Integrated analysis of relationships between 3D-structure, leaf photosynthesis, and branch transpiration of mature Fagus sylvatica and Quercus petraea trees in a mixed forest stand

Integrated analysis of relationships between 3D-structure, leaf photosynthesis, and branch transpiration of mature Fagus sylvatica and Quercus petraea trees in a mixed forest stand Dissertation zur Erlangung der Doktorwürde (Dr. rer. nat.) der Fakultät für Biologie, Chemie und Geowissenschaften der Universität Bayreuth vorgelegt von Stefan Fleck aus Hohensolms Bayreuth, August 2001 2 1. Gutachter: Prof. Dr. J.D. Tenhunen 3 4 5 Danksagung Herrn Prof. Dr. John D. Tenhunen danke ich für die Überlassung des interessanten Themas, für die Förderung und die Anregungen zu meiner Arbeit und die gelungene Koordination mit anderen Projekten. Markus Schmidt spreche ich meinen herzlichen Dank aus für die intensive und freundschaftliche Zusammenarbeit im Steigerwald, Diskussionen und Unterstützung in allen Phasen des Projekts sowie die Überlassung von Messdaten. Dr. Eva Falge, Dr. Barbara Köstner und Dr. Ülo Niinemets danke ich für die ständige Diskussionsbereitschaft, fördernde und kritische Anteilnahme in allen Phasen des Projekts. Bei Wolfgang Faltin bedanke ich mich für seine langanhaltende Bereitschaft zur koordinierten Modellentwicklung und die Unterstützung bei Biomasseernten. Dr. Alessandro Cescatti, Dr. Manfred Forstreuter, Prof. Dr. Yoshitaka Kakubari, Dr. Hideyuki Saito und Dr. Jörn Strassemeyer danke ich für die aktive Unterstützung in fachlichen Fragen und für die Überlassung von Messdaten Meiner Frau Regina Dehmel danke ich herzlich für die weitreichende Untersützung im Zuge der Freilandarbeiten, für die kritische Durchsicht von Manuskripten und Literaturliste und das Management unserer Familie. Allen weiteren Mitarbeitern und Helfern bei Freilandund Laborarbeiten danke ich für ihre Ausdauer und Bereitschaft zu meist langwierigen Tätigkeiten: Annett Börner, Liane Chamsai, Alexandra Hahn, Uta Lohwasser, Friederike Mayer, Silke Potthast und Marc Schroeter - Dr. Martina Alsheimer, Dr. Bärbel Heindl-Tenhunen, Dr. Ueli Joss, Friederike Rothe, Hans-Joachim Scharfenberg, Annette Suske und Dr. Reiner Zimmermann gebührt darüber hinaus mein Dank für die freundschaftliche Aufnahme in die Arbeitsgruppe. Dr. Markus Reichstein danke ich für die intensive Durchsicht von Manuskripten und gemeinsam mit Jens-Arne Subke für inhaltliche Diskussionen. Bei Ralph Geyer bedanke ich mich für die Lösung zeitraubender Hardund Software-Probleme. Dr. Pedro Gerstberger, Dr. Alois-Kastner Maresch, Dr. Holger Lange, Gerhard Müller und Iris Whelan danke ich für fachliche und praktische Unterstützung. Die vorliegende Arbeit wurde am Lehrstuhl Pflanzenökologie der Universität Bayreuth im Rahmen des vom Bundesministerium für Forschung und Technologie geförderten Projekts PT BEO 51 - 0339476C “Entwicklung eines 3-D-Mischbestandesmodells des N-abhängigen CO 2 - und Wasseraustausches von Buchen-Mischbeständen in Nordbayern” durchgeführt. 6 7 Contents 1 Introduction ..................................................................................................................10 1.1 Problems in assessment of gas-exchange of mixed forest stands ........................10 1.1.1 The relevance of gas-exchange of mixed forest stands ..........................................10 1.1.2 Structure dependence of mixed stand gas-exchange .............................................11 1.1.3 Unexplored effects of patterns of space capture.....................................................12 1.1.4 The complexity of canopy structure formation.........................................................12 1.1.5 Canopy structure formation is altered under elevated CO 2 and ozone....................13 1.1.6 Patterns of space capture are the relevant structure information for light utilization 14 1.1.7 Necessity of simulation models for the explanation of altered growth patterns........14 1.2 Conclusions .................................................................................................................15 1.2.1 The relevance of complexity of structure.................................................................15 1.2.2 Implications for actual studies on mixed stand gas-exchange.................................16 1.2.3 Scope and organisation of this study......................................................................17 2 Tree crown structures of mature Fagus sylvatica and Quercus petraea trees .......................................................................................................................................18 2.1 Objectives ....................................................................................................................18 2.2 Materials and Methods ...............................................................................................19 2.2.1 Stand descriptions..................................................................................................19 2.2.1.1 Buchenallee.....................................................................................................19 2.2.1.2 Großebene and Steinkreuz..............................................................................20 2.2.2 Soil pH and soil C/N ratio........................................................................................24 2.2.3 Canopy structure determination..............................................................................24 2.2.4 Geodetic location measurements............................................................................26 2.2.5 Description of branch connections..........................................................................27 2.2.6 Leaf cloud oriented biomass harvest and leaf sampling..........................................28 2.2.7 Error estimations.....................................................................................................29 2.3 Results .........................................................................................................................30 2.3.1 Allometric relationships of the branch system.........................................................30 2.3.1.1 Branch basal area versus estimated sapwood area.........................................30 2.3.1.2 Allometric relationships of ramification.............................................................31 2.3.1.3 Allometric relationships between basal area and leaf area or leaf weight.........33 2.3.2 Discussion of allometric relationships of the branch system....................................37 2.3.3 Leaf arrangement in whole tree crowns..................................................................40 2.3.3.1 3D-representation of leaf clumping..................................................................40 2.3.3.2 Tree Leaf Area Indices ....................................................................................43 2.3.3.3 Arrangement of leaf clouds..............................................................................43 2.3.4 Layer oriented description of leaf distribution in the crown......................................46 2.3.4.1 Leaf area of height layers................................................................................46 2.3.4.2 Leaf area densities of height layers .................................................................48 2.3.4.3 Effect of gap correction of leaf area densities..................................................50 2.3.4.4 Volume gap fractions.......................................................................................51 8 2.3.5 Leaf cloud oriented evaluation of leaf arrangement in the crown.............................53 2.3.5.1 Properties of the crown environment of each leaf cloud ...................................57 2.3.5.2 Angles of the leaf cloud plane ..........................................................................60 2.3.5.3 Main growth directions of leaf clouds................................................................61 2.3.5.4 Azimuth angles.................................................................................................65 2.3.5.5 Spatial extension of leaf clouds........................................................................67 2.3.5.6 Leaf area densities of leaf clouds.....................................................................69 2.3.5.7 Wood area densities of leaf clouds...................................................................75 2.4 Interpretation of investigations on leaf clumping and arrangement ........................75 3 Spatial distribution of leaf properties in tree crowns ......................................77 3.1 Materials and methods ................................................................................................77 3.1.1 Structural leaf parameters.......................................................................................77 3.1.2 Relative irradiance...................................................................................................78 3.1.3 Gas-exchange Measurements.................................................................................78 3.1.4 Evaluation of A/C i -curves with RACCIA...................................................................80 3.1.4.1 The H ARLEY /T ENHUNEN model of leaf photosynthesis.......................................81 3.1.4.2 RACCIA routine for species-specific parameterisation .....................................83 3.2 Results ..........................................................................................................................86 3.2.1 Light and height dependence of leaf properties.......................................................86 3.2.1.1 Relative Irradiance...........................................................................................86 3.2.1.2 Leaf angles ......................................................................................................88 3.2.1.3 Angles of neighbouring branches.....................................................................90 3.2.1.4 Leaf Form.........................................................................................................90 3.2.1.5 Leaf mass per area (LMA)................................................................................91 3.2.1.6 Leaf nitrogen and carbon contents...................................................................94 3.2.2 Photosynthesis measurements...............................................................................96 3.2.2.1 Comparison of PAM-2000 and RACCIA estimates of J max ................................96 3.2.2.2 Day respiration (R d )..........................................................................................99 3.2.2.3 Carboxylation capacity Vc max and electron transport capacity J max ..................101 3.2.2.4 Nitrogen dependence of J max and Vc max ..........................................................104 3.2.2.5 The shape of temperature dependence functions for J max and Vc max ..............106 3.2.2.6 Ball-Woodrow-Berry-coefficient of stomatal sensitivity (g fac )...........................109 3.2.3 Nitrogen dependent model of leaf photosynthesis for beech .................................112 3.2.3.1 Model description...........................................................................................112 3.2.3.2 Parameterisation............................................................................................113 3.2.3.3 Validation Measurements...............................................................................114 3.2.3.4 Model validation.............................................................................................117 3.3 Summary and discussion ..........................................................................................118 4 Application of a 3D-light model to the 3D-representation of beech Gr12 and its stand ......................................................................................................................122 4.1 Methods ......................................................................................................................122 4.1.1 STANDFLUX-SECTORS.......................................................................................122 4.1.2 Representation of 3D-data with CRISTO...............................................................123 4.1.2.1 Representation of stand structure with crown approximating polyhedrons......124 4.1.2.2 Volume and leaf area density calculation of polyhedrons...............................125 4.1.2.3 Segmentation of polyhedrons.........................................................................125 9 4.1.3 Parameterisation of STANDFLUX-SECTORS......................................................128 4.1.3.1 Segmentation of leaf cloud enveloping polyhedrons......................................128 4.1.3.2 Segmentation of crown approximating polyhedrons in the stand Großebene.128 4.1.3.3 Parameter determination for single compartments.........................................132 4.1.4 Validation of STANDFLUX-SECTORS..................................................................132 4.1.4.1 Light and LMA simulations.............................................................................132 4.1.5 Validation data......................................................................................................133 4.2 Results .......................................................................................................................134 4.2.1 Stand Structure.....................................................................................................134 4.2.1.1 Crown length and position of oak and beech trees in the Steigerwald stands 134 4.2.2 LMA-calculations ..................................................................................................135 4.2.2.1 Validation of the light model with the LMA/irradiance relationship..................135 4.2.2.2 Estimation of leaf cloud LMA .........................................................................135 4.2.3 Comparison of climate and transpiration data.......................................................136 4.2.3.1 Daily courses.................................................................................................136 4.2.3.2 Dependence of leaf cloud transpiration on climate variables..........................140 4.2.3.3 Summarising concepts...................................................................................142 4.3 Summary and discussion .........................................................................................142 5 Integrating discussion ............................................................................................144 5.1 Characteristics of oak and beech in the stand Großebene ...................................144 5.2 Application of Beer’s law ..........................................................................................146 5.3 Leaf mass per area (LMA)................................................................................. 147 5.4 Implications for gas-exchange modelling ................................................................148 6 Summary .....................................................................................................................151 7 Zusammenfassung ..................................................................................................153 8 Appendix .....................................................................................................................156 8.1 Parameter derivation for chapter 2.3.5 ...................................................................156 8.2 Measured A/C i -curves ..............................................................................................156 8.2.1 Leaves of beech Gr12..........................................................................................157 8.2.2 Leaves of oak Gr13 ..............................................................................................158 8.3 Figures................................................................................................................. 162 9 Literature .....................................................................................................................169 10 Abbreviations .............................................................................................................182 Introduction 16 1.2.2 Implications for actual studies on mixed stand gas-exchange Given that no single study can yet provide a holistic synthesis, a stepwise long-term strategy is required to cope with the complexity of mixed stands, which starts with intensive fine-scale structural measurements and combined gas-exchange measurements and ends with their complete evaluation with fine-scale models for light and gas-exchange. Up-scaling of functional measurements along 3D-structures of tree crowns is inevitably necessary to achieve this aim and a complete evaluation requires in the first place a complete description of structure and related properties. Unfortunately, methods of structural measurements in forest canopies did not develop as rapidly as data processing by computers, so that the documentation of 3D canopy structure of trees is still time consuming. Though some new measurement methods were established for the application on smaller plants (S INOQUET ET AL . 1991, H IROTA & N AKANO 2000) or for a rougher description of 3D canopy structure (K OCH & R EIDELSTÜRZ 1998, L EFSKY ET AL . 2000, T ANAKA ET AL . 1998), 3D structure measurements on mature trees are not accelerated by these techniques, when physiological investigations on specific parts of the canopy shall be referable to them. Therefore, function-related measurements of 3D structure are the bottleneck for the further development towards a holistic understanding of structure and function of tree canopies. While a growing number of spatially explicit 3D-models of forest canopy light climate and gasexchange exists (C ANHAM ET AL . 1999, C ESCATTI 1997, F ALGE 1997, K NYAZIKHIN ET AL . 1997, R ÖHRIG ET AL . 1999, W ANG & J ARVIS 1990) and further refinements are under development (F ALTIN 2001), their spatial parameterisation is mostly rough or general, i.e., tree crowns are not segmented or are partitioned into a small number of symmetrical compartments. Thus, their high potential for detailed up-scaling of leaf and branch level measurements to the canopy is not fully used, which is simply due to the time-consuming process of three-dimensional structure measurements and the just as time-consuming process to recalculate these measurements into a fine-scale parameterisation. The following implications for the actual study were derived: • Canopy structure measurements have to be organised such, that their usefulness for different approaches of structure representation in 3D-models is guaranteed. • Canopy structure measurements need a resolution that is valuable for many different kinds of physiological measurements in tree crowns (which is mostly the branch scale; V ALLADERES 1999) and which is appropriate for the description of light-climate (see 1.1.6). • Functional (gas-exchange) measurements on different scales should be combined with structure measurements to enable the analysis of relations between function and structure on different spatial levels. • Co-operation with other researchers in the same stand is necessary to bring the necessary information together. • As much as possible additional information about factors influencing gas-exchange for the given stand should be gathered. • The results and samples should be stored in a manner that enables their future evaluation in other fields of research. Introduction 17 • The complete description of all gathered data is important to avoid irretrievable losses of potentially significant information, even when the evaluation of all gathered data to a given evaluation level may be impossible. • Methods of automation should be found and used to reduce complexity and to facilitate further studies on structure-function relationships in mixed stands. 1.2.3 Scope and organisation of this study The aim of this study is to provide field methods, a database, up-scaling relationships, and model subroutines for a spatially explicit analysis of mixed stand gas-exchange. The speciesand stand-specific results that were obtained by application of these methods shall indicate where gas-exchange relevant differences in structure and physiology of Fagus sylvatica and Quercus petraea trees can be expected and shall contribute to a spatially explicit consideration of patterns of space capture in the 3D light-model STANDFLUX-SECTORS (F ALGE 1997, F ALTIN 2001, F LECK ET AL . 2001). This required: 1. The development of partially automated methods for the model-independent description of tree crown structures (leaf cloud oriented biomass harvest) and stand structure (tree crown oriented stand survey) 2. The detailed, light-climate oriented, and therefore leaf cloud oriented 3D-description of crown structures of the two tree species and description of stand structure 3. The intensive investigation of tree crown structures for spatial regularities that enable upscaling or are important for light-climate (leaf cloud properties) 4. The analysis of easily measurable quantities for up-scaling of structure (allometric relationships between branch or trunk basal area and leaf area) 5. Photosynthesis measurements on leaves on the standing trees and characterisation of their light-climate (evaluation of fish-eye photos) 6. Development of an optically controllable routine for A/C i -curves’ automatic evaluation (RACCIA) for the parameterisation of Farquhar-type leaf models of gas-exchange. 7. Investigations on light-climate relevant properties of leaves (leaf-angles) 8. Investigation and establishment of relationships between light-climate, leaf mass per area, leaf nitrogen, and leaf photosynthetic capacities of the two species 9. The development of a leaf nitrogen dependent photosynthesis model based on the LEAVES model (H ARLEY & T ENHUNEN 1991) 10. The development of a program for optical control and recalculation of structural measurements into a 3D-parameterisation, that can be applied to different model representations of 3D-structure (optically controlled crown internal structure representation, CRISTO) 11. The fine-scale parameterisation of the 3D-light model STANDFLUX-SECTORS (F LECK ET AL . 2001), its evaluation for branches, whose sapflow was measured (M. S CHMIDT , Lehrstuhl Pflanzenökologie, Universität Bayreuth, unpublished), and its validation using relative light values from hemispherical pictures The chapters report these steps summarising for different spatial levels: Chapter 2: Tree crown structures of mature Fagus sylvatica and Quercus petraea trees Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 18 (level of boughs and branches / leaf clouds) Chapter 3: Spatial distribution of leaf properties in tree crowns (leaf level) Chapter 4: Representation of tree and stand structure with CRISTO and application of the spatially explicit 3D light-model STANDFLUX-SECTORS to three-dimensional patterns of space capture in a mixed stand (stand and tree level) 2 Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 2.1 Objectives Up-scaling of branch level investigations to whole canopies requires the identification of regularities in tree crown structure that can be expressed as mathematical functions and related to easily measured quantities. One fundamental assumption of structural regularity that is used in most canopy gas exchange models is homogeneity throughout the volume or throughout the height range of certain compartments (tree crowns, segments, or layers), which enables the upscaling of leaf-level photosynthesis rates by multiplication with leaf area of the compartment. This assumption is only an approximation to the real situation, and has to be tested in each case for correctness and utility. Because observations of heterogeneity within single tree crowns reject this assumption, the following hypotheses were formulated: H1: The leaf distribution in single tree canopies is not homogeneous. H2: The 3D-arrangement of branches and associated leaf clouds in the tree crowns is regular and its regularity is responsive to and relevant for light interception. H3: Differences in the regularity of tree crown structure are partly species-specific. The hope behind hypotheses H2 and H3 is to find alternative regularities within tree crowns that are useful for up-scaling. Two major implications for the evaluation arise, when these hypotheses are to be tested under natural conditions: - Structural regularity (H2, H3) can have many different forms, so that many different possibilities must be explored with a variety of approaches. - The necessary high resolution of crown structure measurements required in the search for regularities limits the number of trees that can be investigated, thus preventing statistical evaluation among trees. The results, therefore, cannot initially be generalised to other oaks and beeches, and cannot immediately represent species-specific differences (H3). The results must be considered as examples of tree structural properties, that could similarly occur with other oaks and beeches. Thus, the investigations with respect to H2 are of an explorative nature, while H3 can only be examined with respect to the tree crowns sampled. Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 19 Nevertheless, a full in situ characterisation of structural constraints in mature tree crowns of oak and beech is achieved, that is useful in future considerations of light and gas-exchange models for mixed forest stands. 2.2 Materials and Methods 2.2.1 Stand descriptions Results presented in this thesis rely on measurements that have been performed on three beech dominated stands in two mountainous regions in northern Bavaria. In 1997, structureoriented investigations were performed in the 120 year old pure beech stand “Buchenallee” in the Fichtelgebirge highlands (50°03‘N, 11°52‘E) at an elevation of 905m (Fig. 1). Relationships between structure and function were investigated in 1998 in the 120 year old stand “Großebene” in the Steigerwald highlands (49° 52‘N, 10°28‘E) at an elevation of 450m. This stand is separated by 1.3 km from the main investigation site “Steinkreuz” (140 years) of the BITÖK (Bayreuth Institute of Terrestrial Ecosystem Research), where additional structural and LAI-measurements were taken. Großebene and Steinkreuz are mixed stands of Fagus sylvatica and Quercus petraea. The measurements were carried out at the stands Großebene and Buchenallee due to the availability of climate and other measurements at the nearby stands Steinkreuz and Waldstein (G ERSTBERGER 1997), their species composition, sapflow measurements in other projects on the same trees (M. S CHMIDT , D EPT . OF P LANT E COLOGY , U NIVERSITY OF B AYREUTH , UNPUBLISHED ), and because tree height allowed access to dominant trees with the available highlift. 2.2.1.1 Buchenallee The Fichtelgebirge is a mountainous region created by volcanic activity during the Carboniferous and Permian and has a maximum elevation of 1051 m a.s.l. at the Schneeberg mountain, which is the highest elevation in Northern Bavaria. Low temperatures and high Weissenstadt Bayreuth 10 km 0 F i c h t e l - g e b i r g e G e r m a n y Stands in the Fichtelgebirge Waldstein Buchenallee Germany 10 km 0 Stands at the western edge of the Steigerwald Großebene Steinkreuz S t e i g e r - w a l d Fig. 1: Location of the investigated stands in the Steigerwald (left side) and in the Fichtelgebirge (BITÖK - maps created by P. G ERSTBERGER ) Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 20 precipitation are typical for the climate in the upper Fichtelgebirge. Climate measurements at the Waldstein mountain (765m a.s.l.) (unpublished data of the Chair of Microclimatology, BITÖK, University of Bayreuth) indicate an annual mean temperature of 6 °C. Mean annual precipitation at higher elevation in the Fichtelgebirge ranges from 1100 to 1300 mm and from 950 mm to 1100 mm in those parts below 900 m a.s.l. (B AYERISCHER K LIMAFORSCHUNGSVERBUND 1998). About 20% of precipitation is deposited from fog during 1160 h of foggy weather during the year (W RZESINSKY & K LEMM 2000). Low soil-pH values on the mineral poor, silicate rich geological base material (granite) in combination with the cold and wet climate in the upper region promote podzolation of the soil, so that podzolised brown soils and podzolised leptosols (“Ranker”) cover nearly the whole Schneeberg (F ORSTAMT W EISSENSTADT 1989). The investigation area “Buchenallee” is located on the south slope of the Schneeberg with an inclination of 13.5° (measured with a Suunto inclinometer), ranging from 900 m to 915 m above sea level. The partly podzolised brown earth in this area has pH (H2O) -values of around 4.75 in the upper 5 cm of the mineral soil. The C/N ratio of the 5.7 cm (on average) thick humus layer was found to be 17.6, which accounts for rather good nutrient availability. The potential natural climax vegetation of the Fichtelgebirge should be a beech forest with natural admixture of coniferous trees such as spruce and fir (B OHN ET AL . 1999), although slow growth and a high occurrence of damage by pathogens suggest that beech is at its altitudinal limit at the Schneeberg: The oldest beeches at the Buchenallee are 120 years old, but are not higher than 26 m, thus belonging only to yield class 3 (F ORSTAMT W EISSENSTADT 1989). Ten to 20 percent of the beeches are infected with different parasitic fungi, mostly Fomes fomentarius, Nectria ditissima, and Fusarium avenaceum (determination according to B UTIN 1983). Furthermore, the regions above 950 m a.s.l. of the comparable adjacent highlands in Thüringer Wald, Erzgebirge, Böhmerwald, and Bayerischer Wald have mountainous spruce forests as their potential natural vegetation [B OHN ET AL . 1999]. Pure spruce plantations were favoured in the past in the Fichtelgebirge for economic reasons, so that today around 90% of the forest is made up of uniform and even-aged Norway spruce stands (Picea abies (L.) Karst.). 2.2.1.2 Großebene and Steinkreuz The Steigerwald is a hilly region between 200 and 490 m a.s.l., with highest elevations at its steep western edge which is 200m higher than the adjacent plain of the Main river (see Fig. 1). Altitude decreases continuously from the escarpment toward the east, where maximum altitudes of 300m a.s.l. are attained. Three valleys in east-west direction separate the Steigerwald into four chains of low mountains. Climatic conditions change in correspondence with the elevation gradient: 750 mm to 850 mm precipitation are reached in the uplands of the western part, while the lower and the eastern parts experience only 650 mm to 750 mm (B AYERISCHER K LIMAFORSCHUNGSVERBUND 1998). Precipitation is much lower and mean annual temperature (7 – 8 °C; W ELSS 1985) is higher than in the Fichtelgebirge, which leads to arid periods during the summer that are indicated by less precipitation (in mm) than twice the temperature (in °C) according to the definition of W ALTER & B RECKLE (1999). Arid periods occurred even in the relatively wet year 1998 (see Fig. 2). Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 21 The geological formations of the Steigerwald belong mainly to upper triassic sandstones (Sandsteinkeuper). Blasensandstein, Coburger Sandstein and Burgsandstein build 23-27 m, 5-9 m, and 30 m thick layers above the underlying, largely water-impermeable, and clayey-siltic Lehrberg-layer (30 m) (E MMERT 1985). The sandstone layers include multiple inter-bedding of clay and sandstone layers that are usually some dm in thickness (E MMERT 1985). Sandy brown earth soils develop mainly on Coburger Sandstein and Burgsandstein, while two-layer-soils with a stony phase and clayey pelosols occur mainly above Blasensandsteinand Lehrberg-layers (S EILER 1995, W ELSS 1985). Pelosols are typically found on the plains, and two-layer-soils may develop on steeper slopes by solifluction of the Blasensandsein-layers. The investigated stands are located on the south-east side of the Stollberg (max. altitude 475 m a.s.l.), 2-3 km east of the western edge of the Steigerwald. South slopes on the south-western side of this mountain are warm enough to belong to the most eastern areas of viticulture in Bavaria. The potential natural vegetation of this region belongs to the sessile oak / hornbeam forests in warm-dry areas with little or no occurrence of beech (B OHN ET AL . 1999). Both stands are found on strongly acidic brown earth (pH H2O = 3.7 in 0-5 cm depth, measured in November 2000), which was also found by C HANG (1999) for Steinkreuz. Nitrogen availability of both stands was found to be good (C/N-ratio of the humus layer was 15.2 in both stands). Humus layers were found to be 1.5 to 3.5 cm thick. Climate variables 1998, Fichtelgebirge (Waldstein) -5 20 45 70 95 120 1 3 5 7 9 11 month temperature [°C] -10 40 90 140 190 240 precipitation [mm] mean monthly temperature monthly sum of precipitation Climate variables 1998, Steigerwald (Waldklima Ebrach) -5 20 45 70 95 120 1 3 5 7 9 11 month temperature [°C] -10 40 90 140 190 240 precipitation [mm] mean monthly temperature monthly sum of precipitation Fig. 2: Annual course of climate variables at the investigated sites in the year 1998. Arid periods are indicated by less precipitation (in mm) than twice the temperature (in °C) (W ALTER & B RECKLE 1999), i.e., when the temperature curve lies above the precipitation curve in this diagram. Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 22 Großebene and Steinkreuz are mixed stands of Fagus sylvatica and Quercus petraea with a high proportion of beech, that were established by natural regrowth around 1880 (Großebene) and in the period of 1863 to 1872 (Steinkreuz) (F ORSTAMT E BRACH 2000). The dominance of beech is still supported by natural regrowth of seedlings, and this may partly be due to the higher precipitation rates on the western edge of the Steigerwald, where drought resistance is not as important for competition as it is in the lower or eastern parts. High acidity is not necessarily a disadvantage for natural regrowth of beech seedlings (L EUSCHNER ET AL . 1993). Another reason may be found in the fact that oaks in this area are periodically infested by insects of the Tortrix viridiana community. The populations of these insects may increase enormously in some years and infested oaks in the Steigerwald may lose their entire leaf biomass (S CHÄFER 1997). While 1995 – 1997 was a period of high pest activity ( HEAD FORESTER G EIZ , F ORSTDIENSTSTELLE O BERSCHWARZACH , PERS . COMMUNICATION ), no obvious insect damage occurred to the oaks during the investigation year 1998. Forest management in the Steigerwald generally supports the growth of oaks by selective logging of the oak suppressing beeches (S CHÄFER 1997). The main differences between two nearly even-aged stands in the Steigerwald are their height growth, their tree density, the vigour of oaks, and soil depth. Trees in Steinkreuz are approximately 10 m higher than in Großebene and tree density is much lower, causing greater light availability on the ground and greater cover by understorey vegetation and regrowing trees Table 1: Main site factors of the three investigated stands of Fagus sylvatica and Fagus sylvatica mixed with Quercus petraea Stand Buchenallee Großebene Steinkreuz Location Position 11°51’27-34’’ E, 50°02’30-32’’ N 10°26’43-52’’ E, 49°52’41-48’’ N 10°27’38-44’’ E, 49°52’15-19’’ N Region Fichtelgebirge Steigerwald Mountain (maximum elevation) Schneeberg (1051m a.s.l.) Stollberg (475m a.s.l.) Altitude 910m a.s.l. 460m a.s.l. 440m a.s.l. Area 2424m² * 1 3097m² * 1 12900m² * 2 Inclination 13.5° 2° 5,5° Exposition SSW SE SSE Climate Mean annual precipitation (long term; ’97; ’98) 1100mm - 1300mm 968mm* 3 1299mm* 4 650mm - 800 mm 653mm 807mm Annual mean temperature (long term; ’97; ’98) - 6.0 °C * 4 5.9°C * 4 7.5°C; 7.1°C; 8.3°C Range of monthly mean temperatures (long term; ’97; ’98) - -4.5°C – 17.1°C * 4 -2.5°C – 14.2°C * 4 -1.5°C - 16°C ; -3.7°C - 15.7°C; 0.0 °C - 16.2°C Days p.a. with mean temperature > 5°C (long term; ’97; ‘98) - 189 * 4 199 * 4 215 185 249 Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 23 Soil Geology Coarse-grained coregranite of the Fichtelgebirge Middle Keuper (Upper Triassic), inter-bedding of coarse-grained sandstone (“Blasensandstein”) and clayey layers Middle Keuper (Upper Triassic), inter-bedding of coarseor finegrained sandstone (“Blasensandstein, Coburger Sandstein”) and clayey layers Soil type (FAO-Classification; S CHEFFER & S CHACHTSCHABEL 1998) Loamy-sandy, partly podzolic brown soil (Dystric Cambisol) Loamy-sandy brown soil with stony phase (Cambisol) Sandy brown soil (Cambisol) Soil-depth 30-100cm 5-40cm 50-80cm Humus-layer 5.7 ± 0.8 cm 2.6 ± 0.9 cm 2.4 ± 0.9cm Soil-pH (H2O) in 0-5cm 4.75 ± 0.13 3.72 ± 0.21 3.65 ± 0.29 C/N of humus layer 17.55 ± 0.45 15.16 ± 2.66 15.15 ± 2.25 Vegetation Tree Species composition 99% Fagus sylvatica, 1% Pseudotsuga menziesii 66% Fagus sylvatica, 34% Quercus petraea 75% Fagus sylvatica, 24% Quercus petraea , 1% Carpinus betulus Stand age 120a 120a 140a LAI* 7 8.1 6.1 6.2 Yield class 3 1 1 Trees per ha 524 526.3 358.1 Max. stand height 26m 30m 39m Understorey cover 2% <1% 5 -10% Main understorey species Deschampsia flexuosa, Oxalis acetosella, mosses Anemone nemorosa, tree seedlings Luzula albida, Deschampsia flexuosa, geophytes, mosses Human Impact Forest management Periodic thinning (up to 30% removal) Single stem harvests, supporting growth of oaks No management but ecological research since 1994 Ca 2+ -deposition 4.8 (1.6) kg/(ha*a) * 6 10.6 (2.8) kg/(ha*a) * 5 Mg 2+ -deposition 2.0 (0.4) kg/(ha*a) * 6 2.8 (0.5) kg/(ha*a) * 5 Na + -deposition 11.3 (4.5) kg/(ha*a) * 6 7.6 (3.8) (kg/(ha*a) * 5 K + -deposition 26.1 (2.9) kg/(ha*a) * 6 33.0 (3.1) kg/(ha*a) * 5 Cl - -deposition 19.1 (6.8) kg/(ha*a) * 6 11.6 (5.1) kg/(ha*a) * 5 SO 42+ -deposition 35.1 (9.2) kg/(ha*a) * 6 18.6 (7.6) kg/(ha*a) * 5 NH 4+ -deposition 16.7 (7.2) kg/(ha*a) * 6 12.5 (5.5) kg/(ha*a) * 5 NO 3- -deposition 18.5 (6.2) kg/(ha*a) * 6 11.6 (4.8) kg/(ha*a) * 5 * 1 horizontally projected area of measured tree crown extensions * 2 fenced area * 3 Measurement at DWD-station Bischofsgrün (675m a.s.l) * 4 Measurement at Waldstein investigation site (765m a.s.l.) * 5 Measurement in bulk precipitation (portion in brackets), canopy drip, and stemflow at the Steinkreuz investigation site 1996/1996 (L ISCHEID & G ERSTBERGER 1997) * 6 Measurement in bulk precipitation (portion in brackets) and canopy drip in the Norway spruce stand at the Waldstein investigation site 1993-1998 (M ANDERSCHEID & A LEWELL 2000) * 7 calculated from tree diameters and allometric relationships (Fig. 14) that were adjusted with a constant factor based on leaf area determinations of the harvested trees from each stand Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 24 in a shrubby stage. Steinkreuz is of much lower density and this cannot be due solely to its slightly greater age. The retardation of growth and development of the Großebene stand is probably due to its restricted soil depth which is often less than 10 cm and around 30 cm on average. Thus, root growth at this site for younger as well as old trees appears limited, as observed from the root stock of wind-thrown beeches in the stand. Another difference in the stands concerns the vigour of oaks. While oaks in Großebene are healthy and greater in height than the beeches (height measured with the forest survey laser Criterion 400, Laser Technology Inc., Englewood, Colorado), Steinkreuz oaks appear out-competed by very tall beeches and they have much less dense crowns. The investigation year 1997 was with 968 mm precipitation (DWD-Climate Station Bischofsgrün, 675 m a.s.l.) and a mean temperature of 6.0 °C (BITÖK investigation site Waldstein, 765 m a.s.l.) in the Fichtelgebirge, and 653 mm and 7.1 °C in the Steigerwald (LFW Forest Climate Station Ebrach) a relatively dry but not warm year with a relatively short summer season. The year 1998 (1299 mm precipitation and 5.9 °C at the Waldstein investigation site and 803 mm / 8.3 °C at the LFW Forest Climate Station Ebrach) was a very wet year with high temperatures and long summer season in the Steigerwald (see Fig. 2). 2.2.2 Soil pH and soil C/N ratio Five soil cores per stand were removed in November and December 2000 and separated into humus layer and 5cm thick stratified samples of the mineral soil (0-5cm, 5-10cm, 10-15cm, 1520cm). Thickness of the humus layer (including organic layer) was measured in the field, and samples were brought to the laboratory. Twenty gram of each sub-sample were mixed with 50ml deionized water for 4 – 24 hours and pH was measured with a pH-electrode. The remainder of the soil samples was sieved with a 2mm sieve and oven-dried at 90°C for at least 48 hours for C and N determination in a C/N-analyser (CHN-O-Rapid, Foss Heraeus GmbH, Hanau, Germany). 2.2.3 Canopy structure determination Canopy structure of selected trees was determined in order to develop a “leaf cloud” oriented description of tree crowns of beech and oak. A quantitative description of foliage clustered in leaf clouds (see 2.2.4 for a definition) will allow testing of up-scaling methods for gas-exchange from leaves to canopies by including the intermediate level of organisation associated with branches. Thus, canopy structure is viewed from the perspective of gas-exchange as it is influenced by the spatial arrangement of physiologically distinguished tissues (sun leaves, shade leaves, respiring organs) and their impact on light-climate. Measurements included the geodetic location of branches and leaf clouds inside the crown, the description of the branch system, sampling of leaves for determination of leaf structure, and leaf cloud oriented biomass harvest. Geodetic measurements were mostly done in the leafless state in early spring, and leaves were sampled between June and August to reduce the effects of decreasing leaf mass per area (LMA) and nitrogen retranslocation on nitrogen tissue concentrations (D AY & M ONK 1977, K LOEPPEL ET AL . 1993, S CHULTE 1992). Biomass harvest started mid of August and was completed in the first days of September before yellowing of the leaves. The necessarily high resolution of these measurements limited the number of trees investigated to three beeches and one oak, thus preventing statistical evaluation among trees. The findings, Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 25 therefore, cannot be generalised to other oaks and beeches, but must be considered as examples of tree structural properties, that could similarly occur with other oaks and beeches. Two beech trees in the Buchenallee stand (Bu38, Bu45) and one beech and one oak at the Großebene (Gr12, Gr13) were chosen for study (see Fig. 3). Their size and social position were selected to obtain leaves in all levels of light exposure. Thus, trees had to be tall enough to project above the uppermost leaf-layer of the stand, but small enough to reach with the available highlift. Oak and beech in the Großebene stand were required to stand adjacent to each other. Atypical trees with gross anomalies, such as severe pathogen damage, or atypical crown architecture due to early ramification into two stems, or broken tops, or due to proximity to gaps or roads were excluded from consideration as objects for this study. Großebene: Fagus sylvatica 0 1 2 3 4 5 6 7 8 9 10 15 20 25 30 35 40 45 50 maximum DBH [cm] basal area [m²/ha] 0 5 10 15 20 25 30 35 40 tree height [m] cumulated basal area [m²] average tree height [m] Großebene: Quercus petraea 0 1 2 3 4 5 6 7 8 9 10 15 20 25 30 35 40 45 50 maximum DBH [cm] basal area [m²/ha] 0 5 10 15 20 25 30 35 40 tree height [m] cumulated basal area [m²] average tree height [m] Steinkreuz: Fagus sylvatica 0 1 2 3 4 5 6 7 8 9 10 15 20 25 30 35 40 45 50 55 60 65 70 DBH-class [cm] basal area [m²/ha] 0 5 10 15 20 25 30 35 40 tree height [m] cumulated basal area [m²] average tree height [m] Steinkreuz: Quercus petraea 0 1 2 3 4 5 6 7 8 9 10 15 20 25 30 35 40 45 50 55 60 65 70 DBH-class [cm] basal area [m²/ha] 0 5 10 15 20 25 30 35 40 tree height [m] cumulated basal area [m²] average tree height [m] Buchenallee 0 1 2 3 4 5 6 7 8 9 10 15 20 25 30 35 40 45 50 maximum DBH [cm] basal area [m²/ha] 0 5 10 15 20 25 30 35 40 tree height [m] cumulated basal area [m²] average tree height [m] Fig. 3: Investigated trees, DBH and height distributions in the investigated stands Buchenallee, Großebene, and its compared neighbouring stand Steinkreuz, where additional investigations took place. The diameter classes of investigated trees are indicated by vertical arrows. Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 32 same maximum height in oak Gr13, while its lower boughs were very different in maximum height. The beech trees showed a more continuous extension of boughs throughout their crown’s height range. In the transition zone between the arbitrarily classified sun and shade boughs, higher boughs occurred with extreme south extension while lower boughs were oriented away from the south direction (Table 2). Because south-extended boughs are likely to experience more light than north extended boughs, these boughs were classified as sun boughs, while the lower, north oriented boughs were classified as shade boughs. Table 2: Shadeand Sun-boughs of the investigated trees Quercus petraea Fagus sylvatica Gr13 Gr12 Bu38 Bu45 B o u g h Min. / Max. height [m] Max. south [m] B o u g h Min. / Max. height [m] Max. south [m] B o u g h Min. / Max. height [m] Max. south [m] B o u g h Min. / Max. height [m] Max. south [m] G 19.16 19.23 0.92 C 14.45 15.08 4.19 H 16.38 17.63 0.69 C 11.92 12.32 0.61 A 18.41 20.89 4.75 B 15.69 16.35 2.66 D 16.32 17.87 -0.15 A 9.66 14.47 3.54 B 18.89 21.77 -0.14 G 17.4 18.86 1.64 i 17.75 18.81 0.52 F 14.96 15.18 0.75 L 21.48 23.14 0.94 F 17.3 18.92 -1.18 F 15.57 19.9 0.95 I 15.46 15.96 1.38 E 17.44 23.57 5.37 A 14.0 18.96 1.45 Z 18.23 20.19 0.1 B 11.05 15.96 3.45 F 20.92 23.64 4.22 O 18.58 19.77 2.11 J 19.17 20.47 1.1 E 14.35 16.08 3.6 M 23.95 24.74 2.24 N 19.47 20.11 -1.16 C 15.15 21.48 0.07 G 15.47 16.98 1.28 C 16.92 24.75 0.22 Q 20.69 21.12 -1.38 B 14.39 21.82 9.84 N 17.34 17.94 1.72 D 16.92 24.78 3.12 M 20.7 21.31 1.04 A 13.2 22.26 4.63 O 17.92 18.73 2.49 H 20.85 24.90 3.87 L 19.22 21.43 3.35 L 19.49 22.55 1.7 P 18.19 18.84 2.13 N 23.04 25.00 0.89 D 16.74 22.04 1.94 E 15.66 22.57 2.01 Q 18.5 19.03 1.91 K 23.64 25.30 0.98 K 21.14 22.95 1.03 K 18.34 22.59 1.83 M 17.03 19.06 2.07 I 21.91 25.58 2.65 E 15.9 23.22 4.05 J 16.03 19.44 2.26 i 17.97 23.38 3.59 L 16.34 19.66 1.57 H 18.45 23.83 1.45 H 16.27 20.41 3.12 R 21.92 24.08 -2.27 D 13.79 20.59 4.97 T 22.73 24.68 -0.4 U 23.16 24.78 -0.56 P 20.89 25.08 2.91 V 23.09 25.09 0.91 S 21.9 25.5 -0.41 Table 2: Classification of boughs as shade boughs (dark coloured cells) and sun boughs (light grey coloured cells) according to the extension of their leaf biomass in height and toward the south. Boughs in the table are sorted by maximum height extension of the appending leaf-biomass. Height ranks (x = line numbers of the table) and maximum height extensions (y, in meters) are visualised in the graphs below. The vertical lines in the graphs indicate the border between the two classes and were drawn arbitrarily, considering the steep light gradient in the upper crown and between south and north side of the crown, which is especially valid for the Buchenallee trees that are standing on a slope. The differentiation between the lowest sun bough and the highest shade bough was often facilitated by the higher maximum south extension of the lowest sun bough (see pairs of white cells in the table). 18 20 22 24 26 0 5 10 15 17 19 21 23 25 0 5 10 15 20 17 18 19 20 21 22 23 0 5 10 12 14 16 18 20 0 5 10 15 Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 33 The relationship between basal area of leaf cloud supporting branches and the cumulated area of the affiliated leaf cloud branches that support the second 1m-segment of the leaf cloud was analysed based on data of the Großebene trees. Here branches with a high proportion of dead wood were excluded. The basal area reduction per meter was 84% in leaf clouds of oak Gr13 and 81% in leaf clouds of beech Gr12 (Fig. 8). Fig. 8: Basal area relationship between leaf cloud supporting branches and the connected branches in the second 1m-segment of the leaf cloud 2.3.1.3 Allometric relationships between basal area and leaf area or leaf weight The pipe-model theory (S HINOZAKI 1964) first advanced the principle that sapwood area in trees is related proportionally to foliage biomass (M ÄKELÄ 1986). The theory reasons that each unit of foliage requires a unit pipeline of wood to conduct water from the roots and to provide physical support. As leaf area is a quantity that is interesting in terms of light interception and gasexchange, the correlations presented here utilise leaf dry weight and one-sided leaf area as key variables. Though in the past, pipe-model relations have usually expressed biomass in relation to sapwood area, which yields strong linear correlations to leaf area and leaf weight of several species (G RIER & W ARING 1974, K AUFMANN & T ROENDLE 1981, R OGERS & H INCKLEY 1979, W ARING ET AL . 1977) the current investigations are - like some newer publications (B ARTELINK 1997, S UMIDA & K OMIYAMA 1997) - based on basal area of branches, boughs and stems, because sapwood area is difficult to measure non-destructively and, therefore, not suitable as an input-parameter for up-scaling and modelling purposes. In leaf clouds of oak Gr13, basal area of the branch and appending leaf biomass was better correlated than basal area and leaf area (Fig. 9). The same was found for beech, when all beech observations were pooled: The leaf biomass / basal area ratio was 27.3 with an r² of 0.93, while the leaf area / basal area ratio over all beeches (0.364) had a lower r² of 0.89. The opposite was true if the beeches are analysed separately (see Fig. 9). The individual differences between the beech trees may partly be explained by lower leaf biomass and area of the subdominant and infected tree Bu45. In general, the concept of constant ratios between leaf area or biomass and basal area of the respective branch was better supported for beech leaf clouds than for those of oak Gr13. Fagus sylvatica y = 0.8109x R 2 = 0.9343 0 5 10 15 20 25 30 0 10 20 30 leaf cloud basal area [cm²] cumulated basal area of 2nd 1m-segments [cm²] beech Gr12 Quercus petraea y = 0.8387x R 2 = 0.9441 0 5 10 15 20 25 30 0 10 20 30 leaf cloud basal area [cm²] cumulated basal area of 2nd 1m-segments [cm²] oak Gr13 Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 34 Fig. 9: Allometric relationships between leaf area or leaf biomass and basal area of the associated branch. The same relationships on the level of trunk connected main boughs are illustrated in Fig. 10: Very high correlations were found for the ratio of leaf area or leaf biomass to basal area of sunboughs of oak Gr13, while shade-boughs have lower leaf area and mass. A similar tendency was found in beeches, where the subdominant (shade-) tree Bu45 has less leaves per basal area than the dominant one (Bu38) of the two fully harvested beeches. Again, correlations for beech are higher when considered on a single tree basis. The ratios for the pooled data of beeches are 0.319 for leaf area and 0.0196 for leaf biomass and both have rather high coefficients of determination (r² = 0.896 and 0.904, respectively). Coefficients of determination on the spatial level of boughs were, thus, higher than on the level of leaf clouds. Ratios of leaf area to total basal area of boughs are compared to estimates of leaf area per trunk basal area in Fig. 11 to investigate, if this relationship may be extrapolated: Only the stem basal area of the subdominant beech tree Bu45 is compatible with a linear extrapolation from boughs to the stem. The stems of oak Gr13 and beech Bu38 support less leaf area, leaf biomass, and bough basal area per trunk basal area. An overview of the different leaf area / basal area ratios for leaf cloud branches, boughs and stems indicates that the slope of all these linear regression lines decreases with increasing basal area of the woody element for all trees (see Table 3). Thus, an allometric relationship for all kind of wood from an individual tree becomes non-linear, although linear regression lines with high r² values may be determined on distinct levels of organisation. Fagus sylvatica y = 0.4384x R 2 = 0.9155 y = 0.2904x R 2 = 0.9138 y = 0.3495x R 2 = 0.9186 0 2 4 6 8 10 12 0 10 20 30 leaf-cloud basal area [cm²] leaf area [m²] beech Bu38 beech Gr12 beech Bu45 Quercus petraea y = 0.4129x R 2 = 0.743 0 2 4 6 8 10 12 0 10 20 30 leaf-cloud basal area [cm²] leaf area [m²] oak Gr13 Fagus sylvatica y = 27.333x R 2 = 0.8124 y = 19.126x R 2 = 0.8469 y = 30.488x R 2 = 0.8906 0 200 400 600 800 1000 0 10 20 30 leaf-cloud basal area [cm²] leaf dry weight [g] beech Bu38 beech Gr12 beech Bu45 Quercus petraea y = 32.69x R 2 = 0.8043 0 200 400 600 800 1000 0 10 20 30 leaf-cloud basal area [cm²] leaf dry weight [g] oak Gr13 Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 35 Fagus sylvatica y = 0.1548x R 2 = 0.952 y = 0.3616x R 2 = 0.9808 0 20 40 60 80 100 0 50 100 150 200 250 main bough basal area [cm²] leaf area [m²] beech Bu38 beech Bu45 Quercus petraea y = 0.3756x R 2 = 0.9539 0 20 40 60 80 100 120 0 100 200 300 main bough basal area [cm²] leaf area [m²] sun main boughs shade main boughs Fagus sylvatica y = 0.0109x R 2 = 0.852 y = 0.0218x R 2 = 0.9656 0 1 2 3 4 5 6 0 50 100 150 200 250 main bough basal area [cm²] leaf dry weight [kg] beech Bu38 beech Bu45 Quercus petraea y = 0.0271x R 2 = 0.939 0 2 4 6 8 10 0 100 200 300 main bough basal area [cm²] leaf dry weight [kg] sun main boughs shade main boughs Quercus petraea y = 0.0271x R 2 = 0.939 0 10 20 30 40 50 0 500 1000 1500 main bough basal area [cm²] leaf dry weight [kg] sun boughs trunk Gr13 Fagus sylvatica y = 0.0088x R 2 = 0.9873 y = 0.0218x R 2 = 0.9656 0 5 10 15 20 25 0 200 400 600 800 1000 main bough basal area [cm²] leaf dry weight [kg] beech Bu38 beech Bu45 trunk Bu45 trunk Bu38 Fagus sylvatica y = 0.1469x R 2 = 0.9983 y = 0.3616x R 2 = 0.9808 0 50 100 150 200 250 300 350 0 200 400 600 800 1000 main bough basal area [cm²] leaf area [m²] beech Bu38 beech Bu45 trunk Bu45 trunk Bu38 Quercus petraea y = 0.355x R 2 = 0.8984 0 100 200 300 400 500 600 0 500 1000 1500 main bough basal area [cm²] leaf area [m²] oak Gr13 trunk Gr13 Fig. 10: Allometric relationship between leaf area or biomass and basal area of the associated bough Fig. 11: Comparison of allometric relationships on the bough level with those of the trunk level. The correlation for beech Bu45 includes the trunk data Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 36 Table 3: Leaf vs. woody element ratios on different spatial levels Oak Gr13 Beech Bu38 Beech Bu45 Allometric relationship Leaf clouds 0,4129 32,69 0,4384 30,49 0,2904 19,13 Boughs 0,3756 27,1 0,3616 21,8 0,1548 10,9 Stem 0,2433 18,1 0,2216 13,3 0,1464 8,7 The transition from approximate linear to non-linear behaviour can be described with a power function, which increases the overall coefficients of determination. A linear regression line or model is only a special case of a power function (power function with exponent 1). Indeed r²values increased to more then 0.99 when using a power function for the regression. All resulting fits have exponents lower than 1, which indicates the slight decline of the ratio between leaf area or mass and basal area of woody elements with increase in basal area as more stand structural complexity is included. (Fig. 12). Fig. 12: Power function approximation of the areaand mass-based allometric relationship between basal area (cm²) and leaf area (m²) or leaf dry weight [kg] of boughs and stems of the three fully harvested trees. When estimating parameters for the power function regressions it was found that trendlines produced by Microsoft Excel are based on the logarithmic transformed data of both variables (log-log-transformation), which is justified only for the special case that the log-log-transformed data show a better agreement with the normal distribution than the original data, because in this case the potential effect of lacking data would be considered. Because the agreement with the normal distribution was not tested separately in each case, only approximations to the original data were done using the programming and calculation software Mathematica (Wolfram Research, Champaign, Illinois). These approximations generally yield the best fit to the available data (compare Fig. 13). Leaf area H m² L basalarea H cm² L Leaf biomass H g L basal area H cm² L 400 800 1200 cm² 5 10 15 20 25 30 kg 300 600 900 1200 cm² 5 10 15 kg 200 400 600 800cm² 5 kg 400 800 1200 cm² 200 400 m² 300 600 900 1200 cm² 100 200 m² 200 400 600 cm² 100 m² cm² cm² Oak Gr13 Oak Gr13 Beech Bu38 Beech Bu38 Gr13 Beech Bu45 Beech Bu45 0.68x 0.859 0.048x 0.867 0.074x 0.755 0.016x 0.908 1.27x 0.751 0.17x 0.975 Leaf area H m² L basalarea H cm² L Leaf area H m² L basalarea H cm² L Leaf biomass H g L basal area H cm² L Leaf biomass H g L basal area H cm² L Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 37 A comparison was made between the allometric relationships of 2 beech species, 5 oak species and 5 additional broad-leaved tree species to examine, whether the decrease in ratios of leaf area to total basal area with increasing basal area of the stems may be systematically and generally described with a power function, and most data for this study were taken from literature. The investigated tree species are Fagus crenata (K AKUBARI & M ARUYAMA , UNPUBLISHED ), Fagus sylvatica (B ARTELINK 1997, P ELLINEN 1986, L EBAUBE ET AL . 2000 AND THE OWN MEASUREMENTS ), Quercus spp. (including Quercus petraea and Quercus robur, B URGER 1947 AND THE OWN DATA ), Quercus alba (M ARTIN ET AL . 1998, R OGERS & H INCKLEY 1979), Quercus coccinea, Quercus prinus, and Quercus rubra, Acer rubrum, Betula lenta, Carya spp. (including Carya glabra, Carya ovata and Carya tomentosa), Liriodendron tulipifera and Oxydendrum arboreum (M ARTIN ET AL . 1998). The decrease in stem basal area to leaf area ratio at the level of main trunks was found in 11 of the 12 tree species, only the data set for Betula lenta showed a slight increase in this relationship, which seems to be an artefact due to one data point that represents the largest harvested Betula lenta tree (see Fig. 14). The power function approximation to all available tree data was 0,463 * x 0,903 . 2.3.2 Discussion of allometric relationships of the branch system The inter-individually constant and inter-specifically similar relationship between basal are and sapwood area or area of outer rings of branches (Fig. 6) strengthens the hypothesis, that both relationships describe the same phenomenon. On the one hand, this constancy suggests that the distinguished central part of the cross-section of branches grows in constant relationship to the whole branch cross-section, which in turn indicates physiological changes in the central part of branches with increasing diameter, though heartwood formation has been shown not to take place in branches of several different species (S CHWEINGRUBER 1978). On the other hand, it shows that the allometric relationship between basal area and leaf area at the level of leaf cloud supporting branches of both species is not influenced by alterations of sapwood area, because a constant ratio between basal area and sapwood area exists at this hierarchical level, but not on the level of boughs or trunks (Fig. 6, N AIR 1995). 500 1000 1500 cm² 100 200 300 400 m² Quercus petraea y = 0.533x 0.8769 0 100 200 300 400 0 500 1000 1500 basal area [cm²] leaf area [m²] oak Gr13 y = 0,68*x 0,859 Fig. 13: Comparison of power function trendline (Excel) and power function approximation (Mathematica) on the same data set. The sum of squared errors ( χ ²) was 3749,8 for the trendline and 2020.98 for the approximation. Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 38 Fig. 14: Decrease of ratio between leaf area and basal area of 11 of 12 investigated tree species with increasing basal area. Quercus petraea and Quercus robur are not distinguished (“ Quercus spp .”) and Carya spp . stands for Carya glabra , Carya ovata and Carya tomentosa . 500 1000 1500 2000 2500cm² 50 100 150 200 250 300 m² 500 1000 1500 2000 2500cm² 20 40 60 80 100 120 m² 500 1000 1500 2000 2500cm² 100 200 300 400 500 600 m² 500 1000 1500 2000 2500cm² 50 100 150 200 250 300 350 m² 500 1000 1500 2000 2500cm² 100 200 300 400 m² 500 1000 1500 2000 2500cm² 50 100 150 200 250 300 m² 500 1000 1500 2000 2500cm² 50 100 150 200 250 m² 500 1000 1500 2000 2500 cm² 50 100 150 200 250 300 m² 1000 2000 3000 4000cm² 200 400 600 800 1000 m² 500 1000 1500 2000 2500 3000 cm² 200 400 600 m² 1000 2000 3000 4000cm² 100 200 300 400 m² 500 1000 1500 2000 2500cm² 100 200 300 400 500 m² Fagus crenata 1 Fagus sylvatic Quercus coccinea Quercus Quercus alba Quercus prinus Quercus rubra Acer rubrum Betula lenta Carya spp. Liriodendron tulipifera Oxydendrum arboreum 0,542*x 0,749 0,686* x 0,849 4,878*x 0,542 0,807*x 0,759 1,388*x 0,694 0,526*x 0,825 1,44*x 0,564 0,429*x 0,837 0,068*x 1,16 0,219*x 0,953 1,086*x 0,692 0,942* x 0,847 Oak Gr13 Bu 38 Gr12 1000 2000 3000 4000cm² 200 400 600 800 1000 m² Quercus spp. 0,836*x 0,859 500 1000 1500 2000 2500cm² 100 200 300 400 500 m² Fagus sylvatica 0,745*x 0,833 Bu45 Bu38 Gr12 Gr13 Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 39 The leaf area vs. basal area relationship is very robust (Fig. 9) and, thus, well suitable for upscaling of leaf area along branch diameters of a crown. This could reduce the necessary work in biomass harvests to 10-20% of the leaf clouds, as is shown for beech Gr12. Nevertheless, the established relationship for oak shows considerable variation that can not solely be explained by measurement errors. The inter-individual differences between beeches and the scatter between leaf clouds may relate to variation in the regulation of processes affecting wood formation and differing demands placed on hydraulic conductivity according to the orientation, size and position of the leaf cloud on individual branches (M ATTHECK 1995, P ROTZ ET AL . 2000, M AHERALI ET AL . 1997). The leaf area / basal area ratio of boughs may also be useful for upscaling, but here differences between sunand shade-boughs of oak occur, and the interindividual differences between beeches were larger than those observed at the branch level. The azimuth direction of growth of main boughs from the stem was important for structure formation in the crown, at least in the case of oak. Also in beech trees Bu38 and Gr12, several main boughs reach the upper 1-2m of the crown, while one or two lower boughs exhibited an extreme extension to the south. This could be interpreted as light driven competition between boughs and gives a hint to the asymmetrical distribution of favourable conditions in the tree crown. The much lower number of living shade boughs in the oak crown and the phenomenon of several dead boughs below the living crown of oaks contrasts to the high number of living shade boughs in the three beech crowns. This indicates – together with the low leaf area / basal area ratio of shade boughs of oak - the higher shade tolerance of beech branches. Species-specific differences in heartwood formation occur at the stem and bough level, but not at the level of leaf cloud supporting branches. Nevertheless, allometric relationships of ramification were remarkably similar at all three spatial levels for oak Gr13 and for beech trees (Fig. 7 and Fig. 8), which may be due to the common requirements in crowns of this size for structural stability. The ratio between supported leaf area and basal area of stems declines in most species with increasing basal area. This trend is also found in the investigated oak and beech trees, considering the integration from branches to boughs and to main stems. Exponents lower than 1 for a power function relationship were also found in power function approximations for stemconnected boughs of Quercus mongolica, Acer sieboldianum, Magnolia obovata, Betula platyphylla and Betula maximowicziana (S UMIDA & K OMIYAMA 1997). Similar relationships at different spatial levels may indicate a common reason for the decline. While the leaf area / basal area ratio was linear and inter-individually constant at the level of branches (Fig. 9), differences between sun and shade boughs of oak and between the subdominant, infected tree and the dominant beech tree in the same stand occurred at the level of boughs (Fig. 10). These differences may be explained by cavitation due to dying of appertaining branches of the shade main boughs of oak. Cavitation may also be the reason for the generally lower leaf area / basal area ratio of the wholly infected beech Bu45. The linearity of all investigated leaf area vs. basal area relationships on the bough and branch level apart from that for the shade boughs of oak strengthens this explanation. Cavitation is expected to have less impact on the leaf area / basal area ratio of young branches, because of the relatively short time of their exposition to stress situations. A linear relation in the leaf area / basal area ratio can also result, if cavitation affects all boughs or branches with the same probability due to their similar age, similar conditions in the same tree crown, or similar vitality (same exposure regarding infection as in Bu45). The age of trees, boughs, and branches may, Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 40 thus, explain the general decline of leaf area / basal area ratios across spatial scales. Different species-specific mechanisms to avoid cavitation under their different living conditions may be responsible for the high numerical differences in the investigated leaf area / basal area ratio between species, which may especially be seen between the biggest and therefore oldest trees (for example of Fagus crenata and Quercus spp. in Fig. 14 and Fig. 15). 2.3.3 Leaf arrangement in whole tree crowns 2.3.3.1 3D-representation of leaf clumping The arrangement of leaves in the canopy has a major influence on light climate in the tree crown and the light-dependent function of all assimilating tissues. In most tree species, leaf distribution is clumped along leaf cloud supporting branches, though there may also be some single leaves close to the stem or to a main bough that are far away from other leaves, and therefore, not part of a leaf cloud (as was found in the investigated Quercus petraea crown). A full description of the three-dimensional arrangement of leaf clouds in the crown was achieved for beech Bu38 (139 leaf clouds) and for oak Gr13 (88 leaf clouds) via direct measurement of the whole leaf biomass, while the leaf biomass of leaf clouds of beech Gr12 (66 leaf clouds) was calculated using the relationship found on a sub-sample of its branches (see Fig. 9). The results are shown below in 3-D-illustrations. The data listing the exact co-ordinates of all leaf cloud enveloping polyhedrons are long-term stored and available via the BITÖK sample collection. 500 1000 1500 2000 2500 3000 3500 200 400 600 800 1000 Oxydendrum arboreum Liriodendron tulipifera Carya spp. Betula lenta Acer rubrum Quercus rubra Quercus prinus Quercus coccinea Quercus alba Quercus spp. Fagus sylvatica Fagus crenata Fig. 15: Inter-specific variation of the ratio between basal area and leaf area of 261 trees of different species. cm ² m² Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 41 3-D-graphs in the following are constructed with the software Mathematica (Wolfram research, Champaign, Illinois) using a light reflection model [Phong 1975] that simulates the reflectance of surfaces considering their orientation to light sources, thereby distinguishing between specular (low scatter-) and diffuse (high scatter-) light reflection. The resulting 3-D-effect can only be Oak Gr13 - 2.5 0 2.5 5 7.5 North H m L 5 10 15 20 25 Height H m L 5 10 15 20 25 Height H m L Beech Gr12 -4-202 4 North HmL 5 10 15 20 25 Height HmL 5 10 15 20 25 Height HmL Beech Bu38 - 4 - 2 0 2 4 North H m L 5 10 15 20 25 Height H m L 5 10 15 20 25 Height H m L Leaf area density (m²/m³) 5 15 25 35 45 55 65 Fig. 16: 3-dimensional maps of tree crown structures and leaf area densities of leaf cloud enveloping polyhedrons in the canopies of beech Bu38, beech Gr12 and oak Gr13. Though beech Bu38 is smaller than the “Großebene”-trees, it is a dominant tree in its stand “Buchenallee” (see also Fig. 3). The y-axis of the graphs represents height above the floor (m). The origin of the coordinate system for oak Gr13 is the same as for beech Gr12, so that the stem base point of oak Gr13 is (-4,79 | 2,96 | 0,14 ) [East/North/Height], while the other stem base points are situated in the origin. This and the legend are also valid for Figure 19 a and b, where horizontal sections of the polyhedrons of 1m thickness can be viewed from above. This and all following tree crown figures rely on the 3-D-representation model CRISTO (see chapter 4) that was built using the Mathematica programming language. Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 48 Leaf area calculations on the base of volumetric homogeneity confirm the non-monotone distribution over height layers that was shown for height range homogeneity (Fig. 22). The same maxima and minima are apparent though the lower resolution smoothes the data so much that information from the finer resolution data is necessary to interpret the results. For example, the height layers 17.6m and 18.6m of beech 38 are here difficult to view as minimum layers. The volumetric homogeneity assumption tends to shift leaf area minima and maxima to lower levels. This is a consequence of the volume distribution over height range of the leaf clouds, which are usually wider in their lower, darker extent and smaller in the lighter and upper portion. Considering that leaf clouds usually grow towards lighter and higher regions (development of new leaves) and away from the lower and darker parts (die off of shaded parts) , both methods seem to be justified approaches for examining structure. 2.3.4.2 Leaf area densities of height layers Light harvest of tree crowns is not only influenced by the amount of leaf area at different heights, but also by the shadows cast on and by competing trees and on self-shading (L EUSCHNER 2000). The effective leaf area densities of height layers of single tree crowns depend on leaf area of the layer but also on the horizontal extension of the height layer, which is usually not constant. Height layer-related leaf area densities (LAD L ) were calculated on the base of LA L, dm –data, assuming that the volume of height layers may adequately be described by multiplying the layer height by the convex hull area of projected polygon corner points in that height layer. This assumption requires the height layers not be too small. For the sake of 14.5 15.5 16.5 17.5 18.5 19.5 20.5 21.5 22.5 23.5 24.5 25.5 10 20 30 40 50 60 70 Layer leaf area H m² L upper limit of height layer (m) upper limit of height layer (m) 17.2 18.2 19.2 20.2 21.2 22.2 23.2 24.2 25.2 26.2 10 20 30 40 50 60 70 Layer leaf area H m² L upper limit of height layer (m) Oak Gr13 Beech Gr12 13.6 14.6 15.6 16.6 17.6 18.6 19.6 20.6 21.6 22.6 10 20 30 40 50 60 70 Layer leaf area H m² L Beech Bu38 Layer leaf area (m²) Fig. 22: Leaf area of 1m height layers calculated on the assumption of volumetric homogeneity of leaf clouds. Axes were scaled to represent the same ordinate range. Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 49 simplicity, a height of 1m was chosen for all height layers and leaf area densities were calculated according to where V L denotes the layer volume. The LAD L / height relationship was approximated by a polynomial function of LAD L versus relative height in the canopy (ranging from 0 to 1, see Fig. 23). The results demonstrate a partly different situation in comparison to Figs. 21 and 22. A greater distribution of leaf area density toward the upper part of the crown occurs. Skewness of the LAD L -distribution was positive in all cases (see Table 5), indicating that the trees produce some single layers (those in the upper crown) with extremely high leaf area densities as compared to other layers. Especially the beech trees Gr12 and Bu38 had the highest leaf area densities in their uppermost crown layer, while oak Gr13 had its highest LAD L -values 2,5m below the apex. While oak Gr13 had the greatest amount of leaf area in a higher region than the neighbouring beech Gr12 (Fig. 21), and even though this was more than twice as much leaf area than that of beech Gr12 in the peak layers, beech Gr12 (and also beech Bu38) had a higher maximum LAD L than oak Gr13. Furthermore, even though beech Gr12 was 0.7m shorter LAD L= ⁄ i = 1 10 LA L,dm V L , (2) 13.6 14.6 15.6 16.6 17.6 18.6 19.6 20.6 21.6 22.6 upper limit H m L 0.5 1 1.5 2 2.5 3 Leaf Area Density H m² ê m³ L 14.5 15.5 16.5 17.518.5 19.520.5 21.5 22.5 23.5 24.5 25.5 upper limit @ m D 0.5 1 1.5 2 2.5 3 Leaf Area Density @m²êm³D 17.2 18.2 19.2 20.2 21.2 22.2 23.2 24.2 25.2 26.2 upper limit H m L 0.5 1 1.5 2 2.5 3 Leaf Area Density H m² ê m³ L Leaf area density [m²/m³] Leaf area density [m²/m³] Leaf area density [m²/m³] upper limit of height layer [m] upper limit of height layer [m] upper limit of height layer [m] Fig. 23: Leaf area densities of 1m-height layers of the investigated canopies. The volume calculation is based on the convex hull of the projected polygon corner points of each layer times layer height (1m), and the LAD calculation assumes equal distribution of leaves over the height range of a leaf cloud. Polynomial approximations on the base of x = mean relative height in the canopy for beech Bu38, Gr12 and oak Gr13 were (respectively): Oak Gr13 Beech Gr12 Beech Bu38 LAD L = 335.8 x 6 - 990.9 x 5 + 1119.2 x 4 - 615.2 x 3 + 174.7 x 2 - 22.8 x + 1.3 LAD L = 1111.3 x 6 - 3245.9 x 5 + 3605.8 x 4 - 1897.2 x 3 + 477.5 x 2 - 48.2 x + 1.6 LAD L = 211.9 x 6 - 544 x 5 + 495.9 x 4 - 176.9 x 3 + 11.4 x 2 + 5.2 x - 0.1 Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 50 than oak Gr13, beech Gr12 managed to produce its maximum LAD L in a higher region than the maximum LAD L of oak Gr13, which should be important in terms of shading. The lower maximum LAD L of oak Gr13 is not due to a generally higher volume of the whole tree crown, because the sum of all layer volumes of the two trees (=LAD Crown ) was nearly the same (see Table 5). Moreover, oak Gr13 had a higher absolute leaf area density related to the whole crown volume (LAD Crown , Table 5), so that the higher maximum LAD L of beech Gr12 only arises because of the much more positively skewed distribution of LAD L -values in comparison to the distribution of oak Gr13 LAD L -values , i.e., the high maximum LAD L -value of beech Gr12 can under these circumstances only be achieved due to many height layers with low LAD L -values. The crown of oak Gr13 on the other hand expands to enormously high layer volumes (40.1 - 58.8m³, compare Table 5) in the 2 nd to 6 th layer below apex, which leads despite their high amounts of leaf area to rather moderate LAD L -values for these upper layers. Table 5: canopy data Bu38 Gr12 Gr13 Leaf area (m²) 240.7 236.6 328.3 Height range (m) 13.13 - 22.6 14.0 - 25.5 16.92 - 26.2 Crown volume (m³) 229.3 312.0 310.1 Range of layer volumes (1m-layers, m³) 4.8 – 39.5 3.6 - 37.6 0.6 - 58.8 Crown leaf area density LAD Crown (m²/m³) 1.05 0.76 1.06 Range of layer leaf area densities LAD L (m²/m³) 0.11 - 2.37 0.07 - 2.38 0.20 - 2.03 Skewness* of LAD L –distribution 0.18 1.31 0.41 Standard deviation of LAD L -values 0.74 0.61 0.60 Projected crown area (m²) 42.8 52.4 69.4 Projected crown area (gap corrected, m²) 36 47.5 54.8 Tree leaf area index TLAI (m²/m²) 5.6 4.5 4.7 Tree leaf area index TLAI g (gap corrected, m²/m²) 6.7 5.0 6.0 *: Skewness calculation was based on maximum likelihood estimates of standard deviations 2.3.4.3 Effect of gap correction of leaf area densities Separating the canopy into layers of constant depth does not relate in any way to a natural phenomenon and, therefore, the choice of other boundaries which could significantly influence the volume dependent determination of LAD L –values could be considered. While horizontal boundaries spread the foliage by separating leaves of leaf clouds that are naturally clumped, vertical boundaries can additionally consider the form of the cross-section of a height layer in a finer or coarser manner. Reasonable definitions of layer projected areas are the same as those for projected crown areas and the convex hull area represents a definition that considers the overall shape of the cross-section but explicitly no cavities along the border of the cross-section. Another reasonable definition would be for example to consider all cavities of a given size or to consider only the biggest cavity, which can have a strong effect on the height dependence of LAD L –values, when the roughness of the border of the cross-section of height-layers varies. The potential magnitude of this effect can be seen, when the calculated tree leaf area indices of the investigation trees with or without gap correction are understood as leaf area densities of a single large layer with constant height: Gap correction led to an increase of TLAI in the range of 10 - 28% (Table 5). A tree and cavity oriented layer definition assuming volumetric homogeneity of leaf clouds was tested for comparison on the data of beech Gr12: The height of horizontal boundaries between Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 51 layers was chosen by eye such that bigger cavities along the border of the cross-section were not hidden by leaf clouds above or below the cavities. The irregular form of horizontal crosssections was approximated by 8 or 12 sectors of circles with different radii (see Figs. 112a, 112b). The assumption of volumetric homogeneity of leaf clouds again required the use of the program CRISTO (see chapter 4). Using this approach led to a slightly different LAD L vs. height relationship (Fig. 24). The lowest and the uppermost layer were no longer extreme and their LAD L -values were shifted towards values closer to the average. The highest LAD L now occurs in the second layer from the top. This was again due to the assumption of volumetric homogeneity instead of height range homogeneity. The leaf area of leaf cloud top segments in the uppermost layer is overestimated and that of leaf cloud bottom segments in the lowest layer are underestimated, when their leaf area is assumed to be equally distributed over the height range. Though this is principally also true for the other layers, the effect appears to be weaker in the middle layers: The overall relationship between the middle layers agrees well with that obtained from 1mheight layers, which accounts for the fact that the middle layers contain bottom and top segments of leaf clouds, so that their contributions to relative overand underestimation may cancel each other out. The general trend is still a monotonous and nearly exponential increase in LAD L towards the uppermost layers. If no fundamental changes in the opposite direction would occur when oak Gr13 would be layered in this manner, the layer with highest LAD L of beech Gr12 (mean height: 24.1m) would still be in a slightly higher region than that of oak Gr13 (mean height: 23.7m), though the beech is 0.7m shorter. 2.3.4.4 Volume gap fractions The meaning of layer leaf area densities for light transmission and absorption in a canopy is strongly dependent on clumping of leaves and discontinuity of the tree canopy (C ESCATTI 1998). Therefore the question arises, whether the leaf area density distribution from top to bottom of the canopy is due to changes in leaf area density of leaf clouds or in the leaf cloud density in different layers, i.e., the fraction of their volume with respect to the layer volumes (which can be inversely expressed as volume gap fraction). Volume of leaf cloud segments as calculated with the program CRISTO was summed for each layer and related to the layer-specific convex hullbased layer volume V L for the calculation of layer gap fractions as 0 0.5 1 1.5 2 2.5 15.1 16.1 17.2 18.4 19.3 20.2 21.2 22.6 22.9 23.8 24.4 25.5 upper limit of height layer [m] Leaf area density [m²/m³] . Fig. 24: Leaf area densities of irregular chosen height layers of beech Gr12. Layer volume is calculated as the sum of cylinder sector volumes with different radii and the LAD calculation is based on the assumption of volumetric homogeneity. The polynomial approximation on the base of x = mean relative height in the canopy was: LAD L = - 313.7 x 6 + 766.2 x 5 - 687.7 x 4 + 280 x 3 - 49.3 x 2 + 2.8 x + 0.6 Beech Gr12 Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 52 where V P i denotes the volume of a polyhedron or polyhedron segment and n the number of polyhedrons and polyhedron segments in that layer. The 1m-height layer leaf area density was estimated from the leaf cloud leaf area data assuming volumetric homogeneity: Here, V C i denotes the volume of the whole polyhedron, i. e., the leaf clouds volume and LA C i is the leaf clouds leaf area. Finally, average leaf area density of polyhedrons and polyhedron segments in the layer ( )was calculated according to Volume gap fractions within the crown layers were rather high (90%, 82% and 89% on average for beech Bu38, beech Gr12 and oak Gr13), and ranged from 82% to 98%, 58% to 96%, and 72% to 98% for the three trees, respectively. While the lowest gap fraction of oak Gr13 was in LAD P ` Gap =1- ⁄ i = 1 n V P i V L , (3) LAD L,m = „ i = 1 n V Pi VCi ¥ LA Ci V L (4) LAD P ` = „ i = 1 n V Pi V Ci ¥ LA C i ⁄ i = 1 n V P i . (5) 13.6 14.6 15.6 16.6 17.6 18.6 19.6 20.6 21.6 22.6 0.2 0.4 0.6 0.8 1 Layergapfraction H - L 14.515.516.517.518.519.520.521.522.523.524.525.5 0.2 0.4 0.6 0.8 1 Layer gapfraction H - L 17.2 18.2 19.2 20.2 21.2 22.2 23.2 24.2 25.2 26.2 0.2 0.4 0.6 0.8 1 Layer gap fraction H - L upper limit of height layer (m) upper limit of height layer (m) upper limit of height layer (m) Oak Gr13 Beech Gr12 Beech Bu38 Fig. 25: Layer gap fractions of 1m height layers, calculated on the assumption of volumetric homogeneity Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 53 its uppermost layer, the lowest gap fraction of beech Bu38 and Gr12 was 2.5m and 3.5m below the apex (Fig.25). In any case, the general trend was a more or less continuous decrease in gap fractions as one moved towards the top layer. Gap fractions explained 64%, 89%, and 89% of the variability of layer leaf area densities (Bu38, Gr12, and Gr13 respectively), which were significant relationships at the 1%-level. The regression on was only significant for oak Gr13 (r² = 0.51), leading to the conclusion that the increase of layer leaf area densities of the beeches with height was basically due to decreasing gap volumes; which is also valid for oak Gr13, even though increasing leaf area densities of leaf clouds also occurred. 2.3.5 Leaf cloud oriented evaluation of leaf arrangement in the crown Spatial and qualitative properties of leaf clouds were investigated because of their potential importance for up-scaling of photosynthesis and also because the arrangement of leaf clouds appeared to be quite regular (compare Fig. 16). The growth of tree crowns is generally understood as dependent on a complex interaction of species-specific rules and the research on this topic has been described in chapter 1. But though it has repeatedly been shown that the consequent application of growth rules in simulations over several growth periods leads to regular shaped, typical crown forms (K URTH & S LOBODA 1999, DE R EFFYE ET AL . 1997, L IST & K ÜPPERS 1997, S IEVÄNEN ET AL . 1997), a regular structure of real tree crown shapes in a mature forest has not yet been described in detail, while general concepts of typical crown forms exist already for a long time (H ALLÉ ET AL . 1978). Therefore, it becomes questionable, if fractal simulations of tree growth are an adequate method for their description (L IST & K ÜPPERS 1997). A common argument for these doubts is that the influence of tree growth patterns may become less visible in ageing trees due to the growing and accumulating influence of changing environmental conditions during its life-span and the influence of an inhomogeneous environment. Regularities in canopy structure may have a significant impact on up-scaling methods since they suggest underlying patterns in flows of mass and energy. For example, as the directed separation of electrical charges across the thylakoid membrane of the chloroplast by the spatial organisation of the electron transport chain causes a powerful charge gradient (K ARLSON 1999), the spatial organisation of tree crowns could influence the distribution of photosynthetically active radiation in the canopy via transmission and reflection. Transmittance and reflectance of PAR on typical leaf surfaces varies between 2 and 7%, and between 8 and 15%, respectively, with an average value of ca. 5% for transmittance and ca. 10% for reflectance (J ONES 1992). Both processes are in virtually all canopy light models assumed to be randomly directed, knowing that reflection is dependent on the angle between incoming radiation and reflecting surface, and thereby considering the leaves and other crown elements to be randomly oriented. Even though 10% of the incoming radiation is a small proportion, the resulting irradiance after the first reflection lies often in the range of light saturation of photosynthetic light response curves of shade leaves (achieved at 100 – 200 µmol/(m²*s) for beech, L ICHTENTHALER ET AL . 1981, S CHULTE 1992), while the incoming global radiation above the canopy is often higher than the saturation value for sun leaves (600 - 700 µmol/(m²*s) for beech). It would be possible for tree crowns to optimise the use of radiation for photosynthesis, if the surplus of PAR in the upper part of the forest canopy could be passed to the lower layers by LAD P ` Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 54 directed reflection. Additionally, shade leaves could be spatially arranged such that the amount of reflected and transmitted radiation in the lower layers is optimally used. The leaf cloud oriented three-dimensional description of the investigated trees can not be used to test the reflection of each leaf, but it can be used to check, whether regularities exist that support the use of reflected and transmitted light in the lower layers. Leaf cloud properties may be described with a group of parameters that describe where the leaf cloud is situated in relation to the stem, to the canopy base, or to the forest floor; a second group of parameters that describe the influence of other crown elements on the environmental situation of the leaf cloud; a third group of quantities that describe the spatial properties (angles and extensions) of the leaf cloud, and, finally, a group of qualitative properties. Location properties include the quantities: H: relative height of the leaf cloud centre in the canopy (-), H abs : absolute height of the leaf cloud centre above the floor (m) E: distance of the leaf cloud centre to the stem in east direction (m), N: distance of the leaf cloud centre to the stem in north direction (m), stemd: horizontal distance of the leaf cloud centre to the stem (m), AZ s : azimuth of the horizontal vector stem → leaf cloud centre, measured anti-clockwise from the north (°). Crown environmental properties are: CLA: sum of tree canopy leaf area above the leaf cloud (m²), CVOL: tree canopy volume above the leaf cloud (m³), CLAD: average tree canopy leaf area density above the leaf cloud (m²/m³). Leaf cloud spatial properties are: AZ P : azimuth of the exposition of the leaf cloud plane, mathematically defined as azimuth of the upwards directed normal vector of the leaf cloud plane, measured anti-clockwise from the north (°), α αα α h : leaf cloud angle; steepest angle of the leaf cloud plane towards a horizontal plane (°, positive and negative values), α αα α AZ : inclination of the main growth direction of a leaf cloud towards the horizon. The main growth direction is here determined as that vector in the leaf cloud plane, that goes through the leaf cloud centre and comes from the stem. (°, positive and negative values), α αα α s : angle of the main growth direction vector towards the idealised surface of the crown (°), H s : height of the intersection of main growth direction vector and idealised canopy surface (m), D s : derivative of the idealised canopy shape function at the point of intersection with the main growth direction vector(m/m), area: vertically projected area of the leaf cloud (m²), volume: volume of the leaf cloud (m³), Hrange: vertical extension of the leaf cloud (m). Qualitative properties include: LAD: Leaf area density of leaf clouds (leaf area per leaf cloud volume, m²/m³), Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 55 WAD: Wood area density of leaf clouds (projected area of branches and twigs per leaf cloud volume, m²/m³) CLA was calculated based on the cloud-related height and leaf area data, summing up leaf area of all leaf clouds whose centre lies above a certain relative height. CVOL relies on the volume calculations for height layers (compare Fig. 23), summing up all layer volumes above the relative height of the leaf cloud centre and the height-proportional upper part of that layer to which the leaf cloud centre belongs. CLAD, in contrast, is not related to crown form oriented layer volumes, but assumes a constant volume of each layer above the leaf cloud, thus considering the tree crown as a cylinder. This was done to enable an estimation of the selfshading effect of crown leaf area densities on leaf clouds on the basis of an application of Beer’s law to height layers (see below). The volume of these height layers was, therefore assumed to equal the maximum of height layer volumes of each tree. Volume (volume) of leaf clouds has been estimated by calculation of their enveloping polyhedron’s volume (see chapter 4.1.2.2). The variables α αα α AZ , α αα α s , H s , and D s were introduced for the investigations on spatial regularities in the tree crown and require an approximate description of the canopy shape. The discontinuous real crown shape may not be used for their calculation, which reveals the idealising concept behind the word “canopy shape”. The chosen concept to approximate the measured crown extensions shall enable the consideration of deterministic relationships between properties of crown elements and the canopy shape and therefore tries to describe a typical canopy shape for the given trees in a forest environment: It is assumed that homogeneously changing conditions of the environment do not fundamentally change the typical canopy shape, and that the observed variety of canopy shapes from the same species mainly results from their spatially inhomogeneous environments. Thus, the typical canopy shape may not be found in inhomogeneous environments like a forest, and it may be difficult to reconstruct it from the actual spatial situation, because this situation has changed during the life-span of a tree. The described typical crown shape therefore equalises the crown development in all horizontal directions by taking the maximum extension of height layers as the typical extension in every other direction. It is assumed that the canopy would have developed to this maximum extension in all horizontal directions, if no competition effects due to the inhomogeneity of the forest environment would exist. The canopy surface was defined to be a surface of revolution around the stem on the basis of 5 th order polynomial functions that were approximated to the maximum stem distances in each 1m-height layer. The lowest height layer of each tree was not considered in the approximation and the polynomial function was cut at the bottom of the tree crown (see Fig. 26). The approximations show a similar crown shape of both beeches which is different from the canopy surface shape for the oak. This can definitely be shown by a comparison of the derivatives of the three shape functions (Fig. 27). While the derivative of both beech crown shape functions has two maxima in the height range of the tree canopies, the oak’s had only one, which is due to a great height range in the shape function curve, where the height layers have nearly constant and very high maximum stem distances, while the layers above and below this part are much smaller, so that the shape function monotonously decreases from the five maximum layers towards both ends of the crown. Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 56 Fig. 26 : Polynomial approximations to the maximum stem distance in each layer (first row). The canopy surface was assumed to be a surface of revolution of these functions around the x-axis (second row, all units in meters). The functions for the dependence of stem distance (Y) to height (X) are displayed below (Bu38, Gr12, and Gr13, respectively). The angle between leaf cloud plane and canopy surface ( α αα α s ) was determined at the point of intersection of a straight line through the leaf cloud and the calculated canopy surface (right side, side view). The straight line represents the main growth direction of the leaf cloud and goes through the central axis of the stem and the leaf cloud centre and lies in the leaf cloud plane. While α αα α h is the steepest inclination of the leaf cloud plane, α αα α AZ is the inclination of the leaf cloud plane when measured in direction of its stem relative azimuth orientation AZ S , which is illustrated in the graph below (view from above) 14 16 18 20 22 height H m L 1 2 3 4 5 6 7 8 mets ecnatsid H m L beech Bu38 16 18 20 22 24 26 height H m L 1 2 3 4 5 6 7 8 mets ecnatsid H m L beech Gr12 18 20 22 24 26 28 height H m L 1 2 3 4 5 6 7 8 mets ecnatsid H m L oak Gr13 15 20 25 -5 -2.5 0 2.5 5-5 -2.5 0 2.5 5 15 20 25 -5 -2.5 0 2.5 5 15 20 25 -5 -2.5 0 2.5 5 -5 -2.5 0 2.5 5 15 20 25 -5 -2.5 0 2.5 5 15 20 25 -5 -2.5 0 2.5 5 -5 -2.5 0 2.5 5 15 20 25 -5 -2.5 0 2.5 5 Y = - 0.000827421 x 5 + 0.06824115 x 4 - 2.22255 x 3 + 35.64606 x 2 - 280.825 x + 871.535 Y = - 0.000455346 x 5 + 0.04100925 x 4 - 1.45066 x 3 + 25.09886 x 2 - 211.399 x + 694.228 Y = - 0.0000366738 x 5 + 0.00210313 x 4 - 0.0402233 x 3 + 0.27228 x 2 - 0.0546 x + 0.039 Direction of inclination calculations for α αα α s and α αα α AZ AZ S N Direction of steepest inclination of the leaf cloud plane ( α αα α h ) α αα α AZ α αα α s horizon Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 57 An important consequence of the described canopy shapes is that the maximum extension of the canopy of oak Gr13 lies in the upper half of the crown, while it is in the lower third of both beech canopies. Empirical evidence for the relatively higher position of the maximum extension of oak canopies was found in stand investigations on all trees from the Großebene and from the Steinkreuz stand: While the height of maximum extension in south, east, north, and west direction was on average 80% of the total tree height of 48 oak trees, it was on average 67% of the tree height of 58 beeches. Only trees higher than 15m were considered in this comparison and the range between first and third quartile was 76.7 - 84.9 % for oak trees and 57.2 - 75.6% for beech trees. The same value for all 80 beech trees higher than 15m from the Buchenallee stand was 45% with an interquartile range of 41% - 50.2%. α αα α s was calculated by prolonging the main growth direction of the leaf cloud (a straight line in the leaf cloud plane that goes through the stem and the leaf cloud centre) to the canopy surface, thus considering the azimuth of the leaf cloud relative to the stem (AZ s ) (Fig. 26). The angle was calculated between the main growth direction and the derivative D s of the polynomial function at the point of intersection of both lines in a two-dimensional co-ordinate system in the plane of the main growth direction and the stem (x = H abs , y = stemd). The derivation of the parameters is described in the appendix. 2.3.5.1 Properties of the crown environment of each leaf cloud Tree crown leaf area above each leaf cloud (CLA) reflects the pattern of leaf area in different height layers (Fig. 21) from the view point of a leaf cloud, thus, cumulating the leaf area above it. Though big changes in leaf area were found for 10cm height layers, these changes cause 16 18 20 22 24 26 height H m L - 4 - 3 - 2 - 1 0 1 d dmets ê d thgieh Oak Gr13 14 16 18 20 22 24 height H m L - 4 - 3 - 2 - 1 0 1 d dmets ê d thgieh Beech Gr12 14 16 18 20 22 height H m L - 4 - 3 - 2 - 1 0 1 d dmets ê d thgieh Beech Bu38 Fig. 27: Derivatives of the 5 th order polynom that approximates the maximum horizontal extensions of 1m-layers of the three trees. While the derivative of the beech functions has two maximums in their canopies’ height range, only one maximum is to be found in the height range of oak Gr13, which is a consequence of the outstanding position of the 5 largest layers with nearly constant maximum stem distance relative to the other layers. 0 0.2 0.4 0.6 0.8 relative height H - L 50 100 150 200 250 300 350 ALC H ²m L Oak Gr13 0 0.2 0.4 0.6 0.8 relative height H - L 50 100 150 200 250 300 350 ALC H ²m L Beech Gr12 0 0.2 0.4 0.6 0.8 relative height H - L 50 100 150 200 250 300 350 ALC H ²m L Beech Bu38 Fig. 28: Cumulative leaf area of leaf clouds in relation to relative height H . The curvilinear relationship was approximated with one-parametric functions of the form: CLA = Tree leaf area – k * H ². The coefficient k was 358.3, 302.6, and 358.4, respectively with r²values 0.97, 0.98, and 0.96 for the trees Bu38, Gr12, and Gr13. Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 64 The angle between main growth direction of leaf clouds and the idealised canopy surface (α αα α S ) had a similar height dependence for both beech trees, while it was different from that of oak Gr13 (Fig. 37). The range of achievable values in this relationship is partly limited by the tree-specific canopy shape function that was derived from measured data for all trees using the same polynomial function. Fig. 38 shows that the similarity in the α αα α S vs. height relationship of beech crowns was not completely due to the similar canopy shape of both trees: The consideration of all α αα α AZ - angles of beech Bu38 allows a much bigger range of α αα α S -values than was measured and this is even true, when only the lower variation in α αα α AZ -angles from the bottom part of the crown is considered in the simulation of α αα α S -angles for their height range. The similarity of main growth directions of leaf clouds from the two beech trees may also be observed without relating them to the idealised canopy shape: Fig. 39 shows the vector fields of the main growth directions of leaf clouds from both trees, i. e., the graphs from Fig. 35 twodimensionally scaled to a common height range and superimposed. Leaf clouds of both trees occupied nearly the same space relative to apex and crown base, which would not be the case when the vector field from oak Gr13 would be superimposed. Thus, the similar crown shape with a dent between 0.45 and 0.6 relative height is still visible. Neighbouring vectors from both trees follow often the same direction and the main patterns that have been described for beech Bu38 vectors are still valid. The alternation of height ranges with Fig. 39: Main growth direction of leaf clouds of beech Gr12 (entire, dark, and longer arrows) and of beech Bu38 (dotted, light (red), and shorter arrows). The graphs from Fig. 35 were twodimensionally scaled to a common height range for both crowns. 0 0.1 0.2 0.3 0.4 0.5 stem distance H scaled L 0 0.2 0.4 0.6 0.8 l e r . t h g i e h H d e l a c s L beech trees Bu38 and Gr12 Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 65 more upwards and more downwards inclined leaf clouds in the lower part of the crown may still be shown, when the absolute height ranges from beech Bu38 are recalculated to relative heights (Fig. 40). Assuming that these similarities reflect a species-specific trend in mature beech crowns, the α αα α S vs. height relationship of both trees was approximated with a single curve for both data sets (Fig. 41). The geometrical meaning of this curve is that leaf clouds in the crown were on average fanned-up towards the canopy surface. 2.3.5.4 Azimuth angles Though significant correlations were not found between the azimuth orientation of the leaf cloud plane ( AZ P ) and any other tree inherent quantity, the comparison between the neighbouring trees Gr12 and Gr13 reveals a significant similarity in both distributions (r²=0.41, p<0.01, Fig. 42). Thus, the AZ P -distribution appears not to be regularly distributed, but is possibly dependent on environmental factors that affect both trees. A regularity of AZ S angles could only be found in relation to the azimuth of the slope where the trees were standing. While the largest portion of leaf clouds of beech Bu38 was oriented towards the Buchenallee slope azimuth, this was not true for the Großebene trees. No significant correlations were found to the AZ S frequency distributions, which indicates if the tree crown was developed symmetrical in all directions. The 30° angle classes of the AZ S frequency distributions correspond to radial sectors of the tree crown. While the beech trees had the relatively most leaf clouds in the azimuth direction of the slope of their stand, oak Gr13 had the highest frequency of leaf clouds in that angle class, that was 30° closer to south (Fig. 43). 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 relative height H - L 0 20 40 60 a ZA H ° L Beech trees Bu38 and Gr12 Fig. 40: Average inclination of the main growth direction of leaf clouds towards the horizon ( α αα α AZ ) in layers of beech trees. Open triangles represent beech Bu38, while the rhombi stand for the superimposed vector field of both beech trees (Fig. 39). Fig. 41: A unique relationship has been drawn for the similar relationships between α αα α S and relative height for both beech trees (Bu38: filled triangles, Gr12: open squares). The approximated fourth order polynomial function was y = 1259.85 x 4 - 1778.46 x 3 + 569.83 x 2 + 96.89 x + 54.83. 0 0.2 0.4 0.6 0.8 relative height H - L 25 50 75 100 125 150 175 a s H ° L Beech trees Bu38 and Gr12 Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 66 Upper limit of AZ P –class (°) Upper limit of AZ P –class (°) Upper limit of AZ P –class (°) Fig. 42 : Frequency distributions of the azimuth orientation of leaf cloud planes ( AZ P ). While the frequency distribution of the beech trees is completely different, the distributions of the neighbouring oak Gr13 and beech Gr12 appear to be similar (r² = 0.41). The azimuth of the slope of the stand is 157.5° for Buchenallee and 225° for Großebene. 30 60 90 120 150 180 210 240 270 300 330 360 0.025 0.05 0.075 0.1 0.125 0.15 probability BeechBu38 30 60 90 120 150 180 210 240 270 300 330 360 0.025 0.05 0.075 0.1 0.125 0.15 probability BeechGr12 30 60 90 120 150 180 210 240 270 300 330 360 0.025 0.05 0.075 0.1 0.125 0.15 probability OakGr13 Upper limit of AZ S -class (°) Upper limit of AZ S -class (°) Upper limit of AZ S -class (°) Fig. 43: Frequency distributions of AZ S , the leaf cloud centres’ azimuth orientations relative to the stem (0° = north). The azimuth of the slope of the stand is 157.5° for Buchenallee and 225° for Großebene. While the beech trees had the relatively most leaf clouds in the azimuth direction of the slope of their stand, oak Gr13 had the highest frequency of leaf clouds in that angle class, that is 30° closer to south. No significant correlations were found between the AZ S frequency distribution and that of AZ P . 30 60 90 120 150 180 210 240 270 300 330 360 0.05 0.1 0.15 0.2 probability BeechGr12 30 60 90 120 150 180 210 240 270 300 330 360 0.05 0.1 0.15 0.2 probability BeechBu38 30 60 90 120 150 180 210 240 270 300 330 360 0.05 0.1 0.15 0.2 probability OakGr13 rel. frequency rel. frequency rel. frequency rel. frequency rel. frequency rel. frequency Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 67 A comparison of the average leaf cloud azimuth angles ( AZ P ) in 30° AZ S -sectors is shown in Fig. 44. While the mean leaf cloud azimuth ( AZ P ) in most sectors of beech Bu38 was between south-east and south-west (135°-225°), the leaf clo uds in direction of the slopes azimuth (157.5°) are oriented towards north. The prevailing average leaf cloud azimuth of beech Gr12 sectors was between east-south-east and north-north-east (247.5°-337.5°). No unique range of AZ P -angles was preferred in the sector averages of oak Gr13. These results are only examples of the azimuth orientations of growth in these trees, that were evaluated in order to assure a complete representation of the data set. Further studies on other trees would be necessary to investigate if the found tendencies have a general meaning. 2.3.5.5 Spatial extension of leaf clouds The quantities which describe the spatial extension of leaf clouds are partially dependent on each other, because projected area and height range may be used to calculate a volume around the leaf cloud plane with two horizontal borders above and below and vertical borders along the leaf cloud shape towards the side. The relationship between projected area times height range ( area * Hrange ) and calculated volume ( volume ) of the leaf cloud enveloping polyhedron is shown in Fig. 45. It was better correlated for oak Gr13 (r²=0.9) than for beech Bu38 (r²=0.67) and beech Gr12 (r²=0.74). The slope of the linear equations was very similar for all trees (0.30, 0.30, and 0.33 for the trees Bu38, Gr12, and Gr13, respectively). Fig. 44: Average azimuth of the leaf cloud planes in 30° sectors of each tree crown. While the mean leaf cloud azimuth ( AZ P ) in most sectors of beech Bu38 was between south-east and south-west (135°-225°), the leafclouds in direction of the slopes azimuth (157.5°) are oriented towards north. The prevailing average leaf cloud azimuth of beech Gr12 sectors was between eastsouth-east and north-north-east (247.5°- 337.5°). No unique range of AZ P –angles was preferred in the sectors of oak Gr13. 30 60 90 120 150 180 210 240 270 300 330 360 50 100 150 200 250 300 350 AZ P BeechBu38 30 60 90 120 150 180 210 240 270 300 330 360 50 100 150 200 250 300 350 AZ P BeechGr12 30 60 90 120 150 180 210 240 270 300 330 360 50 100 150 200 250 300 350 AZ P OakGr13 Upper limit of AZ S -class (°) Upper limit of AZ S -class (°) Upper limit of AZ S -class (°) Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 68 0 0.5 1 1.5 2 2.5 3 area * hrange H m³ L 0 0.2 0.4 0.6 0.8 1 1.2 1.4 emulov H ³m L Beech Bu38 0 1 2 3 4 5 6 7 area * hrange H m³ L 0 0.5 1 1.5 2 emulov H ³m L Oak Gr13 0 2 4 6 8 10 area * hrange H m³ L 0 1 2 3 4 emulov H ³m L Beech Gr12 Fig. 45: The relationship between projected area times height range ( area * Hrange ) and calculated volume (volume) of the leaf cloud enveloping polyhedron was better correlated for oak Gr13 (r²=0.9) than for beech Bu38 (r²=0.67) and beech Gr12 (r²=0.74). The slope of the linear equations was 0.30, 0.30, and 0.33 for the trees Bu38, Gr12, and Gr13, respectively. area * Hrange (m³ ) area * Hrange (m³ ) area * Hrange (m³ ) 0 0.2 0.4 0.6 0.8 relative height H - L 0 0.5 1 1.5 2 2.5 3 thgieh egnar H m L Beech Bu38 0.2 0.4 0.6 0.8 relative height H - L 0.5 1 1.5 2 2.5 3 3.5 4 thgieh egnar H m L Beech Gr12 0.2 0.4 0.6 0.8 relative height H - L 0.5 1 1.5 2 2.5 thgieh egnar H m L Oak Gr13 Fig. 46: The height extension of the leaf clouds ( Hrange ) showed a significant (p<0.001) tendency to increase with relative height in the canopy. R²-values were higher for the beech trees (0.38 and 0.28, respectively) than for oak Gr13 (0.14). 30 60 90 120 150 180 210 240 270 300 330 360 2.5 5 7.5 10 12.5 15 projected area H m² L OakGr13 30 60 90 120 150 180 210 240 270 300 330 360 5 10 15 20 25 projected area H m² L BeechBu38 30 60 90 120 150 180 210 240 270 300 330 360 5 10 15 20 projected area H m² L BeechGr12 Upper limit of AZ S -class (°) Upper limit of AZ S -class (°) Upper limit of AZ S -class (°) projected area ( m² ) projected area ( m² ) projected area ( m² ) Fig. 47: Projected area of leaf clouds ( area ) summed for twelve different AZ S -angle classes (radial sectors of the tree crown). The distribution pattern is similar to Fig. 43 and shows that the beeches had the highest amount of leaf cloud projected area in direction of the slope of their stand (157.5° and 225°) and that they preferred a unique range of angles for strengthened development, while area of oak Gr13 leaf clouds was highest in that angle class that is 30° closer to south than the slope of the Großebene stand (225°). Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 69 area , volume , and Hrange were only weakly correlated to height or position of the leaf cloud. The strongest relationship was found between Hrange and H (Fig. 46) with coefficients of determination below 0.4. R²-values were only in some cases higher than those of Fig. 46, when the relations are based on the crown environmental properties CLA , CVOL , or CLAD . For example the relationship between Hrange and CVOL had an r² of 0.45 for beech Bu38 and the relationship between Hrange and CLAD slightly improved the r²-value of oak Gr13 to 0.16. Only minor changes to the patterns of frequency distributions of AZ S in Fig.43 were detected, when volume (data not shown) or projected area ( area ) of the leaf clouds in each 30° angle class of AZ S are considered. The position of the leaf cloud centre relative to the stem was decisive for the classification of leaf clouds. Figure 47 shows that the beeches had the largest amount of leaf cloud projected area in the direction of the slope of their stand (157.5° and 225°) and that they preferred a unique range of angles for strengthened development, while area of oak Gr13 leaf clouds was highest in that angle class that is 30° closer to south than the slope of the Großebene stand (225°). In addition to this, oak Gr13 shows strengthened development in three different AZ S -angle ranges (90-120°, 180-210°, and 300-390°) wh en compared to the sectors between these ranges. 2.3.5.6 Leaf area densities of leaf clouds Leaf area densities of leaf clouds could be key parameters to a leaf cloud oriented 3D-lightmodel of single trees and it was therefore necessary to investigate in some detail if they are randomly distributed in the canopy space or if they depend on any other quantity, which would facilitate the parameterisation of a leaf cloud oriented light model. Measured leaf area densities were partly influenced by the measurement method. Leaves of very small leaf clouds were often arranged along one branch axis or in one plane, so that gaps between two branches or between different leaf-layers did not occur. This increased their calculated leaf area density. Additionally, very small leaf clouds often had a more regular form that fits more accurately into a plane bordered polyhedron than those of larger leaf clouds. Both 0.5 1 1.5 2 2.5 3 3.5 Volume H m³ L 10 20 30 40 50 60 Leaf Area Density H m² ê m³ L BeechGr12 BeechBu38 Oak Gr13 Fig. 48: Leaf area densities of all harvested leaf clouds. Different resolutions in the 3D-description of tree crowns result from the defined minimum diameter of a leaf cloud supporting branch, which was 2cm in the Buchenallee stand and 3cm in the Großebene stand. Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 70 effects led to some extremely high leaf area densities in very small leaf clouds of beech Bu38, as can be seen in Fig. 48. Therefore, geodetic measurements on the Großebene trees were performed without considering very small leaf clouds as separate units (see methods). Then no similar effects were observed (compare Fig. 48). Leaf area densities were in the range of 1.6367.7 m²/m³ in beech Bu38 (139 leaf clouds), 1.31-10.2 m²/m³ in beech Gr12 (66 leaf clouds) and 0.26-13.5m²/m³ in oak Gr13 (88 leaf clouds). No clear relationship of leaf area density could be demonstrated by regression analysis on each of the investigated leaf cloud properties (see above) for each tree. However, when leaf area densities of leaf clouds were averaged per height layer, all trees showed a more or less clear tendency to increase leaf area densities of leaf clouds with height. (Fig. 49). The average leaf area densities of leaf clouds in distinct radial sectors of the trees are shown in Fig. 50. A weak similarity in the angular distributions of LAD has been found between the beeches in the different stands (r² = 0.22) and it turned out that this was due to a remarkable similarity of the angular distribution in the north half of the crowns (r² = 0.80, p<0.05), which was also found, when the angle classes were larger (45°: r²=0.93, p<0.05) or smaller (15°: r²=0.56, p<0.01). Though no similarity was found to the oaks angular distribution of LAD , this might be chance and can not be interpreted as species-specific. Apart from this similarity, LAD was irregularly distributed over AZ S -angle classes. A comparison of the angular LAD -distribution of the neighbouring trees oakGr13 and beech Gr12 (Fig. 51) shows that neighbourhood effects could have an influence on LAD of oak leaf clouds: The sectors with high average LAD of leaf 13.1 14.1 15.1 16.1 17.1 18.1 19.1 20.1 21.1 22.1 2.5 5 7.5 10 12.5 15 LAD H m² ê m³ L BeechBu38 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 1 2 3 4 5 LAD H m² ê m³ L BeechGr12 16.7 17.7 18.7 19.7 20.7 21.7 22.7 23.7 24.7 25.7 2 4 6 8 10 12 LAD H m² ê m³ L Oak Gr13 Average height of layer (m) Average height of layer (m) Average height of layer (m) Fig. 49: Average leaf area density of leaf clouds in 1m-height layers. The classification is based on the positions of the leaf cloud centres. Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 71 4.84m 7.82m 4.12m 30 60 90 120 150 180 210 240 270 300 330 360 5 10 15 20 LAD H m² ê m³ L BeechBu38 30 60 90 120 150 180 210 240 270 300 330 360 1 2 3 4 5 6 LAD H m² ê m³ L BeechGr12 30 60 90 120 150 180 210 240 270 300 330 360 2 4 6 8 10 12 LAD H m² ê m³ L OakGr13 Fig. 50: Average leaf area densities ( LAD ) of leaf clouds in radial sectors of the tree crown given by the azimuth of the leaf cloud centre relative to the stem (AZ S ). Upper limit of azimuth class (°) Upper limit of azimuth class (°) Upper limit of azimuth class (°) 300 330 36030 60 90 120 150 180 210 240 270 300 330 36030 60 90 120 150 180 210 240 270 Fig. 51: Average leaf area densities of leaf clouds in radial sectors of the canopies of beech Gr12 and oak Gr13. The crowns are situated in their stems’ relative angular position to each other. Angles and distances towards the nearest neighbouring trees are indicated. North Average leaf area density of leaf clouds (m²/m³) 126 10842 5.63m 7.62m 5.70m 3.40m Gr12 Gr13 Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 72 clouds were more or less clearly directed towards the three closest tree stem positions of neighbouring trees. Beech Gr12 did not show this coincidence. Data of the three trees were separately used for a multiple regression analysis of LAD on 8 quantities ( H, N, E, α αα α h , absolute value of α αα α h , AZ p, AZ s , Area ). The quantities were chosen because of their expected potential to explain leaf area density distribution inside tree crowns: • Leaf area densities are likely to increase with height ( H ), because leaves cannot survive without light and the lower parts of the crown get less light than the upper parts. Nevertheless it is questionable if this effect may be found in leaf area densities of leaf clouds, because the absolute amount of leaves in a height layer depends on leaf area density of leaf clouds and as well on leaf cloud density in the height layer. Though number and leaf area density of leaf clouds were low in the lowest layers of crowns of oak and beeches (Fig. 19b), no obvious trend in leaf area densities of leaf clouds was found in relation to height (data not shown). • A dependence of leaf area density on distances to the stem in east and north direction, leaf cloud inclination at the point of attachment, or azimuth orientation relative to the stem ( E, N, α α α α b , AZ p, AZ s ) could reflect a species-specific internal organisation scheme of the tree crown. For example, if the leafless space in the central part of the crown develops via partial thinning of leaves of leaf clouds over time, this should have a remarkable effect on the relationship between distances ( E,N ) and leaf area density, or if leaf clouds on the south side of the canopy would have generally higher leaf area densities when they were oriented to the east, this would affect the relationship between LAD and the azimuth angles. • Angle and projected area of the leaf cloud plane (α αα α p , Area ) may be correlated with leaf area density because they have a major influence on light harvesting of the leaf cloud and, thus, may be influential if leaf area densities partly depend on the light situation. Because regression analysis assumes normal distribution of the dependent variable (E NGEL 1997), the probability density functions of leaf area density data was analysed. A first logarithmic transformation showed much better agreement with the normal distribution than the original distribution (for example beech Bu38, see Fig. 52). Fig. 52: Comparison of the distribution of leaf area densities of leaf clouds of beech Bu38 (left side) with the normal distribution. The same data after logarithmic transformation are in better agreement with the normal distribution. The original data were standardised by shifting their mean value to zero and scaling their variance to unity. This was confirmed by an r²-value of 0.97 for the relationship between probability densities of Log( LAD ) and the corresponding values of the normal distribution. The original data were - 2 0 2 4 6 8 Standardised LAD 0 0.2 0.4 0.6 0.8 ytilibaborp ytisned - 3 - 2 - 1 0 1 2 3 4 Standardised Ln H LAD L 0 0.1 0.2 0.3 0.4 0.5 ytilibaborp ytisned beech Bu38 beech Bu38 Tree crown structures of mature Fagus sylvatica and Quercus petraea trees 73 standardised for comparison with the normal distribution by shifting their mean value to zero and scaling their variance to unity. A scatter plot of both quantities (normal probability plot, see Fig. 53) reveals a curvilinear relationship behind this r²-value, indicating that the log-normal distribution is left skewed in the case of beech Bu38 (compare Fig. 52). Fig. 53: Normal probability plots of logarithmic transformed LAD data of beech Bu38 against corresponding quantiles of the normal distribution and the cubic root logarithmic transformation of LAD against corresponding quantiles of the normal distribution. The cubic root transformation made the relationship more linear and improved the regression from r²=0.97 to r²=0.993. Thus, a second transformation taking the cubic root of Log( LAD ) was employed to make the relationship more linear, resulting in an r²-value of 0.993 to the normal distribution. The cubic root transformation was found by the maximum-likelihood method according to (B OX & C OX 1964), where the conditional maximised log likelihood of a given power transformation with respect to the normal distribution is calculated and iteratively evaluated for a range of exponent values. The same procedure for the Großebene trees led to the transformation Log 3/2 ( LAD ) for both trees (r²=0.986 for beech Gr12 and r²=0.996 for oak Gr13). Because the natural logarithm of the lowest LAD-value of beech Gr12 was negative (-0.48), a constant of 0.5 had to be added to enable the Box-Cox transformation, which requires positive values. Fig. 54: Normal probability plots of transformed LAD data of beech Gr12 (left) and oak Gr13 (right) against corresponding quantiles of the normal distribution. Multiple regressions were based on a linear combination of all quantities of the form where y i is the i th response, f pi is the p th quantity evaluated at the i th case, and e i is the error of the i th case. Estimates of the coefficients β ββ β i are calculated to minimise the residual sum of squares. y i = b 1 f 1 i + b 2 f 2 i + … + b p f p i + e i , (8) 1 2 3 4 5 LogHLADL - 3 - 2 - 1 1 2 3 corresponding quantile 0.8 1.2 1.4 1.6 è!!!!!!!!!!!!!!!!!!!! Log H LAD L 3 - 3 - 2 - 1 1 2 3 corresponding quantile Log(LAD) beech Bu38 beech Bu38 1 2 3 4 5 6 Log 3 ÅÅÅÅÅÅ 2 H LAD L - 3 - 2 - 1 1 2 3 corresponding quantile 1 2 3 4 H Log H LAD L + 0.5 L 3 ÅÅÅÅÅÅ 2 - 3 - 2 - 1 1 2 3 corresponding quantile corresponding quantile beech Gr12 oak Gr13 Spatial distribution of leaf properties in tree crowns 80 The results allowed the calculation of temperature normalised values for carboxylation capacity ( Vc max ), electron transport capacity ( J max ) and day respiration ( R d ) with the program RACCIA (see below). Additional estimations of J max , the electron transport capacity were achieved by chlorophyll fluorescence measurements. They were performed using the portable pulse-modulation fluorometer PAM-2000 (Heinz Walz GmbH, Effeltrich, Germany), equipped with leaf clip holder 2030-B, on some of the oak leaves before the gas-exchange measurement on the same leaves. These leaves were darkened for at least 30 minutes with aluminium foil to enable one measurement of minimum and maximum fluorescence, F 0 and F m , with a saturating light pulse on dark adapted leaves (S CHREIBER ET AL . 1994). Fluorescence of the illuminated leaves ( F m ’ ) was afterwards determined with saturating light pulses of increasing light intensities up to 2500 µmol/(m²*s) or even more, when the resulting light response curve of the electron transport rate did not yet appear to saturate. At least three repetitions per light level were done. Quantum yield of the illuminated leaves ( Y ) was calculated as (S CHREIBER ET AL . 1994). The electron transport rate J was calculated according to G ENTY ET AL . (1989): where I is incident quantum flux density and the factor 0.84 accounts for absorptance of leaves. Electron transport capacity J max was found as electron transport rate J at a quantum flux density of 2000 µmol/(m²*s), which was determined by extrapolation of the measured electron transport rates at other quantum flux densities on the base of equation (29), which was fitted to the maximum measured values per light level. 3.1.4 Evaluation of A/C i -curves with RACCIA The measurement of A/C i -curves has been described as a cumbersome procedure in the past (L AISK & L ORETO 1996), which is probably due to the necessity of long stabilisation times for the conditions in the chamber after changing the C a -value and to the use of large CO 2 -storage and mixing systems, that made it necessary to work in the laboratory. This situation has changed to some extent due to the development of small portable photosynthesis measurement systems with small CO 2 -mixing units, small cuvettes, short distances for gas-supply and IRGAmeasurements, and automatic immediate calculations on the measured data, which facilitate the assessment of stability of cuvette conditions. Therefore much more data can be measured in the same time and have to be evaluated. The program RACCIA ( R outine for A/C i c urve ev a luation) was developed to automate the time-consuming derivation of species-specific key parameters of leaf photosynthesis from these measurements, as they are used in different variations of the Farquhar model of leaf photosynthesis (F ARQUHAR & VON C AEMMERER 1982). Because this is typically done by non-linear fits on a low number of data points along the A/C i curve (H ARLEY & T ENHUNEN 1991), a plausibility check is enabled by automatic graphical representation of the data and each fit on the screen during the automatic evaluation process. RACCIA is based on the equations of the H ARLEY /T ENHUNEN photosynthesis model (H ARLEY & T ENHUNEN 1991), which links a modification of the biochemical Farquhar model (F ARQUHAR & Y = I F m - F m ' M ë F m ' (20) , (21) J = 0.5 * 0.84 * Y * I Spatial distribution of leaf properties in tree crowns 81 VON C AEMMERER 1982) with the Ball/Berry model of stomatal conductance (B ALL ET AL . 1987), and on the calculation of day respiration and CO 2 -compensation point according to B ROOKS and F ARQUHAR (1985). 3.1.4.1 The H ARLEY /T ENHUNEN model of leaf photosynthesis The H ARLEY /T ENHUNEN model basically expresses net assimilation rate ( A ) as the sum of carboxylation rate ( Vc ), oxygenation rate ( Vo ), and day respiration ( R d ), i. e., the rate of CO 2 - evolution from processes other than photorespiration that continues in the light: (all quantities in µmol/(m²*s)). Photorespiration losses are expressed dependent on C i and the photocompensation point Γ ΓΓ Γ * (µmol/mol), that C i -value, at which A would be 0, if no other source of respiration than oxygenation of ribulose-1,5-bisphosphate catalysed by rubisco would occur. It is assumed that Vc is limited by the velocity of three processes, so that equation (22) is transformed to the common form of balance equation of most photosynthesis models: W c denotes the carboxylation rate limited by rubisco activity and W j is the carboxylation rate limited by regeneration of RuBP in the Calvin-cycle, which is light dependent. The phosphate limited carboxylation rate W P is not included in most photosynthesis models and was not considered in the parameter derivation with RACCIA nor in leaf gas exchange calculations with the H ARLEY /T ENHUNEN model. The remaining two expressions for W c -limited assimilation rate ( A v ) and W j -limited assimilation rate ( A j ) are basically the same as in (F ARQUHAR & VON C AEMMERER 1982): Here Vc max stands for the enzyme-specific maximum rate of carboxylation, K M,C (µmol/mol) and K M,O (mmol/mol) stand for the Michaelis-Menten constants of rubisco (ribulose-1,5-bisphosphate carboxylase-oxygenase) for carboxylation and oxygenation of ribulose-1,5-bisphosphate, and O (209 mmol/mol air at 101.3 kPa atmospheric pressure) is the leaf internal O 2 -concentration. W j is given as with P m (µmol/(m²*s)), the CO 2 saturated rate of photosynthesis at any given irradiance and temperature. On the assumption that 4 electrons are required for the regeneration of a single RuBP in the Calvin cycle, A j is expressed as A V = Vc max C i - G * K M,C H 1 + O ê K M,O L + C i - R d (24) A=Vc-0.5 Vo-R d (22) A= i k 1G * C i y { min 8 W c ,W j ,W p < -R d (23) W j = P m 1 + 2 G * ê C i , (25) A J = J C i - G * 4 C i + 8 G * - R d , (26) Spatial distribution of leaf properties in tree crowns 82 where J (µmol e - /(m²*s)) is the electron transport rate over the thylakoid membrane and equals 4 P m . Γ ΓΓ Γ * in the above equations is defined as with the dimensionless rubisco specificity factor τ ττ τ . Temperature dependence of this parameter and also of K M,C , K M,O , and R d is expressed in exponential equations, which were converted in the used version of the leaf model to be based on the parameter values at a temperature of 298.16K: parameter 298 stands for the temperature dependent parameter at a temperature ( T ) of 298.16K, R is the gas constant, and H a (J/mol) is the activation energy for the parameter. P m and thereby J is the only light dependent quantity: (Smith-equation). Here I (µmol/(m²*s)) is incident quantum flux density, P ml is P m at light saturation, and α α α α (mol/mol) stands for the initial slope of the curve relating CO 2 -saturated photosynthesis to irradiance. P m and P ml in this equation may be replaced by J and J max (maximum electron transport rate), when α αα α is multiplied by four. The temperature dependence of P ml and Vc max is described in a 4-parametric thermodynamic equation (J OHNSON ET AL . 1942, S HARPE & D E M ICHELE 1977), which may be expressed based on the parameter value at a temperature of 298.16K: Here, Vc max, 298 stands for the parameter value at T = 298.16 K, H a and H d (J/mol) are the energies of activation and deactivation for Vc max , and S (J/(K*mol)) stands for a Vc max -specific entropy term. The same equation with P ml - or J max -specific energies and entropy term is applied for P ml or J max . A in the above equation system is dependent on C i , which is in turn dependent on A and stomatal conductance g sw : C a (µmol/mol) stands for the external CO 2 -concentration and 1.6 accounts for the different diffusivities of water vapour and CO 2 in air. Additionally, g sw is linearly dependent on A and C a as was first described by B ALL ET AL . (1987): parameter = parameter298 * Exp B H a * H T - 298.16 L 298.16 R T F (28) G * = 0.5 O t , (27) P m = a I $ 1 + a 2 I2 Pml2 (29) Vc max = Vc max, 298 Exp B H a H T - 298.16 L 298.16RT F 1 + Exp B 298.16 S - H d 298.16R F 1 + Exp B ST - Hd R T F (30) (31) C i = C a - 1.6A ê g sw (32) g sw = g min + g fac A h s C s Spatial distribution of leaf properties in tree crowns 83 Here g min (mol/(m²*s)) is the constant cuticular conductance for water vapour, h s (-) and C s (µmol/(m²*s)) are relative humidity and CO 2 -concentration on the leaf surface and g fac is an empirically found factor that is derived from (B ALL ET AL . 1987). To calculate h s and C s from rh (external relative humidity) and C a , the boundary layer conductance for water vapour ( g aw , mol/(m²*s)) is taken into account (F ALGE 1997): The used version of the model solves iteratively for C i , thereby finding that C i -value that is compatible with net assimilation rate A (equation (23)) and stomatal conductance g sw (equations (32), (33), and (34) combined), and where A and g sw are related according to equation (31). 3.1.4.2 RACCIA routine for species-specific parameterisation The species-specific parameterisation of the H ARLEY /T ENHUNEN model and other Farquhar models with RACCIA is focused on the determination of three key parameters that are not rubisco-specific. Due to the - among higher plants - similar structure of the rubisco molecule and its highly conserved active sites (K ELLOGG & J ULIANO 1997), species-specific variations in rubisco kinetic parameters ( K M,C , K M,O , τ ττ τ , Γ ΓΓ Γ * ) are expected to be relatively small (B ERNACCHI ET AL . 2001). In vitro measured values for τ ττ τ and Γ ΓΓ Γ * of many different species generally vary about ±20% around a mean value of 2560 (dimensionless) and 42 µmol/mol at 25°C for all species (E PRON ET AL . 1995), and rather big (±10%) intra-specific variations were found under the same measurement conditions (P ARRY ET AL . 1987). However, also single outlying measurements (-50% for τ ττ τ and +100% for Γ ΓΓ Γ * ) exist for Fagus sylvatica and Castanea sativa (E PRON ET AL . 1995). The in vivo derivation of τ ττ τ and Γ ΓΓ Γ * from Nicotiana tabacum and Spinacia oleracea ( VON C AEMMERER ET AL . 1994) yielded τ ττ τ -values of 2710 and 2975, which equals Γ ΓΓ Γ*-values of 38.8 and 35.3 µmol/mol at 25°C, when oxygen concentration O is assumed to equal 210000 µmol/mol (equation 29). These measurements are the only ones, where carboxylation dependent limitation of the assimilation rate is assured by the use of transgenic plants with low rubisco content. The term K M,C (1+210 / K M,O ) from the calculation of A V (equation (24)) varies for the low number of measured species between 410 and 750, (M AKINO ET AL . 1988, H ARLEY & T ENHUNEN 1991, VON C AEMMERER ET AL . 1994, B ERNACCHI ET AL . 2001), though K M,C and K M,O are not expected to vary among higher plants ( VON C AEMMERER ET AL . 1994). It has been argued that this variation might be due to the in vitro measurement method. The two newer measurements use transgenic Nicotiana tabacum plants that shall assure the rubisco limitation of assimilation for in vivo measurements and end up with 710 and 746 for the term mentioned above ( VON C AEMMERER ET AL . 1994, B ERNACCHI ET AL . 2001). Rubisco-specific parameters and their temperature dependencies may, thus, be considered as constant among higher plants, meaning that species-specific variations in assimilation rates that are not due to stomatal limitations prevailingly result from the quantities P ml , Vc max , R d , and α αα α . (33) h s = rh - rh - 1 1 + gaw gsw (34) C s = C a - 1.37 H C a - C i L 1.37 + 1.6 gaw g sw Spatial distribution of leaf properties in tree crowns 84 RACCIA and the appertaining photosynthesis measurements were designated to estimate the quantities P ml , Vc max , and R d that are crucial for the calculation of leaf gas-exchange, because α αα α is the most conservative parameter out of the four and may approximately be estimated to equal 0.06 mol CO 2 /mol photons among C 3 species under most conditions (H ARLEY & T ENHUNEN 1991, E HLERINGER & B JÖRKMAN 1977). While equations (24) and (26) are a common part of most so-called Farquhar models, different types of equations are employed to describe light dependence of electron transport rate J , temperature dependencies, and effects of stomatal regulation, if considered. The original Farquhar model (F ARQUHAR & VON C AEMMERER 1982) for example employs a hyperbolic relationship instead of equation (29) to express the saturating relationship of electron transport rate J on irradiance I : The factor 2.1 in this equation has to be changed under certain conditions. J max stands here for the electron transport capacity, the maximum electron transport rate under saturating light conditions, and it is by definition of J and P m equal to 4 P ml . RACCIA can be used to derive both quantities, when A/C i -measurements are made at light saturation, because it then only uses the common equations (24) and (26). Published values for J max and Vc max range from 17 to 372 µmol/(m²*s) and from 6 to 194 µmol/(m²*s) (W ULLSCHLEGER 1993), which has due to the multiplication in equations (24) and (26) an immense impact on calculated species-specific photosynthesis rates. The effect of day respiration ( R d ) is often smaller due to its additive consideration and rather low absolute values: Published estimates of R d at about 25°C according to the method of L AISK (1977) and B ROOKS & F ARQUHAR (1985) lie prevailingly in the range from 0 to 0.8 µmol/(m²*s) (H ÄUSLER ET AL . 1996, H ÄUSLER ET AL 1999, J ACOB & L AWLOR 1993, H ERPPICH ET AL . 1998, B ROOKS & F ARQUHAR 1985, S UMBERG & LAISK 1995, LAISK & L ORETO 1996, A TKIN ET AL . 1997), but also higher values were measured (3.4 µmol/(m²*s) for Encelia farinosa, Z HANG ET AL . 1995), partly with another method (1.1 µmol/(m²*s) for Pinus sylvestris, W ANG ET AL . 1996). RACCIA first calculates R d as the negative assimilation rate that would be measured at C i = Γ ΓΓ Γ * , prolonging the linear initial slope of each A/C i -curve towards lower values (see Fig. 57, B ROOKS & F ARQUHAR 1985). The needed Γ ΓΓ Γ * -value is calculated from the temperature dependence of Γ ΓΓ Γ * and τ ττ τ , which are connected by equation (27). The used temperature dependence has been found by J ORDAN & O GREN (1984) on spinach and was confirmed by later measurements on spinach and wheat (B ROOKS & F ARQUHAR 1985), French bean (G HASHGHAIE & C ORNIC 1994), potato (H ÄUSLER ET AL . 1999), and Eucalyptus pauciflora (A TKIN ET AL . 2000), where it is expressed as a formula: However, a different temperature dependence was found for Epilobium hirsutum at temperatures below 18°C (G HASHGHAIE & C ORNIC 1994). A Γ ΓΓ Γ * -value of 38.8 µmol/mol at 25°C and 210,000 µmol/mol oxygen concentration in the air was derived from the measurements of J = J max I I + 2.1 J max (35) (36) G * = G * 25 + 1.88 H T - 298.16 L + 0.036 H T - 298.16 L 2 Spatial distribution of leaf properties in tree crowns 85 VON C AEMMERER ET AL . (1994) and was applied considering equation (27) and correcting O for air pressure of the measurement. The temperature dependent Michaelis-Menten constants for rubisco catalysed oxygenation and carboxylation, K M,O and K M,C , are calculated according to equation (28) based on the measurements of VON C AEMMERER ET AL . (1994) and the specific H A -values of H ARLEY & T ENHUNEN (1991), which are similar to those from B ERNACCHI ET AL . (2001). The data points below 350 µmol/mol CO 2 -concentration inside the leaf intercellular spaces ( C i ) are then used for a non-linear regression (based on the Levenberg-Marquardt method) of equation (24) on each curve, thereby assuming that Vc max is limiting photosynthesis in that part of the curve, so that A = A V (Fig. 57). Similarly, equation (26) is fitted to the points above 350µmol/(m²*s), where Vc max is not limiting and J max is equal to J due to saturating irradiance (2000µmol/(m²*s)) during the measurement. RACCIA then evaluates groups of A/C i -curves that belong to the same leaf (or to the same group of leaves, if desired) and were measured at different temperatures. A non-linear regression of equation (30) is performed on the calculated Vc max values of these A/C i -curves versus temperature. An additional data point in the Vc max versus temperature diagram results from complete enzyme inactivation of rubisco, which was shown to occur at 60°C (G EZELIUS 1975). At least three additional Vc max values at different temperatures are necessary, because equation (30) is used to estimate four parameters. The same equation for J max is fitted to the J max values of at least three A/Ci -curves at different temperatures again completed by a Zero-value, which was estimated from A RMOND ET AL . (1978) and N OLAN & S MILLIE (1976) to occur at 50°C. 4 data points were sometimes not enough for these approximations, especially when the measured values were close to each other, so that a completely different shape of the curve better fulfilled the requirements of the χ 2 merit function given by the sum of squared residuals. In this case, data points were weighted and an additional Zero-value at -30°C was added with 10% of the weight of the measurement-derived data to assure that the functional relationship starts with low values at 0°C instead of very high ones. 500 1000 1500 2000 2500 Ci H µmol ê H m² * s L L 0 10 20 30 40 50 60 70 A H lomµ ê ²m * s L L 2 A V A J 20 40 60 80 100 Ci H µmol ê H m² *s L L -1.5 -1 -0.5 0 0.5 1 1.5 2 A H l o m µ ê H ² m * s L L Γ * R d Fig. 57: Determination of Vc max and J max with non-linear approximations of equations (24) and (26) (left graph), and determination of R d from the initial slope of the A/C i -curve. Spatial distribution of leaf properties in tree crowns 86 3.2 Results 3.2.1 Light and height dependence of leaf properties 3.2.1.1 Relative Irradiance Beer’s law is the reason to expect an exponential decrease of relative irradiance with depth in the canopy (M ONSI & S AEKI 1953). The decrease of relative irradiance at the position of sampled leaves with vertical distance from the tree apex was close to exponential in the dominant beech Bu38 (r²=0.91) and no significant differences were found in the decrease of relative irradiance between its 4 vertical lines of investigation points. Relative irradiances from the subdominant tree Bu45 were much more scattered (r² =0.44, Fig. 58). An explanation for the higher scatter in the data of the subdominant tree Bu45 is that its light climate is much more dependent on neighbouring trees than that of beech Bu38. Therefore, depth in the canopy is often higher than the vertical distance to the tree apex. This has been considered by separate approximations on the four vertical lines of investigation points based on a modification of the exponential fit for beech Bu38, which allows for the correction of vertical distance (Fig. 59). The resulting idealised height correction (parameter b) was in the range from –0.68 m to 1.72 m. The height correction improved the coefficient of determination for data of beech Bu45 to 0.8. 2 4 6 8 10 height below apex H m L 0.2 0.4 0.6 0.8 1 evitaler ecnaidarrI Beech Bu38 Fig. 58: Exponential decrease of relative irradiance in the tree crowns with vertical distance to their apex. The approximated lines were y = Exp[-0.3764x] (r² = 0.91) for beech Bu38 and y = Exp[-0.4428x] (r² = 0.44) for beech Bu45. 2 4 6 8 10 12 height below apex H m L 0.2 0.4 0.6 0.8 1 evitaler ecnaidarrI Beech Bu45 2 4 6 8 10 12 14 corrected height b. apex H m L 0.2 0.4 0.6 0.8 1 evitaler ecnaidarrI Beech Bu45, all lines 2 4 6 8 10 12 height below apex H m L 0.2 0.4 0.6 0.8 1 evitaler ecnaidarrI Beech Bu45, line 1 b = 1.72 r² = 0.63 2 4 6 8 10 12 height below apex H m L 0.2 0.4 0.6 0.8 1 evitaler ecnaidarrI Beech Bu45, line 3 b = -0.68 r² = 0.75 2 4 6 8 10 12 height below apex H m L 0.2 0.4 0.6 0.8 1 evitaler ecnaidarrI Beech Bu45, line 4 b = 0.41 r² = 0.71 2 4 6 8 10 12 height below apex H m L 0.2 0.4 0.6 0.8 1 evitaler ecnaidarrI Beech Bu45, line 2 b = 1.25 r² = 0.89 r²=0.8 Fig. 59: Separate approximations of y = Exp[0.3764*(x+b)] to data of the four lines of investigation points. The derived height correction b is indicated in the graphs. The graph below shows all investigation points after application of the height correction. Spatial distribution of leaf properties in tree crowns 87 Fig. 60: Leaf angle distributions for 1m-height layers of the tree crown of beech Bu45 in angle classes of 10°. 0 0.1 0.2 0.3 0.4 0.5 10 20 30 40 50 60 70 80 90 11m-12m below apex 0 0.1 0.2 0.3 0.4 0.5 10 20 30 40 50 60 70 80 90 10m-11m below apex 0 0.1 0.2 0.3 0.4 0.5 10 20 30 40 50 60 70 80 90 9m-10m below apex 0 0.1 0.2 0.3 0.4 0.5 10 20 30 40 50 60 70 80 90 8m-9m below apex 0 0.1 0.2 0.3 0.4 0.5 10 20 30 40 50 60 70 80 90 7m-8m below apex 0 0.1 0.2 0.3 0.4 0.5 10 20 30 40 50 60 70 80 90 6m-7m below apex 0 0.1 0.2 0.3 0.4 0.5 10 20 30 40 50 60 70 80 90 5m6m below apex 0 0.1 0.2 0.3 0.4 0.5 10 20 30 40 50 60 70 80 90 4m5m below apex 0 0.1 0.2 0.3 0.4 0.5 10 20 30 40 50 60 70 80 90 3m4m below apex 0 0.1 0.2 0.3 0.4 0.5 10 20 30 40 50 60 70 80 90 2m3m below apex 0 0.1 0.2 0.3 0.4 0.5 10 20 30 40 50 60 70 80 90 1m2m below apex 0 0.1 0.2 0.3 0.4 0.5 10 20 30 40 50 60 70 80 90 0m-1m below apex Spatial distribution of leaf properties in tree crowns 88 3.2.1.2 Leaf angles Leaf angles to the horizon from both Buchenallee beech trees were in the range from 0° to 86°, low inclinations being much more abundant than steep inclinations. Data of investigation points were grouped in 1m-height layers to assure that at least 30 leaf angles are evaluated per data point. In a first approximation, leaf angle distributions of height layers did not appear to be regular, despite the fact that very steep inclinations above 70° did not occur in the lower half of both crowns, but were relatively abundant in the upper two metres (compare Fig. 60). A general trend towards higher average leaf angles in regions of higher irradiance was observed (Fig. 61), but large variations occurred in this relationship. Anyway it turned out that these leaf angle distributions are regular and belong to the same family of distributions: A more detailed analysis of skewness and kurtosis of the angle distributions of both trees revealed that a close to linear relationship can be drawn between both properties. This has among other things the meaning that leaf angles in each crown region were never normal distributed, because skewness and kurtosis of the normal distribution are 0 and the point (0,0) lies apart from the close to linear relationship. The non-normal distribution of leaf angles is also apparent from Fig. 60. Instead, the relationship between skewness and kurtosis of the measured leaf angle distributions lies close to that relationship that is obtained for the ellipsoidal distribution derived from an oblate spheroid, which was proposed for the description of leaf angle distributions (C AMPBELL 1989), thereby providing empirical evidence for the adequacy of this type of distribution for the description of leaf angle distributions in beech crowns (Fig. 60). k -values of each ellipsoidal distribution, derived by non-linear approximations of the ellipsoidal distribution function (integrated over 10° angle classes, average r² = 0.73), showed a strong dependence on absolute vertical distance from the apex, which was similar for both beech trees (Fig. 62). However, only a weak dependence on relative irradiance was found: While the height dependence shows a clear linear increase of k -values up to 6 or 7 m below apex and a linear decrease from this point towards the bottom of both tree crowns, no linear decrease can be observed in the region of lower irradiances. This is mainly due to the steep light gradient which y = -0.0017x 6 + 0.0193x 5 - 0.076x 4 + 0.113x 3 + 1.3028x 2 - 0.1062x - 1.07 -1.5 -1 -0.5 0 0.5 1 1.5 -0.5 0 0.5 1 1.5 Skewness Kurtosis beech Bu38 beech Bu45 average leaf angles of height layers 0 5 10 15 20 25 30 35 40 0 0.2 0.4 0.6 0.8 relative irradiance average leaf angle (°) beech Bu45 beech Bu38 Fig. 61: General increase of average leaf angles of height layers with relative irradiance (left) and relationship between kurtosis and skewness of all leaf angle distributions (right). The curve in the right graph indicates the relationship between kurtosis and skewness of ellipsoidal distributions with varying parameter k, which may also be expressed as a 6 th order polynomial function (r² = 1). R² for the regression between this line and the data points was 0.83. average leaf angles of height layers 0 5 10 15 20 25 30 35 40 0 0.2 0.4 0.6 0.8 1 relative irradiance a v e r a g e l e a f a n g l e ( ° ) beech Bu45 beech Bu38 Spatial distribution of leaf properties in tree crowns 89 condenses the points that belong to leaf angle distributions of lower layers to a cloud of points in the graph. The relationship between average leaf angle of height layers and the k-value of the associated ellipsoidal leaf-angle distribution was slightly different for both trees as can be seen in Fig. 63. 0 1 2 3 4 5 0 5 10 vertical distance to apex (m) k-value Beech Bu38 Beech Bu45 0 1 2 3 4 5 0 0.2 0.4 0.6 0.8 relative irradiance k-value Beech Bu45 Beech Bu38 Fig. 62: Dependence of the k-value of the approximated ellipsoidal distribution of leaf angles on vertical distance to the tree‘s apex (left) and relative irradiance (right). The trendlines in the left graph were drawn by hand and equal y = 0.24x +1.67 and y = -0.38x + 5.85 in the case of beech Bu38. 0 1 2 3 4 5 0 0 . 2 0 . 4 0 . 6 0 . 8 1 r e l a t i v e i r r a d i a n c e k - v a l u e B e e c h B u 4 5 B e e c h B u 3 8 y = -0.104x + 6.0716 R 2 = 0.6781 y = -0.0913x + 5.0359 R 2 = 0.7428 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 15 20 25 30 35 40 average leaf angle (°) k-value Beech Bu38 Beech Bu45 Fig. 63: Relationship between k-value and average leaf angle of leaf angle distributions of both beech trees. Fig. 64: Average branch angles of branches and twigs closely above the leaf at each investigation point as dependent on height (m below apex) and relative irradiance. R² - values were 0.68 and 0.64. 0.2 0.4 0.6 0.8 relative Irradiance 10 20 30 40 50 hcnarb elgna H ° L beeches Bu38 and Bu45 y = 56.22 x 0.44 2 4 6 8 10 12 vertical distance toapex H m L 0 10 20 30 40 50 hcnarb elgna H ° L Beeches Bu38 and Bu45 y= -3.67 x +46.34 Spatial distribution of leaf properties in tree crowns 96 of leaves of the Buchenallee trees was therefore dependent on relative irradiance (r² = 0.87, Fig. 75). The same was principally true for carbon concentrations. 3.2.2 Photosynthesis measurements 3.2.2.1 Comparison of PAM-2000 and RACCIA estimates of J max J max estimations from fluorescence and gas exchange measurements on the same leaf should lead to comparable results, when they are performed under the same conditions, thus principally providing an opportunity to check accuracy of the measurements. But field conditions were variable and they could only partly be manipulated: While the LICOR-6400 portable gas exchange measurement system can alter temperature in the measurement chamber in the range of ambient temperature ± 7°C and maximum light intensity of the appertaining LED light source (LED 6400-02B) is 2000µmol/(m²*s), fluorescence measurements with the PAM-2000 under field conditions do not allow any adjustment of temperature, but light intensity can be varied in a wide range. Additionally, time of day of the measurement may play a role for the result and differences could also occur between subsequent days at the same hour. A comparison between results of both methods was enabled by measuring a light response curve of J with the fluorometer PAM-2000 at a more or less constant (± 2°C) temperature and a temperature dependence curve of J with the LICOR-6400 at the constant maximum PPFD of 2000 µmol/(m²*s) on the same leaf. The temperature variation in the light response curve is a result of the variation in ambient conditions and warming of the leaf due to the light source. Assuming that the maximum electron transport rate J max is achieved at 2000 µmol/(m²*s), the evaluation of A/C i -curves with RACCIA can provide a segment of the temperature dependence curve of J max , representing the maximum temperature range that can be obtained with the LICOR-6400 under the actual ambient conditions. The extrapolation of this curve to the temperature of the PAM-2000 measurement can be compared with the electron transport rate at 2000µmol/(m²*s) that is derived from the light response curve using a non-linear fit of equation (29) for interpolation. Fig. 75: Area related nitrogen content of leaves versus leaf mass per area (left) and relative irradiance (right). Open squares in the left graph stand for leaves from 2 beeches in the Steinkreuz stand, beech Gr12, and 3 additional beeches in the Großebene stand, all other symbols are the same as in Fig. 73. Data points of beeches Bu38 and Bu45 are averages of at least 3 neighbouring leaves, r² for these data only against LMA was 0.97 and 0.99, respectively. The relationships to relative irradiance were y = 2.64x 0.383 (r² = 0.88) for beech Bu38, y = 2.48x 0.405 (r² = 0.9) for beech Bu45, and y = 2.54x 0.389 (r² =0.87) for both beech trees. 40 60 80 100 120 LMA H g ê m² L 1 1.5 2 2.5 3 3.5 fael negortin H g ê ²m L all trees Beech leaves: y = 0.025x + 0.025 r² = 0.92 Oak leaves: y = 0.025x + 0.124 r² = 0.89 0.2 0.4 0.6 0.8 1 relative irradiance 1 1.5 2 2.5 fael negortin H g ê m 2 L beeches Bu38 and Bu45 Spatial distribution of leaf properties in tree crowns 97 Five leaves of oak Gr13 were selected in different light expositions and fluorescence measurements were performed directly after gas-exchange measurements, except in one case (leaf eb2_1, 20°C), where no gas-exchange measurements could be performed due to a sudden rain event (30.7.99). This leaf was measured twice on two subsequent days during the same hours of the day (11.00 h - 13.00 h), but at different temperatures. The results of fluorescence and gas-exchange measurements are shown in Figs. 76 and 77. The light response curve of leaf 3eb2_1 was different at both measurement temperatures in its initial slope, which was 0.25 in the 20°C and only 0.1 in the 28°C measurement, while maximum values did not differ so much. The light response curve at the highest temperature (leaf 3eb2-2, 32°C) had also a rather low initial slope (0.12), while all other estimations for the initial slope were in the range from 0.22 to 0.3. It can therefore not be excluded that the two leaves under the highest temperatures suffered stress to some extent, though they were able to achieve high Fig. 76: Light response curves of electron transport rate J of 5 leaves of oak Gr13, derived from fluorescence measurements with the PAM-2000 fluorometer at 6 different temperatures (sorted by nitrogen content). The highest measured value per light level was used for a non-linear approximation of the light dependence function for J from the H ARLEY /T ENHUNEN model (equation 29). 500 1000 1500 2000 2500 PPFD H µmol ê H m² * s L L 50 100 150 200 250 J H lomµ ê H ²m * s L L leaf 3h4 - 1, 24°C N = 2.71 g/m² 500 1000 1500 2000 2500 PPFD H µmol ê H m² * s L L 50 100 150 200 250 J H lomµ ê H ²m * s L L leaf 3c4 - 2, 27°C N = 2.41 g/m² 500 1000 1500 2000 2500 PPFD H µmol ê H m² * s L L 50 100 150 200 250 J H lomµ ê H ²m * s L L leaf 3c4 - 3, 25°C N = 1.82 g/m² 500 1000 1500 2000 2500 PPFD H µmol ê H m² * s L L 50 100 150 200 250 J H lomµ ê H ²m * s L L leaf 3eb2 - 2,32°C N = 1.7 g/m² 500 1000 1500 2000 2500 PPFD H µmol ê H m² * s L L 50 100 150 200 250 J H lomµ ê H ²m * s L L leaf 3eb2 - 1,20°C N = 1.52 g/m² 500 1000 1500 2000 2500 PPFD H µmol ê H m² * s L L 50 100 150 200 250 J H lomµ ê H ²m * s L L leaf 3eb2 - 1,28°C N = 1.52 g/m² Spatial distribution of leaf properties in tree crowns 98 maximum electron transport rates. Some fluorescence measurements seem to indicate that the light dependence of J was not monotonously increasing, but achieved a maximum value below 2000 µmol/(m²*s). But this may also be attributed to effects of the long measurement period before measuring the high PPFD values and the effect of the 1-2°C higher temperature at these PPFD values due to leaf warming by the lamp. Shade leaves with lower nitrogen content per area had generally lower J max values than sun leaves according to both methods. A high correlation (r²=0.93) was found between the J max estimations of both methods (Fig. 78). The PAM-2000 estimations were generally slightly higher than those derived with RACCIA from gas-exchange measurements, and this situation improved a bit, when average values instead of 5 10 15 20 25 30 35 40 Temperature H °C L 50 100 150 200 250 xamJ H lomµ ê H ²m * s L L leaf 3eb2-2 5 10 15 20 25 30 35 40 Temperature H °C L 50 100 150 200 250 xamJ H lomµ ê H ²m *s L L leaf 3eb2 - 1 5 10 15 20 25 30 35 40 Temperature H °C L 50 100 150 200 250 xamJ H lomµ ê H ²m * s L L leaf 3c4 - 3 5 10 15 20 25 30 35 40 Temperature H °C L 50 100 150 200 250 xamJ H lomµ ê H ²m * s L L leaf 3c4 - 2 5 10 15 20 25 30 35 40 Temperature H °C L 50 100 150 200 250 xamJ H lomµ ê H ²m *s L L leaf 3h4 - 1 Fig. 77: Temperature dependence of J max of the same leaves as in Fig. 76, estimated with RACCIA from A/C i -curves at three different temperatures and PPFD = 2000 µmol/(m²*s). Leaves are sorted by N-content per area. N = 1.52 g/m² N = 2.71 g/m² N = 2.41 g/m² N = 1.82 g/m² N = 1.7 g/m² R 2 = 0.9339 0 50 100 150 200 0 50 100 150 200 RACCIA estimation of Jmax (µmol/(m²*s)) PAM 2000 estimation of Jmax (µmol/(m²*s)) R 2 = 0.9212 0 50 100 150 200 0 50 100 150 200 RACCIA estimation of Jmax (µmol/(m²*s)) PAM 2000 estimation of Jmax (µmol/(m²*s)) Fig. 78: Comparison of J max estimations from two different methods (RACCIA and PAM-2000). The circles in the left graph represent J max esitmations with the PAM-2000 based on approximations to the maximum measured values per light-level, while the crosses in the right graph rely on approximations to average values. Spatial distribution of leaf properties in tree crowns 99 maximum values were used for the approximation of equation (29) to the measured data of the light response curve, though correlation was somewhat lower then (r²=0.92). 3.2.2.2 Day respiration (R d ) All determined day respiration rates were in the range from 0 to 2.7 µmol/(m²*s) for leaves of beech Gr12 and from 0 to 2.7 µmol/(m²*s) for leaves of oak Gr13. R d of the same leaf was generally higher under higher temperatures and the gradual increase with temperature was greater for sun leaves with high nitrogen content per area than for shade leaves of both species. Therefore, temperature dependence of day respiration was investigated for groups of leaves with similar nitrogen content separately using equation (28). All following approximations of equations (28) and (30) are done to interpolate between measurements at different temperatures. For this, A/C i -data of leaves were sorted by nitrogen content (see appendix) and Fig. 79: Temperature dependence of day respiration R d of oak Gr13. Each point represents the R d estimate of a single A/C i -curve. A/C i - curves of three leaves with similar nitrogen content per area were pooled for each approximation to raise the number of data points per approximation. Nitrogen content is the average over all data points in each graph. 5 10 15 20 25 30 35 Temperature H °C L 1 2 3 4 5 dR H lomµ ê H ²m * s L L N = 1.25 g ê m² 5 10 15 20 25 30 35 Temperature H °C L 1 2 3 4 5 dR H lomµ ê H ²m * s L L N = 1.4 g ê m² 5 10 15 20 25 30 35 Temperature H °C L 1 2 3 4 5 dR H lomµ ê H ²m * s L L N = 1.47 g ê m² 5 10 15 20 25 30 35 Temperature H °C L 1 2 3 4 5 dR H lomµ ê H ²m * s L L N = 1.57 g ê m² 5 10 15 20 25 30 35 Temperature H °C L 1 2 3 4 5 dR H lomµ ê H ²m * s L L N = 1.67 g ê m² 5 10 15 20 25 30 35 Temperature H °C L 1 2 3 4 5 dR H lomµ ê H ²m * s L L N = 1.79 g ê m² 5 10 15 20 25 30 35 Temperature H °C L 1 2 3 4 5 dR H lomµ ê H ²m * s L L N = 2. g ê m² 5 10 15 20 25 30 35 Temperature H °C L 1 2 3 4 5 dR H lomµ ê H ²m * s L L N = 2.19 g ê m² 5 10 15 20 25 30 35 Temperature H °C L 1 2 3 4 5 dR H lomµ ê H ²m * s L L N = 2.32 g ê m² 5 10 15 20 25 30 35 Temperature H °C L 1 2 3 4 5 dR H lomµ ê H ²m * s L L N = 2.37 g ê m² 5 10 15 20 25 30 35 Temperature H °C L 1 2 3 4 5 dR H lomµ ê H ²m * s L L N = 2.55 g ê m² 5 10 15 20 25 30 35 Temperature H °C L 1 2 3 4 5 dR H lomµ ê H ²m * s L L N = 2.77 g ê m² 5 10 15 20 25 30 35 Temperature H °C L 1 2 3 4 5 dR H lomµ ê H ²m * s L L N = 2.87 g ê m² Spatial distribution of leaf properties in tree crowns 100 groups of consecutive leaves in this row were combined in the evaluation. Groups were partly overlapping. Fig. 79 shows that the gradual increase of R d of oak leaves with temperature was very low for some shade leaves, while it was greater for most of the sun leaves. For comparison: The occasionally determined gas-exchange rate of an oak leaf with 2.33 g N/m² at 25°C, measured after 6 minutes of darkness, was -1.85 µmol/(m²*s). The low number of data points and their concentration on a narrower range of temperatures was a problem for the approximations with the exponential equation (28) for beech, because extremely high curvatures ( H a in equation (28)) gave the best approximation even when the beech data were splitted in only two groups. Because this would have resulted in unrealistic or at least never measured R d -values of more than 10 µmol/(m²*s) at temperatures above 30°C, H a in the regressions for beech (Fig. 80) and beech seedlings (Fig. 81) was not allowed to reach values above 50 kJ/mol. This was also done considering recent observations that respiration continuing in the light not necessarily follows an exponentially increasing function, but may also decrease above a maximum value at 25 or 30°C (A TKIN ET AL . 2000). Additional A/C i -measurements have been searched to enlarge the data basis for beech. M. F ORSTREUTER AND J. S TRASSEMEYER (Technische Universität Berlin) meritoriously made available their partly published A/C i -measurements (M EDLYN ET AL . 1999) on beech seedlings at different temperatures for the evaluation with RACCIA. The nitrogen content per area of these investigated leaves varied in a narrower range than that of the leaves of mature trees in Steigerwald or Fichtelgebirge (0.71 - 0.98 g/m² for these investigated leaves, 0.5 - 1.5 g/m² for all measured seedling leaves, 0.6 - 2.6 g/m² for beech leaves from the Fichtelgebirge, and 1.0 - 3.4 g/m² for beech leaves from the Steigerwald), which was due to less variation in leaf mass per area. Nitrogen content per area was on average lower than that of shade leaves from mature trees in both stands. A/Ci-curves of seedlings were separated into three groups (low, middle, and high nitrogen) and were analysed separately (Fig. 81). H a in these approximations was between 33.9 and 42 kJ/mol, while it reached the maximum allowed value of 50kJ/mol in the approximations for beech Gr12. Respiration rates at 25°C ( Rd 298 ) did not show a clear dependence on nitrogen content, though leaves with similar nitrogen content tended to have similar values of Rd 298 (Fig. 82). The results Fig. 80: Temperature dependence of day respiration R d of beech Gr12. All R d -values were splitted into two non-overlapping groups with low and high nitrogen contents. The approximation with equation (28) was performed with the condition that H a does not exceed a threshold value of 50kJ/mol. 10 20 30 40 Temperature H °C L 0.5 1 1.5 2 2.5 3 3.5 4 d R H l o m µ ê H ² m * s L L N = 1.23 g ê m² 10 20 30 40 Temperature H °C L 0.5 1 1.5 2 2.5 3 3.5 4 d R H l o m µ ê H ² m * s L L N = 2.41 g ê m² Fig. 81: Approximation of equation (28) to R d - estimations from A/C i - curves measured on seedlings ( A / C i - measurements of Forstreuter and Strassemeyer (M EDLYN ET AL . 1999)) 10 20 30 40 Temperature H °C L 0.5 1 1.5 2 2.5 3 3.5 4 d R H l o m µ ê H ² m * s L L N=0.73 g ê m² 10 20 30 40 Temperature H °C L 0.5 1 1.5 2 2.5 3 3.5 4 d R H l o m µ ê H ² m * s L L N = 0.84 g ê m² 10 20 30 40 Temperature H °C L 0.5 1 1.5 2 2.5 3 3.5 4 d R H l o m µ ê H ² m * s L L N = 0.97 g ê m² Spatial distribution of leaf properties in tree crowns 101 for oak Gr13 show a slight increase in respiration from the shade leaves with low nitrogen content towards a nitrogen content of 1.7 g/m², slightly lower respiration rates between 1.7 and 2.5 g/m² and a sudden increase towards the leaves with nitrogen contents above 2.5 g/m². The general trend over all leaves is an increase of respiration rates with nitrogen per area. 3.2.2.3 Carboxylation capacity Vc max and electron transport capacity J max Non-linear approximations of equation (30) were used for the description of temperature dependence of Vc max and J max of both species (Figs. 83 - 87). Because both quantities had obviously lower values for shade leaves than for sun leaves, A/C i -data were grouped in the same manner as for the evaluation of R d versus temperature (see 3.2.2.2) in order to separate nitrogen classes. Vc max of oak leaves was generally higher than Vc max of leaves of beech Gr12, reaching a maximum value of 158 µmol/(m²*s) at 33°C in the investigated leaf with the highest nitrogen content (3.1 g/m²), while the maximum determined value of beech leaves was 63 µmol/(m²*s) at 24°C (N = 2.8 g/m²). This corresponds to the maximu m values for J max , which were 231 µmol/(m²*s) ( 32°C, N = 2.3 g/m²) for oak Gr13 and only 132 µmol/(m²*s) for beech Gr12 (25°C, N = 2.2 g/m²). Vc max and J max generally increased with nitrogen content per leaf area, which was also true for seedlings (see below). Additional A/C i -curves from beech seedlings (M EDLYN ET AL . 1999) were investigated and showed to have much lower Vc max - and J max -values (Fig. 87), which may be a consequence of their low nitrogen contents per area. Maximum values were 47µmol/(m²*s) and 56 µmol/(m²*s) at a temperature of 31°C and 30°C, respectively, me asured on a leaf with a nitrogen content of 0.96 g /m². Thus, Vc max and J max of beech seedlings appear to lie closer to each other than those of beech Gr12. Nearly all Vc max -values of oak Gr13, beech Gr12, and beech seedlings were found to be on the ascending part of the approximation curve, while J max -values from the same A/C i -curves were more often on the descending part, indicating a lower temperature optimum for J max than for Vc max . The relationship between both capacities was found to be relatively constant for a high number of species (W ULLSCHLEGER 1993, L EUNING 1997), with an average J max / Vc max ratio between 2.16 and 2.68 at 20°C (depending on the used temperature function). The above temperature dependencies were therefore used to interpolate for a temperature corrected value of Vc max and J max at 20°C for each nitrogen class in order to investigate the general relationship between Fig. 82: Variation of day respiration at 25°C with nitrogen per leaf area. Temperature interpolation was done based on the results of Figs. 79-81. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 0.5 1 1.5 2 2.5 3 3.5 N (g/m²) R d at 25°C (µmol/(m²*s)) oak Gr13 beech Gr12 beech seedlings Spatial distribution of leaf properties in tree crowns 102 5 10152025303540 Temperature H °C L 50 100 150 200 250 x a m c V H l o m µ ê H ² m * s L L N = 1.25 g ê m² 5 10152025303540 Temperature H °C L 50 100 150 200 250 x a m c V H l o m µ ê H ² m * s L L N = 1.4 g ê m² 5 10152025303540 Temperature H °C L 50 100 150 200 250 x a m c V H l o m µ ê H ² m * s L L N = 1.47 g ê m² 5 10152025303540 Temperature H °C L 50 100 150 200 250 x a m c V H l o m µ ê H ² m * s L L N = 1.57 g ê m² 5 10152025303540 Temperature H °C L 50 100 150 200 250 x a m c V H l o m µ ê H ² m * s L L N = 1.67 g ê m² 5 10152025303540 Temperature H °C L 50 100 150 200 250 x a m c V H l o m µ ê H ² m * s L L N = 1.79 g ê m² 5 10152025303540 Temperature H °C L 50 100 150 200 250 x a m c V H l o m µ ê H ² m * s L L N = 2. g ê m² 5 10152025303540 Temperature H °C L 50 100 150 200 250 x a m c V H l o m µ ê H ² m * s L L N = 2.19 g ê m² 5 10152025303540 Temperature H °C L 50 100 150 200 250 x a m c V H l o m µ ê H ² m * s L L N = 2.32 g ê m² 5 10152025303540 Temperature H °C L 50 100 150 200 250 x a m c V H l o m µ ê H ² m * s L L N = 2.37 g ê m² 5 10152025303540 Temperature H °C L 50 100 150 200 250 x a m c V H l o m µ ê H ² m * s L L N = 2.55 g ê m² 5 10152025303540 Temperature H °C L 50 100 150 200 250 x a m c V H l o m µ ê H ² m * s L L N = 2.77 g ê m² 5 10152025303540 Temperature H °C L 50 100 150 200 250 x a m c V H l o m µ ê H ² m * s L L N = 2.87 g ê m² Fig. 83: Temperature dependence of Vc max of leaves of oak Gr13. Each data point represents the Vc max estimation of one A/C i -curve at a certain temperature. Each approximation uses data of three leaves with similar nitrogen content per area and is based on equation (30). N-content is given as the average for all data points. 10 20 30 40 Temperature H °C L 20 40 60 80 100 120 140 x a m c V H l o m µ ê H ² m * s L L N = 1.18 g ê m² 10 20 30 40 Temperature H °C L 20 40 60 80 100 120 140 x a m c V H l o m µ ê H ² m * s L L N = 1.29 g ê m² 10 20 30 40 Temperature H °C L 20 40 60 80 100 120 140 x a m c V H l o m µ ê H ² m * s L L N = 1.68 g ê m² 10 20 30 40 Temperature H °C L 20 40 60 80 100 120 140 x a m c V H l o m µ ê H ² m * s L L N = 2.15 g ê m² 10 20 30 40 Temperature H °C L 20 40 60 80 100 120 140 x a m c V H l o m µ ê H ² m * s L L N = 2.44 g ê m² 10 20 30 40 Temperature H °C L 20 40 60 80 100 120 140 x a m c V H l o m µ ê H ² m * s L L N = 2.66 g ê m² 10 20 30 40 Temperature H °C L 20 40 60 80 100 120 140 x a m c V H l o m µ ê H ² m * s L L N = 2.73 g ê m² Fig. 84: Same type of figure as Fig. 83, but for leaves of beech Gr12. Data of two leaves were used per approximation. Spatial distribution of leaf properties in tree crowns 103 5 10152025303540 Temperature H °C L 50 100 150 200 250 x a m J H l o m µ ê H ² m * s L L N = 1.25 g ê m² 5 10152025303540 Temperature H °C L 50 100 150 200 250 x a m J H l o m µ ê H ² m * s L L N = 1.4 g ê m² 5 10152025303540 Temperature H °C L 50 100 150 200 250 x a m J H l o m µ ê H ² m * s L L N = 1.47 g ê m² 5 10152025303540 Temperature H °C L 50 100 150 200 250 x a m J H l o m µ ê H ² m * s L L N = 1.57 g ê m² 5 10152025303540 Temperature H °C L 50 100 150 200 250 x a m J H l o m µ ê H ² m * s L L N = 1.67 g ê m² 5 10152025303540 Temperature H °C L 50 100 150 200 250 x a m J H l o m µ ê H ² m * s L L N = 1.79 g ê m² 5 10152025303540 Temperature H °C L 50 100 150 200 250 x a m J H l o m µ ê H ² m * s L L N = 2. g ê m² 5 10152025303540 Temperature H °C L 50 100 150 200 250 x a m J H l o m µ ê H ² m * s L L N = 2.19 g ê m² 5 10152025303540 Temperature H °C L 50 100 150 200 250 x a m J H l o m µ ê H ² m * s L L N = 2.32 g ê m² 5 10152025303540 Temperature H °C L 50 100 150 200 250 x a m J H l o m µ ê H ² m * s L L N = 2.37 g ê m² 5 10152025303540 Temperature H °C L 50 100 150 200 250 x a m J H l o m µ ê H ² m * s L L N = 2.55 g ê m² 5 10152025303540 Temperature H °C L 50 100 150 200 250 x a m J H l o m µ ê H ² m * s L L N = 2.77 g ê m² 5 10152025303540 Temperature H °C L 50 100 150 200 250 x a m J H l o m µ ê H ² m * s L L N = 2.87 g ê m² Fig. 85: Temperature dependence of J max of leaves of oak Gr13. Each data point represents the J max estimation of one A/C i -curve at a certain temperature. Each approximation uses data of three leaves with similar nitrogen content per area and is based on equation (30). N-content is given as the average for all data points. 10 20 30 40 Temperature H °C L 50 100 150 200 250 x a m J H l o m µ ê H ² m * s L L N = 1.18 g ê m² 10 20 30 40 Temperature H °C L 50 100 150 200 250 x a m J H l o m µ ê H ² m * s L L N = 1.29 g ê m² 10 20 30 40 Temperature H °C L 50 100 150 200 250 x a m J H l o m µ ê H ² m * s L L N = 1.68 g ê m² 10 20 30 40 Temperature H °C L 50 100 150 200 250 x a m J H l o m µ ê H ² m * s L L N = 2.15 g ê m² 10 20 30 40 Temperature H °C L 50 100 150 200 250 x a m J H l o m µ ê H ² m * s L L N = 2.44 g ê m² 10 20 30 40 Temperature H °C L 50 100 150 200 250 x a m J H l o m µ ê H ² m * s L L N=2.66 g ê m² 10 20 30 40 Temperature H °C L 50 100 150 200 250 x a m J H l o m µ ê H ² m * s L L N = 2.73 g ê m² Fig. 86: Same type of figure as Fig. 85, but for leaves of beech Gr12. Data of two leaves were used per approximation. Spatial distribution of leaf properties in tree crowns 104 both quantities. Those temperature dependence functions without Vc max or J max values below 21°C were excluded from this analysis. Fig. 88 shows that all data lie relatively close to the regression line, which represents a general ratio of 2.28 (r² = 0.86) and lies in the range of previously found ratios (L EUNING 1997). Nevertheless, J max / Vc max ratios varied: While the ratio for investigated leaves of oak Gr13 was nearly the same as the mean response (2.24, range: 1.97 - 2.79), leaves of beech seedlings had a lower average J max / Vc max ratio (1.58, range: 1.51 -1.64) and leaves of beech Gr12 a higher one (2.72, range: 2.38 - 3.23). Thus, the high coefficient of determination for the overall relationship does not necessarily mean that Vc max may be derived from J max estimations, because speciesor age-specific differences are evident. 3.2.2.4 Nitrogen dependence of J max and Vc max The increase of J max and Vc max with nitrogen content of the leaves is obvious from Figs. 83 - 86 and was investigated on the base of the temperature corrected value at 25°C for each nitrogen class of leaves, which is one parameter of equation (30) ( J max, 298 and Vc max, 298 ) and was 10 20 30 40 Temperature H °C L 50 100 150 200 250 x a m J H l o m µ ê H ² m * s L L N = 0.73 g ê m² 10 20 30 40 Temperature H °C L 50 100 150 200 250 x a m J H l o m µ ê H ² m * s L L N = 0.84 g ê m² 10 20 30 40 Temperature H °C L 50 100 150 200 250 x a m J H l o m µ ê H ² m * s L L N=0.96 g ê m² 10 20 30 40 Temperature H °C L 20 40 60 80 100 120 140 x a m c V H l o m µ ê H ² m * s L L N = 0.73 g ê m² 10 20 30 40 Temperature H °C L 20 40 60 80 100 120 140 x a m c V H l o m µ ê H ² m * s L L N = 0.84 g ê m² 10 20 30 40 Temperature H °C L 20 40 60 80 100 120 140 x a m c V H l o m µ ê H ² m * s L L N = 0.96 g ê m² Fig. 87: Temperature dependence of Vc max (upper row ) and J max (below) of beech seedlings as determined with RACCIA. 3 3 Fig. 88: Ratio between J max and Vc max at 20°C for investigated nitrogen classes of leaves of beech Gr12, oak Gr13, and beech seedlings (M EDLYN ET AL . 1999). The interpolation to 20°C was based on the temperature response curves of Figs. 83-87, except those without values below 21°C. The mean ratio for all data was 2.28 (r² = 0.86, long solid line) y = 2.2824x R 2 = 0.8603 y = 1.5814x y = 2.2496x y = 2.7202x 0 20 40 60 80 100 120 140 160 0 10 20 30 40 50 60 70 Vcmax at 20°C (µmol/ (m²*s)) Jmax at 20°C (µmol/(m²*s)) beech seedlings oak Gr13 beech Gr12 Spatial distribution of leaf properties in tree crowns 105 measured or could be interpolated for all described nitrogen classes. Fig. 89 confirms the strict tendency of increasing capacities with increasing nitrogen content, but it also shows that the relative increase with increasing nitrogen content per area became smaller and finally disappeared at higher nitrogen contents of leaves in the upper sun crown. Above a nitrogen threshold of around 2.2 g/m², additional nitrogen per area did not raise photosynthesis capacities of leaves of beech Gr12. While Vc max of oak Gr13 was nitrogen saturated at a nitrogen content of 2.3 g/m², J max of oak Gr13 still increased with increasing nitrogen per area up to 2.9 g/m², but the slope of the J max vs. nitrogen relationship was already decreasing at this nitrogen content. The non-linear approximation of arbitrarily chosen functions of the type y = a x b / (x b + c) represents the data very well (r² ≥ 0.96) and may be extrapolated to a saturating nitrogen content above 4.5 g/m² in this case. 6 additional A/Ci-curves from leaves of mature Fagus crenata (Blume) trees (S AITO & K AKUBARI 1999), measured at 21°C, were evaluated with RACCIA and the nitrogen dependence of their Fig. 89: Variation of J max and Vc max at 25°C of leaves of oak Gr13 (open stars) and bee ch Gr12 (filled squares) with nitrogen content per area. Each data point represents the temperature interpolated value from nitrogen classes of leaves as in Figs. 83 - 86. The observed saturation at higher nitrogen contents was described with an approximation function of the type y = a x b / (x b + c). Coefficients a, b, and c were 120.3, 5.94, and 3.02 ( J max , r² = 0.99) and 53.9, 5.85, and 3.68 ( Vc max , r² = 0.99) for beech Gr12. Coefficients for oak Gr13 were 221.1, 3.07, and 4.44 ( J max , r² = 0.99) and 93.7, 4.93, and 5.9 ( Vc max , r² = 0.96), respectively. 0.5 1 1.5 2 2.5 3 N H g ê m² L 20 40 60 80 100 xamcV H lomµ ê H ²m * s L L 0.5 1 1.5 2 2.5 3 3.5 N H g ê m² L 50 100 150 200 250 xamJ H lomµ ê H ²m * s L L 0 5 10 15 20 25 30 35 40 45 0 0.5 1 1.5 2 2.5 3 N (g/m²) Vcmax at 21°C (µmol/(m²*s)) beech Gr12 beech seedlings Fagus crenata 0 20 40 60 80 100 120 0 0.5 1 1.5 2 2.5 3 N (g/m²) Jmax at 21°C (µmol/(m²*s)) beech Gr12 beech seedlings Fagus crenata Fig. 90: Comparison of Vc max (left) and J max (right) at 21°C of beech Gr12 with data from beech seedlings and from mature Fagus crenata trees. Spatial distribution of leaf properties in tree crowns 112 extreme shade leaves was lowest (9.8) and increased linearly with increasing nitrogen content up to a maximum value of 16.3 at 2.4g/m². Above this value, g fac of oak Gr13 leaves tended to decrease. 3.2.3 Nitrogen dependent model of leaf photosynthesis for beech 3.2.3.1 Model description Nitrogen per leaf area correlated with those leaf properties of oak Gr13 and beech Gr12 that are most important for the determination of photosynthesis rates and it has been shown to be dependent on relative irradiance in tree crowns of beech. It is therefore well suitable for upscaling along light gradients in tree crowns. The nitrogen dependent model of leaf photosynthesis extends the model of H ARLEY and T ENHUNEN (1991) as described above in order to consider the found nitrogen dependent variation in photosynthesis capacities of leaves in tree crowns of beech. Thus, it combines the above findings on nitrogen dependence of J max , Vc max , and R d in the calculation of photosynthesis rates for single leaves. The N-dependent parameterisation of equation (30) for J max and Vc max is done according to the equations displayed in Figs. 89, 92, 95, and 96. Thus, rates at 25°C are dependent on nitrogen, H a is dependent on the rate at 25°C and S and H d depend on H a according to the following equations: J max -specific: J max,298 = 120.3 N 5.94 N 5.94 + 3.02 (37) H a =4.1659 J max,298 0.5224 (38) 0.01 0.02 A*rH ê Ca H mol ê H m²*s L L 0.05 0.1 0.15 0.2 ecnatcudnoC H lom ê H ²m *s L L N=1.18 g ê m² 0.01 0.02 A * rH ê Ca H mol ê H m² * s L L 0.05 0.1 0.15 0.2 ecnatcudnoC H lom ê H ²m * s L L N = 1.29 g ê m² 0.01 0.02 A * rH ê Ca H mol ê H m² * s L L 0.05 0.1 0.15 0.2 ecnatcudnoC H lom ê H ²m * s L L N = 1.68 g ê m² 0.01 0.02 A * rH ê Ca H mol ê H m² * s L L 0.05 0.1 0.15 0.2 ecnatcudnoC H lom ê H ²m * s L L N = 2.15 g ê m² 0.01 0.02 A * rH ê Ca H mol ê H m² * s L L 0.05 0.1 0.15 0.2 ecnatcudnoC H lom ê H ²m * s L L N = 2.44 g ê m² 0.01 0.02 A * rH ê Ca H mol ê H m² * s L L 0.05 0.1 0.15 0.2 ecnatcudnoC H lom ê H ²m * s L L N = 2.66 g ê m² Fig.100: Same type of figure as Fig. 98, but for nitrogen classes of leaves of beech Gr12. 0.01 0.02 0.03 A * rH ê Ca H mol ê H m² * s L L 0.1 0.2 0.3 ecnatcudnoC H lom ê H ²m * s L L N = 2.73 g ê m² S H d + 7.8 = 0.004563H a + 2.925 (39) Spatial distribution of leaf properties in tree crowns 113 Vc max -specific: H d in equations (39) and (42) is assumed to follow the relationship R d was also described as nitrogen dependent. While H a from equation (28) for R d was held constant at 70 kJ/mol, a linear increase of R d,298 with nitrogen per leaf area ( N ) was assumed, that was derived from the two data points for beech Gr12 in Fig. 82: (compare Fig. 80). While g min was held constant equalling 0, gfac was varied according to a quadratic fit to the beech data in Fig. 100 (R² = 0.9): 3.2.3.2 Parameterisation Nearly all parameters that are not rubisco-specific constants were replaced by a nitrogen dependent function, so that the number of parameters for the calculation of photosynthesis and transpiration of single leaves was reduced from 18 to 8, as can be seen in table 7. rubisco-specific constants ( K M,C , K M,O , τ ττ τ ) and the K M,C - and K M,O - specific H a -values for equation (28) were taken from the in vivo measurements of VON C AEMMERER ET AL . (1994). The τ τ τ τ -specific H a -value was taken from H ARLEY & T ENHUNEN (1991), which produced Γ ΓΓ Γ * -values very close to those from equation (36), when equations (27) and (28) were applied in the model (Fig. 101). This formulation was preferred, because it includes the dependence of Γ ΓΓ Γ * on oxygen concentration of the atmosphere. α αα α was set constant to 0.06 mol CO 2 /mol photons. g fac = 5.0071 N 2 - 22.704N + 31.884 (45) (44) R d,298 = 0.874N - 0.269 Vc max,298 = 53.9 N 5.85 N 5.85 + 3.68 (40) H a= 7.9856 Vc max,298 0.5314 (41) S Hd+7.8 =0.003381Ha+2.89 (42) H d = 0.311S - 0.8521 . (43) 270 280 290 300 310 Temperature H K L 0 10 20 30 40 50 60 70 G * H lomµ ê lom L Fig. 101: Similar result of alternative formulations for the temperature dependence of Γ ΓΓ Γ * . While the entire line represents equation (36) (A TKIN ET AL . 2000), the dotted line is the result of equations (27) and (28) for an atmospheric oxygen concentration of 209 mmol/mol, using parameters τ τ τ τ from VON C AEMMERER ET AL . (1997) and H a from Harley & Tenhunen (1991). Spatial distribution of leaf properties in tree crowns 114 Table 7: Parameters of the leaf models H ARLEY /T ENHUNEN model Nitrogen dependent model Numerical value in the nitrogen dependent model K M,O K M,O 248 mmol/mol K M,O -specific H a K M,O -specific H a 35000 J/mol K M,C K M,C 404 µmol/mol K M,C -specific H a K M,C -specific H a 63500 J/mol τ ττ τ τ ττ τ 2710 Rubiscospecific constants τ ττ τ -specific H a τ ττ τ -specific H a -28990 J/mol α αα α α αα α 0.06 mol CO 2 /mol photons P ml,298 H a S Light-use parameters H d Vc max,298 H a S Carboxylation parameters H d R d,298 Respiration parameters H a g fac Conductance parameters g min Nitrogen N variable 3.2.3.3 Validation Measurements While A/Ci-measurements took place between 27 th of July and 6 th of August 1998, validation measurements at ambient CO 2 -concentrations were performed on 7 th and 8 th of August 1998, which were two of the driest and warmest days of that year in the Steigerwald (Fig. 102). Photosynthesis was measured two to four times during the day for around 20 minutes on each leaf, alternating between different leaves of both trees, whereby single points of the daily course 5 10 15 20 25 30 35 1/5/98 1/6/98 2/7/98 2/8/98 2/9/98 date temperature (°C) 0 2 4 6 8 10 12 14 16 18 VPD (hPa) Daily mean temperature Daily mean VPD 8/8/98 7/8/98 Fig. 102: Time course of VPD and temperature of summer 1998. 7 th and 8 th of August were two of the driest days of this year. Spatial distribution of leaf properties in tree crowns 115 0 200 400 600 800 1000 1200 1400 1600 1800 2000 6:00 10:00 14:00 18:00 22:00 2:00 6:00 10:00 14:00 18:00 date PPFD (µmol/(m²*s)) 0 5 10 15 20 25 30 35 40 temperature and VPD (°C, hPa) hourly mean PPFD hourly mean air temperature hourly mean VPD A C D D C B B A A A Fig. 103: Course of climate variables during the measurement period, measured five metres above the floor on a nearby clear-cut. Vertical lines indicate the average point of time of each measurement. The letters above each line indicate the name of the leaf. 10 15 20 25 30 35 40 06:00 12:00 18:00 00:00 06:00 12:00 18:00 time air temperature (°C) Air temperature 5m above the floor Air temperature in the canopy 0 10 20 30 40 50 60 70 06:00 12:00 18:00 00:00 06:00 12:00 18:00 time VPD (hPa) VPD 5m above the floor VPD in the canopy Fig. 104: Course of air temperature and VPD during 7 th and 8 th of August 1998. The measured values in the canopy were recorded in a height of 19 m above the floor on the south side of beech Gr12 and oak Gr13, while the values 5m above the floor were measured above a clearcut. time Spatial distribution of leaf properties in tree crowns 116 of photosynthesis could be determined for each leaf. The objective to measure leaves with different nitrogen content and light exposition in the crowns of both species was only partly reached, because leaves of oak Gr13 were even in the morning hours not responding to light and stomata of most measured oak leaves remained at low conductances during the whole day. Less of the measured leaves of beech Gr12 seemed to be affected by drought, and their nitrogen content turned out to range from 1.8 to 2.3 g/m². All beech leaves were measured in the same height above the floor (19m), two leaves with 1.83 and 1.85 g N/m² represent a position shaded by other leaves and closer to the stem (leaves B and C), while leaves A and D were fully sun-exposed and had nitrogen contents of 1.96 g/m² and 2.28 g/m². Day time of these measurements and climate conditions are depicted in Fig. 103. PPFD, air temperature, and VPD were measured five metres above the floor on a nearby clear-cut. Though they differ from the conditions at the positions of the leaves, they may give insight into the relative changes of climate conditions over the two days. The deviation from these conditions at the position of a leaf in the canopy may be derived from the validation measurements in the canopy (Fig. 104). Air temperature was on average 4.2°C higher than 5m above the floor and a maximum temperature difference of 9°C was reached in the afternoon. VPD was on average 12.3 hPa higher with a maximum difference of 25 hPa. This may partly be attributed to the fact that the clear-cut is surrounded by forest, which casts a shadow in the early morning and in the late evening on the measurement station and may be the source of cooler and more humid air that is exchanged even at low wind velocities. On the other hand it may reflect the increased temperature of sun-exposed leaves and branches that are sun-exposed and poorly cooled by wind and transpiration, thus warming up the surrounding air. Between 12:00 and 16:00 MET, the average measured difference between temperature of leaves and air temperature was 1.1°C with a maximum value of 3.1°C , measured at 13:51 MET on 8 th of August at a sun-exposed oak leaf. Increasing irradiances were under these circumstances generally accompanied by dramatic changes in VPD, which is probably the reason for an unusual light response that was observed when the photosynthesis rates of all leaves are viewed against PPFD (Fig. 105). The photosynthesis rates of beech leaves at above 1000µmol/(m²*s) PPFD were all lower than the rate of leaf A at 660µmol/(m²*s). 0 0.5 1 1.5 2 2.5 3 3.5 4 0 300 600 900 1200 1500 PPFD (µmol/(m²*s)) A (µmol/(m²*s)) leaf A leaf B leaf C leaf D T = 39°C VPD = 56.6 hPa T = 33.2°C VPD = 36.7 hPa T = 36.2°C VPD = 47.5 hPa T = 35°C VPD = 42.2 hPa T = 29.1°C VPD = 25.9 hPa Fig. 105: Light dependence of assimilation rates of four different leaves in the crown of beech Gr12. Average leaf temperature and VPD at the leaf’s position during the measurement are given for the measurements under high PPFD. Nitrogen contents of the leaves were A: 1.96 g/m², B: 1.83 g/m², C: 1.85 g/m², and D: 2.28 g/m² Spatial distribution of leaf properties in tree crowns 117 3.2.3.4 Model validation The comparison between modelled and measured values of assimilation ( A ) and stomatal conductance ( g sw ) revealed a general overestimation by the model: The difference between modelled and measured values was on average 0.52 µmol/(m²*s) and 1.89 mmol/(m²*s), respectively, which corresponds to 34% and 9% of the mean of measured values (mean absolute error, M AYER & B UTLER 1993). The high percentage for A is a consequence of the relatively low photosynthesis rates that were measured during the validation measurements, but it also reflects the partly big deviations from the 1:1 line in Fig. 106. The agreement between measured and modelled values may adequately be described by the root mean square error ( , J ANSSEN & H EUBERGER 1995), which was 1.1 µmol/(m²*s) for A and 6.8 mmol/(m²*s) for g sw . This overestimation was already expected from their unusual light response (Fig. 105), which must be seen with respect to the unusually dry conditions for the leaves on the measurement days. The strongest observed impact of the low relative humidity on leaf photosynthesis was that oak leaves had permanently low conductances, thus reducing assimilation to values below 1µmol/(m²*s). Though only some beech leaves with extremely low conductances were observed (data not shown), the question arises, if their stomatal reaction to drought has been assessed as accurately as necessary. It has been shown that stomatal aperture of several species including beech is generally not uniform but patchy distributed over the leaves (K ÜPPERS ET AL . 1999, E CKSTEIN 1997). The phenomenon of stomatal patchiness may lead to an overestimation of photosynthesis rates, when - like in the used model - only the average response of the stomata is considered (C HEESEMAN 1991). This overestimation is expected to be most severe in heterobaric leaves, where lateral gas diffusion is restricted, which causes different C i -values in different parts of the leaf ( VON W ILLERT ET AL . 1995). In leaves of mediterranean plants, but also of Quercus petraea, Picea abies, and Abies alba, selective stomatal closure is known to be a response to low air humidity and may cause more or less big parts of the leaf to be excluded from photosynthetic activity, while other parts remain physiologically active (E PRON & D REYER 1993, B EYSCHLAG ET AL . 1992, B EYSCHLAG ET AL . 1994). Stomatal patchiness has also been shown to be light induced (K ÜPPERS ET AL . 1999) and has been discussed as a mechanism to avoid photoinhibition (B EYSCHLAG & E CKSTEIN 1997). $ 1 n ⁄ ε εε ε 2 Fig. 106: Modelled versus measured values of assimilation rate A (left) and stomatal conductance to water vapour g sw (right). The line represents the ratio 1 between modelled and measured data. -1 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 A measured (µmol/(m²*s)) A modelled (µmol/(m²*s)) leaf A leaf B 0 10 20 30 40 50 60 0 10 20 30 40 50 60 g sw measured (mmol/(m²*s)) g sw modelled (mmol/(m²*s)) leaf C leaf D Spatial distribution of leaf properties in tree crowns 118 Since Fagus sylvatica leaves have a septate leaf anatomy due to sklerenchymatic tissues (“Sklerenchymscheide”) around the leaf veins, which causes the leaf to be heterobaric ( VON W ILLERT ET AL . 1995), it seems to be plausible, that the measured assimilation rates and conductances may be influenced by stomatal patchiness. A simple test was performed to evaluate the effect of inactivated leaf parts on the model calculations: It was assumed that the shaded leaves inside the crown (B and C) still behave as the model expects, while the sun-exposed leaves (leaves A and D) are partly inactivated. 30% of their leaf area is assumed to be completely inactivated, while the rest of the leaf is physiologically active and behaves as the model expects. Under these circumstances, Vc max , J max , and R d have to be reduced to 70% (B EYSCHLAG & E CKSTEIN 1997), while the average sensitivity of the stomata to humidity, assimilation, and CO 2 ( g fac ) remains unchanged. The effect of these changes on the comparison between model results and measurements is shown in Fig. 107. The previously reported overestimation of assimilation ( A ) and conductance ( g sw ) disappeared: The average difference between modelled and measured values was 0.17 µmol/(m²*s) for A and -1.1 mmol/(m²*s) for g sw , which is an overestimation of 11% of the mean of measured assimilation rates and an underestimation of 5% of the mean of measured stomatal conductances. The root mean square of errors improved to 0.48 µmol/(m²*s) and 4.9 mmol/(m²*s), when the inactivation of parts of the sun-exposed leaves was considered this way. This improvement in modelled assimilation rates was a consequence of lowered assimilation rates (due to decreased Vc max and J max ) as well as of one increased assimilation rate of leaf A, which is attributed to the decrease in R d . 3.3 Summary and discussion The investigations to relative irradiance above leaves along vertical lines confirm the general validity of Beer’s law in the investigated beech crowns, though deviations from a strictly exponential decrease were also found. These deviations were mainly found on the smaller tree, whose light climate is strongly influenced by the different height of neighbouring trees and they may partly be attributed to the effects of gaps between leaf clouds. Additional deviations occur in the lowest third of both crowns, where relative irradiances are not as low as an exponential approximation would suggest. The scatter in the relationship between relative irradiance and distance to apex allows one to -1 0 1 2 3 4 5 6 7 01234567 A measured (µmol/(m²*s)) A modelled (µmol/(m²*s)) leaf A leaf B 0 10 20 30 40 50 60 0 10 20 30 40 50 60 g sw measured (mmol/(m²*s)) g sw modelled (mmol/(m²*s)) leaf C leaf D Fig. 107: Modelled versus measured values of A (left) and g sw (right) under the condition that the photosynthetically active leaf area of the two sun-exposed leaves is reduced to 70%. The line represents the ratio 1 between modelled and measured data. Spatial distribution of leaf properties in tree crowns 119 distinguish between deterministic and adaptive leaf properties: While height below apex may not be experienced by a leaf, irradiance is the most important driver for its physiological activity. Hence, strongly light dependent quantities appear to be a consequence of the environmental conditions, while height dependent quantities may simply be determined by regularities of growth. In this sense, leaf angle distributions in the canopies of beech trees were found to be deterministic: The leaf angle distribution of each height level was an ellipsoidal distribution and the single parameter k of these distributions was linearly dependent on height, while it did not show a clear relationship to relative irradiance. That the linear dependence changes its direction in the lower third of the tree crowns may not be the result of changing irradiance, because only very small differences in relative irradiance occur in this part of the crown. The theory of PPFD extinction in homogeneous canopies with ellipsoidal leaf angle distribution (C AMPBELL & N ORMAN 1989) would expect a functional relationship that allows the calculation of a constant extinction coefficient for Beer’s law from an assumed constant parameter of the ellipsoidal distribution and the zenith angle, but the assumption is not confirmed by this investigation. The vertical gradient in parameter k of the ellipsoidal leaf angle distributions must be considered in such calculations with the consequence of deviations from a strictly exponential decrease of irradiance with height. Thus, the deviations from Beer’s law in beech Bu45 and beech Bu38 are partly a consequence of the deterministic change in leaf angle distributions. Comparable results have been found for a mature tree crown of Quercus robur (K ULL ET AL . 1999) and were interpreted as light dependent. The low number of six data points in this data set allows to draw an exponential relationship on canopy light transmittance with r² = 0.89, but the re-evaluation of these data shows, that also a linear relationship to height exists (r² = 0.85, data not shown). A deterministic and adaptive change of leaf properties was found in the branch angles of their above neighbourhood. This may be understood on the assumption of autonomous growth of branches towards a better light situation, which would result in more horizontal growth towards the surface of the canopy in the lower part and increasing branch angles with increasing height, as was found in the measurements. Since this adaptive growth form was probably more successful in evolution than others it may have become part of a deterministic growth scheme and may therefore not be classified as adaptive or deterministic. Width of leaf space is a more important quantity for light transmission through the canopy than width of leaf blade. Similarly to the parameter k of leaf angle distributions it followed a quasilinear trend and increased up to 7m below apex but then the direction of the quasi-linear relationship changed towards decreasing widths. This effect contributes to the “better than by Beer’s law expected” relative irradiances in the lower third of the canopies since it increases the transmission through the lowest leaf layers. The much more scattered relationship between width of leaf blade and height indicates the relative irrelevance of this quantity for light absorption and transmission. Height of leaf space was surprisingly not simply a consequence of leaf bending by width reduction, but had together with width of leaf space a meaning for the relationship between light interception and chemical composition of the leaf, as may be derived from Fig. 74. Though it is not easy to find reasons for this highly significant relationship, it shows that leaf bending is more important for the interception of radiation than could be expected. The similar relationship in Fig. Spatial distribution of leaf properties in tree crowns 120 73 describes a relationship between leaf space dimensions and nitrogen and carbon concentration of the leaf biomass and may be interpreted in terms of structural requirements to achieve a given leaf form. Leaf mass per area was primarily light dependent and not as strictly height dependent, which suggests an adaptation to environmental conditions. Stand-specific differences are obvious from Figs. 68 and 69, whereas species-specific differences between oak Gr13 and beech Gr12 were not detected. Because nutrient and deposition situation of both stands were similar, other growth conditions like length of vegetation period, average humidity, or average temperature come into question as reasons for stand-specific differences. Though stand-specific differences exist, it is probably not chance that the maximum leaf mass per area measured on beech Gr12 was the highest value when compared with published values from the last 110 years. The estimated average leaf mass per area of all three investigated beech trees was more than double that of mature trees from 1945! The same was also found for oak Gr13 when compared with data from 1947. Fig. 108 shows that the data from the studies mentioned in table 5 describe a more or less continuous increase of maximum LMA-values during the last decades. Thus, the extremely high maximum LMA-value from beech Gr12 is not interpreted as a special quality of the stand but as part of a general trend towards increasing leaf mass per area in beech leaves in Europe during the last 110 years. A potential reason for this trend is the parallel change in the environmental situation due to CO 2 -increase and nitrogen depositions. However, (P ETERSON ET AL . 1999) describe only weak effects of high CO 2 on LMA of leaves of beech seedlings, while other seedlings were more susceptible to CO 2 -induced increases of LMA. The strong relationship between relative irradiance and leaf mass per area (r² = 0.88, Fig. 68) was even valid for the variation of LMA in leaf clouds. It corresponds to the similar relationship between relative irradiance and nitrogen per leaf area (Fig. 75) and both together provide a solid basis for up-scaling purposes, since the variation in most photosynthesis parameters has been found to be nitrogen dependent. The measured leaf nitrogen contents were partly very high. While the ‘normal range’ of nitrogen concentrations per dry weight of leaves in adult forest stands is 1.8 to 2.91% of dry weight (Quercus petraea, VAN DEN B URG 1990) and 1.8 to 2.78% of dry weight (Fagus sylvatica, VAN DEN B URG 1990), a range from 2.2 to 3.1% has been found in beech leaves from the upper third of the crowns along a European transect (B AUER ET AL . 1997). Thus, oak Gr13 had leaves with extremely high nitrogen concentrations, while beech Gr12 had normal to high concentrations Fig. 108: Increase of maximum and estimated average values of leaf mass per area of mature beech trees during the last 30-110 years as derived from published values. Average values for the newer studies since 1970 were estimated as the mean of minimum and maximum values, which was a 10% overestimation in the case of beech trees from the own harvest. The range of means from older whole tree harvests is indicated as error bars. 0 20 40 60 80 100 120 140 1875 1900 1925 1950 1975 2000 investigation year LMA (g/m²) average LMA maximum LMA Spatial distribution of leaf properties in tree crowns 121 and the Buchenallee beeches had leaves with absolutely normal nitrogen concentrations per dry weight. These concentrations combined with the found high LMA-values result in the presented high leaf nitrogen contents per area for the Großebene trees. A direct effect of nitrogen depositions on these values could not be found due to the similar amount of nitrogen depositions in Buchenallee and Großebene, although the C/N ratio of the humus layer was slightly higher in the Buchenallee stand. The dependence of carbon concentrations on relative irradiance may be interpreted as a consequence of increasing leaf mass per area with relative irradiance, which leads in addition to the construction of additional tissue to increased requirements for mechanical stability of the leaf, thus requiring more structural carbon. The production of more excess carbohydrates for storage under higher irradiance may not be the cause due to the low carbon content of carbohydrates (N IINEMETS & K ULL 1998). Extremely high LMA-values and nitrogen concentrations correspond to relatively high Vc max and J max values that were derived for oak and beech, when compared with previously published data: While mean values of an overview of temperate hardwoods were 47µmol/(m²*s) ±33(SD) for Vc max and 104 µmol/(m²*s) ±64(SD) for J max (W ULLSCHLEGER 1993), oak Gr13 reached at 25°C maximum values that were 100% and 81% higher. Vc max,298 and J max,298 of beech Gr12 were 21% and 15% higher than the mean values for temperate hardwoods. The reported values for Fagus sylvatica seedlings at 20°C from T AYLOR & D OBSON (1989) were much lower (11 µmol/(m²*s) and 35µmol/(m²*s)). Values for different Quercus species (Q. alba, Q. rubra, Q. stellata) from this overview were also lower and varied between 18 and 51 µmol/(m²*s) ( Vc max ) and 29 and 127µmol/(m²*s) ( J max ). Only D REYER ET AL . (2001) report similar values to those found in this study from an experiment with N-fertilised seedlings, that were 8% and 18% lower for Quercus petraea and 16% and 7% higher for Fagus sylvatica than the values measured on the Großebene trees and, thus, confirm this study. The good agreement between the nitrogen dependence of Vc max and J max of both species with a saturating curve (Fig. 89) may be interpreted as nitrogen saturation of photosynthesis. Though a nitrogen dependence of Vc max and J max or of the maximum photosynthesis rate A max has also been observed by other investigators (H ARLEY ET AL . 1992, N IINEMETS & T ENHUNEN 1997, P ORTÉ & L OUSTEAU 1998, L E R OUX ET AL . 1999, M EDLYN ET AL . 1999, K AZDA ET AL . 2000, and K AKUBARI 2000 (personal communication)), a saturation has not yet been observed. This may have several reasons: First, nitrogen per leaf area in the mentioned studies was often in a lower range than that of the Großebene trees (0.3 - 2.4 g/m², 0.4 - 1.1 g/m², 1.3 - 2.4 g/m², 0.9 - 3.0 g/m², 0.5 - 1.7 g/m², 1.3 - 2.8 g/m², and 0.5 - 2.5 g/m² in the order of studies mentioned), while oak Gr13 reached 1.3 - 2.8 g/m² and beech Gr12 reached 1.3 - 2.7 g/m². Thus, an effect that appeared above 2.3 g/m² may hardly be recognised in some of these studies. Secondly, differences between mature trees and seedlings or annual plants, that were used in some studies (H ARLEY ET AL . 1992, M EDLYN ET AL . 1999) might exist. And thirdly, all studies with maximum nitrogen contents above 2.4 g/m² were interpreted as linear relationship, though more or less clear tendencies towards saturation may be observed, when the data are re-evaluated. This is especially valid for the study with the highest nitrogen contents on Juglans regia (L E R OUX ET AL . 1999), where maximum Vc max and J max are achieved at 2.4 g/m², while 3 more data points up to 3 g/m² show lower or even high rates. The A max - data of K AZDA ET AL . (2000) for Quercus robur (1.4 - 2.8 g/m²) are partly scattered, but nearly Application of a 3D-light model to the 3D-representation of beech Gr12 and its stand 128 4.1.3 Parameterisation of STANDFLUX-SECTORS 4.1.3.1 Segmentation of leaf cloud enveloping polyhedrons Boundaries of height layers, sectors, and sections as well as section height ranges have been chosen in order to construct compartments with as homogeneous conditions as possible, thereby explicitly representing larger gaps and inhomogeneity of the crown. This is best achieved, when the resulting compartments are either empty or densely filled with leaves. As less intersections as necessary were required on the other hand to reduce the number of compartments that have to be parameterised and calculated in the light-model. Height layer boundaries for beech Gr12 have been chosen in an average vertical distance of around 1m with deviations due to canopy gaps. Figs. 113 a and b show the chosen sector boundaries in each height layer: 4-6 vertical intersection planes cut the polyhedrons in each layer into 3 - 12 filled sectors. The sector boundaries were chosen such that gaps in the crown may well be represented by additional cylinder shaped boundaries. The 94 resulting sectors were cut into 410 sections using the optical representation of beech Gr12 in CRISTO (Fig. 114). 4.1.3.2 Segmentation of crown approximating polyhedrons in the stand Großebene The convex shape and gradients of leaf area density or leaf angles in the crown could be represented by division of the homogeneous tree crown approximating polyhedrons into eight 45°-sectors in the main azimuth directions and four height layers per sector. The height layer boundaries of opposite sectors are the same due to the segmentation scheme (Fig. 115): 20 20.1 20.220.320.4 20 20.2 20.4 20.6 24.5 24.6 24.7 20 20.1 20.220.320.4 19.6 19.8 20 20 20.2 20.4 20.6 24.6 24.8 25 19.6 19.8 20 1 5 4 3 2 Fig. 1 12: The intersection of a concave polyhedron with a vertical plane produces two incomplete polyhedrons (left side, the incomplete polyhedron which was on the left side of the intersection plane is displayed below and has been turned around). The intersection area is concave. The Delaunay triangulation is based on the convex hull of the intersection points and therefore has to be corrected by removing the indicated triangle (below). Application of a 3D-light model to the 3D-representation of beech Gr12 and its stand 129 - 5 0 5 East H m L - 5 0 5 North H m L - 5 0 5 North H m L - 5 0 5 East H m L - 5 0 5 North H m L - 5 0 5 North H m L - 5 0 5 East H m L - 5 0 5 North H m L - 5 0 5 North H m L - 5 0 5 East H m L - 5 0 5 North H m L - 5 0 5 North H m L - 5 0 5 East H m L - 5 0 5 North H m L - 5 0 5 North H m L - 5 0 5 East H m L - 5 0 5 North H m L - 5 0 5 North H m L 0 - 1.05m 4.1 - 5.25m 1.75 - 2.55m 2.95 - 4.1m 1.05 - 1.75m 2.55 - 2.95m Fig. 113a: Segmentation of height layers of beech Gr12 into sectors of the light-model STANDFLUX-SECTORS. The height range of each layer is given in m below apex. Application of a 3D-light model to the 3D-representation of beech Gr12 and its stand 130 - 5 0 5 East H m L - 5 0 5 North H m L - 5 0 5 North H m L - 5 0 5 East H m L - 5 0 5 North H m L - 5 0 5 North H m L - 5 0 5 East H m L - 5 0 5 North H m L - 5 0 5 North H m L - 5 0 5 East H m L - 5 0 5 North H m L - 5 0 5 North H m L - 5 0 5 East H m L - 5 0 5 North H m L - 5 0 5 North H m L - 5 0 5 East H m L - 5 0 5 North H m L - 5 0 5 North H m L 5.25 - 6.15m 10.35 - 11.5m7.05 - 8.35m 9.35 - 10.35m 6.15 - 7.05m 8.35 - 9.35m Fig. 113b: Segmentation of height layers of beech Gr12 into sectors of the light-model STANDFLUX-SECTORS. The height range of each layer is given in m below apex. Application of a 3D-light model to the 3D-representation of beech Gr12 and its stand 131 Height boundaries for opposite sectors (east/west, south/north, north-east/south-west, northwest/south-east) were drawn in the middle between neighbours in height of 4 points: 2 measured outermost border points, crown-base and apex. The horizontal extension of 45°- sectors was given by the maximum extension of a linear approximation to the crown form (Fig. 115). This kind of segmentation results in cylinders, when tree crowns are symmetrical to the stem and may represent bigger cavities along the shape of the canopy. - 5 0 5 - 5 0 5 - 5 0 5 1 2 3 4 5 6 - 1 - 0.5 0.5 1 1 2 3 4 5 6 23 23.2 23.4 23.6 SSE-Sector Radius (m) Height (m) Radius (m) Sector width (m) North (m) East (m) 1.75 - 2.55m below apex Fig. 114: Division of the South-South-East-sector of the third height layer of beech Gr12 into 7 sections, visually supported by an optical representation routine in CRISTO. The SSE-sector is shown from above with cylinder-shaped section boundaries (right side, above) and from the west side, where the cylinder shaped section boundaries occur as vertical lines (right side, below). The section boundaries were chosen in a way that allows to draw the height boundaries close to the border of leaf clouds, thereby enabling the representation of larger gaps. East Apex Crown base West Fig. 115: Segmentation of tree crowns of the Großebene trees (vertical cross-section through the stem in west-east direction). The dotted line represents the cross-section of a tree crown approximating polyhedron with its corners at the western and eastern border points of the crown as explained above. The original crown form (thickest line) of most trees was more convex than the form of the polyhedron, which is considered in the segmentation. Height boundaries were set in the middle between the heights of measured points. The horizontal extensions of 45°-sectors (grey fields) are given by the maxim um extension of the crown approximating polyhedron in each specific layer and direction. Application of a 3D-light model to the 3D-representation of beech Gr12 and its stand 132 4.1.3.3 Parameter determination for single compartments Each compartment of beech Gr12 was automatically parameterised based on leaf area and volume share of included leaf cloud enveloping polyhedrons assuming volumetric homogeneity of leaf area density in the leaf clouds. The relationship between projected wood area and leaf area of leaf clouds from Fig. 56 was employed to calculate wood area density of each compartment. The stem was considered as a cylinder with its diameter in 1.35m height, that reaches the middle height of the crown (19.75m above the floor, 5.75m below apex) and builds the central compartment of the simulated tree. Average leaf angles of each compartment were calculated based on the average height of the compartment below apex using the relationships found for beech Bu38 (Figs. 61 and 62), which were recalculated to in the upper part of the crown (range of 0 - 6.75m below apex) and to in the lower part of the crown. Branch angles in each compartment were calculated using the linear relationship from Fig. 64. Transmissivity and reflectance were assumed to equal 10% and 6%, using the values of F ALGE (1997). The leaf area densities of tree sectors from the surrounding stand were derived from the height dependence of leaf area density as displayed in Fig. 24. All other parameters for the surrounding tree crowns were derived in the same manner as those of beech Gr12, because specific data for Quercus petraea trees were not available. From former studies it was expected that leaf and branch angles of neighbouring trees play a minor role for the light calculation and that the main impact of the different tree species is a result of their canopy form. 4.1.4 Validation of STANDFLUX-SECTORS 4.1.4.1 Light and LMA simulations All light calculations are based on PPFD measurements with a Li-Cor quantum sensor above a clear-cut 1300m south-east of the investigated stand between 19.6.1998 and 2.7.1998 (measurements of M. S CHMIDT ). The matrix points were placed in a 10cm grid spread over the volume of a vertical projection of 6 leaf cloud enveloping polyhedrons that represent leaf clouds whose sapflow was measured by M. S CHMIDT (D EPARTMENT OF PLANT ECOLOGY , UNPUBLISHED ) - see Fig. 116. The volume of a vertical projection with the same height extension as the leaf cloud enveloping polyhedron was chosen because the segmentation in STANDFLUXSECTORS allows only vertical borders. Direct and diffuse irradiation were calculated hourly (336 hours) for each of 125058 matrix points - 5460 points in the volume of leaf cloud E and 33670 points in the volume of leaf cloud B, for example. The maximum integrated value over 336 hours of diffuse plus direct irradiance of all matrix points from a leaf cloud was expressed relative to the measured irradiance above the clear-cut as maximum relative irradiance of each leaf cloud. Assuming that the site of maximum relative irradiance in the volume of a leaf cloud is angle = - 2.63 H heightbelowapex L + 36.86 (51) angle = 4.162 H heightbelowapex L - 8.92 (52) Application of a 3D-light model to the 3D-representation of beech Gr12 and its stand 133 the location of its leaves with maximum LMA, maximum LMA was calculated from maximum relative irradiance based on the relationships in Fig. 75 adjusted to beech Gr12 (see below). The integrated average of all matrix points in the uppermost 10cm-layer of each leaf cloud projection was calculated as an estimation of the leaf cloud’s light climate and expressed as average relative irradiance above the leaf cloud. Whole leaf mass divided by whole leaf area of each leaf cloud (leaf cloud LMA) was assumed to follow the same light dependence as that of single leaves and was calculated based on the equations in Fig. 75 and an adjustment to beech Gr12 (see below). 4.1.5 Validation data Leaf clouds A,C,D,E, and F were harvested on 10 th - 12 th of August 1998 determining minimum and maximum LMA of each of their 1m branch segments with 5 leaves from the proximal part and 5 leaves from the distal part of the segment. Each of these leaf clouds consisted of 11-20 - 4 - 2 0 24 North H m L 15 20 25 Height H m L 15 20 25 Height H m L - 4 - 2 0 2 4 East H m L - 4 - 2 0 2 4 North H m L - 4 - 2 0 2 4 North H m L - 4 - 2 0 2 4East H m L - 4 - 2 0 2 4North H m L 22 23 24 25 Height H m L 22 23 24 25 Height H m L - 5 - 2.5 0 2.5 5 East H m L - 4 - 2 0 2 4 North H m L - 4 - 2 0 2 4 North H m L Fig. 116: Sapflow has been measured on 3 shade leaf clouds (A, B, C) and 3 sun leaf clouds (D, E, F) of beech Gr12 using the thermal dissipation method (G RANIER 1985, 1987, measurements of M. S CHMIDT , D EP . OF P LANT E COLOGY ). The measured average transpiration rates of the 6 leaf clouds during 19.6.98 - 2.7.98 are indicated by intensity of their colour. The left figures show a view from above the tree (above) and from above the shade crown in height 20.25m (below). One hidden sun-leaf cloud may only be seen from west side above (right above), while all other leaf clouds are visible from the west side of the tree (right side, below). Leaf cloud F was inserted as one of the two last branches directly below the apex leaf cloud that is visible between the letters E and F. 20 30 40 50 Transpiration ( mol/( m²*d)) A FED C B FED Application of a 3D-light model to the 3D-representation of beech Gr12 and its stand 134 1m branch segments. Leaf dry mass of the oven-dried samples was separately divided by the average LMA of each segment to calculate the leaf cloud’s leaf area. Maximum LMA of the leaf clouds was the maximum LMA that was measured on any leaf sample from the leaf cloud. Leaf cloud B lost all its leaves during the vegetation period 1998 by itself and its leaf area during the measurement period could only be estimated by eye to equal 2.25m². Its leaf dry mass was calculated based on allometric relationships to 144.1 g. Maximum LMA of this leaf cloud was not determined. 4.2 Results 4.2.1 Stand Structure 4.2.1.1 Crown length and position of oak and beech trees in the Steigerwald stands Oak and beech trees in the stands Großebene and Steinkreuz had different crown lengths with respect to their stems’ basal area (Fig. 117): While crown length of beech trees in both stands increased with basal area to values between 15 and 20m (Großebene) or even 30m (Steinkreuz), oak trees had much shorter crowns (length around 10m) in both stands. In contrast to this, mean heights (average of heights of apex and crown base) of the same crowns were higher for oaks than for beech trees in the same basal area class (Fig. 117, right). Therefore, oaks in both stands occupy spaces in the above part of the stand and are underrepresented in the lower parts (compare Figs. A1 and A2 in the appendix), which is confirmed by the observation of a high proportion of dead branches in the lower part of oak canopies (compare chapter 1). Beech crowns on the other hand often produced leaves rather close to the floor, sometimes even when the trees were large and old. 0 5 10 15 20 25 30 35 0 1000 2000 3000 4000 basal area (cm²) crown length (m) Oak Steinkreuz Beech Steinkreuz Oak Großebene Beech Großebene 0 5 10 15 20 25 30 35 0 1000 2000 3000 4000 basal area (cm²) mean height (m) Oak Steinkreuz Beech Steinkreuz Oak Großebene Beech Großebene Fig. 117: Length of beech and oak canopies from the two mixed stands in the Steigerwald (left) and mean height (average of apex and crown base) of these canopies (right). The log-logtransformed data were approximated with linear functions to show the general trend for both species. The fits are indicated in the re-transformed data by fat (Großebene) and thin (Steinkreuz) lines. Application of a 3D-light model to the 3D-representation of beech Gr12 and its stand 135 4.2.2 LMA-calculations 4.2.2.1 Validation of the light model with the LMA/irradiance relationship The relationship between relative irradiance and LMA from the Buchenallee leaves leads to an underestimation of 14.3g/m² (mean absolute error), when combined with the maximum relative irradiance simulations of STANDFLUX-SECTORS to calculate maximum LMA-values of leaf clouds (Fig. 118). This underestimation equals 13.5% of the mean of measured values and is mainly due to the relatively high maximum LMA-values of the three sun leaf clouds (D, E, F). The root mean square error for this comparison was 17.5 g/m². The main reason for this underestimation is the difference between maximum LMAvalues of beech Gr12 (128 g/m²) and the beech trees from the Buchenallee stand (110 g/m²). Therefore, the equation of the approximation line from the Buchenallee produces LMA-values close to 110g/m² (104.6) at relative irradiance 1, which cannot be adequate for the Großebene beech. This individual or stand-specific difference may be considered by adjusting the equation for the LMA vs. relative irradiance ( Q rel ) relationship to thereby assuming the general shape of the curve to be conserved. Making this adjustment leads to a smaller overestimation (6.1g/m², = 5.9% of mean of measured values) with a root mean square error of 10.3 g/m², indicating that the corrected formula leads to relevant improvements. Thus, equation (55) should be preferred due to its adjustment to beech Gr12 LMA data. 4.2.2.2 Estimation of leaf cloud LMA An additional indication of the validity of LMA calculation based on STANDFLUX-SECTORS and equation (55) was gained from the estimation of leaf cloud LMA (Fig. 119). When leaf cloud Fig. 118: The dependence of LMA on relative irradiance has been measured on leaves of beeches Bu38 and Bu45 (left side, triangles) and the approximation line equals y = 104.6 ((relative( relative irradiance) 0.377 , r² = 0.87. The measured maximum LMA of five leaf clouds in relation to maximum simulated relative irradiance above each leaf cloud (filled squares) is compared for validation of STANDFLUX-SECTORS. The maximum LMA of leaf cloud B (open square) was not measured and may be estimated to equal approximately that of leaf cloud C. When STANDFLUX-SECTORS and the adjusted equation (eq. 53) are used to model maximum LMA of each of the 5 leaf clouds, modelled vs. measured maximum LMA are compared with an r² of 0.87 (right side), a mean absolute error of -6.1 g/m² (-5.9% of mean of measured values), and a root mean square error of 10.3 g/m². 0.2 0.4 0.6 0.8 1 relative irradiance 40 60 80 100 120 AML H g ê m 2 L A C B EDF y = 1.04x R 2 = 0.87 0 30 60 90 120 150 0 30 60 90 120 150 maximum LMA measured (g/m²) maximum LMA modelled (g/m²) (relative , (53) LMA = 128Q rel 0.377 Application of a 3D-light model to the 3D-representation of beech Gr12 and its stand 136 LMA was estimated from averaged relative irradiance above it, thereby treating the whole leaf cloud as a large leaf, the mean absolute error was +1.5 g/m² (2% of mean of measured values) and the root mean square error equalled 10.28 g/m². Thus, leaf cloud LMA could be modelled with a similar accuracy as that of single leaves using the same relationship. The effect of the used LMA vs. relative irradiance relationship has been shown to be rather big when applied to single leaf data and so is its effect in the leaf cloud LMA calculation: Using the original LMA vs. relative irradiance relationship from the Buchenallee trees (Fig. 75) turns the slight overestimation into a stronger underestimation (-9.9g/m² mean absolute error) and increases the root mean square error to 13.1 g/m². Both model comparisons (maximum LMA and leaf cloud LMA) show that the relative irradiance simulation with STANDFLUX-SECTORS may provide a reasonable basis for LMA calculations. 4.2.3 Comparison of climate and transpiration data 4.2.3.1 Daily courses Absolute values of climate variables above a clear-cut near the BITÖK investigation site Steinkreuz were measured by G. L ISCHEID , University of Bayreuth and are shown in Fig. 120. The days during the two weeks from 19.6. -2.7.1998 were mostly cloudy, though not very rainy: Only the days 21.6., 22.6., and 25.6. had permanently clear, sunny conditions. These days were also the warmest days, so that the first week was generally warmer than the second week. Main rain events occurred during the evening or night hours of 21.6., 26.6., and 27.6., while smaller rain events took place on 19.6., 23.6., 26.6., and 1.7.1998. The daily courses of VPD, PPFD, and temperature were more or less parallel on the three clear sunny days, on 24.6., and during A C B E D F Fig. 119: The LMA of leaf clouds is given as their whole leaf mass divided by their leaf area and equals the average LMA of their leaves. Leaf cloud LMA has been set in relation to the average of simulated relative irradiance values in all matrix points directly above the leaf cloud (left side, filled squares). Equation (55) is plotted in the same graph for comparison. Error bars represent the range of LMA values occurring in each leaf cloud apart from leaf cloud B, where this was not measured. Modelled leaf cloud LMA on the base of averaged simulated relative irradiance and the corrected LMA vs. relative irradiance relationship is well correlated to the measured leaf cloud LMA values (right side, r²=0.87). The model slightly overestimates leaf cloud LMA values by 1.5 g/m² (mean absolute error), equalling 2% of the mean of measured values. The root mean square error was 10.28g/m². 0 0.2 0.4 0.6 0.8 1 relative irradiance 0 20 40 60 80 100 120 fael duolc AML H g ê m 2 L y = 0.99x R 2 = 0.87 0 30 60 90 120 0 30 60 90 120 leaf cloud LMA measured (g/m²) leaf cloud LMA modelled (g/m²) (53) Application of a 3D-light model to the 3D-representation of beech Gr12 and its stand 137 26.6. - 29.6.. Opposite tendencies in the courses of VPD and PPFD were due to temperature and were observed on 19.6., 24.6., 30.6., and 2.7.. Some observations may be summarised about the course of transpiration rates of sun and shade leaf clouds during the investigation period: • The daily course of transpiration rates of sun leaf clouds was generally smoother than that of shade leaf clouds: while sun leaf clouds D, E, and F had wide and round daily peaks of transpiration (Fig. 122), the peaks in the course of transpiration rates from shade leaf clouds A, B, and C were more pointed (Fig. 121). • When a continuous increase in irradiance was given, transpiration rates of leaf cloud D and the other sun leaf clouds steeply increased early in the morning and then approached to a maximum value at noon. Discontinuities in the irradiance increase with parallel discontinuities of the usual VPD increase in the morning - probably due to dew fall or smaller rain events - caused a decrease in transpiration rates even if irradiances just stayed constant, which may be observed on 19.6., 22.6., and 26.6. on all sun and shade leaf clouds. • The shade leaf clouds often did not yet start to transpire on these days, when such a discontinuity occurred, which may indicate that a critical light or VPD level was not yet reached before that time. Their later start is one reason for the more pronounced peaks in transpiration. • Another reason was that the course of PPFD above these leaf clouds consists also of pointed peaks, thereby inducing high irradiances for a short time. Fig. 120: Synopsis of climate variables during the investigation period 19.6.1998 - 2.7.1998. While temperature and VPD are scaled on the left y-axis, PPFD (in mmol/(m²*s) ! ) and precipitation are scaled on the right side. All measurements were performed at the BITÖK investigation site Steinkreuz, 5m above a clear-cut approximately 1300m in distance to the Großebene stand by G. L ISCHEID , University of Bayreuth. 0 5 10 15 20 25 30 19/06/98 21/06/98 23/06/98 25/06/98 27/06/98 29/06/98 01/07/98 03/07/98 Date temperature (°C) | VPD(hPa) 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 PPFD (mmol/(m²*s)) | precipitation (mm) temperature (°C) VPD (kPa) precipitation (mm) PPFD (mmol/(m²*s)) Integrating discussion 144 A very high coefficient of determination (r²=0.98) was found between leaf mass and the sum of transpired water of each leaf cloud during the investigation period (Fig. 126). Further investigations are necessary to analyse, if this useful relationship is also valid for other conditions or even other trees and species. Further conclusions may be derived with this model combination and this data base since additional sapflow measurements on branches and stem of oak Gr13, as well as on stems of other trees in the stand were not yet evaluated. 5 Integrating discussion 5.1 Characteristics of oak and beech in the stand Großebene Many characteristics of oak and beech in the Großebene stand have been collected on different levels of organisation and it seems worthwhile to compare these properties species-oriented to evaluate if they draw a reasonable picture of ecological specialization of the species in their stand, though general conclusions can not be drawn due to the low number of investigated trees. Table 9 summarises the clearest differences between the species found in this study. Characteristics Fagus sylvatica Quercus petraea Natural regrowth in the mixed stands Yes (Fig. 3) No (Fig. 3) Height position of crowns in the stand All height positions (Fig. 117) Uppermost 8-12m of the stand (Figs. 19b, 117 ) Crown length Long (Fig. 117) Short (Fig. 117) Proportion of dead branches and boughs in the lower crown Low (Figs. 7, 10) High (Figs. 7, 10) Growth pattern of branches More deterministic (Figs. 9, 33, 34, 46) Less deterministic (Figs. 9, 33, 34, 46) Crown construction Fan-shaped opening towards the surface (Figs. 16, 35, 37,40,41) More irregular (Figs. 16, 35, 37) Crown shape Convex borders, greatest diameter in the lower part, long and pear-shaped (Figs. 18, 26) Concave borders, greatest diameter in the upper part, short and strawberry-shaped (Figs. 18, 26) Directions of strengthened development One main direction, not towards a neighbouring tree (Figs. 43, 47, 51) Several directions towards neighbouring trees (Figs. 43, 47, 51) Total leaf area density Lower (Table 5) Higher (Table 5) Leaf area densities in the crown Highest leaf area density in the uppermost meter of the crown, continuously low densities in the lower half (Fig. 23) Highest leaf area density 2-3m below the apex, decreasing towards the apex and the bottom (Fig. 23) Self-shading Less severe (Figs. 31, 32) Stronger (Figs. 31, 32) Leaf photosynthesis capacities Low (Figs. 83-86, 89) High (Figs. 83-86, 89) Stomatal sensitivity ( gfac ) High in shade leaves, low in sun leaves (Fig. 98) High in medium sun leaves, lower in uppermost sun leaves, low in shade leaves (Fig. 98) Integrating discussion 145 Oak crowns in the stands Großebene and Steinkreuz occupy only the most sun-exposed positions in the stand, but are not able to reach this position by natural regrowth in the dense stand. This is in accordance with the forest management practice to save oaks from competition of neighbouring beeches by felling these beech trees. Once in the top of the canopy, the strategy of oak seems to be the occupation of high volumes in the upper region, producing a high overall leaf area density and thereby shading competing species below that region - and itself. The stronger self-shading of oak may be one reason for its short crown with several dead boughs in the lower part. This may also be seen as a specialization of oak in the use of only high light positions. The occupation of high volumes in the upper part of the canopy is visible in the oak’s crown shape. It is open to speculation if the concave (=rugged) and approximately strawberry-shaped crown form is a consequence of a general multi-directional development of oaks towards competing trees. Such a growth reaction to the spatial situation would require flexibility in the growth pattern of branches, which is apparently better achieved in oak than in beech. The investment into high photosynthesis capacities makes sense for a tree in a high-light environment. That stomatal sensitivity ( gfac ) is high in medium sun leaves indicates that oak allowed high transpiration especially to these leaves, even when their CO 2 use efficiency (assimilation per CO 2 -concentration) and relative humidity were not very high. The risk of high water losses in sun leaves is more reasonable when leaves have high photosynthesis capacities and may provide the resources for expansive growth in the region of these leaves. The lower transpiration support for shade leaves probably causes them to die earlier and again indicates the consequent adaptation of oak to high light environments. Beech on the other hand was generally more carefully avoiding high water losses due to low coefficients of stomatal sensitivity. Only the lowest shade leaves were allowed to have high conductances when CO 2 use efficiency and relative humidity were not very high. This seems not as hazardous as allowing it to sun leaves, because relative humidity in the lowest part of the crown is usually higher than in the upper part. But it includes the possibility of useless transpiration due to the lower chance for sufficiently high assimilation gains of shade leaves. While beech, thus, seems to have supported shade leaves in allowing them high transpiration rates, oak mainly supported medium sun leaves in their water consumption. The water support for the lowest shade leaves may help them to achieve a positive CO 2 - balance and this could be one factor that allows beech to maintain high amounts of shade leaf biomass and to develop extensive shade crowns. The generally sparing equipment of beech leaves concerning photosynthesis capacities may additionally be advantageous in maintaining the high number of shade leaves. Another factor for the survival of shade leaves may be found in the fan-shaped formation of beech leaf clouds towards the canopy surface which probably improves the light situation of shade leaves. The more deterministic growth of branches of a beech tree, its unidirectional development, and the conserved convex crown projection may indicate that a pre-formed internal organisation scheme could be relevant for the CO 2 -balance of shade leaves. A strengthened development towards several directions in order to compete with horizontal neighbours would hardly be possible, if a pre-formed pattern is to be conserved, while a general drift towards the most promising gap in the surrounding stand seems to be possible, especially since the fan-shaped formation of leaf clouds appears to be gap-oriented anyway. A generally and mainly in the shade crown lower leaf area density also improves the conditions for shade leaves due to less self-shading. Integrating discussion 146 All these factors together with the rather low leaf photosynthesis capacities of beech may be seen as adaptations to shade conditions that are necessary for a tree with a large shade crown. The height distribution of leaf area densities in beech shows that it may on the other hand also be very competitive with regard to the most sunny positions in the stand. Its relative success in a mixed stand of oak and beech may, thus, be explained with two complementary, defensive and aggressive strategies: A light-oriented organisation of the shade crown can make the whole tree relatively insensible to shading by a neighbouring tree, which is supported by a growth pattern of the sun crown that avoids self-shading by occupying only small volumes. This could allow it to survive in the shade of other trees for years and even provide the resources for the growth of the sun crown. The concentration of highest amounts of leaf area in the uppermost layer of the sun crown on the other hand can assure high shading efficiency of this part of the crown, because shadow cast of this layer is relevant for the biggest possible part of the surrounding stand canopy. This may on the long run improve the conditions for the whole tree by effectively reducing growth rates of competitors (L EUSCHNER 2001). The double strategy of beech may also be expressed in its crown shape that is more clearly separated in sun crown and shade crown than that of the oak. Thus, the characteristics found on single trees of both species fit into a reasonable description of their ecological specialization, though they can not prove the general validity of this concept. 5.2 Application of Beer’s law The description of light profiles in the stand with Beer’s law was in a first approximation applicable to the beech crowns in the Buchenallee stand (Figs. 58, 59). However, two assumptions of Beer’s law have been shown to be violated in these crowns: • The leaf angle distribution was not constant throughout the canopies of beeches Bu45 and Bu38 (Figs. 62, 63). The frequency of steep inclinations that allow more light to penetrate a leaf layer decreased from the apex to a depth of around 6 m (Bu38) or 7 m (Bu45) in the crown, where horizontal inclinations were most abundant. The frequency of steep inclinations increased again from there towards deeper parts of the crown. The extinction coefficient of Beer’s law was, therefore, variable along a vertical gradient through the crown. • Leaf area density of crown layers was not constant and exhibited the general pattern of 2-3 “peak”-layers with higher leaf area density that were separated by layers with lower leaf area density (Figs. 21-23). The peak-layers of leaf area density of beech Bu38 were in a height of 3 m and 6 m below apex. The variation of leaf area density has to be included in the calculation of light profiles according to Beer’s law. The significance of the layer 6 - 7 m below apex of both crowns for the light profile is increased through the observed trend in width of leaf space and in angles of leaf cloud planes: While width of leaf blade did not show a clear dependence on irradiance or height below apex, the effective width of leaf space was widest in this layer and decreased from there towards both ends of the crown (Fig. 66). This trend increases the effective leaf area density (based on projected leaf area instead of leaf area) of the layer 6 - 7 m below apex relative to the other layers. The angles of leaf clouds were nearly horizontal in the layer 6 - 7m below apex and became negative below that layer, while they were positive above (Figs. 33 and 35). Thus, light extinction on a leaf cloud basis is maximum in this layer. Integrating discussion 147 The consequence of the leaf angle variability for light profiles would be a stronger light gradient than calculated with Beer’s law (using constant coefficients) in the upper 6 - 7 m of the crown and a less strong decrease in light intensity below that height. Leaf area density variability would strengthen this effect in the upper 3 m of the crown of beech Bu38 and in the lowest part below 7 m below apex, while it would damp the decrease of light intensity in the crown part between 3 m and 7 m below apex. Thus, a stronger light gradient is to be expected in the upper 3 m of the beech crown Bu38 and a weaker light gradient in the lowest part below 7 m below the apex. This expectation is confirmed in a comparison with the measured relative irradiance in beech Bu38 (Fig. 58). Relative irradiance in the upper 3 m decreased stronger than an exponential fit based on the assumption of constant coefficients in Beer’s law, though this approximation is for mathematical reasons stronger oriented on the relative high irradiance values than on the low irradiance values. This fit is not able to reproduce the “too high” relative irradiance values in the crown part below 6 m below the apex, indicating that no exponential function may adequately express both parts. The high coefficient of determination does not really consider the deviation in the lower crown part, which is big in relative units but small in absolute units. This might be the reason for it to be overlooked in comparable investigations. A “too high” relative irradiance in the lowest crown part was also observed on the data of beech Bu45 (Figs. 58, 59). The “too high” relative irradiance values in the lowest crown part of these both trees may be interpreted as another adaptation of beech trees to the low light environment that they produce themselves for their shade crown. The light distribution inside the crowns becomes more homogeneous through the described variation in angles and density of foliage elements, which lowered relative irradiance in the above crown part and increased it in the lower shade crown. 5.3 Leaf mass per area (LMA) The reported LMA-values of sun leaves of beech from different origins (Table 5, Fig. 108) show an increasing long-term trend since 1968, while it seemingly was lowest around 1943. Since the position of the investigated leaves is not mentioned in the study of B URGER (1945), the apparent relative decrease of average LMA between 1891 and 1943 could also be due to the different exposition and light situation of the investigated leaves (compare Figs. 68 and 69), though trees have been felled in the extensive studies of B URGER and a differentiation between sun and shade leaves was generally made. This could lead - apart from different stand conditions - to an artificial LMA-decrease, because this investigation is the only data point between 1891 and 1968. But even the newer literature since 1970 shows an increasing long-term trend. The lowest LMAvalues (40 - 60 g/m²) of sun leaves in this period were measured 1968 from a tower in 26m height on the outermost leaves of the sun crown of beech “B68” in the IBP stand Solling (international biological program, S CHULZE 1970). Though differences between stands like altitude, exposition, depositions, average temperature, or other differences may be influential, these differences would not necessarily lead to the compiled general increase of LMA of sun leaves. Stand-specific differences are not relevant in the case of beech B68 in the Solling project, whose sun leaves in 26m were investigated again in the period 1986 - 1988 and then had LMA-values of 80 to 110 g/m² (S CHULTE 1992). Since the increase in LMA-values of beech B68 (Solling) goes along with the general trend found on data from various origin, it becomes likely that this difference shows a realistic Integrating discussion 148 structural change in this crown that occurred apparently also on other beech trees in Europe. The newest compared values (those of this study) were also the highest LMA-values. This could mean that LMA of sun leaves of beech trees is still increasing and reasons as well as consequences of this trend need to be assessed, though additional LMA-data have to be evaluated to assure the validity of the LMA-trend. Atmospheric CO 2 , climate change, or nitrogen depositions come into question as potential causes for physiological changes that lead to an increase of LMA of sun leaves of beech. While effects of climate change are unlikely to be detectable in climate data between 1968 and 1987, nitrogen deposition to forests was increasing between 1968 and 1991 and decreasing in the latest years since 1991 (Level II - program, BML 1997). Yearly averages of atmospheric CO 2 concentration as measured at Mauna Loa (Hawaii) continuously and still exponentially increased from the years 1968 (323 µmol/mol) to 1987 (349 µmol/mol) and 1999 (368 µmol/mol) (K EELING & W HORF 2000), which was the strongest increase of this quantity since 1800 when it started to increase from a stable pre-industrial value of 270 ppm (S ALISBURY & R OSS 1992). The time course of CO 2 -concentrations corresponds best with that of the compiled LMA-increase, since the LMA-trend does not show a decrease. A consequence of the LMA-increase in sun leaves of beech trees could be a higher sink strength of sun crowns of beech for CO 2 during the vegetation period, since more assimilates are needed to build up thicker leaves. This point needs further investigation due to a possible opposite trend in the allometric relationship between leaf area and basal area of trees, which was lower in all harvested trees than in the regressions based on former investigations (Fig. 14), so that trees eventually just organise the same leaf mass to a smaller area. Lower leaf area of beech trees and other forest species is also reported from public forestry studies in Germany (HMU 2000). The combination of both trends could potentially lead to a higher water use efficiency due to reduced transpiration rates (as a consequence of reduced leaf area) and increased light availability in the shade crown. Though the deposition rates are decreasing since 1991, it can not be excluded that the LMAincrease is due to high nitrogen deposition, because nitrogen uptake by the trees might still be high. The observed nitrogen saturation of photosynthesis capacities of leaves of oak and beech indicates that the investigated sun leaves contained more nitrogen than they need for photosynthesis (Fig. 89). 5.4 Implications for gas-exchange modelling It has been shown that homogeneity is not given on the level of tree crowns and, therefore, on the level of stands. Thus, the assumption of homogeneous conditions in smaller or bigger compartments (big leaves, layers, or 3D-compartments) is generally violated to some extent, though many effects of small scale inhomogeneity are probably neutralized on larger scales. The latter seemed also to be valid for the decrease of relative irradiance with depth in the canopy, since the general shape of the function of Beer’s law was in a first approximation confirmed by fish-eye photos in beech canopies (Figs. 58, 59) and the found deviations were small in absolute units. Nevertheless these small deviations need consideration even in large scale models since gas-exchange models are very sensitive to changes in light profiles and the deviations are likely to represent a general phenomenon. An indication of the relevance of these deviations is given by the application of layer-oriented gas-exchange models in net ecosystem exchange (NEE) calculations of beech stands: Such Integrating discussion 149 models often use variations of Beer’s law to describe the light gradient in stand canopies and then typically consider the leaves in the lower half of beech canopies as CO 2 -sources on each day of the vegetation period due to light intensities below the light compensation point of these leaves (own simulations with the layer model GASFLUX (S ALA & T ENHUNEN 1996), data not shown). This is a consequence of the use of an exponential function that inevitably approaches zero in the lower part of the crown when it is fitted to represent the higher light values in the upper canopy. It is not impossible but unlikely that beech trees can afford this waste of resources. The found deviations from Beer’s law are likely to represent general properties of beech canopy structure that have an equalizing effect on the light profile, thereby inducing a steeper gradient in the upper canopy and a much lower gradient in the lower part of the crown. Thus, the height dependent leaf angle distributions and naturally layered leaf area density distributions (see 5.2.) should be considered in layered gas-exchange models. Most gas-exchange models do not consider the leaves as bent and, therefore, probably consider about 20% too much leaf area in the crowns at least of beech, since projected leaf area is the relevant quantity for light transmission and absorption. Since bending has been found to be height dependent (Fig. 66), the area reduction may easily be included in gasexchange models. More complex evaluations would be necessary to investigate the effect of leaf cloud inclinations and their orientation towards the canopy surface, which probably improves the use of reflected and transmitted radiation in the shade crowns of beech due to a fan-shaped formation towards the canopy surface. Such an effect would again improve the light situation of shade leaves. This could affect gas-exchange calculations especially when leaves are wet and their reflectance may reach values above 50% (dependent on the angle of incident light, G ATES 1980). Not all models of gas-exchange consider the changes in transmission and reflectance occurring on wet leaves. A fine-scale 3D-representation of forest stands might be the most accurate way to represent inhomogeneity of stands and to evaluate small-scale effects, but it is not suitable for an application to large areas. This situation may change to some extent due to up-scaling relationships like those of the nitrogen dependent leaf gas exchange model, which may use the structure dependent light climate of leaves for the derivation of nitrogen per leaf area (r² ≥ 0.87, Fig. 75) and thereby yields a completely parameterised leaf gas-exchange model that is valid for this spatial situation. Thus, an integrated and very detailed model of stand gas-exchange results from the combination of the nitrogen dependent leaf gas exchange model with STANDFLUXSECTORS or any other 3D light model and estimations of soil and wood respiration (F LECK ET AL . 2001). Such an integrated 3D model may be validated on many different scales using light measurements, LMA-distributions, leaf nitrogen contents, photosynthesis measurements on leaves and branches, sapflow measurements on branches and stems, or even eddy measurements, when extensive structure information has been gathered and soil respiration has been estimated. It thus may improve the reliability of stand gas exchange models in a way that allows up-scaling from sapflow measurements on trees to stand gas-exchange along canopy structures and could thereby be useful to provide reliable estimations of gas-exchange of stands, where eddy measurements can not be performed (for example stands in Integrating discussion 150 mountainous regions). Reliable estimations of gas-exchange in these regions could be useful to validate regional NEE calculations. The data set from the Großebene stand combines sapflow measurements on stems of beech Gr12, oak Gr13, other tree stems, and on branches from oak Gr13 with a detailed structure description that allows further testing of an integrated model. Automated methods of structure measurement are under development (K OCH & R EIDELSTÜRZ 1998, L EFSKY ET AL . 2000, T ANAKA ET AL . 1998) and might soon provide the necessary structure information for larger scale applications of a reliable integrated 3D model. Summary 151 6 Summary The gas exchange of mixed forest stands is - due to their high proportion within the forested area - an important quantity for the estimation of CO 2 - and water balances on larger scales, but difficult to verify. This thesis assumes that a fundamentally new situation in terms of theory of cognition has emerged in this field of research due to the rapid development of computer-based data processing in recent years, since it allows for the first time the explicit consideration of spatial heterogeneity in process-oriented models. This provides the opportunity to validate models across spatial scales, thereby improving the reliability of forest stand gas-exchange calculations. The bottle-neck for this kind of evaluation is not data-processing or simulation, but rather the co-ordinated recording of all information relevant to the multiple verification of a process-oriented model of mixed stand gas-exchange. The contribution of this investigation lies in the comprehensive representation and comparative fine-scale analysis of the spatially explicit description of trees in a 120 year old mixed stand of oak and beech in the Steigerwald. The 3-dimensional structure description is associated with the measured variability of photosynthesis parameters and validation data on different spatial scales. These data are discussed together with data from compared stands. Subroutines of an integrating up-scaling model were improved and verified with measurements. The canopy structures of two beech trees and one oak were simulated in an optically controllable way based on branch-oriented harvests, branch-oriented geodetic measurements (Figs. 4, 5), and allometric relationships (Figs. 9, 14). The newly developed program CRISTO for spatial analysis is based on the representation of branches and their appending leaf biomass (leaf clouds) as polyhedrons and enables the calculation of height profiles of leaf area density in layers of 1m height (Fig. 23). A tendency to build single layers with very high leaf area densities was detectable. The canopies consisted of 2-3 natural layers of leaves, which contrasted with the optical impression of the trees (Figs. 20, 21). The proportion of gaps between leaf clouds was higher than 80% in most layers of all three trees (Fig. 25). Measured species-specific differences between the crown shapes of 186 oak and beech trees were also found in the characteristic canopy shapes of the three investigated trees that were derived from maximum horizontal extensions of layers of 1m height (Fig. 26). Stronger selfshading of the oak tree was a consequence of its different canopy shape (Figs. 30 - 32). Leaf clouds of both beech trees showed striking similarities in their main growth directions (Figs. 35, 37, 39 - 41), which affected light penetration into the canopy by the variation of leaf cloud angles towards the horizon (Fig. 33) and their orientation towards the canopy surface (Fig. 41). The leaf area density of leaf clouds was largely independent of any of 8 investigated crown structure parameters (Fig. 55). The light profiles of beech crowns were measured using fish-eye-photos and were shown to differ from Beer’s law (Fig. 58) in a way that may be explained by the variation of leaf area density and extinction coefficient, the latter of which was due to the variability of leaf angles. A height dependent variation of leaf angle frequency distributions of beech was found that could be described by single-parametric ellipsoidal distribution functions (Figs. 60, 62). While the relationship between height or light and the width of leaf blades was scattered, the projected width of the beech leaves (which considers leaf bending) was shown to be height and light dependent (Fig. 66). Clear light dependencies were also established for leaf mass per area Summary 152 (LMA, Fig. 69), leaf carbon concentration (Fig. 71), and area-related leaf nitrogen content (Fig. 75). Occasionally very high LMA-values and area-related nitrogen contents have been measured. LMA-values from the Steigerwald were the highest when compared to literature data from 110 years and fit into a general tendency of increasing LMA-values of sun leaves of beech. The program RACCIA has been developed for the automated derivation of photosynthesis capacities ( J max , Vc max ) from A/C i -curves that were measured on oak and beech in the Steigerwald. The program is based on the H ARLEY /T ENHUNEN (1991) - model and was verified using chlorophyll fluorescence measurements (Fig. 78). J max and Vc max were shown to increase with nitrogen per leaf area up to a certain nitrogen level, where leaf photosynthesis becomes apparently nitrogen saturated (Fig. 89). Nitrogen saturation of photosynthesis capacities and measured temperature dependencies were considered in the development of a nitrogen dependent model of leaf photosynthesis (Fig. 97) that reduces the number of necessary parameters by more than 50% (Table 7). The model validation was based on measured daily courses and provided evidence of the potential effects of stomatal patchiness (Figs. 106, 107). The application of the highly resolving 3D light model STANDFLUX-SECTORS to the geometric representation of a beech tree and its surrounding stand in the Steigerwald was enabled by the development of a segmentation and parameterisation routine in the framework of CRISTO (Fig. 112 - 114). A beech crown was segmented into 410 parameterised homogeneous compartments. The light model was verified using the light dependence of LMA (Fig. 118, 119). A stronger light sensitivity of transpiration was derived for shade leaf clouds of beech and was attributed to the higher sensitivity of stomata of shade leaves to CO 2 use efficiency and relative humidity ( gfac ) (Fig. 98, 125). Totals of transpiration over 14 days of the investigated branches were well correlated to the calculated quantum sum above the leaf clouds and to their leaf biomass (Fig. 126). The results provide a reasonable picture of the ecological specialization of oak and beech in a mixed stand: While beech has a strategy to cope with a shady environment that keeps a high amount of shade leaf biomass alive and reduces the tree’s susceptibility to shadow cast from competing trees, oak secures a once achieved position in the upper canopy by expansive growth of the upper crown layers and is largely specialized in the more efficient photosynthesis of sun leaves. Implications for gas-exchange models are derived from their high sensitivity to the used light profile. The use of exponential functions for the calculation of light profiles may lead to strong underestimations of CO 2 -uptake when the height dependence of leaf angle distributions and the multi-layered canopy structure are not adequately considered in the equation. Light absorbing leaf area is overestimated in most gas-exchange models by around 20%, because leaf bending is mostly not considered. The high reflectance of wet leaves should be considered due to the potentially higher irradiance in shade crowns under these conditions. The model subroutines presented in this thesis may be combined to an integrated 3D model that may improve reliability of gas-exchange models, when further validation on different scales is performed. This is possible on additional data from the Großebene stand. The integrated model might be very useful in combination with automated structure measurements in future validation of NEE calculations in mountainous regions, where eddy measurements are more uncertain. Zusammenfassung 153 7 Zusammenfassung Der Gaswechsel von Waldmischbeständen ist aufgrund ihres hohen Flächenanteils eine bedeutende, aber nur schwer zu verifizierende Größe in überregionalen Berechnungen von CO 2 - und Wasseraustausch. Die vorliegende Arbeit geht davon aus, dass durch die rasche Entwicklung der computergestützten Datenverarbeitung der letzten Jahre eine neue erkenntnistheoretische Situation in diesem Forschungsgebiet eingetreten ist, die erstmals die explizite Berücksichtigung räumlicher Heterogenität in prozessorientierten Modellen ermöglicht. Hierdurch werden skalenübergreifende Validierungsmöglichkeiten eröffnet, die Gaswechselberechnungen auf Bestandesebene verlässlicher machen können. Engpässe bestehen durch diese Entwicklung weniger in der Datenverarbeitung und Simulation als in der koordinierten Erfassung aller relevanten Informationen, die zur mehrfachen Verifizierung eines prozessorientierten Modells des Mischbestandsgaswechsels notwendig sind. Der Beitrag dieser Arbeit besteht in der umfassenden Darstellung und vergleichenden feinskaligen Analyse der räumlich expliziten Beschreibung von Bäumen eines 120-jährigen Eichen-Buchen-Mischbestands im Steigerwald. Die zu Simulationszwecken verwertbare 3dimensionale Strukturbeschreibung ist mit der gemessenen räumlichen Variabilität von Photosyntheseparametern und mit Validierungsdaten auf verschiedenen räumlichen Ebenen verknüpft. Diese Daten werden zusammen mit Vergleichsbeständen diskutiert. Subroutinen eines skalenübergreifenden Modells wurden weiterentwickelt und anhand von Messdaten überprüft. Der Kronenaufbau von zwei Buchen und einer Eiche wurde auf der Basis astbezogener Ernten, astbezogener geodätischer Messungen (Abb. 4, 5) und allometrischer Beziehungen (Abb. 9, 14) optisch verifizierbar simuliert. Die räumliche Analyse mit dem dafür entwickelten Programm CRISTO beruht auf der Repräsentation von Ästen mit ihrer anhängenden Blattmasse (Blattwolken) als Polyeder und ermöglicht durch Zerlegung der Kronen in 1m-Schichten die Berechnung von Höhenprofilen der Blattflächendichte (Abb. 23). Hieran war eine Tendenz zur Bildung einzelner sehr dichter Schichten erkennbar. Der Kronenaufbau erwies sich entgegen dem äußeren Anschein als natürlicherweise mehrschichtig hinsichtlich der Verteilung von Blattflächen (Abb. 20, 21). Der Anteil blattfreier Räume außerhalb der Blattwolken lag in den meisten Höhenschichten aller drei Bäume über 80% (Abb. 25). Gemessene artspezifische Unterschiede in der Kronenform von 186 Buchen und Eichen spiegeln sich in den charakteristischen Kronenformen der drei Untersuchungsbäume wider, die aus der maximalen horizontalen Ausdehnung von Höhenschichten abgeleitet wurden (Abb. 26). Als Konsequenz der unterschiedlichen Kronenform wurde eine höhere Selbstbeschattung der Eichenkrone im Vergleich zu den Buchen ermittelt (Abb. 30-32). Blattwolken in beiden Buchenkronen wiesen auffällige Übereinstimmungen hinsichtlich ihrer Wuchsrichtung auf (Abb. 35, 37, 39 - 41), die sich aufgrund des höhenabhängigen Blattwolkenwinkels (Abb. 33) und der Stellung zur Kronenoberfläche (Abb. 41) auf die Lichtverteilung in der Krone auswirken. Die Blattflächendichte von Blattwolken war weitgehend unabhängig von 8 untersuchten Strukturparametern (Abb. 55). Die mittels Fish-eye-Fotografie erstellten Lichtprofile von Buchenkronen zeigten Abweichungen vom Lambert-Beer’schen Gesetz (Abb. 58), die sich aus der von Blattstellungswinkeln verursachten Variabilität des Extinktionskoeffizienten und der inhomogenen Blattflächendichtenverteilung erklären lassen. Es konnte eine höhenabhängige Variation der