Combining empirical models and the process-based model 3-PG to predict Eucalyptus nitens plantations growth in Spain

1 COMBINING EMPIRICAL MODELS AND THE PROCESS-BASED MODEL 3-PG 1 TO PREDICT Eucalyptus nitens PLANTATIONS GROWTH IN SPAIN 2 3 César Pérez-Cruzado1, Fernando Muñoz-Sáez2, Fernando Basurco3, Guillermo Riesco1, 4 Roque Rodríguez-Soalleiro1* 5 1 Unit of Sustainable Forest Management, University of Santiago, E-27002 Lugo, Spain 6 Tel.: (+34) 982 285900 Ext 23120, Fax: (+34) 982 285926 7 2 University de Concepción, Chile 8 3 CIT Ence, Lourizán, 36153-Pontevedra, Spain 9 *e-mail: [email protected]. Corresponding author 10 11 Abstract 12 Empirical, statistically based models were used to describe the growth and 13 development of Eucalyptus nitens plantations for a range of site productivities and the 14 standard biomass and pulp silvicultural regime currently applied in northern Spain. The 15 results obtained, along with data gathered from a network of 68 plots, 48 trees felled for 16 biomass estimations and 73 trees sampled for foliar area estimation were used to parameterize 17 the 3-PG model (Landsberg and Waring, 1997) for this species in Northern Spain. Most 18 parameters associated with allometric relationships and partitioning (i.e. bark and branch 19 fraction, basic density, age modifier and mortality) were derived from local data, and the 20 remaining parameters were obtained from published studies on E. nitens or default values 21 previously used for E. globulus. The parameterized model was validated with data from three 22 trials measured from age 3 years until age 8-14 years, and performed better than the empirical 23 model in terms of total stand under bark volume, mean diameter at breast height, basal area 24 and foliar biomass. The process-based model was then used to forecast changes in plantations 25 *Manuscript Click here to download Manuscript: Prez Cruzado et al, 2011.doc Click here to view linked References 2 subjected to a clearwood regime, initializing the model at age 3 years, considering 3 prunings, 1 2 thinnings and lengthening the rotation to 18 years. This integrated regime was able to 2 provide biomass for bioenergy, pulp or fibreboard wood and also solid wood, with thinning 3 operations assisting the financial viability, and was a potentially good alternative for 4 productive sites. 5 KEYWORDS: process models, silviculture, clearwood, biomass, Eucalyptus nitens. 6 1. Introduction 7 Eucalyptus nitens is one of the most promising hardwoods for plantations in cool 8 temperate regions of the world. The total planted area has been estimated at 340000 ha, 9 distributed throughout Australia (Tasmania and Victoria), Chile, New Zealand, South Africa 10 and Spain (Muñoz et al., 2005). In Spain the plantations have spread out to the north, and now 11 cover approximately 30000 ha in the regions of Galicia and Cantabria. As a frost resistant 12 species, the species was first planted in 1992 in frost prone areas, above 500 m, but the 13 promising growth results and its relatively low susceptibility to damage by Gonipterus and 14 Mycosphaerella soon led to establishment of plantations at lower altitudes, where E. globulus 15 was previously used (Pérez et al., 2006; Pérez-Cruzado and Rodríguez-Soalleiro, 2011). The 16 Barrington Tops provenance was used between 1992 and 1996, and the McAlister provenance 17 thereafter (Astorga, pers. comm.). 18 Plantations are managed by intensive regimes, including mechanical soil preparation, 19 fertilization at establishment and planting of 1000-1500 containerized seedlings per ha. Brush 20 weeding is applied frequently before canopy closure, and clearcutting is carried out at age 10 21 to 12 years. The timber is commonly used as a raw material in the manufacturing of medium 22 density fibreboard (Pérez-Cruzado, 2009). Nevertheless, Spanish pulp factories are beginning 23 to use the timber, although the basic density of the wood is lower than that in E. globulus 24 (Pérez et al., 2006). Logging residues and small diameter logs are also used for energy 25 3 purposes, through the use of bundlers and further chipping once the bundles are air dried. A 1 poor coppicing ability has been reported for the species (Little and Gardner, 2003), although 2 good examples of resprouting have been found in Northern Spain. Declining pulp prices 3 worldwide and the need for product diversification are leading to the increased popularity of 4 plantations of this species managed for solid wood products (Medhurst et al., 2001). There is 5 an increasing interest in Spain in silvicultural regimes aimed at obtaining clearwood through 6 pruning and thinning, and lengthening the rotation age to 18 to 25 years (Nutto and Touza-7 Vázquez, 2004). 8 Plantation yield prediction has been dominated by empirical modelling, but process-9 based models of forest growth and production have increasingly become part of the forest 10 management decision making process. These models have been used to study different 11 situations, including the response to management of established plantations, in terms of yield 12 prediction (Battaglia et al., 2007). The site index approach defines invariant growth 13 trajectories for top height, an assumption known from practical experience to be false. The SI 14 concept is in fact a logically circular concept, which limits the flexibility of the empirical 15 models and their capacity to simulate the results of environmental stresses or departures from 16 the climatic conditions during the periods of plot measurement (Fontes et al., 2006). These 17 problems can be overcome by the use of process-based models, which provide estimates that 18 depend directly on site conditions. 19 The 3-PG model of forest growth (Landsberg and Waring, 1997) is the most used 20 process-based forest model (Landsberg et al., 2003; Almeida et al., 2004; Sands and 21 Landsberg, 2002; Battaglia et al., 2007). It has been parameterized for several species of 22 eucalypts and conifers and used for research and teaching purposes, as well as in the 23 management systems of forest companies. A user-friendly version is available (Sands, 2002) 24 and the information required to run the model is readily obtained from national 25 4 meteorological agencies or site assessment studies. A study has already applied the Sands and 1 Landsberg (2002) parameterization of 3-PG for E. globulus to test the performance of this 2 model in Northern Spain (Rodríguez-Suárez et al., 2010). 3 The aims of the present study were: i) to parameterize the 3-PG model for Eucalyptus 4 nitens plantations in the site conditions of northern Spain, ii) to compare 3-PG with an 5 empirical based model for current silvicultural regimes applied in three trials, measured at age 6 3 - 8 years (one trial), and 3 - 14 years (two trials), and iii) to apply the 3-PG to an alternative 7 silvicultural regime aimed at production of clear wood, for two representative sites of high 8 and low productivity in northern Spain, based on current knowledge of the species response to 9 pruning and thinning treatments. This regime will be evaluated in terms of growth and 10 production. 11 2. Materials and methods 12 2.1. Empirical models and productivity levels 13 Empirical individual-tree and stand models are available for E. nitens in northern 14 Spain (Pérez-Cruzado, 2009). These models have been obtained for the observed range of site 15 productivity and silvicultural treatments applied in the region, which in most cases involves 16 maximizing chip and biomass production. The structure of the empirical models is based on a 17 site index system H2=f1(H1, t1, t2), relating top height (H) to age (t), where H2=SI (site index) 18 for t2=reference age, which has been chosen as 6 years in Spain (Fig. 1). This system was 19 used in the present study to classify the productivity levels of each permanent trial (PT) used 20 to compare the empirical model and 3-PG and the temporary plots (TP) used to propose an 21 alternative silvicultural regime. 22 A second equation in the empirical models is a static model to predict quadratic mean 23 diameter (dg). Because neither the TP nor the PT have been thinned, dg may be directly related 24 to stand density (N) and top height (dg=f2(H, N)). This equation is based on the relationship 25 5 between average tree size, density and a productivity indicator. The change in tree density (N) 1 was thus only dependent on mortality, and stem reduction closely followed a modified Candy 2 (1997) mortality model (N2=f3(N1, t1, t2, SI). 3 These three equations enable calculation of the changes in three stand state variables 4 (H, basal area, G and N), from which several derived variables can be obtained, in particular 5 the stand biomass components: wood biomass (Ww), bark biomass (Wb), branches biomass 6 (Wbr) and foliage biomass (Wf). These functions were fitted simultaneously to produce the 7 system of equations shown in Table 1. The under-bark volume was obtained from the wood 8 biomass, considering an average value of basic density. The equations were used to initialize 9 the process-based model at age 3 years and to calculate stand production in terms of wood or 10 biomass. 11 2.2. Experimental data for calibrating 3-PG 12 A simple process-based model (3-PG) was used to predict the stand evolution as an 13 alternative to empirical models (Landsberg and Waring, 1997). 3-PG is driven by intercepted 14 radiation, with radiation-use efficiency for carbon fixation affected by temperature, vapour 15 pressure deficit, available soil water, stand age and site fertility (Sands and Landsberg, 2002). 16 The model calculates monthly net carbon fixation, stand growth, biomass (considering three 17 compartments, foliage, stems and branches) and water use from monthly values for solar 18 radiation, modified by several soil, climate and management factors. The 3-PG version used 19 in this study was 3-PGpjs2.5, which is implemented as a Microsoft Excel spreadsheet with a 20 user-interface that facilitates data entry and interpretation of results (Sands, 2002). 21 The use of 3-PG required prior parameterization for E. nitens, which was performed 22 with different data sets: 23 i) a sample of 48 trees covering the full range of diameter and height classes existing 24 in Spanish plantations was felled and the following variables were recorded: diameter at 25 6 breast height (cm), tree age, stem biomass (considering wood, bark and branches together) 1 and foliage biomass. The trees were felled and cut into 0.5 m logs until a thin-end diameter of 2 7 cm. Wood density was calculated from the wood dry biomass and the volume calculated by 3 applying the Smalian equation to each log. Basic density data were available for these 48 trees 4 and an additional sample of 14 trees. 5 ii) a set of 68 plots in which diameter and height of all trees were recorded, and stand 6 variables, including site index, were calculated. The plots, in which the trees were aged 1 to 7 18 years, were either circular, of radius 10 m, or square plots of 20x20 m. It was possible to 8 apply the empirical model to them to calculate the predicted annual increment and relate this 9 value to the maximum volume increment for the same site index, thus evaluating the age 10 modifier of 3-PG. The plots were also used to adapt the mortality model, and to evaluate the 11 fraction of mean single-tree biomass lost per dead tree, assuming no foliage biomass is lost 12 because of mortality. 13 iii) the average value of the specific leaf area for young leaves was determined from a 14 set of 73 trees in which foliar samples were obtained in a pruning trial for the species. The 15 trees were pruned to 2-4 m, and a composite sample of fresh leaves was weighed, scanned and 16 oven-dried to constant weight, for calculation of the dry weight. The leaf area was calculated 17 after digitalization of the scanned images. A single composite value was used per tree. 18 The models required to obtain the 3-PG parameter values were fitted with the NLIN 19 procedure of SAS (SAS Institute, 2004). 20 No attempts were made to evaluate the allocation of net primary production (NPP) to 21 roots, but biomass allocation to foliage (ηF) and stems (ηS) was determined by considering the 22 derivatives of the allometric functions for mean single-tree foliage and stem biomass and 23 considering the ratio pFS= ηF/ηS to be an allometric function of diameter at breast height 24 (Sands and Landsberg, 2002). A detailed analysis of allometric relations and their 25 7 applicability to different ages and sites is available for Tasmania (Medhurst et al., 1999), and 1 was considered for comparisons. A temperature modifier of quantum efficiency was used, 2 considering the minimum, optimum and maximum temperatures for net photosynthetic 3 production. Rodríguez et al. (2009) applied values of 2, 20 and 32ºC for this species in Chile 4 and Battaglia et al. (1996; 1998) reported the higher ability of E. nitens than of E. globulus to 5 maintain high photosynthetic rates at low temperatures. Although Battaglia et al. (1996) 6 showed a platykurtic response of net photosynthesis to temperature for E. nitens, it seems 7 reasonable to consider a lower optimum temperature than the value applied to parameterize 3-8 PG to E. globulus (16ºC, Sands and Landsberg, 2002; Fontes et al., 2006). 9 Litterfall should vary in response to local conditions, and so the monthly litterfall rates 10 γF should ideally be site dependent (Sands and Landsberg, 2002), but as no information was 11 available on litterfall, the default value for very young stands was applied, and the maximum 12 litter fall rate was derived from the study of Moroni and Smethurst (2003). The default values 13 used by Sands and Landsberg (2002) for parameters related to stomatal conductance were 14 considered, applying a sensitivity analysis to the maximum canopy conductance, because 15 stomatal conductance and growth are more sensitive to water stress in E. nitens than E. 16 globulus (White et al., 1999). 17 Several sources of information were used to determine other parameters, but especially 18 the references related to specific studies in Tasmania. Default values for E. globulus were 19 considered if no more specific information was available (Sands and Landsberg, 2002), and 20 affected mostly to parameters reported to have a low sensitivity for volume or leaf area 21 estimations (Esprey et al, 2004). 22 2.3. Site data 23 To test whether the parameterization proposed can accurately predict growth, three PT 24 of the species with continuous measurements were employed. In addition, two TP 25 8 representative of high and low levels of productivity for simulating clear wood regimes were 1 identified and the soil and climatic data required to run 3-PG were recorded. 2 Climatic data was obtained from series of the last 30 years (www.meteogalicia.es), 3 and solar radiation or average number of frost days were derived from the same weather 4 stations (but for 5-year series). Monthly average values were used as input data in the model 5 (Table 2). All five plots were in the latitude range 42.6 to 43.4ºN. The three PT were 6 established in June, 1992, with a spacing of 1283 trees per ha, and all diameter and heights 7 were measured annually till age 6 years, and then at age 8 (all trials) and 14 (two trials). 8 Wood volumes inside bark were calculated from single tree equations, considering 3 years as 9 the initializing age. The values of site index and volumes were the average values for 7 to 9 10 rectangular plots of 420 to 520 m2 per trial. The three trials were similar in terms of summer 11 temperatures, although Lalín was the most elevated (700 m) and more exposed to frost. There 12 were clear differences in terms of soil (see Table 2) and parent material: quartziferous schists 13 at Lalín, granites at Antas and slate at Xermade. 14 The two TP are representative of the area where most commercial plantations are 15 located, and the sites were rather similar in terms of summer precipitation, annual 16 precipitation and elevation (600 m), although total annual radiation was 38.4% higher in the 17 more productive site. There were also fewer frost days for Guitiriz. The clearest differences 18 were in soil depth and, correspondingly, the maximum available soil water. The texture of 19 both soils was similar, as was the parent material (schists). 20 Available soil water capacity was calculated from soil depth, soil organic matter and 21 soil texture, using the model proposed by Domingo et al. (2006). The fertility rate of 3-PG, 22 which varies between 0 and 1, was evaluated according to the information on parent material, 23 soil depth, soil pH, C:N ratio of organic matter, soil nutrient concentrations and texture, 24 considering reference values for the optimum soil conditions for growth in the area (Table 3). 25 9 The forests soils in the region are highly acidic and usually shallow, with fertility directly 1 related to the organic mater content and its mineralization rate or to the Al content (Alvarez et 2 al., 2002). Foliar levels of P, Ca and Mg are usually low in E. globulus planted in shallow and 3 stony soils (Merino et al., 2005). We used the approach of Almeida et al. (2010), which takes 4 into account the principal factors that limit nutrient availability (equation 1): 5 [1] TLMLOLWLFLFR 1.02.01.02.04.0  6 Where FL is fertility limitation, WL is water limitation, O oxygen, M management and 7 T topography. The limitation (L) may be null (1.0), slight (0.8), moderate (0.6), strong (0.4) 8 and very strong (0.2). A complete soil analysis including available content of nutrients and 9 soil expert assessment was used to establish the initial FR values for the three PT and the two 10 TP. In all plots, fertilizer was initially added to the planting hole, and had a short-lived effect. 11 During calibration, FR was allowed to vary within ±0.1 units from the field estimation values 12 (Fontes et al., 2006). 13 2.4. Silvicultural regimes and model evaluation 14 Details of the silvicultural alternatives were obtained by a literature review of pruning 15 and thinning experiments in the species (Medhurst et al., 2001; Gerrand, 1997), as well as 16 from the result of local trials. The first regime is usually applied to produce chipwood and 17 bioenergy, i.e., as in the plots inventoried, whereas the alternative regime is used to produce 18 mainly solid wood at the end of the rotation. 19 1. Fiber alternative, with no thinning or pruning. This regime was used for the three 20 PT to validate the 3-PG calibration, tune the FR and evaluate the differences between the 21 empirical and the process-based model. The observed data were used to initialize both the 22 empirical model and 3-PG at age 3 years, and the models were then run until the age of the 23 last measurement. The accuracy of the 3-PG model in relation to the empirical model was 24 16 Cantabria. The allometry of E. nitens has been studied, particularly in Tasmania (Medhurst et 1 al., 1999; Pinkard and Battaglia, 2001), often with the goal of obtaining useful relationships to 2 predict leaf area. Previous studies on E. globulus show that biomass partitioning and 3 allometry are the main drivers of the poor performance of 3-PG when applied with the 4 original Australian parameters and so a specific calibration for Portugal was necessary 5 (Fontes et al., 2006). The sensitivity analysis carried out in the present study shows the 6 dramatic effect of the power parameter nS on basal area and breast height diameter 7 predictions. 8 The average value of SLA0 in Spain is higher than reported values for healthy leaves of 9 E. nitens seedlings in Tasmania (8.3 m2 kg-1, Pinkard et al., 2006). A decreasing trend has 10 been reported, with values of 4.75 to 4.93 in 7-year-old stands (Pinkard and Neilsen, 2003) 11 and the value used in this study, calculated as the weighted average of the values observed by 12 Medhurst and Beadle (2001) in 8-year-old stands. The equation proposed in the present study 13 for the changes in basic density with age provide lower values than those observed for 9-year-14 old stands in Tasmania (0.49 Mg m-3, Raymond and Muneri, 2001). 15 Nutrition is clearly an important variable for forest growth, and even if a numerical 16 procedure was applied to calculate FR (Almeida et al., 2010), it seems reasonable to consider 17 FR as a tuneable parameter (Fontes et al., 2006). Although some studies have considered the 18 FR to be correlated with SI (Dye et al., 2004), we assigned the values exclusively according 19 to soil expert knowledge, by comparison with the optimum values, which are known to 20 provide growth conditions not limited by nutrition. 21 The maximum photosynthetic rate αCx=0.07 mol C (mol quanta)-1 considered in this 22 study is the maximum value proposed by Landsberg et al. (2003) as realistic and applicable to 23 fast growing eucalypts species. The sensitivity analysis shows important changes in the 24 predictions derived from modifications of this parameter. This value is consistent with the 25 17 parameterization for E. globulus (Sands and Landsberg, 2002; Fontes et al., 2006) and the 1 higher rate for net assimilation for E. nitens reported by Battaglia et al. (1996) in relation to E. 2 globulus. 3 4.2. Predictions of E. nitens growth after thinning 4 The 3-PG has been already applied to predict the development of thinned stands and it 5 has been shown that, under usual thinning regimes, a variety of thinning intensities can be 6 adequately described by a simple multiplicative model relating the proportion of volume and 7 foliage mass removed to the corresponding proportion of stem number (Landsberg et al., 8 2005). This provides the necessary information about the reduction in all state variables at 9 each thinning to run the model between thinning events, as carried out in this study. 10 Even so, there may be some limitations derived from the dramatic change in leaf area 11 resulting from a high intensity of thinning. The discontinuous canopy resulting from thinning 12 affects the radiation available to individual trees and may alter the structure of tree crowns 13 and the stand as a whole (Medhurst and Beadle, 2001). These authors found that the relative 14 rate of increase in LAI was much greater in stands of lower stocking (more intensively 15 thinned), suggesting a higher proportion of assimilated carbon being allocated to canopy 16 development in these widely spaced stands. Moreover, the Beer–Lambert law for estimating 17 light attenuation is more appropriate for closed canopies, and heavily thinned stands are 18 unlikely to return to full canopy closure (Medhurst et al., 2001). 19 The growth response to thinning has been quantified for E. nitens in Tasmania 20 (Gerrand et al., 1997) and also in Chile (Muñoz et al., 2005). The latter authors found the 21 volume yield at 14 years in plots thinned to 400 stems per ha was 56-75% of that in non 22 thinned stands. On the other hand, for thinned plots at age 18 years and productivity similar to 23 the SI 17 m, the Chilean growth simulator EUCASIM (2010) estimated 72-85% of the yield 24 of unthinned plots. This means that Eucalyptus nitens has a good ability to recover growth 25 18 after thinning, even for intense fellings (Gerrand et al., 1997), and the predictions obtained by 1 applying 3-PG are probably underestimates. The response to thinning may be attributed to the 2 effects of increase in SLA after thinning, a reduction in the attenuation of light in the crown 3 and increases in the photosynthetic capacity of old and mature foliage in the lower and middle 4 crown zones (Medhurst and Beadle, 2005). This suggests the need to refine some of the 3-PG 5 parameters (k, SLA1, αCx) to apply the model after thinning, which was not possible with the 6 information available in the present study. 7 Another limitation of the 3-PG model is that it produces the mean stand diameter B as 8 output, although it is the stem size distribution that is the most important feature in the 9 commercial value of timber. Landsberg et al. (2005) fitted regressions relating the parameters 10 of the Weibull distribution to B and obtained results that were good enough to provide 11 preliminary indications of likely product quality. This may be a further step in improving the 12 predictions made in the present study. 13 The present study provides a set of values for the parameters to include in 3-PG in 14 order to predict E. nitens stand growth and development. The model can be used to simulate 15 the stand evolution for various silvicultural systems or using observed climate data instead of 16 the average climate values used in this study. 17 The results obtained in the simulations indicate that the silvicultural regimes described 18 are likely to produce clear wood, particularly in highly productive areas. The existence of a 19 market for biomass makes the thinning to waste operations proposed in other studies 20 unnecessary (Candy, 1997), showing the possibility of integrating biomass and solid wood 21 production in the same stand. Medhurst et al. (2001) recommended a final density in the range 22 of 200–300 trees per ha, which would improve the growth during a rotation of 20 to 25 years, 23 thus largely preventing under-utilization of site resources. Washusen et al. (2009) found that 24 19 trees of equivalent size grown under different competitive regimes did not differ substantially 1 in their performance in sawmill processing. 2 5. Conclusions 3 The parameterization of the process-based model 3-PG proposed for E. nitens 4 plantations in Northern Spain provided accurate and unbiased predictions of the inside bark 5 volume for three permanent trials of the species. The predictive ability for mean diameter, 6 basal area and foliar biomass was better than that provided by the empirical model available. 7 An alternative silvicultural regime aiming to obtain clearwood as the main product, 8 integrating the production of pulpwood and biomass for bioenergy was simulated using the 9 model 3-PG, which can be used to quantify the timber and biomass yield for this regime and 10 for the conventional pulpwood regime currently applied. 11 Acknowledgements 12 Funding for this research was provided by the Spanish Ministry of Science and 13 Technology (AGL2010-22308-C02-01). Fernando Muñoz was supported by a research grant 14 from the Chilean CONYCIT for a stay at the University of Santiago (Spain). 15 References 16 Almeida, A.C., Landsberg, J.J., Sands, P.J., 2004. Parameterisation of 3-PG model for fast-17 growing Eucalyptus grandis plantations. For. Ecol. 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Quantifying the 5 effect of cumulative water stress on stomatal conductance of Eucalyptus globulus and E. 6 nitens: a phenomenological approach. Aust. J. Plant Physiol. 26, 17-27. 7 8 25 Tables 1 Table 1. Equations fitted to estimate aboveground stand biomass components. Ww is wood 2 biomass Wb is bark biomass, Wbr is branch biomass and Wf is foliage biomass (oven dry, kg 3 ha-1). Sub index i in each parameter refers to the corresponding component in each file. 4 5 Model Parameter estimates Adj. R2 b1i b2i b3i b4i 41 31 21 011 b b b wNHdgbW  11 10-6 2.2067 0.8808 0.9631 0.9984 42 32 22 012 b b b bNHdgbW  13 10-6 2.3318 0.0463 1.0031 0.9993 43 33 23 013 b b b br NHdgbW  18 10-6 2.3522 0.0914 0.9648 0.9909 44 34 24 014 b b b fNHdgbW  5.03 10-6 2.3607 0.0510 1.0035 0.9992 6 7 Table 2. Climate data for the sites used to parameterize and validate the 3-PG model. PT are 8 permanent plots. TP are temporary plots. Tav is the average temperature for the three summer 9 and three winter months, S-W radiation is total annual short wave incoming radiation, MASW 10 is maximum available soil water and FR is the fertility rate. 11 12 Site Treatment type Site index (m) Age measurement (years) Tav summer (ºC) Tav winter (ºC) Annual frost (days) Precipitation (mm) S-W radiation MJm2year-1 Soil depth (cm) MASW FR Xermade PT 14 3, 4, 5, 6, 8, 14 16 6.3 14 2100 4480 50 145 0.5 Antas PT 12 3, 4, 5, 6, 8, 14 17 6.2 20 1180 4770 85 170 0.5 Lalín PT 10 3, 4, 5, 6, 8 16.2 5.5 64 1360 4770 15 30 0.15 Guitiriz TP 17 7 17.8 6.2 16 1090 4460 120 300 0.7 Begonte TP 11 14 16.5 6.1 21 1110 3220 30 50 0.3 13 14 Table 3. Soil parameters for the upper 30 cm layer used to propose a fertility rate for the three 15 permanent trials of Eucalyptus nitens. FL is fertility limitation, WL is water limitation, O is 16 oxygen, M is management and T is topography. MASW is maximum available soil water 17 18 Soil property Optimum Xermade Antas Lalín Guitiriz Begonte pH (water) 5.5 4.4 4.3 4.4 5.1 4.9 OM (%) 10 10 9.8 5.6 4.6 7.9 C/N 10 13.5 11.4 15.4 10.2 12.5 N (%) 0.5 0.43 0.5 0.21 0.26 0.38 P (kg ha-1) 200 13 36 9 36 85 K (kg ha-1) 400 230 450 170 480 89 Mg (kg ha-1) 300 76 324 164 247 28 Ca (kg ha-1) 650 279 830 100 357 53 Soil depth (cm) 100 50 85 20 80 40 FL 1 0.42 0.68 0.33 Sand (%) 60 79 80 72 62 57 0 50 100 150 200 250 300 350 400 450 345678910 11 12 13 14 Age (years) Volume inside bark (m3ha-1) Observed Empirical model 3-PG PT: Xermade 0 5 10 15 20 25 3 4 5 6 7 8 9 10 11 12 13 14 Age (years) Mean diameter (cm) Observed Empirical model 3-PG PT: Xermade 0 10 20 30 40 50 60 3 4 5 6 7 8 9 10 11 12 13 14 Age (years) Basal area (m2ha -1) Observed Empirical model 3-PG PT: Xermade 0 2 4 6 8 10 12 3 4 5 6 7 8 9 10 11 12 13 14 Age (years) Foliar biomass (Mgha-1) Observed Empirical model 3-PG PT: Xermade Figure 7. Observed changes in the inside bark volume, mean diameter, basal area and foliar biomass in the permanent trial Xermade in relation to the predictions of 3-PG and the empirically based model.. 0 50 100 150 200 250 300 350 400 3 4 5 6 7 8 9 10 11 12 13 14 Age (years) Volume inside bark (m3ha-1) Observed Empirical model 3-PG PT: Antas 0 5 10 15 20 25 3 4 5 6 7 8 9 10 11 12 13 14 Age (years) Mean diameter (cm) Observed Empirical model 3-PG PT: Antas 0 5 10 15 20 25 30 35 40 45 50 3 4 5 6 7 8 9 10 11 12 13 14 Age (years) Basal area (m2ha -1) Observed Empirical model 3-PG PT: Antas 0 1 2 3 4 5 6 7 8 9 345678910 11 12 13 14 Age (years) Foliar biomass (Mgha-1) Observed Empirical model 3-PG PT: Antas Figure 8. Observed changes in the inside bark volume, mean diameter, basal area and foliar biomass in the permanent trial Antas in relation to the predictions of 3-PG and the empirically based model. ns -100 -75 -50 -25 0 25 50 75 100 % aS -40 -30 -20 -10 0 10 20 30 40 % ns -100 0 100 200 300 % ns -100 0 100 200 300 % Vub B G Wf g cx -40 -30 -20 -10 0 10 20 30 40 % +20% +10% -10% -20% ns -100 -75 -50 -25 0 25 50 75 100 % aS -40 -30 -20 -10 0 10 20 30 40 % ns -100 0 100 200 300 % ns -100 0 100 200 300 % Vub B G Wf g cx -40 -30 -20 -10 0 10 20 30 40 % +20% +10% -10% -20% aS -40 -30 -20 -10 0 10 20 30 40 % ns -100 0 100 200 300 % ns -100 0 100 200 300 % Vub B G Wf g cx -40 -30 -20 -10 0 10 20 30 40 % +20% +10% -10% -20% ηRn -40 -30 -20 -10 0 10 20 30 40 % αCx -40 -20 0 20 40 % Vub B G Wf g cx -40 -30 -20 -10 0 10 20 30 40 % +20% +10% -10% -20% ηRn -40 -30 -20 -10 0 10 20 30 40 % αCx -40 -20 0 20 40 % Vub B G Wf Vub B G Wf g cx -40 -30 -20 -10 0 10 20 30 40 % +20% +10% -10% -20% fN0 -40 -30 -20 -10 0 10 20 30 40 % Vub B G Wf gCx -40 -30 -20 -10 0 10 20 30 40 % g cx -40 -30 -20 -10 0 10 20 30 40 % +20% +10% -10% -20% fN0 -40 -30 -20 -10 0 10 20 30 40 % Vub B G Wf Vub B G Wf gCx -40 -30 -20 -10 0 10 20 30 40 % g cx -40 -30 -20 -10 0 10 20 30 40 % +20% +10% -10% -20% Figure 9. Estimated sensitivity of selected 3-PG outputs to the parameters: stem constant (aS), stem power (nS), maximum canopy quantum efficiency (αCx) minimum biomass partitioning to roots (ηRn), minimum site nutrition growth modifier (fN0) and maximum canopy conductance (gCx). The bars show the effects of +20, +10, -10 and -20% variation in each parameter in inside bark volume (Vub), breast height diameter (B), basal area (G) and foliage biomass (Wf). . 0 50 100 150 200 250 300 350 400 450 0 2 4 6 8 10 12 14 16 18 Age (years) Volume under bark (m3 ha-1) 3-PG solid wood Guitiriz 3-PG solid wood Begonte Observed Begonte Observed Guitiriz 3-PG No thinning Guitiriz 3-PG No thinning Begonte Figure 10. Changes in the inside bark simulated with 3-PG for two productivity levels.