A spatial valuation approach of timber provisioning in Finnish forests

Master thesis - Author's personal copy Author: Valentin Ştefan Warsaw University of Life Sciences - SGGW Faculty of Forestry Eberswalde University for Sustainable Development - HNEE University of Applied Sciences Faculty of Forest and Environment Valentin Ştefan SGGW Student ID 164687 HNEE Student ID 12208281 A spatial valuation approach of timber provisioning in Finnish forests Master thesis Forest Information Technology Thesis supervised by: Prof. Dr. Jan-Peter Mund Faculty of Forest and Environment University for Sustainable Development (HNEE), Eberswalde Prof. Dr. Christian Ammer Faculty of Forest Sciences and Forest Ecology University of Göttingen, Göttingen Warsaw, Eberswalde, 2015 Master thesis - Author's personal copy Author: Valentin Ştefan Master thesis - Author's personal copy Author: Valentin Ştefan iii Oświadczenie promotora pracy Oświadczam, że niniejsza praca została przygotowana pod moim kierunkiem i stwierdzam, że spełnia ona warunki do przedstawienia jej w postępowaniu o nadanie tytułu zawodowego. Tutor’s declaration I declare, that the diploma thesis was prepared under my supervision and I state it fulfils the conditions for present it in the professional title proceedings. Erklärung des Betreuers Ich erkläre, dass die vorliegende Arbeit durch mich betreut wurde und die Voraussetzungen für die Durchführung eines Master-Verfahrens erfüllt. Data ................................... Podpis promotora pracy ...................................... Date Tutor’s signature Datum Unterschrift des Betreuers Master thesis - Author's personal copy Author: Valentin Ştefan iv Oświadczenie autora pracy Świadom odpowiedzialności prawnej oświadczam, że niniejsza praca dyplomowa została napisana przeze mnie samodzielnie i nie zawiera treści uzyskanych w sposób niezgodny z obowiązującymi przepisami. Oświadczam również, że przedstawiona praca nie była wcześniej przedmiotem procedur związanych z uzyskaniem tytułu zawodowego w wyższej uczelni. Oświadczam ponadto, że niniejsza wersja pracy jest identyczna z załączoną wersją elektroniczną. The author’s declaration Being aware of legal liability I declare, that the Master thesis was written by myself and it does not include any contents obtained in the illegal way. I also declare that the presented thesis was not a subject of any university professional title’s proceedings previously. In addition I declare, that the presented version of the thesis is identical with the electronic version included. Erklärung des Verfassers Ich versichere, dass die vorliegende Arbeit durch mich angefertigt wurde und kein unrechtmäßig erworbenes Material enthält. Über die Konsequenzen einer Verletzung dieses Grundsatzes bin ich mir bewusst. Ich versichere weiterhin, dass die vorliegende Arbeit zuvor keiner anderen Universität zur Erlangung eines wissenschaftlichen Grades vorgelegt wurde. Zusätzlich erkläre ich, dass die schriftliche Fassung dieser Arbeit mit der beigefügten digitalen Fassung übereinstimmt. Data .................................. Podpis autora pracy Valentin Ştefan Date The author’s signature Datum Unterschrift des Verfassers Master thesis - Author's personal copy Author: Valentin Ştefan v Streszczenie Oprócz stworzenia mapy ekosystemów oraz oszacowania ich stanu oraz ich usług do roku 2014 Strategia Bioróżnorodności EU2020 również zobowiązala kraje członkowskie do określenia ekonomicznej wartości ich usług do 2020 roku. Ekosystemy dają różne materialne i nie materialne korzyści dla ludzi. Niestety te często bardzo ważne korzyści są często ignorowane ponieważ nie można ich wartości zmierzyć w pieniądzu i nie są postrzegane jako towar. Drewno wszelako jest dobrem namacalnym oraz może byc nabyte na rynku za określoną cenę. W fińskich lasach przeprowadzono studium przypadku w celu wykazania potrzeby wyceny przestrzennej w zaopatrzeniu w drewno. Podejście bazowane na GIS, używajace dokładnej inwentaryzacji lasów w celu oszacowania aktualnej wartości fińskich lasów i równego ekwiwalentu rocznego oraz umieszczenia ich na mapie w rozdzielczosci przestrzennej 100 metrów na 100 metrów. Wzrost lasów był szacowany na 3 sposoby: modelowanie regionalnej wydajności, użycie inwentaryzacyjnej bazy danych EFISCEN oraz symulatora MOTTI. Używajac domyślnych wytycznych MOTTI wybrano 4 główne grupy gatunków do oceny spośród 16 lokalizacji. Przy stopie procentowej w wysokosci 1%, aktualna wartość netto lasu sosnowego sięga maksymalnie 8,920 za hektar z roczną równowartością 243 € za ha za rok. Za las świerkowy maksymalna wartość to 12,355 € za hektar z roczną równowartością 293 € za hektar za rok. Brzoza oraz inne szerokolistne gatunki sa mniej dochodowe. Przy stopie procentowej w wysokości 5% większość lasów była niedochodowa oprócz niektórych lasów sosnowych i świerkowych rosnących na żyznych minerałowych południowych glebach. To studium nie sugureje, że lasy mniej dochodowe lub niedochodowe nie są cenne. Rezultaty sugerują, że wybór obu metod szacowania wydajności i scenariuszy zarządzania może mieć wyraźny wpływ na rentowność, szczególnie na terenach z obniżoną stopą procentową oraz na żyznych glebach. Słowa kluczowe: przestrzenna wycena wartości, aktualna wartość netto, równy ekwiwalent roczny, mapa rentowności lasów, usługi ekosystemów, modelowanie wielkości wzrostu, funkcje dochodu. Master thesis - Author's personal copy Author: Valentin Ştefan vi Abstract The EU 2020 Biodiversity Strategy, in addition to mapping and assessing the state of ecosystems and their services by 2014, also required the Member States to assess the economic value of such services by 2020. Forest ecosystems provide several tangible and intangible benefits to humankind. Unfortunately, such vital benefits are usually ignored by policy makers since they lack monetary value and are not perceived as commodities. However, wood is usually a tangible good that can be bought in markets for a certain price. A case study was conducted across Finnish forests in order to address the need of spatially valuating timber provisioning. A GIS based approach making use of detailed national forest inventory data was explored for estimating and mapping the net present values of Finnish forests and their equal annual equivalent at 100×100 m spatial resolution. Forest growth was approximated in three ways: with yield functions, using the EFISCEN inventory database and the MOTTI forest stands simulator. Given the default MOTTI management guidelines, four main groups of species within sixteen different site conditions were considered for appraisal. At a discount rate of one per cent, the net present value of pine forest stands reached a maximum of 8,920 € ha-1 with an annual equivalent of 243 € ha-1year-1. For the spruce stands, the maximum net present value was 12,355 € ha-1 with an annual equivalent of 293 € ha-1year-1. Birch and other broad-leaved species were less profitable. At a discount rate of five per cent, most of the forests were unprofitable except for certain pine and spruce stands on fertile southern mineral soils. However, this study does not suggest that less profitable or unprofitable forest stands are not valuable. The results indicate that the choice of both the yield estimation method and the management scenario can significantly impact profitability predictions, particularly at low discount rates and on fertile sites. Key words: timber spatial valuation, net present value, equal annual equivalent, forest profitability map, ecosystem services, forest growth modelling, yield functions Master thesis - Author's personal copy Author: Valentin Ştefan vii Zusammenfassung Die Biodiversitätsstrategie der Europäischen Union bis 2020 sieht vor, dass alle EUMitgliedsstaaten bis 2014 den Zustand ihrer Ökosysteme und die von ihnen erbrachten Dienstleistungen kartieren und beurteilen sollen. Darüber hinaus soll bis 2020 der ökonomische Wert dieser Dienstleitungen geschätzt werden. Waldökosysteme sind für Menschen sowohl materiell als auch immateriell von Nutzen. Leider werden wesentliche Funktionen von Entscheidungsträgern meist ignoriert, wenn sich ihr Wert nicht finanziell beziffern lässt und sie nicht als Güter wahrgenommen werden. Demgegenüber stellt Holz ein materielles Gut dar, das auf Märkten zu einem gewissen Preis gehandelt werden kann. In finnischen Wäldern wurde eine Fallstudie zum Zwecke der räumlichen Bewertung der Holzbestände durchgeführt. Ein GIS-basierter Ansatz in Kombination mit detaillierten Daten der nationalen Forstinventur wurde erforscht, um den Kapitalwert finnischer Wälder und den entsprechenden jährlichen Gegenwert mit einer räumlichen Auflösung von 100 m mal 100 m zu schätzen und zu kartieren. Das Waldwachstum wurde auf drei Weisen angenähert: durch Modellierung regionaler Ertragsfunktionen, mittels der EFISCEN Inventurdatenbank und mit dem MOTTI Waldbestandssimulator. Unter den gegebenen Standard-Management-Richtlinien von MOTTI wurden vier Hauptartengruppen innerhalb von sechzehn unterschiedlichen Standortbedingungen für die Schätzung berücksichtigt. Bei einer Zinsrate von einem Prozent erreichte der Kapitalwert von Kiefernbeständen ein Maximum von 8920 € ha-1 mit einem jährlichen Gegenwert von 243 € ha-1 Jahr-1. Für Fichtenbestände lag der maximale Kapitalwert bei 12355 € ha-1 mit einem jährlichen Gegenwert von 293 € ha-1 Jahr-1. Birken und andere Laubgehölzarten waren weniger profitabel. Bei einer Zinsrate von fünf Prozent waren die meisten Wälder unprofitabel, mit Ausnahme einiger Kiefernund Fichtenbestände auf fruchtbaren Mineralböden im Süden. Die Ergebnisse dieser Studie bedeuten jedoch keinesfalls, dass weniger profitable oder unprofitable Waldbestände wertlos sind. Die Studie weist darauf hin, dass die Wahl der Ertragsschätzmethode und des Managementszenarios entscheidenden Einfluss auf die Profitabilität haben, besonders bei niedrigen Zinsraten und fruchtbaren Böden. Schlüsselwörter: räumliche Holzwertschätzung, Kapitalwert, jährlicher Gegenwert, Waldprofitabilitätskarte, Ökosystemdienstleistungen, Waldwachstumsmodellierung, Ertragsfunktionen Master thesis - Author's personal copy Author: Valentin Ştefan viii Acknowledgements I am grateful to the European Forest Institute for providing a paid traineeship opportunity and the needed support which led to this study. I would like to express my sincere thanks to Jo Van Brusselen, project manager, in the former EFICENT - OEF office, France. I would also like to thank the rest of the OEF team, Barbara Lacor and Paul Rougieux for the nice working environment. I am also grateful to my supervisors, Prof. Dr. Jan-Peter Mund and Prof. Dr. Christian Ammer, for their role in this thesis. I thank Ari Talkkari from the Karelia University of Applied Sciences for his helpful comments and criticisms with the methodology. I also thank Hannu Salminen from the Natural Resources Institute Finland for his valuable feedback with the MOTTI stand simulator. I thank Nikolai Knapp for helping me with the translation to German and Marcin Naworski for the translation to Polish. I thank my friends Stephanie Pollhammer and Adrian Dănescu for their support and for proofreading this document. Last but not least I would like to thank my parents and family for supporting me morally during the writing of this thesis. Master thesis - Author's personal copy Author: Valentin Ştefan ix Table of contents Tutor’s declaration ...................................................................................................... iii The author’s declaration ............................................................................................. iv Streszczenie ................................................................................................................. v Abstract ....................................................................................................................... vi Zusammenfassung ...................................................................................................... vii Acknowledgements ................................................................................................... viii Table of contents ......................................................................................................... ix List of figures .............................................................................................................. xi List of tables ............................................................................................................... xii List of abbreviations ................................................................................................... xii 1. Introduction ........................................................................................................ 1 1.1. Context and motivation for the study ............................................................... 1 1.1.1. The need for valuating forest ecosystem services....................................... 1 1.1.2. The need for mapping the value of forest ecosystem services .................... 3 1.2. Literature review and concepts related to valuation and profitability ................ 3 1.2.1. Stumpage and consumption value ............................................................. 5 1.2.2. Profitability indices: the net present value (NPV) and its equal annual equivalent (EAE) ................................................................................................... 7 1.3. Aim, scope and significance of the study ....................................................... 10 2. Material and methods........................................................................................ 12 2.1. Data acquisition and description .................................................................... 12 2.2. Data processing for the computation and mapping of profitability indices ...... 16 2.2.1. Geoprocessing the raw spatial data .......................................................... 16 2.2.2. Defining forest stand addresses (FSA) ..................................................... 19 2.2.3. Predicting stand growth with yield functions ........................................... 22 2.2.4. Forest stand management and simulation with MOTTI ........................... 27 2.3. Computation and mapping of profitability indices ......................................... 29 2.3.1. The concept of net present value (NPV) and its equal annual equivalent (EAE) in forest stand management ....................................................................... 29 2.3.2. NPV and EAE computation ..................................................................... 30 2.3.3. NPV and EAE mapping .......................................................................... 33 2.4. Sensitivity analysis ........................................................................................ 34 Master thesis - Author's personal copy Author: Valentin Ştefan 4 Häyhä & Franzese 2014). However, the economic value of an ecosystem service is more informative for policy makers (Häyhä et al. 2015). Several studies have already dealt with mapping the economic value of FESS, using benefit transfer as a valuation method (e.g. Troy & Wilson 2006; Elsasser et al. 2009; Liu 2010b; Carrasco et al. 2014; Frélichová et al. 2014). Specialized online databases have already been developed for ESS valuation, which can include studies that also mapped the economic values of FESS. For example, currently, the Canadian EVRI 1 database (de Civita et al. 2011) offers almost one thousand studies when queried for the word ‘forest’. The number of studies is reduced to less than one hundred when the key words combination ‘map AND forest’ is used. One major drawback of this database is the fact that is accessible only to researchers from the United Kingdom and France (Elsasser et al. 2009). Another example is given by Carrasco et al. (2014); they use The Economics of Biodiversity and Ecosystems dataset (Van der Ploeg & De Groot 2010; de Groot et al. 2012) to map the total ESS values of tropical forests. Schägner et al. (2013) mentioned the UK NEA (UK NEA 2014) as a promising initiative in ESS value mapping, which includes maps of the value of timber across the United Kingdom. Furthermore, a compilation of valuation databases is provided by The Ecosystem Services Partnership (ESP 2014). Nevertheless, they are not focused solely on FESS studies and therefore specific searches are needed. However, a comprehensive and up to date review on mapping the economic value of ESS (FESS included) was found to be the one of Schägner et al. (2013). They found only 69 studies on mapping the economic value of ESS of which a quarter were focused on forest ecosystems with 8 tackling timber provision. It seems that there is no review tackling solely the mapping of the economic values of FESS. Nevertheless, Ninan & Inoue (2013) presented a review on studies concerned solely with estimating the value of FESS, although no mapping approach was reviewed. Another relatively recent review, Barrio & Loureiro (2010), focused solely on forest values but without considering economic valuation mapping methods. 1 Environmental Valuation Reference Inventory Master thesis - Author's personal copy Author: Valentin Ştefan 5 Valuating FESS is no different from the valuation approaches used for ESS in general. There are many ways of valuating ecosystem services and their applicability is mostly context related (La Notte et al. 2012). For further details, in a review covering the research development of ESS valuation, Liu 2010a summarized several non-monetizing and monetary valuation methods used in ESS valuation. However, 'countries are free to choose the methods best suited for valuing their forest assets' (Eurostat 2000). This study is limited to valuating wood growing stock per hectare. Such valuation falls into market methods because wood is commonly perceived as an ecosystem good that can be bought in markets (Fisher et al. 2009). Furthermore, stumpage prices are recommended to be used for the valuation of standing timber (Eurostat 2000). After investigating the literature, two main monetary valuation methods were identified for the timber provision of cultivated forests: stumpage value and net present value (NPV). These monetary valuation methods are further discussed in the next section with corresponding literature references. The NPV also represents a form of estimating the profitability of forest investments (Soucy & Kershaw 2010). The NPV method is further used in this study. 1.2.1. Stumpage and consumption value At a given time along the management cycle of a forest stand, the growing stock (m3/ha) has a certain stumpage value based on the current market prices for different assortments that can be harvested. The Eurostat pilot programme in forest accounting specified that the stumpage value can be calculated by multiplying the total growing stock (m3/ha) with an average stumpage price or by multiplying the growing stock per species with the average stumpage prices of corresponding species (Eurostat 2000). The consumption value method can be seen as a more detailed variant of the stumpage value method because the timber is categorized in terms of species and age or diameter classes with corresponding stumpage prices (Eurostat 2000). The stumpage value is a simple method and has been embraced by many authors. For example, in Finland, Juutinen et al. (2008) considered that the stumpage value of growing stock located on a given site can be used to estimate the opportunity costs of Master thesis - Author's personal copy Author: Valentin Ştefan 6 protecting that particular site. Merry et al. (2009) and Ahmed & Ewers (2012) applied the stumpage value method when estimating the monetary value of standing timber across the Amazon. When mapping the direct use value of forests located in Zhejiang province of southeast China, Chen et al. (2009) applied a slightly different approach by deciding to multiply the stumpage prices with the net annual volume-increments. Certain authors felt the need to introduce harvesting costs in their economic estimations. For example, Grêt-Regamey et al. (2008), when estimating the value of wood production in a district in the Swiss Alps, mentioned that timber production was not profitable given the harvesting costs. In this first study they didn't include such costs but later on the same area was considered for further investigation and the harvesting costs were included (Grêt-Regamey et al. 2013). Remaining within the context of multiplying a quantity with a price, a different valuation approach was used by Li et al. (2006) to map the monetary value of the annual production of organic matter in the Qinba mountains of Shaanxi Province of China. They argued that the value of organic matter can be calculated by multiplying the dry weight of organic matter with the market price of standard coal. However, valuating growing stock by multiplying with the corresponding local market prices does not consider the expected growth of forest nor the land value. On the other hand, these two factors could be neglected for mature forests (Juutinen et al. 2008). Moreover, the European System of Accounts recommends separating forest land from timber values by suggesting that the value of forest land should be best assessed through market prices only (Eurostat 2000). Both the stumpage value and consumption value methods can be considered as simplified versions of the net present value approach with the strong assumption that the discount rate is identical with the growth rate of the forest (Eurostat 2000; Lange 2004). The complexity of the net present value method is that it considers forest growth. Master thesis - Author's personal copy Author: Valentin Ştefan 7 1.2.2. Profitability indices: the net present value (NPV) and its equal annual equivalent (EAE) Effectively, timber continues to grow with a certain rate until the moment of final cut. This natural growth accrues to the initial stumpage value creating future benefits and their present value has to be taken into account, justifying the use of present value methods as recommended by the Eurostat pilot programme in forest accounting (Eurostat 2000). Computing the net present value (NPV) of a forest based on estimated cash flows is regarded as 'probably the most common method currently used for assessing forest estate value' (Holopainen et al. 2010). The NPV approach is in accordance with Faustmann’s theory that the real value of timber is given by the discounted future stumpage value of mature timber after subtracting the costs that occurred during reaching maturity (Eurostat 2000; Lange 2004). Additionally, the NPV is also one of the main profitability indicators of the cost-benefit analysis used in assessing and comparing competing investment projects (Prokofieva & Thorsen 2011; Snowdon & Harou 2013). Also, the annualized form of the NPV, the equal annual equivalent (EAE), can be used in the same manner (e.g. Hynynen et al. 2005; Olssen et al. 2012). The EAE brings the advantage of evaluating investments with different time spans (Prokofieva & Thorsen 2011). Illustrating the meaning of discounting, Prokofieva & Thorsen (2011) argue that an individual will prefer receiving a certain amount of money today rather than in the future. Thus, a high discount rate indicates a higher preference to the present consumption of a given amount of money. Related to the time span of environmental investments, high discount rates imply a low importance of long-term investments, that is, preference for immediate benefits (Yi, Wong, et al. 2014). Even though the NPV method was recommended by Eurostat, this approach is regarded as being rather cumbersome because it requires precise knowledge of the cash flows, that is, knowing the exact benefits and costs and at what time they occur during the management cycle of a forest stand (Eurostat 2000; Lange 2004). Furthermore, predicting benefits requires information concerning forest growth (e.g. yield tables, Master thesis - Author's personal copy Author: Valentin Ştefan 8 curves or equations 2 ). A severe limitation is that this kind of information is not always available. Moreover, results of the Eurostat pilot programme in forest accounting showed that the stumpage value method (presented in the previous section) is more suitable for international comparisons because of higher data availability for its calculation (Eurostat 2000). Nevertheless, with all its drawbacks regarding data availability, the NPV approach still remains a sound way of valuating forests (Eurostat 2000; Holopainen et al. 2010). One of the pioneer studies in mapping timber NPV is the Ph.D. thesis of Bateman (1996). The author first estimated yield class models for Sitka spruce and beech in Wales, United Kingdom based on several environmental variables and then he produced yield class maps. In parallel, he developed tables of NPVs across various yield classes for the two species at various discount rates. Next, he connected the yield class maps with the corresponding NPVs. One of the most recent studies concerned with modelling and mapping NPV is from Yi, Cannon, et al. (2014) who mapped the NPV of rubber plantations in southwest China. Their methodology is similar to the one developed by Bateman (1996). Yemshanov et al. (2007) mapped NPVs for red pine, Norway spruce and black walnut in southern Ontario, Canada and assessed the economic feasibility of the species. The authors used site index maps and corresponding growth and yield models combined with information regarding the intensity of silvicultural management. The authors stressed the high demand of data not only for wood prices and management costs but also for growth and yield estimates. Chan et al. (2011) mapped the economic values for harvestable timber, carbon storage and recreational angling in the Central Interior of British Columbia. Instead of using or computing growth and yield models, they used timber supply reviews for estimating the volume of harvestable timber. The authors also underlined the difficulties of data availability. They discussed the bias that might arise by using timber supply reviews instead of modelling the growth of the forest stands. 2 The yield tables, curves or equations predict the total volume production attained at a specified age. Master thesis - Author's personal copy Author: Valentin Ştefan 9 Polasky et al. (2011), among other objectives of their study, also used a detailed dataset to compute NPVs for Douglas fir stands of the Willamette Basin in Oregon, USA. The authors had access to information regarding yield for each site index at desired forest stand ages. The net price of timber was modelled based on logging and hauling costs. Computing and mapping a form of NPV without costs was done by Ojea et al. (2012) for the Spanish Mediterranean region. They also did not consider yield functions but used data from the national forest inventory. The authors underlined that the desire to differentiate stumpage prices between age classes, management regimes, spatial locations, or assortments was hindered by scarcity and lack of reliable data. Using a map of the Atlantic forests of Paraguay, Naidoo & Ricketts (2006) estimated and mapped the NPV of five different ecosystem services: bushmeat, timber, bioprospecting ('value for new pharmaceutical products'), existence value, and carbon storage. The authors assumed a 30 years harvest cycle with a harvest rate of four trees per hectare. Using other studies, they constructed estimates for an average per-tree value. Many other studies tackled solely the computation of NPV or the Faustmann’s land expectation value (LEV) without considering the spatial variation of these profitability indicators. The difference between LEV and NPV is that in computing LEV all future rotations of timber are included, while in the case of NPV only one rotation is considered (Straka 2007). For example, using a forest growth simulator, Hanewinkel et al. (2010) deducted the cash flows for Norway spruce and European beach stands of Baden-Württemberg. They computed LEV using the net stumpage value at the end of the rotation time, the net revenue for thinning and the cost for replanting. The strength of their study is the complex analysis of the sensitivity of results by changing interest rates, risk levels, and rotation lengths. Additionally, including natural risks (storms and insects), Dieter (2001) created an economic simulation model for beech and Norway spruce in the site conditions of southern Germany. He used the Faustmann approach and simulated forest growth. Creedy & Wurzbacher (2001) also used the Faustmann approach for modelling the economic value of forested areas of the Thomson Catchment in Central Gippsland, Australia. They computed the timber value at a certain age by multiplying stumpage prices with the output of a timber growth function. Master thesis - Author's personal copy Author: Valentin Ştefan 10 Garcia-Gonzalo et al. (2007) used a process-based ecosystem model (FinnFor) to analyse the effects of climate change and management on timber yield and NPV. The scale of their study was limited to a management unit of ca. 1450 ha in central Finland. The authors ran NPV simulations for Scots pine, Norway spruce and silver birch. Even if the above mentioned studies did not aim at mapping economic indicators, they are valuable examples of NPV or LEV computation for the economic assessment of tree species or management scenarios. All in all, the studies that computed and mapped the NPV used various methods for estimating costs and benefits. Apparently, the wider the spatial extent of the study, the less complex the method. Presently, there are no studies aimed at mapping NPV for forests across the whole of Finland at 100×100 m spatial resolution, the task that was addressed in this study. In the second chapter further details are provided about the NPV method and its equal annual equivalent (EAE), NPV computation, three approaches of computing benefits for forests in Finland considering their growth, and mapping the NPV for Finnish forests at one hectare forest stand spatial resolution. 1.3. Aim, scope and significance of the study While there are many studies focused on estimating the value of various ESS, few aspired to map such values at a fine spatial resolution. To date, there are no studies tackling the mapping of the NPV or its EAE for the entire Finnish forests at fine spatial resolution. Finland was an appealing case study because of the available and free data. In this Master's thesis I aimed at investigating the development of NPV and EAE maps of pure cultivated stands in Finland. In order to achieve this aim, I used various datasets coming from the national forest inventory of 2011. The NPV and its EAE were modelled and mapped for various stand types across Finland at 100×100 m spatial resolution. The study is narrowed down to valuating wood timber provision. There is a need for such limitation because assessing the total value of forests is a complex process, which demands access to various data. Integrating other forest ecosystem services could form the aim of further research. Master thesis - Author's personal copy Author: Valentin Ştefan 11 One intended outcome of the study, on a theoretical level, is to contribute to the growing research trend of ESS and FESS valuation studies. Specifically, I focus on mapping the economic value of Finnish forests at the hectare level. Consequently, this study represents a spatial valuation approach of wood provisioning in Finnish forests. A second intended outcome of the study is to clarify benefit estimation methods. Specifically, I focus on three methods for estimating the total standing volume used in the computation of benefits. Finally, a third concern in the research is the detection of differences in terms of profitability between species and site conditions. Thus, to assess which species and site conditions are economically feasible. Master thesis - Author's personal copy Author: Valentin Ştefan 12 2. Material and methods The previous chapter broadly introduced the general concept of economic valuation of ecosystem services, with a focus on forest ecosystem services related to timber provisioning. As pointed out earlier, computing the NPV is a common method in forest valuation and its annualized form (EAE) allows a better comparison of investments with different time spans. In this chapter, computing and mapping of two economic indicators for Finnish forests are presented. Their computation required detailed information regarding forest stand growth, stand management and economic data (stumpage prices and management costs). 2.1. Data acquisition and description Data regarding average stumpage prices and silvicultural management costs by forestry centres 3 were retrieved from the Finnish statistical yearbook of forestry (Ylitalo 2011). Details are provided in Appendix 2. The spatial distribution of the 14 forestry centres across Finland (Figure 3) was built using the Nomenclature of Territorial Units for Statistics - NUTS 2010 (EC 2010). In this study, three methods were used for obtaining forest stand growth data: - predicting stand growth with yield functions, based on the Multi-source National Forest Inventory Raster Maps (METLA 2013a), hereafter MS-NFI; - using the EFISCEN inventory database (Sevola 1997; Schelhaas et al. 2006); - using the MOTTI forest stand simulator (LUKE 2015a), which also provided guidelines for the stand management operations. Datasets for predicting stand growth with yield functions The MS-NFI covers the entire country (Figure 1 and Figure 2) and consists of thematic forest maps in georeferenced raster format. The raster maps are set in the ETRS-TM35FIN coordinate system and have a spatial resolution of 20×20 m (Tomppo et al. 2011). They are provided in GeoTIFF format and can be downloaded using a UTM 200 division grid (METLA 2013b). There are a total of 37 tiles defined by 3 Regional forest districts are mentioned as 'forestry centres' in the Finnish statistical yearbook of forestry. The term 'forestry centre' was adopted in this study. Master thesis - Author's personal copy Author: Valentin Ştefan 13 the UTM grid over Finland. The raster datasets contain the total volume (m3/ha), age (years), canopy cover (percent) and the main site class. The total volume is available for four species groups: Scots pine, Norway spruce, birch and other broad-leaved trees (Figure 2). Metadata is provided in Appendix 1. The four site classes can be interpreted similarly to those used in the EFISCEN inventory database for Finland: site 1 - grass herb forest, site 2 - Myrtillus or Hylocomium-Myrtillus type, site 3 - Vaccinium or Empetrum-Myrtillus type and site 4 - Calluna or Cladina type (Kuusipalo in Yrjölä 2002). Moreover, two types of soil conditions were considered: mineral soil and peatland. A soil raster layer was retrieved from the European Soil Database (EC 2004) and was further clipped to the extent of Finland (Figure 4A). These thematic soil maps are grids in the ETRS89 Lambert Azimuthal Equal Area (ETRS_LAEA) coordinate system with a spatial resolution of 1×1 km. The EFISCEN inventory database The EFISCEN inventory database provides average standing volumes for pure, evenaged stands across several age classes for the same species groups as in MS-NFI. The database differentiates between southern and northern Finland, two types of soil conditions, mineral soil and peatland and four site classes (as described above for MS-NFI). In the present study, these tables were treated as yield tables, even though they only describe the state of the forests at the time of forest inventory. The MOTTI forest stand simulator 4 MOTTI is a forest stand simulator which was built to simulate stand development under alternative management regimes and growth conditions in Finland (Hynynen 2002; Salminen, H., Lehtonen, M., & Hynynen 2005). Additionally, MOTTI can compute the profitability of forest management (NPV) and even support biodiversity and carbon sequestration analyses. MOTTI is equipped with distance-independent individual-tree growth models that can predict tree growth (diameter and height) and mortality rates for 5-year periods. It is calibrated to be applicable to all growth conditions across Finland. (Hynynen et al. 2005). 4 MOTTI version 3.3.1, downloadable from http://www.metla.fi/metinfo/motti/motti-asennus-en.htm. Master thesis - Author's personal copy Author: Valentin Ştefan 20 Figure 5 - Depicting growth conditions and regions as codes. A) Codes assigned to dominant species. B) Codes assigned to site classes. C) Codes assigned to soil classes. D) Codes assigned to regions and forestry centres. D) A) B) C) Master thesis - Author's personal copy Author: Valentin Ştefan 21 Defining dominant species stands and their codes A forest stand was represented by a cell of 100×100 m (1 ha). Because all four species could be present in one stand, the species with the highest relative contribution to total standing volume was defined as the dominant species. For example, if a stand had a total volume of 100 m3/ha and the stand composition was 50 m3/ha pine, 40 m3/ha spruce and 10 m3/ha birch, then pine was considered the dominant species. Subsequently, the NPV would be computed for the cash flow of managing a pine stand. Such simplification had to be made given the complex dynamics of mixed stands and the limited scope of this study. For the purpose of finding the dominant species in each stand, a Python script was built and run in the Python window of ArcMap (script given in Appendix 5). Essentially, the script detects the maximum volume at the stand level (one cell), then tests to which species this maximum value belongs to, and returns a presence-absence grid for each species (Figure 6 B, C, D, E). Finally, all these raster datasets are merged together and a code is attributed to each species (Figure 6A). Figure 6 - Dominant species stands. A) All dominant species stands with corresponding codes; B) Scots pine stands; C) Birch stands; D) Norway spruce stands; E) Other broad-leaved trees stands. A) B) C) D) E) Master thesis - Author's personal copy Author: Valentin Ştefan 22 Defining codes for the four site classes The site classes within the geoprocessed MS-NFI datasets are coded as 1, 2, 3 and 4. In order to distinguish them from the species codes defined above, the cell values of the site classes raster dataset (Figure 1A) where changed to 10, 20, 30 and 40 with the 'Reclassify' tool (Figure 5B). Defining codes for the two soil classes Using the 'Reclassify' tool, the cell values of the soil classes raster dataset (Figure 4B) where changed as follows: 100 for mineral soils and 200 for peatlands (Figure 5C). Defining codes for the forestry centres and regions There are 14 forestry centres across Finland and their default codes (Figure 3B) are given in the Finnish statistical yearbook of forestry (Ylitalo 2011). The 'Reclassify' tool was used to assign new codes (Figure 5D). In the same manner, 100 000 was assigned to northern Finland and 200 000 to southern Finland (Figure 5D). 2.2.3. Predicting stand growth with yield functions General considerations Regional yield functions were computed using the MS-NFI datasets. There were 16 site conditions which resulted from considering all combinations of the two regions (northern and southern Finland) and the two soil classes (mineral soils and peatlands) for each of the four site classes. As each of the 16 site types had to be considered for each of the four species groups, a total of 64 regional yield functions were computed. Spatial processing of growth conditions Considering a resolution of 100×100 m (1 ha), a raster cell represented a forest stand. Initially, the goal was to compute yield functions only for pure stands. However, this was not possible due to the small number of observations available for some combinations of species and site types. Consequently, stands with some mixing and mixed stands had to also be considered and their definition is given in Table 1. Generally, stands with a canopy cover higher than the third quartile of the canopy cover distribution were considered for yield function computation. If there were still not Master thesis - Author's personal copy Author: Valentin Ştefan 23 enough stands in order to observe a pattern for a yield curve to be computed, then the median or the first quartile were considered (e.g. on site classes 4 or 3 where canopy cover was usually low). The analysis concerning canopy cover was carried out in R (R Development Core Team 2015). Table 1 - Type of stands considered for defining regional yield functions Type of stands Dominant species’ share of stand total volume Pure stands over 95%. Pure stands and stands with some mixing over 75% Pure stands, stands with some mixing and mixed stands over 50% NOTE: Adapted from (METLA 2012a) The diagram in Figure 7 illustrates the entire process of building regional yield functions for the four species across Finland. The process involved using various predefined ArcGIS tools, user-defined Model Builder tools, R (R Development Core Team 2015) and Python (Python Software Foundation 2015) code. Scripts are provided in Appendix 6 and 7. Shortly, the procedure consisted in segregating stands by regions, soil classes, site classes, tree species and imposing certain thresholds for volume and canopy. Appendix 8 illustrates the yield curves computed for each site and provides details about the volume and canopy cover thresholds. Two models (tools) were built with the Model Builder application of ArcMap. One model extracts the canopy cover of the forest stands on each regionalized site for each species. The workflow of this model is presented by the diagram in Figure 8. The second model tabulates volume by age for every forest stand on every regionalized site. The workflow is presented by the diagram in Figure 9. Master thesis - Author's personal copy Author: Valentin Ştefan 24 Figure 7Workflow for computing regional yield functions. Clip sites by regions (Extract by Mask) Clip by soil classes (Extract by Mask) Canopy cover Soil classes Sites by NS regions Site classes Species' volume Selected species' volume Stand age Regional yield tables (*.txt) Canopy cover statistics Nonlinear yield function modelling Northern and southern regions (NS) Select volume above certain threshold Regionalized sites Regionalized canopy cover Delete canopy cover below certain threshold (Set Null) Relevant canopy cover Attribute tables (*.txt) Extract canopy cover for each species on each regionalized site Tabulate volume by age on each regionalized site Yield functions Legend: Input rasters Python code R code ArcGIS Tool Model Builder tool Data files InputOutput rasters Input raster Master thesis - Author's personal copy Author: Valentin Ştefan 25 Figure 8 - Workflow of the model which extracts the canopy cover of forest. Nonlinear regression modelling and model selection for yield functions A common way to model volume growth in even-aged stands is to use various nonlinear functions of the form v=f(a), where v is the stand volume (m3/ha) and a is the stand age (years). In this study the logistic and Gompertz functions were used. Both are sigmoid functions which reflect well-known stand dynamics, i.e. that growth rates increase during early developmental stages, reach a maximum, and then decrease in mature and over-mature stands. The equation of the logistic function used in this study is given by Eq. 1, where v is the stand volume, age is the stand age, Asym, xmid and scal are parameters. 𝑣= 𝐴𝑠𝑦𝑚 1+𝑒(𝑥𝑚𝑖𝑑−𝑎𝑔𝑒)/𝑠𝑐𝑎𝑙 (𝐸𝑞.1) The logistic function is symmetric about the inflection point (age=xmid, v=Asym/2) and presents an asymptote at v=Asym (Vera Sit, Melanie Poulin-Costello 1994). The equation of the Gompertz function is described by Eq. 2, where v is the stand volume, age is the stand age, Asym, b2 and b3 are parameters. 𝑣=𝐴𝑠𝑦𝑚∙𝑒−𝑏2∙𝑏3𝑎𝑔𝑒 (𝐸𝑞.2) Gompertz function is not symmetric about an inflection point and has asymptotes at v=0 and v=Asym (Vera Sit, Melanie Poulin-Costello 1994). Legend: ArcGIS Tool Raster dataset Clip volume by sites (Extract by Mask) Regionalized sites Volume Regionalized volume Canopy cover Clip canopy cover by volume (Extract by Mask) Regionalized canopy cover Master thesis - Author's personal copy Author: Valentin Ştefan 26 For both cases the functional form can be linearized by a log-transformation if the parameter Asym is known. In this study, no transformation was applied and the estimates for the parameters of the models were obtained by using the nonlinear least squares technique. The nonlinear regression analysis was conducted in R, using the functions nls and nls2 from the libraries stats and nls2, respectively. The code is provided in Appendix 7 and statistical results regarding the coefficient estimates are provided in Appendix 9. Whenever possible, the self-starting R functions SSlogis and SSgompertz were used. When they failed to converge and find estimates for the parameters, naive guesses were made for the starting values and/or the convergence algorithm was adjusted Regionalized sites Relevant canopy cover Clip canopy cover by sites (Extract by Mask) Volume Regionalized relevant canopy cover Clip volume by canopy cover (Extract by Mask) Regionalized volume under relevant canopy cover Tabulate volume by age (Tabulate Area) Stand age Regionalized tables of volume-age pairs (*.txt) Data files Legend: ArcGIS Tool Raster dataset Figure 9 - Workflow of the model which tabulates volume by age for forest stands. Master thesis - Author's personal copy Author: Valentin Ştefan 27 (e.g. gradually increasing the number of iterations or the convergence tolerance). Only models with significant estimates (five percent significance level) were kept for further investigation and statistical inference. Gompertz and logistic models were compared using the Akaike Information Criterion (AIC). The preferred model was the one with a smaller AIC value. A model selection approach similar to the one proposed by Burnham & Anderson (2002) was used. The authors suggest the rule of thumb according to which models with AIC difference smaller or equal than 2 (AIC ≤ 2) have substantial empirical support, those with 4 ≤ AIC ≤ 7 have considerably less and those with AIC > 10 have essentially none. On the other hand, they also suggest that the model with AIC > 10 might still be used for inference if the sample size is large. Additionally, the under-fitting or over-fitting of the data by the analysed models were very important criteria for model selection. This was assessed visually using the figures of Appendix 8. 2.2.4. Forest stand management and simulation with MOTTI Running the MOTTI simulator involved the following steps: stand initialization, running the automatic stand simulation and saving the results as Excel files. The workflow for the MOTTI simulations is presented in Figure 10. A) Stand initialization B) Stand simulation: default - recommendations of the Forestry Development Centre Tapio MOTTI simulations C) Save results: save as *.xls-file (64 simulations = 64 *.xls-files); post-process *.xls-files with R 1) Choose municipality: - Orivesi if south - Pudasjärvi if north 2) Choose soil type: - mineral - peatland 4) Choose Established stands 5) Choose main species - Regeneration method: planted - Age: 3 years - Height (H): 1 m - Number of seedlings per hectare: - 2000 for spruce, pine, and others - 1600 for silver birch 3) Choose site type: 1 = grove 2 = grovelike 3 = fresh 4 = dry Mineral soil 1 = eutrophic fern 2 = Vaccinium myrtillus type 3 = Vaccinium vitis idaea type 4 = dwarf-shrub type Pine peatland for: pine, birch and other broad-leaved Spruce peatland for spruce Peatland Figure 10 - Workflow for MOTTI simulations. Master thesis - Author's personal copy Author: Valentin Ştefan 28 Stand initialization required choosing a location out of 351 possible municipalities across Finland. Each municipality was characterized based on the following growth factors: temperature sum, latitude, longitude and altitude. Theoretically, all 32 stand conditions 6 could have been considered for each of the 351 municipalities. However, running MOTTI so many times would have been extremely cumbersome. Consequently, the analysis was narrowed down to two representative municipalities: Orivesi and Pudasjärvi for southern and northern conditions, respectively. This resulted in 64 MOTTI simulations comparable with the 64 defined regional yield functions and the EFISCEN tables. The two locations were in the interval described by 0.1 standard deviations from the average conditions 7 of south and north Finland. An R script was used in order to automate the selection. The next step in stand initialization was to choose the site type. A correspondence was established between the site conditions considered in the EFISCEN database and the MS-NFI, on the one hand, and the site types used by the MOTTI simulator, on the other hand (Figure 10). Descriptions of the site factors used in MOTTI were provided by The Natural Resources Institute Finland (Salminen H. 2015, pers. comm.). All stands were artificially established (option 'Established stand') and the plantation density was adjusted to 2000 seedlings per hectare for spruce, pine and other broad-leaved species, and 1600 seedlings/ha for silver birch (Niskanen 1999). All other options related to stand initialization were kept unchanged. Concerning stand simulation, the MOTTI simulator considers by default the practical management recommendations for private forests issued by the Forestry Development Centre Tapio (LUKE 2015b). The management of a forest stand can include the following silvicultural operations: artificial regeneration, cleaning (for stands in the sapling stage), pre-commercial thinning, commercial thinning and a clear cut at the end of the management cycle. The artificial regeneration and the final cut are obligatory operations, while the others are optional. 6 The 32 growth conditions are given by the four group tree species (Scots pine, Norway spruce, birch, other broad-leaved trees), four site classes and two soil classes (mineral soils and peatlands). 7 Temperature sum and latitude were used for the north region. The longitude was additionally used for the south region in order to narrow down the location options only to one. Master thesis - Author's personal copy Author: Valentin Ştefan 29 Running MOTTI for the 64 site conditions resulted in 64 *.xls-files. These files were processed with R and the resulting management guidelines for the 64 stand types are provided in Appendix 10. These guidelines offer details about the timing (stand age) of the silvicultural operations and about the harvestable wood volumes (%) per operation for each of the two considered assortments, i.e. logs and pulpwood. 2.3. Computation and mapping of profitability indices 2.3.1. The concept of net present value (NPV) and its equal annual equivalent (EAE) in forest stand management Computing present values requires the use of discount rates (d) and both future benefits (B) and costs (C) have to be discounted to the present moment. The future benefits (€/ha) are actually the product between stumpage prices (€/m3) and standing timber (m3/ha) at a certain moment (t). Consequently, yield functions or tables detailing the development of a forest stands are required (Figure 11). Figure 11 - A model of stand management cycle. Modified from Saramäki (2012). The net present value (NPV) is mathematically defined as: 𝑁𝑃𝑉= ∑ 𝐵𝑡 (1+𝑑)𝑡−∑ 𝐶𝑡 (1+𝑑)𝑡 𝑇 𝑡=1 𝑇 𝑡=1 ,[€/ℎ𝑎] Master thesis - Author's personal copy Author: Valentin Ştefan 36 The significant parameter estimates (p-value less than 5% significance level) of the functions together with their statistics are provided in Appendix 9. The graphs from Appendix 8 illustrate the models with the cloud of observations for every site condition. 3.1.2. EFISCEN inventory database Figure 16 shows standing volumes at various ages as given by the EFISCEN inventory database for Finland. The points connected by lines are located at the centre of age classes. One age class has an amplitude of 20 years. In general, there is an agreement between the information given by the regional yield curves and the EFISCEN data. Figure 16 - Standing volumes provided by the EFISCEN inventory database. Regional yield curves are plotted in the background. Master thesis - Author's personal copy Author: Valentin Ştefan 37 3.1.3. Forest stand management and simulations with MOTTI Figure 17 shows the development of forest stands for the four species groups on 16 site conditions considering the default MOTTI forest management guidelines. In general, on mineral soils, standing volumes are visibly higher than those given by regional yield functions. Some exceptions appear on peatlands. The corresponding management guidelines are summarized in a tabular form in Appendix 10. They offer details about the timing of silvicultural operations and about harvestable percentages per operation for each wood assortment, i.e. logs and pulpwood. Figure 17 - Stand growth and management given by the MOTTI stand simulator. Regional yield curves are plotted in the background. Master thesis - Author's personal copy Author: Valentin Ştefan 38 3.2. Profitability indices 3.2.1. NPVs and EAEs by levels of ecological factors The 417 unique forest stand addresses (FSAs) defined in section 2.2.2 were considered for analysing. A forest stand dominated by one of the four species groups, depending on its location, could fall within one of the 16 site conditions mentioned in section 2.2.3 and also within one of the 14 forestry centres (896 combinations). Site conditions influenced the standing volume and management, consequently the economic benefits, and the forestry centres dictated the costs and the stumpage prices. Southern forests are divided into 11 forestry centres, while northern forests are divided into three. Whereas all possible site conditions could exist in every northern forestry centre, in the case of southern centres some sites were not identified (e.g. stands dominated by other broad-leaved on site class 4 with peat appeared only in two southern forestry centres). Due to unbalanced distribution of forestry centres across north and south and unbalanced spatial distribution of site conditions, the 417 FSAs were unevenly distributed when grouped by ecological factors (Table 3). Table 3 also informs about the surfaces corresponding to each of the four species groups within 16 site conditions across Finnish forests. Average values and standard deviations of the 417 NPVs and EAEs grouped by site conditions and by the three yield estimation methods are presented in Table 4 - Table 9. The values were computed at a discount rate of one percent. Profitability indices (NPV and EAE) could be computed for all type of stands in the case of volume estimations based on MOTTI stand simulator (Table 4 and Table 5). However, some exceptions occurred in the case of estimations based on regional yield functions and EFISCEN inventory database. For example, reliable yield functions could not be computed for other broad-leaved species on all site conditions. (Table 6 and Table 7). Additionally, in the case of EFISCEN inventory database (Table 8 and Table 9), missing data did not allow the computation of profitability indices on all site conditions for other broad-leaved species, spruce and birch. Master thesis - Author's personal copy Author: Valentin Ştefan 39 Table 3 - Number of unique forest stand addresses (FSA) and forest stands (FS) aggregated by levels of ecological factors Region Species Soil: Mineral Site classes S1 S2 S3 S4 FSA FS (ha) FSA FS (ha) FSA FS (ha) FSA FS (ha) South Pine 11 4,198,955 11 142,413 11 1,143,336 11 5,056 Spruce 11 2,769,850 11 184,215 11 27,967 11 1,360 Birch 11 1,306,327 11 154,690 11 62,398 11 1,815 Other 11 269,666 11 3,975 10 1,018 8 258 North Pine 3 3,301,412 3 63,763 3 1,235,616 3 34,561 Spruce 3 531,257 3 67,283 3 45,869 3 2,061 Birch 3 822,549 3 136,333 3 124,716 3 3,072 Other 3 29,906 3 2,234 3 1,825 3 180 Soil: Peat South Pine 10 601,785 10 33,758 10 383,063 10 2,043 Spruce 10 205,011 10 27,840 10 5,285 9 149 Birch 10 118,593 10 26,528 10 16,719 9 271 Other 10 17,199 10 612 9 319 2 5 North Pine 3 2,578,195 3 69,465 3 1,653,156 3 63,328 Spruce 3 383,420 3 71,389 3 71,972 3 5,278 Birch 3 294,250 3 121,976 3 129,542 3 3,769 Other 3 17,501 3 622 3 2,595 3 178 NOTE: One NPV corresponds to one unique forest stand address (FSA) defined in section 2.2.2. One forest stand (FS) represents one hectare (100×100 m) thus the figures also represent surfaces. The type of soil (mineral or peat) had a major influence on the mean values of both NPV and EAE profitability indices, independent of species or the method used for yield estimation. Stands on mineral soils were, on average, more profitable than stands on peatlands with most of species not yielding profit on sites with peat. For example, when predicting yield with the MOTTI stand simulator, Scots pine stands on southern S1 sites with mineral soil yielded an EAE up to 243 € ha-1year-1 (SD: 28.4 € ha-1year-1). However, the EAE dropped to an unprofitable level of -28 € ha-1year-1 (SD: 1.8 € ha-1year-1) on peatlands (Table 5). This shift in profitability due to soil conditions happened for all site classes and for both southern and northern regions. This trend was also observed for the other two yield estimation methods (for regional yield functions - Table 6, Table 7 and for EFISCEN inventory database - Table 8, Table 9). Only Norway spruce stands remained profitable on peatlands, yielding an average yearly return per hectare up to 181 € (SD: 2.6 € ha-1year-1) on southern peatlands Master thesis - Author's personal copy Author: Valentin Ştefan 40 and 95 € (SD: 4.5 € ha-1year-1) on northern ones (site class S1 - Table 5). However, this profitability abruptly declined from site class S1 to S2, after trickling down without significant variations to S3 and S4. The abrupt decline was independent of region (southern or northern) and yield estimation method. Generally, all species manifested a decline pattern in profitability from site class S1 towards S4. Another trend in profitability was observed when comparing northern and southern regions. On average, southern stands were more profitable than northern ones. For instance, considering the MOTTI estimations and a discount rate of one percent (Table 5), Scots pine stands on southern site class 1 with mineral soil yielded an EAE of 243 € ha-1year-1 but only 104 € ha-1year-1 on northern sites. Given the same conditions, the profitability of spruce stands dropped from an EAE of 293 € ha-1year-1 on southern sites to 110 € ha-1year-1 on northern ones. For both pine and spruce that was a decrease in profitability of around 60%. The EAE of birch stands decreased with 70%, dropping from 109 € ha-1year-1 (south) to 32 € ha-1year-1 (north). Stands dominated by other broad-leaved went from an EAE of 69 € ha-1year-1 (south) to 12 € ha-1year-1 (north), which meant a decrease of around 80%. The same decreasing trend was also observed on peatlands, where, for instance, the EAE of spruce stands dropped from 181 € ha-1year-1 (south) to 95 € ha-1year-1 (north), meaning a decrease of around 50% (Table 5). Furthermore, the results show that the standard deviation (S.D.) of both NPV and EAE decreased with decreasing site quality. In general, the S.D. fallowed the same trend as the one described above. Master thesis - Author's personal copy Author: Valentin Ştefan 41 Table 4 - Summary statistics for NPVs - MOTTI by levels of ecological factors (1% discount rate; yield estimations based on MOTTI simulations) Region Species Soil: Mineral Site classes S1 S2 S3 S4 Mean S.D. Mean S.D. Mean S.D. Mean S.D. South Pine 8,920 1,042 7,435 890 7,313 871 2,861 395 Spruce 12,016 1,501 12,355 1,543 7,978 1,029 782 186 Birch 5,168 653 3,480 489 2,608 408 -146 123 Other 3,271 476 1,699 328 539 85 -330 83 North Pine 4,737 253 3,628 210 3,727 211 1,315 92 Spruce 5,847 325 5,279 304 3,274 198 -70 53 Birch 1,342 458 262 128 111 65 -718 64 Other 518 97 1 83 -235 76 -735 63 Soil: Peat South Pine -1,539 100 -1,469 100 -1,443 100 -1,037 88 Spruce 9,950 145 2,635 82 1,549 82 2,378 97 Birch -720 73 -895 72 -875 72 -904 74 Other -420 76 -641 74 -750 77 -676 23 North Pine -610 76 -992 43 -1,060 46 -1,055 44 Spruce 5,088 240 803 72 484 66 618 65 Birch -760 85 -892 82 -959 80 -956 80 Other -546 90 -854 83 -926 81 -909 81 NOTE: Mean and standard deviation (S.D.) expressed in €/ha Table 5 - Summary statistics for EAEs - MOTTI by levels of ecological factors (1% discount rate; yield estimations based on MOTTI simulations) Region Species Soil: Mineral Site classes S1 S2 S3 S4 Mean S.D. Mean S.D. Mean S.D. Mean S.D. South Pine 242.9 28.4 152.8 18.3 147.2 17.5 53.5 7.4 Spruce 293.2 36.6 262.3 32.8 173.3 22.3 14.2 3.4 Birch 108.5 13.7 73.1 10.3 54.8 8.6 -3.1 2.6 Other 68.7 10.0 35.7 6.9 11.3 1.8 -6.9 1.8 North Pine 104.1 5.6 62.2 3.6 59.8 3.4 18.8 1.3 Spruce 110.2 6.1 91.1 5.2 54.6 3.3 -1.0 0.8 Birch 31.8 10.9 6.2 3.0 2.6 1.5 -17.0 1.5 Other 12.3 2.3 0.0 2.0 -5.6 1.8 -17.4 1.5 Soil: Peat South Pine -28.0 1.8 -26.8 1.8 -24.4 1.7 -16.0 1.4 Spruce 181.3 2.6 48.0 1.5 28.2 1.5 43.3 1.8 Birch -15.1 1.5 -18.8 1.5 -18.4 1.5 -19.0 1.6 Other -8.8 1.6 -13.5 1.5 -15.7 1.6 -14.2 0.5 North Pine -9.4 1.2 -15.3 0.7 -15.6 0.7 -14.3 0.6 Spruce 95.1 4.5 11.5 1.0 6.9 0.9 8.9 0.9 Birch -18.0 2.0 -21.2 1.9 -22.8 1.9 -22.7 1.9 Other -13.0 2.1 -20.3 2.0 -22.0 1.9 -21.6 1.9 NOTE: Mean and standard deviation (S.D.) expressed in € ha-1year-1. Master thesis - Author's personal copy Author: Valentin Ştefan 42 Table 6 - Summary statistics for NPVs - Yield Functions by levels of ecological factors (1% discount rate; yield estimations based on regional yield functions) Region Species Soil: Mineral Site classes S1 S2 S3 S4 Mean S.D. Mean S.D. Mean S.D. Mean S.D. South Pine 1,733 291 818 201 2,368 357 1,249 234 Spruce 6,034 812 5,336 732 1,243 260 84 117 Birch 1,038 222 605 183 187 145 -802 66 Other 1,944 332 465 181 - - - - North Pine 1,719 125 1,046 100 987 92 -700 25 Spruce 1,775 146 1,211 122 -1,022 26 -563 57 Birch -84 206 -355 82 -524 47 -714 64 Other -20 82 -399 72 - - - - Soil: Peat South Pine -1,086 105 -1,276 102 -1,229 102 -1,142 86 Spruce 6,230 108 2,048 80 222 69 553 70 Birch -356 76 -403 76 -765 73 -1,068 73 Other 257 85 -513 75 - - - - North Pine -422 74 -937 42 -981 45 -1,280 46 Spruce 1,693 111 179 48 -570 75 -467 74 Birch -590 89 -760 85 -932 81 -964 80 Other -761 85 - - - - - - NOTE: Mean and standard deviation (S.D.) expressed in €/ha Table 7 - Summary statistics for EAEs - Yield Functions by levels of ecological factors (1% discount rate; yield estimations based on regional yield functions) Region Species Soil: Mineral Site classes S1 S2 S3 S4 Mean S.D. Mean S.D. Mean S.D. Mean S.D. South Pine 47.2 7.9 16.8 4.1 47.7 7.2 23.3 4.4 Spruce 147.2 19.8 113.3 15.5 27.0 5.7 1.5 2.1 Birch 21.8 4.7 12.7 3.8 3.9 3.1 -16.8 1.4 Other 40.8 7.0 9.8 3.8 - - - - North Pine 37.8 2.7 17.9 1.7 15.8 1.5 -10.0 0.4 Spruce 33.5 2.7 20.9 2.1 -17.0 0.4 -8.1 0.8 Birch -2.0 4.9 -8.4 1.9 -12.4 1.1 -16.9 1.5 Other -0.5 2.0 -9.5 1.7 - - - - Soil: Peat South Pine -19.8 1.9 -23.2 1.9 -20.8 1.7 -17.6 1.3 Spruce 113.5 2.0 37.3 1.4 4.0 1.3 10.1 1.3 Birch -7.5 1.6 -8.5 1.6 -16.1 1.5 -22.4 1.5 Other 5.4 1.8 -10.8 1.6 - - - - North Pine -6.5 1.1 -14.4 0.7 -14.4 0.7 -17.3 0.6 Spruce 31.6 2.1 2.6 0.7 -8.2 1.1 -6.7 1.1 Birch -14.0 2.1 -18.0 2.0 -22.1 1.9 -22.9 1.9 Other -18.1 2.0 - - - - - - NOTE: Mean and standard deviation (S.D.) expressed in € ha-1year-1. Master thesis - Author's personal copy Author: Valentin Ştefan 43 Table 8 - Summary statistics for NPVs - EFISCEN by levels of ecological factors (1% discount rate; yield estimations based on EFISCEN inventory database) Region Species Soil: Mineral Site classes S1 S2 S3 S4 Mean S.D. Mean S.D. Mean S.D. Mean S.D. South Pine 4,223 549 3,371 461 2,427 363 557 167 Spruce 6,016 811 4,143 597 1,333 274 29 112 Birch 1,776 292 1,321 254 380 161 -830 65 Other 2,512 388 1,084 253 - - - - North Pine 3,334 201 1,538 122 450 70 -14 47 Spruce 2,052 162 866 114 -836 30 - - Birch 60 221 -768 51 -1,054 32 -817 61 Other 258 90 -359 73 - - - - Soil: Peat South Pine -977 106 -1,100 104 -1,359 101 -1,215 85 Spruce 4,334 93 1,026 79 20 68 - - Birch -81 80 -245 78 -763 73 -926 74 Other -215 78 - - - - - - North Pine -517 75 -843 41 -1,032 46 -1,185 45 Spruce 740 67 -36 43 -352 73 - - Birch -648 88 -819 84 -956 80 - - Other -333 95 - - - - - - NOTE: Mean and standard deviation (S.D.) expressed in €/ha Table 9 - Summary statistics for EAEs - EFISCEN by levels of ecological factors (1% discount rate; yield estimations based on EFISCEN inventory database) Region Species Soil: Mineral Site classes S1 S2 S3 S4 Mean S.D. Mean S.D. Mean S.D. Mean S.D. South Pine 115.0 14.9 69.3 9.5 48.9 7.3 10.4 3.1 Spruce 146.8 19.8 88.0 12.7 28.9 5.9 0.5 2.0 Birch 37.3 6.1 27.7 5.3 8.0 3.4 -17.4 1.4 Other 52.8 8.1 22.8 5.3 - - - - North Pine 73.3 4.4 26.4 2.1 7.2 1.1 -0.2 0.7 Spruce 38.7 3.1 15.0 2.0 -13.9 0.5 - - Birch 1.4 5.2 -18.2 1.2 -25.0 0.8 -19.4 1.4 Other 6.1 2.1 -8.5 1.7 - - - - Soil: Peat South Pine -17.8 1.9 -20.0 1.9 -23.0 1.7 -18.7 1.3 Spruce 79.0 1.7 18.7 1.4 0.4 1.2 - - Birch -1.7 1.7 -5.1 1.6 -16.0 1.5 -19.4 1.6 Other -4.5 1.6 - - - - - - North Pine -8.0 1.2 -13.0 0.6 -15.1 0.7 -16.0 0.6 Spruce 13.8 1.3 -0.5 0.6 -5.1 1.0 - - Birch -15.4 2.1 -19.4 2.0 -22.7 1.9 - - Other -7.9 2.3 - - - - - - NOTE: Mean and standard deviation (S.D.) expressed in € ha-1year-1. Master thesis - Author's personal copy Author: Valentin Ştefan 44 3.2.2. Sensitivity of the equal annual equivalent (EAE) The discount rate considerably influenced the EAE profitability index. As expected, the average yearly return per hectare indicated by EAE decreased with increasing discount rate, independent of species, ecological factor or yield estimation method (Figure 18Figure 22). For Scots pine (Figure 18) the decline in profitability was exponential on sites with mineral soil and linear on peatlands. Stands on peatlands were not profitable at any discount rate. However, for MOTTI simulations, the southern stands on site class 1 with mineral soil were profitable even at a discount rate of five percent. Figure 18 - The EAE sensitivity of Scots pine to yield estimation method and discount rate by ecological factors. Master thesis - Author's personal copy Author: Valentin Ştefan 45 Differences in profitability level due to yield estimation methods were more distinct on mineral soils than on peatlands. The EAE on mineral soils was distinctively higher when considering the MOTTI yield estimations. On mineral soils, the EAE fell off when using the EFISCEN inventory database and decreased further for the estimations given by the regional yield functions. On mineral soils, differences in profitability due to yield estimation methods were more distinct on southern sites than on northern ones. Additionally, these differences became less distinct from site class 1 towards site class 4. This trend was more evident for southern forest stands, which on average, were more profitable. In the case of Norway spruce (Figure 19) the decrease in profitability was exponential both on mineral soil and peatlands. For the MOTTI simulations, all types of spruce stands were profitable at a discount rate of one percent, including stands on peatlands. Additionally, the southern stands on site class 1 with mineral soil were profitable even at a discount rate of five percent. These type of southern stands cover 2.8 million ha out of the 4.4 million ha of all spruce stands across Finland (Table 3). As in the case of pine, differences in profitability due to yield estimation methods were, on average, more distinct on mineral soils than on peatlands. However, for spruce the differences remained distinct for all stands on site class 1, independent of soil conditions. In contrast, for stands on site class 4 the differences in profitability were significantly less distinct. Note, however, that missing data in the EFISCEN inventory database did not allow the computation of profitability indices for some stands on site class 4. On the whole, the EAE was noticeably higher for MOTTI simulations. The EAE fell off roughly at the same level when using yield estimations given by both the EFISCEN inventory database and the regional yield functions. Thus, differences between the EAEs due to these two yield estimation methods were, on average, less distinguishable. As in the case of pine, on mineral soils, differences in profitability due to yield estimation methods were more distinct on southern sites than on northern ones. These differences became less distinct from site class 1 towards site class 4. Master thesis - Author's personal copy Author: Valentin Ştefan 52 MOTTI simulations EFISCEN inventory databse Regional yield functions Figure 24 - Spatial distribution of EAE for Finnish forests. Unprofitable Unprofitable Master thesis - Author's personal copy Author: Valentin Ştefan 53 MOTTI simulations EFISCEN inventory databse Regional yield functions Figure 25 - Profitability assessment for Finnish forests. Unprofitable Unprofitable Master thesis - Author's personal copy Author: Valentin Ştefan 54 4. Discussions In this study, a GIS-based approach was used for estimating and mapping the net present values and their equal annual equivalent across Finnish forests at a high spatial resolution (100×100 m). The computation required detailed information on forest stand growth, stand management and economic data (i.e. stumpage prices and management costs). The volume increment at the forest stand level was estimated in three ways: developing regional yield functions, using the EFISCEN inventory database and the MOTTI forest stand simulator. 4.1. Yield estimates, challenges Computing net present values is not possible without estimating the standing volume at various ages throughout the rotation. Other studies have also underlined the high importance of using growth and yield models mentioning the drawback regarding data availability (e.g. Yemshanov et al. 2007; Chan et al. 2011). However, it is worth mentioning that the task of fitting stand yield models was one of the greatest challenges in this study. An important limitation when estimating standing volumes with regional yield functions was that reliable models could not be computed for the group of species 'other broad-leaved' for all site conditions (Figure 15). In most cases observations were either completely lacking or their numbers were insufficient to allow fitting models (Appendix 8 - Figure 34 and 35). Other limitations are related to the statistical modelling per se and are discussed below, in section 4.2. The same issue regarding the lack of observations was also encountered for the EFISCEN inventory database. However, when modelling the stand growth with the MOTTI simulator it was possible to overcome the issue of insufficient data. The MOTTI forest stand simulator has been already used in studies of forest economic indicators across Finland. For example, Hynynen et al. (2005) used the MOTTI simulator to analyse the profitability (NPV) of different management scenarios in several types of spruce stands. Kojola et al. (2012) used MOTTI in a similar manner for Scots pine stands on drained peatlands. Master thesis - Author's personal copy Author: Valentin Ştefan 55 Ahtikoski et al. (2004) simulated the growth of silver birch stands with MOTTI in order to examine the NPV changes under the influence of alternative thinning intensities. Other forest growth simulators have also been used in studies related to forest stand profitability. For example, in the site conditions of southern Germany, Dieter (2001) simulated the growth of spruce and beech stands with an individual-tree growth model for calculating the land expectation value. To analyse the effects of climate change and management on timber yield and NPV, Garcia-Gonzalo et al. (2007) applied a processbased ecosystem model (FinnFor) for a forest management unit in Finland. Hanewinkel et al. (2010) used the distance-dependent, individual-tree growth simulator SILVA to evaluate the economic effects of a forest biome shift under climate change in southwest Germany. Generally, the profitability was higher when using the estimates returned by the MOTTI simulator than when using those based on the EFISCEN inventory database or the regional yield functions. Importantly, the differences between the values of the profitability indicators returned by the three yield estimation methods increased with site quality, that is, from peatlands to mineral soils, from site class S4 to S1 and also from north to south for each group of species (Figure 18 - Figure 21). This reflects the high impact of the yield estimation method on the final results, especially on sites of higher quality. These results concerning the variation in profitability are consistent with results from earlier studies. For instance, Holopainen et al. (2010) indicated that around one third of the observed variation in NPV was attributable to errors in growth predictions. They also reported a higher variation of NPVs at low discount rates. Similarly, in the present study the discrepancies between EAEs returned by different yield estimation methods increased with decreasing discount rate (Figure 18 - Figure 21). 4.2. Modelling regional yield functions Approximately 15.6 million stands dominated by pine, 4.4 with spruce, 3.3 dominated by birch and 0.4 with other broad-leaved tree species were considered for constructing regional yield functions based on the stand conditions at the time of inventory. Imposing conditions regarding the shares of stand volume occupied by the dominant Master thesis - Author's personal copy Author: Valentin Ştefan 56 species and also a canopy cover threshold resulted in a reduction of the abovementioned figures. These imposed thresholds were needed in order to stratify data into more homogenous layers and reduce the number of extreme values as much as possible. Additionally, these thresholds had to also be within the boundaries of the stand structures and compositions usually observed in situ. This aspect was partially accounted for by choosing flexible thresholds as described in section 2.2.3. In this study, the logistic and Gompertz sigmoid functions were used to model forest stand growth. In such studies it is common to log-transform the dependent variable. This operation is supposed to ensure a normal error distribution and also homogenize the variance, which sometimes tends to increase with age. However, in this study, the yield functions were fitted directly to the untransformed data of age (independent variable) and standing volume (dependent variable). There were several reasons behind the decision to use untransformed data. First, such linearizing transformations have been reported to lead to numeric problems in case of nonlinear regressions due to the complex error structure (Seber & Wild 2003). Second, maintaining the original scaling of the data was suggested to be more expressive (Seber & Wild 2003). Moreover, backtransforming the predicted yield values to the original scale also introduces a new source of bias into the analysis (Sprugel 1983). Third, it appears that a normal error distribution is not a strong prerequisite for the nonlinear least squares method (Seber & Wild 2003). The other issue concerning heteroscedasticity can be solved using weighted nonlinear least squares techniques (Bates & Watts 1988). All in all, it may be best to avoid transformations (Zuur et al. 2010). Consequently, in this study no transformations were applied and the estimates for the parameters were obtained with nonlinear least squares techniques. However, these advanced statistical techniques are not a panacea and come with the important cost of complexity. Nonlinear least squares techniques also require initial guesses for the starting parameter values. This can represent a drawback because the convergence algorithms used for computing parameter estimates sometimes fail because of the initial naive guesses. In this study, a solution to this problem was to gradually increase the number of iterations or the convergence tolerance. However, this indeed made convergence possible but with the cost of altering the standard errors of the parameter estimates. Master thesis - Author's personal copy Author: Valentin Ştefan 57 In the case of birch stands on northern site class 1, both on mineral soils and peatlands, certain heavily clustered observations were eliminated. Generally, these stands were characterized by low volumes at old ages, resulting in clusters of extreme values on the volume-age scatter plots. Removing these outlier-values was considered acceptable for the purpose of this study. It is highly probable that these observations belong to a particular species of birch or even aspen, therefore more accurate data based on further stratification should be considered in future studies. Both considered models (logistic or Gompertz) had significant parameter estimates, yet only one was selected for further inference. The choice was based both on AIC values and visual assessments of overor underfitting the data. As Burnham & Anderson (2002) suggest, a model with AIC > 10 has essentially no support for further consideration. In this study, if one of the models had an AIC up to 10 units bigger but obviously fitted the data better, then it was the one considered for further inference. All in all, model selection was not a purely mechanical operation based only on AIC. 4.3. Profitability of forest stands in Finland This study represents a unique approach for spatially valuating timber provisioning of Finnish forests at a 100×100 m resolution. Two profitability indices (NPV and EAE) were considered in this endeavour. However, other indices can be used in the costbenefit analysis of investments and further details related to the forestry sector are reviewed by Prokofieva & Thorsen (2011). The reasoning behind choosing the NPV and EAE were provided in the Introduction. Generally, the results suggest a major influence of the soil type (mineral or peat) on profitability indices, independent of species, discount rates or the method used for yield estimation. Under the tested management guidelines, stands on mineral soils were more profitable than stands on peatlands. Even though not profitable for timber production, stands located on peatlands are still valuable given their capacity of carbon assimilation, their role in biodiversity conservation and through the provision of other ecosystem services. Indeed, peatland ecosystems are regarded as the most efficient carbon sink on Master thesis - Author's personal copy Author: Valentin Ştefan 58 the planet (Hugron et al. 2013). Future research should urgently consider the valuation of such non-timber ecosystem services. In this study, only a management scenario with no thinnings before the final cutting was considered for the species’ groups Scots pine, birch and other broad-leaved on peatlands (Figure 17; Appendix 10). Kojola et al. (2012) suggested that such a 'passive regime' would severely impact the profitability of Scots pine. On peatlands, a management scenario with thinnings was considered only for spruce. Overall, according to the output from the MOTTI simulator, spruce remained the only profitable species on peatlands at a discount rate of one percent (Figure 19). These results suggest a positive impact of thinnings on the profitability of stands on peatlands. Generally, this underlines the high influence of the management scheme on stand profitability. This is an important factor which was tackled by many studies (e.g. Ahtikoski et al. 2004; Hynynen et al. 2005; Yemshanov et al. 2007; Kojola et al. 2012). The profitability also decreased from south to north. Even if unprofitable peatlands are dominating the north (Figure 4B; Figure 25), the profitability decrease in northern forests was also observed on mineral soils. Whereas the silvicultural costs were slightly lower in the three forestry centres of the northern region, timber prices were slightly lower as well (Appendix 2). The main factor consists probably in the less favourable growing conditions, reflected in lower yield estimates (Figure 17). On the profitability maps the border between south and north appears to be very sharp (Figure 23 - Figure 25). Additionally, the central area of the southern region was the most profitable. This may be, however, relate to the strong presence of Norway spruce in that region (Figure 5A). The comparison between species (Figure 22) revealed the influence of yield estimates and management on profitability (Figure 17). Overall, spruce was the most profitable species, followed by pine, but only on mineral soils (Figure 22). Moreover, the average stumpage prices were slightly higher for spruce than for pine (Appendix 2). These results are consistent with other valuation studies. For instance, Triviño et al. (2015) found that in the conditions of Central Finland the best stands for providing harvest revenues and carbon services (storage and sequestration) were those dominated by spruce. Master thesis - Author's personal copy Author: Valentin Ştefan 59 The results of the sensitivity analysis regarding the influence of the discount rate on the profitability of each species under 16 different site conditions across Finland could be useful to inform decision makers. Target policies could be related to conservation incentives programs. For instance, Juutinen et al. (2008) suggested that timber value maps can inform policy makers in the process of designating potential conservation areas. For example, policy makers could use the monetary value of the timber as an estimate for the opportunity cost of introducing harvesting restrictions or even stopping management on a particular site. Nevertheless, all forest ecosystem services should be considered in such appraisals. Further arguments are provided in the section 4.5 below. Despite considering detailed forest stand simulations, current management guidelines, the variation of growth conditions, discount rates and the spatial variation of costs and stumpage prices, the approach proposed in this study has several limitations. For instance, inherent fluctuations of the timber assortment price during a management cycle were not considered. A simple approach to integrate such variability was suggested by Ojea et al. (2012), who make the simplifying assumption that stumpage prices rise annually by a constant rate. However, the impact of price fluctuations on the final profitability results is probably smaller than that of yield estimates (Holopainen et al. 2010). Moreover, Hynynen et al. (2005) showed that changes in future stumpage prices do not significantly alter the financial ranking of alternative management schedules. The approach used in the current study also ignores the possible occurrence of hazards like wind, snow, fire, grazing, insect and fungi, which would imply additional costs. For instance, Dieter (2001) included the impact of storm and insects in his economic simulations. Another concern is related to the possible transfer and applicability of the proposed approach to other conditions than the ones of Finnish forest. Generally, the restricted access to detailed forest growth and economic data represents a serious limitation, an issue already under debate in other studies (e.g. Pearce 2001; Yemshanov et al. 2007; Ojea et al. 2012). Note that in the approach used in this study the cash flows were computed only for pure even-aged stands with a clear cut at the end of the management cycle followed always by an artificial regeneration. All mixed stands were modelled as pure stands dominated by the species with the highest share of standing volume. Such simplifying assumptions were unavoidable considering the complex dynamics of mixed stands and the limited scope of this study. However, considering their growing importance worldwide, an important Master thesis - Author's personal copy Author: Valentin Ştefan 60 goal of future studies should be to integrate complex and more flexible cash flows adapted to mixed stands. It is also worth mentioning that in Finland pure stands 8 represent around 55% of the total forest land and stands with a low degree of mixing 9 represent 31% (METLA 2012a). 4.4. The 'sustainable' discount rate Hepburn & Koundouri (2007) mentioned that there is an important academic debate with respect to choosing the 'right' discount rate. They criticized the fact that this rate is kept constant over time and recommended using a declining one due to the uncertainty of future economic conditions. They showed that differences in computing NPV based on constant discount rates and computing NPV based on declining discount rates are significant. The highest impact is on long forest management cycles for which the NPV can be negative for constant discount rates, making long term investments not profitable and therefore posing threats to sustainability. The results of this study are consistent with such critics. For instance, the default MOTTI management scenario for pine stands on peatlands suggests a higher age for the final cut than for any other species (Figure 17 or Appendix 10). However, pine stands are the worst in terms of profitability on southern peatlands and it gets worse at higher constant discount rates. Moreover, the lack of thinning aggravates the situation, as already discussed. As a result of this debate, many authors embraced the approach of running a sensitivity analysis, that is, calculations are done for several discount rates. The Eurostat pilot programme in forest accounting suggested a range between 0.5 and 3.5% for European forests (Eurostat 2000). In the most recent appraisal guide, the European Commission suggested a range between 2.8 and 7.7% for the social discount rate within the EU member states with the specification that ‘France, Germany and the UK have autonomously adopted values for their national projects’ (Table B.2, EC 2008 p. 209). It is reasoned that considering higher discount rates should results in a better evaluation of competing investments (EC 2008; Prokofieva & Thorsen 2011). However, for forest investments it has been observed that high and constant discount rates tend to reduce 8 Dominant species’ share of stand total volume is over 95%. 9 Dominant species’ share of stand total volume is between 75 and 95%. Master thesis - Author's personal copy Author: Valentin Ştefan 61 the incentives for long term investments, resulting in lower harvesting ages, which in turn contradicts the sustainable forest management concept (Hepburn & Koundouri 2007; Ojea et al. 2012). 4.5. Further valuating other ecosystem services The present thesis focuses only on the economic valuation and mapping the economic value of timber provisioning. Even though is easier to value timber provision, other forest ecosystem services need to be considered because all ecological functions of forests are equally economic functions (Pearce 2001). Furthermore, many authors underlined the fact that numerous goods and services remain unvalued and ignored in economic decision-making (e.g. Costanza et al. 1997; Navrud & Pruckner 1997; Krieger 2001; Pearce 2001; Bateman et al. 2003; Maes et al. 2012; Snowdon & Harou 2013). However, valuating such goods and services is a very challenging task. On the one hand, because it requires very good knowledge and understanding of ecosystem services (Troy & Wilson 2006). On the other hand, because their benefits often returns almost entirely to local communities, making it hard to quantify their value in economic units per hectare (Pearce 2001). This also offers a justification for policies that conserve local forests ecosystems to better focus on the local context and values (Ninan & Inoue 2013). However, as discussed by Costanza et al. (1997), ecosystem services can also be considered to have an infinite value to humankind, rendering their valuation to a superfluous act. All in all, further research needs to address the complex issue of valuating and mapping the economic value of other forest ecosystem services (e.g. Häyhä et al. 2015). Master thesis - Author's personal copy Author: Valentin Ştefan 68 Forestry, 10, pp.53–66. Sprugel, D.G., 1983. Correcting for bias in log-transformed allometric equations. Ecology, 64(1), pp.209–210. Straka, T., 2007. Valuation of bare forestland and premerchantable timber stands in forestry appraisal. Journal of American Society of Farm Managers and Rural Appraisers, 70, pp.142–146. Tervo, L., 2000. Technical Development in Forest Regeneration in Finland. Baltic Forestry, 6(1), pp.68–73. Tomppo, E. et al., 2011. The Multi-source National Forest Inventory of Finland – methods and results 2011. Working Papers of the Finnish Forest Research Institute, 319, p.224. Triviño, M. et al., 2015. Managing a boreal forest landscape for providing timber, storing and sequestering carbon. Ecosystem Services [In Press], p.11. Available at: http://linkinghub.elsevier.com/retrieve/pii/S2212041615000212. Troy, A. & Wilson, M.A., 2006. Mapping ecosystem services: Practical challenges and opportunities in linking GIS and value transfer. Ecological Economics, 60(2), pp.435–449. UK NEA, 2014. The UK National Ecosystem Assessment (UK NEA). Available at: http://uknea.unep-wcmc.org/. Vera Sit, Melanie Poulin-Costello, W.B., 1994. Catalogue of curves for curve fitting, Forest Science Research Branch, Ministry of Forests. Yemshanov, D. et al., 2007. An integrated spatial assessment of the investment potential of three species in southern Ontario, Canada inclusive of carbon benefits. Forest Policy and Economics, 10, pp.48–59. Yi, Z.-F., Wong, G., et al., 2014. Can carbon-trading schemes help to protect China’s most diverse forest ecosystems? A case study from Xishuangbanna, Yunnan. Land Use Policy, 38, pp.646–656. Yi, Z.-F., Cannon, C.H., et al., 2014. Developing indicators of economic value and biodiversity loss for rubber plantations in Xishuangbanna, southwest China: A case study from Menglun township. Ecological Indicators, 36, pp.788–797. Ylitalo, E., 2011. Finnish statistical yearbook of forestry, Finnish Forest Research Institute. Yrjölä, T., 2002. Forest management guidelines and practices in Finland, Sweden and Norway. EFI Internal Report No. 11, European Forest Institute. Zuur, A.F., Ieno, E.N. & Elphick, C.S., 2010. A protocol for data exploration to avoid common statistical problems. Methods in Ecology and Evolution, 1(1), pp.3–14. Master thesis - Author's personal copy Author: Valentin Ştefan 69 Appendix Appendix 1. Extracts from metadata of MS-NFI 2011 Extract regarding the theme 'Total volume': 'The volume of a tree is defined as the volume of the stem wood above stump until the top of the tree. [...]. The unit and class interval of the volume is 1 m3/ha [...].' Extract regarding the theme 'Canopy cover': 'The canopy cover of trees is the vertical projection area on the horizontal plane of the canopies of the individual trees on a field plot (without double counting the overlapping canopies). In NFI10, it was assessed in the field as a shares (0-99%) on a fixed radius plot. For the NFI11 plots, it was estimated using k-NN method and the NFI10 plot data. [...] The canopy cover proportion of broad-leaved trees is derived from the total cover using the volume of the growing stock. However, in the seedling stands, the canopy cover of broad leaved trees is assessed using the shares of the stem numbers.' Extract regarding the theme 'Age': 'The age of the growing stock on a forest stand is the weighted average of the trees, the basal area of the tree as the weight. The age is assessed in the field for the field plot stands on forest land and poorly productive forest land in the classes of one year.' Appendix 2. Unit costs and average stumpage prices Table 10 - Unit costs of silvicultural and forest improvement work, 2010 (€/ha). A = Non-industrial, private, etc.; B = Forest industries and state Forestry centre Clearing of regeneration areas Disc trenching Mounding Planting Improvement of young stands A B A B A B A B A B Whole country 157 128 168 162 317 304 692 630 359 477 0 Ahvenanmaa - - - - 261 - 925 - 295 - 1 Rannikko 163 117 167 200 347 324 712 615 373 510 2 Lounais-Suomi 160 138 184 196 344 352 715 653 406 524 3 Häme-Uusimaa 189 161 203 214 334 381 785 714 388 515 4 Kaakkois-Suomi 195 126 220 187 341 320 618 638 295 495 5 Pirkanmaa 223 171 193 206 312 373 719 764 390 519 6 Etelä-Savo 193 113 175 206 318 339 707 649 344 478 7 Etelä-Pohjanmaa 173 121 172 145 321 342 676 616 407 501 8 Keski-Suomi 159 166 185 215 321 360 698 679 297 506 9 Pohjois-Savo 270 129 156 197 314 327 735 633 365 451 10 Pohjois-Karjala - 129 - 218 - 322 - 604 - 430 11 Kainuu 195 106 141 149 302 307 633 671 251 481 12 Pohjois-Pohjanmaa 93 125 165 143 274 280 550 584 380 500 13 Lappi 89 131 148 160 311 237 651 581 358 454 Source: Finnish statistical yearbook of forestry (Ylitalo 2011) Master thesis - Author's personal copy Author: Valentin Ştefan 70 Table 11 - Average stumpage prices in non-industrial, private forests by forestry centre, 2010 (€/m3) Forestry centre Logs Pulpwood Pine Spruce Birch Pine Spruce Birch Whole country 54.03 55.17 39.43 15.52 18.61 15.45 0 Ahvenanmaa 35.22 34.35 28.14 11.04 13.18 8.77 1 Rannikko 54.55 54.89 38.39 15.49 19.37 15.45 2 Lounais-Suomi 55.33 56.20 35.81 15.73 19.76 15.35 3 Häme-Uusimaa 54.70 55.63 39.55 14.66 19.26 15.00 4 Kaakkois-Suomi 54.29 55.19 39.16 15.19 18.72 14.66 5 Pirkanmaa 54.59 55.83 37.99 15.30 19.44 15.25 6 Etelä-Savo 53.77 53.99 40.51 14.75 17.86 14.74 7 Etelä-Pohjanmaa 54.42 55.97 37.34 16.03 19.06 16.34 8 Keski-Suomi 53.54 55.12 39.93 15.00 18.31 15.24 9 Pohjois-Savo 53.67 55.37 38.91 14.89 17.74 15.21 10 Pohjois-Karjala 55.18 56.15 40.16 15.81 18.04 14.94 11 Kainuu 55.32 54.25 36.61 16.53 18.93 15.80 12 Pohjois-Pohjanmaa 53.31 53.35 37.16 16.35 18.69 16.65 13 Lappi 49.34 48.55 - 16.08 19.42 15.80 Source: Finnish statistical yearbook of forestry (Ylitalo 2011) Appendix 3. Geoprocessing the NUTS 2010 dataset Table 12 - Aggregation of NUTS 2010 units into forestry centres - correspondence between forestry centres and NUTS 2010 codes Forestry centre NUTS 2010 code 0 Ahvenanmaa FI200 1 Rannikko FI195; F1B1 2 Lounais-Suomi FI196; FI1C1 3 Häme-Uusimaa FI1C2; FI1C3 4 Kaakkois-Suomi FI1C5; FI1C4 5 Pirkanmaa FI197 6 Etelä-Savo FI1D1 7 Etelä-Pohjanmaa FI194; FI1D5 8 Keski-Suomi FI193 9 Pohjois-Savo FI1D2 10 Pohjois-Karjala FI1D3 11 Kainuu FI1D4 12 Pohjois-Pohjanmaa FI1D6 13 Lappi FI1D7 Displacement adjustment with the 'Shift' tool: In the case of the raster dataset depicting northern and southern Finland, the X coordinates were shifted by -25.3525 m and the Y coordinates by -35.8734 m. For the raster dataset depicting the 14 forestry centres, the X coordinates had to be shifted by -11.3605402 m and the Y coordinates by -29.21625 m. Master thesis - Author's personal copy Author: Valentin Ştefan 71 Appendix 4. Geoprocessing the soil raster dataset Displacement adjustment with the 'Shift' tool: The software required precise number of digit after decimal point: X coordinates were shifted by 13.8471929 m and Y coordinates by -45.85521 m. Filling the mismatching gaps with estimated neighboring soil values: The 'Focal Statistics' tool was applied, computing the 'majority' statistics within a 11 km radius circle neighborhood around each water body cell. The 'majority' statistics type computes the most frequent value of the cells within the neighborhood area. A mismatching example is given below in Figure 26. Figure 26 - Overlapping imperfections between MS-NFI and soil raster datasets. The MS-NFI datasets have a spatial resolution of 100×100 m and the soil is given at 1×1 km. The procedure involved the separation of all null values (includes water bodies) as polygons (Figure 27A) and then computing their area and perimeter. The next step was computing the radius that satisfied the corresponding circle of given area and given perimeter of each polygon. First step was to transform all null pixel values to zero and this was done by using the 'Raster Calculator' with the expression Con(IsNull("Soil_raster"), 0, "Soil_raster"). Then all zero values were extracted as a separate raster dataset by using the 'Extract by Attributes' tool with the expression Value = 0. Further, the raster dataset was transformed to a polygon feature dataset using the 'Raster to Polygon' tool. The attribute table of the new feature was exported as *.csv file and processed in Excel and the radiuses were computed as mentioned above. For each polygon of area (A) and perimeter (P), the radius that satisfies the circle of given area A and given perimeter P is R=2A/P. The maximum radius was around 5.5 km and its double size of 11 km was considered for computing in 'Focal Statistics'. Further, the 'Focal Statistics' raster output (hereafter: soil_FS_rst) was resampled from 1×1 km to 100×100 m resolution. Then a 'Raster Calculator' conditional statement was used to replace the water bodies values of the initial soil raster dataset (hereafter: soil_gaps_rst) with the values derived from the neighboring cell values (from soil_FS_rst - Figure 27B). The conditional statement used was Con(IsNull("soil_gaps_rst"), " soil_FS_rst", "soil_gaps_rst"). MS-NFI dataset soil raster dataset Water body Master thesis - Author's personal copy Author: Valentin Ştefan 72 Figure 27 - Intermediate raster datasets for filling the soil gaps. A) Null values and water bodies; B) Soil classes after applying the 'Focal Statistics' tool. Appendix 5. Python script for defining dominant species stands # Import required libraries and modules import arcpy import os import numpy from arcpy import env from arcpy.sa import * # Set environment settings (provide path to the workspace - geodatabase) env.workspace = "F:\EFI\Server\Finland\Finland1ha.gdb" # Set local variables (the total volume raster datasets) spruce = arcpy.Raster('F:\EFI\Server\Finland\Finland1ha.gdb\VTotRealSpruce1ha') pine = arcpy.Raster('F:\EFI\Server\Finland\Finland1ha.gdb\VTotRealPine1ha') birch = arcpy.Raster('F:\EFI\Server\Finland\Finland1ha.gdb\VTotRealBirch1ha') othersp = arcpy.Raster('F:\EFI\Server\Finland\Finland1ha.gdb\VTotRealOtherSp1ha') # Create a list with the above local variables (raster datasets) # - takes all raster datasets from geodatabase (which was set in env.workspace) which start with 'VTotReal' rstlist = arcpy.ListRasters("VTotReal*", "All") # Compute maximum pixel value from the list ' rstlist' maxrst = CellStatistics(rstlist, "MAXIMUM", "DATA") # Save the result raster with changing the pixel depth for optimal memory usage arcpy.CopyRaster_management(maxrst, "F:\EFI\Server\Finland\Finland1ha.gdb\MaxVol", "DEFAULTS", "0", "", "", "", "16_BIT_UNSIGNED") # Attribute the saved raster to a variable (maxrst) maxrst = arcpy.Raster('F:\EFI\Server\Finland\Finland1ha.gdb\MaxVol') # Using the conditional function ('con'): if maximum volume equals given species total volume, then return corresponding species code; otherwise NoData will be returned. The commands will output raster datasets for each dominant species. arcpy.CopyRaster_management((Con((spruce - maxrst) == 0, 1)), "F:\EFI\Server\Finland\Finland1ha.gdb\LogicDominSpruce1ha", "DEFAULTS", "0","","","","16_BIT_UNSIGNED") A) B) Master thesis - Author's personal copy Author: Valentin Ştefan 73 arcpy.CopyRaster_management((Con((pine - maxrst) == 0, 10)), "F:\EFI\Server\Finland\Finland1ha.gdb\LogicDominPine1ha", "DEFAULTS", "0","","","","16_BIT_UNSIGNED") arcpy.CopyRaster_management((Con((birch - maxrst) == 0, 100)), "F:\EFI\Server\Finland\Finland1ha.gdb\LogicDominBirch1ha", "DEFAULTS", "0","","","","16_BIT_UNSIGNED") arcpy.CopyRaster_management((Con((othersp - maxrst) == 0, 1000)), "F:\EFI\Server\Finland\Finland1ha.gdb\LogicDominOtherSp1ha", "DEFAULTS", "0","","","","16_BIT_UNSIGNED") # Create a list with the dominant species raster datasets (previously defined) # - takes all raster datasets from geodatabase which start with ' LogicDomin' rstlistLogic = arcpy.ListRasters("LogicDomin*", "All") # Sum up the cell values (containing species codes) LogicSum = CellStatistics(rstlistLogic, "SUM", "DATA") # Save the sum raster dataset arcpy.CopyRaster_management(LogicSum, "F:\EFI\Server\Finland\Finland1ha.gdb\LogicSumVol", "DEFAULTS", "0","","","","16_BIT_UNSIGNED") # A reclassification was done using Reclassify tool (not used as script but in the GUI) # - raster LogicSumVol becomes LogicSumVol4Sp # - reclassification tackled those stands were more than one species was dominant (species having same maximum standing volume) # 11=1 (pine & spruce becomes spruce stand), # 101=100 (birch & spruce becomes birch stand), # 110=100 (birch & pine becomes birch stand) , # 111=100 (birch & pine & spruce becomes birch stand), # 1001=1000 (other broad-leaved & spruce becomes other broad-leaved stand), # 1010=1000 (other broad-leaved & pine becomes other broad-leaved stand), # 1011=1000 (other broad-leaved & pine & spruce becomes other broad-leaved stand), # 1100=100 (other broad-leaved & birch becomes birch stand), # 1101=100 (other broad-leaved & birch & spruce becomes birch stand), # 1110=100 (other broad-leaved & birch & pine becomes birch stand), # 1111=100 (other broad-leaved & birch & pine & spruce becomes birch stand) # Attribute the reclassification raster previously created to a variable (LogicSum) LogicSum = arcpy.Raster('F:\EFI\Server\Finland\Finland1ha.gdb\LogicSumVol4Sp') # Assign final codes: #1 - birch #2 - pine #3 - spruce #4 - other broad-leaved arcpy.CopyRaster_management((Con(LogicSum==1, 3, Con(LogicSum==10, 2, Con(LogicSum==100, 1, Con(LogicSum==1000, 4))))), "F:\EFI\Server\Finland\Finland1ha.gdb\Species_code", "DEFAULTS", "0","","","","8_BIT_UNSIGNED) Appendix 6. Python script for selecting stands with a certain volume proportional share of the dominant species # The script will sum up all species by total volume. Then compares the ratio between species volume and the summed volume with a certain threshold. If the ratio is above the threshold then the forest stand is selected. # Import required libraries and modules import arcpy import os import numpy from arcpy import env from arcpy.sa import * # Set environment settings (provide path to the workspace - geodatabase) env.workspace = "F:\EFI\Server\Finland\Finland1ha.gdb" # Set local variables spruce = arcpy.Raster('F:\EFI\Server\Finland\Finland1ha.gdb\VTotRealSpruce1ha') pine = arcpy.Raster('F:\EFI\Server\Finland\Finland1ha.gdb\VTotRealPine1ha') birch = arcpy.Raster('F:\EFI\Server\Finland\Finland1ha.gdb\VTotRealBirch1ha') othersp = arcpy.Raster('F:\EFI\Server\Finland\Finland1ha.gdb\VTotRealOtherSp1ha') # Create a list with the above local variables (raster datasets) # - takes all raster datasets from geodatabase (which was set in env.workspace) which start with 'VTotReal' rstlist = arcpy.ListRasters("VTotReal*", "All") # Sum up the total volume of all species arcpy.CopyRaster_management(CellStatistics(rstlist, "SUM", "DATA"), "F:\EFI\Server\Finland\Finland1ha.gdb\VolSumAllSp", "DEFAULTS", "0","","","","16_BIT_UNSIGNED") # Attribute the summation volume raster to a variable (SumVol) SumVol = arcpy.Raster('F:\EFI\Server\Finland\Finland1ha.gdb\VolSumAllSp') # Transform the summation raster dataset from 32 bit to 16 bit pixel depth (for memory usage) Master thesis - Author's personal copy Author: Valentin Ştefan 74 arcpy.CopyRaster_management(SumVol, "F:\EFI\Server\Finland\Finland.gdb\SumVol", "DEFAULTS", "0","","","","16_BIT_UNSIGNED") # Assign value 1 to NoData in SumVol raster dataset arcpy.CopyRaster_management(Con(IsNull(SumVol), 1, SumVol), "F:\EFI\Server\Finland\Finland.gdb\SumVol_1ND", "DEFAULTS", "0","","","","16_BIT_UNSIGNED") # Overwrite SumVol raster dataset with the output raster of previous command SumVol = arcpy.Raster('F:\EFI\Server\Finland\Finland.gdb\SumVol_1ND') # At cell level if sum of volumes is different from 1 (representing NoData) then divide species volume by sum volume. 'Divide' function was used in order to have real number division (otherwise is truncated). If the ratio is above a certain threshold then retrieve the pixel value (volume) otherwise NoData will be attributed by default. # Depending on the value of the threshold the following type of stands were considered: pure (95%), stand with some mixing (75%), mixed stands (50%) # For Scots pine on sites 1, 2 and 3 the proportional share of the dominant species of the volume was set to over 95%, consequently defining pure stands arcpy.CopyRaster_management(Con(SumVol != 1, Con(Divide(Float(pine),Float(SumVol)) >= Float(0.95), pine)), "F:\EFI\Server\Finland\Finland1ha.gdb\VolPurePine", "DEFAULTS", "0","","","","16_BIT_UNSIGNED") # For Scots pine on some sites 4, due to reduced number of stands, the threshold of 75% was used for defining stand with some mixing arcpy.CopyRaster_management(Con(SumVol != 1, Con(Divide(Float(pine),Float(SumVol)) >= Float(0.75), pine)), "F:\EFI\Server\Finland\Finland1ha.gdb\VolPurePine_75", "DEFAULTS", "0","","","","16_BIT_UNSIGNED") # For Norway spruce on sites 1, 2 and 3, the threshold of 75% was used for defining stand with some mixing arcpy.CopyRaster_management(Con(SumVol != 1, Con(Divide(Float(spruce),Float(SumVol)) >= Float(0.75), spruce)), "F:\EFI\Server\Finland\Finland1ha.gdb\VolPureSpruce_75", "DEFAULTS", "0","","","","16_BIT_UNSIGNED") # For Norway spruce on sites 4, due to reduced number of stands, the threshold of 50% was used for defining mixed stands arcpy.CopyRaster_management(Con(SumVol != 1, Con(Divide(Float(spruce),Float(SumVol)) >= Float(0.50), spruce)), "F:\EFI\Server\Finland\Finland1ha.gdb\VolPureSpruce_50", "DEFAULTS", "0","","","","16_BIT_UNSIGNED") # For birch on all four sites the threshold of 75% was used for defining stand with some mixing arcpy.CopyRaster_management(Con(SumVol != 1, Con(Divide(Float(birch),Float(SumVol)) >= Float(0.75), birch)), "F:\EFI\Server\Finland\Finland1ha.gdb\VolPureBirch_75", "DEFAULTS", "0","","","","16_BIT_UNSIGNED") # For other broad-leaved species on sites class 1 and some sites class 2 the threshold of 75% was used for defining stand with some mixing arcpy.CopyRaster_management(Con(SumVol != 1, Con(Divide(Float(othersp),Float(SumVol)) >= Float(0.75), othersp)), "F:\EFI\Server\Finland\Finland1ha.gdb\VolPureOtherSp_75", "DEFAULTS", "0","","","","16_BIT_UNSIGNED") # For other broad-leaved species on some sites class 2, sites class 3 and 4 the threshold of 50% was used for defining mixed stands arcpy.CopyRaster_management(Con(SumVol != 1, Con(Divide(Float(othersp),Float(SumVol)) >= Float(0.50), othersp)), "F:\EFI\Server\Finland\Finland1ha.gdb\VolPureOtherSp_50", "DEFAULTS", "0","","","","16_BIT_UNSIGNED") Appendix 7. R script for nonlinear yield functions modelling # Get the path of the txt file that contains the tabulation of volume by age. The file represents the output of Tabulate Area (Spatial Analyst) tool from ArcGis path <- file.choose() # Read the content of the txt file data <- read.table(file=path, dec=".", sep=",", header=T) # Check for type of format str(data) # Convert factor to numeric for convenience considering that comma is used as thousands separator within the factor data <- sapply(data, function(f) {as.numeric(gsub(",","", as.character(f)))}) # Convert back from matrix to data frame (previous sapply function creates matrices) data <- data.frame(data) # Obtain the number of pixels (frequencies) by dividing with 10 000 m2 (100*100 m2) # the columns OBJECTID & VALUE should not be affected by the operation, therefore they are saved separately objectid <- data$OBJECTID value <- data$VALUE data <- round(data/(100*100)) data$OBJECTID <- objectid data$VALUE <- value # Transform the original contingency table to frequency table # import required libraries (packages) Master thesis - Author's personal copy Author: Valentin Ştefan 75 library(data.table) library(stringr) library(reshape2) # convert data frame to data table mydata <- as.data.table(melt(data, na.rm=T, id=c("OBJECTID","VALUE"), variable.name="Vol", value.name="Count")) # convert string to numeric for convenience mydata[,Vol := as.numeric(str_sub(Vol, start=7, end=9))] # order by VALUE and Vol columns setkey(mydata, OBJECTID, Vol) # generate an index column (key) mydata[, num := 1:.N] mydata <- mydata[rep(num, Count)] Ytbl <- mydata[,list(OBJECTID, VALUE, Vol)] setnames(Ytbl, "VALUE", "Age") # -------------------------------------------------------------------------------------- # Nonlinear regression # Import required libraries (packages) library("nls2") # Plot the cloud of points corresponding to the volume - age pairs windows(record=T) plot(Ytbl$Vol~Ytbl$Age, xlab="Age", ylab="Vol") # ---------------------------- # Logistic model # Self starting Logistic model # ---------------------------- logistic.nls <- nls(Vol ~ SSlogis(Age, Asym, xmid, scal), data=Ytbl) # when convergence problems occur then try to adjust some convergence factors logistic.nls <- nls(Vol ~ SSlogis(Age, Asym, xmid, scal), data=Ytbl, control=nls.control(tol=0.1)) # display the regression's summaries summary(logistic.nls) # test if residuals are normally distributed (Kolmogorov-Smirnov Test) ks.test(residuals(logistic.nls, type="pearson"), "pnorm") # test if the average of the residual is statistically different from zero t.test(residuals(logistic.nls, type="pearson")) # display the nonlinear model dummy.age <- with(Ytbl, seq(1, 100,1)) lines(dummy.age, predict(logistic.nls, newdata=data.frame(Age=dummy.age)), col="red", lwd=2) # Logistic model with starting values # ------------------------------------ equation <- Vol ~ Asym/(1+exp((xmid-Age)/scal)) start.values <- data.frame(Asym = c(20,40), xmid = c(15,30), scal = c(1,6)) # search for an approximate model with starting values model.trial <- nls2(equation, start=start.values, data=Ytbl, algorithm="random-search", control=nls.control(maxiter = 100)) # use the best guessed starting values to attempt fitting a model to the data logistic.nls2 <- nls2(equation, start=model.trial, data=Ytbl) # when convergence problems occur then try to adjust some convergence factors logistic.nls2 <- nls2(equation, start=model.trial, data=Ytbl, control=nls.control(tol=0.5)) # display the regression's summaries summary(logistic.nls2) # test if residuals are normally distributed (Kolmogorov-Smirnov Test) ks.test(residuals(logistic.nls2, type="pearson"), "pnorm") # test if the average of the residual is statistically different from zero t.test(residuals(logistic.nls2, type="pearson")) # display the nonlinear model dummy.age <- with(Ytbl, seq(1, 100,1)) lines(dummy.age, predict(logistic.nls2, newdata=data.frame(Age=dummy.age)), col="red", lwd=2) # ----------------------------- # Gompertz model # Self starting Gompertz model # ----------------------------- gompertz.nls <- nls(Vol ~ SSgompertz(Age, Asym, b2, b3), data=Ytbl) # when convergence problems occur then try to adjust some convergence factors gompertz.nls <- nls(Vol ~ SSgompertz(Age, Asym, b2, b3), data=Ytbl, control=nls.control(tol=0.1)) # display the regression's summaries summary(gompertz.nls) # test if residuals are normally distributed (Kolmogorov-Smirnov Test) ks.test(residuals(gompertz.nls, type="pearson"), "pnorm") # test if the average of the residual is statistically different from zero t.test(residuals(gompertz.nls, type="pearson")) Master thesis - Author's personal copy Author: Valentin Ştefan 76 # display the nonlinear model dummy.age <- with(Ytbl, seq(1, 100,1)) lines(dummy.age, predict(gompertz.nls, newdata=data.frame(Age=dummy.age)), col="green", lwd=2) # Gompertz model with starting values # ------------------------------------ equation2 <- Vol ~ Asym*exp(-b2*b3^Age) # starting values should be adjusted accordingly start.values <- data.frame(Asym = c(70,90), b2 = c(3,10), b3 = c(0.9,1)) # search for an approximate model with starting values model.trial <- nls2(equation2, start=start.values, data=Ytbl, algorithm="random-search", control=nls.control(maxiter = 100)) # use the best guessed starting values to attempt fitting a model to the data gompertz.nls2 <- nls2(equation2, start=model.trial, data=Ytbl) # when convergence problems occur then try to adjust some convergence factors gompertz.nls2 <- nls2(equation2, start=model.trial, data=Ytbl, control=nls.control(tol=0.5)) # display the regression's summaries summary(gompertz.nls2) # test if residuals are normally distributed (Kolmogorov-Smirnov Test) ks.test(residuals(gompertz.nls2, type="pearson"), "pnorm") # test if the average of the residual is statistically different from zero t.test(residuals(gompertz.nls2, type="pearson")) # display the nonlinear model dummy.age <- with(Ytbl, seq(1, 100,1)) lines(dummy.age, predict(gompertz.nls2, newdata=data.frame(Age=dummy.age)), col="green", lwd=2) # ----------------------------- # Compare models using AIC AIC(gompertz.nls, logistic.nls) # compute AIC difference AIC(logistic.nls) - AIC(gompertz.nls) # Extract the RMSEs of the models summary(gompertz.nls)$sigma summary(logistic.nls)$sigma # ----------------------------- # Create the final yield table # choose the desired model vol.tbl <- predict(gompertz.nls, newdata=data.frame(Age=dummy.age)) YtblFinal <- data.frame(dummy.age, vol.tbl) # save the table as TAB delimited *.txt file write.table(YtblFinal, "D:/R/Yield/Table.txt", sep="\t") # save the coefficients of the Logistic and Gompertz models on the storage device Master thesis - Author's personal copy Author: Valentin Ştefan 77 Appendix 8. Regional yield curves Site class Northern region - mineral soil Northern region - peatland 1 Share of stand volume: 95%; Canopy cover: 45% Share of stand volume: 95%; Canopy cover: 50% 2 Share of stand volume: 95%; Canopy cover: 65% Share of stand volume: 95%; Canopy cover: 60% 3 Share of stand volume: 95%; Canopy cover: 50% Share of stand volume: 95%; Canopy cover: 40% 4 Share of stand volume: 95%; Canopy cover: 10% Share of stand volume: 75%; Canopy cover: 10% Figure 28 - Yield curves for Scots pine in northern region. NOTE: The first percent value represents dominant species’ share of stand total volume. The second percent value represents the minimum canopy cover of the stands analysed for building the yield curve (corresponds to the third quartile of the canopy cover distribution). Age is expressed in years and standing volume ('Vol') in m3/ha. Logistic model is represented by the red line and Gompertz model by the green line. Master thesis - Author's personal copy Author: Valentin Ştefan 84 Site class Southern region - mineral soil Southern region - peatland 1 Share of stand volume: 75%; Canopy cover: 30% Share of stand volume: 75%; Canopy cover: 20% 2 Share of stand volume: 75%; Canopy cover: 20% Share of stand volume: 75%; Canopy cover: 15% 3 Share of stand volume: 50%; Canopy cover: 20% [m] Share of stand volume: 50%; Canopy cover: 15% [m] 4 No data available Share of stand volume: 50%; Canopy cover: 20% Share of stand volume: 50% Figure 35 - Yield curves for broad-leaved species in southern region. NOTE: The first percent value represents dominant species’ share of stand total volume. The second percent value represents the minimum canopy cover of the stands analysed for building the yield curve (usually corresponds to the third quartile of the canopy cover distribution, or to the median [m] if there were not enough stands to cover all age classes). Age is expressed in years and standing volume ('Vol') in m3/ha. Logistic model is represented by the red line and Gompertz model by the green line. Master thesis - Author's personal copy Author: Valentin Ştefan 85 Appendix 9. Significant parameter estimates of regional yield functions No. Species Region Soil Site Selected model Coefficient estimates Standard error Asym coef1 coef2 Asym coef1 coef2 1 Pine North mineral 1 Gompertz 109.978 4.160 0.946 0.134 0.079 0.0005 2 Pine North mineral 2 Logistic 106.369 51.611 17.806 2.417 0.935 1.184 3 Pine North mineral 3 Logistic 105.181 45.778 15.715 0.360 0.211 0.290 4 Pine North mineral 4 Logistic 27.102 17.222 4.288 0.547 0.948 0.805 5 Pine North peat 1 Gompertz 118.277 2.383 0.961 0.250 0.040 0.0004 6 Pine North peat 2 Logistic 86.773 43.679 12.605 1.311 0.801 1.005 7 Pine North peat 3 Logistic 81.218 42.813 12.245 0.187 0.202 0.203 8 Pine North peat 4 Logistic 25.393 15.326 4.215 0.248 0.439 0.404 9 Pine South mineral 1 Gompertz 145.616 3.492 0.945 0.300 0.079 0.001 10 Pine South mineral 2 Logistic 128.256 43.747 20.696 1.949 0.742 1.078 11 Pine South mineral 3 Gompertz 136.682 8.245 0.930 0.321 0.766 0.002 12 Pine South mineral 4 Gompertz 122.308 3.418 0.963 16.946 0.200 0.005 13 Pine South peat 1 Gompertz 145.085 3.905 0.939 0.406 0.170 0.001 14 Pine South peat 2 Gompertz 130.416 3.312 0.964 4.622 0.618 0.005 15 Pine South peat 3 Gompertz 130.431 5.723 0.947 0.663 0.582 0.002 16 Pine South peat 4 Gompertz 87.690 3.656 0.960 29.777 0.614 0.015 17 Spruce North mineral 1 Logistic 131.146 40.721 8.241 0.296 0.608 0.496 18 Spruce North mineral 2 Gompertz 115.784 2.859 0.951 1.038 1.143 0.007 19 Spruce North mineral 3 Gompertz 72.974 2.257 0.991 18.260 0.170 0.002 20 Spruce North mineral 4 Logistic 46.912 35.082 9.026 2.900 3.464 3.721 21 Spruce North peat 1 Logistic 125.953 50.051 16.082 0.418 1.056 0.854 22 Spruce North peat 2 Gompertz 124.291 2.447 0.970 2.177 0.915 0.005 23 Spruce North peat 3 Gompertz 65.750 3.427 0.984 8.847 0.381 0.003 24 Spruce North peat 4 Logistic 45.430 39.510 9.093 1.613 1.524 1.557 25 Spruce South mineral 1 Gompertz 270.669 3.892 0.949 0.270 0.044 0.0003 26 Spruce South mineral 2 Logistic 225.027 35.687 10.058 0.712 0.420 0.416 27 Spruce South mineral 3 Logistic 86.183 21.357 5.053 3.106 3.101 2.478 28 Spruce South mineral 4 Gompertz 99.677 4.265 0.934 2.518 1.160 0.012 29 Spruce South peat 1 Gompertz 255.329 4.696 0.943 0.800 0.246 0.001 30 Spruce South peat 2 Gompertz 210.637 4.744 0.951 1.526 0.760 0.003 31 Spruce South peat 3 Logistic 103.864 38.395 14.935 12.227 6.222 5.644 32 Spruce South peat 4 Gompertz 104.419 3.265 0.960 6.961 0.778 0.008 33 Birch North mineral 1 Gompertz 135.487 2.500 0.966 3.201 0.043 0.001 34 Birch North mineral 2 Gompertz 135.583 1.772 0.969 6.134 0.099 0.003 35 Birch North mineral 3 Gompertz 94.603 3.442 0.945 1.886 0.459 0.004 36 Birch North mineral 4 Logistic 48.935 20.731 14.632 9.422 5.991 5.296 37 Birch North peat 1 Gompertz 86.527 3.402 0.937 1.504 0.279 0.004 38 Birch North peat 2 Gompertz 92.613 5.885 0.917 0.962 1.043 0.006 39 Birch North peat 3 Gompertz 70.416 4.835 0.918 0.809 1.031 0.007 40 Birch North peat 4 Logistic 38.079 15.290 5.129 1.823 1.978 2.081 41 Birch South mineral 1 Gompertz 138.610 3.420 0.933 0.769 0.056 0.001 42 Birch South mineral 2 Gompertz 118.264 3.099 0.937 1.353 0.185 0.003 43 Birch South mineral 3 Gompertz 94.018 3.498 0.920 1.286 0.691 0.007 44 Birch South mineral 4 Logistic 37.640 7.855 2.598 2.217 0.736 0.761 45 Birch South peat 1 Gompertz 115.121 3.576 0.923 1.768 0.267 0.004 46 Birch South peat 2 Gompertz 135.338 2.058 0.961 8.021 0.219 0.006 47 Birch South peat 3 Gompertz 92.178 6.480 0.902 1.819 2.252 0.013 48 Birch South peat 4 Logistic 30.062 6.575 1.985 2.254 1.033 0.943 49 Other North mineral 1 Gompertz 86.223 5.482 0.888 3.345 0.504 0.008 50 Other North mineral 2 Gompertz 52.852 5.232 0.877 1.836 2.440 0.023 51 Other North mineral 3 Gompertz 94.603 3.442 0.945 1.886 0.459 0.004 52 Other North mineral 4 Logistic 48.935 20.731 14.632 9.422 5.991 5.296 53 Other North peat 1 Gompertz 38.452 4.942 0.855 1.416 0.752 0.013 54 Other North peat 2 Logistic 92.613 5.885 0.917 0.962 1.043 0.006 55 Other North peat 3 Gompertz 70.416 4.835 0.918 0.809 1.031 0.007 56 Other North peat 4 Logistic 38.079 15.290 5.129 1.823 1.978 2.081 57 Other South mineral 1 Logistic 154.395 19.594 5.573 1.228 0.158 0.169 58 Other South mineral 2 Gompertz 127.651 4.590 0.935 32.161 1.526 0.023 59 Other South mineral 3 Gompertz 94.018 3.498 0.920 1.286 0.691 0.007 60 Other South mineral 4 Logistic 37.640 7.855 2.598 2.217 0.736 0.761 61 Other South peat 1 Logistic 194.547 24.930 6.893 8.783 0.892 0.522 62 Other South peat 2 Gompertz 102.741 9.716 0.892 14.890 3.602 0.022 63 Other South peat 3 Gompertz 92.178 6.480 0.902 1.819 2.252 0.013 64 Other South peat 4 Logistic 30.062 6.575 1.985 2.254 1.033 0.943 NOTE: coef1 is xmid for logistic (Eq.1) or b2 for Gompertz model (Eq.2); coef2 is scal for logistic or b3 for Gompertz model Master thesis - Author's personal copy Author: Valentin Ştefan 86 Appendix 9. Continued No. Species t - value AIC (for model selection) RMSE (for model selection) Asym coef1 coef2 Gompertz Logistic Dif. Gompertz Logistic Dif. 1 Pine 820.1 52.9 2101.4 2693236 2693408 172 31.182 31.192 0.010 2 Pine 44.0 55.2 15.0 38962 38948 -13 30.327 30.276 -0.051 3 Pine 292.3 217.0 54.2 799469 799442 -27 24.415 24.411 -0.004 4 Pine 49.5 18.2 5.3 10812 10708 -104 15.649 15.033 -0.617 5 Pine 473.7 58.9 2166.7 1686118 1686123 5 31.087 31.087 0.000 6 Pine 66.2 54.5 12.5 40312 40308 -4 30.886 30.872 -0.014 7 Pine 433.5 211.7 60.3 1339116 1338934 -182 23.794 23.779 -0.015 8 Pine 102.3 34.9 10.4 44383 44370 -13 14.339 14.322 -0.017 9 Pine 485.4 44.4 1474.9 2368876 2369089 213 45.865 45.887 0.022 10 Pine 65.8 59.0 19.2 81386 81374 -12 37.019 36.992 -0.028 11 Pine 425.9 10.8 505.7 627294 627824 529 34.156 34.299 0.143 12 Pine 7.2 17.1 177.9 7063 7060 -4 22.195 22.143 -0.051 13 Pine 357.0 23.0 791.8 615357 615439 82 38.049 38.074 0.026 14 Pine 28.2 5.4 208.8 16336 16332 -4 35.918 35.876 -0.042 15 Pine 196.7 9.8 484.1 325771 329514 3743 30.385 32.120 1.735 16 Pine 2.9 6.0 65.5 1705 1703 -2 20.725 20.613 -0.113 17 Spruce 443.7 67.0 16.6 481034 480940 -94 59.604 59.540 -0.064 18 Spruce 111.6 2.5 142.8 22882 22881 -1 31.978 31.973 -0.005 19 Spruce 4.0 13.3 413.9 9532 9533 2 17.748 17.760 0.012 20 Spruce 16.2 10.1 2.4 3473 3494 20 31.581 32.483 0.902 21 Spruce 301.3 47.4 18.8 266660 266634 -26 55.955 55.925 -0.030 22 Spruce 57.1 2.7 180.4 18108 18106 -1 31.091 31.079 -0.012 23 Spruce 7.4 9.0 333.7 9792 9785 -7 21.379 21.311 -0.068 24 Spruce 28.2 25.9 5.8 10041 10227 185 25.002 27.238 2.236 25 Spruce 1003.4 88.3 3267.9 2422628 2423129 501 46.833 46.884 0.051 26 Spruce 316.2 85.0 24.2 49148 49118 -29 39.811 39.690 -0.121 27 Spruce 27.7 6.9 2.0 3485 3471 -14 47.194 46.174 -1.019 28 Spruce 39.6 3.7 76.2 2336 2335 -2 21.053 20.989 -0.064 29 Spruce 319.2 19.1 728.8 160453 160453 0.4 46.666 46.667 0.001 30 Spruce 138.0 6.2 308.4 36459 36461 2 40.604 40.615 0.011 31 Spruce 8.5 6.2 2.6 1045 1053 8 46.328 48.205 1.877 32 Spruce 15.0 4.2 117.0 1044 1040 -4 19.025 18.742 -0.283 33 Birch 42.3 57.5 736.9 133624 133632 9 21.798 21.804 0.006 34 Birch 22.1 17.8 284.1 51445 51444 -1 23.882 23.879 -0.002 35 Birch 50.2 7.5 214.0 42550 42543 -7 21.765 21.749 -0.016 36 Birch 5.2 3.5 2.8 1978 1976 -2 13.577 13.512 -0.064 37 Birch 57.5 12.2 258.2 43084 43091 7 21.310 21.325 0.015 38 Birch 96.2 5.6 164.0 40739 40733 -6 21.869 21.854 -0.015 39 Birch 87.0 4.7 132.6 41218 41211 -7 22.601 22.583 -0.018 40 Birch 20.9 7.7 2.5 1333 1286 -47 11.500 10.027 -1.473 41 Birch 180.3 61.1 1027.4 513106 513207 102 22.729 22.749 0.020 42 Birch 87.4 16.7 361.8 64555 64554 -1 23.671 23.669 -0.002 43 Birch 73.1 5.1 123.8 14275 14285 10 20.066 20.128 0.062 44 Birch 17.0 10.7 3.4 1358 1357 -1 14.243 14.195 -0.048 45 Birch 65.1 13.4 242.5 54809 54818 9 23.255 23.273 0.018 46 Birch 16.9 9.4 161.1 11971 11969 -2 24.651 24.629 -0.023 47 Birch 50.7 2.9 69.7 5052 5091 38 19.948 20.628 0.681 48 Birch 13.3 6.4 2.1 471 479 8 11.755 12.532 0.777 49 Other 25.8 10.9 114.7 14349 14366 17 17.466 17.555 0.089 50 Other 28.8 2.1 37.5 4587 4577 -10 16.322 16.174 -0.148 51 Other - - - - - - - - - 52 Other - - - - - - - - - 53 Other 27.2 6.6 64.3 11648 11640 -8 13.009 12.972 -0.037 54 Other - - - - - - - - - 55 Other - - - - - - - - - 56 Other - - - - - - - - - 57 Other 125.8 123.9 33.0 98577 98497 -80 50.617 50.397 -0.219 58 Other 4.0 3.0 40.6 475 477 2 18.842 19.133 0.292 59 Other - - - - - - - - - 60 Other - - - - - - - - - 61 Other 22.2 28.0 13.2 6789 6773 -16 40.652 40.168 -0.483 62 Other 6.9 2.7 40.8 257 257 0.1 11.089 11.098 0.009 63 Other - - - - - - - - - 64 Other - - - - - - - - - NOTE: coef1 is xmid for logistic (Eq.1) or b2 for Gompertz model (Eq.2); coef2 is scal for logistic or b3 for Gompertz model Master thesis - Author's personal copy Author: Valentin Ştefan 87 Appendix 10. Management guidelines and standing volumes from MOTTI simulator Final cut (FC) P% 36 30 30 39 100 100 100 100 31 26 24 31 100 100 100 100 25 23 28 79 20 36 68 73 18 19 22 73 14 45 75 65 L% 64 70 70 61 - - - - 69 74 76 69 - - - - 75 77 72 21 80 64 32 27 82 81 78 27 86 55 25 35 R% 98 99 98 98 91 91 90 91 98 98 98 98 91 92 94 94 98 98 98 88 98 97 95 96 98 99 99 90 99 97 95 97 Vol 176 177 220 137 78 75 64 83 343 332 259 153 69 79 89 104 293 287 223 119 214 158 121 149 373 419 304 159 346 222 197 192 Age 61 88 98 121 105 105 115 135 46 67 69 77 80 80 90 105 76 87 92 120 77 120 120 120 53 64 62 80 80 80 80 80 Third thinning (T3) P% 59 56 71 79 - - - - - - 46 73 - - - - - - - - 56 - - - - - - - - - - - L% 41 44 29 21 - - - - - - 54 27 - - - - - - - - 44 - - - - - - - - - - - R% 30 30 29 33 - - - - - - 34 33 - - - - - - - - 28 - - - - - - - - - - - Vol 208 207 193 138 - - - - - - 286 157 - - - - - - - - 207 - - - - - - - - - - - Age 55 78 74 97 - - - - - - 57 63 - - - - - - - - 64 - - - - - - - - - - - Second thinning (T2) P% 92 89 96 100 - - - - 75 74 84 100 - - - - 71 65 72 - 91 78 98 100 50 47 59 - 40 - - 96 L% 8 11 4 0 - - - - 25 26 16 0 - - - - 29 35 28 - 9 22 2 0 50 53 41 - 60 - - 4 R% 28 29 28 33 - - - - 33 33 32 33 - - - - 26 27 28 - 28 27 25 26 31 30 32 - 33 - - 28 Vol 162 163 150 107 - - - - 240 249 232 111 - - - - 224 236 192 - 164 146 120 110 317 338 242 - 357 - - 192 Age 41 55 54 69 - - - - 31 44 41 44 - - - - 58 67 72 - 54 96 100 87 42 49 47 - 58 - - 69 First thinning (T1) P% 98 100 100 100 - - - - 100 87 96 100 - - - - 84 82 94 - 100 100 100 100 77 72 85 - 78 81 100 100 L% 2 0 0 0 - - - - 0 13 4 0 - - - - 16 18 6 - 0 0 0 0 23 28 15 - 22 19 0 0 R% 32 30 31 32 - - - - 30 29 29 32 - - - - 25 25 25 - 29 28 26 22 33 31 29 - 33 31 27 25 Vol 142 117 119 99 - - - - 168 171 159 106 - - - - 172 175 135 - 121 107 116 97 217 257 168 - 261 205 137 131 Age 32 37 39 54 - - - - 23 30 29 36 - - - - 45 50 52 - 45 72 83 72 31 37 35 - 48 68 58 53 PT age 9 9 10 12 - 10 18 12 11 11 12 10 11 12 13 10 10 10 11 - - 14 - - 9 8 9 - 11 12 - - CL age - - - - - - - - 4 4 4 - 4 4 5 - 7 7 7 - 7 7 - - 5 5 6 - 5 5 - - Site 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 Soil mineral mineral mineral mineral peat peat peat peat mineral mineral mineral mineral peat peat peat peat mineral mineral mineral mineral peat peat peat peat mineral mineral mineral mineral peat peat peat peat Region North North North North North North North North South South South South South South South South North North North North North North North North South South South South South South South South Species Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine Pine Spruce Spruce Spruce Spruce Spruce Spruce Spruce Spruce Spruce Spruce Spruce Spruce Spruce Spruce Spruce Spruce No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 Abbreviations: CL - cleaning of sapling stands (year to apply); PT - Pre-commercial thinning (year to apply); Age - time from regeneration when the operation is applied; Vol - standing volume (m3/ha); R% - percentage of removed volume (applied to Vol); L% - percentage of log assortment (applied to removed volume); P% - percentage of pulpwood assortment (applied to removed volume) Master thesis - Author's personal copy Author: Valentin Ştefan 88 Appendix 10. Continued Final cut (FC) P% 83 95 100 100 100 100 100 100 53 61 67 100 100 100 100 100 100 100 100 100 100 100 100 100 66 86 93 100 100 100 100 100 L% 17 5 - - - - - - 47 39 33 - - - - - - - - - - - - - 34 14 7 - - - - - R% 97 93 93 41 59 32 14 16 98 98 97 77 91 83 56 47 85 78 69 38 72 29 18 23 98 96 89 77 93 81 62 62 Vol 205 168 154 44 47 43 46 43 377 278 225 148 63 42 67 74 148 93 101 43 70 61 56 51 245 235 169 86 102 82 86 81 Age 55 55 55 55 55 55 55 55 65 65 65 65 65 65 65 65 55 55 55 55 55 55 55 55 65 65 65 65 65 65 65 65 Third thinning (T3) P% - - - - - - - - - - - - - - - - - - - - - - - - 88 - - - - - - - L% - - - - - - - - - - - - - - - - - - - - - - - - 12 - - - - - - - R% - - - - - - - - - - - - - - - - - - - - - - - - 31 - - - - - - - Vol - - - - - - - - - - - - - - - - - - - - - - - - 237 - - - - - - - Age - - - - - - - - - - - - - - - - - - - - - - - - 52 - - - - - - - Second thinning (T2) P% - - - - - - - - 88 86 88 - - - - - - - - - - - - - 100 100 - - - - - - L% - - - - - - - - 12 14 12 - - - - - - - - - - - - - 0 0 - - - - - - R% - - - - - - - - 31 30 29 - - - - - - - - - - - - - 25 24 - - - - - - Vol - - - - - - - - 250 249 259 - - - - - - - - - - - - - 158 158 - - - - - - Age - - - - - - - - 37 48 57 - - - - - - - - - - - - - 36 44 - - - - - - First thinning (T1) P% 100 - - - - - - - 95 95 96 - - - - - 100 100 - - - - - - 100 100 100 100 - - - - L% 0 - - - - - - - 5 5 4 - - - - - 0 0 - - - - - - 0 0 0 0 - - - - R% 30 - - - - - - - 30 30 31 - - - - - 21 20 - - - - - - 23 21 23 20 - - - - Vol 173 - - - - - - - 201 206 222 - - - - - 101 107 - - - - - - 128 118 106 102 - - - - Age 41 - - - - - - - 28 36 43 - - - - - 39 49 - - - - - - 29 34 40 60 - - - - PT age 15 16 17 - - - - - 12 12 13 - - - - - - - - - - - - - - - - - - - - - CL age - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Site 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 Soil mineral mineral mineral mineral peat peat peat peat mineral mineral mineral mineral peat peat peat peat mineral mineral mineral mineral peat peat peat peat mineral mineral mineral mineral peat peat peat peat Region North North North North North North North North South South South South South South South South North North North North North North North North South South South South South South South South Species Birch Birch Birch Birch Birch Birch Birch Birch Birch Birch Birch Birch Birch Birch Birch Birch Other Other Other Other Other Other Other Other Other Other Other Other Other Other Other Other No. 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 Abbreviations: CL - cleaning of sapling stands (year to apply); PT - Pre-commercial thinning (year to apply); Age - time from regeneration when the operation is applied; Vol - standing volume (m3/ha); R% - percentage of removed volume (applied to Vol); L% - percentage of log assortment (applied to removed volume); P% - percentage of pulpwood assortment (applied to removed volume) Master thesis - Author's personal copy Author: Valentin Ştefan 89 Wyrażam zgodę na udostępnienie mojej pracy w czytelniach Biblioteki Wyższej Szkoły Zrównoważonego Rozwoju Eberswalde oraz Biblioteki Szkoły Głównej Gospodarstwa Wiejskiego. I give my consent to release my thesis in reading rooms of the library of the University for Sustainable Development Eberswalde and the library of the Warsaw University of Life Sciences. Ich stimme der Einsichtnahme in meine Arbeit in den Leseräumen der Bibliothek der Hochschule für nachhaltige Entwicklung Eberswalde und der Bibliothek der Naturwissenschaftlichen Universität Warschau zu. Valentin Ştefan ................................................................. czytelny podpis autora the author’s legible signature Unterschrift des Verfassers