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1. Introduction
Forest site productivity may be assessed in different ways, but commonly used methods are site index models (dominant height growth models) and site index prediction models (site index prediction from site variables). Such models are fundamental components of growth and yield models, and therefore need to be precise over the entire range of forest growth conditions. A challenge with the existing and most frequently applied Norwegian site index models (Tveite, 1977; Tveite and Braastad, 1981) and site index prediction models (Nilsen and Larsson, 1992) is that they do not properly represent the entire range of forest growth conditions in Norway. The site index models are lacking data from the western and northern parts of Norway, and are therefore likely to be biased for these regions (Blingsmo, 1985;
Øyen and Nes, 1997; Tveite, 1994; Orlund, 2001). Site index models are also dominant height growth models, and may therefore be used to predict maximum possible (potential) height growth in individual tree based growth models (e.g. Pretzsch et al., 2002). However, the presently applied Norwegian site index models (Tveite, 1977; Tveite and Braastad, 1981) cannot be used for the purpose, because the potential height growth derived from them is inconsistent and unrealistic, i.e., height growth culminates at unrealistic ages. Also, the site index prediction models developed by Nilsen and Larsson (1992) are lacking data from large parts of the Norwegian forests. Another challenge is that significant age trends in the
residuals of these models were observed, but age was not included in the models. Bøhler and Øyen (2011) tested the models for samples of Norway spruce and found biased site index predictions.
A large part of the Norwegian productive forests is uneven-aged, a mixture of species, or of heterogeneous structure (NIJOS, 2000). For a description of the dynamics of such forests regarding radial (diameter or basal area) growth, individual tree diameter and basal area growth models have been developed (Andreassen and Tomter, 2003; Bollandsås et al., 2008;
Bollandsås and Næsset, 2009). However, individual tree height growth models are still lacking for Norway to describe forest dynamics.
Heights for individual trees on sample plots are often needed for estimation of volume, biomass and carbon. Because of high inventory costs, measuring heights for all trees is not possible, and therefore only a sample of trees is usually measured for heights. This means that the missing height measurements need to be predicted. This can be done, for example,
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with height-diameter models. A requirement for such models is that they are able to predict height with an appropriate accuracy. By applying a mixed effects modelling approach, which takes the sample plot-level random variations into account, accuracy of the predictions can be improved. A weakness of the presently applied height-diameter models in Norway (Øyen and Andreassen, 2002; Bollandsås, 2007) is that sample plot-level random effects were not included when they were developed. Another weakness is that they did not include height of dominant tree as covariate, which represents the stand development stage over time (e.g.
Adame et al., 2008; Crecente-Campo et al., 2010).
Individual tree based forest simulators have been developed in various countries such as BWIN (Nagel, 1997) and SILVA in Germany (Pretzsch et al., 2002), MOSES (Hasenauer et al., 2006) and PROGNAUS (Monserud and Sterba, 1996; Sterba and Monserud, 1996) in Austria, HEUREKA in Sweden (Lämås and Eriksson 2003), and MOTTI in Finland (Hynynen et al., 2005) as decision-making tools for practical forest management planning.
Together with several other models, these simulators comprise spatially explicit or spatially non-explicit individual tree height growth models. In Norway, the individual tree based forest simulator -T (Gobakken et al., 2008) has been developed. This simulator comprises of
various models such as diameter and height growth models, mortality models, recruitment models, height-diameter models and volume functions. To predict heights, the simulator currently applies height-diameter models (Bollandsås, 2007) for old even-aged and uneven-aged stands and dominant height growth models (Tveite, 1977; Tveite and Braastad, 1981) for young even-aged stands. These models may be replaced with more accurate mixed effects height-diameter models for prediction of heights. Alternatively, height growth predictions accuracy could also be improved by implementing individual tree height growth models in the simulator
The present study used national forest inventory (NFI) data as main data source while data from other sources (long-term experimental plots, stem analysis, meteorological stations) were used as supplementary data. In recent years, NFIs have started to supply permanent sample plot data in various European countries including Norway. These data are useful for growth modellers because individual trees are repeatedly measured on the permanent sample plots. The repeatedly measured individual tree data allow deriving the increments that may be used to model growth at the individual tree-level. In addition, tree positions are in most
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countries also recorded in the NFIs and this allows developing spatially explicit individual tree based growth models. The NFI data cover a wide range of tree sizes, ages, growth
conditions, and management practices across the country. Since NFI data are not collected for growth modelling, they often contain measurement errors that are acceptable for the main purpose (large scale resource assessments), but are very large for growth modelling. In addition, NFI data still represent short time periods, which may cause challenges in growth modelling. Despite these challenges, NFI data have frequently been used to develop various forest models such as dominant height growth models (e.g. Huuskonen and Miina, 2007), individual tree radial growth models (e.g. Monserud and Sterba, 1996; Sterba and Monserud, 1997; Adame et al., 2008; Condés and Sterba, 2008), individual tree height growth models (Hasenauer and Monserud, 1997; Condés and Sterba, 2008), individual tree mortality models (e.g. Monserud and Sterba, 1999), and height-diameter models (Mehtatalo, 2004, 2005;
Nanos et al., 2004; Adame et al., 2008; Crecente-Campo et al., 2010). In Norway, stand basal area and volume growth models (Gizachew and Brunner, 2011), individual tree radial growth models (Andreassen and Tomter, 2003; Bollandsås and Næsset, 2009), individual tree
mortality models (Eid and Tuhus, 2001; Bollandsås, 2007), and height-diameter models (Bollandsås, 2007) have been developed from NFI data.
Norwegian forests are mainly dominated by Norway spruce (Picea abies (L.) Karst.) and Scots pine (Pinus sylvestris L.), both in area coverage and standing volume (Larsson and Hylen, 2007), and these two species were therefore in the focus of this thesis. The main objective of the thesis was to develop dominant height growth models, site index prediction models, individual tree height growth models and mixed effects height-diameter models using NFI data. All these models may be used in the present Norwegian individual tree based forest simulator - T (Gobakken et al., 2008) or in any other simulator that may be developed in the future.
The thesis is divided into four different papers to cover the main objective, each of them corresponding to the following sub-objectives:
1. To develop dominant height growth models for Norway spruce and Scots pine in Norway (Paper I)
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2. To develop site index prediction models from site and climate variables for Norway spruce and Scots pine in Norway (Paper II)
3. To develop individual tree based height growth models for Norway spruce and Scots pine in Norway (Paper III)
4. To develop height-diameter models for Norway spruce, Scots pine, and Downy birch in Norway (Paper IV)
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