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Generalized height-diameter curves based on a re-parameterized version of the Korf function for Norway spruce (Picea abies (L.) Karst.), Scots pine (Pinus sylvestris L.) and silver birch (Betula pendula Roth) in Norway are presented. The Norwegian National Forest Inventory (NFI) is used as data base for estimating the model parameters. The derived models are developed to enable spatially explicit and site sensitive tree height imputation in forest inventories as well as future tree height predictions in growth and yield scenario simulations.
Generalized additive mixed models (gamm) are employed to detect and quantify potentially non-linear effects of predictor variables. In doing so the quadratic mean diameter serves as longitudinal covariate since stand age, as measured in the NFI, shows only a weak correlation with a stands developmental status in Norwegian forests. Additionally the models can be locally calibrated by predicting random effects if measured height-diameter pairs are available. Based on the model selection of non-constraint models, shape constraint additive models (scam) were fit to incorporate expert knowledge and intrinsic relationships by enforcing certain effect patterns like monotonicity.
Model comparisons demonstrate that the shape constraints lead to only marginal differences in statistical characteristics but ensure reasonable model predictions. Under constant constraints the developed models predict increasing tree heights with decreasing altitude, increasing soil depth and increasing competition pressure of a tree. A two-dimensional spatially structured effect of UTM-coordinates accounts for the potential effects of large scale spatially correlated covariates, which were not at our disposal. The main result of modelling the spatially structured effect is lower tree height prediction for coastal sites and with increasing latitude. The quadratic mean diameter affects both the level and the slope of the height-diameter curve and both effects are positive.
In this investigation it is assumed that model effects in additive modelling of height-diameter curves which are unfeasible and too wiggly from an expert point of view are a result of quantitatively or qualitatively limited data bases. However, this problem can be regarded not to be specific to our investigation but more general since growth and yield data that are balanced over the whole data range with respect to all combinations of predictor variables are exceptional cases. Hence, scam may provide methodological improvements in several applications by combining the flexibility of additive models with expert knowledge.
Generalized height-diameter curves based on a re-parameterized version of the Korf function for Norway spruce (Picea abies (L.) Karst.), Scots pine (Pinus sylvestris L.) and silver birch (Betula pendula Roth) in Norway are presented. The Norwegian National Forest Inventory (NFI) is used as data base for estimating the model parameters. The derived models are developed to enable spatially explicit and site sensitive tree height imputation in forest inventories as well as future tree height predictions in growth and yield scenario simulations.
Generalized additive mixed models (gamm) are employed to detect and quantify potentially non-linear effects of predictor variables. In doing so the quadratic mean diameter serves as longitudinal covariate since stand age, as measured in the NFI, shows only a weak correlation with a stands developmental status in Norwegian forests. Additionally the models can be locally calibrated by predicting random effects if measured height-diameter pairs are available. Based on the model selection of non-constraint models, shape constraint additive models (scam) were fit to incorporate expert knowledge and intrinsic relationships by enforcing certain effect patterns like monotonicity.
Model comparisons demonstrate that the shape constraints lead to only marginal differences in statistical characteristics but ensure reasonable model predictions. Under constant constraints the developed models predict increasing tree heights with decreasing altitude, increasing soil depth and increasing competition pressure of a tree. A two-dimensional spatially structured effect of UTM-coordinates accounts for the potential effects of large scale spatially correlated covariates, which were not at our disposal. The main result of modelling the spatially structured effect is lower tree height prediction for coastal sites and with increasing latitude. The quadratic mean diameter affects both the level and the slope of the height-diameter curve and both effects are positive.
In this investigation it is assumed that model effects in additive modelling of height-diameter curves which are unfeasible and too wiggly from an expert point of view are a result of quantitatively or qualitatively limited data bases. However, this problem can be regarded not to be specific to our investigation but more general since growth and yield data that are balanced over the whole data range with respect to all combinations of predictor variables are exceptional cases. Hence, scam may provide methodological improvements in several applications by combining the flexibility of additive models with expert knowledge.
Brezger A, Lang S (2006) Generalized structured additive regression based on Bayesian P-splines. Comput Stat Data Anal 50(4):967-991
Calama R, Montero G (2004) Interregional nonlinear height-diameter model with random coefficients for stone pine in Spain. Can J For Res 34:150-163
Corral-Rivas S, Álvarez-González JG, Crecente-Campo F, Corral-Rivas JJ (2014) Local and generalized height-diameter models with random parameters for mixed, uneven-aged forests in Northwestern Durango, Mexico. Forest Ecosystems 1:6. DOI:10.1186/2197-5620-1-6
Eerikäinen K (2003) Predicting the height-diameter pattern of planted Pinus kesiya stands in Zambia and Zimbabwe. Forest Ecol Manag 175(1-3):355-366. DOI:10.1016/S0378-1127(02)00138-X
Hökkä H (1997) Height-diameter curves with random intercepts and slopes for trees growing on drained peatlands. For Ecol Manag 97:63-72
Lappi J (1997) A longitudinal analysis of height/diameter curves. For Sci 43(4):555-570
López Sánchez CA, Gorgoso JJ, Castedo F, Rojo A, Rodríguez R, Álvarez González JG, Sánchez Rodríguez F (2003) A height-diameter model for Pinus radiata D. Don in Galicia (Northwest Spain). Ann Forest Sci 60:237-245
Mehtätalo L (2004) A longitudinal height-diameter model for Norway spruce in Finland. Can J For Res 34:131-140
Mehtätalo L (2005) Height-diameter models for Scots pine and birch in Finland. Silv Fenn 39(1):55-66
Mehtätalo L, de-Miguel S, Gregoire T (2015) Modeling height-diameter curves for prediction. Can J For Res 45(7):826-837. DOI:10.1139/cjfr-2015-0054
Nanos N, Calama R, Montero G, Gil L (2004) Geostatistical prediction of height/diameter models. For Ecol Manag 195(1-2):221-235
Schmidt M, Kiviste A, Gadow K (2011) A spatially explicit height-diameter model for Scots pine in Estonia. Eur J For Res 130:303-315. DOI:10.1007/s10342-010-0434-8
Temesgen H, Gadow K (2004) Generalized height-diameter models-an application for major tree species in complex stands of interior British Columbia. Eur J Forest Res 123(1):45-51
Wood SN (2004) Stable and efficient multiple smoothing parameter estimation for generalized additive models. J Am Stat Assoc 99:673-686
Wood SN (2011) Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models. J Royal Stat Soc (B) 73(1):3-36
Zhang S, Burkhart HE (1997) The influence of thinning on tree height and diameter relationships in loblolly pine plantations. South J Appl For 21:199-205
We would like to thank two anonymous reviewers for constructive comments.
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