Ecological Modelling 337 (2016) 48–62 Contents lists available at ScienceDirect Ecological Modelling journal homepage: www.elsevier.com/locate/ecolmodel A dynamic environment-sensitive site index model for the prediction of site productivity potential under climate change Chaofang Yue a , Hans-Peter Kahle b , Klaus von Wilpert a , Ulrich Kohnle a,∗ a Forest Research Station Baden-Württemberg, Wonnhaldestr. 4, 79100 Freiburg, Germany b Albert-Ludwigs-University Freiburg, Institute of Forest Sciences, Chair of Forest Growth and Dendroecology, Tennenbacher Str. 4, 79106 Freiburg, Germany a r t i c l e i n f o Article history: Received 22 December 2015 Received in revised form 29 April 2016 Accepted 6 June 2016 Keywords: Norway spruce Space-for-time substitution Nonlinear state space approach Longitudinal data structure Prediction error minimization method a b s t r a c t Accurate and reliable predictions of the future development of forest site productivity are crucial for the effective management of forest stands. Static models which simply extrapolate productivity into the future are inappropriate under conditions of environmental change since they lack a close link between fundamental environmental drivers and forest growth processes. Here we present a dynamic environment-sensitive site index model formulated in the framework of a nonlinear state space approach based on longitudinal data from long-term experimental plots. Estimation of the model parameters was carried out using the prediction error minimization method. Our aim was to identify dynamic relation- ships between site index and environmental variables and to make conditional predictions of the future development of site index under climate change scenarios. Nonlinear, interactive, as well as accumula- tive effects of environmental factors (climate/weather and nitrogen influx) on the growth response were considered in the model. In the study, we estimated the dynamic environment-sensitive site index model using data from 604 Norway spruce (Picea abies [L.] Karst.) long-term experimental plots in southwest Germany with measurement data covering a period of more than 100 years from the end of the 19th century until today. We used the calibrated model to project future site index changes under increas- ing growing season temperature scenarios. Conventional climate change impact studies usually utilize a gradient approach and apply space-for-time substitution for the parameterization of models that are calibrated using spatial variability in the data. In contrast, the approach presented here utilizes the longi- tudinal data structure of multiple real growth time series to simultaneously exploit spatial and temporal variation in the data to provide more reliable and robust projections. Limitations of the space-for-time substitution approach in forest growth modelling are discussed. © 2016 Elsevier B.V. All rights reserved. 1. Introduction Accurate and reliable predictions of the future development of forest site productivity are crucial for the effective management of forest stands. In the context of the management of forests for wood production forest site productivity is defined as a quantitative mea- sure of the potential of a specific forest stand on a specific site type to produce wood (Hägglund, 1981). In forestry the most widespread indicator of forest site productivity is site index (Skovsgaard and Vanclay, 2008). Site index is usually defined as the mean (or domi- nant) stand height of a specific tree species at a predefined reference age (Assmann, 1970; Hägglund, 1981). Since site index is highly ∗ Corresponding author. E-mail addresses: chaofang.yue@forst.bwl.de (C. Yue), hans-peter.kahle@iww.uni-freiburg.de (H.-P. Kahle), klaus.wilpert@forst.bwl.de (K. von Wilpert), ulrich.kohnle@forst.bwl.de (U. Kohnle). sensitive to site potential but (almost) insensitive to stand density it is the most commonly used measure of forest site productivity. From a biological point of view forest site productivity describes a highly complex multigenic trait with various interconnected physiological and biogeochemical processes involved, which are further modified by natural and anthropogenic factors. Conse- quently, beside site index there is a variety of different approaches to define, assess and analyze forest site productivity (Skovsgaard and Vanclay, 2008, 2013). Under changing environmental conditions process-based mod- els are considered more adequate than purely descriptive empirical models for projecting the development of site productivity into the future (Bontemps and Bouriaud, 2014; Johnsen et al., 2001; Vanclay and Skovsgaard, 1997). In process-based modelling, forest site pro- ductivity is formulated as a function of primary site factors like solar radiation, air temperature, tree available soil moisture and nutri- ents, tropospheric carbon concentration as well as of tree species http://dx.doi.org/10.1016/j.ecolmodel.2016.06.005 0304-3800/© 2016 Elsevier B.V. All rights reserved.