Author's personal copy Ecological Modelling 247 (2012) 135–143 Contents lists available at SciVerse ScienceDirect Ecological Modelling jo ur n al homep ag e: www.elsevier.com/locate/ecolmodel Variance-based sensitivity analysis of a forest growth model Xiaodong Song a,b,∗ , Brett A. Bryan b , Keryn I. Paul c , Gang Zhao b,d a Institute of Urban Environment, Chinese Academy of Sciences, Xiamen 361021, China b CSIRO Ecosystem Sciences, Waite Campus, Urrbrae, SA 5064, Australia c CSIRO Ecosystem Sciences, Black Mountain, Canberra 2601, Australia d Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China a r t i c l e i n f o Article history: Received 31 May 2012 Received in revised form 21 July 2012 Accepted 7 August 2012 Keywords: 3-PG2 Sensitivity analysis Variance-based Elementary effects Group effect a b s t r a c t Computer models are increasingly used to simulate and predict the behaviour of forest systems. Uncer- tainties in both parameter calibration and outputs co-exist in these models due to both the incomplete understanding of the system under simulation, and biased model structure. We used sensitivity analysis, including both screening and global variance-based methods, to explore these uncertainties. We applied these techniques to the widely used forest growth model Physiological Principles for Predicting Growth (3-PG2) using field data from 141 plots of Corymbia maculata and Eucalyptus cladocalyx in Australia. The screening method was used to select influential input parameters for the subsequent variance-based analysis and thereby reduce its computational cost. We assessed model outputs including biomass parti- tioning and water balance, and the sensitivities of the soil texture group, which includes 7 parameters. We also compared the screening and variance-based methods, and assessed the convergence of the variance- based method, and the change in sensitivities over time. Using these techniques, we quantified the relative sensitivities of each model output to each input parameter. The variance-based method exhibited good convergence and stable sensitivity rankings. The results indicated changes in input parameter sensitiv- ities over longer simulation periods. The variance-based global sensitivity analysis can be very effective in calibration and identification of important processes within forest models. © 2012 Elsevier B.V. All rights reserved. 1. Introduction Computer models are routinely used to understand forest sys- tems (Battaglia et al., 2004; Landsberg and Waring, 1997; Pan et al., 2011; White et al., 2000). This is in part due to their ability to incor- porate high levels of complexity that are characteristic of these systems. Although a computer model can be seen as series of math- ematic functions that connect certain inputs and outputs, they are often complex, and this presents a barrier to the quantitative anal- ysis of model performance (Morris, 1991). Another consequence of complex models is that the uncertainties in model structure, estimates of the model parameters, and the unexplained random variation in observed variables all increase greatly (Chatfield, 1995). For model parameters with high uncertainty and high sensitivity, a small perturbation in parameter values may have exaggerated effects on the outputs (Makler-Pick et al., 2011; Xu and Gertner, 2007). Thus, understanding the contribution of model structure and parameter estimation to the total model uncertainty is important in both model application and development (Cariboni et al., 2007; ∗ Corresponding author at: Institute of Urban Environment, Chinese Academy of Sciences, Xiamen 361021, China. Tel.: +86 592 6190663; fax: +86 592 6190 977. E-mail address: xdsongy@gmail.com (X. Song). Makler-Pick et al., 2011; Saltelli and Annoni, 2010; Saltelli et al., 2008). To quantify the effect of different sources of uncertainty in forest model inputs on variability of model outputs, sensitivity analysis (SA) can be applied (Saltelli et al., 2008). SA evaluates the relative importance of each input parameter and can be used to identify the most influential parameters in determining the variability of model outputs. Uninfluential parameters can also be identified and be safely set in relatively wide ranges (Cariboni et al., 2007). In general, SA methods can be categorized as either local or global. Local SA is usually derivative-based and belongs to the class of “one- factor-at-a-time” (OAT). OAT methods involve changing one input parameter at a time whilst holding all others at their central values and variation in the outputs is measured. A critique of OAT methods is that they are only informative at the central point where the calculation is executed and do not cover the whole input parameter space. Thus, local SA methods are inadequate for analysing complex biophysical process models which may have many parameters, and may be high-dimensional and/or non-linear (Saltelli and Annoni, 2010; Yang, 2011). A model-independent global SA technique is preferable for these models (Helton et al., 2006; Nossent et al., 2011; Saltelli, 2000; Saltelli and Annoni, 2010). Compared with local SA, global SA explores the full input param- eter space, and the contribution of each input parameter to the 0304-3800/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ecolmodel.2012.08.005