Validation of a dynamic stem diameter variation model and the resulting seasonal changes in calibrated parameter values

Abstract

Validation of ecological models is not a straightforward task and much controversy exists in the published literature on the exact definition. A lot of approaches have been suggested, without one being clearly superior. In this paper, we use the earlier published dynamic ‘RCGro’ tree water flow and storage model as an illustrative example to address some model validation issues. We show that the model fails validation when confronted with a data set not used during model building and calibration. We apply and discuss therefore several validation criteria, including visual comparison between model output and measured data using both time series and scatter plots, calculation of the slope, the intercept and the R 2 statistic of the regression line, computation of the model efficiency, and visual analysis of the residual errors. We then investigate Rykiel's [Rykiel Jr., E.J., 1996. Testing ecological models: the meaning of validation. Ecol. Model. 90, 229–244] suggestion to re-calibrate the model in order to deal with validation failures. Using three different data sets representing spring, summer and late summer growth of beech ( Fagus sylvatica L.) and oak ( Quercus robur L.), we show that model re-calibration is necessary to successfully pass both the visual and the quantitative validation tests. Recalibration caused the values of some of the hydraulic parameters to change ( C(stem) and C(crown)) as well as parameters related to radial stem growth ( β and ϕ). From these changes, information regarding the overall seasonal behaviour could be derived (e.g., cessation of growth). Additionally, it was shown that general conclusions about the differences between beech and oak (e.g., a higher hydraulic capacitance and a lower hydraulic xylem resistance for oak compared to beech) remained valid across the seasons as well. We finally demonstrate that the recalibrated model parameter values are not transferable across the growing season and underscore the need for caution when applying a model or application developed for one temporal or spatial situation to another.