Procedures for validation of forest management growth models: an application to continuous forest inventory data

After a careful reading of available literature on forest growth models validation a framework to validate this type of models is proposed. Three different areas of concern should be considered: (i) verification of the models behavior such as the biological validity of forest growth functions used 35 its components, the correctness of stand property-time or property-property relations or the correct model responses to alternalive management decisions as evaluated by "experienced" people directly involved in forest management (potential model users), (ii) characterization of model error through the analysis of the prediction residuals (computation of summary statistics and graphical analysis), the computation of critical errors and confidence intervals, the detection of error correlations with projection length or initial stand conditions and the identification of the effect of each individual model component on total error, (iii) statistical testing, through the use of several parametric and non parametric statistical tests. While in the first area the analyst (modelbuilder or potential user) gains confidence on the logical structure of the model, the second and the third, usually considered as "the" validation, means testing the agreement between available information from the real system and the corresponding responses emanating from the model. In this paper some of the procedures that are usually used to validate forest growth models were selected to validate a diameter distribution model (PBRAVO), using procedures from each one of the three areas of concern in model validation. Data provided by the forest management inventory carried out each five years in a National Forest in the center of Portugal were used. Although validation is problem dependent this example clearly shows that at least some testing in each one of these areas is needed in order to be confident in using the model. The importance of the identification of the effect of each individual model component on total error is also evidenced by the example