Spatial prediction of diameter distribution models

The prediction of the diameter distribution of a stand is of great interest to forest managers for the evaluation of forest resources and scheduling the future silvicultural treatments. In the present paper, we present a geostatistical approach for the prediction of diameter distributions. The advantage of the proposed method over traditional prediction systems is that it is possible to estimate the diameter distribution at locations, where no secondary variables are measured. The Weibull and the Chaudhry–Ahmad probability density functions were fitted by maximum likelihood to the diameter distribution of 176 plots of pure, even aged stands of Pinus pinaster Ait. located in the province of Segovia of central Spain. Data were taken from the Second National Forest Inventory of Spain. The spatial “behaviour” of the parameters of the density functions was studied by variogram analysis and the results showed that all parameters were spatially correlated to some extent. Kriging was used for the interpolation of parameters of the diameter distributions over the study area. Cross-validation was performed separately for every parameter. Results showed that the Weibull function gave smaller relative bias in the prediction of the diameter sum. Additionally, the likelihood ratio was used to compare the fit of the density functions. This ratio was computed twice: firstly when parameters were estimated by maximum likelihood and secondly, when parameters were predicted by kriging-cross-validation. The Chaudhry–Ahmad function fitted better the actual diameter distributions when maximum-likelihood was used for parameter estimation. Nevertheless, the fit of the Weibull was much better when kriging was used for parameter prediction. The prediction of the diameter distribution was made using data from the National Forest Inventory, therefore predictions should be used for regional planning and estimation of forest resources at this spatial scale (national). For forest management purposes at a local scale, data sources taken at fine spatial scales should be preferred. The spatial discontinuities that the forest compartments introduce during kriging interpolation are finally discussed and some solutions are proposed.