Combining a predicted diameter distribution with an estimate based on a small sample of diameters

Abstract

The diameter distribution of a forest stand is of great interest in many situations, including forest management planning and the related prediction of growth and yield. The estimation of the diameter distribution may be based on, for example, a measured sample of diameters or the application of previously estimated parameter prediction models (PPMs), which relate the parameters of an assumed distribution function to some stand characteristics. We propose combining these two information sources. The approach is adopted from the mixed-effects modelling theory. The PPMs are treated as mixed-effects models, the residuals being stand effects. These stand effects are predicted using a small sample of tree diameters with the best linear predictor. A study conducted with a Spanish pine data set showed that in a situation where the predictors of the PPM include errrors, the prediction can be improved even by using a sample plot of as few as five sample trees. Vice versa, a distribution based on a sample plot of 3–15 sample trees can be significantly improved by utilizing existing PPMs. An additional simulation study was conducted to further investigate how the violation of different underlying assumptions of the method affects the performance.