Incorporating environmental and geographical information in forest data analysis: a new fitting approach for universal kriging

Universal kriging gives the optimal linear model to incorporate auxiliary information in data analysis in the presence of spatial dependence of observations if the underlying variogram is known. However, in practice, the variogram is typically unknown and its estimation constitutes one of the major problems in universal kriging theory. In this paper, a new method is proposed to estimate the variogram and the mean function in universal kriging based on the relationship between the second moments of the variable Z(s) and the auxiliary variables. The performance of the proposed method is analysed in three case studies: the prediction of site index in an Italian stone pine ( Pinus pinea L.) forest, the estimation of growing stock in a Scots pine ( Pinus sylvestris L.) stand, and the assessment of the environmental factors involved in the distribution of a Meliosma species in a tropical montane cloud forest. The results show that the proposed method performs as well as the maximum likelihood and least squares methods in terms of unbiasedness and precision of the kriging predictor and prediction error variance estimation. The proposed method allows the spatial variability linked to environmental and geographical factors to be identified in the analysis of data from forest ecosystems.