Modelling a system of nonlinear additive crown width models applying seemingly unrelated regression for Prince Rupprecht larch in northern China

Abstract

Crown width (CW) is an arithmetic mean of two diameters perpendicular to each other and obtained from measurements of four crown radii (crown components) consisting of east, west, south and north crown width. CW is one of the important tree variables in forest growth and yield modelling, and forest management. An accurate approach of obtaining crown measurements can lead to a high accuracy of prediction. Since the additivity properties of CW components and their inherent correlations have not been addressed so far, in this study we introduced a nonlinear seemingly unrelated regression (NSUR) emphasizing the additivity and inherent correlations to develop a system of CW models. We used a large dataset from a total of 3369 Prince Rupprecht larch (Larix principis-rupprechtii Mayr.) trees within 116 permanent sample plots allocated in northern China. The results from NSUR were compared with those from two commonly used additive approaches: adjustment in proportion (AP) and ordinary least square with separating regression (OLSSR). In addition, regional effect on CW components was introduced into the CW model system through an indicator-variable modelling approach. The results showed that (1) the effect of region on CW components was highly significant; and (2) NSUR, AP and OLSSR well ensured the additivity property of a system of the CW models. It was also found that overall the prediction accuracy of NSUR was much higher than those of AP and OLSSR. This study focuses more on the development of methodology that can be applied to develop a system of CW models for other tree species.