Soil-Sensitive Weibull Distribution Models of Larix principis-rupprechtii Plantations across Northern China

Tree diameter distribution models are important tools for forest management decision making. Soil variables affect tree growth and thus diameter distribution. However, few studies have been conducted on diameter distribution models describing the effects of soil. This study developed a soil-sensitive diameter distribution model based on 213 sample plots of Larix principis-rupprechtii plantations in northern China. The Weibull distribution model was modified by a compatible simultaneous system and the percentile method with the inclusion of soil variables. The most significant factors influencing the diameter distribution of L. principis-rupprechtii in terms of both scale and shape were stand characteristics and available K and alkali-hydrolysable N. The adjusted coefficient of determination for parameter gamma significantly improved by 16.0%, while the root mean square error for parameter beta decreased by 10.4%. The F test indicated a substantial difference between the models with and without soil variables. From the perspective of adjustable R-2 values, the Akaike information criterion, root mean square error, relative error index, and absolute error index, the inclusion of stand and soil factors in the tree diameter distribution model enhanced its performance compared to the model that did not consider soil factors. The soil-sensitive diameter distribution model is proven to be effective and accurate.