A distribution-independent approach to predicting stand diameter distribution

Abstract

A new approach to projecting future stand diameter distribution was proposed without assuming a predefined probability density function. The Lebesque-Stieltjes integral was applied to derive a group of equations for the relationships between current and future stand diameter distributions and stand-level attributes. The parameters in the tree survival function and diameter growth function were recovered using these equations based on independent estimates of future stand mean diameter, quadratic mean diameter, and survival from a whole stand model. This disaggregation approach ensured that the resolutions at size-class distribution and/or individual tree levels were compatible with the stand-level aggregates. A stochastic error component was incorporated into the tree diameter growth function. This allowed us to mimic the tree diameter differentiation process over time, and it improved prediction accuracy for future stand diameter distributions. The proposed approach can also be used to allocate stand growth and yield to a list of individual trees. The fluctuation of tree growth and survival for each tree can be implemented by simulating the variance of tree diameter growth and survival probability using Monte Carlo or error propagation methods.