Propagating uncertainty through individual tree volume model predictions to large-area volume estimates

Abstract

The effects on large-area volume estimates of uncertainty in individual tree volume model predictions were negligible when using simple random sampling estimators for large-area estimation, but non-negligible when using stratified estimators which reduced the effects of sampling variability. Forest inventory estimates of tree volume for large areas are typically calculated by adding model predictions of volumes for individual trees at the plot level and calculating the per unit area mean over plots. The uncertainty in the model predictions is generally ignored with the result that the precision of the large-area volume estimate is optimistic. The primary objective was to estimate the effects on large-area volume estimates of volume model prediction uncertainty due to diameter and height measurement error, parameter uncertainty, and model residual variance. Monte Carlo simulation approaches were used because of the complexities associated with multiple sources of uncertainty, the non-linear nature of the models, and heteroskedasticity. The effects of model prediction uncertainty on large-area volume estimates of growing stock volume were negligible when using simple random sampling estimators. However, with stratified estimators that reduce the effects of sampling variability, the effects of model prediction uncertainty were not necessarily negligible. The adverse effects of parameter uncertainty and residual variance were greater than the effects of diameter and height measurement errors. The uncertainty of large-area volume estimates that do not account for model prediction uncertainty should be regarded with caution.