Effects of height imputation strategies on stand volume estimation

Subsampling and subsequent imputation of tree heights can improve the predictive performance of stand volume estimation but may also introduce biases. Using coastal Douglas-fir data from southwest Oregon, USA, the predictive performance of several height imputation strategies for estimating stand volume was evaluated. A subsample of 1-15 trees was randomly selected per stand, and missing heights were imputed using a regional Chapman-Richards function with diameter only and diameter plus stand density measures, fitted using a nonlinear least-squares model (NFEM) and a nonlinear mixed-effects model (NMEM). Missing heights were imputed using the regional height-diameter equation and by adjusting the equation with a correction factor (NFEM) or with predicted random effects (NMEM) to calibrate the height-diameter relationship to each stand. Differences in actual stand volumes, calculated with measured heights, and predicted stand volumes, calculated using measured heights for the subsampled trees and predicted heights for those with missing heights, were used to compare the alternative height imputation methods. Precision and bias were poorest for the regional models, especially NMEM, and best for the adjusted models also using NMEM. Results suggest that a similar subsample of heights (n = 4) is required for precise stand volume estimation as has been reported for height.