Retrieval of among-stand variances from one observation per stand

Abstract

Forest inventories provide predictions of stand means on a routine basis from models with auxiliary variables from remote sensing as predictors and response variables from field data. Many forest inventory sampling designs do not afford a direct estimation of the among-stand variance. As consequence, the confidence interval for a model-based prediction of a stand mean is typically too narrow. We propose a new method to compute (from empirical regression residuals) an among-stand variance under sample designs that stratify sample selections by an auxiliary variable, but otherwise do not allow a direct estimation of this variance. We test the method in simulated sampling from a complex artificial population with an age class structure. Two sampling designs are used (one-per-stratum, and quasi systematic), neither recognize stands. Among-stand estimates of variance obtained with the proposed method underestimated the actual variance by 30-50%, yet 95% confidence intervals for a stand mean achieved a coverage that was either slightly better or at par with the coverage achieved with empirical linear best unbiased estimates obtained under less efficient two-stage designs.

Model-Based Estimation of Forest Inventory Attributes Using Lidar: A Comparison of the Area-Based and Semi-Individual Tree Crown Approaches

“…The impact that estimates of σ v may have on the mean squared error estimates of stand-level predictions, especially for unsampled stands ( Table 6), suggesting that careful consideration should be given for the estimate of this parameter. Recent studies have investigated the estimation of σ v under different sampling scenarios using simulated data [16,42,43] and suggest that small stand-specific sample sizes may introduce a negative bias in the estimation of stand-specific, model-based mean squared errors under the unit-level model. Our study area had sample sizes that widely varied from stand to stand (Table 1), and in this situation, the possibility of negative bias is not as clear.…”