Approximating covariances between nested plot sizes in forest inventory

The use of nested plot sizes in forest inventories that encounter a wide range of conditions is relatively common. In straightforward situations, data from the different nested plot sizes are usually combined to create a single plot observation for estimation purposes. However, circumstances may occur where nested plot size estimates are obtained separately and subsequently combined via addition to obtain the final result. In these cases, covariances among the nested plots must be considered in the calculation of estimator variance. However, there are several potential approaches that might be considered given that only partial information is known for all but the smallest nested plot size. In this paper, three approaches to estimating the covariance were examined: (1) a modified form of a partially-dependent sample adjustment factor method, (2) explicit subsetting of trees to the area in common among nested plots, and (3) typical covariance estimation ignoring the lack of common area basis. Although the adjustment factor and subsetting methods showed strong consistency in outcomes, the estimated covariances were much smaller than those from ignoring the area basis issue. A subsequent simulation exercise revealed the most accurate covariances were obtained by ignoring the area issue. Thus, covariance estimation calculations can proceed without the additional complications of accounting for different nested plot sizes.