National forest inventories typically estimate individual tree volumes using models that rely on measurements of predictor variables such as tree height and dia

National Forest Inventories (NFIs) provide estimates of forest parameters for national and regional scales. Many key variables of interest, such as biomass and

Model-based inference is an alternative to probability-based inference for small areas or remote areas for which probability sampling is difficult. Model-based mean square error estimators incorporate three components: prediction covariance, residual variance, and residual covariance. The latter two components are often considered negligible, particularly for large areas, but no thresholds that justify ignoring them have been reported. The objectives of the study were threefold: (i) to compare analytical and bootstrap estimators of model parameter covariances as the primary factors affecting prediction covariance; (ii) to estimate the contribution of residual variance to overall variance; and (iii) to estimate thresholds for residual spatial correlation that justify ignoring this component. Five datasets were used, three from Europe, one from Africa, and one from North America. The dependent variable was either forest volume or biomass and the independent variables were either Landsat satellite image bands or airborne laser scanning metrics. Three conclusions were noteworthy: (i) analytical estimators of the model parameter covariances tended to be biased; (ii) the effects of residual variance were mostly negligible; and (iii) the effects of spatial correlation on residual covariance vary by multiple factors but decrease with increasing study area size. For study areas greater than 75 km² in size, residual covariance could generally be ignored.

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.

Forest structural diversity was estimated for an ecological province in the north-central region of the United States of America using data for nearly 350 000 trees observed on >12 000 forest inventory plots. Each plot was 672 m² in area, and the sampling intensity was approximately 1 plot/2400 ha. Two indices were used for each of two commonly and accurately measured inventory variables: species count and the Shannon index for tree species and standard deviation and the Shannon index for tree diameter. The primary results of the study were fourfold: (i) ranges of spatial correlation for diversity indices were small, on the order of 5–10 km, (ii) high proportions of provincewide diversity were realized for circular areas with radii as small as 15 km, (iii) diversity for both species and diameter exhibited strong northwest to southeast spatial patterns, and (iv) plot-level α diameter diversity was highly correlated with mean plot-level tree diameter.