Analysis of spatial correlation in predictive models of forest variables that use LiDAR auxiliary information

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Abstract
Accounting for spatial correlation of LiDAR model errors can improve the precision of model-based estimators. To estimate spatial correlation, sample designs that provide close observations are needed, but their implementation might be prohibitively expensive. To quantify the gains obtained by accounting for the spatial correlation of model errors, we examined (i) the spatial correlation patterns of residuals from LiDAR linear models developed to predict volume, total and stem biomass per hectare, quadratic mean diameter (QMD), basal area, mean and dominant height, and stand density and (ii) the impact of field plot size on the spatial correlation patterns in a standwise managed Mediterranean forest in central Spain. For all variables, the correlation range of model residuals consistently increased with plot radius and was always below 60 m except for stand density, where it reached 85 m. Except for QMD, correlation ranges of model residuals were between 1.06 and 8.16 times shorter than those observed for the raw variables. Based on the relatively short correlation ranges observed when the LiDAR metrics were used as predictors, the assumption of independent errors in many forest management inventories seems to be reasonable and appropriate in practice.

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