Estimating timber volume loss due to storm damage in Carinthia, Austria, using ALS/TLS and spatial regression models

A spatial regression model framework is presented to predict growing stock volume loss due to storm Adrian which caused heavy forest damage in the upper Gail valley in Carinthia, Austria, in October 2018. Model parameters were estimated using growing stock volume measured with a terrestrial laser scanner on 62 sample plots distributed across five sub-regions. Predictor variables were derived from high resolution vegetation height measurements collected during an airborne laser scanning campaign. Non-spatial and spatial candidate models were proposed and assessed based on fit to observed data and out-of-sample prediction. Spatial Gaussian processes associated model intercepts and regression coefficients were used to capture spatial dependence. Results show a spatially-varying coefficient model, which allowed the intercept and regression coefficients to vary spatially, yielded the best fit and prediction. Two approaches were considered for prediction over blowdown areas: 1) an areal approach that viewed each blowdown as a single prediction unit indexed by its centroid; and 2) a block approach where each blowdown was partitioned into smaller prediction units to better align with sample plots' spatial support. Joint prediction was used to acknowledge spatial dependence among block units. Results demonstrated the block approach is preferable as it mitigated change-of-support issues encountered in the areal approach. Despite the small sample size, predictions for 55% of the total 564 blowdown areas, accounting for 93% of the total loss, had a coefficient of variation less than 25%. Key advantages of the proposed regression framework are the ability to quantify uncertainty in spatial covariance parameters, propagate parameter uncertainty through to prediction, and provide statistically valid prediction point and interval estimates for individual blowdowns and collections of blowdowns.