Prediction of stand-level growing stock by using a spatial regression model in an Austrian protection forest

A digital forest inventory is proposed to estimate growing stock in a mountainous protection forest near Ebensee, Austria. As protection forests cover 42% of Austria's forest area and safeguard against natural hazards, continuous monitoring is essential but challenging due to steep terrain and coarse sampling in the Austrian National Forest Inventory. This study proposes a monitoring system combining airborne laser scanning and ground-based personal laser scanning (PLS). ALS data supplement spatial regression models that interpolate inventory data collected on 273 sample plots via PLS. Spatially varying intercept and coefficient models were developed to predict growing stock at both total and stand levels within the 4898-ha Ebensee forest district. Models were fitted under a Bayesian framework using Markov Chain Monte Carlo (MCMC) methods. Compared to non-spatial modeling, this spatial approach significantly improves precision; compared to traditional design-based inventories, it enables high-resolution stand-level estimates and reduces fieldwork and costs. Model performance was evaluated via leave-one-out cross-validation, yielding a root mean squared error of 89.0 m 3 /ha and a bias of 0.392 m 3 /ha. This study highlights the efficiency of integrating ALS, PLS, and spatial models in forest inventory, supporting both ecological and economic assessments. • What are the main findings? A digital forest inventory combining airborne laser scanning (ALS), personal laser scanning (PLS), and spatially varying coefficient models yields precise growing stock estimates in heterogeneous mountain protection forests. • The Bayesian spatial modeling framework improves precision over non-spatial and traditional design-based inventories and enables stand-level mapping. • What is the implication of the main finding? Establishes a reproducible workflow for monitoring protection forests under steep-terrain constraints, delivering high-resolution outputs from fewer ground plots. • Offers a scalable approach for integrating advanced remote sensing and spatial models into operational protection forest monitoring programs.