Linear models for airborne-laser-scanning-based operational forest inventory with small field sample size and highly correlated LiDAR data

Modern operational forest inventory often uses remotely sensed data that cover the whole inventory area to produce spatially explicit estimates of forest properties through statistical models. The data obtained by airborne light detection and ranging (LiDAR) correlate well with many forest inventory variables, such as the tree height, the timber volume, and the biomass. To construct an accurate model over thousands of hectares, LiDAR data must be supplemented with several hundred field sample measurements of forest inventory variables. This can be costly and time consuming. Different LiDAR-data-based and spatial-data-based sampling designs can reduce the number of field sample plots needed. However, problems arising from the features of the LiDAR data, such as a large number of predictors compared with the sample size (overfitting) or a strong correlation among predictors (multicollinearity), may decrease the accuracy and precision of the estimates and predictions. To overcome these problems, a Bayesian linear model with the singular value decomposition of predictors, combined with regularization, is proposed. The model performance in predicting different forest inventory variables is verified in ten inventory areas from two continents, where the number of field sample plots is reduced using different sampling designs. The results show that, with an appropriate field plot selection strategy and the proposed linear model, the total relative error of the predicted forest inventory variables is only 5%–15% larger using 50 field sample plots than the error of a linear model estimated with several hundred field sample plots when we sum up the error due to both the model noise variance and the model’s lack of fit.