No abstract

Hyperspectral remote sensing data carry information on the leaf area index (LAI) of forests, and thus in principle, LAI can be estimated based on the data by inverting a forest reflectance model. However, LAI is usually not the only unknown in a reflectance model; especially, the leaf spectral albedo and understory reflectance are also not known. If the uncertainties of these parameters are not accounted for, the inversion of a forest reflectance model can lead to biased estimates for LAI. In this paper, we study the effects of reflectance model uncertainties on LAI estimates, and further, investigate whether the LAI estimates could recover from these uncertainties with the aid of Bayesian inference. In the proposed approach, the unknown leaf albedo and understory reflectance are estimated simultaneously with LAI from hyperspectral remote sensing data. The feasibility of the approach is tested with numerical simulation studies. The results show that in the presence of unknown parameters, the Bayesian LAI estimates which account for the model uncertainties outperform the conventional estimates that are based on biased model parameters. Moreover, the results demonstrate that the Bayesian inference can also provide feasible measures for the uncertainty of the estimated LAI.

While the analysis of airborne laser scanning (ALS) data often provides reliable estimates for certain forest stand attributes -such as total volume or basal area -there is still room for improvement, especially in estimating species-specific attributes. Moreover, while information on the estimate uncertainty would be useful in various economic and environmental analyses on forests, a computationally feasible framework for uncertainty quantifying in ALS is still missing. In this article, the species-specific stand attribute estimation and uncertainty quantification (UQ) is approached using Gaussian process regression (GPR), which is a nonlinear and nonparametric machine learning method. Multiple species-specific stand attributes are estimated simultaneously: tree height, stem diameter, stem number, basal area, and stem volume. The cross-validation results show that GPR yields on average an improvement of 4.6% in estimate RMSE over a state-of-the-art k-nearest neighbors (kNN) implementation, negligible bias and well performing UQ (credible intervals), while being computationally fast. The performance advantage over kNN and the feasibility of credible intervals persists even when smaller training sets are used.

Nonparametric models are popular in area-based approach (ABA) using airborne laser scanning. It is unclear, however, what are the number of predictors and the number of observations needed for different modeling approaches to provide accurate predictions without overfitting. This work aims to determine these limits for various approaches: ordinary least squares regression (OLS), generalized additive models (GAM), least absolute shrinkage and selection operator (LASSO), random forest (RF), support vector machine (SVM), and Gaussian process regression (GPR). We modeled timber volume (m³ ha-1) using ABA with 2–39 predictors and 20–500 training plots. OLS, GAM, LASSO, and SVM overfitted as the number of predictors approached the number of training plots. They required ≥15 plots per predictor to provide accurate predictions (RMSE ≤30%). GAM required ≥250 plots regardless of the number of predictors. The number of predictors hardly affected RF and GPR, but they required ≥200 and ≥250 training plots, respectively, to ensure accurate predictions. RF did not overfit in any circumstances, whereas GPR overfitted even with 500 training plots. Overall, increasing model predictors up to 39 did not necessarily result in overfitting and, in most models, it resulted in better accuracy as long as the training dataset was sufficiently large (≥250 plots).