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• Bayesian inversion of PARAS model produced promising LAI retrieval accuracy. • Non-uniform priors improve inversion by counteracting optical saturation effects. • Landsat 8 OLI data showed better LAI retrieval accuracy than Sentinel-2 MSI. • We highlight benefits of uncertainty quantification in reflectance model inversion. The inversion of reflectance models is a generalizable tool to obtain estimates on forest biophysical parameters, such as leaf area index, with theoretically little information need from a study area, instead relying on the knowledge about physical processes in the forest radiation regime. The use of prior information can greatly improve the reflectance model inversion, however, the literature does not yet provide much information on the selection of priors and their influence on the inversion results. In this study, we used a Bayesian approach to invert the PARAS forest reflectance model and retrieve leaf area index from Sentinel-2 MSI and Landsat 8 OLI multispectral satellite images. The PARAS model is based on the theory of spectral invariants, which describes the influence of wavelength-independent parameters on forest radiative transfer. The Bayesian inversion approach is highly flexible, provides uncertainty quantification, and enables the explicit incorporation of prior knowledge into the inversion process. We found that the choice of prior information is crucial in inverting a forest reflectance model to predict leaf area index. Regularizing and informative priors for leaf area index strongly improved the predictions, relative to an uninformative prior, in that they counteracted the saturation effect of the optical signal occuring at high values for leaf area index. The predictions of leaf area index were more accurate for Landsat 8 than for Sentinel-2, due to potential inconsistencies in the visible bands of Sentinel-2 in our data, and the higher spectral resolution. [ABSTRACT FROM AUTHOR]

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 the 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 paper, 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 root mean square error over a state-of-the-art $k$ -nearest neighbors (kNNs) 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. [ABSTRACT FROM AUTHOR]

In this paper, Bayesian inversion of a physically-based forest reflectance model is investigated to estimate of boreal forest canopy leaf area index (LAI) from EO-1 Hyperion hyperspectral data. The data consist of multiple forest stands with different species compositions and structures, imaged in three phases of the growing season. The Bayesian estimates of canopy LAI are compared to reference estimates based on a spectral vegetation index. The forest reflectance model contains also other unknown variables in addition to LAI, for example leaf single scattering albedo and understory reflectance. In the Bayesian approach, these variables are estimated simultaneously with LAI. The feasibility and seasonal variation of these estimates is also examined. Credible intervals for the estimates are also calculated and evaluated. The results show that the Bayesian inversion approach is significantly better than using a comparable spectral vegetation index regression. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, we propose an approach to quantify the plot-level uncertainty in species-specific growing stock volume estimated from airborne laser scanning data and aerial imagery. This is accomplished by adopting the framework of Bayesian inference in the area-based estimation of stock volume. The results show that the proposed approach performs well in quantifying the estimate uncertainty and produces optimal interval estimates for species-specific volumes when sufficient training data are available. Also the point estimate accuracy is competitive with current state-of-the-art methods. Furthermore, we demonstrate how the quantified uncertainties of the stand attributes can be utilized to determine the uncertainty in classification done using the estimated stand attributes. [ABSTRACT FROM AUTHOR]

The article focuses on effects of numbers of observations and predictors for various model types on the performance of forest inventory with airborne laser scanning.