Validating a reflectance model based on photon recollision probability in single tree crowns

Abstract:

Spectral invariants and photon recollision probability theories provide a solid theoretical framework for developing relatively simple, i.e. intuitive and relatively easily invertible, models of forest canopy reflectance. Empirical validation of these theories has been, however, rarely performed. Here we present results of a first empirical validation of a model based on photon recollision probability in individual tree crowns. Multiangular spectra of small pine, spruce, and oak trees (height = 0.38–0.7 m) were measured using a goniometer, tree hemispherical reflectance was derived from those measurements, and the agreement between modeled and measured tree reflectance was evaluated. The model predicted the spectral signatures of the trees in the wavelength range between 400–­2300 nm well, with wavelength-specific bias between -0.048 and 0.034 in reflectance units. In relative terms, the model errors were the smallest in the near-infrared (relative RMSE up to 4 %, 7 %, and 4 % for pine, spruce, and oak, respectively) and the largest in the visible wavelength region (relative RMSE up to 34 %, 20 %, and 60 %). The errors in the visible region could be partly attributed to wavelength-dependent directional scattering properties of the leaves. Including woody parts of trees in the model improved the results by reducing the relative RMSE by up to 10 % depending on species and wavelength. Spectrally invariant model parameters, i.e. total and directional escape probabilities, depended on spherically averaged silhouette to total area ratio (STAR) of the trees. Overall, the modeled and measured tree reflectance mainly agreed within measurement uncertainties, but the results indicate that the assumption of isotropic scattering by the leaves can result in large errors in the visible wavelength region for some tree species. Our results help increasing the confidence when using photon recollision probability and spectral invariants -based models to interpret satellite images, but they also lead to an improved understanding of the assumptions and limitations of these theories.