Physically-based methods in remote sensing provide benefits over statistical approaches in monitoring biophysical characteristics of vegetation. However, physically-based models still demand large computational resources and often require rather detailed informative priors on various aspects of vegetation and atmospheric status. Spectral invariants and photon recollision probability theories provide a solid theoretical framework for developing relatively simple models of forest canopy reflectance. Empirical validation of these theories is, however, scarce. Here we present results of a first empirical validation of a model based on photon recollision probability at the level of individual trees. Multiangular spectra of pine, spruce, and oak tree seedlings (height = 0.38–0.7 m) were measured using a goniometer, and tree hemispherical reflectance was derived from those measurements. We evaluated the agreement between modeled and measured tree reflectance. The model predicted the spectral signatures of the tree seedlings in the wavelength range between 400 and 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 seedlings, 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 tree seedlings 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 tree seedlings. 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.

遥感中基于物理的方法在监测植被生物物理特征方面优于统计方法。然而，基于物理的模型仍然需要大量的计算资源，并且常常需要有关植被和大气状况各个方面的相当详细的先验知识。光谱不变性和光子碰撞概率理论为开发相对简单的森林冠层反射率模型提供了坚实的理论框架。但是，对这些理论的经验验证很少。在这里，我们提出基于光子重碰撞概率的单个树模型的模型的第一个经验验证的结果。使用测角仪测量了松树，云杉和橡树幼苗（高度= 0.38–0.7 m）的多角度光谱，从这些测量结果得出树的半球反射率。我们评估了模型反射率与测量树反射率之间的一致性。该模型很好地预测了树苗在400至2300 nm波长范围内的光谱特征，反射率单位为-0.048至0.034之间的波长特定偏差。相对而言，模型误差在近红外范围内最小（相对RMSE分别为松树，云杉和橡树幼苗分别达到4％，7％和4％），在可见波长范围内最大（相对RMSE最高可达34％，20％和60％）。可见光区域的误差可能部分归因于叶片的波长相关定向散射特性。该模型中包括树木幼苗的木本部分，通过根据种类和波长将相对RMSE降低多达10％，从而改善了结果。光谱不变的模型参数，即总和定向逃逸概率，取决于树苗的球形平均轮廓与总面积之比（STAR）。总体而言，建模和测量的树木反射率主要在测量不确定性范围内一致，但是结果表明，叶子的各向同性散射假设可能会导致某些树木在可见波长范围内产生较大误差。我们的结果有助于提高使用光子重碰撞概率和基于光谱不变性的模型来解释卫星图像时的置信度，但是它们也导致人们对这些理论的假设和局限性有了更好的了解。