Rugged terrain, including mountains, hills, and some high lands are typical land surfaces around the world. As a physical parameter for characterizing the anisotropic reflectance of the land surface, the importance of the bidirectional reflectance distribution function (BRDF) has been gradually recognized in the remote sensing community, and great efforts have been dedicated to build BRDF models over various terrain types. However, on rugged terrain, the topography intensely affects the shape and magnitude of the BRDF and creates challenges in modeling the BRDF. In this paper, after a brief introduction of the theoretical background of the BRDF over rugged terrain, the status of estimating land surface BRDF properties over rugged terrain is comprehensively reviewed from a historical perspective and summarized in two categories: BRDFs describing solo slopes and those describing composite slopes. The discussion focuses on land surface reflectance retrieval over mountainous areas, the difference in solo slope and composite slope BRDF models, and suggested future research to improve the accuracy of BRDFs derived with remote sensing satellites.

Topography complicates the modeling and retrieval of land surface albedo due to shadow effects and the redistribution of incident radiation. Neglecting topographic effects may lead to a significant bias when estimating land surface albedo over a single slope. However, for rugged terrain, a comprehensive and systematic investigation of topographic effects on land surface albedo is currently ongoing. Accurately estimating topographic effects on land surface albedo over a rugged terrain presents a challenge in remote sensing modeling and applications. In this paper, we focused on the development of a simplified estimation method for snow-free albedo over a rugged terrain at a 1-km scale based on a 30-m fine-scale digital elevation model (DEM). The proposed method was compared with the radiosity approach based on simulated and real DEMs. The results of the comparison showed that the proposed method provided adequate computational efficiency and satisfactory accuracy simultaneously. Then, the topographic effects on snow-free albedo were quantitatively investigated and interpreted by considering the mean slope, subpixel aspect distribution, solar zenith angle, and solar azimuth angle. The results showed that the more rugged the terrain and the larger the solar illumination angle, the more intense the topographic effects were on black-sky albedo (BSA). The maximum absolute deviation (MAD) and the maximum relative deviation (MRD) of the BSA over a rugged terrain reached 0.28 and 85%, respectively, when the SZA was 60° for different terrains. Topographic effects varied with the mean slope, subpixel aspect distribution, SZA and SAA, which should not be neglected when modeling albedo.

This study assessed accuracies of MCD43A3, Global Land-Surface Satellite (GLASS) and forthcoming Multi-source Data Synergized Quantitative Remote Sensing Production system (MuSyQ) albedos using ground observations and Huan Jing (HJ) data over the Heihe River Basin. MCD43A3 and MuSyQ albedos show similar high accuracies with identical root mean square errors (RMSE). Nevertheless, MuSyQ albedo is better correlated with ground measurements when sufficient valid observations are available or snow-free. The opposite happens when less than seven valid observations are available. GLASS albedo presents a larger RMSE than MCD43A3 and MuSyQ albedos in comparison with ground measurements. Over surfaces with smaller seasonal variations, MCD43A3 and MuSyQ albedos show smaller RMSEs than GLASS albedo in comparison with HJ albedo. However, for surfaces with larger temporal variations, both RMSEs and R² of GLASS albedo are comparable with MCD43A3 and MuSyQ. Generally, MCD43A3 and MuSyQ albedos featured the same RMSEs of 0.034 and similar R² (0.920 and 0.903, respectively), which are better than GLASS albedo (RMSE = 0.043, R² = 0.787). However, when it comes to comparison with aggregated HJ albedo, MuSyQ and GLASS albedos are with lower RMSEs of 0.027 and 0.032 and higher R² of 0.900 and 0.898 respectively than MCD43A3 (RMSE = 0.038, R² = 0.836). Despite the limited geographic region of the study area, they still provide an important insight into the accuracies of three albedo products.

The importance of the bidirectional reflectance distribution function (BRDF) has been well documented in quantitative remote sensing. The semiempirical, kernel-driven BRDF model is widely used to generate operational BRDF/albedo products due to its simplicity and accuracy. However, the effect of topography is rarely coupled with a kernel-based BRDF model. In this paper, a new kernel-driven reflectance model for sloping terrain (KDST) was developed based on the framework of the RossThick-LiSparse-Reciprocal (RTLSR) model. The slope, aspect, geotropic nature of the tree crown governed by gravity, component spectra contrasts, and diffuse irradiance were considered in the KDST model. The performance of KDST was evaluated by 3-D discrete anisotropic radiative transfer (DART) simulations, in situ measurements, and HJ-1A/B constellation charge-coupled device satellite observations. Using DART simulations, KDST reduces the maximum biases of the RTLSR from 15.6% and 29.7% to 7.1% and 4.8% for the surface bidirectional reflectance factor and hemispherical-direction reflectance factor, respectively. Compared with in situ measurements, KDST improves the reflectance simulation accuracy for the red and near-infrared bands from 0.0172 (18.65%) and 0.022 (4.77%) to 0.0060 (6.51%) and 0.0043 (1.05%), respectively. The preliminary comparison results indicate that KDST is promising for reflectance simulation over rugged terrain.

The issue for the validation of land surface remote sensing albedo products over rugged terrain is the scale effects between the reference albedo measurements and coarse scale albedo products, which is caused by the complex topography. This paper illustrates a multi-scale validation strategy specified for coarse scale albedo validation over rugged terrain. A Mountain-Radiation-Transfer-based (MRT-based) albedo upscaling model was proposed in the process of multi-scale validation strategy for aggregating fine scale albedo to coarse scale. The simulated data of both the reference coarse scale albedo and fine scale albedo were used to assess the performance and uncertainties of the MRT-based albedo upscaling model. The results showed that the MRT-based model could reflect the albedo scale effects over rugged terrain and provided a robust solution for albedo upscaling from fine scale to coarse scale with different mean slopes and different solar zenith angles. The upscaled coarse scale albedos had the great agreements with the simulated coarse scale albedo with a Root-Mean-Square-Error (RMSE) of 0.0029 and 0.0017 for black sky albedo (BSA) and white sky albedo (WSA), respectively. Then the MRT-based model was preliminarily applied for the assessment of daily MODerate Resolution Imaging Spectroradiometer (MODIS) Albedo Collection V006 products (MCD43A3 C6) over rugged terrain. Results showed that the MRT-based model was effective and suitable for conducting the validation of MODIS albedo products over rugged terrain. In this research area, it was shown that the MCD43A3 C6 products with full inversion algorithm, were generally in agreement with the aggregated coarse scale reference albedos over rugged terrain in the Heihe River Basin, with the BSA RMSE of 0.0305 and WSA RMSE of 0.0321, respectively, which were slightly higher than those over flat terrain.