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.

As an essential climate variable (ECV), land surface albedo plays an important role in the Earth surface radiation budget and regional or global climate change. The Tibetan Plateau (TP) is a sensitive environment to climate change, and understanding its albedo seasonal and inter-annual variations is thus important to help capture the climate change rules. In this paper, we analyzed the large-scale spatial patterns, temporal trends, and seasonal variability of land surface albedo overall the TP, based on the moderate resolution imaging spectroradiometer (MODIS) MCD43 albedo products from 2001 to 2019. Specifically, we assessed the correlations between the albedo anomaly and the anomalies of normalized difference vegetation index (NDVI), the fraction of snow cover (snow cover), and land surface temperature (LST). The results show that there are larger albedo variations distributed in the mountainous terrain of the TP. Approximately 10.06% of the land surface is identified to have been influenced by the significant albedo variation from the year 2001 to 2019. The yearly averaged albedo was decreased significantly at a rate of 0.0007 (Sen’s slope) over the TP. Additionally, the yearly average snow cover was decreased at a rate of 0.0756. However, the yearly average NDVI and LST were increased with slopes of 0.0004 and 0.0253 over the TP, respectively. The relative radiative forcing (RRF) caused by the land cover change (LCC) is larger than that caused by gradual albedo variation in steady land cover types. Overall, the RRF due to gradual albedo variation varied from 0.0005 to 0.0170 W/m², and the RRF due to LCC variation varied from 0.0037 to 0.0243 W/m² during the years 2001 to 2019. The positive RRF caused by gradual albedo variation or the LCC can strengthen the warming effects in the TP. The impact of the gradual albedo variations occurring in the steady land cover types was very low between 2001 and 2019 because the time series was short, and it therefore cannot be neglected when examining radiative forcing for a long time series regarding climate change.

The semiempirical kernel-driven model is commonly used for global surface reflectance characterization because of its simplicity and underlying physical meaning. However, the current kernel-driven reflectance models assume that the terrain is flat and homogeneous, and can induce significant errors in the surface reflectance estimation and subsequent parameter retrievals over rugged terrain. In this study, an improved topography-coupled kernel-driven (TCKD) reflectance model with the correction of diffuse skylight effects was proposed based on the diffused-equivalent slope model (dESM) and RossThick-LiTransit (RTLT) kernel-driven model. The TCKD model's accuracy and effectiveness were evaluated using surface reflectance simulated by the radiosity approach and the Moderate Resolution Imaging Spectroradiometer (MODIS) data. Against simulated data, the results show that the TCKD model can accurately capture the distortion of the reflectance shape and hemispherical distribution caused by the topographic effects. Compared to MODIS data, the TCKD model has an overall better performance than the RTLT model across different spatial scales and land cover types. When the mean slope is larger than 35° at the 500-m resolution, the TCKD model's near-infrared (NIR) root-mean-square error (RMSE) and the regression slope of the fitting line are 0.037 and 0.752, respectively, whereas those of the RTLT model are 0.049 and 0.645. Neglecting the diffuse skylight in the TCKD model can also lead to great bias in the reflectance retrievals. When the mean slope is 31°, as the ratio of diffuse skylight varies from 0 to 1, the NIR RMSE of the TCKD model decreases from 0.012 to 0.005, whereas that increases from 0.012 to around 0.02 if the diffuse skylight effects are neglected. These preliminary results demonstrate that the TCKD model is capable of improving the fitting ability of the kernel-driven model over rugged terrain and provides potentials for better retrieving and interpreting land surface parameters such as land surface albedo in mountainous areas.

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.