Daily mean albedo is a critical variable in surface energy budget and climate change studies. Currently, satellite-based daily mean albedo is typically estimated from the diurnal variation of albedo, derived from multi-angle reflectance observations using a Bidirectional Reflectance Distribution Function (BRDF) kernel-driven model. However, this model assumes flat terrain and neglects topographic effects. This study evaluates the estimation errors of daily mean albedo derived from the BRDF kernel-driven model over rugged terrain. Experiments were conducted for rugged terrains with different mean slopes (10°, 20°, and 30°) and aspects (north and west) at spatial scales of 500 m and 1 km, using large-scale remote sensing data and the image simulation framework (LESS) model. The results demonstrate that topography significantly influences the daily mean albedo derived from the BRDF kernel-driven model, with the largest relative error exceeding 50%. The estimation error increases as the slope of the terrain becomes steeper and is also strongly influenced by the aspect of the terrain. When the solar azimuth angle aligns with the aspect of the rugged terrain, the estimation error becomes particularly pronounced. These findings highlight the necessity of accounting for topographic effects when estimating daily mean albedo.

Quantitative evaluation of errors caused by Digital Elevation Model (DEM) geolocation bias is crucial for the multiscale validation of land surface albedo (LSA) over rugged terrain, as it provides a deeper understanding of topographic effects and helps minimizing validation uncertainties. This letter simulates the near-infrared band (NIR, 850 nm) fine scale albedo maps and coarse scale albedo by (large-scale remote sensing data and image simulation framework) LESS model, and shifts the DEMs along the different directions to aggregate to different coarse scales. The Mountain-Radiation-Transfer-based (MRT-based) albedo upscaling model was used to aggregate to the coarse scale. The results demonstrate that the errors distribution caused by DEM offsets is related to the terrain features. The primary factors influencing these errors are the average slope and coarse scale. Error increases with steeper slopes and decreases with larger coarse scales. Specifically, at 250 m, for terrains with a mean slope of approximately 25°, when the DEM is shifted by 4 pixels in both row and column directions, the errors can exceed 0.08, which is 4.5 times greater than those for gentle slopes (mean slope ≈ 5°). Minor DEM offsets are generally acceptable for gentle slopes and larger scales (>1 km), whereas precise DEM geolocation is essential for steeper slopes (mean slope > 15°), particularly at smaller coarse scales.

The diurnal variation of high spatial resolution albedo is crucial for understanding the energy budget over mountainous areas. Topography significantly affects the diurnal variation of albedo, making its accurate estimation challenging. In this study, we propose a novel algorithm for estimating the diurnal variation of albedo over sloping terrain using high-resolution satellite data. The diurnal variation of albedo is represented as the product of instantaneous albedo at the time of satellite overpass and a diurnal variation factor. Instantaneous albedo is derived from Landsat data and prior BRDF information from the Polarization and Directionality of the Earth’s Reflectances (POLDER) database. The diurnal variation factor is calculated using a fine-scale digital elevation model (DEM) and prior BRDF information, capturing the shape of diurnal variation. Validation against in situ measurements demonstrates the algorithm’s high accuracy ($R^{2} = 0.902$and root-mean-square error (RMSE) = 0.029). In addition, this study examines the differences in the diurnal variation patterns between horizontal/horizontal sloped albedo (HHSA) and inclined/inclined sloping surface albedo (IISA). The results reveal a notable difference between the two: diurnal variation of HHSA is more sensitive to topography, showing a J-shaped pattern, whereas that of IISA consistently follows a U-shaped pattern, better reflecting the sloping surface properties.

Characterizing the anisotropic features at the Top of Atmosphere (TOA) is crucial for vegetation monitoring and retrieval of biophysical parameters. The core challenge lies in modeling the mutual interactions between land surface and atmosphere, particularly in the context of rugged terrains and cloudy conditions. The GOSAILTA is proposed to extend the top-of-canopy (TOC) anisotropic reflectance Geometric Optical and mutual shadowing and Scattering-from Arbitrarily-Inclined- Leaves model coupled with Topography (GOSAILT) model to TOA reflectance/radiance by integrating Santa Barbara DISORT Atmospheric Radiative Transfer (SBDART) model. The interactions between atmosphere and land surface are characterized for the effects of the sloped surface and its surrounding terrains under both clear and cloudy conditions. The model was validated against Discrete Anisotropic Radiative Transfer (DART) simulations, airborne observations from Wideangle Infrared Dual-model line/area Array Scanner (WIDAS), and satellite observations from HJ-1A/B constellation Charge- Coupled Device (CCD). Results demonstrate high overall accuracy in the red band (coefficient of determination (R2) = 0.993; root-mean-square error (RMSE) = 0.008; mean absolute percentage error (MAPE) = 5.481%) and near-infrared (NIR) band (R2 = 0.933, RMSE = 0.025; MAPE = 6.227%) compared to DART simulations. The simulations show strong agreement with WIDAS and HJ, achieving an R² of 0.9. However, the accuracy is slightly lower for top-of-cloud reflectance, with an R² and MAPE of 0.311 and 14.972%, respectively, primarily due to limitations in cloud parameterization.

The diurnal variation of land surface albedo (DVLSA) is crucial for understanding energy budgets and climate change. As topography complicates the radiative transfer processes, the estimation of DVLSA over rugged terrain becomes challenging. In this study, the topography-coupled DVLSA model (DVLSA_T) is developed to estimate DVLSA over rugged terrain. DVLSA_T represents DVLSA as a multiplication between the basic albedo and a diurnal variation factor. The basic albedo is the albedo at local noon with topographic effects removed, while the diurnal variation factor extends the albedo from local noon to different times of the day, accounting for topographic effects. Specifically, the diurnal variation factor of black-sky albedo (BSA) changes with the illumination geometry, integrating the topographic effects and U-shaped pattern of DVLSA. In contrast, the diurnal variation factor of white-sky albedo (WSA) is independent of illumination geometry and is solely influenced by topography. DVLSA_T shows good performance when compared with the 3-D radiative transfer simulations by the large-scale remote sensing data and image simulation framework (LESS) (BSA: coefficient of determination (${R}^{2}$) = 0.977; root-mean-square (RMSE) = 0.013; WSA:${R}^{2} =0.982$; and RMSE = 0.012) and sandbox measurements (blue-sky albedo:${R}^{2} = 0.904$and RMSE = 0.012). DVLSA_T also has a good agreement with in situ measurements, with an RMSE of 0.024 and an${R}^{2}$of 0.738. Our results demonstrate that DVLSA_T can effectively characterize DVLSA over rugged terrain.