Soil models are widely used to characterize the reflectance properties of dry and wet soils. By considering detailed physical processes, the improved multilayer radiative transfer model of soil reflectance (MARMIT-2) model significantly improves the accuracy of simulating wet soil properties. However, the MARMIT-2 model relies on measured dry soil reflectance as an input, which limits its applicability in practical scenarios, especially when detailed information about specific soils is unavailable. To address this issue, this study first evaluated the ability of the general spectral vector (GSV) model of dry soil to represent the reflectance properties of dry soil. Then, we coupled these dry soil vectors with the MARMIT-2 model to propose the GSV + MARMIT-2 model. Finally, we assessed the accuracy of all three models using a wet soil database. The main conclusions of this study include: 1) the dry soil spectral vectors from the GSV model demonstrated high accuracy in describing the reflectance properties of dry soil, achieving an$R^{2}$of 0.988 and a root mean square error (RMSE) of 0.016. 2) All three soil models exhibited high fitting accuracy for the wet soil database ($R^{{2}} = \sim 0.992$and RMSE$= \sim 0.012$). Compared to the GSV and MARMIT-2 models, the GSV + MARMIT-2 model showed slightly improved accuracy under different soil moisture content (SMC) conditions. This study developed a more versatile and flexible soil model framework as it directly integrates the dry soil spectral vectors from the GSV model into the MARMIT-2 model. This coupling significantly expanded the applicability and improved the stability of the MARMIT-2 model.

Sloping terrain distorts the sun-target-sensor geometry, resulting in biases of the optical reflectance measured by remote sensors relative to flat situations. Performing topographic correction (TC) is, therefore, deemed mandatory to foster the full exploitation of satellite images worldwide to support various applications in mountainous regions. Various TC models have already been proposed and developed, while most of them were previously evaluated at local or regional scales using a few images with various evaluation criteria. Therefore, a systematic and comprehensive assessment has yet to be done on these TC models in the global mountainous regions. In the present study, 10523 Landsat 8 OLI images filtered by land cover types and seasons sampled in the global mountains are corrected by ten popular TC models (SE, b correction, VECA, CC, SCS, DS, SCS+C, PLC, Minnaert, and Minnaert+SCS) with a unified evaluation criterion on the Google Earth Engine platform. The outcomes are that: (1) global TC effects on Landsat 8 OLI images generally increase with sun zenith angles and latitudes; (2) six models (SE, b correction, CC, VECA, Minnaert, and Minnaert+SCS) show good adaptability among the ten models for the global mountainous placing a disregard to land cover types and seasons; (3) considering permanent snow and ice, needle-leaved forests in winter, and null values might appear in b correction, SE is deemed to be with the most global adaptability. This study pioneers an evaluation of fashionable TC models concerning mountainous regions worldwide and will be useful for applying TC to Landsat images for the benefit of making global TC products in the future and a fair inter-comparison of OLI surface reflectance measured in various mountainous areas of the globe.

Terrain elevation over forested areas is important for studies such as hydrological modeling and soil erosion. The spaceborne full-waveform LiDAR missions including Geoscience Laser Altimeter System (GLAS) and Global Ecosystem Dynamics Investigation (GEDI) provide freely available terrain elevation products indirectly and directly. However, the accuracies have seldom been evaluated in the same region. Here, we examined the terrain elevation accuracy and assessed the influence of terrain slope in forested areas using high-resolution airborne LiDAR data as a reference. The root mean square error (RMSE) of terrain elevation computed from all the data of GLAS and GEDI is 5.1 m and 8.4 m, respectively. Even though the footprint diameter of GEDI is much smaller than GLAS (25 m vs. 65 m), we still found a significant terrain effect with the increase of slope in GEDI. The RMSE of terrain elevation from GLAS is 3.4 m, 7.6 m, and 10.5 m when the slope ranges from 0° to 30° with an increment of 10°. The RMSE of terrain elevation from GEDI is 5.2 m, 8.8 m, 12.2 m, 14.1 m, and 16. 9 m when the slope ranges from 0° to 50° with an increment of 10°.

Information about the composition and distribution of dominant tree species is crucial for sustainable forest management. A global ecosystem dynamics investigation (GEDI) offers unique advantages in detecting the vertical spatial structure of forest stands, which may improve the common issues of spectral similarity and saturation in traditional spectral-based tree species mapping. However, the effects of its application have not been explored. This study examines temperate and subtropical forests in eastern China, which are dominated by deciduous and evergreen species, respectively. We employed GEDI-derived forest vertical structure characterization (FVSC) to complement Sentinel-2 spectral features for dominant tree species mapping. The results indicate that FVSC significantly improved the mapping accuracy for 11 tree species in both temperate and subtropical forest regions across seasons, with greater benefits observed for broadleaf species than for coniferous species. During the main phenological stages of spring, summer, and autumn, the accuracy of tree species mapping in the temperate region improved by 6.99%–9.85%. The key contributing factors were the cumulative plant area index (PAI) from the ground to the canopy top and cumulative vegetation coverage (COVER) from 5 m to the canopy top. In the subtropical region, the accuracy improvement ranged from 7.75% to 9.5%, with the highest contributions from the plant gap probability (Pgap_theta) and cumulative COVER from 5 m to the canopy top. These findings demonstrate that FVSC can effectively support spectral feature data in the detailed mapping of dominant tree species at regional scales. Moreover, the method shows good stability and applicability across seasons and climatic regions.

The asymptotic radiative transfer (ART) model has been widely used in snow remote sensing. However, the anisotropic effects of snow reflectance challenge this model because of its underestimation in the forward-scattering direction. To exhibit these strong scattering properties of the snow surface, a microfacet specular kernel has been supplemented with the ART model (hereinafter named the ARTS model). In this study, we propose a method of multiplying by a correction term for improving the ART model (hereinafter named the ARTF model). We validate the performance of the ARTF model using various data sources. Our results demonstrate that: 1) the ARTF model has higher accuracy in characterizing snow bidirectional signatures, with$R^{2}$and root mean square error (RMSE) values in the ranges from 0.722 to 0.990 and 0.007 to 0.041, respectively, than the ART ($R^{2} =0.507$–0.802 and RMSE = 0.038–0.088) and ARTS ($R^{2} =0.686$–0.962 and RMSE = 0.021–0.044) models, especially in the long-wave near-infrared region and 2) the ARTF model can effectively represent snow hyperspectral reflectance, while the ART and ARTS models significantly underestimate snow reflectance in the visible and shortwave near-infrared region. The$R^{2}$values of these three models reach ~0.99, and the RMSE values of the ARTF model range from 0.012 to 0.024, which are smaller than those of the ART (RMSE = 0.021–0.061) and ARTS (RMSE = 0.021–0.049) models. These results demonstrate that the ARTF model is better than the ART and ARTS models for characterizing snow hyperspectral bidirectional reflectance.

Surface albedo plays a key role in global climate modeling as a factor controlling the energy budget. Satellite observations were utilized to estimate surface albedo at global and regional scales with good precision over flat areas. However, because topography greatly complicates radiative transfer (RT) processes, estimating the albedo of rugged terrain with satellite data remains a challenge. In addition, albedo definitions over sloping terrain differ from that for flat areas. They include horizontal/horizontal sloped surface albedo (HHSA) and inclined/inclined sloped surface albedo (IISA). Methods for retrieving HHSA and IISA in mountains have not been well-explored. Here, we retrieved HHSA and IISA on sloping terrain from Landsat 8 using a direct estimation algorithm. We simulated a dataset of Landsat top-of-atmosphere (TOA) reflectance and surface albedo with discrete anisotropic radiative transfer (DART) model, for variable atmospheric, vegetation, soil, and topography properties. Then, we used artificial neural networks (ANNs) to derive an empirical relationship between TOA reflectance and surface albedo. The accuracy of our method was verified within situmeasurements: root mean squared error (RMSE) and bias equal to 0.029 and −0.010 for HHSA, and 0.023 and −0.001 for IISA, respectively. Several albedo results (HHSA, IISA, values without topographic consideration) were evaluated and compared. HHSA was found similar to albedo without topographic consideration, but IISA, considered as the “true albedo” for sloping terrain, showed large difference from them. This study demonstrated the feasibility of surface albedo estimation from Landsat TOA reflectance directly in rugged terrains and advanced our understanding of energy budget in mountains.

Surface albedo is closely related to the Earth’s energy budget and is usually estimated by integrating remotely sensed bidirectional reflectance distribution function (BRDF) data based on the widely used Ross–Li kernel-driven models. However, for large solar zenith angles (i.e., SZAs > 70°), albedo estimation using the operational algorithm of the Moderate Resolution Imaging Spectroradiometer (MODIS), i.e., RossThick-LiSparseReciprocal (RTLSR), is not recommended because it is reported to somewhat underestimate the black-sky albedo (BSA) at large SZAs based on ground albedo measurements. Recently, various combinations of the Ross–Li BRDF models with improved capabilities have been developed, and the assessments of these models based on worldwide satellite BRDF data with good spatial sampling, particularly at the large view and solar angles, will be important to improve an understanding of their performance in estimating intrinsic albedos. Following previous studies, the objective of this study is to further assess a series of hotspot-corrected Ross–Li models by demonstrating their ability to fit the POLarization and Directionality of the Earth’s Reflectances (POLDER) data sets and estimate albedo, especially at large SZAs, based on selected concurrent POLDER and MODIS data. The hotspot-corrected RTLSR model obtained by combining the RossThickChen and LiSparseReciprocalChen kernels (RTLSR_C) shows the best fitting ability, with a high cumulative frequency of small root-mean-square errors (RMSEs), thus confirming previous conclusions. Model differences mainly appear in albedo estimates, especially BSA estimates at large SZAs. The BSAs estimated by other models are significantly different from the RTLSR_C estimates in the near-infrared (NIR) and red bands as the SZA increases to approximately 60° and 70°, respectively. In this case, RossThinChen-LiSparseReciprocalChen (RTNLSR_C) yields higher BSA estimates than those of RTLSR_C. Comparisons of the MODIS and POLDER albedos estimated with Ross–Li models show that models with the RossThinChen kernel yield higher BSA estimates than those of the RTLSR_C model as the SZA increases. The results indicate that the retrieved albedo is likely to be more accurate with appropriately selected kernels for BRDF models at large SZAs, providing guidance for selecting suitable combinations of multiple kernels.

Anisotropy information from moderate-to-coarse-resolution sensors [e.g., 500-m Moderate Resolution Imaging Spectroradiometer (MODIS)] is widely applied to estimate high-resolution surface albedo. Simulated albedos using MODIS bidirectional reflectance distribution function (BRDF) parameters as prior knowledge based on the kernel-driven model are employed to build and assess the lookup table (LUT) of the direct-estimation method, which is then used to estimate high-resolution albedos directly from top-of-atmosphere (TOA) reflectance data (e.g., Landsat albedo). Previously, the errors in the simulated albedos were not considered in building and assessing the LUT. In this article, daytime time-series (30 min) of snow-free albedo measurements with sufficient solar zenith angles (SZAs) were introduced to build the LUT for snow-free Landsat TM surface shortwave broadband albedo (TM albedo) retrievals, together with TOA-simulated reflectance by concurrent daily MODIS BRDF parameters. The assessment utilizes an independent data set and shows larger discrepancies between the estimated and measured albedos [root-mean-square errors (RMSEs) of >0.03 at SZAs ≥ 60°] than those in previous articles. To reduce inconsistencies between the MODIS BRDF parameters and the observed albedos, as well as possible spatial resolution differences between the MODIS and Landsat data, we adopted a correction strategy that first linearly adjusts the MODIS BRDF parameters to match the albedo measurements by a magnitude method, and second, the TOA reflectance simulations were further corrected by concurrent TM reflectances. The developed algorithm shows a significant improvement after using such corrections as a priori (RMSE <; 0.02 at SZA ≤ 75°). The validation indicates improved accuracies in the TM albedo estimation. These improvements may provide potential albedo estimations for nadir-viewing high-resolution sensors using coarse-resolution anisotropy information.

Surface albedo is a key parameter controlling the earth energy budget, which can be estimated by integrating the Bidirectional Reflectance Distribution Function (BRDF). The semi-empirical kernel-driven BRDF models has been widely used in BRDF/Albedo products, MODIS products for instance (Schaaf et al., 2002). However, these albedo products are suspect under large SZA (Liu et al., 2009). With the hotspot improved kernel-driven models, it is necessary to assess the property of these models. In this study, two POLDER datasets are utilized to access these models by root-mean-square error (RMSE) and relative RMSE (RMSE_r). Then, cross-comparison between albedos estimated by improved models under several SZAs is analyzed by POLDER and the concurrence MODIS pixels. This study is aimed at choosing suitable models for albedo estimation under different angular situations to retrieve more accurate albedo.

Recently, Jiao et al. developed a snow kernel in the kernel-driven bidirectional reflectance distribution function (BRDF) model framework to better characterize the anisotropic reflectance of pure snow surface. In this study, we assess performances of this snow kernel in the kernel-driven model framework and original kernel-driven model (hereinafter named the RTS and RTR models) in retrieving snow albedo based on the bicontinuous photon tracking (bic-PT) model. Our results show that: (1) The spectral albedo retrieved by these two models has a high consistency with the bic-PT model. However, the results of the spectral albedo for RTR model has a slight underestimation, especially at SZA=0° in the visible bands, and the RTS model performs well compared with simulated data. (2) The albedo retrieved by these two models agrees reasonably well with the simulated data (R2=~0.9). Yet, the result of the RTR model underestimates 0.50% and 0.52% compared simulated albedo in the red and near-infrared bands, respectively, and the RTS model has a negligible bias for all bands. This assessment provide a priori knowledge of these two models performances, and thus, suggests the RTS model can be applied to future researches of estimating snow albedo.

The foliage Clumping Index (CI) is a key vegetation structure parameter for leaf area index (LAI) estimating and ecological modelling. Previously, several global CI products have been retrieved from the Collection V005 Moderate Resolution Imaging Spectroradiometer (MODIS) Bidirectional Reflectance Distribution Function (BRDF) products with a temporal resolution of one year, one month or 8 day. The Collection V006 MODIS BRDF products provide a chance to retrieve a global CI product with higher temporal resolution and data accuracy. However, the large size of the Collection V006 MODIS BRDF products (~150 terabyte from January 2001 to December 2017) and the retrieved CI products (~9 terabyte) increases the difficulty in retrieving and publishing the global CI product. In this study, we develop a software tool that enable users to produce CI product of their desired date, region and temporal resolution based on the Collection V006 MODIS land cover type and BRDF products. The software tool reduces the requirements of the processing and storage capacity for researchers and thus facilitate the publication and widespread application of the CI product.

The linear kernel-driven RossThick-LiSparseReciprocal (RTLSR) bidirectional reflectance distribution function (BRDF) model was originally developed for modeling the simplified scenarios of the continuous and discreet vegetation canopies, and has been widely used to fit the multiangle observations for the vegetation-soil system of the land surface in many fields. However, there is a need to develop this model to characterize the light scattering properties of snow, which tends to exhibit strongly forward scattering behaviors. This study proposes a snow kernel to describe the reflectance anisotropy of snow, mainly based on the asymptotic radiative transfer theory (ART) for a semi-infinite weakly absorbing layer of snow, and then applies this kernel to the framework of kernel-driven BRDF model. This snow kernel adopts the analytic form of the ART model with an improved ability in forward scattering direction, particularly in a case of a large viewing zenith angle (> 60°) where the simulation accuracy of the ART model somewhat decreases in the principal plane (PP). Validation of this method was implemented using observed multiangle data. Pure snow targets were selected from the entire archive of the POLDER BRDF data. This validation demonstrates that this proposed snow kernel in the framework of the kernel-driven RTLSR model show potentials for many potential applications, particularly in the field of Earth's water cycle and radiation budget where snow cover plays an important role.

Clumping index (CI) is an important vegetation structure parameter in the estimation of leaf area index (LAI) and the modeling of ecological and meteorological process. With the development of surface process modeling and remote sensing technology, high resolution CI product is urgently needed but no appropriate high resolution multi-angle reflectance satellite data is currently available to produce such product. In recent years, random forest algorithm has been widely used in the derivation of high resolution products from remote sensing data. In this study, the random forest algorithm was used to estimate Landsat CI basing on MODIS and field data. The developed predictive model was validated using 26 field measurements and the predicted CI shown a good consistency with the field CI (R2=0.63, bias=0.005, RMSE=0.10).

The surface anisotropy plays a key role in the quantitative remote sensing inversion, which is usually described as bidirectional reflectance distribution function (BRDF). Studies show that BRDF sampling has a significant effect on parameter inversion such as albedo. However, BRDF samplings are complex, and only specific samplings were considered in previous studies. In this study, we investigated the sensitivity of BRDF sampling to albedo and the normalized difference between hotspot and dark spot (NDHD) angular index based on the kernel-driven Ross-Li BRDF model. Albedo and NDHD calculated by a set of dense sampling airborne data were used as the reference data, and inversion results from many sparse samplings were compared to the reference results. The result shows the overall number, plane, range and symmetry in observing condition of BRDF sampling can affect albedo and NDHD estimation. Among typical sensors, POLDER shows best sampling while Landsat shows largest errors.

The hotspot effect is a typical angular reflectance signature of vegetation canopies and contains important information for the retrieval of vegetation structural parameters. To date, the hotspot effect of various analytical bidirectional reflectance distribution function (BRDF) models (e.g., the PROSAIL model) has rarely been assessed by multiangular measurements with sufficient hotspot observations due to the lack of accurate hotspot measurements (for field measurements) or appropriate methods (for airborne and spaceborne measurements). In this paper, we develop a method to further improve the hotspot effect of the kernel-driven model and design a framework to utilize the improved kernel-driven model as a bridge to assess the hotspot effect of the PROSAIL model with Polarization and Directionality of the Earth Reflectance (POLDER) hotspot observations. The results indicate that the proposed method further improves the fits between the models and the observations in the vicinity of the hotspot direction, particularly in the rare situations where the geometric-optical scattering component governs the target reflectance. In addition, the hotspot signature indicated by the PROSAIL multiangular data shows a larger variability than that of POLDER observations. C1and C2in the improved kerneldriven model can be used as benchmarked parameters to qualify the amplitude and width of the hotspot effect for the simulated multiangular data of physical BRDF models and thus present the potential for the assessment and analysis of the hotspot effect of physical models, which, in return, helps retrieve the structural parameters of vegetation canopies from hotspot signatures.

The foliage Clumping Index (CI) quantifies the level of foliage grouping within a distinct canopy structure relative to a random distribution. It is a key structure parameter for the ecological, hydrological, and land surface models. In this study, we investigate the influence of snow cover on the seasonal variation of global CI products derived from the Moderate-resolution Imaging Spectroradiometer (MODIS) Bidirectional Reflectance Distribution Function (BRDF) parameter products using the improved RTCLSR kernel-driven model. Results indicated that the cover of snow can lead to a much larger CI and thus considerably decrease the quality of the CI product. Statistics in 2006 indicates that more than 85% low quality pixels are covered by the snow. The average CI for evergreen needleleaf forests in winter will decrease about 0.1 after deducing the influence of snow covered pixels. The influence of snow cover should be carefully considered and corrected when analyzing the seasonal variation of the global CI product.