In this study, a novel algorithm for high spatial resolution leaf area index (LAI) retrieval, specifically tailored for mountain forests, has been developed. As an essential climate variable, LAI has been incorporated into many ecohydrological process simulation models; however, the majority of the algorithms are developed on the assumption of flat terrain. Previous studies have proved that neglecting the influence of topography may introduce significant biases and uncertainties into LAI estimates particularly in rugged areas. As an important species in the mountain area, forests occupy a large land area worldwide; nevertheless, it is still challenging to obtain high-quality LAIs from satellite images due to their complex canopy structures. In spite of numerous attempts having been made to address such issues with topographic correction (TC) or mountain canopy reflectance models, few algorithms were actually available for LAI estimation of mountain forests. Here, we try to employ the geometric optical and mutual shadowing and scattering from the arbitrarily inclined-leaves model coupled with the topography (GOSAILT) model to retrieve forest LAI over complex terrain. GOSAILT is a combined model that incorporates the radiative transfer model (RTM) into the geometrical optical model (GOM) on the slope surface. It is capable of characterizing the bidirectional reflectance of both discrete and continuous canopies. The validations against computer-simulated LAIs reveal root-mean square errors (RMSEs) being 1.7160 and 0.6260, corresponding to terrain-ignored scenario and terrain-considered scenario, respectively. Besides, the validation against in situ LAIs demonstrated that the RMSE is 0.9262 over flat terrain and 0.6402 over sloped terrain. This evidence underscores the robust performance of the newly developed algorithm.

The estimation of satellite-based albedo highly depends on the surface reflectance (SR). In mountainous areas, three types of SRs [i.e., the virtual SR (VSR) that is retrieved from the atmospheric correction model, the topographically corrected SR (TCSR) that is retrieved from the atmospheric and topographic correction model, and the sloping SR (SSR) that is retrieved from the physically bidirectional reflectance distribution function (BRDF)-based mountain-radiative-transfer (MRT) model] are commonly used to retrieve land surface albedo (SA). However, which type of SR is the best option for SA retrieval has not yet been quantitatively addressed. This letter assessed the performance of these three types of SRs on driving SA by comparison within situalbedo measurements over field sites in the Heihe River Basin, China. Our results show that these three types of albedos have consistent accuracy over flat sites with a root mean squared error (RMSE) smaller than 0.0320. Moreover, the sloping SA (SSA) retrieved from SSR shows the best agreement within situalbedo measurements over rugged sites with a bias of 0.0008, RMSE of 0.0338, relative RMSE (RMSER) of 12.92%, and correlation coefficient ($r$) of 0.89, followed by the topographically corrected SA (TCSA) from TCSR with a lager bias of 0.0208, RMSE of 0.0470, RMSERof 20.24%, and$r$of 0.69. The virtual SA (VSA) retrieved from VSR shows the largest uncertainty than the other two types of albedos, with an RMSE of 0.0516. These results illustrate that SSR is the best option of reflectance for satellite-based albedo retrieval over mountainous areas.

Land surface albedo is a crucial variable of earth energy budget and global climate change. Rugged terrain significantly impacts surface bidirectional reflectance distribution function (BRDF) and the subsequent albedo retrieval using satellite remote sensing. Existing studies of estimating surface BRDF/albedo from satellite observations are limited to neglecting topographic impacts, resulting in large uncertainty in satellite albedo product, especially for low spatial resolution satellite sensors that are primarily regulated by subpixel-scale topographic effects. To fill this knowledge gap, we proposed an extended multisensor combined BRDF inversion (EMCBI) model to characterize subpixel-scale topographic effects, and applied this model to estimate BRDF/albedo from the Himawari-8 Advanced Himawari Imager (AHI) and Terra/Aqua moderate resolution imaging spectroradiometer (MODIS) data and finally validated the satellite-derived albedo with ground measurements of two stations located in Tibet plateau. Our results show that: 1) EMCBI can generate a daily BRDF/albedo dataset with more than 90% spatial coverage and 2) EMCBI-derived albedo agrees well with the referenced albedo corrected from ground measurement, with a root-mean-square-error (RMSE) of 0.0537 and 0.0608 for black-sky albedo (BSA) and white-sky albedo (WSA), and a mean absolute percentage error (MAPE) of 21.93% and 25.13% for BSA and WSA, respectively. These results demonstrate EMCBI has great potential for mapping large-scale high temporal resolution BRDF/albedo product over rugged terrain.

Most surface–atmosphere radiative transfer models (RTMs) work only for flat surfaces, with the exception being time-consuming 3-D scene-based models. The deficiency of flat-surface RTMs that do not consider topographic effects is that their applications in earth observation and simulation studies are impaired because rugged terrains make up approximately 24% of the global land surface. Another deficiency of most surface–atmosphere RTMs is that they model reflected and emitted (i.e., solar and thermal) radiative transfer processes separately, which limits RTMs in applications, such as fire detection. This study proposes a unified optical–thermal RTM coupling framework (RTM-CF) that considers topographic effects based on the four-stream approximation theory. The framework couples surface–atmosphere RTMs and can simultaneously simulate a set of parameters at the top-of-atmosphere (TOA) and bottom-of-atmosphere (BOA) levels from optical and thermal spectral ranges. These parameters include the TOA directional radiance/reflectance, TOA exitance/albedo, TOA net radiation, surface radiance/reflectance/albedo, surface downward/upward/net radiation, and FAPAR/APAR. The RTM-CF with topographic effects is compared with the well-known 3-D discrete anisotropic radiative transfer (DART) ray-tracing model and validated by field measurements from three steep sites. The evaluation results show that the simulated reflectance, radiance, and radiation fluxes are consistent with the DART results and the field data, with$R^{2}>0.93$and scatter points close to the 1:1 line for all parameters. In this RTM-CF, atmospheric and topographic effects are simultaneously incorporated, and the surface anisotropy is also effectively considered. This framework is highly modularized, which enables it to be easily adapted to different submodels.

A comprehensive assessment of satellite-derived albedo products is undeniably essential for better use consideration and the further refinement of the retrieval algorithm. Although satellite albedo products have been extensively validated over spatially homogeneous areas, it remains a challenge to validate them over rugged terrain. Consequently, the accuracy of satellite albedo products over rugged terrain is still unknown. This study for the first time systematically evaluated two widely used satellite albedo products (i.e., MCD43A3 V006 and GLASS V04 albedo) over mountainous areas with a Mountain Radiation Transfer (MRT) coupled multi-scale validation strategy. Fine-scale albedo was first generated with a root mean square error (RMSE) smaller than 0.0317. Then they were upscaled to the coarse pixel and as the reference data for validation. The validation results indicated that the accuracy of the two products tends to decrease with the increase of means slopes. The RMSE and relative RMSE (RMSER) of full retrieval MCD43A3 C6 black-sky albedo (BSA) and white-sky albedo (WSA) over abrupt slopes (mean slope >10°) increase to 0.0432 and 31.87% and to 0.0436 and 32.21%, respectively. The RMSE and RMSERof high quality GLASS V04 were 0.0452 and 33.71% of BSA and 0.0458 and 33.92 % of WSA respectively over abrupt slopes. Particularly, if the backup retrievals were included over the abrupt slopes, the RMSE and RMSER of MCD43A3 C6 can reach to 0.0600 and 36.92% for BSA and 0.0613 and 37.67% for WSA, and those of GLASS V04 can reach to 0.0567 and 36.28% for BSA and 0.0540 and 35.72% respectively.

A comprehensive assessment of satellite-derived albedo products is undeniably essential for better use consideration and the further refinement of the retrieval algorithm. Although satellite albedo products have been extensively validated over spatially homogeneous areas, it remains a challenge to validate them over rugged terrain. Consequently, the accuracy of satellite albedo products over rugged terrain is still unknown. This study for the first time systematically evaluated two widely used satellite albedo products (i.e., MCD43A3 C6 and Global Land Surface Satellite (GLASS) V04 albedo) over mountainous areas with a mountain radiation transfer (MRT) coupled multiscale validation strategy. Fine-scale albedo was first generated with a root-mean-square error (RMSE) smaller than 0.0317. Then, they were upscaled to the coarse pixel and as the reference data for validation. The validation results indicated that the accuracy of the two products tends to decrease with the increase of means slopes. The RMSE and relative RMSE (RMSER) of full retrieval MCD43A3 C6 black-sky albedo (BSA) and white-sky albedo (WSA) over abrupt slopes (mean slope >10°) increase to 0.0432 and 31.87% and to 0.0436 and 32.21%, respectively. The RMSE and RMSERof high-quality GLASS V04 were 0.0452 and 33.71% of BSA and 0.0458 and 33.92% of WSA, respectively, over abrupt slopes. In particular, if the backup retrievals were included over the abrupt slopes, the RMSE and RMSERof MCD43A3 C6 can reach 0.0600 and 36.92% for BSA and 0.0613 and 37.67% for WSA, respectively, and those of GLASS V04 can reach 0.0567 and 36.28% for BSA and 0.0540 and 35.72%, respectively.

Topographic and angular corrections on Sentinel-2 imagery are crucial for the generation of consistent surface reflectance. We propose a novel topographic-angular integrated normalization approach based on the combination of the path length correction (PLC) and C-factor approaches. The PLC-C normalization approach is a semiphysical method with limited use of auxiliary data: only a digital elevation model and a fixed set of kernel coefficients, ensuring its transferability for operational implementation. For the validation, we used two Sentinel-2A images over a mountainous area observed in backward (BS) and forward scattering (FS) directions from laterally adjacent orbit swaths. PLC-C significantly reduced both the topographic and directional anisotropy effects: the overlapping ratio between BS and FS observations was increased from 84.1% to 92.8% for the near-infrared band, and from 81.0% to 93.1% for the red band; the coefficient of variation of the reflectances across different aspects, which was used as a criterion of topographic effects, was reduced from 9.8%/12.2% to 3.6%/5.7% in BS/FS direction for the near-infrared band, and from 8.1%/9.7% to 4.5%/4.2% for the red band. PLC-C will contribute to the generation of analysis ready data from Sentinel-2 top of canopy reflectance.

Topographic correction is a prerequisite for generating radiometrically consistent Landsat 8 OLI vegetation reflectances in support of temporally continuous and spatially mosaicked applications. Path length correction (PLC) is a physically solid topographic correction method that avoids the involvement of any empirical parameter and is therefore suitable for reproducing the inherent reflectance of vegetation. This article compared two different implementation pathways of PLC, i.e., the explicit method (EM) and the implicit method (IM), which are based on the numerical inverse and analytical approximation of the PLC model, respectively. The results show that both EM and IM can obviously reduce the topographic effects on Landsat 8 OLI vegetation reflectances. EM performed slightly better than IM in eliminating the correlation between the topographic characteristics and the vegetation reflectances: the coefficient of determination between the green/red/near-infrared (Nir) band reflectance and the local illumination was reduced from 0.257/0.148/0.467 for the uncorrected (UNCORR) case to 0.016/0.004/0.012 and 0.027/0.014/0.094 for the EM and IM corrected results, respectively. The coefficient of variation of the three band reflectances across different aspects was reduced from 16.5%/18.5%/18.7% for the UNCORR case to 3.2%/1.8%/0.9% and 5.3%/7.1%/7.3% for the EM and IM corrected results, respectively. In addition, the intraclass reflectance variability was also reduced after both the EM and IM corrections. Nevertheless, due to the ill-posed nature of the numerical inverse process, EM cannot fully reproduce the inherent vegetation reflectances, and the reflectances after topographic correction overestimated the inherent vegetation values. In contrast, the IM can achieve an appropriate tradeoff between topographic effect elimination and vegetation inherent reflectance preservation. In addition, IM is computationally very efficient compared to EM: using an ordinary laptop, IM can finish the topographic correction for a Landsat OLI image within several seconds, while this would take more than 20 h for EM. This article highlights the potential of using IM for generating radiometrically consistent Landsat 8 OLI vegetation reflectances.

Accurately estimating the spatial–temporal distribution of downward surface shortwave radiation (DSSR) is essential for terrestrial ecological modeling and climate change research. The accurate georegistration of digital elevation model (DEM) has become one of the significant bottlenecks for improving the DSSR accuracy over rugged terrain. To clearly understand and quantitatively evaluate the impact of geolocation bias on the DSSR estimation under clear sky, this letter conducts a systematical simulation research in Dayekou Basin of China based on a developed remote sensing satellite-based DSSR estimation scheme over rugged terrain. The results demonstrate that the proposed approach can accurately capture the high temporal and spatial heterogeneities of DSSR, and the DSSR estimations are sensitive to geolocation bias. When the horizontal bias is lower than half a pixel, the deviations of the direct radiation could lead to above 600 W/m2due to the illumination angle effects and shadow effects. The consequence of the bias on the diffuse and reflected radiation from adjacent terrains is little because of their relatively small values and low-spatial heterogeneities under clear sky in general except for the deep valley areas. The trends of the total radiation errors with the geolocation bias are identical in different days (scenes), and the error is related to the solar zenith angle. In addition, the more rugged the terrain, the greater the influence of geolocation bias on the radiation accuracy.

In[1], the units of sky view factor and terrain view factor are printed incorrectly in the abstract section andFig. 4.

Topographic effects on canopy reflectance play a pivotal role in the retrieval of surface biophysical variables over rugged terrain. In this paper, we proposed a new canopy anisotropic reflectance model for discrete forests, Geometric Optical and Mutual Shadowing and Scattering-from-Arbitrarily-Inclined-Leaves model coupled with Topography (GOSAILT), which considers the effects of slope, aspect, geotropic nature of tree growth, multiple scattering, and diffuse skylight. GOSAILT-simulated areal proportions of four scene components (i.e., sunlit crown, shaded crown, sunlit background, and shaded background) were evaluated using the Geometric Optical model for Sloping Terrains (GOST) model. The canopy reflectances simulated by GOSAILT were validated against two reflectance data sets: Discrete anisotropic radiative transfer (DART) simulations and wide-angle infrared dual-model line/area array scanner (WIDAS) observations. Compared with a horizontal surface, the forest canopy reflectance over a steep slope (60°) is significantly distorted with absolute (relative) bias values of 0.048 (79.60%) and 0.056 (12.02%) for the red and near-infrared (NIR) bands, respectively. The GOSAILT-simulated component areal proportions show close agreements with GOST. Moreover, GOSAILT simulations have high overall accuracy (red band: coefficient of determination (R2) = 0.96; root-mean-square error (RMSE) = 0.003; and mean absolute percentage error (MAPE) = 3.91%; and NIR band: R2= 0.78, RMSE = 0.019; MAPE = 3.94%) when compared with the DART simulations. These extensive validations indicate good performances of GOSAILT in canopy reflectance simulations over sloped surfaces.

Validation of remote sensing albedo products involves comparisons between point-scale in situ observations and footprint-scale satellite retrievals. However, the observed differences between product and in situ observations are not only attributable to intrinsic errors of satellite products but also to inadequate spatial representativeness of in situ observations. Here, representativeness errors of in situ observations and their effects on validation results were quantitatively explored. Furthermore, the contributors and their influences on representativeness errors were quantified. In the case of large representativeness errors, validation result errors are mainly controlled by representativeness errors. When representativeness errors are small, validation result errors are likely affected by other factors and can be so large that cannot be ignored. Surface heterogeneity is most positively related to representativeness errors, followed by the deviation distance of in situ site from the pixel center. The representative area surrounding in situ sites only shows a weak negative correlation with representativeness errors. The range seems to be not a good indicator of spatial representativeness of in situ sites since there is almost no relationship between them. When these factors are combined, surface heterogeneity contributes more to representativeness errors on the 500-m pixel scale, while quantitative impacts of the representative area and location deviation of in situ sites are not fully understood because magnitudes of these effects are dependent on the choice of high-resolution data set. These findings enhance our understanding about spatial representativeness of in situ observations and improve the quality of validation results based on single in situ observations.

Rugged terrain complicates the BRDF modeling mainly by the modulation of sun-target-sensor geometry and shadowing effects. An improved kernel-driven BRDF model coupled with topography (KDCT) is put forward by combining the RTLSR model used in the algorithm for MODIS bidirectional reflectance anisotropies of land surface (AMBRALS) and the anisotropic reflectance model for rugged terrain (dESM). The improved model was compared with the original RTLSR model by using the simulated data based on the radiosity approach and the MODIS reflectance data. The validation results revealed that the improved KDCT model outperforms the RTLSR model without topographic consideration and can significantly improve the ability of the kernel-driven model to process the multi-angular reflectance measurements over rugged terrain.

Surface albedo plays an important role in the local- and regional-scale solar radiation budget. However, the in situ measurement of surface albedo over rugged terrain is usually confused by the radiometer placement. In this study, two commonly measured albedos with different sensor configurations were characterized and illustrated based on the radiometer orientation in the illumination and viewing geometry. They are: horizontal-horizontal sensor measured sloping surface albedo (HHSA), and inclined-inclined sensor measured sloping surface albedo (IISA). The 3-D Discrete Anisotropic Radiative Transfer (DART) model simulations were used to exemplified their difference. Results reveal that these two albedos show distinct patterns with slope and aspect. Therefore, the radiometer placement should be considered in the surface albedo measurement over rugged terrain.

Downward surface solar radiation (DSSR) plays an important role in the earth's surface energy budget. However, it has significant spatial-temporal heterogeneity over the rugged terrain. To accurately capture DSSR, many analytical terrain parameter algorithms based on digital elevation models (DEMs) have been proposed. However, the uncertainties of the DSSR components associated with these algorithms remain unclear. In this letter, we compared three types of terrain parameter algorithms and their respective DSSR component uncertainties at different spatial scales by using 3-D discrete anisotropic radiative model simulations under different atmospheric conditions. The comparison results indicated that differences in slopes, sky view factors, and terrain view factors can be up to 4°, 0.165°, and 0.264°, respectively. For a high atmospheric visibility, the maximum discrepancies of direct solar irradiance and adjacent terrain-reflected irradiance over the high reflective surface (e.g., fresh snow and ice) are 26.7 and 42.8 W·m2, respectively. In addition, for a low atmospheric visibility, a maximum difference of 31 W·m2is identified for diffuse skylight. These uncertainties are nonnegligible when using a high-resolution DEM (e.g., 30 m), but as the DEM resolution becomes coarser, the uncertainties decrease.

Heterogeneous terrain significantly complicates signals received by airborne or satellite sensors. It has been demonstrated that both solar direct beam and diffuse skylight illumination conditions are significant factors influencing the anisotropy of reflectance over mountainous areas. Several models and methods have been developed to account for topographic effects on surface reflectance at the pixel level in remote sensing. However, subtopographic effects are generally neglected for low-spatial-resolution pixels due to the complex law of radiative transfer and the limitations of higher spatial resolution digital elevation models, which can lead to deviations in reflectance estimation. Accurately estimating the subtopographic effects on anisotropic reflectance over composite sloping terrain under different illumination conditions presents a challenge for remote sensing models and applications. In this paper, the diffused equivalent slope model (dESM) was developed, which is an anisotropic reflectance simulation model coupled with diffuse skylight over composite sloping terrain. The corresponding subtopographic impact factor was also proposed to exhibit how microslope topography affects reflectance over composite sloping terrain under different illumination conditions. Simulated reflectance data sets simulated by the radiosity method and Moderate Resolution Imaging Spectroradiometer reflectance data were used to evaluate the performance of the dESM model. The results reveal that the dESM model can accurately capture the reflectance anisotropy over composite sloping terrain under different illumination conditions, and the subtopographic impact factor can account for the effects of microslope topography, shadow, and illumination conditions.

A well understanding of topography effect on the forest reflectance is critical for biophysical parameters retrieval over rugged area. In this paper, a new hybrid bidirectional reflectance distribution function (BRDF) model coupled the geometric optical mutual shadowing (GOMS) and scattering from arbitrarily inclined leaves (SAIL) models with topography consideration (GOSAILT) for sloping forest was proposed.

Geometric-optical (GO) model suitable for forest plantation (GOFP) is a GO model for forest plantations at the stand level developed in this study based on a four-scale GO model a Geometric-Optical Model for Sloping Terrains-II (GOST2), which simulates the bidirectional reflectance distribution function (BRDF) for natural forest canopies. In most previous GO models, tree distributions are often assumed to meet the Poisson or Neyman model in a forest; therefore, these models are suitable for simulating BRDF for natural forest canopies. However, in forest plantations, tree distributions are proven to meet the hypergeometric model rather than the Poisson or Neyman model at the stand level. GOFP, in which the tree distributions are described using the hypergeometric model, is proposed to simulate the bidirectional reflectance factor (BRF) of forest plantations at the stand level. The area ratios of the four scene components (sunlit foliage, sunlit ground, shaded foliage, and shaded ground) of GOFP compare well with those simulated by a 3-D canopy visualization technique. A comparison is also made against discrete anisotropic radiative transfer, showing that GOFP has the ability to simulate BRF of forest plantations. Another comparison is made against operational land imager and Moderate Resolution Imaging Spectroradiometer surface.

Sloping terrain induces distortion of canopy reflectance (CR), and the retrieval of biophysical variables from remote sensing data needs to account for topographic effects. We developed a 1-D model (the path length correction (PLC)based model) for simulating CR over sloping terrain. The effects of sloping terrain on single-order and diffuse scatterings are accounted for by PLC and modification of the fraction of incoming diffuse irradiance, respectively. The PLC model was validated via both Monte Carlo and remote sensing image simulations. The comparison with the Monte Carlo simulation revealed that the PLC model can capture the pattern of slopeinduced reflectance distortion with high accuracy (red band: R2= 0.88; root-mean-square error (RMSE) = 0.0045; relative RMSE (RRMSE) = 15%; near infrared response (NIR) band: R2= 0.79; RMSE = 0.041; RRMSE = 16%). The comparison of the PLC-simulated results with remote sensing observations acquired by the Landsat8-OLI sensor revealed an accuracy similar to that with the Monte Carlo simulation (red band: R2= 0.83; RMSE = 0.0053; RRMSE = 13%; NIR band: R2= 0.77; RMSE = 0.023; RRMSE = 8%). To further validate the PLC model, we used it to implement topographic normalization; the results showed a large reduction in topographic effects after normalization, which implied that the PLC model captures reflectance variations caused by terrain. The PLC model provides a promising tool to improve the simulation of CR and the retrieval of biophysical variables over mountainous regions.

Current bidirectional reflectance distribution function (BRDF) inversions using ordinary least squares (OLS) criterion can be easily contaminated by observations with residual cloud and undetected high aerosols, which leads to abrupt fluctuations in the normalized difference vegetation index (NDVI) time series. The OLS criterion assumes the noise has Gaussian distribution, which is often violated due to positive noise biases caused by clouds and high aerosols. A changing-weight iterative BRDF/NDVI inversion algorithm (CWI) based on a posteriori variance estimation of observation errors is presented to explicitly consider the asymmetrically distributed noise and observations with unequal accuracy in the BRDF retrieval. CWI employs a posteriori variance estimation and an NDVI-based indicator to iteratively adjust the weight of each observation according to its noise level. The validation results suggest CWI performs better than the Li-Gao and OLS approaches. The rmse was reduced from 0.074 to 0.028, and the relative error decreased from 13.4% to 3.8% at the U.S. Department of Agriculture Beltsville Agricultural Research Center site. Similarly, at the Harvard Forest site, the rmse was reduced from 0.086 to 0.031, and the relative error decreased from 9.5% to 2.7%. The average noise and relative noise of the CWI NDVI time series over ten EOS Land Validation Core Sites from 2003-2009 was smaller (0.028, 3.7%) than those of MOD13A2 (0.041, 5.2%), MYD13A2 (0.039, 4.9%) and MCD43B4 (0.030, 4.4%). The results demonstrate the robustness of the CWI approach in suppressing the influence of contaminated observations in BRDF retrievals by producing results that are less affected by undetected clouds and high aerosols.