Bidirectional Reflectance Distribution Function Data Research Articles

BRDF Data for Coniferous Forests Acquired from Multispectral Camera Onboard a Unmanned Aerial Vehicle

Bidirectional reflectance distribution function (BRDF) is a distribution of directional reflectance for varying viewing and solar geometry. BRDF of a target is important in processing optical image data from satellites, because the observed radiance has great dependency on the direction (or angle) of reflection. It is desirable that the BRDF of any targets is characterized for rigorous BRDF correction of satellite data, since the sun-sensor-target geometry of satellites often varies in a very limited range, limiting the full characterization of target BRDF. This study provides BRDF data set for typical coniferous forests in Korea, by using a multispectral camera onboard a unmanned aerial vehicle (UAV). By operating the UAV in a goniometer-like way, reflectance data for all possible viewing zenith and azimuth angles were obtained. The BRDF data collected from the 3 campaigns in different days were visualized in a polar-coordinate, together with the standard deviation calculated for each zenith/azimuth bin made in 1˚ interval. The data sets demonstrated reflectance distribution over the wide range of angles with sound data quality, suggesting commonly known BRDF characteristics for forests such as strong back-scattering and hot spot area in the viewing zenith angle near the solar zenith angle. This data set is expected to be utilized for the BRDF correction of various satellites including Agro-forest satellite of Korea which is to be launched in 2025 that has similar spectral bands with the ones used in this study.

Design of an image-based BRDF measurement method using a catadioptric multispectral capture and a real-time Lambert calibration.

By utilizing a catadioptric system and a calibration Lambertian sample, a compact measurement method of bidirectional reflectance distribution function (BRDF) has been proposed for rapid and accurate measurement. With the help of an ellipsoidal dome mirror, a hyperboloid mirror, and a high-resolution camera, spatial reflectance distributions from reflected directions with a large field of view (FOV) can be obtained. The built-in Lambertian standard allows for real-time calibration to account for fluctuations in the illumination spectrum, effectively reducing the measurement drift and achieving a high accuracy. Moreover, a multispectral camera captures images at 8 spectral bands for accurate spectral color reconstruction from different directions. To verify the method, a prototype capable of fast, high-resolution measurements with a large FOV has been developed for characterizing the scattering properties of objects. It achieves a measured angular range up to 160°. Multispectral BRDF data for each sample can be obtained within 5 minutes with an angular resolution of less than 0.6°. Eight ceramic samples with different colors were selected for the verification of measurement accuracy, and their mean relative bias of BRDF measurement was found to be as low as 2.5%.

An overview of BRDF models in computer graphics

This paper aims to provide an overview of the Bidirectional Reflectance Distribution Function (BRDF) and the various parametric numerical models, known as BRDF models, used to make it easier and more efficient to use BRDF data in computer graphics. It introduces the basics of BRDF and classifies and describes some well-known BRDF models, including their advantages and disadvantages. The paper also covers the concept of data-driven models, which can achieve a high degree of realism by directly acquiring and using measured BRDF data in the rendering process.

Goniometer in the air: Enabling BRDF measurement of crop canopies using a cable-suspended plant phenotyping platform

The Bidirectional Reflectance Distribution Function (BRDF) quantifies the distribution of the spectral reflectance of a target surface at various viewing and illumination angles. In-field measurement of the BRDF of vegetation canopies improves the characterization of off-nadir measurements and informs radiative transfer models of canopy reflectance, where the Lambertian assumption does not hold. However, current field goniometers are unable to measure BRDF efficiently, especially for tall vegetation across the growing season because of the limitations of clearance, field accessibility, and flexibility of the sensor field of view. In this study, we explored the potential of using a large-scale cable-suspended field phenotyping system to quantify BRDF of the canopy reflectance at selected bands and Vegetation Indices (VIs) of maize and soybean canopies. The system performance benefited from the following conditions: no crop damage, full-season field accessibility of tall canopies, automatic measurement, and accurate positioning. Correlation analysis shows that a strong correlation exists among the reflectance, VIs, and the Green Pixel Fraction. The hemispheric distributions of the spectral reflectance at selected bands and VIs were quantified at multiple dates. Hot spots were observed in the backscatter direction at visible and near-infrared (NIR) bands at the largest sensor zenith angle around the Solar Principal Plane (SPP). In contrast, cold spots of the Normalized Difference Vegetation Index (NDVI) and its related VIs were observed in the backscatter direction around solar zenith angles. The row effect was found for the maize canopy at the NIR band and the Near-infrared reflectance of vegetation (NIRv). NDVI had the lowest anisotropy index values among investigated bands and VIs. This system could be further leveraged to generate rapid and detailed BRDF data at a high spatiotemporal resolution using multiple sensors.

Continuous material reflectance map for deep photometric stereo.

Solving calibrated photometric stereo under a sparse set of lights is of great interest for real-world applications. Since neural networks show advantages in dealing with material appearance, this paper proposes a bidirectional reflectance distribution function (BRDF) representation, which is based on reflectance maps for a sparse set of lights and can handle various types of BRDFs. We discuss the optimal way to compute these BRDF-based photometric stereo maps regarding the shape, size, and resolution, and experimentally investigate the contribution of these maps to normal map estimation. The training dataset was analyzed to establish the BRDF data to use between the measured and parametric BRDFs. The proposed method was compared to state-of-the-art photometric stereo algorithms for different datasets from numerical rendering simulations, DiliGenT, and our two acquisition systems. The results show that our representation outperforms the observation maps as BRDF representation for a neural network for various surface appearances on specular and diffuse areas.

Tracking diurnal to seasonal variations of gross primary productivity using a geostationary satellite, GK-2A advanced meteorological imager

The diurnal sampling capability of geostationary satellites provides unprecedented opportunities for monitoring canopy photosynthesis at multiple temporal scales. At the diurnal scale, only geostationary satellites can currently provide sub-daily data at regular intervals, also it can help to minimize data gaps due to clouds at the seasonal scale. However, the potential of geostationary satellites for monitoring photosynthesis has not been explored in depth. In this study, we tracked diurnal to seasonal variations in gross primary production (GPP) using the product of near-infrared reflectance of vegetation and photosynthetically active radiation (PAR) (NIRvP) over deciduous forests, mixed forests and a rice paddy during the growing season. For this purpose, we generated three levels of reflectance and PAR from Geostationary Korea Multi-Purpose Satellite-2A (GK-2A). We examined how NIRvP derived from GK-2A tracked in-situ GPP data collected from five flux tower sites in South Korea. Bi-directional Reflectance Distribution Function (BRDF) normalized NIRvP agreed well with in-situ GPP over the course of the growing season at hourly (R2 = 0.68–0.77) and daily timesteps (R2 = 0.71–0.83). Atmospheric correction and BRDF normalization improved the performance of NIRvP in tracking GPP at both the diurnal and seasonal time scales. Also, GK-2A showed a much higher percentage of available high-quality BRDF data over the whole growing season for all study sites than the Moderate Resolution Imaging Spectroradiometer (MODIS) (GK-2A: 85%; MODIS: 39%), especially during the cloudy monsoon period. Our findings demonstrated that the unique observation characteristics of geostationary satellites can contribute to large-scale monitoring of diurnal to seasonal GPP dynamics.

CANOPY STRUCTURAL EFFECTS ON BIDIRECTIONAL REFLECTANCE SIMULATED BY THE LESS MODEL: A CASE STUDY OF PICEA CRASSIFOLIA FORESTS

Abstract. Surface albedo is a dominant factor affecting the earth energy balance. Bidirectional reflectance distribution function (BRDF) describes the anisotropic surface reflection of solar radiation. Bidirectional effect is especially noticeable in the forest canopies with three-dimensional canopy structure. Thus, it is challenging to evaluate the canopy structural effects on BRDF using traditional radiative transfer modelling methods, where leaf in canopies is generally assumed to be homogeneous. LESS, a ray-tracing-based three-dimensional (3D) radiative transfer model can effectively simulate bidirectional reflectance factor while fully considering multi-component spectral and structural characteristics of vegetation. In this study, we applied the LESS model to evaluate the impacts of changes in leaf area index (LAI) on canopy reflectance in a Picea crassifolia forest. First, canopy structural parameters obtained from forest inventory were used to construct forest scenes and drive the LESS model. Then, we validated the simulation accuracy of the LESS model against BRDF calculated from MODIS BRDF parameter product using kernel-driven Ross-Li bi-directional reflectance function. Finally, we constructed forest scenes with different LAI to investigate the canopy structural effects on BRDF. We found that the BRDF simulated by the LESS model is in good accordance with the MODIS BRDF data in the red (R2 = 0.97, RMSE = 0.03) and NIR (R2 = 0.94, RMSE = 0.05) bands. The simulated canopy reflectance in the red band displayed ‘dome’ shape and decreased with increasing LAI. In contrast, canopy reflectance in the NIR band displayed ‘bowl’ shape and increased with increasing LAI. Our study highlighted the sensitivity of canopy BRDF to changes in canopy structure and have implications for retrieving LAI from BRDF data.

Field Reflectance Measurements at Night of Beach and Desert Sands within a Particulate BRDF Model

The Bidirectional Reflectance Distribution Function (BRDF) of soils is frequently assumed to be Lambertian in remote sensing applications, even though many soils are observed to have a distinct backscatter. This is largely due to the difficulty of obtaining accurate in-situ BRDF of these materials over the entire hemisphere. The objective of the work presented here is to describe a new technique that combines the measurement of field BRDF data on desert and beach sands measured at night with a model that reproduces the backscatter except in a small region around zero phase angle. It is found that this combination produces parameterized BRDF of sufficient accuracy to allow its inclusion in a remote sensing materials database. The measurement technique was developed in the laboratory and transitioned to perform in-plane BRDF field measurements of sands at night. Field measurements were obtained using a portable light source and field spectrometer over the range of 0.4–2.4 micrometers. The spectrometer sensor optics and light source were mounted on a portable, manually operated goniometer allowing in-plane measurements to within 3 degrees of backscatter. Unlike daytime measurements, corrections for background were unnecessary, and BRDF was obtained by referencing to a Spectralon calibration standard. Analysis of the spectrometer field data used a variant of the Shadow Hiding Opposition Effect (SHOE) wherein a series expansion of Legendre Polynomials was substituted for the angularly dependent backscatter function. It is shown that when the out-of-plane scattering and the backscatter peak are small, this model provides an adequate description of the BRDF. The combination of the nocturnal in-situ measurements with an analysis using a model that can describe the backscatter produces parameterized BRDF for these sands of sufficient accuracy to allow inclusion in the NEFDS materials database. Measurement and analysis techniques are assessed, sample results for both the laboratory and field data are shown, and the extension to future soils measurements are discussed.

Evaluation of the Consistency of the Vegetation Clumping Index Retrieved from Updated MODIS BRDF Data

The clumping index (CI) quantifies the foliage grouping within distinct canopies relative to randomly distributed canopies, which plays an important role in the vegetation radiative regime. Among the vegetation structure parameters, the global CI map can be retrieved by using multiangle remote sensing observations. The bidirectional reflectance distribution function (BRDF)/Albedo product (MCD43) of the Moderate-Resolution Imaging Spectroradiometer (MODIS) is the crucial input data of the global CI product, which provides validated spatiotemporal continuous directional reflectance data. To determine the impacts of updating the MCD43 product on the consistency and performance of global CI products, CIs retrieved from different MCD43 versions (Collection V005/V006, C5/6) were compared on a global scale and validated with field-measured CI data. The results showed that the global and seasonal comparisons of C5 and C6 CI data are generally consistent. Compared to C5 CI data, C6 CI data have improved quality with more main algorithm retrievals and fewer case of missing data. The comparisons over the field measurements indicate that both versions of CI data agree with field-measured CI data in terms of values and seasonal variations, while C6 CI data (R2 = 0.89, RMSE = 0.05, bias = 0.02) are closer to field CIs than C5 CI data (R2 = 0.80, RMSE = 0.07, bias = 0.03), indicating a higher accuracy for C6 CI data. The monthly CI is recommended for characterizing the overall seasonal patterns of surface CIs.

Reflectance Anisotropy from MODIS for Albedo Retrieval from a Single Directional Reflectance

Surface reflectance anisotropy and insufficient multi-angular observations are the main challenges in albedo estimation from satellite observations. Numerous studies have been developed for albedo retrieval from a single directional reflectance by associating the anisotropy information extracted from coarse-resolution bidirectional-reflectance distribution function (BRDF) data. The contribution of land-cover type (LCT) and the Normalized Difference Vegetation Index (NDVI) in distinguishing reflectance anisotropy in these methods remains controversial. This study first proposed an approach to extracting a priori BRDF (F) from the MODIS BRDF/albedo product by considering the distribution characteristics of the model parameters. LCT- and NDVI-based F were also extracted from the corresponding subset. Then, the F-based albedo was derived from simulated or satellite directional reflectance and the anisotropic information of F. Finally, the directional reflectance and F-based albedo were compared with the MODIS albedo or ground measurement, in order to show the ability of F to compensate for the effect of reflectance anisotropy in the albedo retrieval process. The method was fully validated by the global and time-series MODIS BRDF data. The results showed that reflectance anisotropy has an aggregated distribution pattern, and F can represent the reflectance anisotropy of most pixels within a tile. The improvement of LCT and NDVI only occurs when the tile contains a large area of vegetated and barren ground. With the exception of the hotspot and large viewing-zenith-angle area in the forward hemisphere, the F-based shortwave albedo has high consistency with the MODIS albedo product. A comparison with the ground measurements and MODIS albedo showed that the F-based albedo from a single directional reflectance generally achieves an absolute accuracy requirement, with a root-mean-square error (RMSE) of 0.027 and 0.036.

Machine‐readable universal data format for bidirectional reflectance distribution function and BiRDview—An open‐source web‐based application for viewing and comparing bidirectional reflectance data

AbstractModern studies of bidirectional reflectance distribution function (BRDF) and its applications using data and machine‐driven science require formatting of BRDF data according to Findable, accessible, interoperable and reusable (FAIR) data principles. As a solution a FAIR universal BRDF file‐format based on Java Script Object Notation (JSON) is proposed. JSON principles as well as file structure are explained and examples are given. Automatic validation of universal BRDF file format is realized with the help of JSON schema. Furthermore, the source code and accompanying documentation are presented in dedicated supporting material files. It is expected that after its wide adoption, the proposed BRDF file format will enhance collaboration between different research groups and benefit machine‐driven science. The uptake is facilitated by introducing a BiRDview—a modern open‐source web‐based application for BRDF visualization.

Bidirectional Reflectance Distribution Function Modeling Considerations in Small Unmanned Multispectral Systems

With the rapid advancement of miniaturized sensors and unmanned airborne system (UAS) platforms, scientific measurements that previously were carried out by large government or academic institution programs can now be successfully accomplished by smaller collection activities. In the case of vegetation assessment (e.g., forestry and agriculture), spatial, temporal, radiometric, and spectral resolution can be rigorously controlled. Although each of these is important, accurate temporal assessment of chemistry and morphological plant attributes is heavily dependent on spectral resolution and correction. A particular phenomenology of interest is the extraction and modeling of bidirectional reflectance distribution function (BRDF) data. In this effort, an approach is discussed to reflectance calibrate and derive BRDF signatures from soybeans through a newly available multispectral sensor integrated to an industry common UAS platform. Methods were developed to extract the reflectance data across the azimuth and elevation observations and fit these field data to previously derived models from the literature. A modular processing pipeline was developed to allow for the implementation of additional algorithms and efficient numerical analysis. Results show that the coefficients derived to fit the modeled BRDF data are consistent across spatial resolution and within cover type. Additionally, the modeled-fit root-mean-square error was inversely proportional to the spatial resolution of the image data used for signature extraction. In conjunction with more traditional spectral and ratio-based analytical indices, this approach provides important dimensionality in both classification and land-cover assessment applications critical to more accurate temporal vegetation assessment.

Directionally dependent Lambertian-equivalent reflectivity (DLER) of the Earth's surface measured by the GOME-2 satellite instruments

Abstract. In this paper we introduce the new concept of directionally dependent Lambertian-equivalent reflectivity (DLER) of the Earth's surface retrieved from satellite observations. This surface DLER describes Lambertian (isotropic) surface reflection which is extended with a dependence on the satellite viewing geometry. We apply this concept to data of the GOME-2 satellite instruments to create a global database of the reflectivity of the Earth's surface, providing surface DLER for 26 wavelength bands between 328 and 772 nm as a function of the satellite viewing angle via a second-degree polynomial parameterisation. The resolution of the database grid is 0.25∘ by 0.25∘, but the real, intrinsic spatial resolution varies over the grid from 1.0∘ by 1.0∘ to 0.5∘ by 0.5∘ down to 0.25∘ by 0.25∘ by applying dynamic gridding techniques. The database is based on more than 10 years (2007–2018) of GOME-2 data from the MetOp-A and MetOp-B satellites. The relation between DLER and bi-directional reflectance distribution function (BRDF) surface reflectance is studied using radiative transfer simulations. For the shorter wavelengths (λ<500 nm), there are significant differences between the two. For instance, at 463 nm the difference can go up to 6 % at 30∘ solar zenith angle. The study also shows that, although DLER and BRDF surface reflectances have different properties, they are comparable for the longer wavelengths (λ>500 nm). Based on this outcome, the GOME-2 surface DLER is compared with MODIS surface BRDF data from MODIS band 1 (centred around 645 nm) using both case studies and global comparisons. The conclusion of this validation is that the GOME-2 DLER compares well to MODIS BRDF data and that it does so much better than the non-directional LER database. The DLER approach for describing surface reflectivity is therefore an important improvement over the standard isotropic (non-directional) LER approaches used in the past. The GOME-2 surface DLER database can be used for the retrieval of atmospheric properties from GOME-2 and from previous satellite instruments like GOME and SCIAMACHY. It will also be used to support retrievals from the future Sentinel-5 UVNS (ultraviolet, visible, near-infrared, and short-wave infrared) satellite instrument.

Imaging Scatterometry with Extrapolation of Missing BRDF Data for Materials Used in Laser Material Processing.

Imaging scatterometry is a method for determining the reflection distribution based on bidirectional reflectance distribution function (BRDF) measurements. However, it has a well-known limitation that results obtained by imaging scatterometry for small illumination angles are practically useless. Therefore, we propose an approach for reconstruction of the reflection distribution based on a series of measurements at different illumination angles and extrapolation of the missing results to overcome this limitation. The developed algorithm was validated using bidirectional transmittance distribution function (BTDF) measurements. The BRDF measurements were carried out for materials that are commonly used in laser material processing, i.e. substrates and functional coatings. The obtained data were subsequently used to determine the total reflection intensity from all considered materials, which were characterized by reconstructed distributions.

Assessment of Improved Ross–Li BRDF Models Emphasizing Albedo Estimates at Large Solar Angles Using POLDER Data

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.

The Application of Bidirectional Reflectance Distribution Function Data to Recognize the Spatial Heterogeneity of Mixed Pixels in Vegetation Remote Sensing: A Simulation Study

Spectral decomposition of mixed pixels can provide information about the abundance of end members but fails to indicate the spatial distribution of end members in vegetation remote sensing. This work is a significant attempt to use the bidirectional reflectance distribution function (<small>BRDF</small>) characteristics of mixed pixels in the prediction of spatial-heterogeneity metrics. Data sets from this function with different spatial distributions were constructed by the discrete anisotropic radiative transfer model, and three spatial aggregation and dispersion metrics were calculated: percentage of like adjacencies, spatial division index, and aggregation index. A simple linear regression method was used to construct the prediction model of spatial aggregation and dispersion metrics. The potential of multiangle remote sensing model for identifying spatial patterns well was demonstrated, and its importance was found to differ for different spatial aggregation and dispersion metrics. Specifically, the precision of the model based on multiangle reflectance used for predicting the spatial division index could meet a minimum root mean square of 5.95%. The reflectance features from backward observation on the principal plane play the leading role in recognizing the spatial heterogeneity of mixed pixels. The prediction model is sufficiently robust to distinguish the same vegetation with different growth trends, but also performs well when the ground objects have a smaller reflectance difference in the mixed pixels in a certain band. This study is expected to offer a new thought for spatial-heterogeneity identification of ground objects and thus promote the development of remote sensing technology in assessing spatial distribution.

Versatile four-axis gonioreflectometer for bidirectional reflectance distribution function measurements on anisotropic material surfaces

The bidirectional reflectance distribution function (BRDF) data are essential for analyzing and modeling the material appearance of anisotropic surfaces. In order to acquire four-dimensional BRDF on the anisotropic material surfaces, a four-axis gonioreflectometer was designed and implemented. The instrument consists of a collimated, broadband light source, a four-axis rotation mechanism, a spectroradiometer, and a control system. The instrument is able to carry out spectral BRDF measurements over most of the incident and reflection hemispheres and the entire visible spectrum. One thousand twenty-four samples are obtained over the spectral range of 380 to 760 nm. The angular resolution of the BRDF measurement is <0.1 deg with good repeatability. A relative calibration method was adopted to obtain the absolute values of BRDFs. Various scanning schemes can be carried out by the instrument to scan the designated angular domains, enabling the instrument to capture material appearance with strong, distinctive anisotropic highlights and translucency. The obtained BRDF data of a textile sample demonstrate the instrument capability of capturing complex light scattering behaviors, including off-specular reflection peaks, off-plane reflection peaks, and backscattering. The designers of novel material appearance and computer graphics community will benefit from this work.

Global 500 m clumping index product derived from MODIS BRDF data (2001–2017)

The vegetation clumping index (CI) quantifies the degree to which foliage deviates from a random distribution, and therefore, is an important canopy structural parameter that governs the photosynthesis and evapotranspiration processes in terrestrial ecosystems. While the temporal variation of CI has been investigated in many field studies, there has not been a global CI product that captured its seasonal and inter-annual variations. In this study, a look-up table (LUT) method was developed based on an improved Normalized Difference between Hotspot and Darkspot (NDHD) method to estimate the daily CI from the MODIS V006 MCD43 BRDF (bidirectional reflectance distribution function) product. This new CI product is consistent with field measurements at 33 sites distributed globally (R2 = 0.38, RMSE = 0.04, and bias = −0.01). CI shows stronger seasonal variations for deciduous broadleaf forest (DBF) and mixed forests than other vegetation types. The large seasonal differences between evergreen and deciduous vegetation, especially for DBF and deciduous shrubs, allow the CI to be used to detect seasonal structural changes and classify vegetation. The global CI shows a negative correlation to the leaf area index (LAI) for all land cover types, especially forests. The global CI demonstrates an inter-annual variation that correlated with global precipitation (R2 = 0.34). In addition, the global CI shows a global decreasing trend from 2001 to 2017 (−0.007/decade) that was consistent with the increasing LAI (0.049/decade). The time series of CI provides a new perspective for understanding the structural characteristics of vegetation in global ecosystem studies.

Evaluation of the Snow Albedo Retrieved from the Snow Kernel Improved the Ross-Roujean BRDF Model

The original kernel-driven bidirectional reflectance distribution function (BRDF) models were developed based on soil-vegetation systems. To further improve the ability of the models to characterize the snow surface scattering properties, a snow kernel was derived from the asymptotic radiative transfer (ART) model and used in the kernel-driven BRDF model framework. However, there is a need to further evaluate the influence of using this snow kernel to improve the original kernel-driven models in snow albedo retrieval applications. The aim of this study is to perform such an evaluation using a variety of snow BRDF data. The RossThick-Roujean (RTR) model is used as a framework for taking in the new snow kernel (hereafter named the RTS model) since the Roujean geometric-optical (GO) kernel captures a neglectable hotspot effect and represents a more prominent dome-shaped BRDF, especially at a small solar zenith angle (SZA). We obtained the following results: (1) The RTR model has difficulties in reconstructing the snow BRDF shape, especially at large SZAs, which tends to underestimate the reflectance in the forward direction and overestimate reflectance in the backward direction for various data sources. In comparison, the RTS model performs very well in fitting snow BRDF data and shows high accuracy for all data. (2) The RTR model retrieved snow albedos at SZAs = 30°–70° are underestimated by 0.71% and 0.69% in the red and near-infrared (NIR) bands, respectively, compared with the simulation results of the bicontinuous photon tracking (bic-PT) model, which serve as “real” values. However, the albedo retrieved by the RTS model is significantly improved and generally agrees well with the simulation results of the bic-PT model, although the improved model still somewhat underestimates the albedo by 0.01% in the red band and overestimates the albedo by 0.05% in the NIR band, respectively, at SZAs = 30°–70°, which may be negligible. (3) The albedo derived by these two models shows a high correlation (R2 > 0.9) between the field-measured and Polarization and Directionality of the Earth's Reflectances (POLDER) data, especially for the black-sky albedo. However, the albedo derived using the RTR model is significantly underestimated compared with the RTS model. The RTR model underestimates the black-sky albedo (white-sky albedo) retrievals by 0.62% (1.51%) and 0.93% (2.08%) in the red and NIR bands, respectively, for the field-measured data. The shortwave black-sky and white-sky albedos derived using the RTR model for the POLDER data are underestimated by 1.43% and 1.54%, respectively, compared with the RTS model. These results indicate that the snow kernel in the kernel-driven BRDF model frame is more accurate in snow albedo retrievals and has the potential for application in the field of the regional and global energy budget.

An assessment of the performance of two snow kernels in characterizing snow scattering properties

ABSTRACTThe kernel-driven RossThick-LiSparseReciprocal (RTLSR) bidirectional reflectance distribution function (BRDF) model has been widely used in the quantitative remote sensing community. However, the performance of this model is challenged when modelling the optical scattering properties of pure snow surfaces. Recently, two snow kernels have been developed to improve the snow anisotropic reflectance in the kernel-driven RTLSR model framework. However, the performances of these two snow kernels must be assessed to identify their potential applications. Therefore, we assess the performances of these two kernels using various BRDF data sources. Our findings demonstrate their differences in several aspects. (1) These two kernels differ in characterizing the variability in BRDF shape as a function of the solar zenith angle (SZA). As the SZA increases, the shape of snow kernel derived by the asymptotic radiative transfer (ART) model (hereinafter named the ART method) changes from a dome shape to bowl shape, which agrees well with the simulation data of the bicontinuous photon tracking (bic-PT) model. The shape of the snow kernel proposed by Qu et al. (hereinafter named the Qu method) based on the Rahman-Pinty-Verstraete (RPV) model maintains a bowl shape for all SZAs. These differences in the kernel performances affect their abilities to fit snow BRDF data with different SZAs. (2) The corrected RTLSR models, with their respective snow kernels, are generally able to model the forward-scattering properties of snow surfaces compared with the original RTLSR model. However, the ART method performs better in capturing the BRDF variations in snow surfaces than the Qu method. This assessment provides an improved understanding of the performance of these two snow kernels and, thus, suggests further applications for the ART snow kernel in the kernel-driven BRDF model framework in the near future.