Bidirectional Reflectance Distribution Function Research Articles

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.

An attention-embedded GAN for SVBRDF recovery from a single image

Learning-based approaches have made substantial progress in capturing spatially-varying bidirectional reflectance distribution functions (SVBRDFs) from a single image with unknown lighting and geometry. However, most existing networks only consider per-pixel losses which limit their capability to recover local features such as smooth glossy regions. A few generative adversarial networks use multiple discriminators for different parameter maps, increasing network complexity. We present a novel end-to-end generative adversarial network (GAN) to recover appearance from a single picture of a nearly-flat surface lit by flash. We use a single unified adversarial framework for each parameter map. An attention module guides the network to focus on details of the maps. Furthermore, the SVBRDF map loss is combined to prevent paying excess attention to specular highlights. We demonstrate and evaluate our method on both public datasets and real data. Quantitative analysis and visual comparisons indicate that our method achieves better results than the state-of-the-art in most cases.

SCIATRAN software package (V4.6): update and further development of aerosol, clouds, surface reflectance databases and models

Abstract. Since the initiation of development at the Institute of Environmental Physics (IUP), University of Bremen, in 1994, the radiative transfer model SCIATRAN (formerly GOMETRAN) has been continuously improved and new versions have been released (Rozanov et al., 1997, 2002, 2005, 2014, 2017). In the course of development, the SCIATRAN software package became capable of simulating radiative transfer processes through the Earth's atmosphere or coupled atmosphere–ocean system with a variety of approaches to treat the sphericity of the atmosphere (plane-parallel, pseudo-spherical, approximately spherical and full-spherical solutions) in both scalar and vector modes. Supported by a variety of built-in databases and parameterizations, these capabilities made SCIATRAN widely used for various remote-sensing applications related to the retrieval of atmospheric trace gases and characteristics of aerosols, clouds and surfaces. This paper presents an overview of the cloud, aerosol and surface (CAS) databases and models implemented in the SCIATRAN software package (V4.6) and provides some recommendations on their usage. The new implementations offer potential users a flexible interface to perform radiative transfer simulations: (1) accounting for multilayer liquid water, ice and mixed-phase clouds; (2) employing typical aerosol-type parameterizations (including vertical variability) used in the satellite and model communities as well as updated databases; (3) including various surface bidirectional reflectance distribution function (BRDF) and albedo models for land, vegetation, ocean, snow and melt ponds on sea ice. The most recent version of the radiative transfer model SCIATRAN is freely available at the website of the IUP, University of Bremen: http://www.iup.physik.uni-bremen.de/sciatran (last access: November 2022).

Influence of structural disorder on plasmonic metasurfaces and their colors—a coupled point dipole approach: tutorial

The optical properties of plasmonic metasurfaces are determined not only by the shape and size of the constituting nanostructures, but also by their spatial arrangement. The fast progress in nanofabrication has facilitated the emergence of many advanced metasurface designs that enable controlling the propagation of light on the nanoscale. While simple metasurface designs can be derived from theoretical considerations, it is inevitable to employ computational approaches for complex manipulations of incident light. However, most of the currently available full-wave simulation approaches such as the finite element method (FEM) or finite difference time domain method come with drawbacks that limit the applicability to certain usually simplified or less complex geometries. Within this tutorial, different approaches are outlined for modeling light propagation in complex metasurfaces. We focus on an approach that approximates the nanostructure ensemble as a coupled set of point dipoles and determine their far-field response via the reciprocity theorem. This coupled point dipole approximation (CPDA) model is used to examine randomly distributed, oriented, and scaled nanostructure ensembles. A disorder formalism to introduce the randomness is developed that allows one to progressively perturb periodic arrangements of identical nanostructures and thereby investigate the effects of disorder and correlation. Several disorder metrics are provided that allow one to quantify the disorder, and the relation with the far-field scattering properties is discussed. Spatially and angle resolved hyperspectral datasets are computed for various disordered metasurfaces to assess the capabilities of the CPDA model for different polarization states and incidence angles, among others. The hyperspectral datasets are converted into sRGB color space to deduce the appearances in the image and Fourier planes. Very good agreement of the simulation results with Mie theory, FEM results, and experiments is observed, and possible reasons for the present differences are discussed. The presented CPDA model establishes a highly efficient approach that provides the possibility to rapidly compute the hyperspectral scattering characteristics of metasurfaces with more than 10,000 structures with moderate computational resources, such as state-of-the-art desktop computers with sufficient memory; 16 GB allow for the simulations in this paper, whereas scaling to up to more memory by the factor of N2 allows for the simulation of N times more dipoles. For that reason, the CPDA is a suitable approach for tailoring the bidirectional reflectance distribution function of metasurfaces under consideration of structural perturbations and experimental parameters.

Road marking BRDF model applicable for a wide range of incident illumination conditions.

To drive safely and comfortably, an adequate contrast between the road surface and road markings is needed. This contrast can be improved by using optimized road illumination designs and luminaires with dedicated luminous intensity distributions, taking advantage of the (retro)reflective characteristics of the road surface and road markings. Since little is known about road markings' (retro)reflective characteristics for the incident and viewing angles relevant for street luminaires, bidirectional reflectance distribution function (BRDF)-values of some retroreflective materials are measured for a wide range of illumination and viewing angles using a luminance camera in a commercial near-field goniophotometer setup. The experimental data are fitted to a new and optimized "RetroPhong" model, which shows good agreement with the data [root mean squared error (R M S E)<0.13, normalized root mean squared error (N R M S E)<0.04, and the normalized cross correlation ratio (N C C)>0.8]. The RetroPhong model is benchmarked with other relevant (retro)reflective BRDF models, and the results suggest that the RetroPhong model is most suitable for the current set of samples and measurement conditions.

A high-precision aerosol retrieval algorithm for FY-3D MERSI-II images

The Medium Resolution Spectral Imager-II (MERSI-II) onboard the recently launched Chinese Fengyun-3D (FY-3D) satellite has great capability in detecting global aerosols as it includes aerosol bands similar to Moderate Resolution Imaging Spectroradiometer (MODIS). However, to date, aerosol retrieval based on MERSI-II is still limited to dark target regions and there is no official aerosol products for the MERSI-II. This study focuses on developing a high-precision algorithm to retrieve aerosol optical depth (AOD) suitable for entire land areas (except snow/ice and inland waters) based on MERSI-II measurements. Considering both the accuracy and retrieval efficiency, a new cost function is constructed based on (1) the fact that the AOD (550 nm) retrieved independently from different bands should be the same with the correct aerosol model, and (2) the assumption that the aerosol types are the same in the 5 × 5 km spatial range. The retrieval method based on the new cost function is nearly 50 times faster than most current methods using iterative calculations. To extend the application adaption of the FY-3D MERSI-II AOD retrieval and avoid the errors caused by the surface Lambertian hypothesis, a bidirectional reflectance distribution function (BRDF) database is built using MODIS products. Eight candidate aerosol models in different natural zones of China are constructed based on AERONET aerosol products from 2010 − 2021. The new method is applied to MERSI-II images over China and validated against ground-based measurements at 14 stations from 2020 to 2021. MODIS aerosol products from three operational algorithms are also used for comparison purposes. The results show that MERSI-II AOD retrievals agree well with the ground-based measurements with correlation coefficient (R), root mean square error (RMSE), and relative mean bias (RMB) of 0.913, 0.123, and 0.955, respectively. In addition, 72.19 % of AOD matchups fall within the expected error (EE) envelopes. The MERSI-II retrievals show higher accuracy than that of MODIS dark target (DT) and deep blue (DB) products and comparable accuracy of the MODIS Multi-Angle Implementation of Atmospheric Correction (MAIAC) product. MERSI-II AOD also shows higher stability in terms of spatial and temporal and better performance under heavy aerosol loading conditions than MODIS products. A good AOD agreement with R from 0.777 to 0.863 between MERSI-II and MODIS products is found over the land of China. The new method showing high retrieval efficiency and accuracy has great potential to be operationally applied on AOD retrieval for MERSI-II.

An unmixing-based BRDF correction in spectral remote sensing data

While extensive research addressed the Bidirectional Reflectance Distribution Function (BRDF) effect and approaches to correct it, too few works have considered the influence of spectral mixture on the correction results.This work studies the BRDF effect in spectral data and presents an approach to correct its undesired impact, considering the likely presence of mixed pixels. We propose an unmixing-based semiempirical model, incorporating endmembers’ (EMs) fractions within the data correction.To evaluate the performance of the proposed methodology, we conducted experiments with laboratory and aerial hyperspectral image data. The outcomes from all experiments reveal vital insights into the influence of the spectral mixture on the BRDF correction accuracy. Nevertheless, the results clearly show that the accuracy of the corrected reflectance significantly improved using the proposed model for reducing the BRDF effect, regardless of the pixel’s microtopography arrangement.Most importantly, a quantitative assessment of the difference in reflectance values within the overlapping region between two aerial images shows that the unmixing-based model outperforms the commonly used one.While the traditional method reduces the influence of the BRDF in the corrected data by a factor of two, with an average Mean Absolute Error (MAE) of≈2.5%, the proposed approach reduces it by a factor of four with an average MAE≈1.2%.

Infrared BRDF spatial scanning measurement with an optimized rotation strategy of a robotic arm

The bidirectional reflection distribution function (BRDF) reflects the optical reflection properties of opaque materials over the entire hemispherical space. Exciting measurements of infrared BRDF systems based on robotic arms are discrete in space since the incident and reflection angles were coupled deeply. In this paper, a mapping from BRDF angles to goniometer angles was developed, and the two sets of angles were decoupled using an optimized spatial rotation strategy with two scanning modes. The measurement covered the full BRDF hemispherical space. The measurement speed and resolution in the specific scanning directions were significantly improved. Meanwhile, the measurement accuracy was not reduced. An infrared BRDF measurement system using the proposed strategy was developed to measure five different samples from high to low reflectance with specular or diffuse reflection qualities. The qualities demonstrated by the calculated BRDF distributions were consistent with the infrared optical characteristics of all samples, verifying the effectiveness of the proposed system.

The effects of surface roughness on the calculated, spectral, conical–conical reflectance factor as an alternative to the bidirectional reflectance distribution function of bare sea ice

Abstract. The conical–conical reflectance factor (CCRF) has been calculated as an alternative to the bidirectional reflectance distribution function (BRDF) for three types of bare sea ice with varying surface roughness (σ= 0.1–10) and ice thicknesses (50–2000 cm) over an incident solar irradiance wavelength range of 300–1400 nm. The comprehensive study of the CCRF of sea ice presented here is paramount for interpreting sea ice measurements from satellite imagery and inter-calibrating space-borne sensors that derive albedo from multiple multi-angular measurements. The calculations performed by a radiative-transfer code (PlanarRad) show that the CCRF of sea ice is sensitive to realistic values of surface roughness. The results presented here show that surface roughness cannot be considered independently of sea ice thickness, solar zenith angle and wavelength. A typical CCRF of sea ice has a quasi-isotropic reflectance over the hemisphere, associated with a strong forward-scattering peak of photons. Surface roughness is crucial for the location, size and intensity of the forward-scattering peak. As the surface roughness increases, a spreading of the CCRF peak is observed. The hemisphere was split in to 216 quadrangular regions or quads. The peak remains specular for the smaller surface roughnesses (σ=0.001 to σ=0.01), whereas for larger surface roughness features (above σ=0.05), the peak spreads out over multiple quads with a lower intensity than for smaller roughness features, and the highest value is displaced further out on the solar principal plane. Different types of sea ice have a similar pattern with wavelength: the CCRF increases by 30 % from first-year sea ice to multi-year sea ice at 400 nm and up to 631 % at 1100 nm, 32 % from melting sea ice to multi-year sea ice at 400 nm and a maximum of 98 % at 900 nm, and 11 % from melting sea ice to first-year sea ice at 400 nm and up to 86 % at 800 nm. The CCRF calculations presented in this study form the first set of complete CCRF values as an approximation of the BRDF for bare sea ice with a wide range of configurations.

Refractive index inversion method for metals based on circular polarization detection of light

Among many optical detection methods, the polarization detection method of light has been proven to be capable of providing outstanding, even unique sometimes, information of targets under test, this includes detecting objects that are difficult to be distinguished by the light intensity or spectrum information alone. However, as for materials identification, the current polarization detection method which usually uses linearly polarized light can only roughly distinguish metallic materials from non-metallic materials but cannot further differentiate among types of metallic materials. Note that the phase of a linearly polarized light may change after being reflected by a metal due to its complex refractive index, and the circular polarization information of the reflected light can be used to sense the phase change property of the metal, therefore, different types of metallic materials can be identified according to their characteristic circular polarization information due to their diverse complex refractive indices. In this paper, based on the circular polarization detection of light, a complex refractive index inversion method for metals is proposed accordingly, and experimental measurements and fitting estimations are carried out for different types of metallic materials using a Bidirectional Reflectance Distribution Function (BRDF) measurement equipment. The experimental results show that the method can accurately invert the complex refractive indices of different metals and distinguish different types of metal samples. Compared to the Mueller-matrix-based measurement method, the proposed method is computationally simple, needless of measuring a large number of parameters and performing complex calculations, it only needs to invert the results of twice measurements. In addition, it also has the advantages of high sensitivity, good stability and intuitive algorithm, which are valuable for identification applications of metallic materials.

Analysis of target surface polarization characteristics and inversion of complex refractive index based on three-component model optimization

Traditional imaging detection techniques are used to collect intensity information and spectral information of the target to generate high-resolution target images, but the imaging system is susceptible to external environmental factors, resulting in system instability and image quality degradation. Polarization detection techniques use the polarization properties of light to determine the polarization state and spatial profile of a target, thereby improving the contrast of the target in the image. In this study, the reflection process of the target surface is investigated from a microscopic perspective. A polarization characteristics model was developed to illustrate the link between the properties of the target surface and the degree of polarization of the reflected light. The results show that the degree of polarization is strongly related to the detection of zenith and azimuth angles. Experimental data are used to invert the complex refractive index of the target. The polarization of the target is greatest in the direction of specular reflection and smallest in the direction of light source incidence. This suggests that the established Polarimatric Bidirectional Reflectance Distribution Function (pBRDF) model can provide theoretical support for the analysis of the polarization properties of the target surface. Targets of different materials have different polarization properties and the extinction coefficient can effectively classify the targets.

Deep Learning-Based Emulation of Radiative Transfer Models for Top-of-Atmosphere BRDF Modelling Using Sentinel-3 OLCI

The Bidirectional Reflectance Distribution Function (BRDF) defines the anisotropy of surface reflectance and plays a fundamental role in many remote sensing applications. This study proposes a new machine learning-based model for characterizing the BRDF. The model integrates the capability of Radiative Transfer Models (RTMs) to generate simulated remote sensing data with the power of deep neural networks to emulate, learn and approximate the complex pattern of physical RTMs for BRDF modeling. To implement this idea, we used a one-dimensional convolutional neural network (1D-CNN) trained with a dataset simulated using two widely used RTMs: PROSAIL and 6S. The proposed 1D-CNN consists of convolutional, max poling, and dropout layers that collaborate to establish a more efficient relationship between the input and output variables from the coupled PROSAIL and 6S yielding a robust, fast, and accurate BRDF model. We evaluated the proposed approach performance using a collection of an independent testing dataset. The results indicated that the proposed framework for BRDF modeling performed well at four simulated Sentinel-3 OLCI bands, including Oa04 (blue), Oa06 (green), Oa08 (red), and Oa17 (NIR), with a mean correlation coefficient of around 0.97, and RMSE around 0.003 and an average relative percentage error of under 4%. Furthermore, to assess the performance of the developed network in the real domain, a collection of multi-temporals OLCI real data was used. The results indicated that the proposed framework has a good performance in the real domain with a coefficient correlation (R2), 0.88, 0.76, 0.7527, and 0.7560 respectively for the blue, green, red, and NIR bands.

3D Surface Reconstruction Method for Microsamples Based on Polarization Modulation Microscopy

A novel microscopic Shape-From-Polarization (SFP) 3D shape reconstruction method is proposed, in which degree of polarization is calculated using Polarized Bidirectional Reflectance Distribution Function (PBRDF) to overcome azimuthal ambiguity for both specular and diffuse polarization microscopic scenes. Based on the calculated degree of polarization, a polarization modulation microscopy oriented variational model is established to estimate surface normal vector and rebuild 3D shape of the sample with “fuzzy guidance” based on atomic force microscopy (AFM). Experiments on different microscopic samples indicate the proposed method can restore the stereoscopic morphology distribution with precision in micrometer.

Global estimates of surface albedo from Sentinel-3 OLCI and SLSTR data for Copernicus Climate Change Service: Algorithm and preliminary validation

The aim of Copernicus Climate Change Service (C3S) is to supply reliable climate data in support of strategies to adaptation and mitigation to climate change. The C3S provides access to high-quality climate data through its Climate Data Records (CDRs) of atmospheric, marine and land Essential Climate Variables (ECVs). Global Earth Surface Albedo (SA) satellite-based products are included in the land (biosphere) portfolio. SA is a magnitude which quantifies the fraction of solar energy reflected by the surface of the Earth. This paper details the retrieval methodology and preliminary validation results for global estimates of surface albedo based on Sentinel-3 observations for the C3S ECVs data (C3S SA v3.0). The retrieval algorithm exploits the synergistic use of the Ocean and Land Colour Instrument (OLCI) and the Sea and Land Surface Temperature Radiometer (SLSTR) on-board Sentinel-3 A and B satellites. Firstly, the atmospherically corrected reflectances are generated in the Copernicus Global Land Service framework. After that, the Bidirectional Reflectance Distribution Function (BRDF) inversion module concludes the BRDF model parameters, which are transferred to the angular integration module in order to generate spectral albedo quantities for the selected OLCI (Oa03, Oa04, Oa07, Oa17 and Oa21) and SLSTR (S1, S2, S5 and S6) bands. At the end, the spectral integration module generates broadband albedo quantities in three different standard broadband spectral regions (visible [0.4μm − 0.7μm ], near infrared [0.7μm − 4μm] and total shortwave [0.3μm − 4μm]). Preliminary validation results over 10-months demonstration period (July 2018–April 2019) show, in terms of spatial and temporal consistency, that C3S Sentinel-3 SA global estimates reached in general good agreement as compared to other satellite operational references derived from MODIS (MCD43A3 C6) and PROBA-V (C3S PROBA-V SA v1.0) acquisitions. The comparison with ground data shows similar results to the MCD43A3 C6 comparisons but opposite sign in differences (marginally positive in case of Sentinel-3), with accuracy of 0.005 (3.7%), precision of 0.016 (11.3%) and uncertainty of 0.032 (22.7%). Our results have demonstrated the feasibility to estimate global fields of SA from Sentinel-3 observations, with similar quality of existing operational products. These Sentinel-3 based SA datasets will give the continuity to the existing C3S SA CDR, introducing improvements in terms of spatial resolution (300 m) and spectral information (9 spectral albedos) in contrast to previous datasets based on Advanced Very High Resolution Radiometer (AVHRR; 4 km, 4 channels) and Vegetation instruments (VGT; 1 km, 4 channels).

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In this article the development of physically correct light reflectance model which is based on the modified Schlick model is discussed. The advantages and disadvantages of main empirical reflectance models are discussed. The necessity of development of the new physically correct bidirectional reflectance distribution functions is shown. The main steps of normalizing coefficient calculation for the modified Schlick model are discussed. The ideal normalizing coefficient values depending on the surface specularity coefficient were calculated. The formula of dependence between coefficient value and was discovered. The absolute error value between and hemispherical integral reflectivity value was calculated for the interval n ∈ [2,1000].

A Novel Inversion Approach for the Kernel-Driven BRDF Model for Heterogeneous Pixels

The bidirectional reflectance distribution function (BRDF) of the land surface contains information relating to its physical structure and composition. Accurate BRDF modeling for heterogeneous pixels is important for global ecosystem monitoring and radiation balance studies. However, the original kernel-driven models, which many operational BRDF/Albedo algorithms have adopted, do not explicitly consider the heterogeneity within heterogeneous pixels, which may result in large fitting residuals. In this paper, we attempted to improve the fitting ability of the kernel-driven models over heterogeneous pixels by changing the inversion approach and proposed a dynamic weighted least squares (DWLS) inversion approach. The performance of DWLS and the traditional ordinary least squares (OLS) inversion approach were compared using simulated data. We also evaluated its ability to reconstruct multiangle satellite observations and provide accurate BRDF using unmanned aerial vehicle observations. The results show that the developed DWLS approach improves the accuracy of modeled BRDF of heterogeneous pixels. The DWLS approach applied to satellite observations shows better performance than the OLS method in study regions and exhibits smaller mean fitting residuals both in the red and near-infrared bands. The DWLS approach also shows higher BRDF modeling accuracy than the OLS approach with unmanned aerial vehicle observations. These results indicate that the DWLS inversion approach can be a better choice when kernel-driven models are used for heterogeneous pixels.

Micro-Defect Inspection on Curved Surface Using a 6-DOF Robot Arm with One-Shot BRDF Imaging

The need for automated visual inspection in Japan is increasing due to labor shortages caused by the declining birthrate and aging population. We have developed an imaging system called One-shot BRDF (Bidirectional Reflectance Distribution Function), which can easily detect even micro-defects that are conventionally difficult to capture using parallel-beam illumination and an image sensor. By color-coding the direction of light, micro-defects can be instantly captured as a clear image. This paper proposes a novel micro-defect inspection system capable of automatically inspecting the surface of materials with complex shapes by mounting One-shot BRDF optics on the tip of a 6-degree-of-freedom (DOF) robot arm and scanning the material's surface. The 6-DOF robot arm can track the scanning trajectory and keep the optics squarely against the curved surface at a constant distance. We developed a simple algorithm to automatically determine the trajectory from the material's 3D CAD data so that the entire surface to be scanned can be inspected quickly and within the 6-DOF robot arm's range of movement. For high-speed and high-precision inspection, we built a nonlinear dynamic model of the 6-DOF robot arm and model-based control to track the trajectory while suppressing vibration. In scanning experiments using mirror-finished aluminum with a curved surface, the position and orientation control errors were sufficiently small in high-speed operation at the limit of the robot arm's performance. Several minute scratches on the mirror-finished aluminum could be detected and their locations were mapped as 3D CAD data.

Sun Glint Correction Based on BRDF Model for Improving the HY-1C/COCTS Clear-Sky Coverage

The Haiyang-1C (HY-1C) satellite was launched on September 7, 2018. The Chinese Ocean Color and Temperature Scanner (COCTS) onboard HY-1C has the capacity for ocean color and sea surface temperature (SST) observations. The sun glint reflected on sea surface can interfere with the radiance reaching the field of view of satellite sensor, leading to the higher reflectance that is misclassified as cloud and restrictions of satellite data availability. Due to the lack of ability to avoid sun glint, the bidirectional reflectance distribution function (BRDF) model is implemented in the sun glint correction of HY-1C/COCTS visible images. The atmospheric direct transmittance is calculated by aerosol optical depth (AOD) and Rayleigh optical depth (ROD). The comparisons before and after sun glint correction of visible images at different locations and different time are discussed and analyzed. The spectra are compared before and after the sun glint correction, and it has an obvious decrease in both radiance and reflectance. The performance of the BRDF model in low, moderate, and severe glint contaminations is compared. The results indicate that the BRDF model is useful in the sun glint correction of visible bands and leading to more HY-1C/COCTS clear-sky coverage, as consequence can be applied as the preprocessing in the cloud detection and SST retrieval to improve the clear-sky coverage.

A Practical Approach to Improve the MODIS MCD43A Products in Snow-Covered Areas

The MODerate Resolution Imaging Spectroradiometer (MODIS) MCD43A products have been extensively applied in the remote sensing field, but recent researchers have demonstrated that these products still had the potential to be further improved by using the latest development of the kernel-driven model [RossThick-LiSparseReciprocal-Snow (RTLSRS)] in snow-covered areas, since the MCD43A product algorithm [RossThick-LiSparseReciprocal (RTLSR)] needed to be improved for the accurate simulation of snow bidirectional reflectance distribution function (BRDF) signatures. In this paper, we proposed a practical approach to improve the MCD43A products, which used the Polarization and Directionality of the Earth's Reflectance (POLDER) observations and random forest algorithm to establish the relationship between the BRDF parameters (MCD43A1) estimated by the RTLSR and RTLSRS models. We applied this relationship to correct the MCD43A1 product and retrieve the corresponding albedo (MCD43A3) and nadir reflectance (MCD43A4). The results obtained highlight several aspects: (a) The proposed approach can perform well in correcting BRDF parameters [root mean square error (RMSE) = ~0.04]. (b) The corrected BRDF parameters were then used to retrieve snow albedo, which matched up quite well with the results of the RTLSRS model. (c) Finally, the snow albedo retrieved by the proposed approach was assessed using ground-based albedo observations. Results indicated that the retrieved snow albedo showed a higher accuracy as compared to the station measurements (RMSE = 0.055, bias = 0.005), which was better than the results of the MODIS albedo product (RMSE = 0.064, bias = −0.018), especially at large angles. These results demonstrated that this proposed approach presented the potential to further improve the MCD43A products in snow-covered areas.

Optimizing the Protocol of Near-Surface Remote Sensing Experiments Over Heterogeneous Canopy Using DART Simulated Images

Optical canopy models that connect land surface properties and satellite-observed radiance must be validated before being used. These models include the bidirectional reflectance distribution function (BRDF) models in the visible and near-infrared domains, and directional brightness temperature (DBT) models in the thermal infrared domain. Near-surface experiments have been extensively conducted to evaluate the modeling accuracy, including ground-, tower-, and aircraft-based measurements. Indeed, it should be noted that in situ measured BRDF/DBT results are sensitive to the experiment protocol, such as sensor moving orientation, flight height, and sampling frequency. A practical tool for optimizing the in situ measurement protocols is needed in the community of remote sensing modeling. For that, we devised a virtual experiment framework based on the discrete anisotropic radiative transfer (DART) 3-D radiative transfer model that is capable of simultaneously simulating both the BRDF/DBT pattern and the images acquired by in situ cameras. Here, as an optimization case, we use it to determine the optimal sensor flight orientation over heterogeneous vegetated canopies (a row-planted scene with three solar angles and a discrete scene with three solar angles) for measuring their DBT distribution. Results showed considerable errors (i.e., image-extracted DBT minus DART-simulated DBT) exist for sensor flight orientation along the canopy rows ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R^{2}$ </tex-math></inline-formula> = 0.24 and root mean square error (RMSE) = 4.32 K), and they become much smaller ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R^{2}$ </tex-math></inline-formula> = 0.94 ~ 0.98 and RMSE = 0.82 ~ 1.03 K) in other typical orientations (e.g., cross row plane, solar principal plane, and cross solar principal plane). The critical azimuth offset relative to the row direction that can ensure an acceptable RMSE < 1 K is quantified as atan(3*Unitwidth/Scenesize) based on a series of intensive simulations by this new tool. However, the RMSE of the discrete scene is not sensitive to the flight orientation. Such accuracy differences in various protocols were experimentally verified over row-planted maize using a 4-D tower in Huailai, Hebei, China. The result highlights the great potential of this newly designed DART-based virtual experiment to optimize near-surface experiment protocols.