A modified version of the kernel-driven model for correcting the diffuse light of ground multi-angular measurements

A visualization tool for the kernel-driven model with improved ability in data analysis and kernel assessment

Previous work has successfully demonstrated the application of a priori knowledge to bidirectional reflectance distribution function (BRDF) model inversion. The a priori knowledge used in the tests is the general knowledge which can be applied to all land cover types. One of the advantages of general knowledge is that it can be applied independently and doesn't need more information. However, the inversion accuracy may be low, compared to results using correct specific knowledge. This paper mainly focuses on the accumulation of a priori knowledge for the linear BRDF model in both general and specific realms. The authors first provide some specific knowledge based on ground and spaceborne BRDF measurements for BRDF model parameters.

Because of the anisotropy of snow surface reflectance, it is essential to select a proper snow bidirectional reflectance model for extracting snow cover and inverting snow properties from remote sensing image, especially during the period of snow rapidly changed. In this letter, the ability of reproducing snow bidirectional reflectance by three semiempirical bidirectional reflectance distribution function (BRDF) models (Ross–Li, Roujean, and Raman–Pinty–Verstraete) and the asymptotic radiative transfer theory (ART) model was evaluated using the polarization and directionality of the earth reflectance (POLDER) data. In addition, the ART model was compared with the bicontinuous geometric optics (bic-GORT) model based on field measurements. The results indicated that the root mean square errors (RMSEs) are small and similar for all models during the stable-snow period. The physical models perform better than the semiempirical models in capturing the bidirectional signatures of snow during the periods of snow rapidly changed. The bic-GORT model achieves higher accuracy, while the ART model holds the advantages of simple and efficient to be used.

An optimized Back-Propagation network (BP network) based on Genetic Algorithm (GA) was introduced to construct bidirectional reflectance distribution function (BRDF) model. To verify the performance of GA-BP network, two different kinds of space target materials were used for experiment. Based on the experimental data, we used GA to simulate the undetermined parameters of a five-parameter BRDF model, and used GA-BP network and BP network to construct a new BRDF model respectively. The fitting results manifest that the GA-BP network is suitable for construct a new BRDF model and outperforms the five-parameter BRDF model in speed and accuracy under the same condition.

Multi-angle remote sensing observations play an important role in the remote sensing of solar radiation absorbed by land surfaces. Currently, the Moderate Resolution Imaging Spectroradiometer (MODIS) and Visible Infrared Imaging Radiometer Suite (VIIRS) teams have successively applied the Ross–Li kernel-driven bidirectional reflectance distribution function (BRDF) model to integrate multi-angle observations to produce long time series BRDF model parameter products (MCD43 and VNP43), which can be used for the inversion of various surface parameters and the angle correction of remote sensing data. Even though the MODIS and VIIRS BRDF products originate from sensors and algorithms with similar designs, the consistency between BRDF parameters for different sensors is still unknown, and this likely affects the consistency and accuracy of various downstream parameter inversions. In this study, we applied BRDF model parameter time-series data from the overlapping period of the MODIS and VIIRS services to systematically analyze the temporal and spatial differences between the BRDF parameters and derived indices of the two sensors from the site scale to the region scale in the red band and NIR band, respectively. Then, we analyzed the sensitivity of the BRDF parameters to variations in Normalized Difference Hotspot–Darkspot (NDHD) and examined the spatiotemporal distribution of zero-valued pixels in the BRDF parameter products generated by the constraint method in the Ross–Li model from both sensors, assessing their potential impact on NDHD derivation. The results confirm that among the three BRDF parameters, the isotropic scattering parameters of MODIS and VIIRS are more consistent, whereas the volumetric and geometric-optical scattering parameters are more sensitive and variable; this performance is more pronounced in the red band. The indices derived from the MODIS and VIIRS BRDF parameters were compared, revealing increasing discrepancies between the albedo and typical directional reflectance and the NDHD. The isotropic scattering parameter and the volumetric scattering parameter show responses that are very sensitive to increases in the equal interval of the NDHD, indicating that the differences between the MODIS and VIIRS products may strongly influence the consistency of NDHD estimation. In addition, both MODIS and VIIRS have a large proportion of zero-valued pixels (volumetric and geometric-optical parameter layers), whereas the spatiotemporal distribution of zero-valued pixels in VIIRS is more widespread. While the zero-valued pixels have a minor influence on reflectance and albedo estimation, such pixels should be considered with attention to the estimation accuracy of the vegetation angular index, which relies heavily on anisotropic characteristics, e.g., the NDHD. This study reveals the need in optimizing the Clumping Index (CI)-NDHD algorithm to produce VIIRS CI product and highlights the importance of considering BRDF product quality flags for users in their specific applications. The method used in this study also helps improve the theoretical framework for cross-sensor product consistency assessment and clarify the uncertainty in high-precision ecological monitoring and various remote sensing applications.

Anisotropic canopy reflectance plays a crucial role in estimating vegetation biophysical parameters, whereas soil reflectance anisotropy affects canopy reflectance. However, woodland canopy bidirectional reflectance distribution function (BRDF) models considering soil anisotropy are far from universal, especially for the BRDF models of mountain forest. In this study, a mountain forest canopy model, named geometric-optical and mutual shadowing and scattering from arbitrarily inclined-leaves model coupled with topography (GOSAILT), was extended to consider the soil anisotropic reflectance characteristics by introducing the simple soil directional (SSD) reflectance model. The modified GOSAILT model (named GOSAILT-SSD) was evaluated using unmanned aerial vehicle (UAV) field observations and discrete anisotropic radiative transfer (DART) simulations. Then, the effects of Lambertian soil assumption on simulating the vi-directional reflectance factor (BRF) were evaluated across different fractions of vegetation cover (Cv), view zenith angles (VZA), solar zenith angles (SZA), and spectral bands with the GOSAILT-SSD model. The evaluation results, with the DART simulations, show that the performance of the GOSAILT-SSD model in simulating canopy BRF is significantly improved, with decreasing RMSE, from 0.027 to 0.017 for the red band and 0.051 to 0.037 for the near-infrared (NIR) band. Meanwhile, the GOSAILT-SSD simulations show high consistency with UAV multi-angular observations (R2 = 0.97). Besides, it is also found that the BRF simulation errors caused by Lambertian soil assumption are too large to be neglected, with a maximum relative bias of about 45% for the red band. This inappropriate assumption results in a remarkable BRF underestimation near the hot spot direction and an obvious BRF overestimation for large VZA in the solar principal plane (PP). Meanwhile, this simulation bias decreases with the increase of fraction of vegetation cover. This study provides an effective technique to improve the capability of the mountain forest canopy BRDF model by considering the soil anisotropic characteristics for advancing the modeling of radiative transfer (RT) processes over rugged terrain.

This paper describes the motivation and an approach for deriving a time series of albedo maps of Australia from historical Advanced Very High Resolution Radiometer (AVHRR) data. Polarization and Directionality of the Earth’s Reflectances (POLDER) measurements will be used to test the angular correction algorithm. Some initial results from a survey of POLDER directional reflectance signatures of Australian land cover are presented. Those results show that, while there is much correspondence between the spatial patterns of directional signatures and land cover types, there is a large spread of signatures within each land cover type. However, the similarity of two of the kernels of the bidirectional reflectance distribution function (BRDF) model used to parameterise the directional signatures can produce spurious variations in the model parameters. Finally, some field measurements of grassland albedo are used to make the point that for the greatest accuracy in the estimation of land surface albedo from satellites, it is necessary to account for the detailed shape of the diurnal variation and the effect of the cloudiness on albedo.KeywordsLand Cover TypeAdvance Very High Resolution RadiometerAdvance Very High Resolution RadiometerSolar Zenith AngleDirectional SignatureThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The accuracy of hotspot signatures is crucial to the development of algorithms for the retrieval of various biophysical parameters of terrestrial surface targets. The hotspot effect determined by the kernel-driven RossThick-LiSparseReciprocal (RTLSR) Bidirectional Reflectance Distribution Function (BRDF) model fully relies on the performance of the two kernels in modeling the hotspot effect. Previously, a method has been developed to correct the volumetric scattering component of the RTLSR model (Jiao et al., 2016); however, in few cases that the weight of the volumetric scattering component (f vol ) is no longer significant (e.g., f vol = 0) in the framework of the RTLSR model, the slight underestimation of the hotspot effect still exists. In this study, we propose a method to enhance the overlap function inherent in the geometric-optical (GO) kernel using a physical hotspot factor. The hotspot observations extracted from the entire archive of the POLDER-3 BRDF database are used to determine two parameters of this hotspot factor. Result shows that the proposed method further improves the model-observation fits in the vicinity of hotspot direction, particularly in some extreme cases where the GO scattering component is fully dominant in the multiangle measurements. Such an improved GO kernel, combining with the hotspot adjustment method for the volumetric scattering kernel, reconstructs hotspot effect more accurately; therefore, necessarily further improves the performance of the kernel-driven BRDF model particularly for the retrieval of the canopy structure parameters that is associated with the hotspot effect.

The commonly used analytic bidirectional reflectance distribution functions (BRDFs) do not model goniochromatism, that is, angle-dependent material color. The material color is usually defined by a diffuse reflectance spectrum or RGB vector and a specular part based on a spectral complex index of refraction. Extension of the commonly used BRDFs based on wave theory can help model goniochromatism, but this comes at the cost of significant added model complexity. We measured the goniochromatism of structual color pigments used for additive color printing and found that we can fit the observed spectral angular dependence of the bidirectional reflectance using a simple modification of the standard microfacet BRDF model. All we need to describe the goniochromatism is an empirically-based spectral parameter, which we use in our model together with a specular reflectance spectrum instead of the spectral complex index of refraction. We demonstrate the ability of our model to fit the measured reflectance of red, green, and blue commercial structural color pigments. Our BRDF model enables straightforward implementation of a shader for interactive preview of 3D objects with printed spatially and angularly varying texture.

This paper proposes a three-component bidirectional reflectance distribution function (3C BRDF) model consisting of diffuse, quasi-specular, and glossy components for calculation of effective emissivities of blackbody cavities and then investigates the properties of the new reflection model. The particle swarm optimization method is applied for fitting a 3C BRDF model to measured BRDFs. The model is incorporated into the Monte Carlo ray-tracing algorithm for isothermal cavities. Finally, the paper compares the results obtained using the 3C model and the conventional specular-diffuse model of reflection.

Abstract. The surface reflection of solar radiation comprises an important boundary condition for solar radiative transfer simulations. In polar regions above snow surfaces, the surface reflection is particularly anisotropic due to low Sun elevations and the highly anisotropic scattering phase function of the snow crystals. The characterization of this surface reflection anisotropy is essential for satellite remote sensing over both the Arctic and Antarctica. To quantify the angular snow reflection properties, the hemispherical-directional reflectance factor (HDRF) of snow surfaces was derived from airborne measurements in Antarctica during austral summer in 2013/14. For this purpose, a digital 180∘ fish-eye camera (green channel, 490–585 nm wavelength band) was used. The HDRF was measured for different surface roughness conditions, optical-equivalent snow grain sizes, and solar zenith angles. The airborne observations covered an area of around 1000 km × 1000 km in the vicinity of Kohnen Station (75∘0′ S, 0∘4′ E) at the outer part of the East Antarctic Plateau. The observations include regions with higher (coastal areas) and lower (inner Antarctica) precipitation amounts and frequencies. The digital camera provided upward, angular-dependent radiance measurements from the lower hemisphere. The comparison of the measured HDRF derived for smooth and rough snow surfaces (sastrugi) showed significant differences, which are superimposed on the diurnal cycle. By inverting a semi-empirical kernel-driven bidirectional reflectance distribution function (BRDF) model, the measured HDRF of snow surfaces was parameterized as a function of solar zenith angle, surface roughness, and optical-equivalent snow grain size. This allows a direct comparison of the HDRF measurements with the BRDF derived from the Moderate Resolution Imaging Spectroradiometer (MODIS) satellite product MCD43. For the analyzed cases, MODIS observations (545–565 nm wavelength band) generally underestimated the anisotropy of the surface reflection. The largest deviations were found for the volumetric model weight fvol (average underestimation by a factor of 10). These deviations are likely linked to short-term changes in snow properties.

In this paper, we compare reflectance and polarization measurements from two different satellite instruments, namely, the imager Polarization and Directionality of the Earth's Reflectances (POLDER) and the spectrometer Scanning Imaging Absorption Spectrometer for Atmospheric Chartography (SCIAMACHY). Both instruments are able to measure not only the Earth reflectance but also the state of linear polarization of the detected light. The aim of this paper is to validate the SCIAMACHY reflectance and polarization data using the fact that POLDER is well calibrated. This validation requires a careful search for suitable, collocated data having identical solar and viewing angles. For the reflectance, there is a disagreement between POLDER and SCIAMACHY of up to 20% in the wavelength interval 400–1000 nm, which we attribute to SCIAMACHY. As for the linear polarization, we present for the first time clear evidence for the existence of discrepancies in the SCIAMACHY polarization retrieval for polarization measurement devices 2, 3, and 4.

Observing system simulations for small satellite formations estimating bidirectional reflectance

This paper presents a novel sparse non-parametric Bidirectional Reflectance Distribution Function (BRDF) model derived using a machine learning approach to represent the space of possible BRDFs using a set of multidimensional sub-spaces, or dictionaries. By training the dictionaries under a sparsity constraint, the model guarantees high-quality representations with minimal storage requirements and an inherent clustering of the BDRF-space. The model can be trained once and then reused to represent a wide variety of measured BRDFs. Moreover, the proposed method is flexible to incorporate new unobserved data sets, parameterizations, and transformations. In addition, we show that any two, or more, BRDFs can be smoothly interpolated in the coefficient space of the model rather than the significantly higher-dimensional BRDF space. The proposed sparse BRDF model is evaluated using the MERL, DTU, and RGL-EPFL BRDF databases. Experimental results show that the proposed approach results in about 9.75dB higher signal-to-noise ratio on average for rendered images as compared to current state-of-the-art models.

Rugged terrain, including mountains, hills, and some high lands are typical land surfaces around the world. As a physical parameter for characterizing the anisotropic reflectance of the land surface, the importance of the bidirectional reflectance distribution function (BRDF) has been gradually recognized in the remote sensing community, and great efforts have been dedicated to build BRDF models over various terrain types. However, on rugged terrain, the topography intensely affects the shape and magnitude of the BRDF and creates challenges in modeling the BRDF. In this paper, after a brief introduction of the theoretical background of the BRDF over rugged terrain, the status of estimating land surface BRDF properties over rugged terrain is comprehensively reviewed from a historical perspective and summarized in two categories: BRDFs describing solo slopes and those describing composite slopes. The discussion focuses on land surface reflectance retrieval over mountainous areas, the difference in solo slope and composite slope BRDF models, and suggested future research to improve the accuracy of BRDFs derived with remote sensing satellites.