Kernel-based Bidirectional Reflectance Distribution Function Research Articles

Derivation of Kernel Functions for Kernel-Driven Reflectance Model Over Sloping Terrain

The importance of the bidirectional reflectance distribution function (BRDF) has been well documented in quantitative remote sensing. The semiempirical, kernel-driven BRDF model is widely used to generate operational BRDF/albedo products due to its simplicity and accuracy. However, the effect of topography is rarely coupled with a kernel-based BRDF model. In this paper, a new kernel-driven reflectance model for sloping terrain (KDST) was developed based on the framework of the RossThick-LiSparse-Reciprocal (RTLSR) model. The slope, aspect, geotropic nature of the tree crown governed by gravity, component spectra contrasts, and diffuse irradiance were considered in the KDST model. The performance of KDST was evaluated by 3-D discrete anisotropic radiative transfer (DART) simulations, in situ measurements, and HJ-1A/B constellation charge-coupled device satellite observations. Using DART simulations, KDST reduces the maximum biases of the RTLSR from 15.6% and 29.7% to 7.1% and 4.8% for the surface bidirectional reflectance factor and hemispherical-direction reflectance factor, respectively. Compared with in situ measurements, KDST improves the reflectance simulation accuracy for the red and near-infrared bands from 0.0172 (18.65%) and 0.022 (4.77%) to 0.0060 (6.51%) and 0.0043 (1.05%), respectively. The preliminary comparison results indicate that KDST is promising for reflectance simulation over rugged terrain.

Superpixel-Based Adaptive Kernel Selection for Angular Effect Normalization of Remote Sensing Images With Kernel Learning

Considering that satellites rarely acquire data from the exact nadir direction, angular effect normalization needs to be conducted as an important preprocessing step to correct reflectance observations from off-nadir directions into the nadir direction. Kernel-based bidirectional reflectance distribution function models have been employed for angular effect correction. The kernels used in the model are often predetermined and fixed for an entire image. However, the fixed kernels are unable to accommodate the various reflective characteristics of different ground cover types present in the imaged area. In this paper, we propose a kernel learning procedure that enables the flexible selection of kernels for different land cover types within a scene. The kernels are selected from kernel dictionaries that contain multiple candidate kernels. The selection is conducted on the superpixel level instead of the pixel level in order to reduce within-class variation and overcome the overfitting problem. Experiments are conducted on multiangular images acquired by the Sentinel-2A satellite over a rural area in southeastern Australia. Cross-validation results show that the proposed method is able to adaptively select appropriate kernels for different land cover types, leading to an improved performance for image normalization.

Regularized kernel-based BRDF model inversion method for ill-posed land surface parameter retrieval

In this paper, we consider the direct solution of the kernel-based bidirectional reflectance distribution function (BRDF) models for the retrieval of land surface albedos. This is an ill-posed problem due to nonuniqueness of the solution and the instability induced by error/noise and small singular values of the linearized system or the linear BRDF model. A robust inversion algorithm is critical for the BRDF/albedo retrieval from the limited number of satellite observations. We propose a promising algorithm for resolving this kind of ill-posed problem encountered in BRDF model inversion using remote sensing data. New techniques for robust estimation of BRDF model parameters are needed to cope with the scarcity of the number of observations. We are reminded by Cornelius Lanczos' dictum: “Lack of information cannot be remedied by mathematical trickery.” Thus identifying a priori information or appropriate constraints, and the embedding of the information or constraints into the regularization algorithm, are pivotal elements of a retrieval algorithm. We develop a regularization method, which is called the numerically truncated singular value decomposition (NTSVD). The method is based on the spectrum of the linear driven kernel, and the a priori information/constraint is based on the minimization of the l 2 norm of the parameters vector. The regularization algorithm is tested using field data as well as satellite data. Numerical experiments with a subset of measurements for each site demonstrate the robustness of the algorithm.

Detecting vegetation structure using a kernel-based BRDF model

The magnitude of the anisotropy of vegetation is mainly determined by its spectral and structural features. It can be described by the bidirectional reflectance distribution function (BRDF). The parameters of physical BRDF models are related to the biophysical structural information. However, for a semiempirical kernel-based BRDF model, the relationship between BRDF parameters and vegetation structure is no longer as clear as with a physical BRDF model. To reveal this relationship, a structural scattering index (SSI) and a relative structural scattering index (RSSI) are derived based on the BRDF parameters in this paper. The investigation of SSI and RSSI show that they have both theoretical and practical meaning and can be used to distinguish different land cover types or to detect structural changes.

Land surface albedo retrieval via kernel-based BRDF modeling: I. Statistical inversion method and model comparison

The land surface albedo is a key parameter influencing the climate near the ground. Therefore, it must be determined with sufficient accuracy. In this paper, a statistical inversion method is presented in support of the application of kernel-based Bi-directional Reflectance Distribution Function (BRDF) models for the calculation of the surface albedo. The method provides the best linear unbiased estimations (BLUE) of the BRDF model coefficients for an arbitrary number of available angular measurements. When the number of measurements exceeds the number of the estimated coefficients, the QR decomposition method is proposed to improve the ill-conditional features of the inversion matrix. In other cases, the singular value decomposition (SVD) method is suggested. The proposed inversion method is innovative in that it provides confidence intervals for each of the BRDF model coefficients with a prescribed significance expressed by a probability level. Five candidate kernel-driven BRDF models were used in the present simulation study: Li–Sparse, Roujean, Li–Sparse–Wanner, Li–Dense and Walthall. A ground-based reflectance measurement data set including 11 surface types forms the background for the inversion experiments. The results show a strong dependence on the solar zenith angle (SZA) and on the land cover type (LCT) for all candidate models. Owing to this, none model could be recommend in a general manner. The Li–Sparse and the Li–Sparse–Wanner models performed the best for the grass and wheat LCT, while the Roujean model appeared as a favorite for the pine and deciduous forests. The implementation of the confidence interval technique shows that the BRDF model coefficients can be retrieved with an uncertainty of 20–30%, and somewhat greater in the case of forest. The measured angular reflectance curves lie, as a rule, within the uncertainty bands related to the 5% significance level (95% probability). The corresponding albedo estimates can be characterized by an absolute uncertainty of 1–2% in the visible band and 5–10% in the near infrared band, or by 10–30% in relative terms. The reflectance measurements at low SZA values are preferable for BRDF model inversion for the grassland and crop, while medium range of SZA seems to provide more information on forest features. For the majority of LCT, the results of BRDF model inversion seem to be less reliable when considering multi-angular measurements for various SZA than for a single SZA.

An Algorithm to Infer Continental-Scale Albedo from AVHRR Data, Land Cover Class, and Field Observations of Typical BRDFs

Abstract A method to derive bottom-of-atmosphere land surface albedos from Advanced Very High Resolution Radiometer (AVHRR) satellite measurements is presented. The algorithm described uses kernel-based bidirectional reflectance distribution function (BRDF) models of land cover but, in contrast to other kernel-based albedo retrievals, assumes a priori knowledge of underlying surface BRDFs, based on a land cover classification and typical field-measured BRDFs for each class in the land cover classification. The BRDF of each land cover is scaled using AVHRR reflectance measurements to take into account within-class variations of albedo, and the resultant scaled BRDF is integrated to retrieve an albedo. An albedo dataset for North America is produced with this scheme from February and July 1995 monthly maximum normalized difference vegetation index value composite images. Spectral-to-broadband albedo conversion is achieved by using spectral albedos to scale a laboratory-measures vegetation spectral reflectan...

An algorithm for the retrieval of albedo from space using semiempirical BRDF models

Spectral albedo may be derived from atmospherically corrected, cloud-cleared multiangular reflectance observations through the inversion of a bidirectional reflectance distribution function (BRDF) model and angular integration. This paper outlines an algorithm suitable for this task that makes use of kernel-based BRDF models. Intrinsic land surface albedos are derived, which may be used to derive actual albedo by taking into account the prevailing distribution of diffuse skylight. Spectral-to-broadband conversion is achieved using band-dependent weighting factors. The validation of a suitable BRDF model, the semiempirical Ross-Li (reciprocal RossThick-LiSparse) model and its performance under conditions of sparse angular sampling and noisy reflectances are discussed, showing that the retrievals obtained are generally reliable. The solar-zenith angle dependence of albedo may be parameterized by a simple polynomial that makes it unnecessary for the user to be familiar with the underlying BRDF model. The algorithm given is that used for the production of a BRDF/albedo standard data product from NASA's EOS-MODIS sensor, for which an at-launch status is provided. Finally, the algorithm is demonstrated on combined AVHRR and GOES observations acquired over New England, from which solar zenith angle-dependent albedo maps with a nominal spatial resolution of 1 km are derived in the visible band. The algorithm presented may be employed to derive albedo from space-based multiangular measurements and also serves as a guide for the use of the MODIS BRDF/albedo product.