are the solar zenith, view zenith and relative azimuth angles, respectively;
f1 and f2 are the geometric and volume scattering
functions, respectively; and k0, k1 and k2 are the function weights
(model parameters).
If these techniques are applied across entire AVHRR subscenes the improvement is no less striking, whether BRDF adjustment of the original 21 orbits of reflectance values or forward-modelling to a new single scene is used. BRDF correction techniques are currently being applied in only a few programmes using AVHRR, the most notable being CNRM-Meteo France, which has produced a new BRDF-corrected 2km vegetation map of Europe from AVHRR; the CSIRO Earth Observation Centre in Australia; and the Canadian Center for Remote Sensing, which was one of the first institutions to take BRDF anomalies in AVHRR seriously by implementing corrections based on the Roujean and Walthall models.
1. BRDF Models. Although physical BRDF models had existed for some time prior to 1992 they were mostly complicated and cumbersome to use and often attempted to extract more information than is practically possible with the sparse and limited angular sampling afforded by current satellite sensors. These models largely remain research tools and have a valuable role to play as such; they may become more feasible at some time in the future with increases in computing power and the launch of new multidirectional sensors.
The only model capable of operational use prior to 1992 was the 1984 Walthall model, an entirely empirical BRDF model based on a set of polynomials. However, since no physical meaning could be ascribed to the parameters retrieved, it was not widely adopted (but see this example of the Walthall model used for BRDF correction of AVHRR).
In 1992 a new type of BRDF model for vegetated surfaces appeared which was at once simple and operationally feasible and at the same time based on the (vastly simplified) physics of geometrical optics and radiative transfer : the Roujean model (Roujean et al, 1992a). This is called a linear semiempirical BRDF model, since it combines the simplicity and ease of inversion of an empirical linear model such as Walthall while retaining some physical meaning in its parameters. The model is formulated so that bidirectional reflectance is a linear combination of three terms weighted by three parameters :
where R is modelled bidirectional reflectance;
are the solar zenith, view zenith and relative azimuth angles, respectively;
f1 and f2 are the geometric and volume scattering
functions, respectively; and k0, k1 and k2 are the function weights
(model parameters).
More information on this type of model is available on Wolfgang Lucht's website, here. This type of model is also called a linear semiempirical kernel-driven model, since new variants based on the same formulation have appeared but using different functions ("kernels") to account for geometric surface and volume scattering. I use the contraction "LiSK" for Linear Semiempirical Kernel-driven, since "Linear Semiempirical Kernel-driven" is a tad unwieldy! The kernels may also be used in an interchangeable manner so that the most appropriate set is used in particular circumstances; this is the approach adopted by the team working on the MODIS BRDF/Albedo product; see also the MODIS website.
2. Sampling the BRDF. Sampling surface BRDF with the AVHRR is hampered by three important factors. First, there is no onboard calibration for channels 1 and 2 allowing consistent calculation of spectral radiance at TOA. This is a problem because the 10-bit sensor outputs are known to degrade postlaunch as a result of outgassing and the harsh space environment. This impacts on comparative use of data from one sensor over long periods and on the use of data from more than one AVHRR simultaneously; however, much work has been done using quasi-static earth surface targets (deserts and ice caps) as stable calibration references and formulae are now available which take postlaunch degradation into account (Rao & Chen, 1993, 1996; Loeb, 1997); see also the NOAASIS Satellite Sensor Calibration site. Second, the presence of clouds and cloud shadow reduces the number of valid surface observations available and restricts the angular sampling. Contamination must be removed through screening, which may make use of the AVHRR thermal IR channels in the detection of clouds (as in the Clouds from AVHRR or CLAVR algorithm), although the success in obtaining an adequate sample depends to some extent on latitude; there are areas in the tropics where cloud is a perennial problem. Less work has been done on detection of the shadows cast by clouds, an important problem in morning satellite scenes since the sun is low in the sky and so clouds do not tend to hide their own shadows; see this series of contaminated observations. Third, the atmosphere has its own BRDF which tends to dampen the anisotropy in surface BRDF (Rahman, 1996), although the unwanted variations in the satellite signal resulting from surface BRDF are often more important than atmospheric effects, including changing path length with scan angle (Roujean et al, 1992b).