The BRDF (Bidirectional Reflectance Distribution Function) describes the angular distribution of outgoing radiation over the upper hemisphere relative to incoming radiation (irradiance). It is a dimensionless quantity (i.e. reflectance, a ratio) and cannot be measured directly (it is defined for all angles) and must be estimated from bidirectional reflectance samples. All land surfaces exhibit some degree of anisotropy in bidirectional spectral reflectance; that is, they exhibit non-Lambertian reflectance properties and incoming radiation is scattered unequally in terms of outgoing direction. This phenomenon is also wavelength dependent; light is scattered and absorbed differently in different regions of the solar spectrum as a result of the different types of interactions with surface materials (plant leaves, tree trunks, soil, concrete...) and this affects the angular distribution of outgoing radiation. The problem is illustrated in this simplified diagram.
Note that BRDF is dynamic in space and time; it varies with land cover type and also with changes owing to : growth and senescence of vegetation, soil moisture content, windblown sand, snow cover, ploughing, logging, harvesting, flooding, appearance of lake beds on dehydration, strong winds flattening erectophile canopies ....and anything else you can think of which changes the optical and/or physical characteristics of a surface.
For great examples of BRDF effects, explanations and further BRDF-related links, see
Wolfgang Lucht's site at Center for Remote Sensing at Boston University
Lewis' site at University College London
Zoltan Hesley's site at the University of Wales at Swansea
Stefan Sandmeier's site at the Remote Sensing Laboratory at the University of Zurich (links well worth following!)
Don Deering's PARABOLA pages and the
Reflectance Phenomenology and Modeling Tutorial at ERIM.
My pet example of surface BRDF is the effect you get when brushing a piece of velvet one way and then the other; its the same material but it can appear alternately light and dark. Think of the everyday experience of seeing a field of wheat on a windy day; the "ripples" in the field are caused by changing shadowing effects as the canopy moves; or look carefully at your favourite houseplant (the one with shiny leaves) under bright sunshine - are the leaves all green, or is there some shiny white stuff in there too? This is owing to specular reflection, where energy in a broad range of wavelengths is scattered directly with little interaction with the leaves.
The BRDF has a major impact on the spectral radiance received at a satellite sensor viewing off-nadir. As a result, calculating surface reflectance values as a function of solar irradiance and atmospheric composition via an atmospheric correction procedure yields values which still retain a significant dependency on the anisotropy of the surface (as well as that of the atmosphere). Moreover, the solar zenith angle can change significantly across the scanline; more than 20 degrees in the case of the AVHRR sensor on NOAA satellites. If reflectance is calculated for scenes acquired from different orbits, the change in viewing and illumination geometry (zeniths and azimuths) introduces unwanted variation in the satellite signal; mosaicking together scenes acquired at different times results in an image in which the join between the two is usually very obvious (see the images at the Canadian Center for Remote Sensing).