The bidirectional reflectance distribution function (BRDF) is the intr
insic measure of the directional properties of the Earth's surface. Ho
wever, it cannot be measured directly by remote sensing. A procedure u
sing the optimum technique is applied to retrieve surface BRDF paramet
ers from multiangle remotely sensed data in which a statistical BRDF m
odel and an analytical model of atmospheric radiative transfer are cou
pled. The atmospheric model decomposes radiant intensity received by a
detector into four parts: scattered only by the (non-Lambertian) surf
ace; singly scattered by the atmosphere; multiply scattered to the sur
face but unscattered to the detector; and multiply scattered before an
d after surface scattering. Analytical solutions are derived for the f
irst two. The third is derived from a two-stream model, but incorporat
es the surface BRDF explicitly. The fourth uses a two-stream model und
er conditions of azimuthal independence. The six-parameter surface BRD
F is modeled as the sum of a modified limacon function, which describe
s the basic bowl-shape of the BRDF, and a negative exponential, which
describes the hotspot. Multiangle observations from the ASAS and PARAB
OLA instruments are analyzed using the coupled models. Experiments sho
w that the simple statistical BRDF can summarize typical directional o
bservations with errors in the range of 3-10 %.