972 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 38, NO. 2, MARCH 2000 Cloud Shadow Detection Under Arbitrary Viewing and Illumination Conditions James J. Simpson, Zhonghai Jin, and James R. Stitt, Member, IEEE Abstract—Relatively little work on cloud shadow detection has been published and many of these papers deal with restricted ge- ometries. Here, arbitrary viewing and illumination conditions are considered. A means is provided to extend more restricted treat- ments of cloud shadow detection and removal to the general case. Index Terms—Clouds, cloud height, cloud shadow. I. INTRODUCTION A CCURATE detection of cloud shadow in satellite data is important for improved prediction and simulation of mesoscale atmospheric circulations ([1], [2]) and for accu- rately estimating continental biomass ([3], [4]). An accurate, automated method for detecting and removing cloud shadow in Advanced Very High Resolution Radiometer (AVHRR) data, which works well under restricted viewing and illumination conditions, was developed in [4]. This note extends their work to arbitrary geometries. II. CLOUD SHADOW DETECTION—THE GENERAL CASE Cloud shadow results from the projection of cloud structure on the local plane of the earth with respect to a direction of in- coming solar radiation. For a flat earth approximation ([4]–[6]), the length of the cloud shadow is given in terms of the solar zenith angle and the cloud height by (1) Cloud shadow is minimal at local solar noon because the sun is highest in the sky for a nadir viewing satellite and large near either sunrise or sunset because tan is large at these times. The positions of the satellite and sun, relative to the position of the cloud, determine the amount of cloud shadow observed (Fig. 1). For nadir viewing (see below), the satellite observes the actual cloud shadow length given by (1). Under more gen- eral conditions, the satellite observes an apparent cloud shadow length . The relevant geometry for the forward edge of the cloud (Fig. 1) yields (2) Manuscript received August 21, 1998; revised May 12, 1999. This work was supported in part by NASA, Washington, DC. The authors are with the Digital Image Analysis Laboratory, Univer- sity of California, San Diego, La Jolla, CA 92093-0237 USA (e-mail: jsimpson@ucsd.edu). Publisher Item Identifier S 0196-2892(00)02473-6. Fig. 1. Sun-cloud satellite geometry (leading cloud edge, point A) for arbitrary viewing and illumination conditions. and are the actual cloud height and cloud shadow length. is the apparent cloud shadow length. with the satellite zenith angle and the relative azimuth angle. is related to apparent cloud height (3) Define , the difference between the apparent and actual cloud shadow lengths, as , and the corre- sponding cloud height difference . Then, the ratio of the error in apparent cloud shadow length (either lengthening or foreshortening) to the actual cloud shadow length becomes (4) Equation (4) applies to arbitrary viewing and illumination con- ditions. If we examine (4) in the principal ( ) plane of Fig. 1 and impose the condition that the satellite and sun are on opposite sides of the nadir line ( ), then (4) becomes (5) 0196–2892/00$10.00 © 2000 IEEE