Proceedings of the International Geoscience and Remote Sensing Symposium IGARSS 2000, 24-28 July 2000, Honolulu,Hawaii, USA, ed. Tammy I. Stein, IEEE Cat. No. 00CH37120, ISBN 0-7803-6359-0, IEEE, Piscataway, NJ, USA, 2000.

0-7803-6359-0/00/$10.00 2000 IEEEE1863

Fresnel reflection by wavy sea surface

Vladimir I. Haltrin, Walton E. McBride III, and Alan D. Weidemann,

Naval Research Laboratory, Ocean Sciences Branch, Code 7333Stennis Space Center, MS 39529-5004, USA. e-mail:

Planning Systems Inc., 115 Christian Lane, Slidell, LA 70458, USAAbstract In studying light and image transfer in seawaters, the influence of Fresnel surface reflection is assignificant as scattering and absorption phenomena. In thesecases knowledge of the reflective properties of sea surface atdifferent wind speeds is very important. At present, little ispublished about these properties. We present here results ofnumerical modeling of angular reflection coefficients of seawater as a function of zenith angle of illumination and windspeed.

INTRODUCTION

The ray-tracing computer model was developed andimplemented as slopes and elevations. The model used thePierson-Moskowitz (PM) [1] and Paul Hwang (PH) [2] waveheight spectrums in order to generate a realistic sea surface{see Fig. 1 and Eqs. (1) and (2)}. The Fresnel reflectioncoefficients were averaged over 10000 pixels of sea surfaceareas and 80 time realizations to produce resulting angulardistributions of Fresnel reflection coefficient.

The Pierson-Moskowitz [1] wave energy spectrum is

Figure 1. Comparison of Pierson-Moskowitz and PaulHwang spectrums at windspeed of 4 m/s.

defined as:

PM k kg

u k( )

.exp

.=

0 00405 0 743

2

4 2 (1)

here g m s= 9 8. / is a gravitational acceleration, u is awindspeed in m s/ , k g u= / is a wavenumber in m1 .

The Paul Hwang [2] wave energy spectrum is defined as:

PH k k

k g u

u k g u k

u k k

u g k k

u k k

( )

. , ,

. , . ,

. , . . , ( )

. . , ,

. , .

=