Wind dependence of quasi-specular microwave sea scatter
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Wind Dependence of QuasiSpecular Microwave Sea Scatter
DONALD E. BARRICK
Abstract-It is shown that a specular-point scattering model adequately predicts the relation between the average quasi-specular microwave scattering cross section of the sea and the mean wind speed. The mean-square sea slope required in this model varies with both the upper and lower ends of the waveheight spectrum, of wind speed. Optical measurewhich in themselves are functions ments of slopes confirm this physical relationship. Finally, the resultant scattering cross section predicted by the slope-dependent specular-point model is compared with a set of recent measurements, lending credence to the model and interpretation suggested here.
The latter two processes involve stationary phase integrat.ions, where the radar wavenumber ko t,imes the typical roughness height. is assumed large. The last approach is equivalent 6o geometrical optics because t.he stationary phaseintegration over space shows that the total scattering is merely the summation of the individual returns from each specular point. Thus all of these models lead to the following result for backscatter2
UO
[TI, [3].
=
K
see4ep, ( - tan S,0) I R (0)
!2
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where e is t.he angle of incidence from the vertical, E ( 0 ) is the Fresnel reflection coefficient of the surface a t normal incidence, and p , (cz,ru)is the joint probability density function of the surface slopes (= a { / a x ) and l v ( = a{/dy), with ( being the surface height above the mean b y ) plane. It. is assumed t,hat the z z plane is the incident plane. The interpretat.ion of (1) is enlightening: Thestrength of the scat.tered signal is merely proportional tothe probability of the surface having "specular" points, or regions tilted a t slope -tan e so as t.obe normal t.0 the incident ray. For the sea, the model is not valid for e greater than about 15'; beyond this angle, microwave scatter is more diffuse and is describable by the Bragg diffraction model postulated in [ 8 ] . The sea surface slopes are nearly Gaussian and isotropic in t.heir distribution, as shown in [SI, and hence f1) for the sea can be written approximately as
I. ISTRODUCTION
Models relating the near-verticalsea-backsratt.ered microwave signal power to pertinent sea-state descriptors are receiving renewed interest with t.he advent. of orbiting short-pulse radar altimeters.' Many independent measurements of t.he average backscattering cross section per unit sea area U O over 6he past 15 yr have confirmed the angular dependence of u0 near the vertical (e.g.,see Skolnik [l] or Barrick [2] for reviews of such data). The near-vertical angular dependence is explained by the specular-point models [3], assuming a (nearly) Gaussian distribution of surface slopes. There is considerable variance, however, between the magnitudes of U O measured bythe various investigators. In addition, it is not clear from the resu1t.s to date to which of t.he various sea-surface descriptors uo is most. sensitive. It. is t.he purpose of t.his note to call attention to an extensive well-calibrated set of measurements of u0 [4] and tosuggest a physically meaningful relationship between u0 and surface wind speed via t,he surface slope used in the specularpoint. model. A comprehensive set of measurements of uo by Rayt.heon in the Atlantic was reported in [4]: these aircraft measurements were made a t 9.0 GHz with ground-truth data takensimult.aneously aboard a IiAS-4 ship beneath the aircraft. During December 1969 andJanuary 1970 sixteen test flights were made, thedata from ten of which aere considered of adequate quality to be st.atistically reduced and presented. The data of interest here consist of averages of U O in the vert.ica1 direction. Each flight typically resulted in incoherent averages over as many as 60 frames of data; each frame, recorded once per second, represented about 50 individually received, square-law-detected pulses averaged over t.he frame (typical travel distance per frame is -300 f t ) . Most. of the flights. were flown a t 10 000 ft with a 2C-m pulse. Radar sensit.ivity was calibrated and later rhecked dynamically by flying over ground support equipment that. recorded and transponded the signal back a t known power levels. The overallrnlssystem error w-as estimated to be 0.9 dB. I<aytheon attempted to correlate uo with the various wind and sea desrriptors available from the NASA support ship. They found little or no correlat.ion between uo (at, vertical incidence) and wave height, wave period, or wave direction. Howcver, there did appear to be a definite trend betR-een uo and (surfate) wind speed;this is shown in Fig. 1 , where the number beside the dot refers to the flight number. A mathematical model that. predicts t.he observed relationship b e b e e n wind speed and u0 will be developed.