Polarimetric Moclelling of Ocean Backscatter and Brightness Temperatures

There has been an increasing interest in the applications of polarimetric microwave ractiotneters for ocean wind remote sensing. Aircraft and spaceborlle radiometers have found a few Kelvins wind direction signals in sea surface brightness temperatures, in addition to their sensitivities on wind speeds. However, it was not clear what physical scattering rnechanistus produced the observed brightness dependence on wind direction. To this end, polarimetric microwave emissions from wind-generated sea surfaces are investigated with a polarimetric two-scale scattering model, which relates the directional wind-wave spectrum to passive microwave signatures of sea surfaces. Theoretical azimuthal modulations are found to agree well with the Jet Propulsion Laboratory (JPL) Wind Radiometer (WINDRAD) observations of all Stokes parameters for a large range of wind speeds. This theoretical interpretation suggests the use of polarimetric brightness temperatures for retrieving the directional wave spectrum of short gravity and capillary waves. The polarimetric backscattering coefficients of sea surfaces are also explored using this scattering model with results in reasonable agreement with airborlm ancl satellite scatterometer measurements and the symmetric relations expected for reflection-symmetric surfaces. I. I N T R O D U C T I O N ‘There has been an increasing i[lterest irl the applicatiolL of polarimetric microwave radiometers for ocean wind velocity (speed and direction) measure[nmlts. Early experime[ltal results, such as those published in [1, 2], have shown the correlation of sea surface brightness tetnperatures with the near surface wind speed. Theoretical investigations by [3, 4] have deterlni~led that a t~vc)-scale scattering model could interpret reasonably well the ~vi[ld speed se[lsitivity of vertically and horizontally polarized b r i g h t n e s s te~uperatures (7; and Ii). In addition to wind speed sensitivity, microwave sea surface radiation has been shown by recent aircraft and spacecraft radiolllcter observations to have a few Kelvin directional sig[~als [5, 6, 7, 8, 9]. A re-exanlillatiotl of theoretical scattering models is therefore required to shed light on the ~)hysics behind the otmrved wind directio[i sig[mtures. Ocea[l wind rougheus surfaces ill the forln of gravity and ca~)illa[-y waves, brcakiug waves alltl foaul. Tile scatterirlg effects of large-scale wraves lMVC bm’[i Inodele(l t]y ttlc geo[n(’tcic o~)tics (G()) scatteri[lg theory [10, 1 1]. 111 GO Illod(!ls, the large-scale waves are modeled by tiltirlg surface facets, atld the scattering coef[icieuts are proportional to the llulubc’r of surface facets with a tiltillg angle satisfying the specular reflection conclitiotl. Stogryll [10] used Cox and Munk’s slope distribution of sea surfaces [12] and studied the se[lsitivity of brightness teml)eratures to wind speed. However, Hollinger’s tower measurelncnts [1] performed at 1, 8 and 19 GHz showed that the GO model failed to account for the observational frequency deperldence and significantly underestimated the wind speed depe[ldence of the horizontally polarized radiation at small incidence angles. With the Bragg scattering mechanism taken into consideration, the two-scale scattering theory [13] was exte[lded by Wu and Fung [3] and Wentz [4] to interpret the brightrless temperatures of sea surfaces. In tk two-scale scattering model, the Bragg scattering by s[nall-scale waves contributes to bistatic incoherent scatteri[lg and modifies the coherent reflection coefficients of large-scale waves. As cortlpared with the geometric optics moclel, the two-scale theory more accurately modeled the dependence of brigbtlless telnperatures on incidence a~lgles and wind velocities [3, 4]. IIo\vevcr, the co~ltributions of short and long waves to the wind direction signals i~l passive microwave radionletet measuremc[lts [5, 6, 7, 8, 9] have not yet been thoroughly ixlvestigatcd. In Jt’u and Fu~lg’s [3] and Wentz’s [4] models, the surface spectrum of short lvaves \vas assutned to be isotropic and the Bragg scattering theory for isotropic surfaces was used. Conseque~ltly, no directional clepcndcnce was predicted by their theoretical models. 1[1 co[ltrast, Stogryll’s GO II1OC1C1 using Cox and Munk’s slope distribution, althougll il[ poor agreement wit~l the wind speed smlsitivity of sea surface brigtltness te[llperatures, did predict an azimuthal brigtltllcss ~’ariatiou of a few Kcl\’ins. The efFects of Ilra,gg scatteri~lg by anisotropic short-gravity and capillary w’aves on all Stokes parameters [15] \vere not studied u[ltll recently [16] a~ld tile t,tleoretical rrsults a~)pearcd to agree with the measurenletlts made at Ilear normal i~lciderlce allgles [6]. Additiorl ally, Irisov et al. [17] ewiluated the differezlce betwww u~nvirld and cross\villd obsmvatiorls of briglltrless teln~wratures usi[lg a twoscalc lnodel based otl the theory of critical 1)lle210tnena slid Cm and hluuk’s slope distrit)utioll, and they SINWW1 ttliit ttle contriblltiorl fronl capillary tvaves ;Vas Illllcll IImrc sig,tlifical}t ttla[l ttlat fr(j~ll lt)ILg Ivav(’s al ttle freque[lcies of 19 MI(I 37 GIIz at Ilorl[d i[lcidellcc angle aIl(l that taki[lg iilt () ;u(x)llrlt all scat teri[lg ltiecliallisl[]s Jvas Ilt’((’ssary ;it t,ll(, illciflc~lcc aIIgle of 78°. Ilow,cv(,rl 1[ isov et, al.’s :Hlalysis W’ilS Iitllit,cd to ttl(! u~)wirl(l :111{1 crx)sswirld asyl[lr[l(,try of 7~, arI(l 7}, with 110 resul ts sir[llllat,(,(l for t,llc otllcr St,ok(,s ~mral[leters, wid t,hey (lid llot, ~)rovi(l(! r)rf!(lict,iorls for the tallg(! of irlci(lcnc{! arigles fro~ll 30° to 70°, where sigllifiCiL[lt, chzulges of u~)wil~(l wid dowilwi]ld asyln}l~ttry were observed irl [7, 8, 9]. The ~JUr~)OSC! of this paper is to examine the applicability of a two-scale model [18, 19] to the w’inrl direction signals in polarimetric sea surface brightness ternpcratures. This model was a generalization of Durden and Vesccky’s scatterillg model [20] to polarimetric microwave emission, extendiu~ the mevious two-scale models (3, 41 to surfaces .,. L,, with an anisotropic directional spectrum and providing theoretical ~redictions for all four Stokes ~)ararncters of . sea surface brightness temperatures. This allows us to examine the relative significance of geometric tiltiug effects of long waves, Bragg scattering by short waves, the excess emission from sea foaln and the modulation of short waves by long waves (hydrodynamic Inodu]ation) [20, 21,22,23, 24]. In Section I I., the theory of polarirnetric radiometry is summarized. Section III. presents a two-scale model for thermal emission from anisotropic wincl waves and foam. Section IV. presents comparison of theoretical results and existixlg microwave brightness temperatures of sea surfaces. Section V. summarizes the results of this paper and discusses the issues for further investigation. II. P O L A R I M E T R I C R A D I O M E T R Y l’he electrornaguetic waves emitted from natural media due to random thermal motion of electric charges are in general partially polarized. To fully characterize the polarization state of partially polarized thermal radiation, four parameters 1, Q, U, and V were introduced by Sir George Stokes. 13ecause conventional radiometers for earth remote sensing perform Tv and Th measurements, an alternate representation of the Stokes vector uses four p a r a m e t e r s , TV, Th, u, and V , T,, atld 7; are the brightness temperatures of vertical a[ld llori~.ontal polarizations, while U al~d V characterize the correlation between these two orthogonal ~)olarizations. N’ote that Z(=T~, + T/, ) represents the total radiated er]er.gy and Q(=~~ – T~) the polarization balauce. Eq. (1) defines the Stokes parameters in terms of the horizontally and vertically polarized components of electric fields (Eh and E,,). The polarizatioll vectors are related to the ctirectio[l of propagation aud are defi[led iu [16]. The atlgular brackets denote the etlsc!mhle average of the argumett, atl(l r is a co[lstarlt relating the brigtlt[iess t,elnperaturc to tllc electric crwrgy de~]sit,y [15, 25]. I{(xxvit interests in the a~)plications of ~)olariluct,ric radiolllctry for rrrnote se[]si[lg were II IOti\’ilt(’(1 by ttle theoretical uwrk [15, 26]. ~;r(]~ttl(l-l)~ls(’(1 (,,x~wrilne[]ts w e r e carri[,(l out to irlvestigate ttl(’ Stokf’s lmriutlcters of t,llerI[ial crllissiotl frottl ~)(,rio(lic soil Sllrfii((’s at, X-l)at]d [ 2 7 ] a[l(l frt)tll si[l[woidal v.’ater surfam,s at Ku ball{] [28], at X I)il[l(l [2!)], illl(l at 94-CIIZ [1 1]. ‘1’11(’ surface ~)rofiles st,lldie(l it] t,tl(’se exiwriltl(![its w(’N’ c~rl(’-(lirll[’[lsiollal w i t h all rills Iwig}lt of a few cc[lt,illlctcrs, I[luctl rougt Ler t}ml tile ca~)illary waves ill the opcm oceans. Herlcej the measllred brightrless temperatures had arl azi[nuthal variation of as large as 20 Kelvins, si,g[lificantly larger than the measureruetlts from ocean surfaces [5, 7, 8] and the theoretical predictiotls [18, 30]. However, these studies clearly show that the Stokes parameters of microwave radiatio~l from surfaces with preferential directional features are functions of az,in~utbal vicxving angles. For wind-generated sea surfaces, the surface spectrum is sylnrnetric with respect to the willd direction (@u, ) or the surfaces are statistically reftcctiou symmetric with respect to ~., [31], if the effects of swell can be ignored. Denoting the azir[luthal observation anmle of radiometer look direc<, tion by ~, and the relative azirrluth angle by @ = @u, – @,, Yueh et al. [31] derived from Maxwell’s equations that T. and Th are even functions of @ and that U and V are odd functions for reftectiorl-symrnctric surfaces. The even and odd symmetry properties allow us to expanc] the Stokes parameters in either cosine or sine series of the azirtlutb auglc O. Hence, expanded to the second harmonic of ~, U R U1 sill@+ U2 sin 2d (4) The first harmonics account for the upwind and clownwind ~ymmetric surface features, while the second harmonics for the upwind and crosswind asymmetry. The coefflcicuts of these Fourier series are functions of oceanic. at[nospheric, aucl some irlstrument parameters, including near surface wind velocity, swell, salinity, air and sea surface temperatures, incidence angle, polarization aucl frequency. The dominant geophysical parameter is the surface wind velocity according to the past experience of oceatl backscatter ~ncasuremeuts. However, other variables which may influence the lviuci stress or frictior[ velocity, could beconle significant at low to moderate \vitLci s~x’eels. LJnderstanding the relation of these harrlmnic coefficiellts with geophysical parameters is crucial to the irlversion of geophysical parameters using polariructric brighttlcss tenlperatures. 111. POLARIMETRIC 2-SCALE SEA SURFACE EMISSION MODEL T~()-S~ill~ sca surface moclels approximate the sea surface as a twc)-scale surface with small-scale ripples or capillary \Yavcs ric!ing oll the top of large-scale surfaces. \Yith ttlis :l~)i)roxit[l:ltioll,” the total tllcrllud er[lission from the $Ilrf;l((, is t]l(~ sul[l of (,lrlissiolls frolll irldilfi(lu;il, s l i gh t ly pt,rt Ilrl)[xl sllrface ~)at (}1(,S tilt,(,(l I)y tile (lll(l(,rlying larges~:tl(L sllrfil(~. Altllotlgtl tt~()-s~;ll~’ IIIO(I(,IS lI:L\(’ (lPHIOIISt Iilt(,(l I(,;lsorlilt)l(, [Illlllerical :L(((lt’;l(j’ [3, ‘~, 17, 20, 2 2 ] , 3 7 G H z 1 9 . 3 5 G H z 220r, ,, r.... ., .!.! ,~~~...i. .L-._--L.-LL–-;. ..;__. l o 10 2 0 30 40 50 60 70