Wind Parameters from Scatterometry

Transcription

1 Wind Parameters from Scatterometr Zorana Jelenak, Moira Sten-Ross and Aleksandar Jelenak Department of Phsics and Electronic Engineering Universit of Waikato Private Bag 3105 Hamilton, New Zealand fa: Abstract We present a preliminar look at the NSCAT data and compare speed and alread derived at the processing ground station at Jet Propulsion Laboratories, USA, with our own theoretical model. Our model adopts a growing sea spectrum (Donelan and Pierson [1987]) and two scale roughness model. We used Level 1.7 of the NSCAT data as our source of backscatter data and compared the speeds and s obtained from the model with Level of the NSCAT data. Introduction Knowledge of speed and over oceans is important in oceanographic, meteorological and climate studies. Satellite scatterometers are radar instruments which transmit and receive (backscattered) power from the ocean surface. The provide frequent measurements in both clear and cloud conditions. Changes in velocit are manifested as variations in ocean surface roughness and thus modification of the radar cross section of the ocean and the magnitude of the backscattered power. Backscatter cross section varies with both speed and when measured at moderate angles. The theor of retrieval from satellites is based on the interaction of electromagnetic waves with rough surfaces. Although this scattering theor has been derived etensivel, current operational algorithms use onl empiricall based relationships; and the application of scattering to ocean retrieval is in need of development. We present a theoretical model of scattering of electromagnetic waves from the ocean surface, based on a two-scale formalism in which capillar waves are superposed on longer wavelength waves. The capillar waves are thought to be predominantl affected b local s, whereas the longer waves are due to local s plus swell. To model the swell effect we introduced local incidence angles which account for the tilting effect of the swell on the scattering ocean surface. Wind parameters are incorporated into the model via the wave spectrum of Donelan and Pierson [1987]. This semiempirical model allows for inclusion of the effects of non locall generated swell, viscosit, surface tension and sea surface temperature on backscatter. The recent launch of the NSCAT scatterometer on board the ADEOS satellite provided researchers with ocean data for the first time since SEASAT mission of The NSCAT scatterometer retained the same working frequenc of the Seasat satellite, 14 GHz, but introduced one more pair of antennas, the so-called middle beam, to enable ambiguit removal from calculations. The NSCAT scatterometer scans the earth surface in two 600 km wide swaths, spaced apart for 400 km to remove an possibilit of specular reflection. Prior to ADEOS's untimel demise earlier this ear, NSCAT had fortunatel alread recorded sufficient scatterometr data to enable scientists to validate and formulate ocean algorithms.

2 Two Scale Composite Model The sea surface can be represented as a surface composed of two wave sizes, one large and the other small compered with the incident wavelength. The shorter waves, known as capillar waves, are tilted in accordance with the slope distribution of the large waves (gravit waves) of the surface. Scattering from such a surface is dominated b the large scale roughness at near normal incidence (qi < 5 o ) and b the small scale roughness at large incidence angles. It has been established that the resonant or Bragg scattering is the most important mechanism in electromagnetic wave ocean surface interaction for midrange incidence angles. On the sea the short waves ride on the larger waves and are thus tilted with respect to the horizontal. The tilt dependence for horizontal polarisation is ver different than that for vertical polarization. The polarization ratio decreases for large angles of incidence as the ocean becomes rougher with speed. For backscatter onl waterwaves of wave number k = k 0 sin q i (which is the Bragg resonance condition) travelling parallel to the line of sight contribute (Valenzuela [1977]). Thus ocean backscatter can be derived using firstorder perturbation theor. The backscatter coefficient in this model is given b Valenzuela (1977) for horizontal polarization: o (q) = 4pk 4 æ a cosd o cos(q) ç M hh (q) + sin d æ ç M vv (q) S(k o a,k o g sin d ) (1) è ø è ø s hh for vertical polarization: o (q) = 4pk 4 æ a cosd o cos(q) ç M vv (q) + sin d æ ç M hh (q) S(k o a,k o g sin d ) () è ø è ø s vv where M hh (q) and M vv (q) are first order scattering coefficients for horizontal and vertical polarization, respectivel. M hh (q) = (e r - 1) cosq+(e r + sin q) 1/ [ ] [ ] [ cosq+(e r + sin q) 1/ ] M vv (q) = (e r - 1) e r (1 + sin q) - sin q e r = i is the comple dielectric constant of water. To account for the tilting of the capillar waves due to the gravit waves the return due to the capillar waves must be integrated over the probabilit distribution of the slopes of the gravit waves. s osea = s o (q)p q (Z òò, Z )dz dz (4) (3) where P q (Z, Z ) is the probabilit distribution of the slope as viewed from an angle q. Z is the local surface slope at the plane of incidence, Z is the local surface slope perpendicular to the plane of incidence, Z is the local surface slope in the of and Z is the local surface slope perpendicular to the. Z, Z and Z, Z are related b a simple coordinate transformation. If c represents then the resultant local incident angle q' is given b g q' q z g ' q= q - g = q - tan -1 (Z cos c + Z sin c) (5) Fig 1 where c is the.

3 The probabilit slope distribution of the ocean viewed from an angle q (Chang and Fung [1977]) is related to the probabilit slope distribution viewed from the vertical b P q (Z, Z ) = [ 1 + Z cos c tan q + Z sin c tan q]p(z,z ) (6) We used the slope probabilit distribution P(Z, Z ) proposed b Co and Munk, [1954]: P(Z, Z ) = F(Z, Z ) 4pv u v c é ep - Z v - Z ê ëê u v c ù ú ûú (7) where F(Z, Z ) = 1 - c 1 + c 4 æ Z ç è v - 1 Z u ø v - c 03 Z 3 3 u 6 v - 3Z æ ç 3 è u v u ø + c æ 40 ç 4 è æ Z æ ç v - 1 Z ç è c ø v c 04 Z 4 4 è u ø 4 v - 6Z æ ç + 3 è u v u ø Z 4 v c 4-6Z + 3 v c ø (8) and vu and vc are the slope variances of the long waves in the up and cross s respectivel. The values of the other coefficients are given b Co and Munk, [1954] as follows: c 40 = 0.4 c = 0.1 c 04 = 0.3 c 1 = U(1.5) c 03 = U(1.5) Donelan and Pierson Spectrum To incorporate the parameters into our model we used the two dimensional wave spectrum of Donelan and Pierson [1987]. This spectrum is obtained b multipling the down spectrum b an angular spreading function. The value of the down spectrum is onl preserved if the value of the spreading function is one when the angle of azimuth is zero. If the spreading function is normalised this condition is not generall met. The situation is further complicated if the normalised factor is a function of wavenumber. Our solution to this problem is to use the spectrum given b Donelan and Pierson [1987] with a normalised spreading function adjusted b factor two to make the variance of the slopes calculated from the spectrum agree with the result of Co and Munk (1987). We defined the two dimensional wave spectrum as S k (k, c) = S(k) D N (k, c) (9) k where D N (k, c) is the normalised spreading function. The form of D N (k, c) used in our calculations is: D N (k, c) = h(sec h (h(c - p)) + sec h (hc) + sec h (h(c + p)) (tanh(ph) + tanh(ph)) (10) where h is a parameter depending on the ratio of k/kp. In our work we defined h as continuos function of k/kp over several ranges of k/k p as follows:

4 ì1.4 0 < k / k p < (k / k p ) < k / k p < 0.90 h = í.30(k / k p ) < k / k p < (k / k p ) < k / k p < 50 î < k / k p (11) The low-wave number part of the spectrum used b Donelan and Pierson [1987] for a full developed generated sea and for 0 < k / k p < 10, is given b where S(k) = U (10) k.5 g 0.5 æ -g epç è k (1.U (10)) F ( k ) (1) ø 0.5 æ æ1.u (10)k F(U (10), k) = epç-1.ç -1 è g 0.5 è ø ø (13) In these equations k is the ocean wave number, U (10) is the speed at 10 m, and g = 9.8 m/s. The peak of the spectrum k p is given b k p = g /(1.U(10)) The Donelan and Pierson [1987) high wave number spectrum (capillar wave spectrum) is given b S(k) = é0.194 r a æ U (p / k) k 3 ç - 1 ëê a r w è C(k) ø - 4nk ù ac(k) ûú 1/n (14) where the speed at p / k is given in terms of U (10) as é U (p / k) = U (10) ( U (10)) 0.5 æ æ ln p k è è 10ø - ln k ù ê ë ø ú û (15) In equation (14) r a represents densit of air and r w densit of sea water. The values a and n depend on the nature of the breaking process, and are parameterized to follow this process as n = (n 1 - n )- g+3gk g+gk ln a = (lna 1 - ln a )- g+3gk b +n where n 1 = 5 and n = 1.15 g+gk b +ln a where ln a 1 =, ln a = 4.6 and b = 3 Parameters n 1 and a 1 are obtained from observation of gravit wave spectra and b, n and a are chosen to give the best fit to the observed datn the K u band. Results We calculated the backscatter for ten different values of the angle of incidence in increments of two from 40 o to while varing speed from m/s to 0m/s assuming 150 o. In our calculations we found that the backscatter for both horizontal and vertical pollarizations was almost independent of surface temperature, and thus set the surface temperature to 10 o C. Fig. shows the backscatter for vertical polarization as a function of incidence angle and speed for constant temperature. Fig 3 shows the calculated backscatter for horizontal polarization.

5 Angle / [deg] U / Angle / [deg] U / 0 Fig. Calculated backscater in [db] 0 Temperature =10 C Vertical polarization Fig.3 Calculated backascater in [db] Temperature = 10 0 C Horizontal polarization NSCAT Model NSCAT used an arra of si antennas that radiated microwave pulses at a frequenc of 14 GHz. These antennas were oriented to make observations at three independent azimuth angles on each side of the satellite. The received return signal was divided b an on-board Doppler processor into 5 s o cells (4 science plus 1 monitor),. where s o is the radar backscatter cross section. NSCAT measured the backscatter at 5 km resolution and retrieved vectors at 50 km. NSCAT science data products include global backscatter data which are grouped and saved as vector cells (WVC) in the Level 1.7 product: Level.0 provides retrieved s. In Februar 1987 The SWT Model Function subcommittee produced the NSCAT model function: A table of s o values. The model function is refined after comparison of NSCAT data with insitu data from validation eperiments. Their model function depends on speed U, azimuth angle c, radar frequenc f, polarization p and incidence angle q: s o = F(U,c, f, p, q, g) where g represents influences of other geophsical phenomena on s o. Due to azimuthal variation of the model function, solutions at approimatel the same speed have different s known as ambiguities. Thus the objective function used to obtain a vector solution has a number of local etrema. The values of the objective function at these etremas characterise the goodness of fit between the so measurements and the model function. The solution to this is found b the additional NSCAT mid-beam antenna which introduces an additional azimuthal look and produces a single solution. The NSCAT objective function is a Maimum-Likelihood Estimator (MLE) defined b N s J =- oi - s m (U, c i ) å - ln( Var(s m ) i ) i=1 Var(s m ) i where s oi are the backscatter measurements, s m are the model backscatter values corresponding to measurements, and Var(s m ) i are the measurement variances. U is the speed; c i are corresponding s.

6 The Wind Speed and Direction Retrieval Method NSCAT dats organised as three dimensional arras: Each element in the arra corresponds to a 5 5 km region of the Earth from which up to 4 different backscatter measurements are provided. Along with the backscatter data, there are also a suite of control flags that determine the qualit of the backscatter measurements. Our retrieval method starts b selected the region from which we wish to retrieve speed and. If the control flags signal good qualit data we proceed with the initialisation of our method. The maimum number of correct backscatter measurements is read, together with the corresponding azimuth and incidence angles. These values are entered in a non linear multidimensional minimisation routine, which calculates the backscatter using the Donellan and Pierson model b changing the speed and for each entered case. Double integrals were calculated using the 48-point Gauss-Legendre integration formula. This formula provided significant speed improvements over the traditional integration methods based on the Simpson's rule. The function minimized is the total error (sum of the square root differences of the NSCAT measured and our computed backscatter data) of the fit. The minimization routine is implemented in MATLAB ver. 5.1 (The MathWorks Inc. Natick, Massachusets, USA). The minimization routine emploed is the Nealder-Meade simple downhill method. Although simple to use we found that the final speed and values are greatl influenced b the first-guess value. Our current work is focused on investigation for a more robust multidimensional minimization procedure. We have tested our retrieval algorithm with a small set of NSCAT data over the Tasman sea. The data were taken on Jun 19, 1997 which corresponds to the ADEOS revolution number Results are given in Table 1. Wind s are given in accordance with the oceanographic convention for where of 0 o implies a flow toward the north. The reference height for all NSCAT vectors is 19.5 meters above the surface and in our model we used 10 meters above the surface as reference heigh. Within each NSCAT WVC there are up to four possible values for speed and. In the first position is placed solution selected b ambiguit removal algorithm with remaining ambiguities in decreasing oredr of MLE likelihood. These solutions are presented in the same order in TableÊ1. Table 1.ÊÊÊÊÊÊÊÊÊÊÊ NSCAT vector solution selected b ambiguit removal algorithm Calculated vectors speed U 1 speed U speed U 3 speed U 4 speed U c 1 [deg] c [deg] c 3 [deg] c 4 [deg] c [deg]

7 Conclusion Wind retrieval algorithm based on theoretical model on the interaction of electromagnetic waves with ocean surface is presented. The advantage of theoretical approach is that the adjustment can be made to calculated s that relate to different conditions on the sea. The comparison of our model and calculated s b empirical NSCAT model is given in Table 1. Our solutions compare well with NSCAT solutions. We found that the multidimensional minimization routine used in our calculations is greatl influenced b the first-guess value. Our current work focusses on improving the minimization procedure. References 1. H.L. Chan and A.K. Fung; "A Theor of Sea Scatter at Large Incidence Angles", J. Geophs. Res. Vol. 8. No. 4, pp , C.Co and W.Munk, "Statistics of the Sea Surface Derived From Sun Glitter", J. Mar. Res., Vol. 13, No., pp , Donelan M.A. and W.J. Pierson, "Radar Scattering and Equilibrium Ranges in Wind Generated Waves with Application to Scatterometr", J. Geophs. Res. Vol. 9 No. C5, pp , C. L. Humphres, "Theoretical Consideration of Microwave Scattering from The Ocean Surface", Msc Theses, Universit of Waikato, G. R. Valenzuela, " Theories for the Interaction of Electromagnetic and Ocean Waves - A review", Boundar-Laer Meteorolog 13 (1978) J. W. Wright " A New Model for Sea Clutter" IEEE Transactions of Antennas and Propagation, Vol. AP-16, No., 1968.