A Review of Models for Polarimetric Thermal Emissionfrom the Sea Surface

Current models for the microwave polarimetric brightness temperature of the sea surface are reviewed. Results from the physical optics (PO), composite surface, and small slope approximation (SSA) theories are illustrated and compared with an empirical model. All models are shown to predict both first and second harmonic azimuthal variations of sea brightnesses, but the physical effects captured are distinct for each model. Both the composite surface and small slope theories are found to show reasonable agreement with empirical results, although some discrepancies exist, while the physical optics model tends to under-predict empirical results. INTRODUCTION Polarimetric radiometry has been proposed as an effective means for retrieving wind speed and direction over the sea surface from spaceborne sensors, and plans to include polarimetric radiometers in future satellite systems are in progress [1]. Several models have been proposed for predicting polarimetric emission from the rough sea surface, although these models are all based on approximations in the solution of the electromagnetic boundary value problem. Solutions based on geometrical or physical optics capture emission from surface features which have small slopes and which are large compared to the electromagnetic wavelength [2]-[3], while composite surface (or “two-scale”) [4] and small slope approximate theories [5]-[9] include both long and short wave effects. Higher order implementations of both the small slope and optical theories can be developed and would provide information on convergence of these methods, but the resulting expressions are typically difficult to evaluate for a multi-scale sea surface. Note it has been shown that both the composite and small slope theories provide predictions similar to those of physical optics for long wave features [9]. MODELS The JPL WindRAD empirical model [10] predicts first and second azimuthal harmonic coefficients of sea polarimetric brightness temperatures as a function of wind speed. The model applies to frequencies 19.35 and 37 GHz, and polar observation angles of 45, 55, and 65 degrees. The 55 degree results are focused on in this paper due to their importance for space-borne sensors. In the results to be shown, physical optics predictions were obtained by integrating over the Cox and Munk slope distrbution for the sea surface [11], and shadowing and multiple scattering effects are neglected. Composite surface model predictions follow the formulation of [4], including the use of a doubled “Durden-Vesecky” spectrum [12], and model the long wave slope distribution as Gaussian. Integrations over the long wave slope distribution were performed using Gauss-Hermite quadrature with 4 x 4 points. Small slope approximation predictions used the second order theory [5]-[6] for second azimuthal harmonic predictions, and the third order theory [8] for first azimuthal harmonic predictions. The doubled “Durden-Vesecky” spectrum was again used, and the long-short wave modulation process described in [4] applied. Of course, all of these predictions are sensitive to the sea surface models included, and continued research in improving these descriptions is of great importance. RESULTS Figures 1 through 4 illustrate the comparison of results from the PO, composite surface, and SSA models with the WindRAD model, in all four polarimetric brightnesses. First azimuthal harmonics in Figures 1 (19.35 GHz) and 2 (37 GHz) show that the third-order small slope theory appears to provide the highest level of agreement with the empirical data, but composite surface results are similar. PO predictions under-predict the empirical data, particularly at low wind speeds, suggesting that short wave effects may be important contributors to these results. An assymetric foam coverage (not modeled here) has also been proposed as an additional source of up-downwind brightness aymmetry [3]. Second azimuthal harmonic results in Figures 3 (19.35 GHz) and 4 (37 GHz) show composite surface and second order small slope theory results are more similar, indicating that “tilting” effects have little influence in the composite model. PO results again underpredict the empirical model. The over-prediction of second azimuthal harmonics at high wind speeds by both the composite and small slope theories is related to the fact that Durden-Vesecky spectral amplitudes do not saturate at high wind speeds. The results of this paper suggest that short wave effects can be important contributors to sea emission signatures, given the difference between the composite/SSA and PO results. While the comparison with the WindRAD model showed a reasonable level of agreement, continued investigation of the accuracy of all sea emission models is warranted. Higher-order implementations of the SSA are currently under development, and should provide a more rigorous means for evaluating the accuracy of composite and lower-order SSA predictions. Some results with higher order implementations of the SSA and PO theories are available in [13]. REFERENCES [1] Gasster, S. D. and G. M. Flaming, “Overview of the Conical Microwave Imager/Sounder development for the NPOESS program,” IGARSS’98 conference proceedings, vol. 1, pp. 268–271, 1998. [2] Stogryn, A., “The apparent temperature of the sea at microwave frequencies,” IEEE Trans. Ant. Prop., vol. 15, pp. 278–286, 1967. [3] Kunkee, D. B. and A. J. Gasiewski, “Simulation of passive microwave wind direction signatures over the ocean using an asymmetric-wave geometrical optics model,” Radio Science, Vol. 32, pp. 59, 1997. [4] Yueh, S. H., “Modeling of wind direction signals in polarimetric sea surface brightness temperatures,” IEEE Trans. Geosc. Remote Sens., vol. 35, pp. 1400-1418, 1997. [5] Irisov, V. G., “Small-slope expansion for thermal and reflected radiation from a rough surface,” Waves in Random Media, vol. 7., pp. 1-10, 1997. [6] Johnson, J. T., and M. Zhang, “Theoretical study of the small slope approximation for ocean polarimetric thermal emission,” IEEE Trans. Geosc. Remote Sens., vol. 37, pp. 2305–2316, 1999. [7] Irisov, V. G., “Azimuthal variations of the microwave radiation from a slightly non-Gaussian sea surface,” Radio Science, vol. 53, pp. 65–82, 2000. [8] Johnson, J. T. and Y. Cai, “A theoretical study of sea surface up/down wind brightness temperature differences,” IEEE Trans. Geosc. Remote Sens., vol. 40, pp. 66–78, 2002. [9] Johnson, J. T., “Comparison of the physical optics and small slope theories for polarimetric thermal emission from the sea surface,” IEEE Trans. Geosc. Rem. Sens., vol. 40, pp. 500–504, 2002. [10] Yueh, S. H., W. J. Wilson, S. J. Dinardo, and F. K. Li, “Polarimetric microwave brightness signatures of ocean wind directions,” IEEE Trans. Geosc. Remote Sens., vol. 37, pp. 949–959, 1999. [11] Cox, C. and W. Munk, “Measurement of the roughness of the sea surface from photographs of the sun’s glitter,” J. Opt. Soc. Am., vol. 44, pp. 838–850, 1954. [12] Durden, S. L. and J. F. Vesecky, “A physical radar cross-section model for a wind driven sea with swell,” IEEE J. Oceanic Eng., vol. OE-10, pp. 445–451, 1985. [13] Johnson, J. T., “Higher order emission model study of bi-sinusoidal surface brightnesses,” unpublished. 0 10 20 −2 −1 0 1 2 3 U19.5 (m/s) Fi rs t A zi m ut ha l H ar m on ic (K ) (a) Th Tv U V JPL 0 10 20 −2 −1 0 1 2 3