Whitecap Observations by Microwave Radiometers: With Discussion on Surface Roughness and Foam Contributions

: Ocean surface whitecaps manifest surface wave breaking. Most of the whitecap data reported in the literature are based on optical observations through photographic or video recording. The air in whitecaps modiﬁes the dielectric properties of microwave emissions and scattering. Therefore, whitecap information is intrinsic to microwave signals. This paper discusses a method to retrieve the ocean surface whitecap coverage from microwave radiometer signals.


Introduction
Observations of whitecaps have traditionally been conducted with optical sensing using photographs or video recording (e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and references therein). The risks involved in conducting observation in inclement weather have limited the availability of high wind data. The maximum wind speed in published observations rarely exceeds 25 m/s [5,13,15]. Spaceborne microwave radiometer measurements offer a great opportunity to obtain whitecap information in a much broader range of wind and wave conditions, as well as to expand the geographic coverage throughout the global ocean [16][17][18][19][20][21]. In [21], it is emphasized that two components contribute to the received brightness temperature T bp : ocean surface roughness and whitecaps; the subscript p refers to polarization, and is either vertical (V) or horizontal (H) in this paper. Quantitative evaluation shows that the roughness term dominates in most situations, and its accurate determination is critical to the retrieval of whitecap information in the microwave radiometer signal. This paper presents a brief description of whitecap retrieval from spaceborne microwave radiometers. The details of retrieving whitecap coverage from microwave radiometer signals have been published in [21]. Section 2 presents a summary of the method and the background theory. Section 3 compares the results derived from microwave sensors with those obtained through conventional approaches, and presents discussions on the surface roughness and foam contributions in the microwave radiometer signal. Section 4 presents conclusions.

Theory
Microwave emission from the sea surface is represented by brightness temperature T bp or emissivity e p =T bp /T s , which is brightness temperature normalized by the sea surface temperature T s . The sea surface emissivity is composed of two terms: The flat surface (specular) term is given by pp is the Fresnel reflection coefficients of p polarization, f is microwave frequency, and θ is incidence angle. The wind contribution is evaluated from the excess emissivity ∆e p = e p − e 0p defined as the difference between the actual measured emissivity e p from wind-roughened sea surface and an ideal flat surface e 0p . The excess emissivity is composed of foam and roughness components: The foam component ∆e pf is defined as the difference between the air-entrained (foamed) specular emissivity e 0pf and foamless specular emissivity e 0psw , that is, where ε sw is the (foamless) sea water relative permittivity and ε e is an effective relative permittivity of air-water mixture, to be further discussed later. The roughness component is defined by where S(k, φ) is the surface wave directional spectrum, k is wavenumber, φ is azimuth angle with respect to the wind direction, and g p is a weighting function describing the thermal emission contribution of each wavenumber-directional surface wave component. The full expression of g p is given in [22][23][24]. The original g p formulation in [22][23][24] defines ε = ε sw , and whitecaps are not explicitly treated.
In [25][26][27], ε = ε e is used to compute the roughness term for the more realistic condition with whitecap presence. Many different formulations of ε e have been published; see discussions in [28]. A short summary is given in ( [27], Appendix B). Based on those analyses, the refractive mixing rule [28][29][30][31] is selected: where ε a = 1 is the relative permittivity of air, and F a is the effective air volume fraction, which is formulated as a function of the whitecap coverage W c [21,[25][26][27].

Retrieval Algorithm
The foundation of microwave radiometer wind sensing is built on the observed ∆e p varying with U 10 . Indeed, the stepped frequency microwave radiometer (SFMR) has become an indispensable surface wind sensor for tropical cyclone (TC) monitoring [32][33][34][35][36][37][38]. The relation can be expressed symbolically as Following the analysis given in Section 2.1, the wind effect on the excessive emissivity is contributed by two major components: roughness and whitecaps. The roughness term is evaluated with (5), for which the wave spectrum S(k, φ) is a critical factor [21,27]. The whitecap term is evaluated by (4) with W c embedded in the effective permittivity ε e (6) through F a . Both surface wave spectrum and whitecaps are determined by the ocean surface wind stress, which is proportional to the square of wind friction velocity u * . Thus, (7) can be expanded as The forward computation to evaluate ∆e p with U 10 as the only atmospheric/oceanographic input requires the implementation of wave spectrum, wind stress, and whitecap coverage models in the computation process. There are many different wind speed functions of S(k, φ), u * , and W c in published literature. Microwave remote sensing measurements have been an important source of data for their analyses. The determination of S(k, φ)-especially for short scale waves-is a complicated problem, and active radar data provide more direct connection with the surface wave spectrum. The passive microwave radiometer data can be used to assist in the validation and verification effort. The details are discussed in [21,27] and the references cited in those studies; they are not repeated here. On the other hand, the large volume of microwave radiometer measurements can be used to optimize the choice of whitecap coverage and surface wind stress models. The analyses presented in [21,27] lead to the selection of the following wind relationship for the whitecap coverage, which is introduced in [25] and established on the whitecap measurements of [11]: The whitecap formula (9) is given as a function of wind friction velocity u * , so a drag coefficient C 10 formula is needed when U 10 is the input. The C 10 formula is derived from microwave radiometer data in TC wind conditions [19,21,27]: Figure 1 shows four examples of comparing microwave thermal emission computations with field observations of ∆e p . The SFMR and three frequencies of WindSat are illustrated here. Detail and more extensive comparisons are given in [21].
The ∆e p is presently used for retrieving U 10 (7). As indicated by (8), it also contains information related to whitecaps, surface wind stress, and surface roughness. A procedure to use the pre-calculated solutions of ∆e p (U 10 , W c , u * ) for retrieving W c and u * from ∆e p in addition to U 10 is described in [21]. Figure 2 illustrates the procedure for W c retrieval. The WindSat 6.8 GHz H polarization data are used as an example; there are 500 (U 10 , ∆e H ) data pairs, and the maximum wind speed is 24.8 m/s. Figure 2a shows ∆e p (U 10 ) and ∆e pf (U 10 ); the data are shown with magenta circles and cyan crosses, and the analytical solutions are illustrated with black solid and dashed lines. The same data can be presented as ∆e p (W c ) and ∆e pf (W c ) in Figure 2b. The model solutions can then be used to obtain W c from ∆e p or ∆e pf ; and the derived W c can be subsequently presented as functions of wind speed, as shown in Figure 2c, in which the W c (U 10 ) model curve (9-10) is illustrated with a black dashed-dotted line. Clearly, the results of W c (U 10 ) obtained with ∆e pf are in better agreement with the model curve and with less data scatter in comparison to those derived from ∆e p . Radiometer measurements from many SFMR, WindSat, SMAP, and SMOS missions in a wide range of frequency (1.4 to 37 GHz) and incidence angle (SFMR: 0 • , SMAP: 40 • , SMOS: 0 • to 65 • , and WindSat:~53 • ) are assembled to optimize various parameters in the whitecap retrieval procedure. The maximum wind speed in the collection exceeds 90 m/s; details are given in [21].  Figure 1 shows four examples of comparing microwave thermal emission computations with field observations of Δep. The SFMR and three frequencies of WindSat are illustrated here. Detail and more extensive comparisons are given in [21]. The Δep is presently used for retrieving U10 (7). As indicated by (8), it also contains information related to whitecaps, surface wind stress, and surface roughness. A procedure to use the precalculated solutions of Δep(U10, Wc, u*) for retrieving Wc and u* from Δep in addition to U10 is described in [21]. Figure 2 illustrates the procedure for Wc retrieval. The WindSat 6.8 GHz H polarization data are used as an example; there are 500 (U10, ΔeH) data pairs, and the maximum wind speed is 24.8 m/s. Figure 2a shows

Whitecap Coverage Retrieved from Microwave Radiometers
From the discussion presented in Section 2, it becomes clear that the whitecap coverage can be retrieved from the ∆e p (U 10 ) data, such as those given in Figure 1. Many datasets from SFMR, WindSat, SMAP, and SMOS missions are analyzed in [21], a large portion of the data is collected in TCs, and the maximum wind speed in the collection exceeds 90 m/s. The retrieval procedure uses the foam component ∆e pf (U 10 ), through the method presented in the discussion of Figure 2. Figure 3 summarizes the results from all microwave sensors (green crosses). For comparison, measurements from conventional optical approaches reported in [2][3][4][5][7][8][9][10][11] are shown with magenta plus signs. The whitecap coverage model, (9)(10), is shown with the black solid line.   The whitecap model (9) specifies that U 10 = 3.3 m/s (u * = 0.11 m/s) is the minimum wind speed for whitecap appearance. Non-zero whitecap coverages are found in optical observations as well as in the retrieved results from microwave radiometers; the magnitude, however, is generally smaller than 10 -4 . For U 10 < 25 m/s, the W c derived from microwave radiometers is similar to that obtained by optical methods, and the data scatter in the radiometer dataset is much smaller. Most significantly, the wind speed coverage of whitecap databases expands considerably by incorporating the microwave radiometer results, from about 25 m/s to 90 m/s.

Foam and Roughness Contributions
The sum, foam, and roughness components, respectively ∆e p , ∆e pf , and ∆e pr , can be obtained from the analytical electromagnetic (EM) model (black, red, and blue curves in Figure 1). Figure 4a,b shows the foam-to-roughness ratio r pfr =∆e pf /∆e pr for vertical and horizontal polarizations. Note that the range of the vertical scale is 10 times larger in the plot of vertical polarization in Figure 4a, than that of the horizontal polarization in Figure 4b. The roughness contributions of the vertical polarization for 10.7, 18.8, 23.0, and 37.0 GHz of WindSat near 53 • are partially or wholly negative, as shown by the examples in Figure 4c,d; therefore, the vertical polarization foam-to-roughness ratios r Vfr are partially or wholly negative for those four frequencies, as shown in Figure 4a. In contrast, the foam and roughness components of the horizontal polarization are all positive. For convenience, the roughness components of the excess emissivity of vertical and horizontal polarizations of the five WindSat frequencies are shown in Figure 4c,d, respectively.
The vertical roughness component ∆e pr transitions from positive to negative near Brewster's angle. This is an important practical consideration in the present design of whitecap retrieval algorithm. The algorithm uses the analytical foam-to-sum ratio r pfs =∆e pf /∆e p to obtain the foam component of the observed excess emissivity ∆e pf . Figure  the examples in Figure 4c,d; therefore, the vertical polarization foam-to-roughness ratios rVfr are partially or wholly negative for those four frequencies, as shown in Figure 4a. In contrast, the foam and roughness components of the horizontal polarization are all positive. For convenience, the roughness components of the excess emissivity of vertical and horizontal polarizations of the five WindSat frequencies are shown in Figures 4c and d, respectively. The vertical roughness component Δepr transitions from positive to negative near Brewster's angle. This is an important practical consideration in the present design of whitecap retrieval algorithm. The algorithm uses the analytical foam-to-sum ratio rpfs=Δepf/Δep to obtain the foam component of the observed excess emissivity Δepf. Figure 5 shows the analytical solutions of rpfs and

Conclusions
Whitecap contribution is an important element in the microwave radiometer signal. There are many published datasets offering the opportunity to obtain the whitecap information in global oceans and under extreme wind conditions. Two major components, roughness (surface waves) and foam (whitecaps), contribute to the microwave radiometer signal from the ocean surface. The roughness component is the dominant one over a wide range of wind speeds, so retrieving whitecap information from microwave radiometer measurements requires an accurate accounting of the surface roughness contribution. An algorithm is described for whitecap retrieval from microwave systems, including SFMR, WindSat, SMAP, and SMOS. Many of the assembled data are collected in

Conclusions
Whitecap contribution is an important element in the microwave radiometer signal. There are many published datasets offering the opportunity to obtain the whitecap information in global oceans and under extreme wind conditions. Two major components, roughness (surface waves) and foam (whitecaps), contribute to the microwave radiometer signal from the ocean surface. The roughness component is the dominant one over a wide range of wind speeds, so retrieving whitecap information from microwave radiometer measurements requires an accurate accounting of Remote Sens. 2020, 12, 2277 7 of 9 the surface roughness contribution. An algorithm is described for whitecap retrieval from microwave systems, including SFMR, WindSat, SMAP, and SMOS. Many of the assembled data are collected in TCs, with the maximum wind speed exceeding 90 m/s. In the wind speed range below 25 m/s, whitecap coverages derived from microwave radiometers are similar to those obtained by optical methods, and the data scatter of the radiometer datesets is much smaller. Incorporating the microwave radiometer results expands the wind speed coverage range of whitecap databases from about 25 to 90 m/s.