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  • View in gallery

    Calculated ΔeV and ΔeH at various microwave frequencies, and comparison with field data. The top two rows (M09 and S19; triangle for V and square for H) show (a) 6.69, (b) 6.8, (c) 10.7, (d) 18.7, (e) 23.8, and (f) 37.0 GHz. Sum, foam, and roughness contributions are given by black, cyan, and green curves; solid and dashed lines show vertical and horizontal polarizations, respectively. The two numbers in parentheses are frequency (GHz) and EIA. The bottom row (L band 1.41 GHz, θ = 40°) shows (g) ΔeV, Y16 and M17 (SMAP); (h) ΔeH, Y16 and M17 (SMAP); and (i) ΔeA, Y16 and M17 (SMAP) and R16 θ = 40° ± 0.1° (SMOS).

  • View in gallery

    Illustration of whitecap and surface wind stress retrieval using Δep; WindSat 6.8-GHz horizontal polarization data are used for an example (p = H): (a) Δep(U10) and Δepf(U10), (b) Δep(Wc) and Δepf(Wc), (c) Δep(u*) and Δepf(u*), (d) Wc(U10) retrieved with Δep and Δepf, (e) comparison of modeled and retrieved Wc from Δep and Δepf, and (f) comparison of modeled and retrieved u* from Δep and Δepf. In (e) and (f), statistics (b0, b1, b2, and b3) of modeled and retrieved Wc and u* with Δep and Δepf are printed at the top.

  • View in gallery

    Snapshots (~10 h) of WindSat global retrieval of (a) Wc and (b) u* on 5 Jan 2014 (in northern winter). The dependence on wind speed is given for (c) Wc and (d) u*, where bin-averaged results shown with colored markers are from four microwave frequencies identified in the legend; unaveraged results for 10.7 GHz are superimposed with cyan dots in the background.

  • View in gallery

    As in Fig. 3, but on 1 Jul 2014 (in southern winter).

  • View in gallery

    Whitecap and wind stress retrieval from five frequencies of the M09 WindSat dataset and comparison with models (9) and (10): (a) Wc and (b) u*.

  • View in gallery

    Whitecap and wind stress retrieval of extreme wind cases of SMAP datasets (Y16 and M17) and comparison with models (9) and (10): (a) Wc and (b) u*; results obtained with both V and H polarizations are presented and statistics (b0, b1, b2, and b3) of comparing the modeled and retrieved Wc and u* with both polarizations are printed at the lower right corners.

  • View in gallery

    Whitecap and wind stress retrieval from the SMOS dataset (R16) and comparison with models (9) and (10): (a) Wc and (b) u*; bin-averaged results obtained for θ = 11°, 15°, 20°, …, 60°, and 64° are illustrated with various markers identified in the legend and unaveraged 35° results are shown with cyan dots in the background.

  • View in gallery

    (a) Whitecap coverage dependence on wind speed; data are from observations tabulated in MTRXLS (Monahan 1971; Toba and Chaen 1973; Ross and Cardone 1974; Xu et al. 2000; Lafon et al. 2004, 2007; Sugihara et al. 2007) and C08 (Callaghan et al. 2008). The solid line is whitecap coverage model (9). (b) Whitecap coverage dependence on surface wave energy dissipation rate computed with wind and wave data reported in TLS (Toba and Chaen 1973; Lafon et al. 2004, 2007; Sugihara et al. 2007). The dashed line is the linear function (11) given in H08 (Hwang and Sletten 2008). [Partially reproducing Fig. 6 of Hwang and Sletten (2008)].

  • View in gallery

    Whitecap and wind stress results combining SFMR, SMAP, SMOS, and WindSat datasets discussed in this paper: (a) Wc, (b) u*, and (c) energy dissipation rate Et converted from whitecap coverage obtained by microwave radiometers and employing the linear relationship obtained by Hwang and Sletten (2008).

  • View in gallery

    Determination of flat surface (specular) emissivity using data with U10 < 2 m s−1: (a),(c) e0H and (b),(d) e0V. Superimposed black lines are fitted polynomial curves; red lines are analytical solutions computed with s = 35 psu and Ts = 290 K. Top and bottom rows show results for data used in Figs. 3 and 4, respectively.

  • View in gallery

    WindSat Δep(U10) of Fig. 3 data (blue markers and light-colored dots for bin-averaged and unaveraged results, respectively), and comparison with M09 (red markers) and analytical solutions (black lines): (a) 10.7, (b) 18.7, (c) 23.7, and (d) 37.0 GHz. Mean and standard deviation of EIA are given in the second set of numbers inside parentheses at the upper-left corner of each panel.

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Whitecap and Wind Stress Observations by Microwave Radiometers: Global Coverage and Extreme Conditions

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  • 1 Remote Sensing Division, U.S. Naval Research Laboratory, Washington, D.C.
  • 2 Laboratoire d’Océanographie Physique et Spatial, Institut Français de Recherche pour l’Exploitation de la Mer, Univ. Brest, CNRS, IRD, Brest, France
  • 3 Remote Sensing Systems, Santa Rosa, California
  • 4 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California
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Abstract

Whitecaps manifest surface wave breaking that impacts many ocean processes, of which surface wind stress is the driving force. For close to a half century of quantitative whitecap reporting, only a small number of observations are obtained under conditions with wind speed exceeding 25 m s−1. Whitecap contribution is a critical component of ocean surface microwave thermal emission. In the forward solution of microwave thermal emission, the input forcing parameter is wind speed, which is used to generate the modeled surface wind stress, surface wave spectrum, and whitecap coverage necessary for the subsequent electromagnetic (EM) computation. In this respect, microwave radiometer data can be used to evaluate various formulations of the drag coefficient, whitecap coverage, and surface wave spectrum. In reverse, whitecap coverage and surface wind stress can be retrieved from microwave radiometer data by employing precalculated solutions of an analytical microwave thermal emission model that yields good agreement with field measurements. There are many published microwave radiometer datasets covering a wide range of frequency, incidence angle, and both vertical and horizontal polarizations, with maximum wind speed exceeding 90 m s−1. These datasets provide information of whitecap coverage and surface wind stress from global oceans and in extreme wind conditions. Breaking wave energy dissipation rate per unit surface area can be estimated also by making use of its linear relationship with whitecap coverage derived from earlier studies.

Supplemental information related to this paper is available at the Journals Online website: https://doi.org/10.1175/JPO-D-19-0061.s1.

© 2019 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Dr. Paul A. Hwang, paul.hwang@nrl.navy.mil

Abstract

Whitecaps manifest surface wave breaking that impacts many ocean processes, of which surface wind stress is the driving force. For close to a half century of quantitative whitecap reporting, only a small number of observations are obtained under conditions with wind speed exceeding 25 m s−1. Whitecap contribution is a critical component of ocean surface microwave thermal emission. In the forward solution of microwave thermal emission, the input forcing parameter is wind speed, which is used to generate the modeled surface wind stress, surface wave spectrum, and whitecap coverage necessary for the subsequent electromagnetic (EM) computation. In this respect, microwave radiometer data can be used to evaluate various formulations of the drag coefficient, whitecap coverage, and surface wave spectrum. In reverse, whitecap coverage and surface wind stress can be retrieved from microwave radiometer data by employing precalculated solutions of an analytical microwave thermal emission model that yields good agreement with field measurements. There are many published microwave radiometer datasets covering a wide range of frequency, incidence angle, and both vertical and horizontal polarizations, with maximum wind speed exceeding 90 m s−1. These datasets provide information of whitecap coverage and surface wind stress from global oceans and in extreme wind conditions. Breaking wave energy dissipation rate per unit surface area can be estimated also by making use of its linear relationship with whitecap coverage derived from earlier studies.

Supplemental information related to this paper is available at the Journals Online website: https://doi.org/10.1175/JPO-D-19-0061.s1.

© 2019 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Dr. Paul A. Hwang, paul.hwang@nrl.navy.mil

1. Introduction

Due to its close connection to wave breaking, there has been an enduring interest in attempting to quantify the ocean surface whitecap coverage. Conventionally, whitecap observations are made with photographs or video recording. The sharp brightness contrast between whitecaps and background water surface is used to determine the fraction of whitecap coverage (e.g., Monahan 1969, 1971; Toba and Chaen 1973; Ross and Cardone 1974; Black et al. 1986; Walker 1994; Xu et al. 2000; Lafon et al. 2004, 2007; Sugihara et al. 2007; Callaghan et al. 2008; Kleiss and Melville 2011; Holthuijsen et al. 2012; Brumer et al. 2017, and references therein). Over many decades of diligent observations, only a small number of published observations are obtained in conditions with wind speed exceeding about 25 m s−1 (e.g., Weather Squadron Two 1952; Black et al. 1986; Holthuijsen et al. 2012). This is mainly caused by the necessity of having a ship or aircraft in the scene to make photographic or video observations, and tower-based operations are suspended during inclement weather.

Microwave radiometer data represent another source of whitecap information. As in ocean surface optical images, microwave brightness temperature Tbp increases sharply in the presence of whitecaps (surface foams); subscript p is polarization and is either vertical (V) or horizontal (H) in this paper. Several investigations of whitecap retrieval from Tbp data have been reported (e.g., Pandey and Kakar 1982; Wentz 1983; Anguelova and Webster 2006; Hwang 2018; Anguelova and Bettenhausen 2019). Utility of Tbp-derived whitecaps for air–sea interaction studies has been demonstrated (Salisbury et al. 2013, 2014; Albert et al. 2016; Anguelova 2016) using WindSat whitecap database built with an earlier version of the Wc(Tbp) algorithm (Anguelova et al. 2010).

In the present investigation, it is emphasized that the ocean surface microwave thermal emission is composed of two major components: surface roughness and foam. The relative weighting of the two components varies as a function of wind speed, microwave frequency, polarization, and incidence angle. In general, the roughness term dominates over a wide range of wind speed (Hwang 2012, 2018, 2019). It is therefore very critical to correctly compute the roughness term in order to minimize errors spilled over to the whitecap term.

Both surface roughness and whitecaps are driven by ocean surface wind stress. Forward solutions of microwave thermal emission, with wind speed as the only oceanographic/atmospheric input, require the information of surface wind stress, surface wave spectrum, and whitecap coverage for the EM thermal emission calculation (e.g., Yueh et al. 1994a,b; Johnson and Zhang 1999; Hwang 2012, 2018, 2019). The forward computation procedure therefore employs wind speed dependence models of drag coefficient C10, whitecap coverage Wc, and directional surface wave spectrum S(k) reported in literature; k is the wavenumber vector of surface waves (roughness). Good agreement between forward solutions and radiometer data is achieved only when the employed C10, Wc, and S(k) models are reasonably accurate. In this respect, microwave radiometer data can be used to evaluate various formulations of the drag coefficient, whitecap coverage, and surface wave spectrum. An example is given in Hwang (2018, Figs. 3a and 4 therein) showing that small perturbations of the drag coefficient formula can result in large changes of the thermal emission solution. Similarly, the forward solution of radar backscattering is severely modified by different assumptions of the drag coefficient (Hwang et al. 2013, their Fig. 12).

Many reports of microwave radiometer measurements in high winds have been published recently (e.g., Meissner and Wentz 2009; Yueh et al. 2010, 2013, 2016; Klotz and Uhlhorn 2014; Meissner et al. 2014, 2017; Reul et al. 2016; Sapp et al. 2019). These references and datasets are denoted M09, Y10, Y13, Y16, K14, M14, M17, R16, and S19, respectively, in this paper. Analyses of these data have led to improved understanding relating surface wind speed with surface wind stress, surface roughness spectrum, and whitecap coverage (Hwang 2012, 2018, 2019). The most recent results are presented in Hwang et al. (2019, hereafter HRMY). With improved understanding, good agreement is achieved between analytical thermal emission computations and microwave brightness temperature measurements over a wide range of frequency, incidence angle, both V and H polarizations, and calm to tropical cyclone (TC) wind conditions (Hwang 2019; HRMY).

Built on this foundation, an algorithm is developed for deriving whitecap coverage and surface wind stress from microwave radiometer measurements. Analytical solutions of wind-induced excess emissivity are precalculated to generate lookup tables that serve as geophysical model functions (GMFs). (Emissivity ep = Tbp/Ts is the ratio of brightness temperature Tbp and sea surface temperature Ts.) The wind-induced excess emissivity is a relatively small portion of the total emissivity that is dominated by the flat-surface specular term. With the specular term removed, the excess emissivity is more sensitive (compared to Tbp) for retrieving wind-related parameters such as whitecap coverage and surface wind stress. Furthermore, analytical thermal emission computation can separate roughness and foam components. By using the foam component, additional improvements are realized in the retrieved results of whitecap coverage and surface wind stress. Microwave data collected in TCs (M09, R16, Y16, M17, and S19) are then processed to yield information of whitecap coverage and surface wind stress in extreme wind conditions.

Section 2 discusses the theoretical aspects of ocean surface microwave thermal emission and the forward computation procedure. The discussion includes a comparison between analytical solutions and field measurements. Section 3 describes the method for retrieving whitecap coverage and surface wind stress using microwave radiometers. Section 4 presents the oceanographic significance of microwave approach and results of retrieved whitecap coverage and surface wind stress from global oceans and in extreme wind conditions. Furthermore, breaking wave energy dissipation rate per unit surface area can be estimated by making use of its linear relationship with whitecap coverage derived from previous studies (Ross and Cardone 1974; Hwang and Sletten 2008). Section 5 is a summary.

2. Ocean surface microwave thermal emission

a. Theoretical background

Sea surface microwave emission is typically given in terms of brightness temperature Tbp or emissivity ep = Tbp/Ts. In the absence of surface roughness and foam, ep is dependent on microwave frequency f, incidence angle θ, polarization p, and bulk seawater properties of sea surface temperature Ts and sea surface salinity s. The fundamental property characterizing emissivity is the seawater relative permittivity (dielectric constant) ε (e.g., Klein and Swift 1977; Meissner and Wentz 2004). Knowing ε the Fresnel reflection coefficients of V and H polarizations can be computed:
RHH(0)=cosθ(εsin2θ)1/2cosθ+(εsin2θ)1/2,RVV(0)=εcosθ(εsin2θ)1/2εcosθ+(εsin2θ)1/2.
The flat surface (specular) emissivities e0V and e0H are given by
e0p(f,θ)=1|Rpp(0)(f,θ)|2.
For a foamless flat sea surface, the specular emissivity term is given as
e0psw=e0p(f,θ,εsw)=1|Rpp(0)(f,θ,εsw)|2,
where εsw is the (foamless) seawater relative permittivity.
In the presence of wind agitation, wave breaking may entrain air into water and change the ocean surface dielectric property. To quantify foam effects from air in whitecaps, an effective relative permittivity εe of air–water mixture is introduced. An extensive discussion of many different formulations of εe is given in Anguelova (2008). A concise description is presented in appendix B of HRMY. The present application employs the refractive mixing rule (Birchak et al. 1974; Sihvola and Kong 1988; Sihvola 2000; Anguelova 2008)
εe=[Faεa1/2+(1Fa)εsw1/2]2,
where εa = 1 is the relative permittivity of air, εsw is the relative permittivity of foamless seawater as mentioned earlier, and Fa is the effective air volume fraction. In practice, Fa is connected to the observed whitecap coverage Wc (Hwang 2012, 2019; HRMY), which is an area fraction. So there is an implicit assumption of homogeneous air distribution in the thin surface layer that interacts with EM waves; the microwave skin depth is about 0.002 m at 10 GHz, and 0.01 m at 1.4 GHz (HRMY, their Fig. 12).
For a foamed flat sea surface, the specular emissivity term is given as
e0pf=e0p(f,θ,εe)=1|Rpp(0)(f,θ,εe)|2.
The wind-induced excess emissivity Δep=epe0p can be separated into foam and roughness components:
Δep=Δepf+Δepr.
The foam component Δepf is defined as the difference between the two specular emissivities of air-entrained (foamed) and foamless seawater surfaces, respectively e0pf and e0psw, that is,
Δepf=e0pfe0psw=e0p(f,θ,εe)e0p(f,θ,εsw)=|Rpp(0)(f,θ,εsw)|2|Rpp(0)(f,θ,εe)|2.
The roughness component is defined by
Δepr(f,θ,ϕ)=002πS(k,ϕ)gp(f,θ,ϕ,ε,k,ϕ)kdϕdk,
where S(k, ϕ) [or S(k)] is the directional spectrum of surface waves (the ocean surface roughness), k is wavenumber, ϕ is azimuth angle referenced to the wind direction, and gp is the EM weighting function describing the thermal emission contribution of each wavenumber-directional surface wave component; the full expression of gp is given in Yueh et al. (1994a,b) and Johnson and Zhang (1999). In the original formulation given by Yueh et al. (1994a,b) and Johnson and Zhang (1999), ε=εsw and whitecaps are not explicitly treated. In Hwang (2012, 2018, 2019) and HRMY, ε=εe is used to compute the roughness term for the more realistic condition with whitecap presence.

The major advance derived from comparing analytical solutions with measurements in a wide range of frequency, incidence angle, and both H and V polarizations is an improved understanding of the dependence on frequency and incidence angle of the foam effects in ocean surface microwave emission. In particular, the effective air fraction Fa can be equated to the whitecap coverage Wc for high EM frequencies (f ≥ 14 GHz) but for lower frequencies Fa is smaller than Wc; more details of the Fa(Wc) function are given in Hwang (2019) and HRMY, and they are not repeated here.

b. Forward computation

In a microwave thermal emission analytical model, the input meteorological parameter is wind speed U10, from which surface wind stress (represented by the wind friction velocity u* or drag coefficient C10), ocean surface roughness spectrum S(k, ϕ), and whitecap coverage Wc are calculated to feed into EM thermal emission computation (section 2a). The Fa needed to evaluate εe [(4)] is calculated from Wc as given by the Fa(Wc) function detailed in HRMY. The whitecap coverage model is determined by comparing microwave emission model results with an extensive dataset (K14) of Stepped Frequency Microwave Radiometer (SFMR) measurements of hurricane reconnaissance and research missions. The comparison analysis (Hwang 2018) confirms the following relationship introduced by Hwang (2012), which is established on the whitecap measurements by Callaghan et al. (2008)
Wc={0,u*0.11ms10.30(u*0.11)3,0.11<u*0.40ms10.07u*2.5,u*>0.40ms1.
The drag coefficient formula to obtain u* from U10 in TC wind conditions is also determined from comparing microwave emission model results with microwave radiometer data:
C10={104(0.0160U102+0.967U10+8.058),U1035ms12.23×103(U10/35)1,U10>35ms1.
The two matching points of three branches in (9), that is, u* = 0.11 and 0.40 m s−1, correspond to U10 = 3.3 and 10.0 m s−1; Hwang (2012, Fig. 2 therein) presents the data of Callaghan et al. (2008) in terms of Wc(u*) and Wc(U10) side by side.

Subsequent analyses show that microwave thermal emission solutions incorporating (9) and (10) are in good agreement with microwave radiometer measurements over a wide range of frequency, incidence angle, and both V and H polarizations. Datasets used for the additional comparisons include six-frequency SFMR (S19), five-frequency WindSat (M09), and L-band airborne (Y10), Soil Moisture Active Passive (SMAP) (Y13, M14, Y16, M17), and Soil Moisture and Ocean Salinity (SMOS) (R16), as described in Hwang (2019) and HRMY. It is emphasized that existing direct observations of Wc are restricted to wind speeds lower than about 25 m s−1 and although the maximum wind speed of published C10 data is much higher, the data scatter is rather large in TC wind conditions. Applicability of (9) and (10) to TC wind conditions is inferred from good agreement between theoretical thermal emission computations and microwave radiometer observations, to be further discussed in section 2c.

The surface wave spectrum model H2018 described in Hwang and Fan (2018) and Hwang (2019) is used to compute the roughness term [(8)]. Independent analyses of H2018 have been performed using active and passive microwave measurements including GMFs of scatterometer L-, C-, and Ku-band backscattering radar cross sections (Wentz and Smith 1999; M14; Stoffelen et al. 2017), WindSat brightness temperature data (M09), and low-pass-filtered mean square slopes (Katzberg and Dunion 2009; Katzberg et al. 2013; Gleason 2013; Gleason et al. 2018) obtained from Global Navigation Satellite System reflectometry (GNSS-R). The details are given in Hwang et al. (2011, 2013), Hwang and Fois (2015), Hwang and Fan (2018), and Hwang (2019).

c. Comparison with field observations

As mentioned in section 1, several datasets of microwave radiometer measurements in high winds have been published (M09, Y10, Y13, K14, M14, R16, Y16, M17, and S19). These datasets are used to examine various formulations of C10 and Wc dependence on U10 (Hwang 2012, 2018, 2019; HRMY). Figure 1 summarizes the results from those studies and shows comparison of microwave thermal emission computations and field observations of Δep for the datasets mentioned above.

Fig. 1.
Fig. 1.

Calculated ΔeV and ΔeH at various microwave frequencies, and comparison with field data. The top two rows (M09 and S19; triangle for V and square for H) show (a) 6.69, (b) 6.8, (c) 10.7, (d) 18.7, (e) 23.8, and (f) 37.0 GHz. Sum, foam, and roughness contributions are given by black, cyan, and green curves; solid and dashed lines show vertical and horizontal polarizations, respectively. The two numbers in parentheses are frequency (GHz) and EIA. The bottom row (L band 1.41 GHz, θ = 40°) shows (g) ΔeV, Y16 and M17 (SMAP); (h) ΔeH, Y16 and M17 (SMAP); and (i) ΔeA, Y16 and M17 (SMAP) and R16 θ = 40° ± 0.1° (SMOS).

Citation: Journal of Physical Oceanography 49, 9; 10.1175/JPO-D-19-0061.1

Data from airborne SFMR 6.69-GHz (S19) and spaceborne WindSat five-frequency (M09) measurements are displayed in Figs. 1a–f; the two numbers in parentheses at the lower left of each panel are f (GHz) and θ. For the SFMR normal incidence data (S19) displayed in Fig. 1a, V and H are identical. The analytical solution (black solid line) is in very good agreement with data except for the maximum wind speed datum (56.9 m s−1), which is suspected of rain contamination; more details are given in S19 and appendix A of HRMY. For WindSat measurements (M09) displayed in Figs. 1b–f, the V and H data and analytical curves are shown with black markers and black lines, respectively; the maximum wind speed is 41.4 m s−1. Again, there is good agreement between analytical solutions and measurements for all frequencies and both polarizations.

The analytical EM model provides solutions of sum, foam, and roughness components, respectively Δep, Δepf, and Δepr, and they are illustrated with black, cyan, and green curves. For the H polarization, the roughness term (green dashed lines) is greater than the foam term (cyan dashed lines) over a wide range of wind speed. The minimum wind speed that Δepf exceeds Δepr is about 22 m s−1 for normal incidence (Fig. 1a), and greater than 50 m s−1 for Earth incidence angle (EIA) θ = ~53° (Figs. 1b–f). The exception to roughness term dominance is for the V polarization of C-band and higher frequencies near 53°EIA where ΔeVr crosses over from positive to negative (Hollinger 1971). The WindSat roughness term ΔeVr (green solid lines in Figs. 1b–f) is nearly zero or negative, and smaller than the foam term ΔeVf (cyan solid lines).

Figures 1g–i show L-band (1.41 GHz) data from SMAP and SMOS satellite missions. Analytical solutions of sum, foam, and roughness components are shown with black solid, cyan dashed, and green dashed–dotted curves. The SMAP data (Y16 and M17, shown with blue and magenta dots, respectively) report V (Fig. 1g) and H (Fig. 1h) polarizations at 40° EIA. The reference wind speed in Y16 is TC best track information with 90.2 m s−1 maximum. The reference wind speed in M17 is collocated SFMR measurements with 70.9 m s−1 maximum. R16 is from five years SMOS measurements of average excess emissivity ΔeA = (ΔeV + ΔeH)/2 containing about 300 TC interceptions with continuous EIA coverage between 10° and 65°. Here we consider only a subset of this database corresponding to the SMOS sensor intercepts with Category 4 hurricane Igor developed in North Atlantic in 2010 (Reul et al. 2012). The wind reference is H*WIND analyzed fields (Powell et al. 1998), with 44.3 m s−1 maximum wind speed after averaging H*WIND at the spatial resolution of the SMOS instrument (~43 km). Altogether, there are 304 602 (U10, ΔeA, θ) triplets. Figure 1i presents the SMAP ΔeA data (Y16 and M17, shown with blue and magenta dots, respectively) combined with the SMOS results extracted within 40° ± 0.1°EIA [2508 (ΔeA, U10) pairs] and given as red contour lines of data density. There is the expected large data scatter of these measurements under TC conditions, and analytical solutions (black lines) provide a good description of their wind speed dependence. The minimum wind speed that Δepf (cyan curves) exceeds Δepr (green curves) is about 45 m s−1 for ΔeV, 62 m s−1 for ΔeH, and 54 m s−1 for ΔeA.

It is gratifying to see that the analytical EM thermal emission model yields solutions in good agreement with a large variety of measurements at different frequencies, incidence angles, and both V and H polarizations. The capability of the EM thermal emission model to separate roughness and foam components presents an excellent opportunity to explore retrieval of whitecap coverage and its driving force (surface wind stress) from microwave brightness temperature measurements.

3. Whitecaps, surface wind stress, and microwave radiometer signal

The microwave thermal emission analytical solution Δep(U10) in fact depends on many more implicit ocean surface parameters and can be written as Δep[U10, Wc, u*, S(k, ϕ), …]. In this paper, we focus on Δep(U10, Wc, u*), which can be precalculated for retrieving U10 and/or Wc and/or u* from Δep. The precalculated solutions can be presented as lookup tables to serve as retrieval GMFs.

The retrieval procedure is illustrated in Fig. 2 as an example using the WindSat 6.8-GHz H polarization data of about 500 (U10, ΔeH) pairs with 24.8 m s−1 maximum wind speed; further discussions of WindSat data are given in section 4a and the appendix. Figure 2a shows Δep(U10) data with magenta circles and analytical solution with black solid line (polarization p is H in this example). Using precalculated Δep(U10, Wc, u*) solutions presented as a lookup table (Table 1), the same data can be presented as Δep(Wc) and Δep(u*) as shown with magenta circles in Figs. 2b and 2c, the corresponding analytical model solutions are given by black solid lines. The model solutions can then be used to obtain Wc and u* from Δep; the derived Wc and u* can be subsequently presented as functions of wind speed. For example, Fig. 2d shows the retrieved Wc(U10) results with magenta circles, and the red dashed–dotted line is the Wc(U10) model curve [(9)].

Fig. 2.
Fig. 2.

Illustration of whitecap and surface wind stress retrieval using Δep; WindSat 6.8-GHz horizontal polarization data are used for an example (p = H): (a) Δep(U10) and Δepf(U10), (b) Δep(Wc) and Δepf(Wc), (c) Δep(u*) and Δepf(u*), (d) Wc(U10) retrieved with Δep and Δepf, (e) comparison of modeled and retrieved Wc from Δep and Δepf, and (f) comparison of modeled and retrieved u* from Δep and Δepf. In (e) and (f), statistics (b0, b1, b2, and b3) of modeled and retrieved Wc and u* with Δep and Δepf are printed at the top.

Citation: Journal of Physical Oceanography 49, 9; 10.1175/JPO-D-19-0061.1

Table 1.

Lookup table (LUT) for retrieving Wc and u* from WindSat 6.8-GHz ΔeH observations. Additional LUTs for SFMR, WindSat, and L-band radiometers at selected incidence angles are given in the supplemental material. (WindSat 6.8 GHz, θ = 53.5°, p = H).

Table 1.

The analytical thermal emission computation can separate roughness and foam components: Δepr and Δepf, respectively. Using the foam component, that is, employing Δepf(Wc) and Δepf(u*), can improve the results of retrieved whitecap and surface wind stress. The “observed” foam component Δepf is calculated from observed Δep multiplied with the analytical ratio Δepfep (interpolated to wind speeds of observed Δep data). In Figs. 2a–c, the observed Δepf are shown with cyan pluses, and the corresponding model solutions Δepf(U10), Δepf(Wc), and Δepf(u*) are given by blue dashed lines. Retrieving Wc or u* from Δepf employs the same procedure outlined in the last paragraph for retrieving Wc or u* from Δep. The results of Wc(U10) obtained with Δepf are given with cyan pluses in Fig. 2d, showing less data scatter and in better agreement with the model curve (red dashed–dotted line) in comparison with those derived from Δep (magenta circles). Figures 2e and 2f compare modeled and retrieved Wc and u* using Δep (magenta circles) and Δepf (cyan pluses), again showing less data scatter and better accuracy in the results derived from Δepf compared to those obtained from Δep. The statistics of bias, slope of linear regression, root-mean-square (RMS) difference, and correlation coefficient (b0, b1, b2, and b3, respectively) of comparing modeled and retrieved Wc (%) and u* (m s−1) from Δepf and Δep are printed above Figs. 2e and 2f.

4. Result and discussion

a. Global coverage

Spaceborne microwave radiometers provide global coverage. Here we use WindSat data to demonstrate the retrieval of global whitecap coverage and surface wind stress. WindSat is a satellite-based polarimetric microwave radiometer developed by the U. S. Naval Research Laboratory (NRL) Remote Sensing Division and Naval Center for Space Technology for U.S. Navy and National Polar-Orbiting Operational Environmental Satellite System (NPOESS) Integrated Program Office (IPO). It was launched in January 2003 to demonstrate the ability to measure ocean surface vector winds with microwave radiometers from space. In addition to surface wind vector, WindSat also measures sea surface temperature, columnar atmospheric water vapor, and columnar atmospheric cloud liquid water (Gaiser et al. 2004; Bettenhausen et al. 2006).

Figures 3 and 4 give examples of retrieved whitecap coverage and surface wind stress over a period of about 10.2 h each in northern and southern winters on 5 January 2014 and 1 July 2014 with maximum wind speeds 29.5 and 27.9 m s−1. The retrieval lookup tables are given in the online supplemental material. Figures 3a and 4a and Figs. 3b and 4b show spatial patterns of Wc and u* obtained from 10.7-GHz ΔeH; Figs. 3c and 4c and Figs. 3d and 4d show Wc(U10) and u*(U10) obtained from 10.7-, 18.7-, 23.8-, and 37.0-GHz ΔeH; and their comparison with the Wc(U10) and u*(U10) models is illustrated with black dashed lines. Results derived from each frequency are averaged into 20 wind speed bins. Consistent Wc and u* retrievals are obtained from different microwave frequencies. To get an assessment of data scatter, unaveraged 10.7-GHz results are displayed with cyan dots in Figs. 3c and 4c and Figs. 3d and 4d.

Fig. 3.
Fig. 3.

Snapshots (~10 h) of WindSat global retrieval of (a) Wc and (b) u* on 5 Jan 2014 (in northern winter). The dependence on wind speed is given for (c) Wc and (d) u*, where bin-averaged results shown with colored markers are from four microwave frequencies identified in the legend; unaveraged results for 10.7 GHz are superimposed with cyan dots in the background.

Citation: Journal of Physical Oceanography 49, 9; 10.1175/JPO-D-19-0061.1

Fig. 4.
Fig. 4.

As in Fig. 3, but on 1 Jul 2014 (in southern winter).

Citation: Journal of Physical Oceanography 49, 9; 10.1175/JPO-D-19-0061.1

M09 represents WindSat Tbp measurements for years 2003 and 2004, and it includes much higher wind speed data (to about 41.4 m s−1 maximum) in comparison to those ~10-h snapshots shown in Figs. 3 and 4. M09 uses National Centers for Environmental Prediction (NCEP) General Data Assimilation System (GDAS) wind vectors and Special Sensor Microwave Imager (SSM/I) atmospheres for training and testing of a wind speed retrieval algorithm that can be applied globally and under all existing rain conditions and low wind speeds. H*WIND analyzed wind fields from 17 hurricanes during 2003 and 2004 are used for training and testing the wind vector retrieval algorithm under TC conditions. Retrieved whitecap and surface wind stress results using M09 WindSat data are shown in Fig. 5, they are in very good agreement with the Wc(U10) and u*(U10) models [(9) and (10)] illustrated with black dashed lines. The global coverage of satellite operation offers an opportunity to obtain measurements in high wind regions that are dangerous, expensive, and difficult to deploy ships or aircraft. More details on WindSat data analysis are given in the appendix.

Fig. 5.
Fig. 5.

Whitecap and wind stress retrieval from five frequencies of the M09 WindSat dataset and comparison with models (9) and (10): (a) Wc and (b) u*.

Citation: Journal of Physical Oceanography 49, 9; 10.1175/JPO-D-19-0061.1

b. Extreme conditions

As mentioned earlier, there are several published microwave radiometer datasets dedicated to TC extreme wind conditions. In particular, the maximum winds of Y16 and M17 are 90.2 and 70.9 m s−1, respectively. Both Y16 and M17 report SMAP radiometer data; the Y16 reference wind is TC best track maximum winds in both Pacific and Atlantic Oceans, whereas the M17 reference wind is collocated SFMR data. Figures 6a and 6b show retrieved Wc and u* from these two datasets using Δepf of both V and H polarizations; the retrieval lookup tables are given in the supplemental material. Statistics (b0, b1, b2, and b3) of comparing Wc(U10) and u*(U10) models with microwave-retrieved results for both datasets are printed at the lower-right corners. Slightly higher RMS difference (b2) and less-linear regression slope (b1) are found in Y16 compared to those in M17, most likely indicating a better quality of the reference SFMR winds used in M17 compared to the TC best track maximum winds used in Y16. The correlation coefficients (b3) are all better than 0.91 even for these extreme wind datasets.

Fig. 6.
Fig. 6.

Whitecap and wind stress retrieval of extreme wind cases of SMAP datasets (Y16 and M17) and comparison with models (9) and (10): (a) Wc and (b) u*; results obtained with both V and H polarizations are presented and statistics (b0, b1, b2, and b3) of comparing the modeled and retrieved Wc and u* with both polarizations are printed at the lower right corners.

Citation: Journal of Physical Oceanography 49, 9; 10.1175/JPO-D-19-0061.1

Another dataset of great interest is R16 SMOS ΔeA measurements, which have continuous θ coverage from 10° to 65°. Figure 7 shows retrieved Wc and u* using ΔeAf with EIA in the ranges of 11° ± 0.25°, 15° ± 0.25°, 20° ± 0.25°, …, 60° ± 0.25°, and 64° ± 0.25°; consistent Wc and u* retrievals are obtained and they are in good agreement with Wc(U10) and u*(U10) models shown with dashed lines. To get an assessment of data scatter, unaveraged 35° ± 0.25° results are shown in the background with cyan dots.

Fig. 7.
Fig. 7.

Whitecap and wind stress retrieval from the SMOS dataset (R16) and comparison with models (9) and (10): (a) Wc and (b) u*; bin-averaged results obtained for θ = 11°, 15°, 20°, …, 60°, and 64° are illustrated with various markers identified in the legend and unaveraged 35° results are shown with cyan dots in the background.

Citation: Journal of Physical Oceanography 49, 9; 10.1175/JPO-D-19-0061.1

c. Wave breaking inference

One of the primary reasons for studying whitecap coverage is to infer wave breaking properties. For example, a linear relationship between whitecap coverage Wc and wave breaking energy dissipation rate per unit surface area Et has been proposed by Ross and Cardone (1974) and Hwang and Sletten (2008). Figure 8 reproduces partially Fig. 6 of Hwang and Sletten (2008), showing Wc dependence on U10 and Et. The whitecap observations described in Hwang and Sletten (2008) are collectively referred to as MTRXLS (Monahan 1971; Toba and Chaen 1973; Ross and Cardone 1974; Xu et al. 2000; Lafon et al. 2004, 2007; Sugihara et al. 2007) and plotted with green dots in Fig. 8a. Here, whitecap observations by Callaghan et al. (2008) are also added (labeled C08 and plotted with magenta diamonds in Fig. 8a). The Et can be calculated for the four references reporting significant wave height Hs and dominant wave period Tp in addition to U10 (Toba and Chaen 1973; Lafon et al. 2004, 2007; Sugihara et al. 2007); these data are displayed with green circles and labeled TLS in the figure. Bin-averaged Et results are given by black circles in Fig. 8b and they can be approximated by the linear Wc(Et) function given by Hwang and Sletten (2008):
Wc=0.014(Et0.014),
where the unit of Et is watts per square meter (W m−2). Plotted in log–log scales in Fig. 8b, the linear function (11) deviates from a straight line when Et is small. Log–log scales are used because the data ranges of Wc and Et stretch from two to five orders of magnitude.
Fig. 8.
Fig. 8.

(a) Whitecap coverage dependence on wind speed; data are from observations tabulated in MTRXLS (Monahan 1971; Toba and Chaen 1973; Ross and Cardone 1974; Xu et al. 2000; Lafon et al. 2004, 2007; Sugihara et al. 2007) and C08 (Callaghan et al. 2008). The solid line is whitecap coverage model (9). (b) Whitecap coverage dependence on surface wave energy dissipation rate computed with wind and wave data reported in TLS (Toba and Chaen 1973; Lafon et al. 2004, 2007; Sugihara et al. 2007). The dashed line is the linear function (11) given in H08 (Hwang and Sletten 2008). [Partially reproducing Fig. 6 of Hwang and Sletten (2008)].

Citation: Journal of Physical Oceanography 49, 9; 10.1175/JPO-D-19-0061.1

The monotonically increasing trend of microwave excess emissivity with wind speed (Fig. 1) is a strong indication that surface wind stress and whitecap coverage also increase monotonically with wind speed. In TC wind fields (U10 > ~35 m s−1) the drag coefficient model (10), with C10U101, specifies that wind stress (proportional to u*2=C10U102) increases linearly with wind speed; and whitecap coverage in (9) increases slightly stronger than linear with wind speed (~U101.25) and reaches 100% at ~108 m s−1. Combining all the microwave radiometers discussed in this paper (SFMR, SMAP, SMOS, and WindSat), the retrieved whitecap and surface wind stress results are given in Figs. 9a and 9b. Applying the Et(Wc) linear dependence from (11), Et(U10) is given in Fig. 9c.

Fig. 9.
Fig. 9.

Whitecap and wind stress results combining SFMR, SMAP, SMOS, and WindSat datasets discussed in this paper: (a) Wc, (b) u*, and (c) energy dissipation rate Et converted from whitecap coverage obtained by microwave radiometers and employing the linear relationship obtained by Hwang and Sletten (2008).

Citation: Journal of Physical Oceanography 49, 9; 10.1175/JPO-D-19-0061.1

d. Remote sensing and ocean surface processes

Ocean remote sensing is interdisciplinary and requires coherent consideration from both remote sensing and oceanographic perspectives. In general, our understanding of the relevant oceanographic processes lags behind EM theories. Pertaining to forward computation in support of remote sensing of the ocean environment, particularly winds and waves, the three most relevant oceanographic parameters are the ocean surface roughness (wave) spectrum, whitecaps from wave breaking, and their driving force: surface wind stress. In this paper, we present a holistic approach incorporating all three oceanographic parameters in the analysis.

The approach is two-way. In forward computations, active and passive microwave remote sensing measurements are used to improve our models of C10, Wc, and S(k) as functions of wind speed U10. In reverse, the improved ocean modules [C10, Wc, and S(k)] provide feedback to improve and enhance the remote sensing effort to derive ocean parameters from microwave measurements.

In addition to wind velocity currently retrieved operationally, our analysis shows that the forward solutions of microwave radiometer thermal emission can serve as the GMFs for retrieving additional ocean surface properties, particularly surface wind stress and whitecap coverage, from microwave radiometer measurements. Furthermore, information such as wave breaking energy dissipation rate per unit surface area can be inferred.

5. Summary

The microwave radiometer signal from ocean surface is composed of two major components: roughness (surface waves) and foam (whitecaps). Both ocean surface roughness and whitecaps are driven by ocean surface wind stress, which is connected to wind speed by a drag coefficient. An extensive collection of microwave radiometer data provides the opportunity to critically examine various wind speed functions of drag coefficient and whitecap coverage by comparing microwave thermal emission model results with microwave radiometer measurements in a wide range of microwave frequency (1.4–37.0 GHz), incidence angle (0°–65°), both horizontal and vertical polarizations, and an expansive wind speed range covering calm to TC wind conditions. These analyses have shown that the whitecap and drag coefficient models (9) and (10) yield very good agreement between analytical microwave thermal emission computations and all the high-wind microwave radiometer measurements we have assembled, as summarized concisely in Fig. 1. The analytical thermal emission model quantifies the relative importance of roughness and foam contributions. In general the roughness term dominates over a wide wind speed range. Retrieving whitecap information using microwave radiometer measurements and based on analytical thermal emission models requires an accurate accounting of the surface roughness contribution.

With a microwave thermal emission model, Δep(U10, Wc, u*) and Δepf(U10, Wc, u*) analytical solutions can be precalculated and presented as lookup tables to serve as GMFs for retrieving Wc and u* from Δep and Δepf. Whitecap coverage and surface wind stress data derived from microwave radiometer measurements in extreme wind conditions and global oceans are presented in this paper and compared to models (9) and (10). In addition, breaking wave energy dissipation rate per unit surface area can be estimated by making use of its linear relationship with whitecap coverage [(11)] established from previous studies (Ross and Cardone 1974; Hwang and Sletten 2008). Based on the whitecap and surface wind stress models (9) and (10), under TC wind conditions (U10 > ~35 m s−1) surface wind stress increases with wind speed linearly and whitecap coverage increases with wind speed slightly stronger than linear (~U101.25) and reaches 100% at ~108 m s−1. Given the linear relationship between Et and Wc, the Et dependence on wind speed is expected to follow the same trend of whitecaps (Fig. 9).

Acknowledgments

This work is sponsored by the Office of Naval Research (Funding Doc. N0001416WX00044). We are grateful for the comments and suggestions from two anonymous reviewers. M. Anguelova, M. Bettenhausen, and P. Gaiser kindly provided the WindSat January and July 2014 data, and the related discussions. Other datasets used in this analysis are given in the references cited. The processing codes and data segments are also available by contacting the corresponding author. NRL Publication Number JA/7260–19-0353.

APPENDIX

Additional Information on the WindSat Analysis

For Figs. 3 and 4 in this study, we have used four high-frequency (10.7, 18.7, 23.8, and 37.0 GHz) WindSat data in January and July 2014, which are in northern and southern winters, respectively. The 6.8-GHz data are only available at a lower resolution (50 km × 71 km) compared to the four higher frequencies (25 km × 35 km). The 6.8-GHz data are used in Fig. 2 to serve as a retrieval example.

Data extracted from WindSat Sensor Data Record (SDR) and Environmental Data Record (EDR) include V and H brightness temperatures (TV and TH), EIAs (θ), sea surface temperature (Ts), wind speed (U10), and measurement location (latitude and longitude). The brightness temperature received at sensor antenna is processed to obtain the brightness temperature at sea surface by correcting for atmospheric emissions and cosmic microwave background radiation (Anguelova and Bettenhausen 2019). Rain-flagged data are excluded in this analysis.

The information of wind-related processes (whitecaps and surface wind stress in this study) is contained in the excess emissivity, which is a small fraction of the total surface emissivity ep = Tbp/Ts. The flat surface (specular) emissivity is estimated by the portion of data with U10 < 2 m s−1 (Fig. A1, measurements are shown with dots of different colors for different frequencies), which can be approximated by polynomial functions of Ts (black curves in the figure). These empirical e0p functions differ slightly for different datasets (the top row in Fig. A1 represents 5 January 2014 data shown in Fig. 3, and the bottom row represents 1 July 2014 data shown in Fig. 4). The coefficients of polynomial functions are listed in Table A1. The empirical e0p functions deviate from analytical solutions computed with single values of sea surface salinity and sea surface temperature (35 psu and 290 K are used and shown with red lines in the figure); the difference also reflects imperfection of corrections applied to obtaining the brightness temperature at sea surface from the brightness temperature received at antenna.

Fig. A1.
Fig. A1.

Determination of flat surface (specular) emissivity using data with U10 < 2 m s−1: (a),(c) e0H and (b),(d) e0V. Superimposed black lines are fitted polynomial curves; red lines are analytical solutions computed with s = 35 psu and Ts = 290 K. Top and bottom rows show results for data used in Figs. 3 and 4, respectively.

Citation: Journal of Physical Oceanography 49, 9; 10.1175/JPO-D-19-0061.1

Table A1.

Polynomial coefficients of WindSat flat surface (specular) emissivity: e0p=A2Ts2+A1Ts+A0.

Table A1.

Figure A2 shows excess emissivity Δep for the same period in Fig. 3; results for the same period in Fig. 4 are similar. Unaveraged data are displayed in the background with light colored dots (cyan for H and green for V) and bin-averaged results are given with blue markers (squares for H and triangles for V). They are in very good agreement with those reported in M09, which are superimposed in the figure with red markers (diamonds for H and triangles for V). Analytical solutions are in excellent agreement with measurements for the H polarization (dashed lines) and slightly underestimate the V polarization (solid lines) in the wind speed range between about 10 and 30 m s−1 (but within about 0.01 ΔeV magnitude).

Fig. A2.
Fig. A2.

WindSat Δep(U10) of Fig. 3 data (blue markers and light-colored dots for bin-averaged and unaveraged results, respectively), and comparison with M09 (red markers) and analytical solutions (black lines): (a) 10.7, (b) 18.7, (c) 23.7, and (d) 37.0 GHz. Mean and standard deviation of EIA are given in the second set of numbers inside parentheses at the upper-left corner of each panel.

Citation: Journal of Physical Oceanography 49, 9; 10.1175/JPO-D-19-0061.1

For θ in the range between 50° and 55°, the ΔeV dependence on wind speed is relatively mild in low to moderate wind speeds. The analytical solutions are in fact nonmonotonic for 18.7, 23.8, and 37.0 GHz. The nonmonotonic trend is also found in the M09 dataset: the lowest wind speed (11.6 m s−1) of the M09 37.0-GHz datum is negative; also, see Fig. 8 in Meissner and Wentz (2012). The lack of wind sensitivity makes it unsuitable to use WindSat ΔeV measured in the neighborhood of 50° to 55°EIA for retrieving whitecap and wind stress (as well as wind speed) except in very high winds. WindSat results of whitecap and wind stress retrieval presented in this paper are based on ΔeH. As a related note, for L band (~1.4 GHz) the critical incidence angle of wind insensitivity moves up to about 70° (see, e.g., Y10; Hwang 2012, 2019). Whitecap coverage and surface wind stress can be retrieved from the full EIA range of R16 SMOS dataset (Fig. 7).

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