We present estimates of whitecap coverage on a global scale from satellite-measured brightness temperature of the ocean surface. This is a first step in a larger framework aiming at more realistic modeling of the high variability of whitecap coverage as a function of wind speed and a suite of additional environmental and meteorological factors. The involvement of oceanic whitecaps in various physical and chemical processes important for climate studies such as production of sea-salt aerosols, enhancement of air-sea gas exchange, and influence on retrievals of ocean surface wind and ocean color motivates this effort. A critical review of the physical variables causing the high variability of whitecap coverage and existing approaches modeling this variability establishes the need for a database of whitecap coverage and concomitant measurements of additional factors. The necessity to build such an extensive database justifies the quest for a method estimating whitecap coverage from satellite data. We describe the physical concept, a possible implementation, error analysis, results, and evaluation of a method for estimating whitecap coverage from routine satellite measurements. The advantages of the concept and the drawbacks and necessary improvements of the implementation are discussed.
 Breaking waves in the ocean entrain air into seawater forming clouds of bubbles beneath and foamy patches on the sea surface. The fraction of the ocean surface covered with sea foam and mixed with bubbles is defined as whitecap coverage (or foam fraction), W. The global average has been cited to be 1–4% [Blanchard, 1963, 1983]. Whitecap coverage is usually modeled as a function of wind speed at 10-m reference height above the sea surface, U10. However, it exhibits high variability, which cannot be predicted with the wind alone. Various environmental and meteorological factors in addition to wind influence it [Williams, 1969; Monahan and O'Muircheartaigh, 1986].
 Whitecaps mark places in the ocean where various physical processes are either enhanced or completely different from those in and on surrounding seawater. Through these physical and many consequent chemical processes, oceanic whitecaps are directly and indirectly involved in the climate system. Inadequate modeling of the high variability of whitecap coverage introduces uncertainty in the modeling of all air-sea processes correlated with W. The importance of whitecap coverage for climate studies motivates the work presented here. The list below of air-sea processes associated with whitecaps justifies our efforts.
 Oceanic whitecaps mark areas with increased surface emission and brightness temperature at microwave frequencies [Ross et al., 1970; Williams, 1971; Smith, 1988a; Swift, 1990]. Together with the surface roughness, they are a key component of the signal used to obtain surface wind vector with satellite-borne radiometric and polarimetric instruments [Wentz, 1997; Yueh, 1997; Gaiser et al., 2004]. The global wind vector field is one of the initializing variables in climate models whose requirements for accuracy constantly increase. The accuracy of wind vector retrievals from physically based algorithms may improve if the geophysical model function includes foam emissivity and whitecap coverage.
 Including parameterizations of all these processes in climate models requires an estimation of global whitecap coverage. Currently, global whitecap coverage is estimated by combining a global wind field, U10, obtained from satellite-borne radiometers or scatterometers, and an empirical relation, W(U10). However, to obtain more accurate predictions of whitecap coverage, a model of W must account for its dependence on a suite of additional factors. To investigate correlations and develop physically sound models for these additional dependences, a database of whitecap coverage under various environmental and meteorological conditions is necessary. Since the existing photographic measurements of whitecap coverage are not enough to organize an adequate database of W with concomitant measurements of environmental and meteorological variables, an alternative approach for measuring whitecap coverage is in order.
 This paper documents results on the first step in this framework, namely estimating whitecap coverage on a global scale from satellite-measured brightness temperature of the ocean surface. Building on the existing knowledge of oceanic whitecaps, section 2 justifies the quest for a new way of measuring whitecap coverage by demonstrating its high variability, identifying the factors causing this high variability, reviewing the existing approaches of modeling it, and establishing the need for an extensive database of whitecap coverage and accompanying variables. Section 3 presents briefly the physical concept, implementation, and error analysis of a method estimating W from routine satellite measurements. Section 4 reports results on satellite-based estimates of whitecap coverage and evaluates them. Finally, section 5 discusses the advantages of the concept and the drawbacks and necessary improvements of the described implementation.
2. Oceanic Whitecaps
2.1. Whitecap Coverage Variability
 The lowest wind speed at which whitecaps may appear is around 3 m s−1 [Monahan and O'Muircheartaigh, 1986; Hanson and Phillips, 1999]. Certainly, wind speed is the main cause for the formation of whitecaps and both oceanographic and remote sensing communities have proposed many empirical expressions for the W(U10) relation, each developed as the best fit to data set(s) at specific locations and conditions. These various parameterizations are summarized in Table 1 and plotted in Figure 1. With a few exceptions, most of the proposed W(U10) expressions are a power law in the form aU10b with b typically around 3 or a(U10−c)3 with c loosely associated with the threshold wind speed for whitecap formation under the specific conditions of the measurements. This functional form of W(U10) conforms to Cardone's [1969, pp. 64–69] (also discussed by Monahan ) suggestion that whitecaps manifest the dissipation of excessive energy transferred from the air flow to the waves. Wu [1979, 1988, 1992b] expressed this on dimensional grounds as whitecap coverage, W, proportional to the cube of wind specified either in terms of friction velocity u* or wind at reference height z, Uz, e.g., W ∼ u*3 ∼ U103. Though measurements roughly confirm this physically sound conclusion, there are wide variations from one parameterization to another: the exponent b ranges from 1 (Bortkovskii , cold waters) to above 5 [Hanson and Phillips, 1999] and the threshold wind speed c is from 0.6 m s−1 [Reising et al., 2002] to above 6 m s−1 (Stramska and Petelski , undeveloped sea). Different values for b or c quantify different water temperatures (cold, moderate, warm), atmospheric stability (neutral, stable, unstable), or wind fetch and duration (developed, undeveloped sea) regimes. Figure 1 clearly demonstrates the wide variability of whitecap coverage, especially at low and moderate winds. This is upward of 3 orders of magnitude variability for winds of 5 m s−1, and nearly 2 orders of magnitude variability for winds of 10 m s−1. Such a high variability implies that other factors, beside the wind, are at play and models in terms of wind speed alone cannot predict W well under various conditions encountered over the globe.
Table 1. Parameterizations of Whitecap Coverage as a Function of Wind Speeda
 At different locations in the world ocean various environmental and meteorological factors act in concert but with different strengths and form a composite effect that either enhances or suppresses the effect of wind alone. Air-to-water energy input, sea state, and bubble lifetime are the physical quantities controlling the formation and spatial and temporal extent of whitecaps. Thus the variables that influence these quantities will influence whitecap coverage as well. Wind speed, U, atmospheric stability (the difference between seawater and air temperatures), ΔT, and surface current velocity, Uc, are variables necessary to completely describe the air-to-water energy flux and wind stress responsible for whitecap formation. Surface current velocity, Uc, wind fetch, X, duration of wind, d, sea surface temperature (SST), Ts, and concentration and type of surface active materials, C, affect sea state characteristics such as significant wave height, wave spectrum, wave dissipation rate, and wave age, and with that wave growth rate and the frequency of wave breaking. Thus these too affect whitecap formation and also determine the spatial extent of whitecap coverage. Finally, Ts, C, and salinity, S, affect water viscosity and surface tension. These, in turn, control (1) bubble formation and bursting by determining bubble size distributions when waves break and push air into the water, (2) bubble rise velocities through the water column to the surface, and (3) rates of coalescence and gravitational draining of bubbles floating on the surface. As a result, spatial extent and lifetime of whitecaps differ over the world ocean. Overall, besides wind speed, a suite of additional factors affect whitecap coverage, namely atmospheric stability, surface currents, wind fetch, wind duration, SST, salinity, and surfactant concentration, W(U, ΔT, Uc, X, d, Ts, S, C).
 How different environmental and meteorological factors affect whitecap coverage can be summarized as follows [Monahan and O'Muircheartaigh, 1986; Stramska and Petelski, 2003]: Even low winds, around 3 m s−1, may create whitecaps under unstable atmospheric conditions (ΔT > 0), while moderate winds of 6 m s−1 may not lead to whitecapping when the lower atmosphere is stable (ΔT < 0). Longer d produces a fully developed sea, which enhances W. In contrast, even high winds may produce fewer whitecaps if they blow for a short time. Fewer whitecaps form in places with limited X. Kraan et al.  documented a decrease in whitecap coverage as the current velocity increased and suggested an explanation with an interaction of current shear and long waves. With Ts increasing, water viscosity decreases, which facilitates wave breaking and prolongs the lifetime of an individual whitecap. Both processes increase W. Organic compounds, such as amino acids, lipids, fatty acids, proteins, and phenols released into seawater from living organisms [Pinet, 1992, p. 128], create a surface-active film on the open ocean surface which damps capillary and short gravity waves [Hühnerfuss et al., 1987; Alpers and Hühnerfuss, 1989]. This process slows down, or even prevents, the breaking process [Scott, 1986] yielding a decrease in W. Surfactants and salinity, S, lower the surface tension of seawater [Garrett, 1967; Scott, 1975] compared to that of fresh water. Systems with low surface tension require less work to create a new interface [Rosen, 1978]. Thus the air entrained from breaking waves in salt water ruptures into more and smaller bubbles compared to bubbles formed in fresh water [Cartmill and Su, 1993; Anguelova, 1997]. Surfactants quickly adsorb to the bubble walls stabilizing them against dissolution in the water column and inhibiting their coalescence and drainage at the ocean surface [Garrett, 1967; Rosen, 1978; Thorpe, 1982; Blanchard, 1983; Scott, 1986]. This results in more persistent and long-lived whitecaps in seawater than in fresh water [Monahan and Zietlow, 1969]. Small variations of S in the open ocean may cause only small variations in W, but large S differences, such as between open ocean and coastal zones, could invoke more significant changes in W.
2.3. Modeling the Variability of Whitecap Coverage
 The understanding that various physical, chemical and biological factors influence whitecap formation and coverage has been around since Williams  first suggested their possible effects on the W(U10) relation. Since the first field campaigns [Monahan, 1971; Nordberg et al., 1971; Ross and Cardone, 1974], measured whitecap coverage has been reported together with wind speed and additional variables such as surface water and air temperatures and wind fetch. Quantifications of the effects of some of these additional factors have been published.
 The usual approach when considering the effect of water temperature on whitecap coverage has been to divide the range of observed Ts values into subranges of cold, moderate, and warm waters. In each Ts subrange different exponents [e.g., Spillane et al., 1986] or even functional expressions [e.g., Bortkovskii, 1987, Table 2.1] are chosen for the wind speed dependence. With a similar approach, Stramska and Petelski  account for the wind duration effect by offering W(U10) relations for developed and undeveloped seas assuming that during their experiment wind duration, not fetch, was the variable determining the sea state. Monahan and O'Muircheartaigh [1986, equation 5] proposed the first explicit relation quantifying the effect of an additional variable, that of atmospheric stability, W(U10, ΔT). Expressions for W(U10, X) or W(X) in fetch-limited conditions have been only recently proposed [Xu et al., 2000; Zhao and Toba, 2001; Piazzola et al., 2002; Lafon et al., 2004]. The dependence of whitecap coverage on the remaining factors (Uc, S, and C) is only qualitatively discussed.
 Another approach to address the necessity to account for additional factors has been the parameterization of W with one parameter or a combination of parameters, which accounts for the action of several variables that affect wave breaking and whitecapping. Proponents of W parameterization in terms of u* or wind stress, τ, instead of U10 [Wu, 1979, 1988; Toba and Koga, 1986], have always had a strong point. Indeed, u* obtained with Monin-Obukhov similarity theory using diabatic profiles [Liu et al., 1979; Large and Pond, 1981; Fairall et al., 1996] can explicitly account for ΔT and Uc. Also, the roughness length, z0, with terms for smooth and rough flows [e.g., Smith, 1988b; Fairall et al., 1996, equation 25] can implicitly account for the factors affecting the wavefield, namely Uc, X, d, and possibly Ts and C. However, even rigorously estimated u* fails to remove the significant scatter of data in plots of W(u*). Compare, for instance, Figures 4 and 5 of Stramska and Petelski  or Figures 2 and 3 of Lafon et al. . A large body of recent publications argues that wavefield characteristics must be explicitly included in z0 for better results [Donelan et al., 1993; Fairall et al., 2000; Taylor and Yelland, 2001; Bourassa, 2004]. This argument is further supported by parameterizations of W in terms of wave spectrum [Ross and Cardone, 1974; Snyder and Kennedy, 1983], wave age [Kraan et al., 1996], wave dissipation rate [Hanson and Phillips, 1999], and the breaking wave parameter (a dimensionless parameter combining u* and wave spectrum) [Zhao and Toba, 2001], all of which demonstrate the strong correlation of W with wavefield characteristics. However, none of them alone suffice to completely describe W variability for, while all these parameterizations would account for energy input and to some extent for wavefield, they do not explicitly address the variables responsible for the whitecap lifetime, Ts, C, and S.
 In summary, the existing knowledge of whitecap coverage helps to identify and qualitatively understand the action of the additional factors affecting W. The effects of some of these factors have been quantified either explicitly, e.g., W(ΔT) and W(X), or implicitly, e.g., W(u*). However, quantification of the effects of all additional factors in the form W(U, ΔT, Uc, X, d, Ts, S, C), admittedly cumbersome, or W(u*, Ts, S), is missing. To extract physically sound model(s) for the effects of these additional factors, a database of whitecap coverage under various environmental and meteorological conditions accompanied with simultaneous measurement of variables describing these conditions is necessary. Do existing measurements of whitecap coverage provide enough data to compile such a database?
2.4. Whitecap Coverage Measurements
 Traditionally, whitecap coverage is determined from still photographs or video images of the sea state collected from research platforms, ships, and aircraft. Facts for 28 data sets of W are summarized in Table 2 (we do not claim that this list of data sets is exhaustive). Figure 2 shows the locations of measurements. Though useful for gaining knowledge on whitecap coverage, the existing data sets do not provide enough information to model its high variability. A database for W built from the existing photographic measurements (here and onward under “photographic measurements” we mean both photographic and video measurements) of whitecap coverage would have the following weak points.
Table 2. Data Sets of Whitecap Coverage Observationsa
Data Set Number
Relative Error, %
U10 Range, m s−1
Add. param. ΔT, S, X , d, C, Uc
Listed chronologically according to the time of the field campaign (time column).
 First, Figure 2 reveals the patchiness of the conditions represented. Most of the data are collected in cold waters; only 5 data sets (156 total data points) represent warm water conditions (Ts > 17°C), see Table 2. With the exception of data sets 10, 13, and to some extent 25, all data have been collected in coastal zones or in confined fetch-restricted seas. Also, only one data set is reported for the Southern Ocean. Overall, experiments conducted over a time span of 42 years have provided 853 data points (not including Mediterranean Sea data reported by Villarino et al. ). No measurements are available for vast areas of the ocean, especially in the Southern Hemisphere. Thus existing data sets largely under represent open ocean conditions and areas with long fetches and persistent winds.
 Another issue with the photographic database is that there is not sufficient documentation of the meteorological and environmental conditions accompanying the whitecap coverage measurements. The conditions encountered during various experiments cover a wind speed range of 0.1–25 m s−1 (Figure 3a), an atmospheric stability range from −8 to + 12°C, and water temperatures from −1.7 to 30.55°C (Figure 3b). While the wind speed and stability conditions are well represented and ensure an empirical derivation of W(U10) and W(ΔT), the Ts range is presented in discrete intervals and cannot be used to extract well constrained relations for W(Ts). Only two of the listed data sets (27 and 28) report accompanying measurements of S. Five data sets report tabulated values for fetch. Only Kraan et al.  report concomitant data for Uc. Wind duration and presence of surfactants are not reported quantitatively.
 Finally, photographs and video images register well the more visible active whitecaps, stage A in Monahan and Woolf's  terminology, while aged whitecaps (stage B), which are thinner and less bright, can be easily overlooked. Since aged whitecaps cover much larger areas than freshly generated active whitecaps [Monahan, 1989], measuring whitecap coverage from photographs and video images tends to underestimate W, especially at low and moderate winds. Moreover, the oblique angle of observation in the photographs and video images prevents detection of the B stage of the whitecaps and introduces additional underestimation; see for example area 2 in Figure 2 of Stramska and Petelski .
 In summary, the existing measurements of whitecap coverage, though of high quality, are not sufficient to quantify the dependence of W on other environmental and meteorological variables in addition to wind speed. Therefore, to model the high variability of whitecaps, a database of W over the entire globe is needed, and this requires an alternative approach for estimating whitecap coverage. Can we use satellite measurements?
2.5. Remote Sensing Signature of Whitecaps
 Being a mixture of air and water, both foamy whitecaps on and bubbly clouds below the surface have dielectric properties very different from those of seawater and this determines their specific signature for remote sensors. Whitecaps can be detected from space-borne remote sensors in various portions of the electromagnetic spectrum. They appear as high reflectivity in the visible or high emissivity in the microwave or a combination of reflectivity and emissivity signals in the IR [Whitlock et al., 1982; Koepke, 1984, 1986; Frouin et al., 1996; Kokhanovsky, 2004; Marmorino and Smith, 2005]. Any of these signals can be used for detection of whitecaps. The preferred choice, however, is the microwave region (frequency of 1 GHz to 3 THz or wavelength of 10 to 0.01 cm) because atmospheric interference is a more manageable problem compared to visible and IR wavelengths [Gordon and Wang, 1994; Swift, 1990]. The variable measured at microwave frequencies and suitable for whitecap coverage detection is brightness temperature, TB, which is connected with the emissivity, e, of foam-covered ocean through the physical temperature, Ts, of the seawater: TB = eTs.
 At microwave frequencies, the radiation available for remote sensing emanates from a thin layer (penetration depth) at the surface. Depending on the wavelength and the dielectric properties of the sensed media (water or foam), this penetration depth differs. For seawater it is from less than a millimeter at 37 GHz to a few centimeters at 6 GHz. For foam with different content of air and water the penetration depth varies over a wider range. Thus passive microwave sensors detect the surface part of the whitecaps, that is, the floating bubble rafts at the surface, not the bubble plumes below. At lower frequencies, however, bubble plumes below thin foam patches can be sensed.
 The use of microwave frequencies to diminish atmospheric interference raises, however, the question of losing resolution. Indeed, none of the current satellite-borne microwave sensors, even with the smallest antenna footprint of 4 km × 6 km (AMSR-E, 89 GHz [Kawanishi et al., 2003]), can resolve an individual whitecap having a length scale of at most 10 m [Bortkovskii, 1987; Dahl and Jessup, 1995]. Whitecap coverage detection, however, does not require resolving and counting individual whitecaps. Rather, what is of interest is how much the average emission of a given ocean area changes with whitecaps appearance and how well these changes can be retrieved from measured data.
3. Method Estimating Whitecap Coverage
3.1. Physical Concept
 The concept of estimating whitecap coverage on a global scale from satellite data relies on changes of ocean surface emission at microwave frequencies induced by the presence of whitecaps. Ocean surface emissivity, e, is a composite of two main contributions: emissivity due to the rough sea surface, er, in places free of whitecaps (1 − W), and emissivity due to foam, ef, in places covered with whitecaps W. The composite surface emissivity therefore can be presented as [Stogryn, 1972]
Provided that the emissivities in (1) can be obtained, whitecap coverage can be determined as
In (2), e can be retrieved from satellite measurements with appropriate atmospheric correction, while emissivities er and ef can be computed using analytical or empirical models. Since e obtained for each point on the globe is a measure of ocean emissivity as it is created by the specific environmental and meteorological factors at this point, the satellite-measured W values will contain information for the additional factors and be more realistic than W predictions from a model developed from regional data elsewhere.
 The surface emissivity model (1) appears deceivingly simple. There are two major requirements for the applicability of (1), which are difficult to fulfill. First, the models for er and ef must clearly separate these two emissivities: er must represent rough sea emission not contaminated by foam emission and ef must strictly represents emissivity of foam. While even simple foam emissivity models can guarantee the latter, existing models for rough surface emission most certainly contain foam contributions making the former the more challenging task. Second, only well validated models for er, ef, and the atmospheric correction of e can guarantee the true utility of (1). However, the existing uncertainty in validation of atmospheric terms, the continuous development of rough surface models, and the insufficient knowledge of foam emission all demand tuning of some parameters in or applying empirical corrections to those models. Moreover, the lack of whitecap coverage values representing a wide range of conditions impedes reliable constraints on such tuning and empirical corrections.
 However challenging, these difficulties are by no means prohibitive. In fact, the idea of using a surface emissivity model (1) in combination with satellite data to obtain whitecap coverage is not completely new and has been tried before. In developing forward models of ocean microwave emission for geophysical retrieval algorithms in the early 80s, the remote-sensing community has used (1) and measurements of TB from the Scanning Multichannel Microwave Radiometer (SMMR) to infer foam coverage [Pandey and Kakar, 1982; Wentz, 1983]. The need to measure whitecap coverage on a global scale and model its high variability more realistically clearly calls for a renewed effort aimed at assessing the feasibility of obtaining W from routine satellite measurements.
 In the following sections, using current better calibrated satellite data, we demonstrate the feasibility of the concept and present the first global estimates of satellite-based whitecap coverage. In this endeavor we do not seek the most rigorous models for computing the emissivities in (2). Rather we use readily available models and empirical parameterizations and accept simplifying assumptions that would allow the implementation to advance to a reasonable end.
3.2. Analytical Expressions
3.2.1. Surface Emissivity e
 The composite surface emissivity, e, can be retrieved from satellite-measured brightness temperature, TB, of the ocean surface. TB, registered by a microwave radiometer viewing the ocean from a satellite, is given by the radiative transfer equation [Stewart, 1985; Swift, 1990]:
Here only the first term, which gives the ocean surface emission influenced by the atmospheric transmission, t, carries information regarding W. The remaining three terms represent the contribution of the atmosphere, namely upwelling and downwelling atmospheric radiation, TBU and TBD, and cosmic background radiation TCB. The factors 1 − e = r, t, and t2 account for the radiation reflected from the ocean surface back to space and its attenuation on the way up and down through the atmosphere. We neglect the so-called omega term [Wentz, 1997], which accounts for nonspecularly reflected downwelling radiation. Solving (3) for e yields the emission from the ocean surface only:
All quantities in (4) may be either measured or analytically evaluated. Satellite-borne sensors provide daily measurements of TB and Ts. Wentz  derived approximate formulae for the atmospheric terms TBU and TBD as a function of columnar water vapor, V [mm], and cloud liquid water, L [mm]. Both of these are derived as geophysical products from measured TB. The cosmic background is known, TCB = 2.725 K [Smoot and Scott, 2000]. The atmospheric transmittance, t, at microwave frequencies involves four major components due to rain, cloud liquid water, molecular oxygen, and water vapor [Wilheit et al., 1980; Swift, 1990; Wentz, 1997]. Correction for rain is a complex problem, thus we model the transmittance of the nonraining atmosphere. The transmittance for a one-layer atmosphere along a viewing path is approximated with [Wentz, 1997]
where θ is the incidence angle of the sensor (the angle measured from the normal to the probing beam), and k is attenuation coefficient accounting for the effects of oxygen with absorption coefficient aO, of water vapor with aV, and of cloud liquid water with aL. Wentz [1997, equations 20–23] gives expressions for each of these absorption coefficients as a function of V, L, and Ts.
3.2.2. Rough Sea Emissivity er
 Over foam-free areas of the ocean surface at low to moderate wind speeds (<10 m s−1), surface roughness is the major contributor to changes of ocean surface emission and consequent changes of brightness temperature [Stogryn, 1972; Swift, 1990]. To model the emission of a rough sea, we have adopted the approach of Pandey and Kakar . The emissivity of rough sea surface, er, is considered as er = es + Δer, where es is specular emissivity of a flat ocean surface, and Δer accounts for changes of es due to wind induced surface roughness.
 Specular emissivity is obtained as es = 1 − rs, where rs is specular reflectivity calculated with the Fresnel formula [e.g., Swift, 1990, equations 6 and 7]. The calculation of rs requires the dielectric constant of seawater, ɛ, usually modeled with the Debye equation [Rosenkranz and Staelin, 1972]. The dielectric constant of seawater is a complex number, ɛ = ɛ′ − iɛ″, whose real component, ɛ′, represents the actual magnitude of the dielectric constant and the imaginary part, ɛ″, is a measure of the attenuation (losses) of incident radiation in the material:
Here ω = 2πfr is the frequency of the radiation (in radians) interacting with the material, fr is the frequency in Hz, ɛ∞ is the dielectric constant at infinite frequency, ɛs is the static dielectric constant, τ is the relaxation time, σ is the ionic conductivity of water, and ɛ0 is the permittivity of free space. Klein and Swift [1977, equations 13–18] proposed empirical expressions for the static dielectric constant, ɛs (Ts, S), and relaxation time, τ (Ts, S), as functions of seawater temperature, Ts, and salinity, S. Values for ɛ∞, ɛ0, and σ are available from the literature [Hasted, 1973; Stewart, 1985]; fr, thus ω, is chosen (section 3.3.1).
 We model the surface roughness correction, Δer, for both horizontal and vertical polarizations, with empirical expressions cited by Pandey and Kakar , but do not use the constant bias that they introduce
Here hi and vi are coefficients (Table 3). U10 values are derived as a geophysical product from SSM/I-measured TB analogously to V and L. The rationale of choosing these simple empirical expressions is that they are developed using Hollinger's  data for which the effect of foam has been excluded, thus providing a clear separation between the contributions of roughness and foam in (1) and (2).
 Foam emissivity is obtained as ef = 1 − rf, where rf is foam reflectivity calculated with the Fresnel formula. The dielectric constant of foam is determined as [Troitsky, 1962; Droppleman, 1970; Wentz, 1974]
where Q is the ratio of the amount of water to total amount of air-water mixture within a unit volume. A more informative quantity for foam is the void fraction, α, defined as the ratio of the amount of air to the total amount of air-water mixture in a unit volume; the higher the void fraction, the more air the foam contains. Both these quantities are simply related as α = 1 − Q.
 For the calculations of foam dielectric constant, we choose a void fraction α = 98% (Q = 2%). This choice is not arbitrary. This value is chosen to account for two main characteristics of microwave emission from sea foam: (1) high, black-body-like emissivity [Williams, 1969; Rose et al., 2002] and (2) a decrease of emissivity as foam thickness decreases [Droppleman, 1970]. According to Droppleman's  model, with the choice of 98% void fraction, the computed ɛf and ef represent all whitecaps thicker than 6 mm. Thinner foam layers will be missed and this may introduce some underestimation of W. This underestimation, however, is compensated for by our assumption of a foam layer with constant void fraction instead of a gradual change from ≈100% at the surface to ≪1% within the bubble clouds. Understanding the possible underestimation and overestimation of W with a choice of a constant void fraction of 98%, we believe that, compared to photographic measurements, this method evaluates more adequately the whitecap coverage because it “feels” both the thick active whitecaps in their initial A stage, and, though not all, most of the B stage of decaying whitecaps.
 Though our approach for calculating foam emissivity ef differs from existing empirical and analytical models [Ulaby et al., 1986, chap. 18], it is suitable for the purpose of proof of feasibility. Indeed, it oversimplifies the foam emission problem considered rigorously in analytical models [Droppleman, 1970; Raiter and Sharkov, 1982; Chen et al., 2003], yet it has a stronger physical foundation than the empirical models [e.g., Stogryn, 1972] because it introduces the necessary dependencies of ef on θ and fr via rf and also involves the specific features of foam as a medium via ɛf.
 Computations of the emissivities in (2) require data for brightness temperature, TB, water vapor, V, cloud liquid water, L, wind speed, U10, SST, Ts, and salinity, S.
3.3.1. SSM/I Data for TB, U10, V, and L
 Special Sensor Microwave Imager (SSM/I) provides TB, U10, V, and L daily on a global scale. SSM/I is a passive microwave sensor, which detects natural microwave emission from the Earth's surface and atmosphere at four frequencies (19.35, 22.2., 37.0, 85.5 GHz) and horizontal (h) and vertical (v) polarizations [Hollinger et al., 1990; Wentz, 1997]. Brightness temperature TB in the range from 100 to 300 K is the basic information the SSM/I collects. Values for U10, V, and L are derived as geophysical products from TB.
 The Global Hydrology Resource Center (GHRC) at Marshall Space Flight Center (MSFC), NASA, distributes TB, U10, V, and L data processed with Wentz's  algorithm in full (swath) and reduced (gridded) resolution in hierarchical data format (HDF) files (http://ghrc.msfc.nasa.gov). Data used in this work are in arrays of 720 × 360 elements representing Earth's surface in 0.5° × 0.5° gridded maps (54 km × 54 km at the Equator). While the TB values are not corrected for atmospheric effect, the U10 values are for the ocean surface. Valid U10 values range from 0 to 40 m s−1, V values are in the range of 0 to 10 g cm−2, and L values are from 0 to 1000 mg cm−2. For the computations, the units of V [g cm−2] and L [mg cm−2] are converted to [mm] using the relation 1 g m−2×10−3 = 1 mm [Wentz, 1997].
 For the estimation of W we choose to use 19.35 GHz, h polarization, for the following reasons. First, changes in ocean surface emissivity should be predominantly due to surface roughness and presence of foam, and not to other factors at the chosen frequency. Ocean emissivity changes not only with surface roughness and the presence of sea foam, but also with salinity, S, and seawater temperature, Ts. Salinity influences ocean emission weakly for frequencies from 5 to 50 GHz, and contributes more strongly for frequencies below 5 GHz [Wilheit, 1978]. At an incidence angle of 55° over the range of 0°–30°C, brightness temperature of the ocean surface, TB, is independent of Ts (i.e., ∂TB/∂Ts ≅ 0) only for two frequencies: around 1.5 GHz and 27 GHz [Wilheit, 1978, Figure 5]. Considering the strong effect of S at low frequencies, the only suitable choice fulfilling the first requirement for the SSM/I incidence angle of 53.4° is around 23 GHz. Second, at the chosen frequency, the atmospheric effects need to be as little as possible. For SSM/I frequencies this requirement is fulfilled for 19 and 37-GHz channels. Combining these possible choices with the outcome of the first requirement singles out 19 GHz as the more suitable frequency. The choice of h polarization is based on results of radiometric experiments showing that the h polarization of TB has higher sensitivity to changes in surface wind speed, and hence to formation of whitecaps [Hollinger, 1971; Webster et al., 1976; Wilheit, 1978; Pandey and Kakar, 1982; Wang et al., 1995]. A 1-m s−1 change of wind speed invokes a change of about 0.5 K in vertically polarized TB while horizontally polarized TB changes with about 1.2 K. The h polarization signal includes both surface roughness and foam effects, which, we believe, are well separated with our choice of model for roughness emissivity (section 3.2.2).
3.3.2. AVHRR Ts Data
 The advanced very high resolution radiometer (AVHRR) provides sea surface temperature, Ts, on a daily basis. AVHRR is a visible/infrared multispectral scanner, which registers the Earth/atmosphere radiation in five channels. The Physical Oceanography Distributed Active Archive Center (PODAAC) at the Jet Propulsion Laboratory (JPL), NASA, distributes global maps of SST data in several temporal and spatial resolutions in various formats including HDF (http://podaac.jpl.nasa.gov/sst/sst_data.html). For consistency with the resolution of the SSM/I data sets, Ts data gridded at 0.5°×0.5° resolution are used in this study. The SST values are obtained with the Pathfinder SST algorithm. The coefficients of the algorithm are calculated by regressing observations of satellite skin SST to buoy measurements of bulk SST thus computing “pseudo-bulk SST” values [Emery et al., 2001]. Therefore the error introduced in the computation of emissivities (e, er and ef) from the difference between skin and bulk SST is not significant, especially at 19 GHz.
 We have used the so-called “best SST” product, which retains only pixels with the highest quality, discarding areas with clouds and areas from the far and distorted portion of the swath. As a result, there is not complete coverage within satellite passes. Because all other data sets used for the computations have more complete coverage, the daily Ts maps determine the cell number and locations for which all necessary data exist and match. Thus, from each Ts map, a mask containing pixels available for the computations is created for each day.
 The range of values used for the calculations is −1.8 to about 33°C. We discarded extremely low SST values (below −1.8 °C) because they are most probably attributed to seawater mixed with ice (slush). Since the emission of sea ice is as high as that of whitecaps, their signals cannot be distinguished. Discarding Ts < −1.8 removes about 2% of all available Ts values.
3.3.3. WOA98 S Data
 The World Ocean Atlas 1998 (WOA98) provides global maps of seawater salinity, S, at 33 standard levels covering depths from 0 to 5500 m [Levitus et al., 1998]. The WOA98 is based on the extensive World Ocean Database 1998 (WOD98) of the National Oceanographic Data Center (NODC), which contains more than 4 million in situ data entries measured with various instruments including historical oceanographic records, bottle seawater samples (ocean station data), and conductivity-temperature-depth (CTD) instruments. Data are offered as text files, which contain several “stacked” 10 × 6480 arrays, one for each depth level (http://www.nodc.noaa.gov/OC5/data_woa.html). We use 1° × 1° maps of monthly climatological means of S at the surface, i.e., the first 10 × 6480 array in a file for a given month. This array is rearranged into 360 × 180 array to represent a 1° × 1° map and then resampled via bilinear interpolation to obtain a 0.5° × 0.5° map (720 × 360 array).
3.3.4. Data Preparation
 Data sets of TB, V, L, U10, and Ts for all 365 days and S for all 12 months of 1998 are used. Data are first processed to obtain consistency in the spatial resolution, validity of the values, unification of the units, and spatial and temporal matching. Next, wind, rain, and clear sky masks are prepared for each day and applied to all data.
 The wind mask is extracted from the daily U10 maps. The wind mask favors cells with wind speeds ≥3 m s−1, the wind speed for whitecap inception, and discards cells (puts 0s) with lower wind. Very high winds, U10 > 35 m s−1 are also excluded since the SSM/I is not designed for high winds and its performance deteriorates under gale conditions. The wind mask removes about 2% of the pixels representing the ocean. An examination of data for the entirety of 1998 showed that wind speed is rarely above 26 m s−1.
 Since the atmospheric transmittance obtained with (5) is for a nonraining atmosphere, a rain mask is necessary. A cell is considered rain-free when two requirements, formed from h and v polarizations of TB at 19 and 37 GHz, are fulfilled simultaneously [Goodberlet et al., 1989]:
where T0 and T1 have different values depending on the latitude (Table 4). The rain mask removes about 14% from the useful “ocean” pixels. Apparently most of the removed cells are associated with high Ts, which could introduce bias in the distribution of Ts values toward lower temperatures. Figure 4a displays the distributions of Ts for one day (27 March 1998) without (black bars) and with (white bars) the mask applied, and the percentage of removed cells for each temperature bin (gray circles and solid line with axis at right). Indeed, the rain mask removes more cells with Ts in the range of 25°–33°C (about 34%) than with lower Ts values (15–25% for 5°–25°C). However, it also removes many cells, around 30%, for the lowest SST. The shape of the masked distribution, however, does not change significantly compared to the initial distribution. There is not noticeable skewness toward lower Ts values. In addition, the averages of the initial (20.02°C) and masked (19.22°C) Ts values differ by only 4%. Thus, despite the apparently preferential removal of high and low Ts, the effect of the rain mask is still tolerable.
Table 4. Temperatures Used in Condition (9) for a Rain Maska
 The clear sky mask, prepared from daily L maps, discards cells with high cloud liquid water content leaving clear sky cells with L ≤ 5 mg cm−2 = 0.05 mm [Wentz et al., 1980]. The expected adverse effect of this mask is the introduction of a bias toward lower wind speed values, thus missing locations with high whitecap coverage. Figure 4b shows the distributions of U10 for the same day (27 March) without (black bars) and with (white bars) the mask applied, and the percentage of removed cells for each wind speed bin (gray circles and solid line with axis at right). Only wind speed bins with more than 200 points are considered; for wind speeds above 22 m s−1 there are very few points in a bin, which compromises the statistics. Figure 4b demonstrates that the removal of wind speed values is roughly proportional to the amount of data in each bin leading to a decrease in the absolute number of cells available for retrieval of whitecap coverage, but not changing the shape of wind speed distribution. The average of the initial wind speed values is 10.53 m s−1, while that of U10 values remaining after application of the mask is 10.5 m s−1. Obtaining W under clear sky conditions, we decrease the uncertainties that would arise from the difficulties in parameterizing and validating cloud liquid water product, L, from radiometric measurements [Wentz, 1997]. Once the feasibility of satellite-based estimates of W is tested, the task of retrieving whitecap coverage under cloudy conditions can be pursued. The application of a clear sky mask removes up to 40% of the “ocean” pixels. For the remaining 60% of “ocean” pixels, we assume L ≅ 0, thus aL ≅ 0. This yields a modified attenuation coefficient in (5b), k = aO + aV, where the absorption coefficients of oxygen and water vapor are determined with high confidence.
 These three masks for wind, rain, and clear sky, together with the mask matching SSM/I products with available Ts, combine to form one composite mask. This composite mask is applied to S, Ts, TB, U10, and V, and with that, all necessary data sets are ready for the computation of the emissivities and W in (2). On that particular day of 27 March the composite mask removes about 83% of the initial ocean pixels for TB, leaving about 15,800 cells available for W estimation. These numbers cited for 27 March 1998 vary from variable to variable (U10, V, Ts, S) and from day to day, yet remain of the same order of magnitude. For all days of 1998, the number of pixels useful for W estimation ranges from a minimum of about 6,700 in November to maximum of 27,000 in October. This constitutes 4% to 17% of all pixels representing the oceans on a 0.5° × 0.5° global map.
3.4. Error Analysis
 The method for estimating global whitecap coverage, W, uses many measured and calculated quantities. Assuming that the models used (section 3.2) are exact, that is, there is no modeling error, the main source of error is the uncertainties in data measurements. These are carried over to the calculated variables and ultimately to the final result. To determine the uncertainty with which the method retrieves W, an analysis of the error propagation and the contributions of the various quantities to the error of W has been made using the approach outlined by Bevington [1969, chap. 4].
 The analysis of each investigated quantity starts with two considerations: (1) on which variables this quantity depends, and (2) which covariant terms are likely to play a role. The error analysis derives the variance of calculated W, σW2, as a function of the variances of the four emissivities and two covariant terms:
where the sensitivity coefficients Wij are calculated using the computed emissivities (Appendix A). The variance of each emissivity (σe2, σes2, σef2, and σer2) is derived as a function of the basic variables whose measurement errors influence them, namely TB, V, U10, Ts, S, ɛ∞, σ, θ, and Q, and whose errors propagate to the errors of the emissivities. For instance, composite sea emissivity emerges as a function of four basic variables, e = f(TB, Ts, V, θ), while more variables affect foam emissivity, ef = f(Ts, S, θ, σ, ɛ∞, Q). The variances of the four emissivities in (10) are listed in Appendix A. The variances and standard deviations of the basic variables are either known from their measurement and calculation or are chosen (Table A1).
4. Whitecap Coverage From Satellite Data
 Having all necessary analytical and error expressions, initial values, and prepared data at hand, the calculation of the emissivities and whitecap coverage in (2) proceeds. On a global map for 27 March 1998, specular emissivity es remains relatively low and varies in a narrow range, from 0.255 to 0.285, conforming to the contention that in the microwave range a smooth flat ocean is a cold body with low emissivity. Emissivity due to roughness, Δer, ranges from 0.0095 to 0.0832, adding little but a measurable correction to es as the wind roughens the sea surface. As expected, foam emissivity, ef, has high values, from 0.913 to 0.942. Finally, composite seawater emissivity, e, ranges from 0.25 to 0.45. With these values, the range of estimated whitecap coverage for 27 March 1998 is from less than 1% to about 24% with 97% of all estimated values in the range of 0.6% to 6%.
Figure 5a shows the global spatial distribution of monthly mean whitecap coverage for March 1998. Whitecap coverage over most of the world ocean is up to 4%. The lowest whitecapping, from less than 1% up to 2%, is evident along the equator, on the western edges of the continents, and east of the tip of South America. The highest whitecapping, up to 6%, is observed in the zonal belts of the trade winds (5° to 30° N and S) and the prevailing westerlies (30° to 60° N and S). The average whitecap coverage for March 1998 in the northern hemisphere is 3.2%, and in the southern hemisphere it is 2.7%.
 Retrieving W at several different values of the void fraction α investigates the effect of the void fraction choice. In Figure 6 the distributions and averaged W at α = 99%, 95%, 85% and 60% are compared with those obtained with α = 98% (equivalent to Q = 2%). The trend is: with α decreasing, the averaged W increases and the distributions become wider, featuring more high W values. The reason is that the lower α (i.e., the more water, Q, the foam contains), the lower foam emissivity ef until eventually it approaches the value of er. With ef lower, (2) gives higher W. For any α in the range of 95–99%, the distributions do not change significantly, and the averaged W differ at most by 23%. As α approaches 85%, the average W is higher than the previous photographic estimates. At α = 60%, W achieves unrealistically high values, including >1. In conclusion, void fraction serves as a tuning parameter for the performance of the method and the choice of α = 98%, which is roughly in the middle of the range giving the most reasonable W values, seems appropriate.
 For each daily map of W a map of standard deviation, σW, is also computed using (10); a relative error for each estimated W value is thus available as σW/W in %. The relative errors of estimating W for 27 March 1998 vary widely, from 9% to more than 6,000%. As anticipated from the analytical investigation of the error [Anguelova, 2002] and previous experiences [Blanc, 1987; Andreas, 1991], high error under certain conditions is not a surprise. Rather the question is: what is the acceptable error for W estimation? An arbitrary choice of 30% relative error as a criterion for a reliable estimation of W deems only 48% of all retrieved W values as acceptable, and discards the remaining W values as “bad” data. Moreover, with no exception, all discarded W estimates are for low whitecapping, which certainly creates a bias toward higher values in the distribution of W. To keep the error as low as possible, yet not discard a statistically significant amount of data featuring low W, we decided to use all estimates with standard deviation σW ≤ W. Applying this criterion to the Ws retrieved for 27 March 1998 leads to the following statistics: (1) only about 5% of all retrieved data is “bad” data with relative error above 100%; (2) about 47% of the retrieved Ws have an error from 30% to 100%; and (3) about 48% of the Ws have error below 30%. Two points are noteworthy: (1) Indeed, the 5% “bad” data all comprise low W values, but this does not introduce a statistically significant change in the W distributions; (2) The method provides many more W data (about half of the estimates) with an error smaller than 30% compared to the photographically measured W (only about 1/3 of the measurements). Figure 7 shows the distribution of the relative errors of W values retrieved for 27 March 1998. Error statistics of the satellite-measured W for all days in 1998 are similar. The minimum number of cells discarded due to large relative error (above 100%) is encountered in July, about 2.5% of all useful cells. The maximum number of cases with large errors is registered in May, about 10.5% of all useful cells.
 While Figure 5a represent the first global whitecap coverage obtained from satellite measurements, the global distribution and seasonal changes of oceanic whitecaps have been previously investigated using W(U10) relations [Blanchard, 1963; Spillane et al., 1986; Erickson et al., 1986]. In estimating global whitecap coverage, all authors discuss possible underestimation of W values for two reasons. First, ships usually avoid areas with stormy weather leading to under sampling of high-wind speed conditions [Spillane et al., 1986]. Second, due to the nonlinearity of the W(U10) dependence, the use of mean winds, usually monthly means, instead of instantaneous winds, also yields underestimation of the whitecap coverage. Blanchard [1963, 1983, 1985] and Erickson et al.  account for this problem by correcting their W estimates for the standard deviation of the wind speed.
 In this study, whitecap coverage is calculated from daily (in a sense instantaneous) fields of satellite data. The daily values of the whitecap coverage are averaged to obtain monthly, seasonal, or annual means of W. These are used to investigate the spatial and temporal characteristics of the global whitecap coverage [Anguelova, 2002, chap. 4]. Globally averaged annual W obtained with satellite-measured data is estimated to be 3.05%, which is consistent with Blanchard's [1963, Table 3] estimates of 3.4%. Comparisons on more regional scales, however, showed that satellite-retrieved estimates are usually higher than the photographic measurements. One possible reason for these higher values is that the satellite retrievals need an improved computational algorithm. However, it is also possible that the method described gives higher estimates of W because it measures both stages (A and B, i.e., active and decaying) of the whitecaps and uses daily instead of monthly data.
 At this time, the photographic data sets (Table 2) are the only available data for comparison with and evaluation of the satellite-derived whitecap coverage. This comparison cannot be considered a rigorous validation because the spatial resolution of the satellite retrievals is much coarser than that of the photographic measurements. However, such a comparison can be used to illustrate the consistency of the satellite retrievals. Measurements of whitecap coverage from the existing data sets, as a function of wind speed, shown in Figure 3a are replotted in Figure 8 (open circles, 646 points; not all data sets listed in Table 2 are included in the figure) together with W values obtained from satellite measurements for 27 March 1998 (shaded circles, about 14,700 points after removing invalid and erroneous estimates). Generally, the two databases are consistent with regard to absolute values and scatter. Differences between the two data sets are seen, however, and are expected.
 Another way to evaluate the performance of the method is to compare satellite-retrieved whitecap coverage with that calculated from existing parameterizations in terms of wind speed. Figure 5b shows results for whitecap coverage obtained with widely recognized and used parameterization of Monahan and O'Muircheartaigh :
For this calculation we use a global 0.5° × 0.5° map of wind speed for March 1998 (average of 31 daily wind speed maps), which ensures temporal and spatial matching with the satellite-retrieved whitecap coverage shown in Figure 5a. Again, a comparison of Figures 5a and 5b shows a general consistency in absolute values, but with large differences in spatial distribution. It is argued here that while issues with the described implementation probably contribute to these differences (section 5.1), a possible reason is that the satellite-measured whitecap coverage incorporates the effects of environmental variables in addition to wind speed (section 5.2).
5.1. Implementation Issues
5.1.1. Conditions for Valid and Accurate Estimates
 For the day under consideration (27 March 1998), nonphysical negative values for whitecap coverage were computed for 335 cells, about 2.1% of all estimated W values for this day. For the entire 1998, the minimum occurrences of nonphysical negative values for W happened in November with about 0.5% of all useful cells. The maximum number of nonphysical negative values occurred in July, when W values were negative for 7% of all useful cells. Since values for foam emissivity ef in (2) are consistently high, we compared values of composite surface emissivity e and foam-free emissivity er = es + Δer in order to identify the cause for these cases. Figure 9a plots data for e (open circles) and es + Δer (squares) as a function of corresponding brightness temperatures for 27 March 1998 along a north-south line at 83°E. In most cases e ≥ es + Δer, as it should be, but there are several cases at the highest TB (from 165 to 168°K) for which e < es + Δer (solid circles). Figures 9b and 9c show that these same low e values are associated with low winds, up to 5.2 m s−1, and high V, 63 to 66 mm.
Pandey and Kakar  also encountered negative values for W in their microwave emissivity model. There are two possible causes in their model that can lead to W < 0: (1) they use the Stogryn  expression for foam emissivity, which underestimates ef; (2) they use TB data from the SMMR, which is known to have calibration problems [Wentz and Francis, 1992], thus affecting their values for e. According to our investigation, however, even if TB is well calibrated and a more comprehensive model is used for ef, cases of W < 0 still would occur. Pandey and Kakar  fixed the problem by subtracting a frequency-dependent bias from Hollinger's expressions (7) for roughness emissivity and adding a bias to the Stogryn's  expression for foam emissivity. Knowing that we have not chosen the most comprehensive models for this study, we decided to investigate but not correct the problem with negative W; at this time we discard all pixels for which W < 0.
Figure 9 helps identify one possible combination of conditions that might lead to unreliable detection of e and W: low wind speed coupled with high humidity, situations usually found at low latitudes. Examination of more cases of e < es + Δer, however, reveals that these conditions are not the only ones restricting the retrieval of valid and accurate e and W. Too low e values are encountered also in cases characterized with moderate winds (7–10 m s−1) and not so high humidity (20–35 mm) at mid latitudes (Figures 10a–10c). It proved difficult to identify a few specific combinations of variables (wind, humidity, water temperature, salinity) responsible for invalid or inaccurate e and W. Instead, numerous restricting conditions are encountered all over the globe. This suggests that drawbacks of the method, not physical reasons, limit the validity and accuracy of whitecap coverage estimates.
5.1.2. Modeling and Validation
 We used simplified models for the emissivities of rough sea and foam, er and ef. While these simple models provide clear separation between er and ef, they may not determine the rough and foam emissivities accurately. The masking of the surface emissivity signal in low-wind/high-humidity conditions revealed in Figure 9 points to the importance of the atmospheric correction model used to compute e. In addition, after applying the clear sky mask, we assumed L ≅ 0 and aL ≅ 0, which may not always hold true. While we did that to avoid the high uncertainty in retrieving L, completely neglecting the effect of the remaining cloud liquid water may introduce some error. Also, by necessity because of the lack of other data at the time of this study, the satellite brightness temperatures and the correction parameters needed to derive e, namely water vapor, V, and cloud liquid water, L, were obtained from the same satellite data set (SSM/I). Therefore the satellite-retrieved whitecap coverage could be somewhat dependent on the assumptions made in the SSM/I retrieval algorithm.
 The most rigorous way to evaluate the performance of the method estimating whitecap coverage from satellite measurements is to investigate the bias, ΔW, between satellite-measured whitecap coverage, Wsat, and true whitecap coverage, Wtrue: ΔW = Wsat − Wtrue. If Wtrue is reliably and accurately measured, then the bias ΔW will be mainly due to issues with the models and data used to obtain the emissivities in (2). Thus the accuracy of Wsat can be evaluated and eventually increased with improvements in models and data sets used (see section 5.3). At this time, however, the magnitude of the bias ΔW cannot serve as a fair measure for the performance of the method because, besides the modeling and data issues listed in the previous paragraph that influence Wsat, ΔW is also affected by uncertainties in Wtrue. True whitecap coverage can be represented either by photographic and video measurements or by predictions from a reliable W(U10) relation. We have shown, however, that existing photographic measurements of whitecap coverage do not fully represent different conditions over the globe (section 2.4) and relation W(U10) cannot model the whitecap coverage variability adequately (section 2.3). Though slowly, new photographic measurements of whitecap coverage will improve Wtrue and provide data for direct validation of Wsat. Meanwhile, the main approach to minimize ΔW is to improve modeling and data usage to obtain Wsat.
5.2. New Physical Insights
 Fully aware of the issues discussed in section 5.1, yet encouraged by the overall consistency between satellite estimates and photographic measurements in Figure 8, we believe that the satellite-based estimates of W can provide new physical insights into global whitecap coverage, which the available photographic data and the W(U10) parameterization do not capture well. Figures 5 and 8 support our interpretation.
 First, the wind speed dependence of the satellite and photographically derived W values in Figure 8 are somewhat different, with the photographically derived W increasing more rapidly with wind speed than the satellite-retrieved measurements. Our error analysis shows that higher error is associated with low estimates of whitecap coverage at low winds, while at high winds the error is consistently lower. Thus, in explaining the difference in wind speed dependence between satellite and photographically derived W values, we look into physical rather than implementation reasons. The slower changes of satellite-derived W with U10 can be interpreted as a result of suppression of the action of strong winds and boosting of the action of moderate winds by local meteorological and environmental conditions. Second, satellite-retrieved whitecap coverage clearly shows the expected high variability of W at moderate winds (6 to 12 m s−1).
 The differences apparent in Figure 8 are manifested as different global distributions in Figures 5a and 5b. As (11) suggests, the conventional W(U10) relation inevitably predicts high whitecap coverage in high latitudes, around 50°–60°N and S (Figure 5b) because average wind speed is high in these regions. In mid and low latitudes, where the wind speeds are lower, the whitecapping is rarely above 1%. Same features (high W at high latitudes, low W at low latitudes) are observed in Spillane et al.'s [1986, Figure 5] climatological whitecap atlas for March since it was produced with an approach similar to (11). These observations are in contrast to the picture in Figure 5a where no such strong gradient from high to low latitudes is observed. Instead, high variability in values makes whitecap coverage more uniform latitudinally: not very high at high latitudes and higher at mid and even low latitudes.
 Though strikingly different from the global distribution predicted by (11) and documented by Spillane et al.'s  climatological whitecap atlas, the features of satellite-derived whitecap coverage in Figure 5a can be explained with the effects of various environmental factors whose concerted action enhances the effect of wind alone in some regions and suppresses wind action in others. For example, it is expected that, with all other conditions similar, whitecap coverage would be higher at 12 m s−1 wind in warm waters than whitecap coverage at 12 m s−1 wind in cold waters due to water viscosity differences. Indeed, Figure 5a shows that satellite-derived whitecap coverage in the Southern Ocean and the northern reaches of the North Atlantic and North Pacific is not the highest because these are regions where high winds are invariably coupled with very low water temperatures (often below 0°C). Furthermore, the persistent trade winds and the long fetches in the tropics further foster whitecapping in warm waters. Also, the central parts of the oceans, regions of downwelling of warm surface waters, are oligotrophic [Pinet, 1992, p. 376] as nutrients are exported from the surface layer. A low concentration of organisms in places with less nutrients leads, presumably, to a low concentration of surface-active materials, thus wave breaking in these warm waters is not suppressed by surfactants and whitecapping is enhanced. In contrast, coastal upwelling west of Africa and South America, as well as Polar upwelling in the Southern Ocean [Pinet, 1992, p. 388, Figure 12–1], brings cold nutrient-laden waters at the surface leading to high primary production, thus more surfactants in the surface water, which would hinder wave breaking and diminish whitecapping.
 It is anticipated that addressing rigorously the modeling and data issues discussed in section 5.1.2 may reduce the strength of or even change the spatial features in Figure 5a to some extent. We suspect, though, that fingerprints of various factors affecting whitecap coverage will still be discernable and the global spatial distribution of satellite-measured whitecap coverage will still be different from that obtained with W(U10) relation. This, however, remains to be seen.
 An independent and completely different study corroborates the global distribution of satellite-measured whitecap coverage revealed in Figure 5a. Haywood et al.  computed the solar irradiance at the top of the atmosphere in several runs of general circulation model (GCM). Once they ran their GCM without any atmospheric aerosols, then in several additional GCM runs they introduced different combinations of aerosols both natural and anthropogenic. For each GCM run, the model results for solar irradiance were compared with those observed by the Earth Radiation Budget Experiment (ERBE). Without aerosols, their GCM underestimated the solar irradiance over the entire globe (Haywood et al.'s Figure 1A). When all aerosol types except sea-salt aerosols were introduced, the bias between GCM predictions and ERBE measurements was only partially eliminated (Haywood et al.'s Figure 1B). The inclusion of sea-salt aerosols with low concentration further decreased but did not fully eradicate the bias between model and measurements (Haywood et al.'s Figure 1C). Sea-salt aerosols with high concentration brought the best balance between model and measurements at low and mid latitudes, but at high latitudes the model overestimated the solar irradiance (Haywood et al.'s Figure 1D). The point of this description is that in Haywood et al.'s figures the solar irradiance exhibits a global spatial distribution whose main features closely resemble those of whitecap coverage in our Figure 5a. This implies that sea-salt aerosols, and perhaps whitecaps albedo as well, are most necessary for the reflected radiance in the same places where we observe high whitecap coverage, which would be the main initial source for sea-salt aerosols.
5.3. Possible Improvements
 The discussion in section 5.1.2 points to two major necessary improvements, namely more comprehensive models for the emissivities in (2) and decoupled data sets for the computations. To minimize correlations and error propagation, it is preferable to use independent data sets for the brightness temperature and atmospheric correction variables to obtain the composite emissivity e (equations (4)–(5)). The recent launch of WindSat [Gaiser et al., 2004] should make this possible. For instance, we can use brightness temperatures from the WindSat sensor and make the atmospheric correction employing data for water vapor and cloud liquid water from SSM/I. Similarly, it is desirable to decouple the quantities used in the models for er and ef (e.g., SST taken from weather forecast analyses) from those directly measured and used to obtain e (e.g., SST from AVHRR). Using various independent data sets, however, raises the necessity of their rigorous matchup in time and space with a potential to introduce a significant source of error.
 Calculations of the emissivity of rough sea surface, er = es + Δer, should be placed on a more sound physical ground. Instead of the empirical expression used in this implementation for surface roughness correction Δer, the so-called two-scale emissivity model can be used to compute er [Wentz, 1983; Durden and Vesecky, 1985; Yueh, 1997, St. Germain et al., 2002]. This model best describes changes of ocean emissivity for winds up to 10–12 m s−1 due to Bragg scattering from short gravity and capillary waves riding on long waves with a Gaussian distribution of slopes. Gains from a better physical model, however, will raise new issues. Though the two-scale model has matured over the years since its first introduction [Semyonov, 1966], it has limitations such as the choices of the wavelength separating short and long waves and of the wave spectrum model [Zhang and Johnson, 2001]. Another anticipated challenge is the clear separation of er and ef in (1). Therefore new theories and models [Johnson, 2002] should also be considered.
 The emissivity of foam, ef, which is modeled with the Fresnel formula for foam reflectivity, also needs improvement. The assumption in this model of constant void fraction, α, throughout the foam layer at the surface and the chosen value of α = 98% ensure a fair prediction of the emissivity of thick, freshly generated whitecaps (stage A), but it is only partially suitable for aged thinner whitecaps in stage B. Since the area of the aged whitecaps is much larger than the area of fresh thick ones, a realistic physical model should have a way to account for the characteristics and emission of both types of whitecaps. A model for ef incorporating void fraction changes with depth and distribution of foam thicknesses can address this requirement.
 The necessity to model realistically the high variability of whitecap coverage has justified the development of a method for estimating whitecap coverage on a global scale from routinely measured satellite data as an alternative to traditional photographic measurements. The concept for satellite-based estimates of W relies on changes of microwave brightness temperature at 19 GHz (horizontal polarization) at the ocean surface as whitecap coverage increases. Models, parameterizations, data sets, and assumptions used to implement the method are described. Though highly simplified, this initial implementation proves the feasibility of the concept. It should be possible to obtain daily global whitecap coverage estimates with an error of at most one standard deviation. Drawbacks of the method are analyzed and necessary changes and improvements are discussed.
 Satellite-derived values for whitecap coverage are of the same order of magnitude as those from previous photographic measurements, but their global distribution is quite different from that predicted from conventional relations using wind speed. This different spatial distribution is plausibly explainable through the effects of various meteorological and environmental factors in addition to the effect of wind alone. Using satellite-based estimates, an extensive database of whitecap coverage under a myriad of conditions encountered over the globe can be assembled. Such a database might be used to improve existing, or to develop new, models and parameterizations for various air-sea interaction processes such as the production of sea-salt aerosols and gas transfer.
Appendix A:: Error Analysis—Sensitivity Coefficients and Variances
 The variances of the four emissivities in (10) are
In (A2), Eej, Esj, Efj, and Erj are the sensitivity coefficients for e, es, ef, and Δer, respectively. The index j show the basic variables contributing to the emissivity errors. Each of the sensitivity coefficients, Eij, is determined by a set of expressions containing numerous terms (not shown). The inequality signs in (10) and (A2) come from Schwarz inequality, ∣σuv2∣ ≤ σuσv.
Table A1 lists the standard deviations (or RMS errors), σx, of the variables used to compute emissivity variances in (A1)–(A2).
Table A1. Variances of the Basic Variables Contributing to the Errors of Emissivities (A2)
 This work was done while the first author was completing her Ph.D. at the College of Marine Studies, University of Delaware, and was partly supported by the NSF Ocean Sciences Division under grant OCE-9730439. The authors wish to thank the reviewers whose careful review of the manuscript and detailed suggestions and comments helped improve the text. M.A. wishes to thank Michael Bettenhausen (NRL, Remote Sensing Division) for valuable discussions on the remote sensing part of the paper.