Does SST matter for scatterometry?
Semyon A. Grodsky1, Vladimir N. Kudryavtsev2, Abderrahim Bentamy3, James A. Carton1
Submitted to Geophysical Research Letters
January 26, 2012
1Department of Atmospheric and Oceanic Science, University of Maryland, College Park, MD20742, USA
2RussianState Hydrometeorological University and Nansen International Environmental & Remote Sensing Centre, St Petersburg, Russia
3 Institut Francais pour la Recherche et l’Exploitation de la Mer, Plouzane, France
Corresponding author:
Abstract
This study quantifies the impact of SST on satellite scatterometer winds.Scatterometry depends on the relationship linking surface stress, surface roughness and microwave radar backscatter.However, changes in SST alter the growthrate of centimeter-scale waves through their impact on airdensity and on water viscosity.This SST-dependence hasnot been included in the standard Geophysical Model Functions of widely used satellite scatterometers.This study uses a radar imaging model to evaluate the SST-dependence and compares the results to observations.The resulting corrections raises wind speed estimates by up to 0.2ms-1 in the storm track region of the Southern Ocean for C-band scatterometers. For the higher frequency Ku-band scatterometers the SST corrections decrease estimated wind speed by up to 0.4ms-1 south of 60oS where SST is cold and winds are moderate.
1. Introduction
Scatterometry has revolutionized analysis of marine winds, but its calibration remains a research problem. Recently Bentamy et al. (2012) compared simultaneous wind estimates from two scatterometers using different Ku and C frequency bands and found a systematic pattern of mean difference whose geographic distribution is related to the mean distribution of SST. They speculated that the pattern of difference resulted from neglecting the impact of SST on atmospheric momentum and oceanic viscous dissipation processes affecting ocean surface wave generation/dissipation. In this paper we employ the Radar imaging model (RIM) of Kudryavtsev et al. (2005) to show that accounting for these neglected effects can explain the Bentamy et al. observations,in turn suggesting that scatterometer algorithms should be modified to include these SST dependencies.
In contrast to this direct impact of SST, much of the recent interest in the impact of SSTon scatterometry relates to its impact on mesoscale winds via the stability of the marine atmospheric boundary layer (see Chelton and Xie, 2010 for a review). The latter effect can be traced back to observations by Weissman et al. (1980) showing that the warm Gulf Streamhas a brighter radar signature than the colder water to its north and east. Reductions in boundary layer stability increase surface winds, thus altering the wave field and the strength of Radar backscatter.The atmospheric stability effect has beenconfirmed in the C-band by Beal et al. (1997) who conducted quasi-simultaneous satellite and in-situ observations in the Gulf Stream. However in the lower frequencyL-band the Gulf Streamsignature is weakcompared to the surrounding water (Grodsky et al., 1999) suggesting a frequency-dependence to impact of the SST-induced atmosphere stratificationeffects on radar backscatter.
Separate from the impact of SST on atmospheric stability, the SST has a direct impact on the growth rate of wind waves, and thus on the sea surface radar backscatter at the same winds. Scatterometers measure wind velocity indirectly through the impact of wind on the amplitude of centimeter-scale waves(e.g. Wright and Keller, 1971). The growth of local wind waves depends on the wind growth coefficient, , in turn proportional to the ratio of air to water density, (Miles, 1957).Hence, stronger waves are generated by denser air over cold SSTs,assuming that the wind itself remains unchanged(Bourassa et al., 2010).In contrast, weaker waves are expected due to higher viscosity, , and stronger viscous dissipation, , of colder water.Thus, for fixed wind, wave energy and radar backscatter may either increase or decrease with SST due to changes in and (Donelan and Pierson, 1987).
To date, the most successful conversions of scatterometer measurements to near-surface wind rely on empirically derived geophysical model functions (GMFs,Dunbar et al., 2006; Hersbach, 2008).Historically scatterometers have used two different frequency bands. The National Aeronautics and Space Administration (NASA) NSCAT and QuikSCATand the Indian OCEANSAT2 use frequencies in the 10.95-14.5GHz Ku-band while European scatterometers have all adopted the 4-8 GHz C-band to allow for reduced sensitivity to rain interference [e.g. Sobieski et al, 1999]. TheNASA Ku-band winds are estimated with the empirical QSCAT-1 GMF[Dunbar et al., 2006]. The European Meteorological Satellite Organization (EUMESAT) C-band winds are estimated with the empirical CMOD5N GMF (Hersbach, 2008). Although neither GMFsaccount for SST variations, careful tuning of the GMFs provides accuracy of 10m neutral wind velocity in the range of±1 ms-1and ±20o, [e.g. Ebuchi et al., 2002].However,an examination by Bentamy et al. (2012) reveals that within these ranges of error there exist systematic errors at high latitudes over very cold SST<5oC. In this paper we employ the Kudryavtsev et al. (2005) RIM to assess errors in scatterometer winds arising from the lack of SST-dependence in current GMFs.
2. Collocated scatterometer data
This study relies ona set of observed differences between spatially and temporally collocated winds from the Ku-band (13.4 GHz, 2.24 cm) SeaWinds instrument onboard QuikSCAT (referred to as QuikSCAT or QS) and the C-band (5.225GHz, 5.74 cm) ASCAT (referred to as ASCAT or AS) onboard the EUMESAT MetOp-A.QuikSCAT was operational June, 1999 to November, 2009, while ASCAT launched in October, 2006. The collocated winds are available during November 2008 – November 2009when both missions were collecting data and when ASCAT processing used the current CMOD5N GMF to derive 10m neutral wind (Bentamy et al., 2012).
3. Radar Imaging Model
The Kudryavtsev et al. (2005)RIM simulates the normalized radar cross section () by accounting fortwo-scale Bragg scattering (),specular reflections (), and scattering by wave breaking (). Bragg scattering component is approximately symmetrical in azimuth because it depends on the folded spectrum of the resonant Bragg waves. It is the only component depending on polarization and is stronger in V-pol than in H-pol (by a factor of 4 to 5). The two other components are specular reflections from regular surface and very rough breaking zones, which don’t depend on polarization. Regular specular reflection ()is weak in the range of incidence angles () utilized by scatterometers, but is not negligible.Rough zones of active wave breaking generate a strong spike-like radar signal. Though their fraction is small, these zones nevertheless significantly contribute to .For centimeter-scale Bragg waves, thewave breaking contributionis produced by longer (a few decimetersor more) waves that are less dependent on SST than the resonant Bragg waves.
Apart from their direct contribution to , the wave breaking also impact the energy balance of shorter waves. Following Donelan and Pierson (1987), the wave spectrum in the equilibrium range,, is balanced by the linear growth and nonlinear dissipation (the first two terms in 1). In addition to the above mechanisms the Kudryavtsev et al. (2005) formulation accounts for the energy input due to breaking of longer waves, , (Kudryavtsev and Johannessen, 2004)
,(1)
where is the saturation spectrum of wind waves, and are empirical parameters. The growth rate, ,is the difference between the wind growth rate,, and the rate of viscous dissipation, . The wind growth rate (2) is parameterized in a functional form suggested by Stewart (1974)
,(2)
where is the angle between wind and wave azimuth, is the wavenumber, is the phase velocity, is the wave frequency that depends on SST via the surface tension , is the air friction velocity, and is wind speed at .
The air temperature ,,effect on the wind growth rate (2) is accounted for by the air density that is calculated at fixed relative humidity of 75% and the normal air pressure. The water temperature, , effect on is accounted for by the kinematic viscosity that is calculated at fixed salinity of 35 psufollowing Sharqawy et al. (2010). All results presented below assume a neutrally stratified marine atmospheric boundary layer so that air temperature is given by SST:.With these parameterizations, the RIM produces that for a given wind,, depends also on temperature, . Because current GMFs don’t depend on SST, theradar calibration, , is assumed corresponding to areference temperature (chosen equal the global mean SST=19oC in this study), andthe temperature-related wind retrieval error is
(3)
4. Results
Although decreases by approximately 10% between 0oC to 30oC (Figure 1) while drops by 50%, the impact of changes in these two factors on are comparable. In Figure 2 the two contributions to wind retrieval error () and ()are evaluated from (3) by varying either or as a function of temperature, keeping the other variable fixed at its value for =19oC.The errors in Figure 2 are illustrated for the extreme case of cold SST, =0oC.The error in the wind estimates due to air density changes, , is mostly positive at these conditions because of denser air. It increases quasi-linearly with and is virtually independent of the radar wavelength. This behavior is the result of the importance of Bragg component. If the wave breaking contribution in (1) is weak, the energy of the Bragg component, thus its contribution to radar backscattering,,both depend on.ATaylor series expansion of (3) in vicinity of following Bentamy et al.(2012) yields:
(4)
If the first term in (4) is linear in wind, .For the Stewart wind growth rate model (2) is quasi-linear in wind with minor dependence on radar wavelength (Figure 2)that refers to the wavenumber dependence of. Surprisingly, becomes negative at weak winds <4ms-1where wind speeds drop below the wave speed (2). At those winds direct interaction with wind extracts energy from the surface waves, rather than adding it, at a rate proportional to .
In contrast to the impact of neglecting temperature-dependence in , the impact of neglecting SST-dependence in is to cause an underestimation of wind over cold water, (Figure 2). Although the two effects tend to cancel each other, they have different wind dependencies. In the C-band at low to moderate winds (<13 m/s) while at higher winds.
The size of the wind error due to water viscosity variations is larger at shorter wavelengths where viscosity can have more impact (Figure 2), as reflected in a larger . But, this relationship switches over at<5ms-1that is explained by . The RIM shows that in the Ku-banddominates the V-polcomponent of in the upwind direction at >4ms-1. But, as decreases toward the threshold wind for the resonant Bragg component(defined by ), which is approximately 4 ms-1 in the Ku band, Bragg scattering decreases sharply and the wave breaking component,which is produced by longer waves,starts dominating, . This results in a weaker temperature dependence of becauseis produced by waves longer than the resonant Bragg component that areless dependent on , thus on temperature. The threshold wind in the C-band (~2.5 ms-1) is lower than that in Ku-band consistent with smaller at these frequencies. As a result, at relatively weak winds <5 ms-1 (Figure 2). It is interesting to note that the RIM suggests in the entire wind speed range ms-1in the Ku-band at H-pol. This difference in the behavior at different polarizations explains why the SST-related wind error is several times weaker for H-pol than for V-pol (not shown). Since QuikSCAT had sensors measuring backscatter at both polarizations this dependence on polarization will impact the response of this instrument.
The dependence of on radar wavelength provides an opportunity to check the model against scatterometer retrievals from different bands. Observed collocated wind speed differencefrom QuikSCAT and ASCAT, , is binned in Figure 3 versus and SST.These results show that in time average is higher than at low (<3ms-1) and high (>12ms-1) winds. The most notorious>0is observed in regions of high winds where exceeds by up to 2ms-1. Thishas been attributed by Bentamy et al. (2012) to the difference in QuikSCAT and ASCAT GMFs rather than impact of SST. The positive for <3ms-1is artificial of theasymmetrical distribution of wind speed for winds approaching the low wind cutoff [Freilich, 1997].
In contrast, ASCAT exceeds QuikSCAT wind speed by at least 0.25 ms-1 over cold SST<7°C under moderate wind 5ms-1<12ms-1, the result of a more negative in the Ku-band than the C-band. The model predicts a qualitatively similar impact of SST at cold SST<10oC and moderate winds (Figure 3). But, the simulated <0 extends into higher winds >15ms-1 for cold SSTs. This behavior can’t be verified by observations, which are dominated by the GMF-related effects at high winds. It is also noticeable that at the very cold SST=0oC examined here the model predicts a somewhat weaker = -0.4ms-1 in comparison with observed values of -0.6ms-1 (Figure 3). In part, these differences are expected because model results presented here are based on a particular set of parameters (V-pol., upwind direction, and =45o) while the scatterometer data result from observations at various angles and polarizations.
In the upwind direction the wind retrieval error, , has a similar dependence on and SST in either frequency band (Figures 4a,b). The way it is defined, = 0. However, it is interesting that it is approximately anti-symmetric with respect to at higher and lower temperatures with some modifications due to the stronger impact of (Figure 1) at colder SSTs. In the Ku-band, the negative values of that occur due to viscous effects dominates at <13ms-1 (Figure 4a). As expected, the negative is weaker in the C-band and is limited to winds <9ms-1 (Figure 4b) due to weaker viscous dissipation (in comparison with that in the Ku-band). In contrast, the positive at high winds is stronger in the C-band due to weaker viscous effects at the longer wavelengths (Figure 2).
We should expect the azimuthal dependence of to be approximately symmetrical in the downwind and upwind directions for conditions where Bragg scattering dominates. Any deviation from this symmetry is explained by , which is less temperature dependent than Bragg scattering, and is stronger in the upwind direction. So, looking downwind in the Ku-bandshows that is stronger than upwind (Figure 4c) due to a weaker downwind. The upwind- downwind asymmetry of is less noticeable in the C-band (Figure 4d) due to the relatively stronger Bragg scattering in that band. In general the strongest negative is expected within the plus/minus 90o downwind azimuth sector at some angles relative to the wind direction where the relative magnitude of azimuth-independent is stronger in comparison with azimuth-dependent (Figures 4c, 4d).
Differences in between the two radar bands are reflected in the geographical patterns of the wind retrieval error (Figure 5). These patterns are calculated from (3) assuming the upwind direction for V-pol and =45o, and using observed ASCAT wind speed and SST from the collocated QuikSCAT/ASCAT data of Bentamy et al. (2012). Results are binned in a 1ox1o longitude/latitude grid and time average at each point. The density error component is very similar in the two bands giving similar patterns in Figures 5a,d. This wind overestimation is up to 0.3ms-1 over regions where cold SSTs and high winds are both present. But, in many regions wind overestimation due to positive is compensated for by wind underestimation due to negative (compare Figures 5b, 5e). In the C-band, positive and negative are of similar magnitudes (Figures 5a,b). Hence, combination of the two error components results in a overall weak total retrieval error (Figure 5c). A slight wind overestimation <0.1ms-1 is expected in the C-band over the tropical warm pools and in the ‘roaring forties’ belt where =0.15ms-1 in the Indian Ocean sector (Figure 5c). Of course the total error is not simply sum of the Taylor series terms because of non-linearity of . This is mostly evident over the warm tropical SSTs where , providing is negligible (Figures 5a-c).
At polar latitudes the total Ku-band error is dominated by ocean viscous effects where SST is cold but winds are moderate (Figure 5f). This leads to an underestimation of wind speed in the Ku-band, where the effects are larger, of up to -0.4ms-1 south of 60oS in line with the Bentamy et al. (2012) assessment. Viscous effects also dominate in the tropical warm pools where wind is overestimated by up to 0.2 ms-1 by the Ku-band instrument. As is the case with the C-band scatteromenter, the total wind error for the Ku-band scatterometer is weaker than the viscous component in the deep tropics (Figures 5e, 5f) where =0.3ms-1.
5. Summary
Wind wave energy and radar backscattervary with SST due to air density-dependence of wind-wave growth rate and temperature dependence in viscous wave dissipation rate. The magnitude of the effect varies with the frequency of the scatterometer. Current empirical scatterometer GMFs do not account for these SST-dependences which are thus misinterpreted as spurious winds. We evaluate their impact on scatterometer wind accuracy using the Kudryavtsev et al. (2005) Radar Imaging Model which takes into account two-scale Bragg scattering, specular reflections, and scattering from breaking waves. The results are then validated using the Bentamy et al. (2012) set of collocated wind speed differences from the QuikSCAT and ASCAT instruments. The wind errors are evaluated at vertical polarization in the upwind direction at 45o incidence angle assuming that the radar calibration corresponds to a global mean value of SST=19oC and that atmospheric stratification is neutral.
The density component of the wind error (due to neglect of temperature-dependence in air density) is very similar in the C- and Ku- frequency bands. Wind overestimation due to this error approaches 0.3ms-1 poleward of 40o where cold SSTs and high winds are both present. Wind overestimation due to this error is compensated for by wind underestimation due to neglect of SST-dependence in the viscous wave dissipation rate . For C-band altimeters such as ASCAT, positive values of and negative values of are of similar size. As a result we expect a weak overestimation <0.1ms-1 of winds over the warm pools of the tropical ocean and in the in the westerly storm track region of the Southern Indian sector where the total error =0.15 ms-1. In contrast, the viscous error dominates the total SST-dependent errors for Ku-band scatterometers at polar latitudes where SST is cold but winds are moderate. This leads to an underestimation of wind speed for these instruments using an uncorrected GMF (neglecting SST-dependence) by up to -0.4ms-1 south of 60oS, a result that is consistent with those presented in Bentamy et al. (2012). In tropical warm pool regions Ku-band altimeters will overestimate wind speed by up to 0.2 ms-1.