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  • View in gallery

    Azimuthal slice of measured antenna gain pattern for WindSat 18.7-GHz vertical polarization and Gaussian approximation based on prelaunch calculations of half-power beamwidth.

  • View in gallery

    WindSat 37-GHz imagery of moderate Tropical Cyclone Asma, observed at 0129 UTC 19 Oct 2008. The storm was classified as a tropical depression at the observation time. The circle shows the best-track location at 0000 UTC, and the parallel lines denote the coincident TRMM PR measurement swath.

  • View in gallery

    ECMWF 10-m wind vector field from the 0000 UTC 19 Oct 2008 reanalysis. The color bar units are (top) m s−1 and (bottom) kt.

  • View in gallery

    ECMWF water vapor field from the 0000 UTC 19 Oct 2008 reanalysis. The color bar units are mm.

  • View in gallery

    TRMM 2B31 surface rainfall rate observed at 0129 UTC 19 Oct 2008. The parallel black lines denote the portion of the swath over which were simulated. The color bar units are mm h−1.

  • View in gallery

    Comparison of simulated and observed for TMI. The color map corresponds to the number of points in each hexbin.

  • View in gallery

    Comparison of simulated and observed for WindSat. The color map corresponds to the number of points in each hexbin.

  • View in gallery

    Hexbin maps of on (top) wind speed (m s−1) and (bottom) water vapor (mm) for rain-free pixels. Grayscale isopleths, from dark to light, denote vertically integrated cloud water paths of 0.1, 0.2, and 0.5 mm.

  • View in gallery

    Hexbin maps of on (top) rainfall rate (mm h−1) and (bottom) wind speed (m s−1) for water vapor between 60 and 65 mm. Grayscale isohyets, from dark to light, denote rainfall rates of 0.5, 2, and 5 mm h−1.

  • View in gallery

    Hexbin maps of on (top) rainfall rate (mm h−1) and (bottom) wind speed (m s−1) for water vapor between 65 and 70 mm. Grayscale isohyets, from dark to light, denote rainfall rates of 0.5, 2, and 5 mm h−1.

  • View in gallery

    Relationship between wind speed difference (WindSat minus ECMWF) and field-of-view averaged rainfall rate. The hexbin pixels are colored with that have been smoothed to match the resolution of the WindSat retrievals, and the color bar units are in kelvins.

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Brightness Temperature Simulation of Observed Precipitation Using a Three-Dimensional Radiative Transfer Model

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  • 1 Remote Sensing Division, Naval Research Laboratory, Washington, D.C.
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Abstract

This study demonstrates the capabilities of a three-dimensional radiative transfer model coupled to a polarized microwave surface emissivity model. Simulations are performed at 10, 19, and 37 GHz for TMI and WindSat using three-dimensional fields of rain, snow, and graupel derived from Tropical Rainfall Measuring Mission observations of moderate Tropical Storm Asma in conjunction with atmospheric profiles and surface fields from ECMWF. Simulations are well behaved and compare well with measured brightness temperatures. Comparisons are made between simulations with a wind-roughened surface and simulations assuming a specular surface. This theoretical study, which is supported with WindSat retrievals, shows the frequencies and conditions under which surface emissions may be detected in the presence of rain.

Corresponding author address: Ian S. Adams, Remote Sensing Division, Naval Research Laboratory, Code 7233, 4555 Overlook Ave. SW, Washington, DC 20375. E-mail: ian.adams@nrl.navy.mil

Abstract

This study demonstrates the capabilities of a three-dimensional radiative transfer model coupled to a polarized microwave surface emissivity model. Simulations are performed at 10, 19, and 37 GHz for TMI and WindSat using three-dimensional fields of rain, snow, and graupel derived from Tropical Rainfall Measuring Mission observations of moderate Tropical Storm Asma in conjunction with atmospheric profiles and surface fields from ECMWF. Simulations are well behaved and compare well with measured brightness temperatures. Comparisons are made between simulations with a wind-roughened surface and simulations assuming a specular surface. This theoretical study, which is supported with WindSat retrievals, shows the frequencies and conditions under which surface emissions may be detected in the presence of rain.

Corresponding author address: Ian S. Adams, Remote Sensing Division, Naval Research Laboratory, Code 7233, 4555 Overlook Ave. SW, Washington, DC 20375. E-mail: ian.adams@nrl.navy.mil

1. Introduction

Radiative transfer models are integral to remote sensing, as they form the basis for physically based retrieval of geophysical parameters. Such models also facilitate studies of sensor response to geophysical phenomena (Roberti and Kummerow 1999; Battaglia et al. 2007; Adams et al. 2008; Battaglia et al. 2011). One area where detailed radiative transfer studies would be useful, but such investigations have been limited, is in the sensing of near-surface ocean winds in the presence of precipitation. The ability to accurately sense winds in precipitation facilitates improved numerical weather prediction as well as improved storm-track and intensity forecasts; however, passive microwave observations of the ocean surface become contaminated even at low and moderate rainfall rates (Adams et al. 2006).

Kim and Lyzenga (2008) developed a model-based method for determining the atmospheric transmittance at the various WindSat frequencies. However, the resulting wind retrievals were not considered valid in cases of heavy precipitation, and no attempt was made to quantify the atmospheric conditions under which wind speed sensitivity was observable at the different WindSat frequencies.

Meissner and Wentz (2009) formulated an empirical approach to retrieve winds from passive microwave observations that have been contaminated by rain, for both general cases and tropical cyclones. By utilizing lower frequencies where atmospheric attenuation is limited, the retrievals demonstrated improved performance. The choice of leveraging 6.8- and 10.7-GHz brightness temperatures () was based upon radiative transfer calculations, but an analysis of the higher-frequency bands was not included. The statistical nature of the algorithm training and geophysical retrieval prohibits discerning the conditions under which the various radiometer frequencies are sensitive to surface emission.

The advent of three-dimensional radiative transfer models coupled with increases in computing power means that problems that depend on the three-dimensional structure of rain may be approached in a physically based manner instead of the simplified approach needed for parallel-plane models, most importantly to address nonuniform beamfilling (Kummerow 1998). While these increases in computational power make three-dimensional Monte Carlo methods attractive, the runtime, when compared to faster 1D models, limits the usefulness for applications such as near-real-time processing. Often the differences between 1D and 3D models, such as slant-path effects, can be reconciled (Liu et al. 1996). Thus, 3D simulations are attractive for understanding remote sensing physics for the purpose of studying assumptions and developing parameterizations that can be applied to simpler 1D models for low-latency applications.

Another aspect of radiative transfer that a three-dimensional model addresses is the distribution of downwelling radiation. Surface emissivity models (Meissner and Wentz 2012; Liu et al. 2011) perturb the specular response of a flat ocean surface to include the effects of wind-induced roughness. Since rough surface scattering is a combination of specular reflection and diffuse scattering, emissivity parameterizations statistically include the effects of nonspecular reflection of nonuniform downwelling radiation due to the change in path with downwelling angle, based on the uniform vertical transmission calculated from a parallel-plane model. For the three-dimensional case, the variation in downwelling atmospheric path, which is further complicated by spatially heterogeneous atmospheric conditions particularly associated with precipitation, is explicitly calculated.

Finally, a three-dimensional approach allows radiation to enter and escape the sensor beam, and to be multiply scattered by the heterogeneous medium within the beam and the medium (leakage) that manifests as polarization signatures that cannot be replicated by one-dimensional models (Petty 1994; Battaglia et al. 2011). Three-dimensional multiple-scattering effects can also affect simulations and retrievals when polarization is less of a concern (Kim et al. 2016).

A three-dimensional approach requires high-resolution fields to characterize hydrometeor-size distributions. Since cloud-resolving models suffer from issues of both correctness and representativeness (Kummerow et al. 2011), they are a poor basis for simulating observed events and discerning the physics from both the observed and simulated . Instead, by using high-resolution profiles, such as those derived from spaceborne radar observations, we can study the effects of precipitation on surface signatures. The drawback to this approach is that any assumptions and simplifications in the retrievals will propagate to the simulated .

The present work couples the Atmospheric Radiative Transfer Simulator (ARTS) (Eriksson et al. 2011) with a polarized surface emissivity model (Meissner and Wentz 2012) for the purpose of investigating precipitation events. This tool is validated against measured microwave radiances at key frequencies, and an analysis of detectable surface wind signatures is presented. The datasets used in this study are listed in section 2, and details of the radiative transfer model components are presented in section 3. Results are discussed in section 4. Section 5 gives concluding thoughts on the impact of this work as well as laying out a path for future research.

2. Data

a. TRMM data

Launched in November 1997, the Tropical Rainfall Measuring Mission (TRMM) is a suite of instruments with the purpose of estimating rainfall over the tropics. The primary instruments for estimating precipitation are the precipitation radar (PR), the TRMM Microwave Imager (TMI), and the Visible and Infrared Scanner (VIRS), and the platform is also equipped with two additional Earth-observing instruments: the Clouds and the Earth’s Radiant Energy System (CERES) and the Lightning Imaging Sensor (LIS) (Kummerow et al. 1998). The present study utilizes products derived from PR and TMI observations. Operation of the TRMM instrument suite ceased on 8 April 2015 and TRMM reentered the earth’s atmosphere on 15 June 2015.

The precipitation radar is the first spaceborne instrument designed to observe the three-dimensional structure of precipitating clouds. PR is a Ku-band (13.8 GHz) radar capable of measuring profiles of reflectivity factor with 250-m vertical resolution. The horizontal resolution at the surface is 5 km. The instrument scans across the satellite ground track, sampling 49 positions for a swath of approximately 250 km.

The TRMM Microwave Imager is a passive radiometer based on Special Sensor Microwave Imager (SSM/I) heritage, with additional X-band capabilities at 10.65 GHz and a shift in the water vapor channel from 22.235 to 21.3 GHz. The channel set and channel characteristics are given in Table 1. The instrument forms a conical scan with a constant nadir angle of 49° that translates to a 52.8° incidence angle. The usable scan comprises 208 (104) high (low)-frequency samples with a swath width of 878 km.

Table 1.

TMI radiometer characteristics.

Table 1.

For the primary input to the radiative transfer model, we used version 7 of TRMM 2B31 combined retrievals (NASA 2011a; Haddad et al. 1997b; Coppens et al. 2000; Kummerow et al. 2000). This product retrieves three classes of hydrometeors (rain, snow, and graupel) using TRMM PR radar reflectivities and TMI . The 85-GHz band is used to determine the ice above the liquid precipitation, and then a rain– parameterization is employed to determine the radar-derived rain profile that best matches the measured .

While the focus of this work is to simulate WindSat , we also simulated TMI to check the consistency of the simulations. For these comparisons, we used version 7 of the 1B11 product (NASA 2011b).

b. ECMWF reanalysis

Since the 2B31 retrievals provide only profiles of precipitation, another source for profiles of temperature, water vapor, and cloud must be used. For this purpose we elected to use the European Centre for Medium-Range Weather Forecasts (ECMWF) interim reanalysis (ERA-Interim) product that has been regridded to a regular N128 Gaussian grid with a nominal horizontal resolution of 0.703125° by the National Center for Atmospheric Research (NCAR) Data Support Section (ECMWF 2009). The NCAR-supplied data retain the 60 vertical levels of the source ECMWF dataset. In addition to vertical profiles, we also ingest 10-m wind vector and sea surface temperature fields from the ECMWF reanalysis.

c. WindSat data

WindSat, which launched in January 2003, is the first space-based polarimetric microwave radiometer (Gaiser et al. 2004). The channel set and channel characteristics are given in Table 2. In addition to the principal polarizations (vertical and horizontal) at each of the frequencies, fully polarized measurements are available at 10.7, 18.7, and 37; however, only the principal polarizations are simulated in this work. To accommodate the large number of horns needed to make the polarimetric measurements, the horns are aligned in three rows on the bench. The result of this configuration is that the incidence angle differs for each of the feed bench rows. The WindSat forward swath is approximately 1000 km. Only forward swath observations are used for the present study, and the Earth incidence angles (EIA) listed in Table 2 are the nominal values for the forward portion of the scan.

Table 2.

WindSat radiometer characteristics.

Table 2.

We use WindSat that are at native resolution and are corrected for spillover and cross-polarization artifacts (P. Gaiser 2013, unpublished data). The have not been resampled to common locations and are densely sampled proportional to frequency. To thin the number of observation points, reducing the necessary simulation points, and to harmonize the number of comparisons across frequencies, we use the WindSat locations closest to the TMI low-frequency footprint locations.

3. Methodology

a. ARTS

For simulating WindSat and TMI , we used the ARTS, version 2.3 (Eriksson et al. 2011). ARTS is a radiative transfer simulation framework that considers spheroidal planetary geometries for computing atmospheric transmission and radiation in one, two, or three dimensions. Within ARTS, two options are available for solving the radiative transfer equation when scattering hydrometeors are present: a discrete ordinate iterative (DOIT) method (Emde et al. 2004) and a reverse Monte Carlo integration (ARTS-MC) (Davis et al. 2005). For this work, we use ARTS-MC, as it is well suited for three-dimensional problems.

ARTS-MC

ARTS-MC is a reverse Monte Carlo scheme for solving the radiative transfer equation in scattering atmospheres. It utilizes importance sampling to handle nondiagonal extinction matrices associated with preferentially aligned particles while employing reverse photon path tracing to efficiently include the contribution of all photons (Davis et al. 2005). One component of ARTS-MC is the ability to approximate the sensor antenna pattern with a Gaussian distribution, thereby facilitating efficient Monte Carlo integration of the antenna pattern by statistically choosing the direction the photon leaves the sensor. The three-dimensional nature of ARTS-MC combined with a finite antenna response inherently handles the spatial distribution of precipitation within the radiometer footprint.

b. Optical properties

Absorption due to water vapor, oxygen, and nitrogen was calculated using gaseous absorption models developed by Rosenkranz (1993, 1998) that are contained within ARTS, and liquid water absorption for suspended clouds was calculated with the Millimeter-Wave Propagation Model (MPM-93) (Liebe et al. 1993), again within ARTS. The complex permittivities of liquid and frozen precipitating hydrometeors were calculated using Stogryn (1997) and Mätzler (2006), respectively. The scattering properties of the precipitating hydrometeors were calculated with the T-matrix code for randomly oriented particles (Mishchenko and Travis 1998); however, only spherical hydrometeor approximations were considered for this work to maintain consistency with the 2B31 retrievals.

c. Surface emissivity

While version 2.3 of ARTS includes the option of using a Fast Emissivity Model (FASTEM) (Liu et al. 2011) for calculating the emissivity of a wind-roughened ocean surface, we computed surface emissivities at four discrete frequencies (10.7, 18.7, 19.35, and 37 GHz) using an empirically based surface emissivity model (Meissner and Wentz 2012) that is more representative of observed WindSat . This representation of surface emissivity assumes that the emissivity of the sea surface can be parameterized with four perturbations to a specular surface: small-scale roughness, large-scale roughness, directional anisotropy, and the nonspecular reflection of nonuniform downwelling radiation due to the variation of pathlength with downwelling incidence angle. For large atmospheric optical depths, the nonspecular correction is small; moreover, while ARTS-MC considers only specular reflections at the surface based on the incidence angle of the incident photon, the Monte Carlo integration explicitly accounts for nonuniform downwelling radiation from both the variation in pathlength and heterogeneous atmospheric conditions. Therefore, we ignore the nonspecular atmospheric path correction detailed by Meissner and Wentz (2012). Since the parameterized permittivity models assume unpolarized downwelling radiation, the resulting Mueller matrix, which translates the incident Stokes vector into the scattered Stokes vector, is not fully characterized. With the terms available from the model, the Mueller matrix takes the form
e1
where , , , and are the emissivity terms for vertical polarization, horizontal polarization, the third Stokes parameter, and the fourth Stokes parameter, respectively. Since the particle models used in the present work consist only of spheres, terms outside of the upper-left block have no consequence to the simulations.

d. Size distribution models

To translate the retrieved precipitation parameters into drop and particle number densities, we employed the parameterization of the gamma size distribution for rain developed by Haddad et al. (1997a) and the inverse exponential distribution for snow and graupel, all of which are consistent with the 2B31 retrievals.

e. Sensor properties

As stated in section 3a(1), ARTS-MC efficiently exploits the Monte Carlo integration for the case of a Gaussian antenna beam. Figure 1 shows the azimuthal and center frequency slice of the WindSat vertical polarization antenna pattern for the 18.7-GHz band. The Gaussian approximation based on prelaunch calculations of the WindSat half-power beamwidth is also shown. The patterns agree well within the first null; although, the Gaussian approximation is slightly narrower and skewed. The skewness results from the offset between the horn and the focal point, and the slight difference in width occurs because the pattern data presented are only a slice of the full dataset used to calculate the beamwidth. The correspondence of the Gaussian approximation here is indicative of the fidelity of the approximations for all frequencies considered in this work. The half-power beamwidths listed in Tables 1 and 2 were used to define the Gaussian antenna pattern approximations. Sensor bands are treated monochromatically using the center frequencies listed.

Fig. 1.
Fig. 1.

Azimuthal slice of measured antenna gain pattern for WindSat 18.7-GHz vertical polarization and Gaussian approximation based on prelaunch calculations of half-power beamwidth.

Citation: Journal of Atmospheric and Oceanic Technology 33, 10; 10.1175/JTECH-D-15-0241.1

4. Results and discussion

To demonstrate the simulator, we chose a coincident observation of moderate Tropical Storm Asma. At the observation time of 0129 UTC 19 October 2008, Asma was still classified as an unnamed tropical depression with maximum sustained winds of 18 m s−1 (35 kt) and a minimum central pressure of 996 mb according to the Joint Typhoon Warning Center (JTWC). WindSat 37-GHz imagery is given in Fig. 2. The ECMWF wind field is given in Fig. 3. The maximum winds in the reanalysis are 14 m s−1 (27 kt), and the center (designated by the circle in Fig. 3 corresponding to the lowest winds) is slightly offset from the center location given by the JTWC best track (denoted by the circle in Fig. 2). The water vapor field from the ECMWF reanalysis is shown in Fig. 4. The ECMWF cloud field (not shown) exhibited significant spatial mismatch when compared with passive microwave cloud retrievals from WindSat (Bettenhausen et al. 2006).

Fig. 2.
Fig. 2.

WindSat 37-GHz imagery of moderate Tropical Cyclone Asma, observed at 0129 UTC 19 Oct 2008. The storm was classified as a tropical depression at the observation time. The circle shows the best-track location at 0000 UTC, and the parallel lines denote the coincident TRMM PR measurement swath.

Citation: Journal of Atmospheric and Oceanic Technology 33, 10; 10.1175/JTECH-D-15-0241.1

Fig. 3.
Fig. 3.

ECMWF 10-m wind vector field from the 0000 UTC 19 Oct 2008 reanalysis. The color bar units are (top) m s−1 and (bottom) kt.

Citation: Journal of Atmospheric and Oceanic Technology 33, 10; 10.1175/JTECH-D-15-0241.1

Fig. 4.
Fig. 4.

ECMWF water vapor field from the 0000 UTC 19 Oct 2008 reanalysis. The color bar units are mm.

Citation: Journal of Atmospheric and Oceanic Technology 33, 10; 10.1175/JTECH-D-15-0241.1

For ingestion into ARTS, TRMM 2B31 profiles (corresponding surface rainfall rates are shown in Fig. 5) and ECMWF profiles are spatially interpolated onto a rectilinear latitude–longitude grid with a resolution of 0.045°. ARTS uses a fixed pressure grid for the vertical coordinates, so we created a composite grid with finer resolution, evenly spaced logarithmically, below 500 hPa, and coarser resolution, again evenly spaced logarithmically, above. Below 500 hPa, this grid consists of 25 cells ranging from 232 to 265 m in height. Above 500 hPa, the grid is 35 cells ranging in height from 343 to 480 m. For the collocation region considered in this work, 500 hPa corresponds to roughly 6 km in altitude. Since the observation time (0129 UTC) is much closer in time to the 0000 UTC reanalysis than the 0600 UTC reanalysis, we do not perform temporal interpolation of the ECMWF reanalysis. Simulated points are all contained within the black lines of Fig. 5, and a buffer of 1° is maintained near the edges of the domain depicted in Fig. 2.

Fig. 5.
Fig. 5.

TRMM 2B31 surface rainfall rate observed at 0129 UTC 19 Oct 2008. The parallel black lines denote the portion of the swath over which were simulated. The color bar units are mm h−1.

Citation: Journal of Atmospheric and Oceanic Technology 33, 10; 10.1175/JTECH-D-15-0241.1

a. Comparisons with measurements

Figures 6 and 7 show comparisons of the simulated with TMI- and WindSat-observed . The simulations compare well with the from the respective platforms. One feature of the scatterplots that is readily apparent is the cold tail at low for 18-/19- and 37-GHz bands. That this feature is not present at 10 GHz suggests an anomaly due to water vapor. Inspection of these points reveals a correspondence with the region of low water vapor (<50 mm) southwest of the storm (see Fig. 4). The water vapor field from the ECMWF reanalysis is biased cold by 5–10 mm when compared with WindSat retrievals (Bettenhausen et al. 2006) (not shown). Since this region of the storm is free of precipitation, as is evident by inspecting either the WindSat 37-GHz (Fig. 2) or the TRMM rainfall rates (Fig. 5), the WindSat retrievals are considered reliable. As was stated previously, there was considerable spatial mismatch between the ECMWF cloud liquid water and the WindSat retrievals. This mismatch contributes to the increase in variance at 37 GHz.

Fig. 6.
Fig. 6.

Comparison of simulated and observed for TMI. The color map corresponds to the number of points in each hexbin.

Citation: Journal of Atmospheric and Oceanic Technology 33, 10; 10.1175/JTECH-D-15-0241.1

Fig. 7.
Fig. 7.

Comparison of simulated and observed for WindSat. The color map corresponds to the number of points in each hexbin.

Citation: Journal of Atmospheric and Oceanic Technology 33, 10; 10.1175/JTECH-D-15-0241.1

Table 3 gives the statistics for each of the simulated channels. While the simulated , in general, compare well with the measurements, there is a noticeable cold bias, especially at the lower frequencies. There are no studies available that analyze the resulting from the 2B31 retrievals; however, by comparing to the results from another combined product (Munchak and Kummerow 2011), we see that the results are reasonable. One feature that merits future investigation is the slope at 10 GHz that results in an increasing cold bias with increasing rainfall rate. The statistics for WindSat show similar but slightly diminished agreement between simulations and measurements when compared with the TMI results. This is expected, as the 2B31 retrieval algorithm uses TMI . Differences in calibration, sensor characteristics, and viewing geometry should account for some of this disparity.

Table 3.

Simulation statistics corresponding to Fig. 6 (TMI) and Fig. 7 (WindSat).

Table 3.

b. Specular versus wind roughened

For a specular ocean surface, the emissivity for vertical polarization is higher than emissivity for horizontal polarization, generally resulting in higher for vertical polarization than for horizontal polarization. Since the horizontal polarization is more sensitive to wind-induced roughness, increases in wind speed cause the horizontally polarized to increase more rapidly than vertically polarized . A useful metric for this phenomenon is the parameter Q of the Stokes vector, which is the vertically polarized minus the horizontally polarized . As such, for a given atmospheric state, Q is at a maximum for zero wind speed, and it decreases with increasing wind speed. While Q is an indicator of wind speed, atmospheric attenuation also decreases Q, and for opaque atmospheres where the surface is not visible, a wind-roughened surface should be indistinguishable from a specular surface. In particular, the spectral dependence of Q on precipitation is much stronger than on wind speed. The spectral behavior of Q, then, is important for separating and determining surface and atmospheric conditions; however, in a tropical storm environment, the geophysical parameters are highly correlated spatially. To isolate the wind-roughened component, with respect to a specular surface, we introduce the term , as the roughness terms are additive as outlined in the perturbative method in section 3c. Unlike Q, the parameter becomes more negative with increasing wind speed while still tending to zero for increasing atmospheric opacity.

Spaceborne radiometers provide an interesting challenge to studying the spectral dependence on geophysical parameters because the resolutions vary greatly between the different frequencies. For radiometers like TMI, which include all horns on a single row on the feedbench, there is a slight spatial offset along the flight track due to spacecraft motion; otherwise, the radiometer observations are collocated in space, all with the same zenith angle. To accommodate the additional feedhorns needed to measure the full Stokes vector at 10.7, 18.7, and 37 GHz, the design of the WindSat feedbench arranges the horns on three rows, resulting in not only in slightly different orientations of the fields of view, but also differing incidence angles for the WindSat bands (Gaiser et al. 2004). Therefore, the simulator detailed in the present work offers a useful tool for investigating the spectral behavior of Q. To avoid incidence angle and resolution differences, we performed additional simulations of 10.7- and 18.7-GHz with the 37-GHz geometry and antenna parameters. The spatial resolution of these simulations is approximately 8 km × 13 km at the surface. To coincide with the simulations, ECMWF wind speeds and vertically integrated water vapor paths have been linearly interpolated to the WindSat field-of-view locations, while the 2B31 surface rainfall rates have been convolved with a Gaussian function characterized by an 8 km × 13 km half-power beamwidth oriented to match the simulations.

Figure 8 shows frequency pairs of simulated versus wind speed (top) and water vapor (bottom) for nonraining pixels. The most notable feature is the strong dependence of at 10.7 and 18.7 GHz on wind speed. Likewise, the relationship between at 18.7 and 37 GHz and water vapor is apparent, as the absorption due to water vapor at the two frequencies is equivalent. The isopleths indicate greater amounts of cloud absorption at 37 GHz, which contaminates the wind and water vapor dependence, and also show the influence of cloud at the lower frequencies.

Fig. 8.
Fig. 8.

Hexbin maps of on (top) wind speed (m s−1) and (bottom) water vapor (mm) for rain-free pixels. Grayscale isopleths, from dark to light, denote vertically integrated cloud water paths of 0.1, 0.2, and 0.5 mm.

Citation: Journal of Atmospheric and Oceanic Technology 33, 10; 10.1175/JTECH-D-15-0241.1

For the simulations containing rain, we partitioned the data by water vapor to minimize the water vapor dependence. Figure 9 shows frequency pairs of simulated versus rainfall rate (top) and wind speed (bottom) for vertically integrated water vapor between 60 and 65 mm, and Fig. 10 shows the same relationships for water vapor between 65 and 70 mm. We ignore cases where the columnar water vapor is less than 60 mm, thus discarding 127 out of 1041 points with surface rainfall rate greater than zero. The obvious feature is the considerably stronger spectral response to rain than to the attenuated surface signatures. There is little sensitivity to surface winds at 37 GHz in the presence of rain. For rainfall rates below 2 mm h−1, both the 10.7- and 18.7-GHz simulations show sensitivity to the wind roughening of the surface. These relationships are less clear for the cases where water vapor is between 65 and 70 mm. Some of this is attributable to the higher water vapor, but the hexbin plots for this water vapor range are also noisier. The number of points is almost half: 321–593 points for 60–65 mm. A principal component analysis of Q for the three simulated frequencies, for nonzero rainfall rates, and for water vapor between 60 and 70 mm supports the claim, based on the qualitative analysis , that there is spectral sensitivity to wind speed for rainfall rates below 2 mm h−1. For rainfall below this threshold, the first principal component, which corresponds to opacity dominated by precipitation, explains 94.8% of the variance. The second component, which can be attributed to wind speed, explains 4.7% of the variance. Above 2 mm h−1, such an analysis is less enlightening due to the nonlinearity of the spectral response and the small number of points available for analysis, but the data suggest little-to-no sensitivity to surface winds.

Fig. 9.
Fig. 9.

Hexbin maps of on (top) rainfall rate (mm h−1) and (bottom) wind speed (m s−1) for water vapor between 60 and 65 mm. Grayscale isohyets, from dark to light, denote rainfall rates of 0.5, 2, and 5 mm h−1.

Citation: Journal of Atmospheric and Oceanic Technology 33, 10; 10.1175/JTECH-D-15-0241.1

Fig. 10.
Fig. 10.

Hexbin maps of on (top) rainfall rate (mm h−1) and (bottom) wind speed (m s−1) for water vapor between 65 and 70 mm. Grayscale isohyets, from dark to light, denote rainfall rates of 0.5, 2, and 5 mm h−1.

Citation: Journal of Atmospheric and Oceanic Technology 33, 10; 10.1175/JTECH-D-15-0241.1

To further demonstrate the impact that precipitation has on surface signatures and the resulting retrievals, we look at how the wind speed difference between WindSat retrievals and ECMWF reanalysis compares to in Fig. 11. The WindSat optimal estimator (Bettenhausen et al. 2006) simultaneously retrieves columnar water vapor, columnar cloud, sea surface temperature, and wind vector. To approximate the footprint matching performed for retrievals, the native resolution simulations discussed in section 4a have been smoothed with a Gaussian function having a half-power beamwidth of 25 km × 35 km and oriented to the 37-GHz geometry. The 10.7-GHz footprints have been left at native resolution: 25 km × 38 km at the surface. The rainfall rates and have been smoothed using the same procedure applied to the 18.7- and 37-GHz . Given the uncertainties of the ECMWF reanalysis in storm conditions, as ECMWF underestimates the finescale variability of tropical cyclone wind fields (Chelton et al. 2006), WindSat and ECMWF winds are in relatively good agreement for rainfall rates up to 1 mm h−1, with decreasing but reasonable agreement between 1 and 2 mm h−1. Above 2 mm h−1 of rainfall, the retrievals greatly overestimate the magnitude of the winds, and this overestimation increases with rainfall rate.

Fig. 11.
Fig. 11.

Relationship between wind speed difference (WindSat minus ECMWF) and field-of-view averaged rainfall rate. The hexbin pixels are colored with that have been smoothed to match the resolution of the WindSat retrievals, and the color bar units are in kelvins.

Citation: Journal of Atmospheric and Oceanic Technology 33, 10; 10.1175/JTECH-D-15-0241.1

5. Summary and conclusions

In this work, we demonstrated the coupling of a three-dimensional radiative transfer model with a polarized surface model. TRMM 2B31 combined retrievals serve as input to the radiative transfer model, supported with analysis fields from ECMWF. Simulated agree well with measured from both TMI and WindSat. Using the model, we are able to discern the conditions under which surface contributions are detectable, and we verify this with comparisons between WindSat retrieval and ECMWF reanalysis of near-surface wind speeds. This analysis of the effects of precipitation on wind speed retrievals does have some deficiencies. The linear interpolation of the high-resolution surface rainfall rates produced by the 2B31 algorithm is a poor proxy for the amount and distribution of liquid and frozen water within the radiometer beam; however, this first-order comparison validates the predictions made by the radiative transfer model. Another source of uncertainty is the presence of nonspherical hydrometeors—in particular, preferentially aligned drops that form a dichroic medium—but future simulations can include such particle and drop models.

Based on the present work, there is a discernible spectral component to the wind speed up to approximately 2 mm h−1 of rainfall. The retrievals mostly confirm this assertion; however, there is some disagreement with ECMWF between 1 and 2 mm h−1. Some of these differences can be attributed to temporal mismatch and spatial smoothing of the reanalysis winds, but incomplete modeling of precipitation and spatial mismatching of the resampled also contribute. Improvements to the forward model and the inclusion of 6.8 GHz could extend the range of conditions for which wind may be retrieved, but the coarse resolution of spaceborne C-band radiometers will exacerbate antenna beamfilling effects. A more comprehensive study of the effects of precipitation on surface winds should be undertaken for a wider range of surface and atmospheric conditions, as well as including the effects of nonspherical particles. Improvements to surface emissivity parameterizations should be investigated, as current parameterizations do not fully account for cross-polarization effects for polarized downwelling radiation, particularly if the framework described in this paper is paired with nonspherical, preferentially aligned hydrometeor models. Characterization for nonspecular reflections would also improve interfacing surface emissivity models with three-dimensional radiative transfer schemes. Given that the ECMWF cloud field did not match observations from WindSat, the use of a combined algorithm that includes cloud water retrievals (Munchak and Kummerow 2011) is currently being investigated.

A focused investigation is needed to determine the full effects of footprint matching. The use of measured antenna patterns should also be considered in future work. While the Gaussian approximations matched well up to the first null, there is some deviation, mostly due to skewing of the pattern because of placement away from the focal point. The Gaussian approximation does not include sidelobes, which could be a source of additional contamination in surface retrievals near cloud edges.

While the framework described in this paper is too computationally intensive for near-real-time retrievals, it is useful for understanding the physics of remote sensing. To that end, it can be a forward model for retrieval studies of individual precipitation events or ground validation campaigns with the aim of refining assumptions that are used in an operational process setting. Finally, the flexibility of this radiative transfer framework can facilitate independent comparisons of differing profiling algorithms, and the three-dimensional nature of the model can be exploited to harmonize retrievals from multiple platforms.

Acknowledgments

This work was supported by the Office of Naval Research through the 6.1 base program (PE-61153N). The authors thank Drs. S. Buehler and P. Eriksson and the ARTS team for making their codebase publicly available.

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