A Consistent Treatment of Microwave Emissivity and Radar Backscatter for Retrieval of Precipitation over Water Surfaces
1. Introduction
Algorithms for estimating precipitation from spaceborne radars at attenuating frequencies [e.g., TRMM PR (Iguchi et al. 2000, 2009), CloudSat (Mitrescu et al. 2010), Global Precipitation Measurement (GPM) dual-frequency precipitation radar (DPR; Grecu et al. 2011)] have long realized the benefit of an estimate of the path-integrated attenuation (PIA) that is independent of the reflectivity profile for the purposes of constraining the integrated and surface precipitation amounts. In general, such an estimate of the PIA is obtained via a form of the surface reference technique (SRT; Meneghini et al. 2000, 2004), which subtracts the surface radar backscatter cross section (
Algorithms that make simultaneous use of passive microwave and radar data (Haddad et al. 1997; Grecu et al. 2004; Munchak and Kummerow 2011) generally use the SRT PIA along with microwave radiances to constrain the precipitation profile (indeed, PIA can be the dominant constraint because of its high resolution relative to the passive microwave footprint, especially when the reliability factor is large). These algorithms also require knowledge of the surface emissivity in order to forward model the brightness temperatures (Tb) for comparison to observations. Since emission and reflection are related processes, it is logical for a combined algorithm to exploit any relationships between 
The purpose of this work is not only to highlight the benefits of unifying the active and passive surface characteristics for the purpose of precipitation retrievals from GPM but also to demonstrate the feasibility of combined DPR–GPM Microwave Imager (GMI) retrievals of surface wind over water, particularly when precipitation is present. This has historically been problematic for both passive and active (scatterometer) wind retrievals (Weissman et al. 2012), despite the high motivation to develop capabilities to monitor the strength of tropical and extratropical cyclones. For passive measurements, higher-frequency channels (>19 GHz) can become opaque to the surface in rain and clouds, and although the surface emission is not fully obscured at lower frequencies, measurements at multiple frequencies near the C band are required to distinguish the surface and rain column contributions from the observed radiances (Uhlhorn et al. 2007). However, the large footprints that are characteristic of spaceborne microwave radiometers at these frequencies are not optimal for retrievals of wind and precipitation due to nonuniformity within the footprint. Even outside of rain, cross talk between wind, water vapor, and cloud liquid water can bias wind retrievals (O’Dell et al. 2008; Rapp et al. 2009). Also, rain creates an additional source of surface waves, which can either enhance or damp surface backscatter, depending on angle, frequency, and wind speed (Stiles and Yueh 2002; Seto and Iguchi 2007). Backscattering from the rain itself can also enhance the measured surface cross section, particularly for scatterometers that are designed to maximize the signal-to-noise ratio by employing relatively long pulse widths and large footprint sizes (Li et al. 2002). Finally, in high winds the sensitivity of 
As of yet, only the short-lived Midori-II AMSR–SeaWinds combination of passive and active instruments has been designed specifically for the measurement of ocean winds, but several investigators have taken advantage of existing platforms with these measurements (e.g., TRMM and Aquarius) or coincident overpasses of scatterometer and passive microwave radiometers to elucidate further information about the atmosphere and sea state than is possible from either instrument type alone. Studies based on the TRMM Microwave Imager (TMI) and precipitation radar (PR) have often used the TMI-based wind retrievals as a reference to develop geophysical model functions (GMFs) for PR, which relate wind speed and 
The growing number of satellites with active and passive microwave instruments (e.g., TRMM, GPM, Aquarius, SMAP), along with airborne platforms [e.g., the NASA Global Hawk Hurricane and Severe Storm Sentinel (HS3)], represents an opportunity to use these combinations to retrieve ocean winds, particularly under conditions (such as rain) where single-sensor methods are underconstrained. This study is based on data from the GPM satellite, which has a particularly useful set of measurements for developing the GMFs due to the well-calibrated, high-resolution GMI instrument (Draper et al. 2015) and DPR, which improves the capability to separate surface effects from rain-induced attenuation. Our strategy (Fig. 1) is to develop a GMF for DPR based upon collocated GMI wind retrievals, and then use this GMF under raining conditions by modifying the GPM Combined Radar–Radiometer Algorithm (CORRA; Olson and Masunaga 2015). To have as accurate a wind reference as possible, we evaluate three emissivity models after calculating offsets under clear and calm conditions to achieve consistency with the GMI calibration. Next, we use all available matchups of GMI and DPR under nonprecipitating conditions to develop the GMFs. This process is presented in section 2. Next, the use of GMFs in the GPM combined GMI–DPR ensemble filter retrieval framework, including validation of winds in regions of precipitation against buoy measurements, is described in section 3, followed by a summary in section 4.
Flowchart of the process by which the DPR GMF is derived and used by the combined DPR–GMI precipitation algorithm.
Citation: Journal of Atmospheric and Oceanic Technology 33, 2; 10.1175/JTECH-D-15-0069.1
2. Development of geophysical model functions for DPR
Although physical models exist to describe the relationship between wind speed, the wave spectrum, and backscatter (Durden and Vesecky 1985; Majurec et al. 2014), the desire for GPM applications is to be as internally consistent as possible between the emissivity model and DPR GMF. Therefore, the strategy in this study is to derive empirical GMFs from clear-sky matchups of DPR- and GMI-derived 10-m wind retrievals, eliminating as much as possible the error from precipitation and cloud cross talk described in section 1, and then applying those GMFs to retrievals under all conditions. The use of empirical GMFs derived in this manner is standard practice in the scatterometer community (Migliaccio and Reppucci 2006).
The components of the optimal estimation retrieval are the state vector (
Because the atmosphere is represented by EOFs and no covariance between the atmosphere and wind/cloud is assumed, the state covariance matrix 
Bias (before applying offsets) and rmse (after applying offsets; K) of clear sky, nearly calm wind (<3.5 m s−1)-simulated Tb forced with buoy observations of SST, and 10-m wind and MERRA atmospheric parameters. No offsets were applied to the 183-GHz channels.
Before the emissivity models can be intercompared, sensor calibration must be considered. Following MW, a calm-wind offset (
Next, each emissivity model was evaluated under the full range of conditions encountered in the GMI buoy overpasses. The retrieval was performed with each emissivity model, and the retrieved winds are compared with observations in Fig. 2. These results were filtered to remove precipitation by applying a maximum threshold of 1.0 for the normalized cost function. It is apparent from these results that the MERRA analysis is biased high at observed wind speeds below 3 m s−1 and biased low above this threshold. The retrievals using the different emissivity models behave similarly to each other up to about 8 m s−1 and remove most of this bias, but they diverge due to different foam models (implicit in MW and explicit in FASTEM 4/5). At observed wind speeds greater than 15 m s−1, FASTEM4 begins to diverge below the observed wind speed, whereas FASTEM5 diverges above more severely. The MW model gives a slight low bias of as much as 1 m s−1 at 10–15 m s−1 but recovers to near zero at higher speeds. The overall root-mean-square error in clear-sky conditions for the MW model is 1.3 m s−1 (equivalent to WindSat) and, because of its low bias over the range of observed wind speeds, is chosen to generate the DPR GMFs.
MERRA and GMI-retrieved wind speed bias relative to ICOADS buoy observations from March to December 2014. Error bars represent 1σ of the difference between observed and retrieved wind speeds in each bin.
Citation: Journal of Atmospheric and Oceanic Technology 33, 2; 10.1175/JTECH-D-15-0069.1
Standard deviation of 
Citation: Journal of Atmospheric and Oceanic Technology 33, 2; 10.1175/JTECH-D-15-0069.1
At moderate and high wind speeds, the standard deviations are much lower and the pattern is shifted slightly to relatively high values near nadir and at the largest off-nadir angles, with minima around 9° for KuPR. Specular effects can again explain the near-nadir maximum, whereas the off-nadir maxima are likely a result of wind direction sensitivity (Wentz et al. 1984). The KaPR standard deviations are slightly higher for the MS than the HS data due to the shorter pulse width and are qualitatively similar to the KuPR data. The effect of more stringent quality control (reduction of the cloud LWP, its spatial variability, and cost function thresholds by 50%; denoted QC2 in Fig. 3) is also most evident here in reducing the KaPR standard deviation, but the differences are negligible enough (0.01 dB) that the original thresholds (QC1) are used to generate databases for the combined algorithm, as these thresholds provide more data, especially at higher wind speeds.
The two-dimensional GMFs of 
The two-dimensional GMFs of 
Citation: Journal of Atmospheric and Oceanic Technology 33, 2; 10.1175/JTECH-D-15-0069.1
3. Combined radar–radiometer retrieval of precipitation and surface wind
The MW emissivity model (optimized for GMI) and DPR wind–
a. Algorithm description
The CORRA algorithm uses an ensemble filter technique (Evensen 2006) to retrieve a set of precipitation profiles that is consistent with observations from KuPR, GMI, and KaPR (where available). The first step in this process is the creation of an ensemble of solutions that fits the observed KuPR reflectivity profile without any consideration of the GMI, KaPR, or KuPR 
The algorithm output is derived from the updated ensemble and includes both mean and standard deviations of the geophysical parameters of the ensemble and forward-modeled observations. This update is done separately for the Ku-only full swath (denoted as NS in GPM products) and Ku+Ka inner swath (MS products).
b. Example case
To illustrate the update process described by Eq. (5), the retrieval algorithm is applied to a GPM overpass of a developing cyclone off the eastern coast of the United States on 26 January 2015 (Fig. 5). This case provides an opportunity to examine the algorithm under a variety of precipitation and surface wind conditions.
False-color GMI composite and KuPR maximum column-observed reflectivity at 2204 UTC 26 Jan 2015. The GMI composite is from the 89-GHz V and H and 36-GHz V channels following the Negri et al. (1989) scheme.
Citation: Journal of Atmospheric and Oceanic Technology 33, 2; 10.1175/JTECH-D-15-0069.1
The correlations (calculated from the initial, unfiltered ensemble) between the each observation type and the surface rain rate, as well as the correlations between each observation type and the 10-m wind speed, are shown in Fig. 6 for both radar frequencies and the horizontally polarized GMI channels from 10 to 36 GHz (which are most sensitive to rain and wind over water surfaces). It is evident from these sensitivities that algorithm adjustments to precipitation rate in convective rain (echoes greater than 40 dBZ; purple colors in Fig. 5) are mostly a response to the initial Ku and Ka 
Correlations of Ku and Ka 
Citation: Journal of Atmospheric and Oceanic Technology 33, 2; 10.1175/JTECH-D-15-0069.1
c. Internal validation
The output from 400 GPM orbits between September 2014 and January 2015 is analyzed to assess the internal consistency between the forward model and observations before and after filtering. The mean bias and rms error between the initial ensemble mean and filtered ensemble mean for both NS (Ku+GMI) and MS (Ku+Ka+GMI) are given in Table 2. There is a general cold bias to the initial simulated Tb at all frequencies (although a warm bias is present in the 18- and 36-GHz channels at rain rates exceeding 10 mm h−1). Both the rms error and magnitude of the bias are reduced after filtering as expected. The MS error and bias are larger than the NS error and bias because the initial ensemble profiles are constrained by the additional Ka-band information and are less free to be adjusted to match the GMI radiances. In other words, the NS retrievals are overfit to the Tb, which suggests that an increase in their error values in 
The rmse and bias of ensemble-mean deconvolved GMI radiances before and after filtering.
The initial and filtered rms errors and bias of 
The (a) rmse and (b) bias of the initial and filtered ensemble mean 
Citation: Journal of Atmospheric and Oceanic Technology 33, 2; 10.1175/JTECH-D-15-0069.1
d. External validation
During September 2014–January 2015, 606 buoy observations from the ICOADS database were identified as being within 30 min of a GPM overpass and in the KuPR swath (308 of these were within the KaPR swath) at the same time that DPR detected precipitation in the pixel nearest to the buoy location. These observations were used to validate the CORRA wind retrieval.
The wind rmse and bias are shown in Fig. 8. Similar to the MERRA data analyzed in section 2, these background winds are biased high below 3 m s−1 and biased low at higher wind speeds relative to the buoy observations. Root-mean-square errors increase from 2 to 4 m s−1 and NS errors are slightly higher than the MS or ENV errors. However, the bias is significantly reduced in the filtered datasets relative to the initial winds, indicating that while the retrievals are noisy, adjustments tend to be in the correct direction (this is consistent with the initial and filtered Tb and 
Background (JMA GANAL; 2A-ENV) and retrieved wind rmse and bias relative to ICOADS buoy observations in precipitating pixels.
Citation: Journal of Atmospheric and Oceanic Technology 33, 2; 10.1175/JTECH-D-15-0069.1
The wind error is shown as a function of incidence angle in Fig. 9. It is evident that the largest errors occur near the 9° incidence angle, where there is little sensitivity of 
Retrieved wind rmse as a function of DPR incidence angle. The data are smoothed using a seven-bin centered average in order to reduce noise from the small sample size in each angle bin.
Citation: Journal of Atmospheric and Oceanic Technology 33, 2; 10.1175/JTECH-D-15-0069.1
e. Impact on precipitation retrieval
Although the retrieval of wind in precipitation is useful for many applications, one of the main purposes of this work is to improve the precipitation retrieval by enforcing an internal consistency between the surface emissivity (which depends on wind) and observed 
Theoretically, the use of 
Change in GPM combined algorithm precipitation, as a function of wind speed and incidence angle, when the SRT PIA is replaced with the observed 
Citation: Journal of Atmospheric and Oceanic Technology 33, 2; 10.1175/JTECH-D-15-0069.1
At moderate (1 mm h−1 < R < 10 mm h−1) precipitation rates, the wind–
The Ku–Ka (MS) retrievals are generally more stable when comparing the SRT and coupled versions of the algorithm, but some changes are still notable. The increase in light precipitation is still present, but moderate and heavy precipitation shows some different behavior from the NS retrievals with increases in light winds (below about 5 m s−1) and little change at higher wind speeds. There is not much sensitivity of Tb to wind at low wind speeds, so this appears to be driven by an increase in the inferred PIA in the coupled model relative to the dual-frequency SRT.
4. Summary
The Global Precipitation Measurement core satellite launched in February 2014 carries a passive microwave imager (GMI) and a dual-frequency radar (DPR) designed specifically to provide the most accurate instantaneous precipitation estimates currently available from space, and they serve as a reference for precipitation retrievals from other passive microwave imagers with similar channel sets (Kummerow et al. 2015). The GPM combined algorithm plays a key role in this process by providing precipitation estimates that are consistent with both GMI and DPR measurements. This algorithm uses physically based forward models to simulate GMI and DPR measurements, and it is desirable that those models use the same geophysical input parameters wherever possible.
This study explored the feasibility of using internally consistent relationships between wind, emissivity, and backscatter for water surfaces in the combined algorithm. We first evaluated the FASTEM 4/5 (Liu et al. 2011) and Meissner and Wentz (2012) emissivity models in a GMI-only nonprecipitation retrieval against buoy observations obtained from ICOADS. The MW model provided the lowest rms error (1.3 m s−1) and was used to create a geophysical model function (GMF) for DPR Ku and Ka 
The MW emissivity model and DPR GMFs were then implemented in the GPM combined algorithm. This coupled forward model indicated that the sensitivity of 
The combined wind/precipitation retrievals were then evaluated against the ICOADS buoy dataset under precipitating conditions, which have been a challenge for surface wind retrievals from stand-alone passive radiometers (e.g., WindSat) or scatterometers. Although the retrievals were noisier than under clear-sky conditions (rmse of 3.7 m s−1 for Ku+GMI and 3.2 m s−1 for Ku+Ka+GMI), there was a significant reduction in the bias from the background data provided by global analysis (GANAL) data (−10%) to the Ku+GMI (−3%) and Ku+Ka+GMI (−5%) retrievals. The impact on precipitation retrievals was also evaluated. Ku+GMI retrievals of precipitation increased slightly on the light end (<1 mm h−1) and decreased in moderate to heavy precipitation (>1 mm h−1) due to compensating effects of wind on 
While GPM was not designed specifically to measure ocean surface winds, this study demonstrates that such measurements are quite feasible in clear-sky conditions. In precipitation, using a coupled emissivity–backscatter GMF produces reasonable results that achieve the goal of internal consistency in the combined algorithm. The results presented here should only be considered as a proof of concept, as additional details that we did not consider, such as wind direction, the effect of rain on the scattering properties of water surfaces, and spatial correlation of the wind field, are left to future work.
Acknowledgments
This work was supported under NASA Cooperative Agreement NNX12AD03A and Precipitation Measurement Missions Program Scientist Dr. Ramesh Kakar. We would also like to thank Dr. Thomas Meissner of Remote Sensing Systems for providing the computational codes for the Meissner–Wentz emissivity model, and Dr. Simone Tanelli of NASA JPL/Caltech for providing the cutoff-invariant two-scale Durden–Vesecky model data. Finally, we thank the three anonymous reviewers, whose comments and suggestions greatly improved the quality of this manuscript.
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Note that the MW model does not include frequencies higher than 90 GHz and FASTEM5 was substituted at these frequencies.
For off-nadir incidence, where there are multiple samples from the surface, a case can be made for integrating over all the data from the surface. This should reduce the standard deviation of the 
The Ka HS GMF is not shown, but it is essentially identical to the MS data with a −0.2-dB offset owing to the inability of the larger pulse width to capture the surface peak as effectively, especially near nadir.
