Abstract

The Global Precipitation Measurement (GPM) Microwave Imager (GMI) and dual-frequency precipitation radar (DPR) are designed to provide the most accurate instantaneous precipitation estimates currently available from space. The GPM Combined Radar–Radiometer Algorithm (CORRA) plays a key role in this process by retrieving precipitation profiles that are consistent with GMI and DPR measurements; therefore, it is desirable that the forward models in CORRA use the same geophysical input parameters. This study explores the feasibility of using internally consistent emissivity and surface backscatter cross-sectional () models for water surfaces in CORRA. An empirical model for DPR Ku- and Ka-band as a function of 10-m wind speed and incidence angle is derived from GMI-only wind retrievals under clear-sky conditions. This allows for the measurements, which are also influenced by path-integrated attenuation (PIA) from precipitation, to be used as input to CORRA and for wind speed to be retrieved as output. Comparisons to buoy data give a wind rmse of 3.7 m s−1 for Ku+GMI retrievals and 3.2 m s−1 for Ku+Ka+GMI retrievals under precipitation (compared to 1.3 m s−1 for clear-sky GMI-only retrievals), and there is a reduction in bias from the global analysis (GANAL) background data (−10%) to the Ku+GMI (−3%) and Ku+Ka+GMI (−5%) retrievals. Ku+GMI retrievals of precipitation increase slightly in light (<1 mm h–1) and decrease in moderate to heavy precipitation (>1 mm h−1). The Ku+Ka+GMI retrievals, being additionally constrained by the Ka reflectivity, increase only slightly in moderate and heavy precipitation at low wind speeds (<5 m s−1) relative to retrievals using the surface reference estimate of PIA as input.

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 () in a precipitating column from a precipitation-free reference. The difference is then assumed to be due to attenuation from precipitation after accounting for multiple scattering (Battaglia and Simmer 2008) and the effect of precipitation on the surface itself (Seto and Iguchi 2007). If the ratio of this difference to the uncertainty in the reference value, known as the reliability factor, is large, then the precipitation retrieval is more strongly constrained, because the PIA is sensitive to the vertically integrated third moment of the particle size distribution, whereas the reflectivity is sensitive to the sixth moment.

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 and emissivity that may exist. Over water surfaces, it is known that wind-induced surface roughness and foam have a large impact on and emissivity; thus, it should benefit a combined algorithm to retrieve the 10-m wind speed in order to achieve internal consistency between the forward-modeled PIA and brightness temperatures.

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 to wind speed is low (Donnelly et al. 1999; Fernandez et al. 2006), limiting the accuracy of retrievals even if rain effects are accredited.

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 (e.g., Li et al. 2002; Freilich and Vanhoff 2003; Tran et al. 2007). These are then used to retrieve the wind field independently with PR (Li et al. 2004) either as a stand-alone product or for use as a reference to estimate the rain-induced attenuation as an input to the rainfall estimation algorithms. In the case of WindSat, a comparison of its retrievals and QuikSCAT wind vectors in coincident overpasses was performed by Quilfen et al. (2007), who found that differences between the two depended on wind speed and water vapor (a consequence of the aforementioned cross talk between parameters). The authors also attempted to combine the two sets of measurements via multiple regression. They found that adding QuikSCAT to WindSat did not improve wind retrievals outside of rain, but they did note a slight improvement under raining conditions. More recently, the Aquarius satellite, which offers active and passive measurements at L band for the purpose of ocean salinity retrieval, was launched. Yueh et al. (2013) developed GMFs based on SSM/I and NCEP reanalysis collocations and found that the resulting combined active–passive retrievals of wind speed and salinity compared favorably to salinity retrievals where ancillary data were used to set the wind vector.

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.

Fig. 1.

Flowchart of the process by which the DPR GMF is derived and used by the combined DPR–GMI precipitation algorithm.

Fig. 1.

Flowchart of the process by which the DPR GMF is derived and used by the combined DPR–GMI precipitation algorithm.

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 first step in this process is to generate the clear-sky wind retrievals and then assess their error relative to buoy observations. In the absence of precipitation, the microwave radiances measured by GMI are primarily sensitive to the surface emission, atmospheric temperature and water vapor profile, and cloud liquid water. These parameters can be solved for using optimal estimation, also known as variational, retrieval techniques. These have been implemented for microwave sensors by Elsaesser and Kummerow (2008) and Boukabara et al. (2011), and a blend of their approaches is used to derive the surface and atmospheric properties from GMI by minimizing the cost function:

 
formula

The components of the optimal estimation retrieval are the state vector () and covariance matrix (), the observation vector () and covariance matrix (), and the forward model . For water surfaces, the state vector consists of the 10-m wind speed, cloud liquid water path, and a set of variables representing the values of the leading empirical orthogonal functions (EOFs) of the atmospheric temperature and water vapor profile. These EOFs were derived from 10 years of MERRA reanalysis (Rienecker et al. 2011; NASA/GMAO 2008) independently in 1-K SST bins. The number of leading EOFs is chosen such that at least 99% of the variance in temperature and water vapor is explained by the selected EOFs. The EOFS are used to simultaneously adjust the initial atmospheric temperature and water vapor profiles in order to match the observed GMI radiances. This is a change from the Elsaesser and Kummerow (2008) method, which assumed a constant lapse rate and scale height for water vapor. These assumptions are sufficient for matching observations near the 22-GHz water vapor absorption line, where radiances are mostly sensitive to the total column-integrated amount of water vapor and are less sensitive to its vertical structure and emitting temperature. However, both the vertical structure of water vapor and temperature matter for modeling the additional channels near 183 GHz on GMI, so some method of adjusting the shape of the profile in mid- and upper levels is necessary. The EOFs represent the climatological covarying structures in temperature and water vapor profiles, and are a robust way to adjust both without requiring temperature sounding channels (e.g., 50–55 GHz). The a priori (and initial) state is the MERRA reanalysis interpolated in time and space to the GMI pixel location.

Because the atmosphere is represented by EOFs and no covariance between the atmosphere and wind/cloud is assumed, the state covariance matrix is diagonal. The observation vector consists of the 13-channel GMI radiances from the GMI level 1C-R (intercalibrated and collocated) product (GPM Science Team 2015). The collocation matches the high-frequency (HF) observations [166 vertical (V) and horizontal (H), 183 ± 3, and 183 ± 7 GHz], which are observed at 49.2° Earth incidence angle, with the lower-frequency (LF) observations, which are observed at 52.8° Earth incidence angle. A diagonal matrix for is also assumed, with values of instrument noise (Hou et al. 2014) plus additional error determined from buoy matchups (Table 1) to account for forward model error and inexact footprint matching.

Table 1.

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.

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.
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.

The forward model is derived from the Community Radiative Transfer Model (CRTM) Emission (nonscattering atmosphere) Model, modified to include the downwelling pathlength correction for roughened water surfaces as described by MW and using the same atmospheric layers that are provided by MERRA products up to 10 hPA. Absorption by atmospheric gases is calculated from Rosenkranz (1998) and Tretyakov et al. (2003). Cloud liquid absorption follows Liebe et al. (1991), and cloud water is assumed to follow an adiabatic profile (Albrecht et al. 1990). Since the surface emissivity and its relationship to wind speed is of fundamental importance to this study, three emissivity models were tested for their ability to produce unbiased clear-sky radiances when forced with buoy-observed surface winds (within 30 min of a GPM overpass) and MERRA atmospheric profiles: FASTEM4/5 (as implemented in CRTM; Liu et al. 2011) and the Meissner and Wentz (2012, hereafter MW) model.1 Wind direction was not considered in this study, as only the MW model is capable of representing wind direction–induced emissivity changes. Instead, we include the wind direction–induced error in the total model error, which is derived from buoy matchups. The source of wind observations in this study is the International Comprehensive Ocean–Atmosphere Data Set, version 2.5 (ICOADS; Woodruff et al. 2011; NOAA/NCDC 2011) from April 2014 to March 2015. Only observations from platforms with a known anemometer height () were considered, and all winds were adjusted to 10 m assuming neutral buoyancy using the relationship (Hsu et al. 1994):

 
formula

Before the emissivity models can be intercompared, sensor calibration must be considered. Following MW, a calm-wind offset () was determined for each emissivity model and each GMI channel. These offsets were obtained by first selecting a subset of ICOADS observations with 10-m winds less than 3.5 m s−1, where the emissivity–wind relationship is linear. To filter out clouds, observations were excluded if the polarization difference at 89 GHz was less than an SST-dependent threshold representing a cloud liquid water path of 0.01 kg m–2 under average atmospheric conditions or the spatial standard deviation (within 15 km) of 89-GHz Tb was greater than 2 K. The radiative transfer model (RTM) was then forced with the observed SST and wind speed and interpolated MERRA atmospheric profile. The offsets were then calculated in order to minimize the bias between observed and simulated GMI brightness temperatures. No offsets were applied to the 183-GHz channels, as these were not sensitive to the surface emissivity in the matchups. The offsets and root-mean-square error (after offsets have been applied) are given for each channel and emissivity model in Table 1. The biases are different for each model at low frequencies but similar or identical at 166 GHz, indicating low sensitivity of the brightness temperatures to emissivity at these channels and therefore low confidence in the offsets, which are likely influenced by the water vapor absorption model and/or absolute calibration of GMI. The root-mean-square error (rmse) values, which are not sensitive to the choice of emissivity model, represent the error from other components of the forward model (such as wind direction and water vapor absorption) plus instrument noise and are used as the diagonal components of .

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.

Fig. 2.

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.

Fig. 2.

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.

The DPR GMF was generated by averaging the observed from the DPR level 2 product (Iguchi and Meneghini 2014), removing the two-way attenuation from gases and cloud liquid water (which are determined from the GMI retrievals), in wind speed bins with 0.5 m s−1 spacing from 0 to 10 m s−1, 1 m s−1 spacing between 10 and 20 m s−1, and 2 m s−1 spacing above 20 m s−1. Note that all of the results presented in this manuscript are from observations taken between 25 August 2014 (when the most recent phase shift code for DPR was implemented) and 30 April 2015. Earlier observations used different phase shift codes and attenuator settings, which had some slight impact on the GMFs (not shown). The standard deviation in each bin is also calculated as is the correlation coefficient in the case of the matched Ku- and Ka-band PR (KuPR–KaPR) beams. The standard deviation serves as an implicit indicator of the quality of the derived GMF: Low values are desirable because they indicate that the 10-m wind speed retrieved by GMI is sufficient to represent the sea state for the purposes of reproducing , and when used in the combined framework, they provide a stronger constraint on the PIA contributed by the precipitation column. The theoretical minimum standard deviation of for DPR, assuming the signal-to-noise ratio is large (true under almost all nonrain conditions), depends on the number of independent samples, N, taken. If the surface is modeled as a Rayleigh target (an incoherent sum from many specular points on the surface without any dominant scattering contribution) and a logarithmic receiver is used, then the standard deviation (dB) is given by (Sauvageot 1992)

 
formula

where N depends on incidence angle and varies between 100 and about 110 . Using these numbers, the nominal standard deviation in , from sampling alone, is a bit more than 0.5 dB.2 Values higher than 0.5 dB could be caused by random errors in the GMI wind reference (this is compounded when the sensitivity of to wind is high) or that something other than wind speed is contributing to the variation of , resulting in the diminished impact of the observation on the precipitation retrieval. In Fig. 3, the standard deviation of for the KuPR, in normal scan (NS) mode, and KaPR, in matched-scan (MS) and high-sensitivity (HS) modes, is shown as a function of DPR incidence angle for three wind speed bins centered on 0.5, 5, and 15 m s−1. At the low wind speed, the standard deviation is quite high (nearly 10 dB), particularly off nadir, but smaller (still 2–4 dB) near nadir at both frequencies (the lower Ku values are likely due to the saturation of the KuPR receiver). As the wind becomes calm, the surface is nearly specular and the sensitivity to small changes in wind speed is quite high off nadir, so random error in the reference wind is thought to primarily contribute to the large standard deviation there. Long-period swell also provides an increasing contribution to variation in (Tran et al. 2007) that is unrelated to the local wind speed. Finally, since the change in with respect to incidence angle is also high at low wind speeds, small changes in the incidence angle (the standard deviation of the DPR incidence angle was around 0.01° in each angle bin) may also contribute to the high standard deviation at off-nadir angles.

Fig. 3.

Standard deviation of in three wind speed bins: (top) 0.5, (middle) 5, and (bottom) 15 m s–1. The different colors represent different frequencies, DPR modes (NS, MS, HS), and quality control of the reference wind.

Fig. 3.

Standard deviation of in three wind speed bins: (top) 0.5, (middle) 5, and (bottom) 15 m s–1. The different colors represent different frequencies, DPR modes (NS, MS, HS), and quality control of the reference wind.

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 are shown in Fig. 4. Most of the variability is exhibited at low wind speeds at both Ku and Ka bands.3 However, continues to decrease near nadir for wind speeds as high as 30 m s−1, which is approximately the upper limit of the reliable data that has been collected so far. Off nadir, appears to reach maxima at increasing wind speeds with incidence angle. The standard deviation of reaches minima near the 0.5-dB sampling limit at 5°–15° and wind speeds between 5 and 10 m s−1. There is also a minimum in the standard deviation at Ku band (but not Ka band) at very low wind speeds near nadir. This is an artifact of the saturation of the Ku receiver when dB (the Ka receiver saturates closer to 40 dB, which is only observed over some land and ice surfaces). The higher standard deviations at the off-nadir angles are likely a result of wind direction–induced variability in . In Fig. 4f the observed Ku-band is compared to the cutoff-invariant two-scale model (Soriano and Guérin 2008) using the Durden–Vesecky single-amplitude wave spectra (Durden and Vesecky 1985). This model appears to produce a flatter when viewed with respect to incidence angle at low wind speeds, but at winds above about 8 m s−1 it has a comparable shape to the observed GMF minus a small (1 dB) offset. These results are consistent with the comparisons of this model to airborne observations of reported by Majurec et al. (2014).

Fig. 4.

The two-dimensional GMFs of , its standard deviation, Ku–Ka correlation, and difference between the Durden–Vesecky single-amplitude model and observations at Ku band are shown as a function of 10-m wind speed and incidence angle.

Fig. 4.

The two-dimensional GMFs of , its standard deviation, Ku–Ka correlation, and difference between the Durden–Vesecky single-amplitude model and observations at Ku band are shown as a function of 10-m wind speed and incidence angle.

The Ku–Ka correlation (Fig. 4e) is an important component of the dual-frequency surface reference technique (DSRT; Meneghini et al. 2012). In the DSRT, is replaced by the differential :

 
formula

and the method provides an estimate of the differential PIA, A(Ka) − A(Ku) where A is attenuation. The errors in both single-frequency SRT and DSRT methods are dominated by the fluctuations in the rain-free reference data: and . As the correlation between (Ku) and (Ka) increases, the variance in decreases, so that the DSRT provides a potentially more accurate estimate of the path attenuations. The correlations, which are near 0.8 in most DPR angle bins when all wind speeds are considered, reduce to 0.1–0.4 for most wind speeds >5 m s−1 and off-nadir incidence angles. This suggests that wind is responsible for most of the covariance in Ku and Ka but near nadir and at low winds the stronger correlations make the DSRT technique particularly useful.

3. Combined radar–radiometer retrieval of precipitation and surface wind

The MW emissivity model (optimized for GMI) and DPR wind– GMFs described in section 2 are implemented in the forward modeling component of the CORRA retrieval algorithm. A description of the radar component of this algorithm is given by Grecu et al. (2011), and a more complete description of the algorithm’s architecture can be found in the algorithm theoretical basis document (Olson and Masunaga 2015); for the purposes of this manuscript, a brief summary and example case are presented in this section followed by validation statistics. It is difficult to directly ascertain the improvement (if any) in rainfall estimates over ocean owing to the lack of reliable direct measurements, but the algorithm can be assessed as to how well the forward model matches GPM observations and buoy observations of wind speed. The impact on retrieved precipitation amounts is also shown in this section.

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 observations. The randomly perturbed properties of each profile solution include the vertical profile of the hydrometer particle size distribution (PSD) intercept parameter (), degree of nonuniform beamfilling, the cloud liquid water profile, relative humidity, and 10-m wind speed. For each solution, the associated Ku and Ka , Ka reflectivities, and GMI radiances are calculated. The calculation of Ka reflectivity accounts for multiple scattering enhancements using the multiscatter library developed by Hogan and Battaglia (2008).

The ensemble is then filtered using the observed Ku , GMI radiances, and Ka reflectivities and (where available). This is done by constructing an vector representing the ensemble variables to be updated, including the perturbed variables (e.g., and 10-m wind) and derived/forward-modeled variables (e.g., precipitation rate and brightness temperature). A separate vector consists of the forward-modeled variables corresponding to the observation vector ( is the corresponding observation error), which contains the observed , brightness temperatures, and Ka reflectivities. The ensemble state vector is then updated using the sample covariance:

 
formula

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.

Fig. 5.

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.

Fig. 5.

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.

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 errors, whereas adjustments in stratiform rain are mostly a response to the Ka and GMI Tb (note that in the heaviest rain, the correlation between rain rate and 36H Tb becomes negative as scattering dominates over emission). Note that in extremely heavy precipitation with large amounts of ice aloft, the variability of Ka due to multiple scattering begins to overwhelm the attenuation and the correlation decreases. In these cases, the algorithm relies mostly on Ku to adjust the initial ensemble rain rates. In light and moderate rainfall, the 10-m wind adjustment is mostly a response to Ku , especially away from the approximately 9° incidence angle at which Ku is insensitive to wind. Nevertheless, there is some sensitivity of the 10- and 19-GHz radiances and Ka to wind under lighter precipitation. Because of the finite number of ensemble members, there are some spurious negative correlations between wind and the Tb in heavier rain, but these are weak and do not substantially impact the output. The degree to which the ensemble spread is reduced after the filtering step is indicative of the overall information content in the observations for each variable of interest, and is provided as part of the standard CORRA output.

Fig. 6.

Correlations of Ku and Ka , and 10.65-, 18.7-, and 36.6-GHz horizontally polarized Tb to surface rain rate and 10-m wind speed, derived from the initial ensemble of solutions to each radar profile.

Fig. 6.

Correlations of Ku and Ka , and 10.65-, 18.7-, and 36.6-GHz horizontally polarized Tb to surface rain rate and 10-m wind speed, derived from the initial ensemble of solutions to each radar profile.

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 is warranted.

Table 2.

The rmse and bias of ensemble-mean deconvolved GMI radiances before and after filtering.

The rmse and bias of ensemble-mean deconvolved GMI radiances before and after filtering.
The rmse and bias of ensemble-mean deconvolved GMI radiances before and after filtering.

The initial and filtered rms errors and bias of are shown as a function of scan angle in Fig. 7. There is a significant reduction in Ku rms error at all scan angles. The Ka error values are higher due to the stronger attenuation and multiple scattering effects, but errors are still reduced by nearly 50% after the filtering step. The bias plots show a pattern of initial errors that is consistent with a low bias in the ENV wind (too high near nadir and too low off nadir), where ENV is the background environmental data used for algorithm input. This bias appears to be more significant than any systematic bias in the precipitation attenuation, which would have the same sign regardless of scan angle.

Fig. 7.

The (a) rmse and (b) bias of the initial and filtered ensemble mean as a function of incidence angle.

Fig. 7.

The (a) rmse and (b) bias of the initial and filtered ensemble mean as a function of incidence angle.

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 biases as well).

Fig. 8.

Background (JMA GANAL; 2A-ENV) and retrieved wind rmse and bias relative to ICOADS buoy observations in precipitating pixels.

Fig. 8.

Background (JMA GANAL; 2A-ENV) and retrieved wind rmse and bias relative to ICOADS buoy observations in precipitating pixels.

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 to wind speed (Figs. 4 and 6 illustrate this behavior). Near nadir and beyond 12° incidence angles, the sensitivity is stronger and the wind errors are much smaller. The NS errors are similar, and the MS errors are smaller than the 4.26 m s−1 error of the Advanced Scatterometer (ASCAT) under raining conditions (Portabella et al. 2012) and the 3.5 m s−1 error of the QuikSCAT retrievals using a neural network to compensate for rain effects (Stiles and Dunbar 2010). These are also within the range of 2–5 m s−1 accuracy (depending on rain rate) of a globally applicable rainy-atmosphere WindSat wind retrieval algorithm (Meissner and Wentz 2009). When stratified by rainfall rate, wind speed errors are similar for light (<1 mm h−1) and moderate (1 mm h−1 < R < 10 mm h−1) precipitation rates, but they increase at heavier precipitation rates as the wind-induced variability in and brightness temperatures are overwhelmed by the precipitation effects.

Fig. 9.

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.

Fig. 9.

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.

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 , which depends on both wind- and precipitation-induced PIA. In this section we show the impact of switching from the SRT PIA (which infers PIA by comparing the observed to a reference outside the precipitation) to the coupled –emissivity model.

Theoretically, the use of as an observation (instead of SRT-derived PIA) should impact the agreement between observed and modeled Tb in two ways: first, through adjustments to the rain column to match the observed by changing the PIA; and second, via changes in the surface emissivity. The relative importance of these mechanisms depends on the relative sensitivity of the Tb and to changes in the rain column and surface wind. Figure 10 shows the change in near-surface precipitation rate retrieved by the GPM combined algorithm over ocean surfaces equatorward of 55° latitude (to eliminate possible sea ice) when the SRT PIA (single frequency for NS retrievals in the top panels; DSRT in the MS retrieval shown in the bottom panels) is replaced with the observed in the observation vector. Light precipitation (<1 mm h−1) is increased slightly in the NS swath, predominantly at wind speeds >10 m s−1 and at incidence angles less than 12°. The discontinuities in the 10°–12° range are an artifact of the unavailability of the low-frequency GMI channels near the edge of the DPR swath (the deconvolution procedure requires coverage of the full footprint within the DPR swath). This suggests that GMI Tb are driving the increase in precipitation, which is consistent with the weak Ku –precipitation correlation in light rain (Fig. 6). Near the edges of the DPR swath, where the GMI Tb are not used, there is not enough information to significantly adjust the precipitation rate because the Ku-band PIA is small relative to the uncertainty in , so the SRT and coupled method have the same information content.

Fig. 10.

Change in GPM combined algorithm precipitation, as a function of wind speed and incidence angle, when the SRT PIA is replaced with the observed in the observation vector and a coupled –emissivity model is used in the forward model. The ENV wind and SRT-based precipitation are used as reference values.

Fig. 10.

Change in GPM combined algorithm precipitation, as a function of wind speed and incidence angle, when the SRT PIA is replaced with the observed in the observation vector and a coupled –emissivity model is used in the forward model. The ENV wind and SRT-based precipitation are used as reference values.

At moderate (1 mm h−1 < R < 10 mm h−1) precipitation rates, the wind– correlation is still larger than the rain correlation at Ku band, whereas Tb are more sensitive to the precipitation (although there is still some wind sensitivity, especially at 10H); this results in some compensating behavior, where it is “easier” for the algorithm to increase the wind speed to satisfy the Ku observation, but it must reduce the precipitation rate to be consistent with the Tb. In heavy rain (>10 mm h−1), the ensemble variance in and the Tb is dominated by variance in the rain column, rather than surface wind, and where both observations are available only a very small reduction in precipitation is noted with the coupled forward model relative to the SRT method. When only Ku is available in the outer swath, however, there is a reduction in precipitation relative to the SRT version. The mean precipitation rate from the coupled model is more consistent across the different scan angles than the SRT version (not shown), which suggests that the SRT PIA may be biased high at the off-nadir angles and wind speeds from 5 to 10 m s−1.

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 as a function of 10-m wind speed and incidence angle by matching the GMI retrievals to DPR observations under clear-sky conditions.

The MW emissivity model and DPR GMFs were then implemented in the GPM combined algorithm. This coupled forward model indicated that the sensitivity of to wind at Ku band dominates the precipitation sensitivity—particularly in light to moderate rain and at low wind speeds, where the brightness temperatures are more sensitive to precipitation (although there is still some wind sensitivity, particularly at 10 and 18 GHz at horizontal polarization in light and shallow precipitation). Therefore, the surface reference (SRT) estimate of the DPR PIA was replaced with in the observation vector. This is desirable because is directly observed by DPR, while the SRT PIA includes implicit assumptions and can be unphysically negative in light rain. Because depends on both the 10-m wind speed and attenuation from atmospheric gases, clouds, and precipitation, the 10-m wind speed was added to the retrieval state vector.

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 and emissivity, requiring changes in the precipitation column to maintain consistency with the observations. The Ku+Ka+GMI retrievals, being additionally constrained by the Ka reflectivity, did not change as much although a slight increase in moderate and heavy precipitation at low wind speeds was noted.

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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Footnotes

This article is included in the Precipitation Retrieval Algorithms for GPM special collection.

1

Note that the MW model does not include frequencies higher than 90 GHz and FASTEM5 was substituted at these frequencies.

2

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 ; however, in the DPR processing, the is based on the peak return power, not the integrated power.

3

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.