Can DSD Assumptions Explain the Differences in Satellite Estimates of Warm Rain?
1. Introduction
Satellites play an important role in measuring, predicting, and understanding precipitation across the globe. Current precipitation missions such as the Global Precipitation Measurement (GPM) mission (Hou et al. 2014; Skofronick-Jackson et al. 2017) and CloudSat (Stephens et al. 2008, 2018) are crucial for monitoring the global hydrologic cycle and constraining climate models, especially over the open oceans where rain gauges, disdrometers, and ground-based radar observations are rarely available. Satellite observations inform many types of precipitation estimates. These include direct estimates from CloudSat (Haynes et al. 2009; Lebsock and L’Ecuyer 2011) and the GPM Core Observatory satellite (Grecu et al. 2016; Seto et al. 2021) along with the earlier Tropical Rainfall Measuring Mission (TRMM; Kummerow et al. 2000), estimates from a constellation of passive microwave radiometers (GPROF; Kummerow et al. 2015), and estimates that combine observations from a variety of different satellite techniques such as the Global Precipitation Climatology Project (GPCP; Adler et al. 2018) and the Climate Prediction Center Merged Analysis of Precipitation (CMAP; Xie and Arkin 1997). Over some regions of the globe, there is reasonable agreement between seasonally averaged precipitation as estimated from these various satellite products, especially when GPM-based and CloudSat-based estimates are combined in ways that take advantage of the fact that GPM/TRMM is more sensitive to moderate and heavy precipitation while CloudSat is more sensitive to light precipitation (Behrangi et al. 2014; Hayden and Liu 2018). However, over the higher latitudes, as well as over stratocumulus dominated regimes, larger discrepancies exist (Berg et al. 2010; Andersson et al. 2011; Behrangi et al. 2016; Behrangi and Song 2020). In particular, north or south of about 40° latitude there are large differences between zonally averaged oceanic precipitation estimates from the GPM combined radar–radiometer algorithm GPM_2BCMB (Grecu et al. 2016) and the CloudSat 2C-RAIN-PROFILE algorithm (Lebsock and L’Ecuyer 2011). Behrangi and Song (2020) find that the GPM estimates can be up to 60%–70% (∼2 mm day−1) lower than the CloudSat estimates at these high latitudes.
There are undoubtedly many factors contributing to the disagreement among satellite precipitation estimates. For example, many light precipitation events do not generate high enough Ku- or Ka-band reflectivities (Z) to be detected by the Dual-Frequency Precipitation Radar (DPR) on the GPM Core Observatory satellite. DPR has a minimum detectable Z of 15.46 dBZ for Ku band, 19.18 dBZ for Ka-band matched beam, and 13.71 dBZ for the Ka-band high-sensitivity beam (Masaki et al. 2021). In terms of rain rates, this corresponds to a nominal threshold of 0.5 mm h−1 for Ku-only retrievals and 0.2 mm h−1 for Ku/Ka retrievals (Kidd et al. 2021). However, Lin and Hou (2012) found that, over the continental United States, 43.1% of precipitation occurs below 0.5 mm h−1 and 11.3% occurs below 0.2 mm h−1, with those occurrences accounting for 7% and 0.8% of total rain volume, respectively. Over stratocumulus areas and at the high latitudes, where drizzle is common, those values are even higher, with as much as 70% of precipitation by frequency (or around 25% by volume) occurring at rain rates below 0.5 mm h−1 (Kidd and Joe 2007; Giangrande et al. 2019). CloudSat’s Cloud Profiling Radar (CPR), on the other hand, struggles with heavy precipitation. The higher-frequency W-band radar is more easily attenuated by water vapor, cloud water, and rainwater, and multiple scattering is also more of a concern. These factors make CPR precipitation estimates at high rain rates unreliable (e.g., Battaglia et al. 2008; Berg et al. 2010). The insensitivity of DPR to light precipitation and the attenuation challenges CPR faces in heavy precipitation together form a natural (if only partial) explanation of the widely reported result that GPM/TRMM retrievals underestimate light rain rates while CloudSat retrievals underestimate heavy rain rates (e.g., Berg et al. 2010; Behrangi et al. 2012; Hayden and Liu 2018).
Another important consideration is surface clutter. DPR radar returns below 1000 m above the surface have too much noise to accurately detect precipitation, rising to up to 1500 m near the edge of swath or over rough terrain (Kidd et al. 2021). For CloudSat, the lowest range bin that can be accurately sensed is around 750 m (Tanelli et al. 2008). Thus, each of these radars misses some shallow precipitation altogether. For example, Kidd et al. (2021) found that only slightly more than 60% of radar profiles over the United Kingdom had rain rates greater than 0.2 mm h−1 at 1000 m above the surface. Even when the radar can detect the presence of precipitation, assumptions must be made to translate the near-surface precipitation rate to the actual precipitation rate at the surface. In some cases, collision–coalescence processes act to enhance the surface rain rate (Porcacchia et al. 2019), while in drier environments all of the rain detected at 750 m might evaporate before it hits the ground (Rapp et al. 2013).
Last, DPR and CPR have different viewing geometries and resolutions. DPR has a spatial resolution of about 5 km and covers a swath that is 245 km wide, while CPR is a nadir-only instrument with a resolution of about 1.4 km cross track and 1.7 km along track (Tanelli et al. 2008). Given these considerations, it is not surprising that there is some discrepancy between GPM and CloudSat estimates of precipitation. Still, there are many other factors, such as algorithm assumptions, that could be contributing to the underestimation of high latitude precipitation by GPM compared to CloudSat. In this paper we focus on one potential source of uncertainty, the drop size distribution (DSD) model assumed by retrieval algorithms, and one particular type of precipitation, warm rain. We make use of the CloudSat–GPM coincidence dataset (Turk et al. 2021) and, using a consistent optimal estimation (OE) framework (thus eliminating many potential sources of discrepancy), we retrieve warm rainfall rates from the CloudSat and GPM observations separately. As expected, the GPM retrievals return less overall rain than the CloudSat retrievals, but we find that most of the difference disappears when we account for surface clutter, radar detection thresholds, and DSD assumptions. We also perform combined retrievals that incorporate observations from both GPM and CloudSat. These experiments strengthen the argument that DSD assumptions account for part of the GPM–CloudSat rain warm discrepancy and offer insight into the kind of retrievals that may be possible with future satellite radars.
2. Data
The CloudSat–GPM coincidence dataset, version 1C (Turk et al. 2021), is a compilation of products for each near-coincident (within 15 min) overpass between CloudSat and GPM from 18 March 2014 to 30 September 2016. This time period covers 6502 instances when the two satellites, due to their unique orbital geometries, sampled the same scene. Each CPR pixel is matched to the pixel contained in the DPR swath whose center is closest in space to the center of the CPR pixel. Because the instruments’ footprints are not the same size, this means that many of the GPM observations are associated with multiple CloudSat pixels. There is also a slight mismatch in vertical resolution for the radars: the DPR vertical resolution is 250 m for matched Ku- and Ka-band footprints, while the CPR vertical resolution is 240 m. When matching radar bins between CPR and DPR, the matched DPR bin is the bin whose top lies just above a given CloudSat bin top.
Each CloudSat–GPM coincident file contains several individual datasets. GPM products are version 4 (V4) and CloudSat products are release 5 (R05). We use the CPR profile of radar reflectivity as reported in the 2B-GEOPROF dataset, along with an estimate of two-way 94 GHz path integrated attenuation (PIA) due to hydrometeors, which comes from 2C-PRECIP-COLUMN (Haynes et al. 2009). For GPM, we use the “matched scan” (MS) profiles of Ku- and Ka-band reflectivity, along with corresponding PIA values, from 2B.GPM.DPRGMI.CORRA (Grecu et al. 2016), while GPM Microwave Imager (GMI) brightness temperatures come from 1C.GPM.GMI. Auxiliary information used by our retrieval, including the surface wind speed and profiles of temperature, pressure, and specific humidity, comes from ECMWF-AUX, i.e., interpolated forecast model fields from the European Centre for Medium-Range Weather Forecasts.
We compare retrieved rain rates from our algorithm with retrieved rain rates reported from the GPM_2BCMB radar–radiometer algorithm (Grecu et al. 2016) and the CloudSat 2C-RAIN-PROFILE algorithm (Lebsock and L’Ecuyer 2011). These values also come from the CloudSat–GPM coincidence files (and thus are V4 and R05, respectively). In our analysis, we consider CloudSat rain rates at two levels: at the surface and at CPR range bin 5, which we will refer to as GPM-base because it corresponds approximately to the lowest DPR range bin (∼1000 m above the surface). The surface values are taken directly from the CloudSat–GPM coincidence files. The CloudSat algorithm assumes that evaporation occurs between cloud base and the surface according to the parameterization given in Kalmus and Lebsock (2017). For a better apples-to-apples comparison with the GPM combined algorithm, which does not include subcloud evaporation, we also consider GPM-base rain rates from 2C-RAIN-PROFILE. While these are not reported directly in the CloudSat–GPM coincidence files, the rainwater content (RWC) retrieved at each range bin is reported, and from this we calculate the rain rate assuming the DSD parameterization given by Abel and Boutle (2012), which is the same parameterization assumed by the 2C-RAIN-PROFILE algorithm.
3. Methods
To retrieve rain rates from the GPM and CloudSat measurements, we use a retrieval algorithm based upon the method of optimal estimation (Rodgers 2000). A simpler version of the algorithm was applied to idealized atmospheric profiles based upon surface disdrometer observations in Schulte et al. (2022). As in that study, we retrieve the column-integrated cloud liquid water path (CLWP); however, unlike that previous study, which assumed a constant RWC throughout the raining profile, we also retrieve the RWC at each radar gate. Like other OE algorithms, ours is a Bayesian algorithm that searches for the atmospheric state vector (x) that, when processed through a forward model f, leads to simulated observations that are most consistent with the actual satellite observations y, subject to measurement and forward model uncertainties described by the error covariance matrix Sy. At the same time, x is constrained by the a priori state vector xa and its assumed uncertainties, described by the error covariance matrix Sa. The algorithm tries to find the state vector that maximizes the conditional probability P(x|y), that is, the probability of that state being the correct state given the observed satellite measurements y. For more information about the mathematical methods we use, we refer the reader to Schulte et al. (2022).
a. State and observation vectors
The state vector x is made up of the column-integrated CLWP plus the RWC at each vertical level in the column at which at least one radar frequency has a reflectivity above −20 dBZ. Specifically, we retrieve log10(CLWP) and log10(RWC) because the OE framework assumes Gaussian distributions and these variables are closer to Gaussian when translated into logarithmic space. In the normalized gamma drop size distribution experiments (NG_DSD, explained in section 3c), the state vector also contains two additional parameters, both of which are retrieved as column-averaged values. These are the mass-weighted mean rain drop diameter (Dm) and the normalized gamma shape parameter (μ). The size of x thus depends both upon the depth of the raining column as well as the DSD model being used. The values used for the a priori state vector xa are given in Table 1.
Values used in the a priori state vector xa, along with their assumed uncertainties included in the Sa matrix.
The makeup of the y vector, on the other hand, depends on whether the observations being considered come from CloudSat, GPM, or both combined. For the CloudSat-only retrievals, y consists of the W-band PIA plus the W-band reflectivities from CPR-base up to the highest range gate with Z > −20 dBZ. For GPM-only retrievals, y contains Tb from the 13 channels of GMI, Ku- and Ka-band PIA, and all valid DPR reflectivities reported in the CloudSat–GPM coincidence file for that pixel (i.e., measurements that are both above the surface clutter and above DPR detection limits). For combined retrievals, y includes all of these observations. We acknowledge that the GMI field of view is much larger than that of the DPR, especially for the lower-frequency channels, and for this reason the forward model errors associated with the GMI observations are assumed to be quite high in the Sy matrix (see section 3d and Table 2). The GMI measurements weakly constrain the total amount of liquid water in the column but are much less important to the retrieval than the radar reflectivities or PIA.
Uncertainties assumed in the Sy error covariance matrix, grouped by observation type.
b. Forward model
For a given state vector, we use a forward model to simulate passive microwave (PMW) brightness temperatures (TB), radar reflectivities, and radar two-way path integrated attenuation to compare with satellite observations from GPM and CloudSat. For simulating TB, we use the MonoRTM radiative transfer model (Clough et al. 2005) to calculate gaseous absorption and the FASTEM6 model to estimate sea surface emissivity (Kazumori and English 2015). We assume spherical cloud and rain drops and use Mie theory (Mie 1908) to calculate the absorption and scattering from these hydrometeors. For more details on the PMW part of the forward model refer to Schulte et al. (2022). For simulating Z and PIA, we use effective reflectivities calculated by the QuickBeam radar simulator (Haynes et al. 2007). Both gaseous and hydrometeor attenuation is included for calculating Z but only hydrometeor attenuation is included in the calculation of PIA, to match the way that PIA is reported in the CloudSat–GPM coincidence dataset. Because our aim is to study the impact of DSD assumptions on rain rates, rather than to retrieve perfect RRs, we have neglected multiple scattering in order to simplify the radiative transfer calculations. This choice is further justified by the fact that we are mostly focused on light rain. However, we note that multiple scattering can be significant at W-band radar frequencies (e.g., Battaglia et al. 2008).
c. DSD models
However, in the third set of experiments (GPM_DSD), μ is prescribed to be equal to 2. This mimics the assumption in the GPM_2BCMB algorithm (Grecu et al. 2016). Furthermore, in GPM_2BCMB, Dm and Nw are retrieved in separate steps. Dm is analytically diagnosed from the Ku radar reflectivity profile, making assumptions about Nw as described in Grecu et al. (2011), and then Nw is retrieved at 9 vertical locations in the raining column, assuming the profile of Dm already diagnosed. Rather than try to copy this process, in the GPM_DSD experiments we fix Dm at each level to be equal to the value reported in the CloudSat–GPM coincidence files, leaving Nw as the only free parameter left to be retrieved.
Finally, it should be noted that because the RWC of a DSD can be obtained via simple integration, it is possible to express any given normalized gamma curve as a function of RWC, Dm, and μ. In our testing, we found that the retrieval algorithm performed slightly better when RWC was retrieved (and Nw then calculated) than when Nw was one of the retrieved parameters. RWC also has the advantage over Nw of being a directly measurable quantity from a disdrometer.
To summarize, in the CS_DSD experiments we retrieve a profile of RWC only while assuming μ = 0 and that Eq. (4) is valid. In the NG_DSD experiments, we retrieve a profile of RWC, as well as column-averaged values of Dm and μ. And in the GPM_DSD experiments, we retrieve the RWC profile, prescribe Dm at each level to be equal to the Dm reported by GPM_2BCMB, and set μ = 2.
d. Covariance matrices
The Sa and Sy covariance matrices are very important in the OE framework, and changes to their values can have nontrivial effects on retrieved values. In addition, determining the proper covariances to assume is a difficult task given the many potential sources of forward model and observational uncertainties and the rather small number of CloudSat–GPM coincident observations of oceanic warm rain that we are considering. We have done our best to make error assumptions that are physically plausible, consistent with other observational algorithms (particularly 2C-RAIN-PROFILE), and that yield reasonable retrieved rain rates. Admittedly, in some cases one could make an equally justifiable but different error assumption and retrieve a different rain rate. However, our goal in this paper is not to validate the retrieved RRs themselves but to look at differences that arise when different DSD models are assumed. We are confident that the differences we report between DSD experiments are robust, because all of the experiments make use of a consistent set of error assumptions.
4. Results
a. Comparison between operational products
Our analysis of the CloudSat–GPM coincidence dataset confirms previous findings that CloudSat retrievals include a much higher frequency of occurrence of rain rates below 0.5 mm h−1 than GPM retrievals, and that CloudSat retrieves more accumulated oceanic warm rain than GPM. Figure 1 shows the frequency of occurrence of various surface rain rates for all oceanic warm rain cases (at any latitude) in the CloudSat–GPM coincident dataset. For a pixel to be included it must meet the following criteria: 1) be within the DPR matched swath and over ocean, 2) have a cloud-top altitude as indicated by CloudSat that is below the altitude of the 273 K isotherm given by ECMWF-AUX, and 3) have a nonzero rain rate as reported by either the GPM_2BCMB product or the CloudSat 2C-RAIN-PROFILE product.
(left) Frequency distribution of surface rain rates from pixels seen by both GPM and CloudSat from the GPM_2BCMB and CloudSat 2C-RAIN-PROFILE algorithms. (right) Cumulative distributions of rain rates, scaled so that each curve represents the precipitation up to a given rain rate as a percentage of the total amount of rain reported by GPM_2BCMB. The solid blue and pink lines represent the reported surface rain rates, but we also include 2C-RAIN-PROFILE rain rates at GPM-base (dashed red) and at GPM-base with the lowest rain rates excluded such that the total rain frequency matches GPM_2BCMB (solid red).
Citation: Journal of Atmospheric and Oceanic Technology 39, 12; 10.1175/JTECH-D-22-0036.1
It should also be noted that precipitation frequencies depend on the spatial scale being considered. Using a coarser resolution will yield a higher frequency of precipitation overall but a lower average precipitation rate per pixel. This complicates comparisons between GPM and CloudSat as their radar footprint sizes are different. In theory, the number of consecutive CPR pixels that should be averaged together for comparison with a DPR pixel should be somewhere between 3 and 11 (Behrangi et al. 2012). The lower limit represents the number of CPR pixels it takes to completely cross a single DPR pixel. The upper limit represents the number of CPR pixels whose combined area is equal to a single DPR pixel. In Fig. 1 and in the analysis that follows we choose to use an averaging bin of seven CloudSat pixels when comparing to GPM estimates, as this falls halfway between these two limits. The choice of averaging bin does not affect total accumulated precipitation.
Figure 1 shows that the GPM combined algorithm retrieves precipitation overall less frequently than the CloudSat 2C-RAIN-PROFILE algorithm, and that retrieved precipitation rates from GPM of below 0.2 mm h−1 are very rare (this is expected given that 2BCMB only performs a retrieval when a radar signal is present). Comparing the blue and pink curves on the right-hand side of Fig. 1, GPM_2BCMB retrieves only about 33% of the total surface rain retrieved by 2C-RAIN-PROFILE. However, this gap is greatly reduced by accounting for surface clutter and radar sensitivity differences. The red dashed line shows the frequency of RRs from 2C-RAIN-PROFILE at GPM-base instead of the surface. This greatly reduces the number of high-RR pixels, putting the frequency much more in line with GPM_2BCMB estimates. This implies either that GPM misses a lot of heavier, near-surface warm rain that is masked by its surface clutter, or that there is something about the CloudSat 2C-RAIN-PROFILE algorithm that causes it to overestimate RRs in the lowest levels of the atmosphere. On the other hand, 2C-RAIN-PROFILE includes many more RRs below 0.5 mm h−1 at GPM-base than at the surface. This is presumably because the rain is so light that it evaporates before it reaches the surface. All told, using GPM-base estimates reduces the total accumulated warm rain from 2C-RAIN-PROFILE to about 175% of the total from GPM_2BCMB, instead of about 300% if surface estimates are used.
Next we attempt to account for radar detection limits. There is no perfect way to do this, because the GPM and CloudSat observations are only near-coincident, and because whether or not a particular RR is able to be seen by DPR is dependent upon the DSD. To overcome these challenges while minimizing the number of assumptions required, we force the frequency of warm rain occurrence from 2C-RAIN-PROFILE at GPM-base to be equal to the frequency of occurrence from GPM_2BCMB. That is, since only 5.1% of GPM pixels in our dataset included measurable precipitation, we set all but the top 5.1% of RRs from 2C-RAIN-PROFILE to be equal to 0. The results are shown by the solid red line in Fig. 1. This further reduces the discrepancy between CloudSat and GPM RRs, such that total accumulated 2C-RAIN-PROFILE warm rain is only 25% higher than GPM_2BCMB. From the accumulation graph, it is clear that most of this difference comes at high RRs (above 2.0 mm h−1), which are not frequent but that contribute significantly to total accumulation.
b. CloudSat-only and GPM-only retrievals
In our next experiment, we perform OE retrievals on either CloudSat-only or GPM-only observations, assuming DSDs models that are consistent with the 2C-RAIN-PROFILE and GPM_2BCMB algorithms, respectively. Figure 2 shows scatterplots of retrieved RR compared to the operational algorithms, and Fig. 3 shows histograms of retrieved RR frequency and the total cumulative distributions. Once again, CloudSat estimates have been averaged with a boxcar window of seven pixels and low RRs have been eliminated to force the total rain frequency to match GPM. The retrieved rain rates do not track perfectly with the operational algorithms, which is expected given that the operational algorithms take slightly different retrieval approaches and make assumptions in their forward models (apart from DSD assumptions) that are different than the ones made in our OE algorithm. Specifically, our retrieved rain rates are biased high compared to the operational algorithms. Looking at Fig. 3, it is clear that the distribution of RRs from our algorithm is wider than from the operational algorithms. This is particularly true for CloudSat, for which we more frequently retrieve both very low RRs and very high RRs than 2C-RAIN-PROFILE. This is likely related to the relatively loose a priori constraints we impose in the OE algorithm. Importantly, however, we obtain a similar result to what is shown in Fig. 1 in that much more total rain is retrieved from CloudSat than from GPM. The gap between CloudSat and GPM estimates is about 17%, similar in magnitude to the 25% gap seen between 2C-RAIN-PROFILE and GPM_2BCMB.
Density plots comparing OE retrieved rain rates from (left) GPM-only or (right) CloudSat-only observations to values from the operational algorithms GPM_2BCMB and CloudSat 2C-RAIN-PROFILE, respectively. The GPM-only retrieval only includes cases where there exists a valid DPR reflectivity value somewhere in the column, and thus includes far fewer cases than the CloudSat-only retrieval. Both OE retrievals assume identical DSD models to the operational algorithms to which they are compared.
Citation: Journal of Atmospheric and Oceanic Technology 39, 12; 10.1175/JTECH-D-22-0036.1
As in Fig. 1, but with distributions included from GPM-only (assuming GPM_DSD) and CloudSat-only (assuming CS_DSD) OE retrievals, and with the CloudSat rain frequency forced to match that of GPM.
Citation: Journal of Atmospheric and Oceanic Technology 39, 12; 10.1175/JTECH-D-22-0036.1
c. GPM retrievals with adjusted DSD assumptions
To test the theory that gaps between CloudSat and GPM retrieved rain rates are at least partially attributable to differing DSD assumptions, we retrieve rain rates from GPM-only observations assuming the NG_DSD and CS_DSD models in addition to the GPM_DSD results presented above. Results are shown in Fig. 4. Assuming the Abel and Boutle (2012) DSD of CS_DSD shifts the entire population of retrieved rain rates higher. This results in 28% more total precipitation being retrieved in the CS_DSD experiment compared to the GPM_DSD experiment, a value that is quite similar to the 25% gap between 2C-RAIN-PROFILE and GPM_2BCMB. Using NG_DSD, the retrieved rain rates tend to be between the GPM_DSD and CS_DSD experiments, with total accumulation about 12% higher than in GPM_DSD.
(left) Frequency distributions and (right) cumulative distributions of GPM-only retrieved RRs assuming either the GPM_DSD, NG_DSD, or CS_DSD drop size distribution models. The cumulative distributions are scaled relative to the total amount of rain accumulation from GPM_2BCMB at GPM-base.
Citation: Journal of Atmospheric and Oceanic Technology 39, 12; 10.1175/JTECH-D-22-0036.1
The idea that the Abel and Boutle DSD could lead to an overestimation of warm rain was first postulated by Schulte et al. (2022). They showed that, for the small RWCs present in many warm rain cases, CS_DSD predicts much more numerous, but also much smaller, drops than are present in surface disdrometer observations. Z scales as D6, or, for a given mass concentration q, as qD3. Thus, if the retrieval assumes smaller drop sizes than are present in reality, much higher water contents are necessary for the retrieval to match the observed Z. This manifests itself in RRs that are biased high, especially at the lowest RWCs for which the CS_DSD model diverges most significantly from disdrometer observations. Our results support the findings of Schulte et al. (2022). It is worth noting that the shift in the distribution of RRs seen in Fig. 4 (in terms of percentages) is particularly pronounced at the lowest RRs (although, because high RRs contribute most to accumulated rainfall, the differences in the cumulative distributions become most apparent only at RRs higher than 2.0 mm h−1).
d. Combined retrievals
In our last set of experiments, we perform retrievals that incorporate observations from both GPM and CloudSat. This can be thought of as a proxy for what a theoretical triple-frequency spaceborne radar would retrieve, though we caution that the observations in the CloudSat–GPM coincidence dataset are not perfectly matched in space and time. Still, using both sets of observations gives a sense for how much of the CloudSat–GPM rain-rate differences are due to the different sensitivities of the satellite instruments, and how much are due to DSD assumptions. We perform these combined retrievals using either the CS_DSD or NG_DSD assumptions (we cannot use GPM_DSD because no Dm is reported for levels at which DPR reflectivities are below the detection thresholds).
An example of one combined retrieval is shown in Fig. 5. This particular profile illustrates several noteworthy principles. From the radar reflectivity profiles, we see that CPR has a greater sensitivity to rain near the surface than DPR, and that CPR measures light rain that reaches much higher than what DPR is able to see. The W-band Z also decreases below 2000 m, even as the Ku- and Ka-band Z are increasing, an indication that significant W-band attenuation is occurring. The profile of RWC from CloudSat 2C-RAIN-PROFILE is much higher than that from GPM_2BCMB, a result that we also see in our own GPM-only and CloudSat-only retrievals. This is in large part explained by the fact that GPM_2BCMB assumes much higher Dm values than 2C-RAIN-PROFILE. With a greater concentration of large drops assumed, less overall rainwater is required in order for the simulated DPR reflectivities to reach the levels observed. In the combined NG_DSD retrieval, which settles on a column-averaged value for Dm that is somewhat between the CloudSat and GPM results, the RWC profile similarly falls in the middle. This tendency of the retrieval to choose a Dm somewhat between 2C-RAIN-PROFILE and GPM_2BCMB is common across the whole coincidence dataset. This can be seen in Fig. 6, which plots the distribution of retrieved Dm (at GPM-base) for all three algorithms. The combined retrieval usually returns a Dm value between 0.5 and 1.0 mm, whereas Dm from CloudSat is usually below 0.5 mm and Dm from GPM is often above 1.0 mm.
Example of the combined (three-frequency) retrieval assuming the NG_DSD model. (top left) Profiles of observed (solid) and simulated (dotted) reflectivity at each DPR or CPR radar frequency. (top right) Profile of retrieved RR is the dotted black line. For comparison, blue lines show RR profiles from GPM-only retrievals from either GPM_2BCMB or our OE assuming GPM_DSD, while red lines show CloudSat-only retrievals from 2C-RAIN-COLUMN or our OE assuming CS_DSD. (bottom left) As in the top-right panel, but for retrieved RWC. (bottom right) Profile of Dm from 2C-RAIN-PROFILE, GPM_2BCMB, and our combined retrieval assuming NG_DSD. Note that our retrieval produces only a column-averaged value.
Citation: Journal of Atmospheric and Oceanic Technology 39, 12; 10.1175/JTECH-D-22-0036.1
Frequency distributions of Dm at GPM-base as retrieved by GPM_2BCMB, 2C-RAIN-PROFILE, and our combined OE algorithm, for near-coincident observations of warm rain from the CloudSat–GPM coincidence dataset.
Citation: Journal of Atmospheric and Oceanic Technology 39, 12; 10.1175/JTECH-D-22-0036.1
Rain-rate distributions from the combined OE retrievals are compared against GPM-only and CloudSat-only retrievals in Fig. 7. The combined retrievals have a greater frequency of retrieved RRs landing between 0.5 and 2.0 mm h−1. In some cases where the CloudSat observations indicate light rain, GPM observations pull the solution toward higher rain rates, and vice versa. This could be for either “good” reasons (having more observables reduces the overall measurement noise) or unphysical ones (e.g., space and time mismatches). Overall, the effect of combining observations is to increase the total amount of retrieved warm rain accumulation. Another noteworthy result is that the NG_DSD version of the combined retrieval retrieves 11% less total accumulated rain than the CS_DSD version. This is consistent with the GPM-only results shown in Fig. 4 and points once again to the important role that DSD assumptions play in satellite warm rain retrievals.
As in Fig. 4, but with retrieved rain rates from GPM-only (GPM_DSD assumed), CloudSat-only (CS_DSD assumed), combined retrieval with CS_DSD assumed, and combined retrieval with NG_DSD assumed.
Citation: Journal of Atmospheric and Oceanic Technology 39, 12; 10.1175/JTECH-D-22-0036.1
5. Discussion and conclusions
Our analysis suggests that a nontrivial portion of the difference in warm RRs retrieved by GPM and CloudSat stems from differing DSD assumptions. We can use our results to roughly partition the GPM–CloudSat discrepancy into three categories: differences in surface clutter, differences in sensitivity, and differences in DSD assumptions. The gap between the total warm rain estimated from CloudSat 2C-RAIN-PROFILE and from GPM_2BCMB reduces from nearly 200% of the GPM_2BCMB total to about 75% when evaluating rain rates at 1000 m above the surface instead of using surface estimates (thus eliminating surface clutter differences). The gap is further reduced to 25% when accounting for radar sensitivity differences by forcing the rain frequencies from the two estimates to match. When using our own OE algorithm, making mostly identical algorithm assumptions but retaining differences in DSD models, total CloudSat warm rain accumulation is about 17% larger than GPM accumulation. This gap is similar in magnitude to the 25% gap seen in the operational products, but disappears completely when we retrieve rain rates from GPM assuming the CloudSat DSD model.
The fact that the GPM_DSD and NG_DSD experiments resulted in lower retrieved RRs than the CS_DSD experiments is explained by the fact that the CS_DSD model assumes a much higher concentration of small rain drops for a given RWC. At first glance, one might think that this would result in lower RRs, since small drops fall more slowly than large drops. For a purely attenuation-based retrieval, such as 2C-RAIN-COLUMN (Haynes et al. 2009), this would likely be the result. However, when reflectivities are considered, which (in the Rayleigh regime) scale to the power of D6, the slower fall speed of small drops is outweighed by the fact that, if smaller drops are assumed, a much higher RWC is required in order to give the same Z. These competing effects are illustrated nicely in Fig. 5, where the retrieved RWC at GPM-base from 2C-RAIN-COLUMN is about twice as high as the retrieved RWC from GPM_2BCMB, but the retrieved CloudSat RR at the same level is only about 40% higher than the GPM RR.
Which DSD model is the “correct” one to assume in satellite precipitation retrievals? That is beyond the scope of this paper, although Schulte et al. (2022) found that the Abel and Boutle (2012) DSD relationship (used in 2C-RAIN-PROFILE) did not closely match observed DSDs from the Azores or the relationships found in other recent studies looking at disdrometer observations (Protat et al. 2019b; Liao et al. 2020). Our combined NG_DSD retrievals tend to result in Dm values that are somewhere between the CloudSat and GPM value but that track slightly more closely to CloudSat, as seen in Fig. 6. Still, this is somewhat dependent on the a priori value for Dm that is used in the retrieval, and we have looked only at warm rain. Results in other types of precipitation could be very different, and could vary regionally. More global observations of oceanic DSDs are needed in order to better understand how DSDs vary in different environments.
Encouragingly, much progress has been made on this front in recent years. The Observations of Aerosols above Clouds and Their Interactions (ORACLES; Redemann et al. 2021) field campaign of 2016/17 made many aircraft flights observing stratocumulus cloud structure, precipitation frequency, and precipitation intensity over the southeast Atlantic Ocean (Dzambo et al. 2019). In addition, a series of coordinated projects between 2016 and 2018 used in situ probes, radar, lidar, and other instruments to measure precipitation properties, including DSDs, over the Southern Ocean (McFarquhar et al. 2021). Dolan et al. (2018) identify six dominant modes of DSDs globally, using a network of ground-based disdrometer observations. Finally, the Ocean Rainfall And Ice-phase precipitation measurement Network (OceanRAIN; Klepp et al. 2018) is a recently compiled in situ ship-based ocean precipitation database that is helping to characterize the variability of global DSDs. The OceanRAIN dataset exhibits different DSD characteristics at high latitudes compared to other parts of the globe and these characteristics translate into different relationships between radar observables and RR (Protat et al. 2019a,b; Duncan et al. 2019).
We also caution that, because CloudSat and GPM are in different orbits, we are limited to statistical comparisons from a relatively small number of near-coincident observations of warm rain. Our contention is not that either the GPM_DSD or CS_DSD model is definitively more appropriate but rather that they make significantly different assumptions about the shape of the rain DSD and that these differences are important for explaining retrieved RR differences. If warm rain satellite retrieval uncertainties are to be narrowed, we must not only design radars that are better able to sample light rain near the surface, but also work to better incorporate our understating of global DSD variability into retrieval algorithms.
Acknowledgments.
We are grateful to the NASA FINESST program, which funded this work (Award 80NSSC19K1325). We also thank the CloudSat science team for helpful feedback. Three anonymous reviewers greatly improved the manuscript.
Data availability statement.
The CloudSat–GPM coincidence dataset is publicly available from the CloudSat Data Processing Center (https://www.cloudsat.cira.colostate.edu/community-products/cloudsat-trmm-gpm-coincidence-dataset).
REFERENCES
Abel, S. J., and I. A. Boutle, 2012: An improved representation of the raindrop size distribution for single-moment microphysics schemes. Quart. J. Roy. Meteor. Soc., 138, 2151–2162, https://doi.org/10.1002/qj.1949.
Adler, R. F., and Coauthors, 2018: The Global Precipitation Climatology Project (GPCP) monthly analysis (new version 2.3) and a review of 2017 global precipitation. Atmosphere, 9, 138, https://doi.org/10.3390/atmos9040138.
Andersson, A., C. Klepp, K. Fennig, S. Bakan, H. Grassl, and J. Schulz, 2011: Evaluation of HOAPS-3 ocean surface freshwater flux components. J. Appl. Meteor. Climatol., 50, 379–398, https://doi.org/10.1175/2010JAMC2341.1.
Battaglia, A., J. M. Haynes, T. L’Ecuyer, and C. Simmer, 2008: Identifying multiple-scattering-affected profiles in CloudSat observations over the oceans. J. Geophys. Res., 113, D00A17, https://doi.org/10.1029/2008JD009960.
Behrangi, A., and Y. Song, 2020: A new estimate for oceanic precipitation amount and distribution using complementary precipitation observations from space and comparison with GPCP. Environ. Res. Lett., 15, 124042, https://doi.org/10.1088/1748-9326/abc6d1.
Behrangi, A., M. Lebsock, S. Wong, and B. Lambrigtsen, 2012: On the quantification of oceanic rainfall using spaceborne sensors. J. Geophys. Res., 117, D20105, https://doi.org/10.1029/2012JD017979.
Behrangi, A., G. Stephens, R. F. Adler, G. J. Huffman, B. Lambrigtsen, and M. Lebsock, 2014: An update on the oceanic precipitation rate and its zonal distribution in light of advanced observations from space. J. Climate, 27, 3957–3965, https://doi.org/10.1175/JCLI-D-13-00679.1.
Behrangi, A., and Coauthors, 2016: Status of high-latitude precipitation estimates from observations and reanalyses. J. Geophys. Res. Atmos., 121, 4468–4486, https://doi.org/10.1002/2015JD024546.
Berg, W., T. L’Ecuyer, and J. M. Haynes, 2010: The distribution of rainfall over oceans from spaceborne radars. J. Appl. Meteor. Climatol., 49, 535–543, https://doi.org/10.1175/2009JAMC2330.1.
Clough, S. A., and Coauthors, 2005: Atmospheric radiative transfer modeling: A summary of the AER codes. J. Quant. Spectrosc. Radiat. Transfer, 91, 233–244, https://doi.org/10.1016/j.jqsrt.2004.05.058.
Dolan, B., B. Fuchs, S. A. Rutledge, E. A. Barnes, and E. J. Thompson, 2018: Primary modes of global drop size distributions. J. Atmos. Sci., 75, 1453–1476, https://doi.org/10.1175/JAS-D-17-0242.1.
Duncan, D. I., P. Eriksson, S. Pfrundschuh, C. Klepp, and D. C. Jones, 2019: On the distinctiveness of observed oceanic raindrop distributions. Atmos. Chem. Phys., 19, 6969–6984, https://doi.org/10.5194/acp-19-6969-2019.
Dzambo, A. M., T. L’Ecuyer, O. O. Sy, and S. Tanelli, 2019: The observed structure and precipitation characteristics of southeast Atlantic stratocumulus from airborne radar during ORACLES 2016–17. J. Appl. Meteor. Climatol., 58, 2197–2215, https://doi.org/10.1175/JAMC-D-19-0032.1.
Giangrande, S. E., D. Wang, M. J. Bartholomew, M. P. Jensen, D. B. Mechem, J. C. Hardin, and R. Wood, 2019: Midlatitude oceanic cloud and precipitation properties as sampled by the ARM Eastern North Atlantic observatory. J. Geophys. Res. Atmos., 124, 4741–4760, https://doi.org/10.1029/2018JD029667.
Grecu, M., L. Tian, W. S. Olsen, and S. Tanelli, 2011: A robust dual-frequency radar profiling algorithm. J. Appl. Meteor. Climatol., 50, 1543–1557, https://doi.org/10.1175/2011JAMC2655.1.
Grecu, M., W. S. Olson, S. J. Munchak, S. Ringerud, L. Liao, Z. Haddad, B. L. Kelley, and S. F. McLaughlin, 2016: The GPM combined algorithm. J. Atmos. Oceanic Technol., 33, 2225–2245, https://doi.org/10.1175/JTECH-D-16-0019.1.
Hayden, L., and C. Liu, 2018: A multiyear analysis of global precipitation combining CloudSat and GPM precipitation retrievals. J. Hydrometeor., 19, 1935–1952, https://doi.org/10.1175/JHM-D-18-0053.1.
Haynes, J. M., R. T. Marchand, Z. Lou, A. Bodas-Salcedo, and G. L. Stephens, 2007: A multipurpose radar simulation package: QuickBeam. Bull. Amer. Meteor. Soc., 88, 1723–1728, https://doi.org/10.1175/BAMS-88-11-1723.
Haynes, J. M., T. S. L’Ecuyer, G. L. Stephens, S. D. Miller, C. Mitrescu, N. B. Wood, and S. Tanelli, 2009: Rainfall retrieval over the ocean with spaceborne W-band radar. J. Geophys. Res., 114, D00A22, https://doi.org/10.1029/2008JD009973.
Hou, A. Y., and Coauthors, 2014: The Global Precipitation Measurement mission. Bull. Amer. Meteor. Soc., 95, 701–722, https://doi.org/10.1175/BAMS-D-13-00164.1.
Kalmus, P., and M. Lebsock, 2017: Correcting biased evaporation in CloudSat warm rain. IEEE Trans. Geosci. Remote Sens., 55, 6207–6217, https://doi.org/10.1109/TGRS.2017.2722469.
Kazumori, M., and S. J. English, 2015: Use of the ocean surface wind direction signal in microwave radiance assimilation. Quart. J. Roy. Meteor. Soc., 141, 1354–1375, https://doi.org/10.1002/qj.2445.
Kidd, C., and P. Joe, 2007: Importance, identification and measurement of light precipitation at mid- to high-latitudes. Joint EUMETSAT Meteorological Satellite Conf. and 15th Satellite Meteorology and Oceanography Conf., Amsterdam, Netherlands, EUMETSAT–Amer. Meteor. Soc., https://www.eumetsat.int/media/5487.
Kidd, C., E. Graham, T. Smyth, and M. Gill, 2021: Assessing the impact of light/shallow precipitation retrievals from satellite-based observations using surface radar and Micro Rain Radar observations. Remote Sens., 13, 1708, https://doi.org/10.3390/rs13091708.
Klepp, C., and Coauthors, 2018: OceanRAIN, a new in-situ shipboard global ocean surface-reference dataset of all water cycle components. Sci. Data, 5, 180122, https://doi.org/10.1038/sdata.2018.122.
Kummerow, C. D., and Coauthors, 2000: The status of the Tropical Rainfall Measuring Mission (TRMM) after two years in orbit. J. Appl. Meteor. Climatol., 39, 1965–1982, https://doi.org/10.1175/1520-0450(2001)040<1965:TSOTTR>2.0.CO;2.
Kummerow, C. D., D. Randel, M. Kulie, N.-Y. Wang, R. Ferraro, S. J. Munchak, and V. Petkovic, 2015: The evolution of the Goddard profiling algorithm to a fully parametric scheme. J. Atmos. Oceanic Technol., 32, 2265–2280, https://doi.org/10.1175/JTECH-D-15-0039.1.
Lebsock, M., 2018: Level 2C RAIN-PROFILE product process description and interface control document. CloudSat Data Processing Center Doc., 14 pp., https://www.cloudsat.cira.colostate.edu/cloudsat-static/info/dl/2c-rain-profile/2C-RAIN-PROFILE-PDICD.P_R04.20110620.pdf.
Lebsock, M., and T. S. L’Ecuyer, 2011: The retrieval of warm rain from CloudSat. J. Geophys. Res., 116, D20209, https://doi.org/10.1029/2011JD016076.
Liao, L., R. Meneghini, T. Iguchi, and A. Tokay, 2020: Characteristics of DSD bulk parameters: Implication for radar rain retrieval. Atmosphere, 11, 670, https://doi.org/10.3390/atmos11060670.
Lin, X., and A. Y. Hou, 2012: Estimation of rain intensity spectra over the continental United States using ground radar–gauge measurements. J. Climate, 25, 1901–1915, https://doi.org/10.1175/JCLI-D-11-00151.1.
Masaki, T., T. Iguchi, K. Kanemaru, K. Furukawa, N. Yoshida, T. Kaubota, and R. Oki, 2021: Calibration of the dual-frequency precipitation radar onboard the Global Precipitation Measurement Core Observatory. IEEE Trans. Geosci. Remote Sens., 60, 5100116, https://doi.org/10.1109/TGRS.2020.3039978.
McFarquhar, G. M., and Coauthors, 2021: Observations of clouds, aerosols, precipitation, and surface radiation over the Southern Ocean: An overview of CAPRICORN, MARCUS, MICRE, and SOCRATES. Bull. Amer. Meteor. Soc., 102, E894–E928, https://doi.org/10.1175/BAMS-D-20-0132.1.
Mie, G., 1908: Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen. Ann. Phys., 330, 377–445, https://doi.org/10.1002/andp.19083300302.
Nuijens, L., K. Emanuel, H. Masunaga, and T. L’Ecuyer, 2017: Implications of warm rain in shallow cumulus and congestus clouds for large-scale circulations. Surv. Geophys., 38, 1257–1282, https://doi.org/10.1007/s10712-017-9429-z.
Porcacchia, L., P.-E. Kirstetter, V. Maggioni, and S. Tanelli, 2019: Investigating the GPM Dual-Frequency Precipitation Radar signatures of low-level precipitation enhancement. Quart. J. Roy. Meteor. Soc., 145, 3161–3174, https://doi.org/10.1002/qj.3611.
Protat, A., C. Klepp, V. Louf, W. A. Peterson, S. P. Alexander, A. Barros, J. Leinonen, and G. G. Mace, 2019a: The latitudinal variability of oceanic rainfall properties and its implication for satellite retrievals: 1. Drop size distribution properties. J. Geophys. Res. Atmos., 124, 13 291–13 311, https://doi.org/10.1029/2019JD031010.
Protat, A., C. Klepp, V. Louf, W. A. Peterson, S. P. Alexander, A. Barros, J. Leinonen, and G. G. Mace, 2019b: The latitudinal variability of oceanic rainfall properties and its implication for satellite retrievals: 2. The relationships between radar observables and drop size distribution parameters. J. Geophys. Res. Atmos., 124, 13 312–13 324, https://doi.org/10.1029/2019JD031011.
Rapp, A. D., M. Lebsock, and T. L’Ecuyer, 2013: Low cloud precipitation climatology in the southeastern Pacific marine stratocumulus region using CloudSat. Environ. Res. Lett., 8, 014027, https://doi.org/10.1088/1748-9326/8/1/014027.
Redemann, J., and Coauthors, 2021: An overview of the ORACLES (Observations of Aerosols above Clouds and Their Interactions) project: Aerosol–cloud–radiation interactions in the southeast Atlantic basin. Atmos. Chem. Phys., 21, 1507–1563, https://doi.org/10.5194/acp-21-1507-2021.
Rodgers, C. D., 2000: Inverse Methods for Atmospheric Sounding: Theory and Practice. Vol. 2. World Scientific, 256 pp.
Schulte, R. M., C. D. Kummerow, C. Klepp, and G. G. Mace, 2022: How accurately can warm rain realistically be retrieved with satellite sensors? Part I: DSD uncertainties. J. Appl. Meteor. Climatol., 61, 1087–1105, https://doi.org/10.1175/JAMC-D-21-0158.1.
Seto, S., T. Iguchi, R. Meneghini, J. Awaka, T. Kubota, T. Masaki, and N. Takahasi, 2021: The precipitation rate retrieval algorithms for the GPM Dual-Frequency Precipitation Radar. J. Meteor. Soc. Japan, 99, 205–237, https://doi.org/10.2151/jmsj.2021-011.
Sinclair, K., B. van Diedenhoven, B. Cairns, M. Alexandrov, A. M. Dzambo, and T. L’Ecuyer, 2021: Inference of precipitation in warm stratiform clouds using remotely sensed observations of cloud top droplet size distribution. Geophys. Res. Lett., 48, e2021GL092547, https://doi.org/10.1029/2021GL092547.
Skofronick-Jackson, G., and Coauthors, 2017: The Global Precipitation Measurement (GPM) mission for science and society. Bull. Amer. Meteor. Soc., 98, 1679–1695, https://doi.org/10.1175/BAMS-D-15-00306.1.
Stephens, G. L., and Coauthors, 2008: CloudSat mission: Performance and early science after the first year of operation. J. Geophys. Res., 113, D00A18, https://doi.org/10.1029/2008JD009982.
Stephens, G. L., D. Winker, J. Pelon, C. Trepte, D. Vane, C. Yuhas, T. L’Ecuyer, and M. Lebsock, 2018: CloudSat and CALIPSO within the A-train: Ten years of actively observing the Earth system. Bull. Amer. Meteor. Soc., 99, 569–581, https://doi.org/10.1175/BAMS-D-16-0324.1.
Stubenrauch, C. J., and Coauthors, 2013: Assessment of global cloud datasets from satellites: Project and database initiated by the GEWEX Radiation Panel. Bull. Amer. Meteor. Soc., 94, 1031–1049, https://doi.org/10.1175/BAMS-D-12-00117.1.
Tanelli, S., S. L. Durden, E. Im, K. S. Pak, D. G. Reinke, P. Partain, J. M. Haynes, and R. T. Marchand, 2008: CloudSat’s Cloud Profiling Radar after two years in orbit: Performance, calibration, and processing. IEEE Trans. Geosci. Remote Sens., 46, 3560–3573, https://doi.org/10.1109/TGRS.2008.2002030.
Testud, J., S. Oury, R. A. Black, P. Amayenc, and X. Dou, 2001: The concept of “normalized” distribution to describe raindrop spectra: A tool for cloud physics and cloud remote sensing. J. Appl. Meteor., 40, 1118–1140, https://doi.org/10.1175/1520-0450(2001)040<1118:TCONDT>2.0.CO;2.
Turk, F. J., and Coauthors, 2021: Applications of a CloudSat-TRMM and CloudSat-GPM satellite coincidence dataset. Remote Sens., 13, 2264, https://doi.org/10.3390/rs13122264.
Witte, M. K., T. Yuan, P. Y. Chuang, S. Platnick, K. G. Meyer, G. Wind, and H. H. Jonsson, 2018: MODIS retrievals of cloud effective radius in marine stratocumulus exhibit no significant bias. Geophys. Res. Lett., 45, 10 656–10 664, https://doi.org/10.1029/2018GL079325.
Xie, P., and P. A. Arkin, 1997: Global precipitation: A 17-year monthly analysis based on gauge observations, satellite estimates, and numerical model outputs. Bull. Amer. Meteor. Soc., 78, 2539–2558, https://doi.org/10.1175/1520-0477(1997)078<2539:GPAYMA>2.0.CO;2.
