1. Introduction
The relationships between passive microwave brightness temperatures (TBs) and the microphysical characteristics of hydrometeors have long been recognized as critical for many aspects of remote sensing, including the derivation of precipitation information (Petty 1994a,b; Smith et al. 1992; Wang et al. 1998; Wilheit 1986). Knowledge of these relationships is essential to develop and assess cloud-resolving models (Tao and Simpson 1993), to improve forward radiative transfer calculations (Smith et al. 1992), to compute vertical diabatic heating profiles (Tao et al. 1993), and to develop precipitation parameter retrieval algorithms (Marzano et al. 1999; Smith et al. 1992). To gain information about these relationships, many theoretical studies (Smith et al. 1992; Yeh et al. 1990) and experimental studies (Bennartz and Bauer 2003; Heymsfield et al. 1996; Liu and Curry 1998; Simpson et al. 1996) have been conducted.
The simulation of individual scattering properties of nonspherical precipitation-sized ice particles and their effects on radar and passive microwave observations of clouds and precipitation has drawn significant attention in the last years. Tremendous progress has been made in understanding the scattering properties of nonspherical ice particles (Ekelund and Eriksson 2019; Eriksson et al. 2015; Hogan and Westbrook 2014; Hogan et al. 2017; Hong 2007; Hong et al. 2009; Kim 2006; Kuo et al. 2016; Leinonen et al. 2018; Liu 2004; Lu et al. 2016; Mason et al. 2019; Ori et al. 2014; Petty and Huang 2010; Tyynelä et al. 2014). New methods and databases based on these findings are currently being used for various purposes including precipitation retrieval (Ringerud et al. 2019; Skofronick-Jackson et al. 2019; Yin and Liu 2019), data assimilation (e.g., Geer and Baordo 2014), and ice water path retrievals (Brath et al. 2018; Buehler et al. 2012; Piyush et al. 2017). The simulated scattering properties of ice particles must ideally and realistically represent the optical properties of actual ice particles in terms of both active and passive microwave remote sensing applications. In this context, closure studies between multifrequency active and passive observations of the scattering signals of ice clouds are of critical importance as they can provide constraints on particles properties in terms of their active scattering properties, radar dual/triple-frequency ratio, for example, Kneifel et al. (2011), and their passive microwave optical properties (Bytheway and Kummerow 2018; Fox et al. 2019; Gong and Wu 2017; Kulie et al. 2010).
Here we use the cross-track scanning Microwave Humidity Sounder-2 (MWHS-2) on board Fengyun-3C (FY-3C) to globally assess the impact of hydrometeor scattering on observed TBs over the range 89–190 GHz including the 118-GHz oxygen absorption channels. Various observation-based and modeling studies have investigated the impact of hydrometeor scattering on passive microwave brightness temperatures (Bennartz and Petty 2001; Bennartz and Bauer 2003; Bennartz et al. 2002; Burns et al. 1997; Gasiewski 1992; Grody 1991; Skofronick-Jackson and Wang 2000; Spencer 1986; Spencer et al. 1989; Weng and Grody 2000). The combination of 89-, 150-, and 183-GHz observations allows for an improved retrieval of precipitation ice microphysical properties using the differential scattering signature (Skofronick-Jackson and Johnson 2011; Skofronick-Jackson and Wang 2000; Weng and Grody 2000). Bennartz and Bauer (2003) studied the response of brightness temperatures to hydrometeor scattering based solely on simulations at 89, 150, and 183 GHz. Their research shows that 150 GHz is highly sensitive to variations in ice scattering, and water vapor channels (183.31 ± X GHz) give additional information because of their low sensitivity to surface emission. While these channels have been exploited to understand ice scattering properties, temperature sounding channels (118.75 ± X GHz) have been relatively unexplored (Bauer and Mugnai 2003). Building conceptually upon these previous findings, we focus on two questions that can be answered by combining active and passive observations. First, at any given frequency, what is the average sensitivity of the brightness temperature to the presence of ice-phase precipitation in the observed atmospheric column? Second, what is the frequency-dependence of this sensitivity in the range 89–190 GHz? To answer these questions, we create a global, ocean-only 1-yr dataset of combined spaceborne radar observations from the Global Precipitation Measurement mission’s (GPM) Dual-Frequency Precipitation Radar (DPR) and FY-3C MWHS-2 TBs. Based on this dataset, we study the sensitivity of observed TBs to changes in vertically integrated radar reflectivity and in hydrometeor water path (HWP), which we define as the total amount of all precipitation ice and all liquid in a vertical column. In our analysis we use “scattering-induced brightness temperature depressions” (ΔTB), which is defined as the difference between observed TBs and simulated cloud-free TBs, the latter based on collocated numerical weather prediction (NWP) fields. We pay particular attention to issues related to the absolute calibration of the passive microwave sensor and its ability to reproduce bias-free and cloud-free observed TBs for all channels. To quantify the effects of scattering alone, rather than the effect of combined scattering and gas absorption, we further develop a method to account for the impact of variable gas transmission that most strongly affects the temperature channels near 118 GHz and water vapor absorption channels near 183 GHz. The approach we use here is very similar to Wu et al. (2009) and Gong and Wu (2014) who deal with high-frequency microwave and submillimeter observations of cloud ice water path (IWP).
MWHS-2 is particularly well suited for the purpose of the current study as it is the first spaceborne sensor equipped with temperature sounding channels around 118 GHz in addition to the more traditional channels around 89, 150, and 183 GHz (Dong et al. 2009; Zhang et al. 2012). In the near future, the Time-Resolved Observations of Precipitation Structure and Storm Intensity with a Constellation of Smallsats (TROPICS) and EUMETSAT’s Microwave Imager (MWI) will also provide observations at 118 GHz (Blackwell et al. 2018; Holmlund et al. 2017; Mattioli et al. 2019). The new channels around 118 GHz are of interest for temperature sounding but also in the context of precipitation retrievals (Bauer and Mugnai 2003; He and Chen 2019).
The rest of this paper begins by describing the MWHS-2 dataset, the DPR reflectivity measurements and associated radar-retrieved hydrometeor profiles, and the method to preprocess the data to obtain collocated and coincident matchups between MWHS-2 and DPR. We then describe the forward modeling process to obtain cloud-free simulated TBs and to develop a bias correction to the MWHS-2 observations. Next, we outline how we account for variable gaseous transmission in the process of comparing HWP and other radar-derived quantities to MWHS-2. We then proceed to study the sensitivity of the individual MWHS-2 channels to the presence of hydrometeors and to evaluate the spectral dependency of this sensitivity.
2. Instruments, data, and methods
a. Description of datasets
The MWHS-2 on board the midmorning polar-orbiting FY-3C satellite, launched by the China Meteorological Administration/National Satellite Meteorological Center (CMA/NSMC) on 23 September 2013, is a cross-track, millimeter-wave radiometer. MWHS-2 includes two window channels at 89 and 150 GHz. Five sounding channels are working near 183.31 GHz. MWHS-2 is also the first spaceborne sensor equipped with eight channels near 118.75 GHz and therefore provides new observations that allow for a global assessment of such channels. With these 15 channels (shown in Table 1 along with polarizations), MWHS-2 can retrieve atmospheric temperature profiles, humidity profiles, and water vapor information simultaneously. The spatial resolution is near 16 km at nadir for 183 GHz and 29 km for 89 GHz.
MWHS-2 channel frequencies and polarization at nadir used in RTTOV (H = horizontal; V = vertical).
We note that the polarization values listed in Table 1 (as well as in Lawrence et al. 2015) are reversed from the polarization values reported for MWHS-2 in the World Meteorological Organization’s Observing Systems Capability Analysis and Review Tool (OSCAR) database (see https://www.wmo-sat.info/oscar/instruments/view/341 for FY-3C’s MWHS-2). The determination of polarization at nadir is a matter of definition, which likely causes this discrepancy. We have numerically verified that the setting reported here align correctly with the values needed in the radiative transfer model we use. MWHS-2 Level-1 files were obtained from the CMA/NSMC (http://satellite.nsmc.org.cn/portalsite/default.aspx).
The GPM Core Observatory carries both a DPR and a GPM Microwave Imager (GMI) (Hou et al. 2014). The GPM orbit inclination of 65° is such that it enables the orbit to cut across the orbits of sun-synchronous satellites, such as FY-3C. It also allows for the gathering of samples at latitudes where most precipitation occurs in terms of absolute amount at various times of the day. The DPR consists of a Ku-band precipitation radar (KuPR at 13.6 GHz) and a Ka-band precipitation radar (KaPR at 35.5 GHz). Data collected from the KuPR and KaPR units provide three-dimensional observations of rain/snow and also provide an accurate estimation of rainfall rate to the scientific community. The radar reflectivity measured by and hydrometeor profiles retrieved from DPR will be compared to the TB of MWHS-2 to study the sensitivity of radiance at microwave high-frequency channels to hydrometeor scattering, which allows us to explore the potential capability of spaceborne observations from these channels for retrieving hydrometeor profiles.
The KuPR has an observation swath of 245 km with 49 beams, each resulting in a circular footprint with a 5.2-km diameter. The KaPR has a swath of 120 km with 49 beams of which 25 beams are matched to the central 25 beams of KuPR. This narrower swath with matched Ka and Ku reflectivities is termed matched scan (MS). The KuPR is more sensitive to heavy and moderate rainfall and the KaPR is more sensitive to light rainfall and snow. The combination of measurements from both radars will allow for a more comprehensive understanding of the ice particle scattering to which the microwave observations are sensitive at different degree levels. Therefore, in this paper we used the 2BCMB product at MS scans, to obtain the reflectivities of both radars and hydrometeor retrievals, including precipitation profiles. The 2BCMB product uses data of KuPR and KaPR, and GMI to determine the precipitation structure that best fits the combined data from these instruments. The resolution of the 2BCMB product is 250 m vertically and 5 km horizontally. To account for the total amount of liquid and ice in a column as fully as possible, we herein consider the HWP to consist of three parts: IWP, precipitation water path (PWP), and cloud liquid water path (LWP), where each of these three is the vertical integral of the corresponding vertically resolved water content. For example, LWP is the vertical integral of liquid water content (LWC). Precipitation water content (PWC) in 2BCMB consists of the mass of all liquid rain and frozen precipitation-sized ice particles and is directly retrieved from GPM observations. Thus, PWP holds the total mass of precipitating particles per square meter in the column. Note that GPM observations are not sensitive to small ice crystals. Therefore, cloud ice water content (IWC), is assigned to be zero in the 2BCMB product. In consequence, the IWP is also zero and HWP = LWP + PWP in this study. The PWC in the 2BCMB product was retrieved from the GPM observations using the GPM combined algorithm and is composed of liquid-phase and ice-phase precipitation. The cloud LWC in this product differs in that it was provided by the “Vertical Profile Submodule” (VER) of the “Radar Algorithm,” which interpolates the Japan Meteorological Agency’s (JMA) analyses and forecasts to the DPR locations/range bins (Grecu et al. 2016; Olson et al. 2018). We discuss the impact of LWP on observed brightness temperatures later in the paper. Table 2 provides the symbols, quantities, units, and supplementary information of these parameters and the others used in this paper. The 2BCMB product was provided by the NASA Precipitation Processing System archived at the NASA GES DISC (https://doi.org/10.5067/GPM/DPRGMI/CMB/2B/06).
Symbols and quantities used in this paper.
b. Collocated and coincident measurements
In this study, observations were regarded as collocated and coincident when MWHS-2 brightness temperatures and GPM profiles fell into the same 0.25° latitude × 0.25° longitude bin and the time difference between the two was less than 15 min. Because the footprint of the MWHS-2 channels 1–9 is about 29 km at nadir, which is approximately equivalent to the grid size (25 km), there were only a few MWHS-2 pixels falling into the same grid (typically fewer than three). Therefore, the measurements from the pixel closest to the center of a grid in distance are extracted to represent that grid. Contrarily, typically dozens of GPM observations fell into one 0.25° latitude × 0.25° longitude bin because the DPR footprint (5 km) is much smaller than the grid size. Thus, we averaged all the GPM measurements within one grid to represent the mean over this grid cell. To limit issues caused by the high zenith angles and the low spatial resolution of MWHS-2 at the outer edge of its scan, the five outermost scan positions on each side of the scan were excluded from the collocated dataset. We further limit this study to open oceans only in order to avoid issues related to the simulation of surface emissivity over land. At the end of the collocation process, a total of more than 1.5 million samples over oceans globally for the year of 2017 were generated.
3. Cloud-free radiative transfer simulations and bias correction
a. Atmospheric profiles and surface parameters
ERA-Interim is a third-generation global atmospheric reanalysis provided by the European Centre for Medium-Range Weather Forecasts (ECMWF). It improves on previous versions (e.g., ERA-40) by using an enhanced atmospheric model and assimilation system (Dee et al. 2011). The spatial resolution of the dataset is approximately 80 km (T255 spectral) on 60 vertical levels from the surface up to 0.1 hPa. Among others, it assimilates a significant amount of satellite radiances, (e.g., SSM/I and SSMIS). ERA-Interim data are available since 1979, and it had been continuously updated until 31 August 2019 when it was replaced by ERA5. For this study, 6-hourly surface as well as vertically resolved moisture and temperature field products were used (downloaded from https://rda.ucar.edu/datasets/ds627.0/).
Each MWHS-2 observation was matched to the closest ERA-Interim reanalysis profile, leading to maximum time differences between the observations and the reanalysis of 3 h. The ERA-Interim profiles, together with sea surface temperature and surface wind speed, formed the basis of the subsequent cloud-free radiative transfer simulations.
b. Radiative transfer simulations
Radiative transfer simulations were carried out using the TIROS Operational Vertical Sounder Radiative Transfer (RTTOV, version 12.2) Model (Hocking et al. 2019; Saunders et al. 2018, 2007), which is widely used both in the operational and research community. All physical parameterizations including absorption by gases, liquid water, and rough ocean surface scattering were applied unchanged from RTTOV. Radiative transfer simulations were implemented for all 15 channels listed in Table 1 with RTTOV polarization at nadir as also listed in this table.
c. Bias correction
The bias correction was performed based on histograms of differences between observed and simulated TBs. Figure 1 serves as an example for this approach. For each channel, the histogram of brightness temperature differences was analyzed and the mode of the histogram was used for bias correction. The idea is that the mode of the histogram corresponds to the observations that are least affected by precipitation and therefore produces a more robust estimate of bias than the mean or median.
Histograms of observed minus simulated brightness temperatures for all 15 channels of MWHS-2. These histograms contain data for scan position 44 for the entire year of 2017. The different colored vertical lines correspond to the same-colored statistics given in the upper-left part of each panel. The mode of each histogram was used as the basis for bias correction.
Citation: Journal of Applied Meteorology and Climatology 59, 7; 10.1175/JAMC-D-19-0293.1
The process was repeated for each channel and each scan position, leading to the bias-correction values shown in Fig. 2. These values can be directly compared with the values reported in Lawrence et al. (2015, see their Figs. 7 and 12). While they use a different version of RTTOV as well as a different underlying NWP model, their bias-correction values and in particular the dependency of bias correction on scan position are very similar to our values shown in Fig. 2. Significant differences between our results and those reported in Lawrence et al. (2015) exist in particular in channel 14. They report biases between 1 and 3.5 K depending on scan position and we report biases between 0.5 and 6 K with a similar dependency on scan position. It is unclear what these large differences in bias can be attributed to. Lawrence et al. (2015) use a slightly different approach of rejecting precipitation-affected observations. They calculate a scattering index (SI) based on observed and simulated TBs in channels 1 and 2. Whenever the SI exceeded 5 K, the data were rejected and the bias was only estimated on the remaining data, which are only weakly affected by scattering. To test whether this different approach led to different values for the bias correction, we implemented this approach as well. However, the results were not significantly different from the results reported in Fig. 2.
Bias-correction values derived and used in this study as function of scan position for all 15 MWHS-2 channels.
Citation: Journal of Applied Meteorology and Climatology 59, 7; 10.1175/JAMC-D-19-0293.1
The biases reported in Fig. 2 are subsequently used to correct observed TBs toward the simulations. That is, the bias reported in Fig. 2 is subtracted from the observations before further analysis.
d. Weighting functions under cloud-free conditions
We use the collocated dataset to study the variability of MWHS-2 weighting functions under cloud-free conditions as function of viewing angle, expressed in terms of relative airmass factor, and total column water vapor amount (TCWV), the latter being a proxy for the general type of atmosphere observed. Midlatitude atmospheres typically exhibit TCWV on the order of 20–30 kg m−2, more tropical atmospheres around 40 kg m−2 or beyond. Figure 3 shows the height of the peak of the weighting function for each channel as function of TCWV and relative airmass factor. Various features can be observed:
Channel 1 (89 GHz) peaks near the surface. Only for very high TCWV and high sensor zenith angles will the peak of the weighting function move up to about 1 km. Channel 1 will therefore be affected by nonprecipitating warm clouds also in the lower atmosphere.
The 118.75-GHz channels 2–4 peak in the lower stratosphere or high up in the troposphere at altitudes between 17 and 26 km and will therefore show little sensitivity to the lower atmosphere. Only in exceptional cases would convection reach so high that these channels show a significant signal.
The 118.75-GHz channels 5 and 6 peak around 10 km altitude and will therefore be affected by most deep convective events.
The 118.75-GHz channels 7–9 and channel 10 (150 GHz) peak between 4 km and the surface. These channels transition from a stronger sensitivity to observation angle (isolines run more vertically), to a stronger sensitivity to atmospheric moisture (isolines run more horizontally). Thus, for example, the lowest-peaking 118-GHz channel 9 (118 ± 5 GHz) and channel 10 show sensitivity to both observation angle and TCWV.
The 183.31-GHz channels 11–15 peak between 7 and 2 km and show stronger sensitivity to water vapor than to zenith angle.
Peak of cloud-free weighting function for all 15 MWHS-2 channels as a function of viewing angle θ, expressed in terms of relative airmass factor, and TCWV. The values given are averaged over all collocated profiles, binned in intervals of 0.1 airmass factors for airmass factors between 1 (observation zenith angle θ = 0°) and 2 (θ = 60°), and 2.5 kg m−2 TCWV intervals in a range between 0 and 60 kg m−2. Isoline labels as well as the color bar are in kilometers. Mean heights μ for each channel and corresponding standard deviations σ are given in each panel’s title.
Citation: Journal of Applied Meteorology and Climatology 59, 7; 10.1175/JAMC-D-19-0293.1
These findings are generally in agreement with earlier studies (Lawrence et al. 2015) and with the general expectations one would have for a MWHS-2-like sounding system under cloud-free conditions. Clouds and precipitation will modify observed brightness temperatures from their cloud-free values only if they reach high enough. For the purpose of precipitation retrievals therefore three findings are relevant. First, the stratospheric channels 2–4 will have little direct information on precipitation because of their high weighting functions. This will be confirmed later. Second, the lower-peaking 118-GHz channels, particularly channels 7 and 8, provide information orthogonal to the 183-GHz water vapor sounding channels, where former are more sensitive to zenith angle changes and the latter more sensitive to TCWV changes. Third, the window channels (1, 9, and 10) have significant sensitivity to the surface and will thus be sensitive also to precipitation and clouds in the lower atmosphere.
We next move on to studying the impact of clouds and precipitation on the observed brightness temperatures. We do this first by studying the difference between observed all-sky brightness temperatures and simulated cloud-free brightness temperatures. After that, we explicitly calculate the amount of precipitation in the column that is visible for each observation and frequency by explicitly accounting for the atmospheric transmission.
4. Brightness temperature response to clouds and precipitation
a. Observed deviation from cloud-free brightness temperatures
In this study, the scattering-induced brightness temperature depression (ΔTB) is defined as the difference between bias-corrected microwave observations, TBobs, and simulated clear-sky background brightness temperatures, as outlined in section 3, TBsim:
Figure 4 shows an example of the observed brightness temperatures and the resulting scattering-induced brightness temperature depression. The convection cell located around 2°N, 68°E shows significant depressions of brightness temperatures with respect to cloud-free simulated brightness temperatures. Channels 10 and 15 both show ΔTBs exceeding −100 K. In contrast, channel 1 shows a ΔTB of only −20 K. In general, going from lower to higher frequencies, one can expect the scattering signature to increase, as the size parameter of the scatterer increases with decreasing wavelength. Additionally, the oxygen and water vapor sounding channels exhibit a strong dependency on how close each channel is to the center of its corresponding absorption line. This effect is caused by the weighting functions of the sounding channels peaking higher in the atmosphere the closer they are to the center of the absorption line. Ultimately, the channels will peak so high in the atmosphere that even deep convection is not visible at all. This is the case for example for channels 2–4 in Fig. 4.
Example of the scattering signature of deep convective clouds observed by MWHS-2. (a) One full orbit of MWHS-2 data (channel 9; 22 Aug 2016, with start time 0554 UTC). (b) The same data as in (a), enlarged around an area in the Indian Ocean that contains isolated deep convection, visible as the blue and green dots in the center-right of the panel. (c) The spectral variation of ΔTB for the center of one of the convective cells, as highlighted by the arrow to (b); the plot in (c) also shows the location of the 118.75-GHz oxygen absorption line, the 183.31-GHz water vapor absorption line, and the MWHS-2 channel numbers corresponding to Table 1. Note that MWHS-2 sounding channels 2–9 and 11–15 are all double sideband (e.g., channel 9 is 118.75 ± 5 GHz). In (b), their corresponding ΔTB are only shown at the location of the upper subband (e.g., 118.75 + 5 GHz).
Citation: Journal of Applied Meteorology and Climatology 59, 7; 10.1175/JAMC-D-19-0293.1
Addressing the sensitivity of ΔTB to ice particle scattering therefore requires disentangling the effect of broad spectral variations in actual scattering intensity from the effect of gas absorption that attenuates the scattering signal near the absorption lines. Further down, we present an approach to do exactly that. However, before we introduce this approach, we first evaluate the range of variability of ΔTB expected for the entire dataset.
Figure 5 presents two-dimensional probability density distribution functions of TBobs and ΔTB for all 15 MWHS-2 channels. Warm TBobs values are mostly from the clear sky, the surface, or from nonscattering clouds, while colder TBobs include scenes with precipitation, in particular precipitation ice, but can also occur under low-wind, cold and dry, cloud-free conditions. Regardless of how warm the absolute TBobs are, a perfect RTM model with perfect clear-sky input would produce near-zero values in ΔTB for all cloud-free conditions, while large negative ΔTB values are generated in the presence of precipitation that includes the ice phase.
Two-dimensional probability density distributions of TBobs and ΔTB for all 15 channels of MWHS-2 and for all collocated data. Note the different scales of both the x axis and the y axis.
Citation: Journal of Applied Meteorology and Climatology 59, 7; 10.1175/JAMC-D-19-0293.1
The typical response of high-frequency channels to hydrometeor scattering can be clearly identified for channels 7–15. While most data lie on around the ΔTB = 0 K line, a subset of the data shows a ΔTB decreasing linearly with decreasing TBOBS and that the ΔTB eventually decreases to −100 K or more. Channels 5 and 6, which peak higher in the atmosphere, show a similar behavior, but less pronounced.
It is important to note here that TBOBS and ΔTB provide independent information. This can be observed for example for channel 9. For TBOBS between 200 and 280 K, the probability density plot shows a bifurcation between those data that follow the ΔTB = 0 K line and those data for which ΔTB decreases approximately linearly with decreasing TBOBS. If only TBOBS was evaluated and a brightness temperature of TBOBS = 220 K was observed, one would not be able to know whether it was observed under conditions compatible with clear sky (ΔTB around 0 K) or whether it was observed under heavy hydrometeor scattering (ΔTB around −50 K). Also, under precipitation-free conditions, observations in channels 1, 9, and 10 (window channels) might be affected by cloud liquid water from nonprecipitating clouds. Since clouds are not represented in the cloud-free simulations, this causes the ΔTB values to be above the ΔTB = 0 line, for cases where there is no significant precipitation in the column.
The highest-peaking channels 2–4 are not sensitive to hydrometeor scattering and only exhibit slight deviations of ΔTB from zero. Because of their insensitivity to hydrometeor scattering, channels 2–4 will be excluded in subsequent analysis.
In addition to hydrometeor scattering, the emission caused by cloud liquid water and liquid precipitation will also affect brightness temperatures as well as ΔTB for those channels that peak low enough in the atmosphere to be sensitive to it. This emission signal has an effect opposite from the scattering-induced brightness temperature depression. It can be most clearly observed for channel 1 (89 GHz), which is the least-opaque of all channels. For channel 1, one can observe not only ΔTB values below zero, but also a significant portion of ΔTB values above zero, up to +100 K. To a lesser extent, channels 7–10 show this behavior, too. Channels 11–15 (183-GHz water vapor absorption channels) show very little of this effect.
To further understand the effect of ice and liquid in the column, we next evaluate the TBOBS with ΔTB in the context of DPR observations. To avoid any potential issues associated with DPR retrievals, we first look at DPR reflectivity profiles, which are direct measurements and not affected by any assumptions made in DPR retrievals.
b. Spectral sensitivity to precipitation
To compare DPR reflectivity profiles with TBOBS and with ΔTB, we calculate for each radar profile two integral properties, namely, the total vertically integrated reflectivity as seen by a given MWHS-2 channel and the average height from which this reflectivity originates. This concept will be used further down in a similar manner for HWP and requires some explanation, which is provided next for a general quantity X(h). The vertical integral of any atmospheric quantity X(h) is
The term X(h) can in principle be any quantity. In this paper, we are mostly concerned with GPM-observed radar reflectivities and hydrometeor products. Consider for example the generic function X(h) to represent cloud LWC in units of kilograms per meter cubed. The corresponding integrated quantity XINT then has units of kilograms per meter squared and is typically called cloud LWP. This principle also applies to PWC and cloud IWC in a vertical column that add up to PWP and IWP, respectively. Note that in the DPR data, cloud ice (IWC) is zero, so that IWP here is also zero, and therefore the HWP in the context of this paper is the sum of LWP and PWP.
As pointed out above, low-frequency passive microwave satellite observations rely on the relative transparency of the atmosphere (window channels) at low frequencies to derive column-integrated quantities, such as LWP. However, sounding instruments, such as MWHS-2, by design, provide several channels at frequencies with strong gas absorption (sounding channels). The weighting functions of these channels peak higher in the atmosphere and lower parts of the atmosphere are obstructed. In addition, the atmosphere is observed at a slant path for any satellite zenith angle larger than zero. The gross impact on weighting functions is discussed in the above section 3a. We now quantify which part of the vertical precipitation column is, in principle, visible to each channel.
Accounting for gas absorption and slant path the definition of XINT can be expanded as follows:
Here τ(h, f, θ) is the transmission between height h and the top of the atmosphere (TOA). The quantity
The transmission-weighted average height H* can then be calculated as
The conceptual model shown in Fig. 6 illustrates the above quantities by example of hydrometeor water content [HWC; [i.e., the generic quantity X(h) is set to mean HWC(h)]. Thus, in this example XINT represents HWP. While H and HWP (black in Fig. 6) refer to the physical properties of the column of the atmosphere, the properties H* and HWP* refer to transmission-weighted average height and the amount of HWP visible for each particular channel. They differ between channels with different vertical weighting function (red and blue in Fig. 6).
Conceptual model relating the different quantities in this section. (left) HWC as an example of a vertically resolved atmospheric parameter. The horizontal line (marked H) shows the average hydrometeor height. (center) The gas transmission for two example channels: one peaking higher in the atmosphere (blue; weighting function peaks at 9 km) and another one peaking lower in the atmosphere (red; weighting function peaks at 4 km). (right) The integrand of Eq. (2). The numbers on the right provide the results of Eqs. (3) and (4) for this case. The values of H* are also shown as colored horizontal lines in the right panel.
Citation: Journal of Applied Meteorology and Climatology 59, 7; 10.1175/JAMC-D-19-0293.1
Based on the above Eqs. (2)–(4), we now calculate the vertical integral of reflectivity
Relation between DPR-derived ZINT and HWP (blue dashed line with light-blue uncertainty range). Also shown are the relations between
Citation: Journal of Applied Meteorology and Climatology 59, 7; 10.1175/JAMC-D-19-0293.1
For lower values of ZINT, considerable spread can be observed among the different curves, which again is a manifestation of the DRP retrieval, likely caused by temperature dependency of the retrieval, and likely physically realistic. For higher peaking channels, the observed reflectivities will be at colder temperatures than for lower peaking channels. Thus, size distributions assumed in the DPR retrieval will change and consequently, the retrieved ice water content and HWP* will change. This effect is most clearly identified in channels 12–15 at around HWP* = 1 kg m−2, for which the corresponding
To understand the relation between MWHS-2-derived ΔTB and the radar-derived quantities, we next bin ΔTB by
Binned representation of mean brightness temperature depression ΔTB as a function of transmission-weighted integrated radar reflectivity
Citation: Journal of Applied Meteorology and Climatology 59, 7; 10.1175/JAMC-D-19-0293.1
As mentioned above, channels 2–4 peak too high in the atmosphere to see significant scattering. The remaining 12 channels can be split up into two groups with different behavior: The first group includes channel 1 and channels 5–10. The second group includes the five water vapor absorption channels 11–15. Channels 1 and 5–10 include the traditional window channels as well as the 118-GHz oxygen absorption channels. Toward large values of
Comparing channels 1 (89 GHz) and 10 (150 GHz), one can see that both channels react very similarly to hydrometeor scattering (blue). However, one significant difference between these two channels is that channel 1 shows a significant warming (ΔTB > 0) for high
Next, we proceed to study the sensitivity of ΔTB of the individual MWHS-2 channels to the presence of hydrometeors. In Fig. 9, the top-left panel shows no clear dependency of sensitivity on frequency. This is not surprising because HWP is just the total column hydrometeor water path and, for example, channel 3 peaking at 20.0 km altitude is not expected to be sensitive to precipitation ice and liquid found in the lower troposphere. The variability seen in sensitivity with respect to HWP is thus driven by two factors. First, the gaseous transmission in each channel, which will depend on the position of the channel relative to the 118 and 183 absorption lines. Second, the actual scattering intensity of hydrometeors, which should be a monotonically increasing function of frequency.
The ΔTB response of the 12 MWHS-2 channels (excluding channels 2–4) to (top left) HWP and (top right) HWP*. Window channels are plotted in black, 118-GHz oxygen absorption channels are plotted in red, and 183-GHz water vapor absorption channels are plotted in blue. (bottom) The corresponding data density for the different plots in the top panels in samples per bin. Note that for the plots on the left-hand side all channels have the same data distributions because HWP is independent of channel number. For plots on the right-hand side, each channel has its unique data distribution because HWP* depends on channel number.
Citation: Journal of Applied Meteorology and Climatology 59, 7; 10.1175/JAMC-D-19-0293.1
The right-hand panel of Fig. 9 disentangles these two effects by plotting ΔTB against HWP*, and thereby accounting for the portion of hydrometeors actually observed in each channel and allows to assess the response of ΔTB as function of frequency alone. The different curves cluster around the four frequency ranges, 89, 118, 150, and 183 GHz, with significant differences in sensitivity between the four. One can identify that over a large range of HWP* the response of ΔTB is approximately linear.
The approximate linearity of ΔTB with HWP* allows for an estimation of the sensitivity of ΔTB to HWP* by calculating the slope of each curve. The results of this analysis are shown in Table 3. The sensitivities of these 12 channels increase in magnitude with frequency from about 11 K (kg m−2)−1 at 89 GHz to 35–53 K (kg m−2)−1 at 183 GHz.
Sensitivity to ice particle scattering of ΔTB of the different MWHS-2 channels expressed in kelvins per kilogram per meter squared of HWP* and sensitivity to
This general increase in scattering intensity with frequency is overlaid by a few other effects. Comparing the scattering sensitivity between the different 118-GHz channels (5–9), one can see from Table 3 that the sensitivity decreases with increasing atmospheric opacity. Contrarily, for the water vapor absorption channels (11–15), the sensitivity increases with increasing opacity. We believe that both effects are physical, but further studies are needed in order to fully understand this effect.
Channel 1 (89 GHz) presents a special case. For low HWP*, ΔTB increases with HWP* and the observed ΔTB on average exceeds zero in the range between zero and about 1.5 kg m−2 in HWP*. This effect is caused by emission of liquid clouds and precipitation and is only very weakly observed in the other channels. We therefore calculated the sensitivity of 89 GHz only for values HWP* > 0.74 kg m−2, where visually the relation starts to decrease linearly. The combined effect of emission and scattering at 89 GHz makes this channel particularly difficult to interpret in the context of precipitation retrieval but also provides additional information when combined with higher-frequency channels, where the emission effect is less pronounced or completely absent.
To explain the principal behavior of the curves shown in Fig. 9, we set up a simple conceptual radiative transfer model following the graph shown on the left-hand side of Fig. 10. The upwelling cloud-free brightness temperature TB,CF is modulated by an absorbing/emitting cloud/precipitation layer and a second layer that is purely scattering. The optical depth of the emitting layer is τe and the optical depth of the scattering layer is τs. To first order, the sum of these two quantities is proportional to HWP, that is, HWP ∝ τe + τs, assuming the mass extinction coefficient of the absorbing and scattering materials to be constant. Assuming the scattering layer to be scattering isotopically (asymmetry parameter g = 0) and conservatively (single-scattering albedo
(left) The setup of a simple two-layer model affecting the observed brightness temperatures. This same model is expressed mathematically in Eq. (5). (right) The response of ΔTB to changes in the total optical thickness of the two layers for two different values of cloud-free background temperatures (black and yellow curves) and for another case in which the optical depth of the scattering layer is increased (red curve). The dashed lines show the range for which the response is approximately linear.
Citation: Journal of Applied Meteorology and Climatology 59, 7; 10.1175/JAMC-D-19-0293.1
One can see from Fig. 10 that the magnitude of the positive “bump” in ΔTB depends on the contrast between TB,CF and the temperature Te of the emission layer. If this contrast is large (black curve, compared to yellow curve, which has a smaller contrast), emission by clouds and precipitation will initially increase ΔTB over the zero line and only as the scattering layer becomes optically thicker, ΔTB will decrease. Large differences between TB,CF and Te are typically observed in window channels over open ocean situations. As frequency increases, these differences become smaller, because surface emissivity increases. Because 89 GHz exhibits the lowest surface emissivity for all MWHS-2 channels, the effect can be observed most strongly in Fig. 9 for 89 GHz and to a much smaller extent for the other channels:
Figure 10 also highlights the limited range in ΔTB responds roughly linearly to increases in cloud and precipitation optical depth (dashed lines). One can see that the slope of the yellow and black dashed lines is approximately identical. Only when the scattering optical depth increases (red curve), the slope becomes steeper. This effect is associated with increase in scattering optical depth with frequency and can be observed in the top-right panel of Fig. 9.
We note that the underlying HWP* value itself is derived from DPR observations and therefore also incorporates assumptions about particle habit and size distribution. For observational validation of radiative transfer model simulations of nonspherical particles, it might be more appropriate to compare the spectral dependency of ΔTB to
As in Fig. 9, but for
Citation: Journal of Applied Meteorology and Climatology 59, 7; 10.1175/JAMC-D-19-0293.1
To better quantify the spectral dependency of ΔTB on HWP* and
(left) Sensitivity of ΔTB to HWP* for the four different bands (89, 118, 150, and 183 GHz). The data are shown in a double-logarithmic plot. To avoid issues with channels peaking too high in the atmosphere, only channels with a peak of the weighting function below 5 km were included. Thus, for 118 GHz only channels 7–9 were included, and for 183 GHz only channels 13–15 were included. The error bars at 118 and 183 GHz show the minimum/maximum range of sensitivity over these channels. The red curve shows a power-law fit through the data with parameters given in the inset, with S being the sensitivity [K (kg m−2)−1] and f being the frequency (GHz). (right) The sensitivity of ΔTB with respect to
Citation: Journal of Applied Meteorology and Climatology 59, 7; 10.1175/JAMC-D-19-0293.1
This observed spectral dependency sheds light on the observed particle scattering behavior over a wide range of frequencies. To first order, the increased response of ΔTB to HWP (and ZINT) is caused by the increased optical thickness of scattering by ice particles. This observed behavior can then be used, statistically, to evaluate the accuracy of theoretical scattering models, which need to reproduce the same spectral behavior. In this context, the above finding of approximate linearity (i) between (ZINT)0.58 and ΔTB as well as (ii) between HWP and ZINT and (iii) between HWP and ΔTB reinforces the notion that the underlying GPM-DPR hydrometeor retrieval (which drives the relation between HWP and ZINT) actually is physically consistent. As pointed out above, if it were not, we would not find linearity between (ZINT)0.58 and ΔTB.
5. Conclusions
In the next few years, several new passive microwave missions will be launched covering the spectral range between 89 and 200 GHz. Some of these missions, as, for example, NASA’s TROPICS mission, will also provide channels at 118 GHz but will not provide low-frequency observations below 89 GHz. In this context, it is important to understand the response of passive microwave observations to ice particle scattering.
Here we present an analysis of ice particle scattering behavior in this frequency range as compared to vertically integrated hydrometeor and reflectivity properties derived from collocated GPM-DPR observations. The results presented here build on earlier analysis by Bennartz and Bauer (2003) in which the scattering signal of precipitation was also investigated using simulation studies. In this current study, we overcome a few limitations of the earlier study, which was based solely on radiative transfer simulations and was geared toward understanding the bulk effect of hydrometeor scattering. Here, we focus on disentangling the effects of gaseous absorption from that of hydrometeor scattering, which allows us to quantify the effects of scattering alone, rather than the effect of combined scattering and gas absorption. We further provide a simple conceptual model that explains the principal dependency of the brightness temperature depression on changes in hydrometeor water path (HWP). With this new approach, we quantify the global response of brightness temperature depressions over a cloud-free background (ΔTB) and its dependency on frequency. Globally averaged, the sensitivity in magnitude of ΔTB to HWP quadruples from about 11 K (kg m−2)−1 at 89 GHz to more than 53 K (kg m−2)−1 around 183 GHz. Comparing the two frequencies least affected by gas absorption (89 and 150 GHz, respectively), we find that our observationally derived sensitivities [11 and 26 K (kg m−2)−1, respectively] are in agreement with the results of Bennartz and Bauer (2003), in which the response at 150 GHz was found to be 2–3 times as strong as at 85 GHz.
Disentangling gaseous absorption from the scattering behavior proves useful for two reasons. First, the profiles of gaseous transmission as well as the cloud-free background brightness temperatures needed for ΔTB can be calculated easily from operational NWP model data. Second, while NWP models do not provide perfectly accurate profiles of temperature and moisture, and collocation errors between NWP models and observed brightness temperatures exist, the simulated cloud-free brightness temperatures are fairly accurate, and their error characteristics are known better than any simulations of precipitation-affected brightness temperatures. Together with the relatively large temperature depressions observed at the frequencies under consideration, the use of ΔTB appears beneficial in the context also of retrievals of hydrometeors. The results and approach reported here will form the basis for such investigations in the future, where we will evaluate the scattering response to different types of precipitation (e.g., deep convective vs frontal) and also address issues related to changes in observed sensitivity within a given band. For example, we found here that different channels within the 118-GHz oxygen band respond differently to scattering than different channels with the 183-GHz water vapor band. In the former band, the sensitivity of ΔTB to HWP decreases with gaseous absorption, whereas in the latter band it increases. Further, from our analysis presented here, it also appears feasible to use the difference between observed brightness temperatures and simulated cloud-free background brightness temperatures to retrieve surface rain rate and hydrometeor water path from passive microwave observations.
Acknowledgments
This work was supported by NASA Grant NNX17AJ09G to Vanderbilt University. The authors thank the NASA Precipitation Processing System (PPS) for providing the GPM 2BCMB data and the China Meteorological Administration/National Satellite Meteorological Center (CMA/NSMC) for providing MWHS-2 L1B data for this research. The authors further acknowledge and support the help of EUMETSAT and the Met Office for providing and maintaining RTTOV.
REFERENCES
Bauer, P., and A. Mugnai, 2003: Precipitation profile retrievals using temperature-sounding microwave observations. J. Geophys. Res., 108, 4730, https://doi.org/10.1029/2003JD003572.
Bennartz, R., and G. W. Petty, 2001: The sensitivity of microwave remote sensing observations of precipitation to ice particle size distributions. J. Appl. Meteor., 40, 345–364, https://doi.org/10.1175/1520-0450(2001)040<0345:TSOMRS>2.0.CO;2.
Bennartz, R., and P. Bauer, 2003: Sensitivity of microwave radiances at 85–183 GHz to precipitating ice particles. Radio Sci., 38, 8075, https://doi.org/10.1029/2002RS002626.
Bennartz, R., A. Thoss, A. Dybbroe, and D. B. Michelson, 2002: Precipitation analysis using the Advanced Microwave Sounding Unit in support of nowcasting applications. Meteor. Appl., 9, 177–189, https://doi.org/10.1017/S1350482702002037.
Blackwell, W. J., and Coauthors, 2018: An overview of the TROPICS NASA Earth venture mission. Quart. J. Roy. Meteor. Soc., 144, 16–26, https://doi.org/10.1002/qj.3290.
Brath, M., S. Fox, P. Eriksson, R. C. Harlow, M. Burgdorf, and S. A. Buehler, 2018: Retrieval of an ice water path over the ocean from ISMAR and MARSS millimeter and submillimeter brightness temperatures. Atmos. Meas. Tech., 11, 611–632, https://doi.org/10.5194/amt-11-611-2018.
Buehler, S. A., and Coauthors, 2012: Observing ice clouds in the submillimeter spectral range: The CloudIce mission proposal for ESA’s Earth explorer 8. Atmos. Meas. Tech., 5, 1529–1549, https://doi.org/10.5194/amt-5-1529-2012.
Burns, B. A., X. Wu, and G. R. Diak, 1997: Effects of precipitation and cloud ice on brightness temperatures in AMSU moisture channels. IEEE Trans. Geosci. Remote Sens., 35, 1429–1437, https://doi.org/10.1109/36.649797.
Bytheway, J. L., and C. D. Kummerow, 2018: Consistency between convection allowing model output and passive microwave satellite observations. J. Geophys. Res. Atmos., 123, 1065–1078, https://doi.org/10.1002/2017jd027527.
Dee, D. P., and Coauthors, 2011: The ERA-Interim reanalysis: Configuration and performance of the data assimilation system. Quart. J. Roy. Meteor. Soc., 137, 553–597, https://doi.org/10.1002/qj.828.
Dong, C., and Coauthors, 2009: An overview of a new Chinese weather satellite FY-3A. Bull. Amer. Meteor. Soc., 90, 1531–1544, https://doi.org/10.1175/2009BAMS2798.1.
Ekelund, R., and P. Eriksson, 2019: Impact of ice aggregate parameters on microwave and sub-millimetre scattering properties. J. Quant. Spectrosc. Radiat. Transfer, 224, 233–246, https://doi.org/10.1016/j.jqsrt.2018.11.013.
Eriksson, P., M. Jamali, J. Mendrok, and S. A. Buehler, 2015: On the microwave optical properties of randomly oriented ice hydrometeors. Atmos. Meas. Tech., 8, 1913–1933, https://doi.org/10.5194/amt-8-1913-2015.
Fox, S., and Coauthors, 2019: Airborne validation of radiative transfer modelling of ice clouds at millimetre and sub-millimetre wavelengths. Atmos. Meas. Tech., 12, 1599–1617, https://doi.org/10.5194/amt-12-1599-2019.
Gasiewski, A. J., 1992: Numerical sensitivity analysis of passive EHF and SMMW channels to tropospheric water vapor, clouds, and precipitation. IEEE Trans. Geosci. Remote Sens., 30, 859–870, https://doi.org/10.1109/36.175320.
Geer, A. J., and F. Baordo, 2014: Improved scattering radiative transfer for frozen hydrometeors at microwave frequencies. Atmos. Meas. Tech., 7, 1839–1860, https://doi.org/10.5194/amt-7-1839-2014.
Gong, J., and D. L. Wu, 2017: Microphysical properties of frozen particles inferred from Global Precipitation Measurement (GPM) Microwave Imager (GMI) polarimetric measurements. Atmos. Chem. Phys., 17, 2741–2757, https://doi.org/10.5194/acp-17-2741-2017.
Gong, J., and D. L. Wu, 2014: CloudSat-constrained cloud ice water path and cloud top height retrievals from MHS 157 and 183.3 GHz radiances. Atmos. Meas. Tech., 7, 1873–1890, https://doi.org/10.5194/amt-7-1873-2014.
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.
Grody, N. C., 1991: Classification of snow cover and precipitation using the special sensor microwave imager. J. Geophys. Res., 96, 7423–7435, https://doi.org/10.1029/91JD00045.
He, J., and H. Chen, 2019: Atmospheric retrievals and assessment for microwave observations from Chinese FY-3C satellite during Hurricane Matthew. Remote Sens., 11, 896, https://doi.org/10.3390/rs11080896.
Heymsfield, G. M., J. M. Shepherd, S. W. Bidwell, W. C. Boncyk, I. J. Caylor, S. Ameen, and W. S. Olson, 1996: Structure of Florida thunderstorms using high-altitude aircraft radiometer and radar observations. J. Appl. Meteor., 35, 1736–1762, https://doi.org/10.1175/1520-0450(1996)035<1736:SOFTUH>2.0.CO;2.
Hocking, J., P. Rayer, D. Rundle, and R. Saunders, 2019: RTTOV v12 users guide. EUMETSAT, accessed 7 December 2019, https://www.nwpsaf.eu/site/software/rttov/documentation/.
Hogan, R. J., and C. D. Westbrook, 2014: Equation for the microwave backscatter cross section of aggregate snowflakes using the self-similar Rayleigh–Gans approximation. J. Atmos. Sci., 71, 3292–3301, https://doi.org/10.1175/JAS-D-13-0347.1.
Hogan, R. J., R. Honeyager, J. Tyynela, and S. Kneifel, 2017: Calculating the millimetre-wave scattering phase function of snowflakes using the self-similar Rayleigh–Gans approximation. Quart. J. Roy. Meteor. Soc., 143, 834–844, https://doi.org/10.1002/qj.2968.
Holmlund, K., B. Bojkov, D. Klaes, and P. Schlüssel, 2017: The joint polar system: Towards the second generation EUMETSAT polar system. Proc. 2017 IEEE Int. Conf. on Geoscience and Remote Sensing Symp., Fort Worth, TX, IEEE, 2779–2782, https://doi.org/10.1109/IGARSS.2017.8127574.
Hong, G., 2007: Parameterization of scattering and absorption properties of nonspherical ice crystals at microwave frequencies. J. Geophys. Res., 112, D11208, https://doi.org/10.1029/2006JD008364.
Hong, G., P. Yang, B. A. Baum, A. J. Heymsfield, F. Weng, Q. Liu, G. Heygster, and S. A. Buehler, 2009: Scattering database in the millimeter and submillimeter wave range of 100–1000 GHz for nonspherical ice particles. J. Geophys. Res., 114, D06201, https://doi.org/10.1029/2008JD010451.
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.
Kim, M. J., 2006: Single scattering parameters of randomly oriented snow particles at microwave frequencies. J. Geophys. Res., 111, D14201, https://doi.org/10.1029/2005JD006892.
Kneifel, S., M. S. Kulie, and R. Bennartz, 2011: A triple-frequency approach to retrieve microphysical snowfall parameters. J. Geophys. Res., 116, D11203, https://doi.org/10.1029/2010JD015430.
Kulie, M. S., R. Bennartz, T. J. Greenwald, Y. Chen, and F. Weng, 2010: Uncertainties in microwave properties of frozen precipitation: Implications for remote sensing and data assimilation. J. Atmos. Sci., 67, 3471–3487, https://doi.org/10.1175/2010JAS3520.1.
Kuo, K. S., and Coauthors, 2016: The microwave radiative properties of falling snow derived from nonspherical ice particle models. Part I: An extensive database of simulated pristine crystals and aggregate particles, and their scattering properties. J. Appl. Meteor. Climatol., 55, 691–708, https://doi.org/10.1175/JAMC-D-15-0130.1.
Lawrence, H., N. Bormann, Q. Lu, A. Geer, and S. English, 2015: An evaluation of FY-3C MWHS-2 at ECMWF. EUMETSAT/ECMWF Fellowship Programme Research Rep. 37, 26 pp., https://www.ecmwf.int/node/10668.
Leinonen, J., S. Kneifel, and R. J. Hogan, 2018: Evaluation of the Rayleigh–Gans approximation for microwave scattering by rimed snowflakes. Quart. J. Roy. Meteor. Soc., 144, 77–88, https://doi.org/10.1002/qj.3093.
Liu, G., 2004: Approximation of single scattering properties of ice and snow particles for high microwave frequencies. J. Atmos. Sci., 61, 2441–2456, https://doi.org/10.1175/1520-0469(2004)061<2441:AOSSPO>2.0.CO;2.
Liu, G., and J. A. Curry, 1998: Remote sensing of ice water characteristics in tropical clouds using aircraft microwave measurements. J. Appl. Meteor., 37, 337–355, https://doi.org/10.1175/1520-0450(1998)037<0337:RSOIWC>2.0.CO;2.
Lu, Y. H., Z. Y. Jiang, K. Aydin, J. Verlinde, E. E. Clothiaux, and G. Botta, 2016: A polarimetric scattering database for non-spherical ice particles at microwave wavelengths. Atmos. Meas. Tech., 9, 5119–5134, https://doi.org/10.5194/amt-9-5119-2016.
Marzano, F. S., A. Mugnai, G. Panegrossi, N. Pierdicca, E. A. Smith, and J. Turk, 1999: Bayesian estimation of precipitating cloud parameters from combined measurements of spaceborne microwave radiometer and radar. IEEE Trans. Geosci. Remote Sens., 37, 596–613, https://doi.org/10.1109/36.739124.
Mason, S. L., R. J. Hogan, C. D. Westbrook, S. Kneifel, D. Moisseev, and L. von Terzi, 2019: The importance of particle size distribution and internal structure for triple-frequency radar retrievals of the morphology of snow. Atmos. Meas. Tech., 12, 4993–5018, https://doi.org/10.5194/amt-12-4993-2019.
Mattioli, V., C. Accadia, J. Ackermann, S. Di Michele, Imke Hans, P. Schlüssel, P. Colucci, and A. Canestri, 2019: The EUMETSAT Polar System–Second Generation (EPS-SG) passive microwave and sub-mm wave missions. PhotonIcs & Electromagnetics Research Symposium–Spring (PIERS-Spring), Rome, Italy, IEEE, 3926–3933, https://doi.org/10.1109/PIERS-Spring46901.2019.9017822.
Olson, W. S., and Coauthors, 2018: GPM combined radar–radiometer precipitation algorithm theoretical basis document (version 5). NASA GES DISC Rep., 68 pp., https://pps.gsfc.nasa.gov/Documents/Combined_algorithm_ATBD.V05.pdf.
Ori, D., T. Maestri, R. Rizzi, D. Cimini, M. Montopoli, and F. S. Marzano, 2014: Scattering properties of modeled complex snowflakes and mixed-phase particles at microwave and millimeter frequencies. J. Geophys. Res. Atmos., 119, 9931–9947, https://doi.org/10.1002/2014jd021616.
Petty, G. W., 1994a: Physical retrievals of over-ocean rain rate from multichannel microwave imagery. Part I: Theoretical characteristics of normalized polarization and scattering indexes. Meteor. Atmos. Phys., 54, 79–99, https://doi.org/10.1007/BF01030053.
Petty, G. W., 1994b: Physical retrievals of over-ocean rain rate from multichannel microwave imagery. Part II: Algorithm implementation. Meteor. Atmos. Phys., 54, 101–121, https://doi.org/10.1007/bf01030054.
Petty, G. W., and W. Huang, 2010: Microwave backscatter and extinction by soft ice spheres and complex snow aggregates. J. Atmos. Sci., 67, 769–787, https://doi.org/10.1175/2009JAS3146.1.
Piyush, D. N., J. Goyal, and J. Srinivasan, 2017: Retrieval of cloud ice water path using SAPHIR on board Megha-Tropiques over the tropical ocean. Adv. Space Res., 59, 1895–1906, https://doi.org/10.1016/j.asr.2017.01.022.
Ringerud, S., M. S. Kulie, D. L. Randel, G. M. Skofronick-Jackson, and C. D. Kummerow, 2019: Effects of ice particle representation on passive microwave precipitation retrieval in a Bayesian scheme. IEEE Trans. Geosci. Remote Sens., 57, 3619–3632, https://doi.org/10.1109/TGRS.2018.2886063.
Saunders, R., and Coauthors, 2007: A comparison of radiative transfer models for simulating Atmospheric Infrared Sounder (AIRS) radiances. J. Geophys. Res., 112, D01S90, https://doi.org/10.1029/2006JD007088.
Saunders, R., and Coauthors, 2018: An update on the RTTOV fast radiative transfer model (currently at version 12). Geosci. Model Dev., 11, 2717–2737, https://doi.org/10.5194/gmd-11-2717-2018.
Simpson, J., C. Kummerow, W.-K. Tao, and R. F. Adler, 1996: On the tropical rainfall measuring mission (TRMM). Meteor. Atmos. Phys., 60, 19–36, https://doi.org/10.1007/BF01029783.
Skofronick-Jackson, G. M., and J. R. Wang, 2000: The estimation of hydrometeor profiles from wideband microwave observations. J. Appl. Meteor., 39, 1645–1656, https://doi.org/10.1175/1520-0450-39.10.1645.
Skofronick-Jackson, G. M., and B. T. Johnson, 2011: Surface and atmospheric contributions to passive microwave brightness temperatures for falling snow events. J. Geophys. Res., 116, D02213, https://doi.org/10.1029/2010JD014438.
Skofronick-Jackson, G. M., M. Kulie, L. Milani, S. J. Munchak, N. B. Wood, and V. Levizzani, 2019: Satellite estimation of falling snow: A Global Precipitation Measurement (GPM) Core Observatory perspective. J. Appl. Meteor. Climatol., 58, 1429–1448, https://doi.org/10.1175/JAMC-D-18-0124.1.
Smith, E. A., H. J. Cooper, X. Xiang, A. Mugnai, and G. J. Tripoli, 1992: Foundations for statistical–physical precipitation retrieval from passive microwave satellite measurements. Part I: Brightness-temperature properties of a time-dependent cloud-radiation model. J. Appl. Meteor., 31, 506–531, https://doi.org/10.1175/1520-0450(1992)031<0506:ffsppr>2.0.co;2.
Spencer, R. W., 1986: A satellite passive 37-GHz scattering-based method for measuring oceanic rain rates. J. Climate Appl. Meteor., 25, 754–766, https://doi.org/10.1175/1520-0450(1986)025<0754:ASPGSB>2.0.CO;2.
Spencer, R. W., H. M. Goodman, and R. E. Hood, 1989: Precipitation retrieval over land and ocean with the SSM/I: Identification and characteristics of the scattering signal. J. Atmos. Oceanic Technol., 6, 254–273, https://doi.org/10.1175/1520-0426(1989)006<0254:PROLAO>2.0.CO;2.
Tao, W. K., and J. Simpson, 1993: Goddard cumulus ensemble model. Part I: Model description. Terr. Atmos. Oceanic Sci., 4, 35–72, https://doi.org/10.3319/TAO.1993.4.1.35(A).
Tao, W. K., S. Lang, J. Simpson, and R. Adler, 1993: Retrieval algorithms for estimating the vertical profiles of latent heat release. J. Meteor. Soc. Japan, 71, 685–700, https://doi.org/10.2151/jmsj1965.71.6_685.
Tyynelä, J., J. Leinonen, D. Moisseev, T. Nousiainen, and A. von Lerber, 2014: Modeling radar backscattering from melting snowflakes using spheroids with nonuniform distribution of water. J. Quant. Spectrosc. Radiat. Transfer, 133, 504–519, https://doi.org/10.1016/j.jqsrt.2013.09.013.
Wang, J. R., J. Zhan, and P. Racette, 1998: Multiple aircraft microwave observations of storms over the western Pacific Ocean. Radio Sci., 33, 351–368, https://doi.org/10.1029/97RS02221.
Weng, F., and N. C. Grody, 2000: Retrieval of ice cloud parameters using a microwave imaging radiometer. J. Atmos. Sci., 57, 1069–1081, https://doi.org/10.1175/1520-0469(2000)057<1069:ROICPU>2.0.CO;2.
Wilheit, T. T., 1986: Some comments on passive microwave measurement of rain. Bull. Amer. Meteor. Soc., 67, 1226–1232, https://doi.org/10.1175/1520-0477(1986)067<1226:SCOPMM>2.0.CO;2.
Wu, D. L., and Coauthors, 2009: Comparisons of global cloud ice from MLS, CloudSat, and correlative data sets. J. Geophys. Res., 114, D00A24, https://doi.org/10.1029/2008JD009946.
Yeh, H.-Y. M., N. Prasad, R. A. Mack, and R. F. Adler, 1990: Aircraft microwave observations and simulations of deep convection from 18 to 183 GHz. Part II: Model results. J. Atmos. Oceanic Technol., 7, 392–410, https://doi.org/10.1175/1520-0426(1990)007<0392:AMOASO>2.0.CO;2.
Yin, M. T., and G. S. Liu, 2019: Assessment of GPM high-frequency microwave measurements with radiative transfer simulation under snowfall conditions. Quart. J. Roy. Meteor. Soc., 145, 1603–1616, https://doi.org/10.1002/qj.3515.
Zhang, S., J. Li, Z. Wang, H. Wang, M. Sun, J. Jiang, and J. He, 2012: Design of the second generation microwave humidity sounder (MWHS-II) for Chinese meteorological satellite FY-3. Proc. 2012 IEEE Int. Conf. on Geoscience and Remote Sensing Symp., Munich, Germany, IEEE, 4672–4675, https://doi.org/10.1109/IGARSS.2012.6350423.