Estimation of Liquid Water Path in Stratiform Precipitation Systems using Radar Measurements during MC 3 E

General comments: The authors present a scheme to retrieve rain liquid water path (RLWP) and cloud liquid water path (CLWP) beneath the melting layer in stratiform precipitation. It is known that LWP retrieved from traditional microwave radiometer (MWR) in rainy conditions might be invalid. The authors consider two situations: (1) no cloud detected below the melting layer; (2) cloud is detected below the melting layer. The retrieval of RLWP (namely, situation 1) is based on the method proposed by Williams et al. (2016). In situation (2), to retrieve CLWP they estimate the layer mean rain rate by using the differential velocity technique proposed by Williams et al. (2016), which is expected to be an improvement to the original method (Matrosov. 2009). Using the proposed technique, the authors found that the CLWP is the main contributor to LWP beneath the melting layer when cloud exists. This is an interesting study that is relevant to the scientific community and is within the scope of AMT. Overall, this manuscript is well written, cites relevant literature and the proposed technique is novel. However, the authors should include a more detailed discussion about the retrieval uncertainty. I recommend it for publication in AMT if the authors take into account the following comments.


Introduction
Clouds in stratiform precipitation systems are important to the Earth's radiation budget.The vertical distributions of cloud microphysics, ice and liquid water content (IWC and LWC), determine the surface and top-of-the-atmosphere radiation budget and redistribute energy in the atmosphere (Feng et al., 2011(Feng et al., , 2018)).Also, stratiform precipitation systems are responsible for most tropical and midlatitude precipitation during summer (Xu, 2013).However, the representation of those systems in global climate and cloud-resolving models is still challenging (Fan et al., 2015).One of the challenges is due to the lack of comprehensive observations and retrievals of cloud microphysics (e.g., prognostic variables IWC and LWC) in stratiform precipitation systems.Liquid water path (LWP) is defined as an integral of LWC in the atmosphere.It is a parameter used to provide the characterization of liquid hydrometeors in the vertical column of atmosphere and study clouds and precipitation.The estimation of LWC and LWP is one of the critical objectives of the US Department of Energy's (DOE) Atmospheric Radiation Measurement (ARM) Program (Ackerman and Stokes, 2003).
LWP can be retrieved using a ground-based microwave radiometer (MWR), which sensed downwelling radiant energy at 23.8 and 31.4GHz (Liljegren et al., 2001).In the last two decades, ARM has been operating a network of  ground-based MWRs to provide a time series of LWP at the ARM Southern Great Plains (SGP) site (Cadeddu et al., 2013).Absorption-based algorithms using multichannels of MWRs have been widely used to retrieve cloud LWP (e.g., Liljegren et al. 2001;Turner, 2007), and they are known to be accurate methods to estimate LWP of nonprecipitating clouds, with a mean LWP error of 15 g m −2 (Crewell and Löhnert, 2003).However, in precipitating conditions, LWP retrieved from conventional MWRs is generally not valid due to the violation of the Rayleigh assumption when large raindrops exist (e.g., Saavedra et al., 2012).In addition, a large increase of brightness temperatures is measured as a result of the deposition of raindrops on the MWR's radome.Unfortunately, it is very hard to model and quantify this increase from the rain layer on the radome (Cadeddu et al., 2017).This "wet radome" issue largely inhibits the retrieval of LWPs using ground-based MWRs during precipitation.Due to the limitations of retrieving LWP from MWRs during precipitation, cloud and precipitation radars were used to simultaneously retrieve LWP (Matrosov, 2010).
In the precipitating system, the liquid water cloud droplets and raindrops often coexist in the same atmospheric layer (e.g., Dubrovina, 1982;Mazin, 1989;Matrosov, 2009Matrosov, , 2010)), indicating that the LWP consists of both cloud liquid water path (CLWP) and rain liquid water path (RLWP).However, the discrimination between suspended small cloud liquid water droplets and precipitating large raindrops is a very challenging remote-sensing problem.Even though the partitioning of LWP into CLWP and RLWP is important in cloud modeling (Wentz and Spencer, 1998;Hillburn and Wentz, 2008), there are few studies in which RLWP and CLWP were retrieved simultaneously and separately (Saavedra et al., 2012;Cadeddu et al., 2017).Battaglia et al. (2009) developed an algorithm to retrieve RLWP and CLWP from the six Advanced Microwave Radiometer for Rain Identification (ADMIRARI) observables under rainy conditions.Saavedra et al. (2012) developed an algorithm using both ADMIRARI and a micro rain radar to retrieve and analyze the CLWP and RLWP for midlatitude precipitation during fall.In addition to these RLWP and CLWP estimations mainly from passive microwave radiometers, there are several studies estimating the LWP using active radar measurements only.Ellis and Vivekanandan (2011) developed an attenuation-based technique to estimate LWC, which is the sum of cloud liquid water content (CLWC) and rain liquid water content (RLWC), using simultaneous S-and Ka-band scanning radars measurements.However, using these techniques to retrieve LWC is not always applicable.If raindrop diameters are comparable to at least one of the radar's wavelength, the "Mie effect" will be included in the measured differential reflectivity; however this Mie effect is not very distinguishable from differential attenuation effects (Tridon et al., 2013;Tridon and Battaglia, 2015).Matrosov (2009) developed an algorithm to simultaneously retrieve CLWP and layer-mean rain rate using the radar reflectivity measurements from three ground-based W-, Ka-, and S-band radars.The CLWP was retrieved based on estimating the attenuation of cloud radar signals compared to Sband radar measurements.Matrosov (2010) developed an algorithm to estimate CLWP using a vertical pointing Ka-band radar and a nearby scanning C-band radar.The layer-mean rain rate was first estimated with the aid of a surface disdrometer, and then CLWP was retrieved by subtracting the rain attenuation from total attenuation measured from two radars.For the estimation of RLWP, Williams et al. (2016) developed a retrieval algorithm for raindrop size distribution (DSD) using Doppler spectrum moments observed from two co-located vertically pointing radar (VPRs) at frequencies of 3 and 35 GHz.The retrieved air motion and DSD parameters were evaluated using the retrievals from a co-located 448 MHz VPR.
In this study, the CLWP retrieval algorithms in Matrosov (2009Matrosov ( , 2010) ) have been modified given the available radar measurements, vertical pointing Ka-and Sband radars, during the Midlatitude Continental Convective Clouds Experiment (MC3E) field campaign.For the estimation of RLWP, we will basically follow the idea described in Williams et al. (2016) to retrieve microphysical properties for raindrops.However instead of retrieving vertical air motion and rain DSDs (Williams et al., 2016), this study aims at retrieving RLWC and then integrating RLWC over the liquid layer to estimate RLWP.Overall, in this study, algorithms from three former publications are modified and combined to estimate the LWP in the stratiform precipitating systems.
The goals of this study are to retrieve the LWP below the melting base, which includes both RLWP and CLWP retrievals using radars measurements, and tentatively answer two questions based on observations and retrievals in the stratiform precipitation systems during MC3E: (1) what is the occurrence of cloud below the melting base in the stratiform precipitation systems?(2) What are the values of simultaneous CLWP, RLWP, and LWP, and how does CLWP or RLWP contribute to the LWP?Note that the CLWP and RLWP are constrained in a stratiform precipitation layer below the melting base and above the surface.The LWP estimations in this study are primarily aimed at stratiform precipitating events exhibiting melting-layer features from radar measurements with lower-to-moderate rain rates (RR < 10 mm h −1 ).The instruments and data used in this study are introduced in Sect. 2. Section 3 describes the methods of retrieving LWP (both RLWP and CLWP).Section 4 illustrates two examples and is followed by statistical results from more samples during MC3E.The last section gives the summary and conclusions.Acronyms and abbreviations are listed in Table 1.(Jensen et al., 2015).MC3E provided an opportunity to develop new retrieval methods to estimate cloud microphysics and precipitation properties in precipitation systems (Giangrande et al., 2014;Williams, 2016;Tian et al., 2016Tian et al., , 2018)).Several stratiform rain cases were observed by the VPRs during MC3E (as shown in Fig. 1).Distinct signatures of the "bright band" are detected by VPRs.To retrieve LWP associated with stratiform precipitation, this study mainly uses the observations from two co-located VPRs operating at 3 and 35 GHz at DOE ARM SGP Climate Research Facility.

Vertical pointing radars
The 3 GHz (S-band) VPR was deployed by NOAA Earth System Research Laboratory for the 6 weeks during the MC3E.The NOAA 3 GHz VPR is a vertical pointing radar with 2.6 • beamwidth monitoring precipitation overhead.This 3 GHz profiler bridges the gap between cloud radars, which are used to provide the structure of nonprecipitat- The Ka-band ARM zenith radar (KAZR) is also a vertical pointing radar, operating at 35 GHz and permanently deployed by DOE ARM at the SGP site.The KAZR measurements include reflectivity, vertical velocity, and spectral width from the near-ground to 20 km.The KAZR data used in this study are the KAZR Active Remote Sensing of Clouds (ARSCL) product produced by the ARM (https://www.arm.gov, last access: 18 May 2017).The KAZR-ARSCL corrects for atmospheric gas attenuation and velocity aliasing.By selecting the mode with the highest signal-to-noise ratio at a given point, data from two simultaneous operating modes (general and cirrus mode) are combined for each profile to provide the best estimates of radar moments in the time-height fields.The vertical and temporal resolutions of KAZR-ARSCL product are 30 m and 4 s, respectively.Since the 3 and 35 GHz VPRs are independent radars with different dwell time and sample volumes (Williams et al., 2016), the radar observations are processed to 1 min temporal and 60 m vertical resolutions in this study.

Disdrometers
The DOE ARM program maintains a suite of surface precipitation disdrometers.Measurements and estimations from the Distromet model RD-80 disdrometer and the NASA two-dimensional video disdrometer (2DVD) deployed at the ARM SGP site are used in this study.The RD-80 disdrometer provides the most continuous raindrop size distribution (DSD) measurements at high spectral (20 size bins from 0.3 to 5.4 mm) and temporal resolutions (1 min), and its minimal detectable precipitation amount is 0.006 mm h −1 .From the 2DVD, the rain DSDs are observed from 41 bins (0.1-10 mm), and its minimal detectable precipitation amount is 0.01 mm h −1 .In addition to rain rate, the mean massweighted raindrop diameter (D m ) is also provided by the 2DVD, which is used for evaluating retrieved D m from radar measurements.

Ceilometer
The Vaisala Laser Ceilometer (CEIL) operates at the SGP Central Facility, sensing cloud presence up to a height of 7700 m with 10 m vertical resolution.The laser ceilometer transmits near-infrared pulses of light, and the receiver detects the light scattered back by clouds and precipitation.It is designed to measure cloud-base height.

Methodology of liquid water path estimation
As mentioned earlier, both RLWP and CLWP contribute to the LWP.With the aid of the cloud-base height detected by the ceilometer, LWP is retrieved under two different situations: (I) the cloud base is higher than the melting base, and (II) the cloud base is lower than the melting base.For situation (I), there are almost no cloud droplets below the melting base (CLWP = 0), and thus the LWP below the melting base is solely from raindrops.The LWP is calculated by integrating RLWC over this layer.The RLWC could be retrieved by analyzing the measured Doppler velocity differences ("DVD algorithm") from two co-located VPRs.In situation (II), the small cloud droplets and large raindrops coexist below the melting base.Both raindrops and cloud particles contribute to LWP.RLWP will still be estimated using the DVD algorithm.CLWP will be retrieved using an attenuation-based algorithm named the "attenuation algorithm".The algorithms for LWP estimation are summarized in a flowchart (Fig. 2).

Situation I (no cloud droplets exist below the melting base)
The algorithm from Williams et al. (2016) was developed based on an assumption that the 3 GHz VPR operates within the Rayleigh scattering regime for all raindrops, while the 35 GHz VPR operates within the Rayleigh scattering regime for small raindrops (diameters < ∼ 1.3 mm) and non-Rayleigh scattering regime for larger raindrops (diameters ≥∼ 1.3 mm).The different scattering regimes for the two operating frequencies result in different estimated radar moments.These estimated radar moments are in functions of rain microphysics.Thus, the rain microphysics could be retrieved with given measured radar moments.The details of this DVD algorithm and uncertainty estimation are introduced in Appendix A.
3.2 Situation II (cloud particles and rain droplets coexist below the melting base) In situation (II), substantial cloud particles exist below the melting base, and both RLWP and CLWP retrievals are needed to estimate the LWP.The total two-way attenuation of 35 GHz VPR signals, A (in decibels, dB), in a layer between the melting base and the cloud base, mainly consists of rain attenuation, liquid cloud attenuation, and gaseous attenuation.The total attenuation (A) is expressed as R m is the layer-mean rain rate, and H (km) is the thickness of the layer (Matrosov, 2009).G is the two-way attenuation/absorption from atmospheric gases, which is relatively small, and the absorption by gases has already been corrected in the KAZR ARSCL dataset and is assumed to be zero in our retrieval.
C and B are the coefficients for rainfall and cloud liquid water attenuation.
where λ is the wavelength of the Ka-band radar, and m is the complex refractive index of water.The unit of B is decibels per gram per meter (dB g −1 m −2 ).
where b is the correction factor considering raindrop fall velocities with changing air density.
where ρ am and ρ a0 are the mean air density in the rain layer and the density under normal atmospheric conditions.Based on Eq. ( 1), CLWP can be written as The attenuation (A) is estimated by comparing the drop in Ka-band reflectivity with the unattenuated S-band reflectivity through the cloud.Assuming the changes in reflectivity with altitude due to changes in raindrop size distributions with altitude are similar for Ka-and S-band reflectivities, then the difference in reflectivities through the cloud is a proxy for attenuation.This can be expressed using Notice that the absolute calibration of the radar was not important to the retrieval results since the retrieval of CLWP used S-and K-band differential attenuation.This avoids radar calibration (Tridon et al., 2015(Tridon et al., , 2017)), which is a serious issue limiting the accuracy of radar retrievals.
The R m is estimated as where h equals 60 m, MB is the melting base, and h 0 is the height of the lowest unsaturated KAZR rang gate (Matrosov, 2010).RRs in the layer between the melting base and the cloud base are calculated from the DVD algorithm.
The uncertainties of retrieved CLWP are mainly due to the uncertainties of estimated R m and observed total attenuation from VPRs.The value of B is on the order of 1 dB kg −1 m −2 .The uncertainty of retrieved CLWP would be ∼ 0.25 kg m −2 , with 0.5 dB uncertainty from the measured radar reflectivity difference or ∼ 0.5 kg m −2 for 1.0 mm h −1 uncertainty from the estimated layer-mean rain rate.Compared to the typical mean rain rate observed in the stratiform system (∼ 2-4 mm h −1 ), 1.0 mm h −1 represents a ∼ 30 % uncertainty.The uncertainty for CLWP retrievals is roughly estimated as ∼ 0.56 kg m −2 ( 0.25 2 + 0.5 2 ) in this study.For reference, the expected uncertainty is reported as ∼ 0.25 kg m −2 for typical rainfall rates (∼ 3-4 mm h −1 ) in Matrosov's (2009)

Case A
On 20 May 2011, an upper-level low-pressure system in the central Great Basin moved into the central and northern plains, while a surface low pressure in southeastern Colorado brought warm and moist air from the southern plains to a warm front over Kansas, and a dry line extended southward from Texas to Oklahoma.With these favorable conditions, a strong north-south-oriented squall line developed over the Great Plains and propagated eastward.The convection along the leading edge of this intense squall line exited the ARM SGP network around 11:00 UTC on 20 May, leaving behind a large area of stratiform rain (Case A in Fig. 1).This stratiform system passed over the ARM SGP site and was observed by two VPRs and disdrometers as shown in Fig. 1a-c.
It clearly shows the 3 GHz radar echo tops are much lower than those from the 35 GHz VPR.Even though there is attenuation at 35 GHz by the raindrops and melting hydrometeors, the 35 GHz radar can still detect more small ice particles near the cloud top.The bright band, which occurs in a uniform stratiform rain region, is clearly seen from the 3 GHz VPR (a sudden increase and then decrease in radar reflectivity) but is not obvious from the 35 GHz VPR due to the non-Rayleigh scattering effects at 35 GHz (Sassen et al., 2005;Matrosov, 2008).
Figure 1a-b clearly show that the ceilometer-detected cloud base is in the middle of the melting layer, indicating almost no cloud particles below the melting layer, and the LWP in the liquid layer is equal to the RLWP.The RLWP is retrieved using the DVD algorithm introduced in Sect.3.1 and Appendix A. Figure 3 shows an example of the DVD retrieval algorithm at 13:40 UTC on 20 May 2011.Radar reflectivity from 3 GHz, Doppler velocities from 3 and 35 GHz, and spectrum variance from 35 GHz are the inputs of the DVD algorithm.The Doppler velocity differences (3-35 GHz) from the surface to 4 km are also plotted in Fig. 3d.The melting base is defined as the height of maximum curvature in the radar reflectivity profile at 3 GHz (Fabry and Zawadzki, 1995), which is clearly seen at 2.5 km in Fig. 3. Below 2.5 km, the Doppler velocity differences between the two VPRs become relatively uniform, indicating that the process of melting snow/ice particles into raindrops is completed.Retrieved profiles of rain microphysical properties and their corresponding uncertainties (horizontal bars at different levels) in the rain layer (0-2.5 km) are shown in Fig. 3f-h.In general, the retrieved D m values from the surface to 2.5 km are nearly a constant of ∼ 2 mm (Fig. 3f), while the retrieved RLWC and rain rate values slightly decrease from 2.5 km to the surface.One of the highlights of this study is, in addition to the surface rain rate, which can usually be observed using surface disdrometers, the vertical profiles of rain microphysical properties are retrieved.These retrieved rain microphysical properties will shed light on the understanding of liquid cloud and rain microphysical processes (like condensation, evaporation, autoconversion, and accretion) in the models.
To evaluate the rain property retrievals, we compare the retrieved rain microphysical properties, the D m , and rain rate at the surface, with the surface disdrometer measurements (Fig. 4).The D m values range from 1.0 to 2.5 mm during a 3.5 h period, with nearly identical mean values of 1.79 and 1.81 mm from both retrievals and 2DVD measurements.There are large variations for rain rates, ranging from 0 to 8 mm h −1 , with means of 3.19, 3.17, and 2.88 mm h −1 , respectively, from the 2DVD, RD-80, and radar retrieval.The mean rain rates from 2DVD and RD-80 measurements are almost the same, although there are relatively large differences during certain time periods, while the retrievals from this study, on average, underestimate the rain rate by ∼ 10 % compared to the disdrometer measurements.More statistics (mean differences, their 95 % confidence intervals of mean differences and root mean square errors) can be found in Table 2. Overall, the mean differences are within the retrieval uncertainties.The variation of RLWP (Fig. 4c) mimics the variation of retrieved rain rate in Fig. 4d.The mean value of RLWP is 0.55 kg m −2 for this case, which is also the LWP below the melting base.

Case B
On 11 May 2011, a surface cold front moved across the Oklahoma-Texas area, and then convections were initiated.At 16:00 UTC, a mesoscale convective system formed with a parallel stratiform precipitation region.A period of 2-3 h later (∼ 18:30 UTC), the mesoscale convective system was transitioned to a trailing stratiform mode passed over the ARM SGP site.The large stratiform regions are observed by two VPRs and disdrometers as shown in Fig. 1d-f Firstly, the surface rain microphysics (D m , RLWC, rain rate, and RLWP) are retrieved using the DVD algorithm.These rain property retrievals are compared with the surface disdrometer measurements (Fig. 5).The D m values at the surface range from 0.90 to 2.30 mm during a 4.5 h period with mean values of 1.41 and 1.52 mm, respectively, from both retrievals and 2DVD measurements.The difference between the retrieval and 2DVD measurements may be due to different sampling volumes between radar and the sur-  face disdrometer, as well as wind shear.The rain rates, in this case, vary quite largely, ranging from 0.02 to 4.78 mm h −1 , with means of 1.36, 1.26, and 1.66 mm h −1 , respectively, from the single 2DVD, RD-80, and our retrieval.It is found that, from both Case A and Case B, the mean value from the RD-80 is smaller than that from the 2DVD.This may be due to the different ranges of measurable drop sizes from two types of disdrometers (0.3-5.4 mm for the RD-80, while 0.1 to 10 mm for the 2DVD).More statistics can be also found in Table 2. Overall, the mean differences are still within the retrieval uncertainties for this case.
Secondly, the CLWP is retrieved using the attenuation algorithm introduced in Sect.3.2.Figure 5c shows the time series of RLWP, CLWP, and LWP retrievals.It is found that the CLWP values (when they exist) are usually larger than RLWP values in the same vertical column.When cloud droplets and raindrops coexist below the melting base, the mean values are 0.11 and 1.64 kg m −2 for RLWP and CLWP, and the corresponding LWP below the melting layer is 0.76 kg m −2 , while when only raindrops exist below the melting base, there is no CLWP (CLWP = 0), and the RLWP and LWP are the same (with average of 0.34 kg m −2 ).It is noticed that even though the occurrence of CLWP is low (11 %) in this case, the value of CLWP can be very large when it exists, and it is about 2 times larger than the mean RLWP.The mean value of LWP is 0.37 kg m −2 for all the samples in Fig. 5c.The blue uncertainty bars in Fig. 5c show the retrieved CLWP uncertainty when assuming both of the uncertainties of attenuation and total rain rate are 30 %. Due to the variations of the attenuation and total rain rate with time, the estimated uncertainties of CLWP vary point to point.More details about the estimation of CLWP are in Appendix B.

Statistical results
Box and whisker plots of retrieved RLWP, CLWP, and LWP for situations (I), (II), and all samples during MC3E are shown in Fig. 6.The horizontal dashed orange and red lines indicate the median and mean, boundaries of the box represent the first and third quartiles, and the whiskers are the 10th and 90th percentiles.During MC3E, a total of 13 h of stratiform rain was observed by VPRs at the ARM SGP Climate Research Facility, in which 91 % and 9 % the samples are categorized into situations (I) and (II), respectively.The mean RLWPs are 0.32 and 0.10 kg m −2 for situations (I) and (II).There are a substantial number of small cloud droplets sustaining in the rain layer that have not yet been converted to larger raindrops, which may partially explain the smaller RLWP in situation (II).The mean value of the surface rain rate is 2.06 mm h −1 when cloud droplets exist, which is also smaller than the mean value (2.38 mm h −1 ) in the rain-only situation.The mean CLWP in situation (II) is as large as ∼ 0.56 kg m −2 , even though their occurrence is very low (9 %), which is much larger than mean RLWP in the liquid layer.The LWP from situation (II) (0.66 kg m −2 ) is much larger than the mean LWP from situation (I) (0.32 kg m −2 ), which is primarily contributed by cloud droplets.The overall mean LWP for stratiform rain during MC3E is 0.34 kg m −2 .
We also processed the ARM MWR-retrieved LWPs during MC3E and compared them with our retrievals as illustrated in Fig. 7a.The corresponding LWP uncertainties are also provided as the grey error bar for each retrieval, with the rain rate indicated by colors.It is noticed that the MWR has no LWP estimation when the rain rate is large.The MWR-retrieved LWPs increase with increased rain rate, and the retrievals from the MWR are much larger than the new LWP retrievals at high rate rates.The newly retrieved LWPs weakly correlate with rain rates, and most values are less than 1.0 kg m −2 , especially at high rain rates.The MWR-retrieved LWPs increase with rain rate generally.The increase of retrieved LWP with rain rate from the MWR is possibly due to the wet radome effect (Cadeddu et al., 2017).In addition to the issue from standing water on the radome, the extinctions due to raindrops also affect MWR retrievals.The extinction for rain is much larger than that for cloud (Sheppard, 1996), and thus, the small amount of rainwater could enhance the measured brightness temperature significantly.More details of extinctions and brightness temperature calculations are shown in Appendix B. Statistical results of the retrieved LWPs from this study and the MWR are averaged for each measured rain rate bin (bin size = 0.25 mm h −1 ).The differences of LWPs from the MWR and this study are shown in Fig. 7b.The LWP differences increase with increased rain rate.The LWP differences between the MWR retrieval and this study could be for the following reasons.(1) MWR-retrieved LWP represents the entire vertical column (RWLP and CLWP below the melting layer, large water coated ice particles in the melting layer, and supercooled LWC above the melting layer), while our retrieval only represents the LWP below the melting base.As Battaglia et al. (2003) pointed out, the brightness temperature generally increases if mixed-phase precipitation is included.
(2) The MWR radome was wet during rain periods, and the deposition of raindrops on the radome can cause a large increase in the measured brightness temperatures (Cadeddu et al., 2017).(3) Large extinctions due to raindrops would affect MWR retrievals.(4) Uncertainties exist in the retrieved LWP from this study.

Summary and conclusions
LWP is a critical parameter for studying clouds, precipitation, and their life cycles.LWP can be retrieved from microwave radiometer measured brightness temperatures during cloudy and light precipitation conditions.However, MWR-retrieved LWPs are questionable under moderate and heavy precipitation conditions due to the wet radome and the large extinction in the unit volume caused by large raindrops.LWPs below the melting base in stratiform precipitation systems are estimated, which include both RLWP and CLWP.The measurements used in this study are mainly from two VPRs, 35 GHz from ARM and 3 GHz from NOAA during the MC3E field campaign.
In this study, the microphysical properties of raindrops, such as D m , RLWC (and RLWP), and RR, are estimated following the method described in Williams et al. (2016) using measurements from co-located Ka-and S-band VPRs.The retrieved rain microphysical properties are validated by the surface disdrometer measurements.Instead of retrieving vertical air motion and rain DSDs (Williams et al., 2016), this study aims at retrieving RLWC and then integrating RLWC over the liquid layer to estimate RLWP.The CLWP is retrieved based on the modifications of the methods in Matrosov (2009Matrosov ( , 2010) ) with available radar measurements, vertical pointing Ka-and S-band VPRs, during the MC3E field campaign.
The applicability of retrieval methods is illustrated for two stratiform precipitation cases (20 and 11 May 2011) observed during MC3E.Statistical results from a total of 13 h samples during MC3E show that the occurrence of cloud droplets below the melting base is low (9 %), while the CLWP value can be up to 0.56 kg m −2 , which is much larger than the RLWP (0.10 kg m −2 ).When only raindrops exist below the melting base, the average RLWP value is 0.32 kg m −2 , which is much larger than the mean RLWP in the situation of coexisting cloud droplets and raindrops.Our retrievals are also compared with ARM MWR-retrieved LWPs.It is noticed that the MWR has no LWP estimation when the rain rate is large.The MWR-retrieved LWPs increase with increased rain rate, and the retrievals from the MWR are much larger than our LWP retrievals at high rate rates.The LWP differences are fully discussed.
Reliable retrievals of RLWC and RLWP are critical for model evaluation and improvement, as RLWC (rain mixing ratio) is an important prognostic variable in weather and climate models.Furthermore, retrievals in the whole rain layer would be useful to understand the microphysical pro- cesses (i.e., condensation, evaporation, autoconversion, and accretion, etc.) and have great potential to improve model parametrizations in the future.Overall, the LWP (CLWP and RLWP) retrievals derived in this study can be used to evaluate the models that separately predict cloud and precipitation and contribute comprehensive information to study cloudprecipitation transitions.Note that the attenuation by liquid is more profound at 94 GHz, and the ratio of attenuation by liquid clouds and by rain is larger at 94 GHz compared to 35 GHz (Matrosov, 2009).Thus, using 94 GHz (W-band) radar measurements to develop a retrieval algorithm may be promising if the W-band radar signals are not fully attenuated.In addition, analyzing co-located multiple-frequency VPRs would also better define the uncertainties of retrievals made with co-located radars operating at different frequency pairs.The variabilities of 3 and 35 GHz VPR observations within each 1 min temporal resolution and 60 m vertical resolution bin are regarded as the measurement uncertainties and will be propagated through the retrieval to produce retrieval uncertainties.The retrieval uncertainties are estimated following two steps: (1) construction of a distribution of input radar measurements.For example, the temporal resolution for 3 GHz VPR is 7 s; thus there are about nine radar reflectivities observed for 1 min.A normal distribution is generated first using the mean and standard deviations of these nine observed radar reflectivities within 1 min and 60 m observations.(2) The DVD retrievals are repeated using samplings from distributions of all input measurements.We randomly select 100 groups of members from those (DVD, SV 35 GHz , Z 3 GHz ) normal distributions to form 100 realizations and then produce 100 separate output estimates.The mean and standard deviation of the 100 solutions are regarded as the final retrieval and the retrieval uncertainty.
The uncertainties of RLWP are estimated based on the uncertainties of RLWC.More specifically, we first estimated the RLWC uncertainties at each height level, and then we calculated the ratios of RLWC uncertainties to the mean retrieved RLWC at each height level, which represent percentage values of retrieval uncertainties.Finally, we calculated the mean ratio of the uncertainties in the whole liquid layer below the melting base and regarded this mean ratio as the uncertainty of RLWP.
It is noted that the uncertainty here only considers estimates of instrument noise, not the uncertainties associated with assumptions used in the retrieval.For example, the gamma size distribution used in Eq. ( A2) is an approximation which may introduce error into the retrieval.However, it is very difficult to quantify this type of retrieval uncertainty.In this study, we further compared our retrievals with independent surface disdrometer measurements to estimate the uncertainties of retrievals.Also, when both radars are observing within the Rayleigh scattering regime for small raindrops, the reflectivity-weighted radial velocities for these particles should be the same.In order to have a difference in radial velocity during the retrieval, large droplets must exist.The maximum diameters in drop size distribution measured by the disdrometer for all the stratiform cases during MC3E are investigated.It is found that the occurrence of small droplets only (maximum diameter < 1.3 mm) is very low (less than 3 %).Thus, it will not have a significant impact on the retrieval results.Notice that this algorithm is not suitable for strong convective rain due to the wind shear and strong turbulence as well as severe attenuation and extinction of the Ka-band radar signal.

Figure 2 .
Figure 2. Algorithm flowchart to retrieve liquid water path (LWP) below the melting base.
retrieval method.More details of the estimation of CLWP uncertainties are in Appendix B. 4 Retrieval results and discussions 4.1 Case studies Even though situation (I) is dominated (Fig. 1), especially in Case A, the ceilometer cloud-base estimates can be lower than the melting base (Cases B to D).Two case studies (20 and 11 May 2011) are given as examples to demonstrate the estimation of LWP in stratiform precipitation systems for two different situations.

Figure 3 .
Figure 3.An example of illustrating the Doppler velocity difference (DVD) retrieval algorithm at 13:40 UTC on 20 May 2011.The inputs of the DVD retrieval algorithm are (a) the 3 GHz vertical pointing radar reflectivity factor (Z e ), (b) the 3 GHz radar Doppler velocities (V d ), (c) the 35 GHz radar Doppler velocities (V d ), and (e) the 35 GHz radar spectrum variance (SV).The Doppler velocity difference between 3 and 35 GHz is shown in (d).The outputs of the DVD retrieval algorithm are (f) mass-weighted mean diameter D m , (g) rain liquid water content (RLWC), and (h) rain rate (RR).Retrieval uncertainties are shown as horizontal thin black lines.
. Figure 1d-f clearly show that the ceilometer-detected cloud bases are occasionally lower than the melting bases.Under this situation, both RLWP and CLWP could contribute to the LWP below the melting base.

Figure 4 .
Figure 4. Time series of (a) retrieved (RET) (red dots) and 2DVD surface disdrometer estimated (grey line) D m , (b) RET (red line), 2DVD (grey line) and RD-80 (black line) surface disdrometer rain rate estimates, and (c) retrieved rain liquid water path (RLWP; red dots) for Case A (20 May 2011).The red shading areas are the estimated retrieval uncertainties.

Figure 5 .
Figure 5.Time series of (a) retrieved (RET) (red dots) and 2DVD surface disdrometer estimated (grey lines) D m , (b) RET (red dots), 2DVD (grey line) and RD-80 (black line) surface disdrometer rain rate estimates, and (c) rain liquid water path (RLWP; red line), cloud liquid water path (CLWP; blue dots), and liquid water path (LWP = RLWP + CLWP, green lines) for Case B (11 May 2011).The red shading area and blue bars are the estimated retrieval uncertainties for rain microphysical properties (D m , rain rate, and RLWP) and CLWP.

Figure 6 .
Figure 6.Box and whisker plots of retrieved RLWP, CLWP, and LWP for situation (I), (II), and all samples.The horizontal orange line within the box indicates the median, boundaries of the box represent the 25th and 75th percentile, and the whiskers indicate the 10th and 90th percentile values of the results.The dashed red lines represent the mean values.

Figure 7 .
Figure 7. (a) Comparisons between LWP from the microwave radiometer (MWR; on x axis) and LWP retrievals from this study (RET; on y axis, with estimated uncertainty in grey lines).The rain rates are indicated by colors.(b) The LWP differences between two estimations (MWR-RET) are shown as a function of rain rate.

Table 1 .
Acronyms and abbreviations used in this study.