Retrievals of ice cloud microphysical propertiesof deep convective systems usingradar measurementsJingjing Tian1, Xiquan Dong1, Baike Xi1, Jingyu Wang1, Cameron R. Homeyer2,Greg M. McFarquhar3, and Jiwen Fan4

1Department of Atmospheric Sciences, University of North Dakota, Grand Forks, North Dakota, USA, 2School ofMeteorology, University of Oklahoma, Norman, Oklahoma, USA, 3Department of Atmospheric Sciences, University of Illinoisat Urbana–Champaign, Urbana, Illinois, USA, 4Pacific Northwest National Laboratory, Richland, Washington, USA

Abstract This study presents newly developed algorithms for retrieving ice cloud microphysicalproperties (ice water content (IWC) and median mass diameter (Dm)) for the stratiform rain and thick anvilregions of deep convective systems (DCSs) using Next Generation Radar (NEXRAD) reflectivity and empiricalrelationships from aircraft in situ measurements. A typical DCS case (20 May 2011) during the MidlatitudeContinental Convective Clouds Experiment (MC3E) is selected as an example to demonstrate the 4-Dretrievals. The vertical distributions of retrieved IWC are compared with previous studies and cloud-resolvingmodel simulations. The statistics from six selected cases during MC3E show that the aircraft in situ derivedIWC and Dm are 0.47 ± 0.29 gm�3 and 2.02 ± 1.3mm, while the mean values of retrievals have a positivebias of 0.19 gm�3 (40%) and negative bias of 0.41mm (20%), respectively. To evaluate the new retrievalalgorithms, IWC and Dm are retrieved for other DCSs observed during the Bow Echo and MesoscaleConvective Vortex Experiment (BAMEX) using NEXRAD reflectivity and compared with aircraft in situmeasurements. During BAMEX, a total of 63, 1min collocated aircraft and radar samples are available forcomparisons, and the averages of radar retrieved and aircraft in situ measured IWC values are 1.52 gm�3 and1.25 gm�3 with a correlation of 0.55, and their averaged Dm values are 2.08 and 1.77mm. In general, the newretrieval algorithms are suitable for continental DCSs during BAMEX, especially within stratiform rain andthick anvil regions.

1. Introduction

Obtaininganaccurate representationof convectiveprocesses innumericalmodels is a challenge for improvingcurrent and future simulations of the Earth's climate system. A primary unresolved issue is the lack of under-standing of the detailed cloud microphysical properties of deep convective systems (DCSs). Although theseproperties can bemeasured by research aircraft, suchmeasurements represent very limited convective stormsampling volumes both spatially and temporally. Thus, developing targeted retrievals from long-term ground-based observations would be beneficial to better understand the cloudmicrophysical properties within DCSs.These retrievals, however, may have large uncertainties. Quantitative analysis on the retrieval uncertainties isrequired, and aircraft in situ measurements can be used to achieve this goal.

The upper layers of DCSs are mainly ice particles, and these ice layers dominate the radiation budget[Feng et al., 2012]. To better estimate the Earth radiation budget and improve numerical climate forecasts,accurate spatial distributions and temporal variations of ice cloud microphysical properties (e.g., ice watercontent (IWC) and median mass diameter (Dm)) in DCSs are needed. Many previous studies [e.g., Liu andIllingworth, 2000;Matrosov et al., 2002;Mace et al., 2002; Sato and Okamoto, 2006] have attempted to retrievecirrus cloud microphysical properties from millimeter-wavelength radar reflectivity. However, studiesinvolving the retrieval of ice microphysical properties of DCSs are limited due to severe attenuation ofhigh-frequency radar, lidar, and radiometer signals during the moderate to heavy precipitation eventsassociated with DCSs. For optically thick ice clouds, Wang et al. [2005] developed a method for retrievingthe microphysical properties using airborne dual-frequency (X- and W-band) radar measurements. Sayreset al. [2008] derived an empirical relationship between IWC and radar reflectivity (Ze) using in situ probes andairborne W-band radar measurements during the Cirrus Regional Study of Tropical Anvils and Cirrus Layers–Florida Area Cirrus Experiment. These aerial view radar reflectivity measurements from a high-altitude ER-2

TIAN ET AL. CONVECTIVE CLOUD MICROPHYSICAL RETRIEVAL 10,820

PUBLICATIONSJournal of Geophysical Research: Atmospheres

RESEARCH ARTICLE10.1002/2015JD024686

Key Points:• Developing new algorithms toretrieve ice cloud IWC and Dm of DCSs

• The 4-D (space-time) ice cloudmicrophysical properties of DCSs

• Evaluation of radar-retrieved IWC andDm using aircraft in situmeasurements

Correspondence to:X. Dong,xdong@email.arizona.edu

Citation:Tian, J., X. Dong, B. Xi, J. Wang,C. R. Homeyer, G. M. McFarquhar, andJ. Fan (2016), Retrievals of ice cloudmicrophysical properties of deepconvective systems using radarmeasurements, J. Geophys. Res. Atmos.,121, 10,820–10,839, doi:10.1002/2015JD024686.

Received 21 DEC 2015Accepted 30 AUG 2016Accepted article online 3 SEP 2016Published online 23 SEP 2016

©2016. American Geophysical Union.All Rights Reserved.

aircraft avoided the attenuation issue in precipitating thick clouds. However, the application of these airborne-derived relationships to ground-based remote sensors is questionable because the ground-based millimeterwavelength radar measurements are severely attenuated for DCSs, especially within the convective core (CC)and stratiform rain (SR) regions. In addition, the W-band Cloud Radar System has not always been availableon board the high-altitude aircraft in different campaigns, which limits the usage of W-band reflectivity-basedretrieval algorithms.Hoganetal. [2006] (hereafterH06) demonstratedan IWCretrievalmethodbasedonS-bandradar reflectivity and cloud temperature.Matrosov [2015] applied theH06 retrieval method to obtain ice waterpath (IWP) in a vertical atmospheric column of precipitating clouds from Next Generation Weather Radar(NEXRAD) reflectivity and evaluated the estimated IWP using cloud microphysical retrievals from CloudSatand auxiliary spaceborne measurements, showing a relative mean difference of 50–60%.

To investigate the microphysical properties and formation-dissipation processes of continental DCSs, theDepartment of Energy (DOE) Atmospheric Radiation Measurement (ARM) and the National Aeronauticsand Space Administration (NASA) Global Precipitation Measurement mission Ground Validation programconducted the Midlatitude Continental Convective Clouds Experiment (MC3E) at the ARM Southern GreatPlains (SGP) site during April–June 2011 [Jensen et al., 2015; Williams, 2016; Wang et al., 2016; Giangrandeet al., 2016; Kumjian et al., 2016]. The campaign employed the largest observing infrastructure currently avail-able in the Central United States combined with an extensive sounding array, NASA ground validationremote sensors, remote sensing, and aircraft in situ observations. The University of North Dakota (UND)Citation II was one of the primary research aircraft deployed during MC3E and was fully equipped to studycloud microphysics. Six DCS cases sampled by the UND Citation II during MC3E were selected to investigatethe ice cloud microphysical properties of DCSs [Wang et al., 2015] (hereafterW15).W15 provided not only themass-dimensional relationship but also empirical fits between ice cloud particle size distribution (PSD) para-meters and NEXRAD reflectivity Ze. In this study, new algorithms for retrieving ice cloudmicrophysical proper-ties of DCSs are developed using these relationships and S-band NEXRAD radar reflectivity. Ground-basedNEXRAD observations advance the temporal continuity and spatial coverage when compared to verticalpointing and airborne radars and can be used to provide continuous four-dimensional (4-D, space-time) mea-surements over large regions within the continental U.S. This in turn makes it possible to retrieve 4-D icecloud microphysical properties of DCSs and study their evolutions.

This paper is organized as follows: the data used in this study are introduced in section 2, and the algorithmdevelopments are presented in section 3. In section 4, a case study is first presented to demonstrate the 4-Dretrievals and then followed by the IWC profile comparisons from different approaches. To further evaluatethe newly developed retrieval algorithms and investigate their suitability over other DCSs, independentaircraft in situ measured ice cloud microphysical properties from the Bow Echo and Mesoscale ConvectiveVortex Experiment (BAMEX) are used. Finally, a brief summary is given in section 5.

2. Data

One of the goals of MC3E was to advance the understanding of cloud microphysical properties in DCSs[Jensen et al., 2015]. The comprehensive measurements, including ground-based radars and research aircraft,are used to aid the selection of DCS cases and development of retrieval algorithms [W15]. The UND aircraftprobes used in W15 and their associated measurements and accuracies are listed in Table 1. In summary,the Rosemount Icing Detector, King and Droplet Measurement Technologies (DMT) Cloud Droplet Probes,and OAP Two-Dimensional Cloud (2DC) and DMT Cloud Imaging Probe images have been used to detect

Table 1. The University of North Dakota Citation II Aircraft Probes Used During MC3E

Instrument Name Description

Nevzorov TWC/LWC sensor Deep cone (60°), range of measured TWC/LWC 0.003–3.0 gm�3, accuracy ±10%King LWC sensor Model KLWC-5, range of measured LWC 0.05–3.0 gm�3, accuracy ±15%Rosemount Icing Detector Model 0971LM, causing a sharp drop in the frequency of oscillation due to accrete and glaciate SLW

droplets on the sensing cylinderCloud Droplet Probe (CDP) 1–50 μmTwo-Dimensional Cloud Probe (2DC) 30–3,000 μm (bins of 1–3, from 30 to 90 μm, were not used in this study)High-Volume Precipitation Spectrometer (HVPS) 300–30,000 μm

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the supercooled liquid water content (LWC) in the ice-dominated cloud layers of DCSs. The Nevzorov sensor(measuring total water content (TWC) and LWC) and 2DC and High-Volume Precipitation Spectrometerprobes have been used to study DCS's ice cloud PSDs, as well as their bulk ice cloud properties (IWC andDm). A series of empirical relationships between gamma-fitted parameters and ground-based NEXRAD obser-vations were established, directly providing the representation of cloudmicrophysical properties for both theremote sensing and modeling communities.

A network of NEXRAD Weather Surveillance Radar-1988 Doppler (WSR-88D) S-band systems (operating at~3GHz)allows for theobservationofagivenatmospheric columnbyseveraldifferent systemsatvarying rangesthat, when combined, can provide denser vertical sampling. In this study, we produce NEXRAD WSR-88Dcomposites with approximately 2 km horizontal, 1 km vertical, and 5min temporal resolutions following themethods of Homeyer [2014] and Homeyer and Kumjian [2015]. Note that at the S-band frequency, attenuationby hydrometeors is often negligible and can be ignored formost practical cases [Matrosov, 2007]. Thus, no cor-rections for attenuation have been applied to the radar composites. During MC3E, an S-band zenith-pointingDoppler radar was deployed by the National Oceanic and Atmospheric Administration (NOAA) at the DOEARM SGP Central Facility during MC3E. This S-band radar can provide the vertical structure of a precipitatingcloud from an altitude of approximately 200m to 16 km above the ground [Ecklund et al., 1999] with 1mintemporal resolution and 62m vertical resolution. The NOAA zenith-pointing radar reflectivity is regarded asthe “best estimate” to evaluate the uncertainty of composite-gridded NEXRAD reflectivity.

The radar reflectivity columns are extracted from 4-D gridded NEXRAD radar data along the aircraft flighttrack every 1min during MC3E. Figure 1 shows the time-height cross sections of NEXRAD radar reflectivityalong with the aircraft flight tracks for six selected cases (27 April and 1, 11, 18, 20, and 24 May 2011). Theaircraft in situ data were sampled from inside the SR and thick anvil (ACthick) regions of DCSs that wereadjacent to the convective cores [W15]. Along the aircraft tracks, DCS ice cloud microphysical properties werebest estimated using multiple probes as discussed in W15.

Data from an additional field campaign, BAMEX, were also used to evaluate the new retrieval algorithms.BAMEX was conducted between 20 May and 6 July 2003 over the Central United States. One of the primary

Figure 1. Time-height cross sections of NEXRAD radar reflectivity (color filled) along with aircraft track (black lines) for sixselected cases of deep convective systems (DCSs): (a) 27 April 2011, (b) 1 May 2011, (c) 11 May 2011, (d) 18 May 2011, (e) 20May 2011, and (f) 24 May 2011 during the Midlatitude Continental Convective Clouds Experiment (MC3E).

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objectives of BAMEX was to study the life cycle of convective systems using airborne and ground-basedobserving networks. The observing facilities for BAMEX and some preliminary results are summarized inDavis et al. [2004]. During BAMEX, the NOAA P-3 aircraft documented the vertical variability of ice cloudmicrophysical properties [McFarquhar et al., 2007a; Grim et al., 2009; Smith et al., 2009]. The NOAA P-3sampled the cloud environment from 6 km to near the surface in the stratiform regions behind the convec-tive lines (Figures 2 and 3), which is similar to the area of aircraft sampling during MC3E. The cloud tempera-tures ranged from nearly �10°C to ~15°C during the eight selected flights, and their dates and time periodsare summarized in Table 2. The ice cloudmicrophysical properties during BAMEX were well calculated follow-ingMcFarquhar et al. [2007a] and Smith et al. [2009], and these ice cloud microphysical properties were usedto evaluate the newly developed retrieval algorithms. Note that there were 17 flights during BAMEX; 8 of

Figure 2. The radar reflectivities at an altitude of 2.5 km for eight selected flights (details listed in Table 2) during the BowEcho and Mesoscale Convective Vortex Experiment (BAMEX). The aircraft flew region is shown as black square.

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which were used to evaluate the radar retrievals due to available NEXRAD radar measurements and coverage.The average of aircraft in situ measured IWC values for all 17 flights during BAMEX was 1.44 ± 0.89 gm�3

[McFarquhar et al., 2007a], while the average value in this study is 1.25 ± 0.89 gm�3 for the 8 selected flights.The small mean difference (0.19 gm�3) and almost the same standard deviation for the two data sets indicatethat the IWC sampled during the eight selected flights are statistically similar to those sampled during theentire project. Smith et al. [2009] further characterize the microphysical properties in context of the locationwithin the storm, where the measurements were made (i.e., in transition zone, notch region, enhanced strati-form region, and rear anvil region).

In addition to the aircraft in situ measurements and NEXRAD observations during MC3E and BAMEX, the icecloud microphysical properties from a cloud-resolving model (CRM) simulated with spectral bin microphysics[Liu et al., 2015] during MC3E were also used for intercomparison. The CRM is a numerical model, which hasbeenwidelyused incloudsystemresearchto investigate the formation,maintenance, structure, anddissipationof cloud systems [e.g., Krueger et al., 1995a, 1995b] and to test innovative cloud parameterizations [e.g., Xu andKrueger, 1991; Xu and Randall, 1995]. Spectral binmicrophysics (SBM), inwhich the size distributions of aerosolsand cloud hydrometeors are discretized by a number of size bins and predicted [Khain et al., 2004], treats cloudmicrophysical processes more physically than the commonly used bulk microphysical schemes [Khain et al.,2015]. Simulationswith SBMare computationally expensivebut oftenare treatedasbenchmarks in cloud simu-lations and parameterization development [Liu et al., 2015]. In this study, the CRM simulations for 20 May caseduringMC3E from Fan et al. [2015] are used. The simulations have a horizontal resolution of nearly 1 km, whichis comparable to our gridded NEXRAD product. More details about themodel simulations can be found in Fanet al. [2015]. In this study, the CRM-simulated IWC values are compared with radar-retrieved IWC values.

The NEXRAD-retrieved and CRM-simulated IWC values are also compared with the IWC values retrieved usingthe H06method. Temperature is one of the inputs in the H06 retrieval in addition to radar reflectivity. Cloudtemperatures used in this study are from the DOE ARM Merged Sounding (MERGESONDE) value-added pro-duct, which uses a combination of measurements of radiosonde, Microwave Radiometer, and surfacemeteorological instruments. The European Centre for Medium-Range Weather Forecasts model outputs with

Figure 3. Time-height cross sections of NEXRAD radar reflectivity (color filled) along with aircraft track (black lines) for eightselected flights (details listed in Table 2) during the Bow Echo and Mesoscale Convective Vortex Experiment (BAMEX).

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a scaling/interpolation/smoothing scheme are also used to generate the merged soundings in order toproduce the atmospheric thermodynamic state profiles in 1min temporal intervals for a total of 266 verticallayers from sea level up to 20 km [Troyan, 2011].

This study focuses on microphysical retrievals of the ice layer of DCSs above the freezing level. The instancesof supercooled liquid water in the ice-dominated cloud layers of DCSs have been eliminated in the aircraft insitu measurements using multisensor detection, including the Rosemount Icing Detector, King and CloudDroplet Probes, and the 2DC and Cloud Imaging Probe images during MC3E as mentioned in Table 2 ofW15. During BAMEX, the lack of a strong peak in the size distributions measured by a forward scattering spec-trometer probe between 5 and 25μm suggests that minimal supercooled water was present at the locationof the observations [McFarquhar et al., 2007b]. However, freezing-level heights are not readily available withacceptable accuracy from conventional NEXRAD data. In this study, the atmospheric temperature (0°C) fromMERGESONDE is also used to detect the melting band level, assuming that the ice particles are dominantabove the melting band [Matrosov, 2015].

Note that the SR and ACthick regions of DCSs are the main interests in this study. The convective-stratiform-anvil (CSA) products were used in this study to separate a DCS into three components [Feng et al., 2011]. Thedefinitions of these components are as follows: (1) CC, vertically oriented reflectivity maximum that producesintense precipitation with contiguous echo top above 6 km; (2) SR, widespread precipitation that has a weakhorizontal reflectivity gradient and enhanced reflectivity near the 0°C level with a contiguous echo top above6 km; and (3) ACthick, neither CC nor SR, but radar reflectivity has an echo base above 3 km. More details aboutthe CSA can be found in Feng et al. [2011].

3. Retrieval Algorithms

The equivalent radar reflectivity factor Ze can be calculated using a Rayleigh scattering approximation as[Heymsfield et al., 2002a; Boudala et al., 2006]

Ze ¼ Kij j2Kwj j2

6ρiπ

� �2

∫Dmax

Dminm Dð Þ2N Dð ÞdD; (1)

where D is the diameter of smallest circle that encloses the ice particle shown on optical array probe images[Heymsfield and Parrish, 1978; Korolev, 2007;W15], N(D) is the number concentration distribution function, ρi isthe solid ice density, |Ki|

2 = 0.176, and |Kw|2 = 0.93. The integration is evaluated from minimum diameter Dmin

up to the maximum diameter Dmax in the PSD. m(D) is the relationship between the particle mass anddiameter given by the expression

m Dð Þ ¼ aDb; (2)

where a is the coefficient and b is the exponent.

The IWC can be derived by integrating the individual particle mass over the PSD

IWC ¼ ∫Dmax

Dminm Dð Þ N Dð ÞdD; (3)

Typically, the size distributions of ice particles in observations and numerical model parameterizations areapproximated by using a gamma-type size distribution [Heymsfield et al., 2002b, 2013; McFarquhar et al.,2007a, 2015; W15]

N Dð Þ ¼ N0Dμe�λD; (4)

where N0 is the intercept, μ is the dispersion, and λ is the slope. For data collected in tropical cyclones,McFarquhar et al. [2015] showed that μ could range from �2 to 8; λ ranged from 0 to 100 cm�1; and the

Table 2. Aircraft Flight Dates and Time Periods for Eight Flights During BAMEX Used in This Study

Flight No. FL1 FL2 FL3 FL4 FL5 FL6 FL7 FL8

Date 24 May 2003 10 June 2003 21 June 2003 29 June 2003 29 June 2003 5 July 2003 6 July 2003 6 July 2003Begin time (UTC) 21:54 07:15 04:54 05:26 07:29 01:37 05:30 06:38End time (UTC) 22:23 07:31 05:00 05:34 07:36 01:49 05:37 06:44

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largest variation among the three PSD parameters is N0, ranging from 10�6 cm�(4 + μ) to 1012 cm�(4 + μ). It isalso important that mutual correlations between the parameters be accounted for, as otherwise inappropri-ate combinations of parameters will yield solutions drastically different from the observed size distributions[McFarquhar et al., 2015]. The uncertainty of estimated N0 is about 2 orders of magnitudes [W15]. Thus, toavoid the high potential uncertainty of N0 in retrievals, the ratio of Ze and IWC, Ze

IWC, is expressed in the form of

Ze

IWC¼

Kij j2Kwj j2

6ρiπ

� �2∫Dmax

Dminm Dð Þ2Dμe�λD dD

∫Dmax

Dminm Dð ÞDμe�λDdD

; (5)

where m(D)= 3.65 × 10�3 g cm�2.1D2.1 as provided in W15 for DCSs measured during MC3E. The new m(D)was determined by W15 noting the following two conclusions: (1) the exponent b of m(D) equals 2.1, whichcan be broadly applied to a variety of habits including aggregates, bullet rosettes, needles, plates, and den-drites [Heymsfield et al., 2010], and (2) the Nevzorov probe can accurately measure IWC at Dmax< 4000μmbut underestimates IWC for Dmax> 4000μm (e.g., for cloud with large ice particles Dmax> 10mm, the IWCmeasured by Nevzorov will underestimate more than 50%) [Korolev et al., 2013]. Thus, when using theNevzorov-measured IWC values at Dmax< 4000μm as the best estimate,W15 determined that the most likelyvalue of the coefficient a for the 5 s samples measured during MC3E was 3.65 × 10�3 g cm�2.1.

For application of aircraft in situ measured PSDs to remote sensing and models, a series of empiricalrelationships between the fitted PSD parameters λ and μ and NEXRAD reflectivity Ze values were providedin W15 as follows:

λ ¼ aλebλZe ; (6)

where aλ=51.465 cm�1 and bλ=�0.091 dBZ�1, and

μ ¼ aμebμZe þ cμ; (7)

where cμ=�2.5 and aμ=7.955 and bμ=�0.0948 dBZ�1 when Ze> 12 dBZ and aμ= 3.498 andbμ=�0.111 dBZ�1 when Ze ≤ 12 dBZ. By assuming fixed Dmax (3 cm) and Dmin (90μm), Ze

IWC can be calculatedfrom equation (5). With the availability of NEXRAD Ze and calculated Ze

IWC in equation (5), IWC can thus beretrieved. In addition to IWC, another ice cloudmicrophysical property, Dm, is also retrieved.Dm is widely usedin the studies of ice cloud microphysical properties [Mace et al., 2002; Heymsfield, 2003; Heymsfield et al., 2004;W15] and is defined as the diameter that splits IWC in half and is expressed by

∫Dm

Dminm Dð ÞN Dð ÞdD ¼ 1

2∫Dmax

Dminm Dð ÞN Dð ÞdD: (8)

By combining equations (2) and (4), equation (8) can be simplified as

∫Dm

DminDμþbe�λDdD ¼ 1

2∫Dmax

DminDμþbe�λDdD: (9)

Given theNEXRADZemeasurements, λ andμ are estimatedusingboth λ-Ze andμ-Ze relationships, and thenDm

canbe retrieved following equation (9). Note that sensitivity studies are presented inAppendixA, including thesensitivities of the retrieved ice cloudmicrophysical properties (IWC and Dm) with respect to the uncertaintiesfrom input variables (Ze), empirical relationships (μ-Ze, λ-Ze, and m(D) relationships), and the validity of theassumptions used in the retrieval (the assumed value of maximum andminimum diameters Dmax and Dmin).

4. Results and Discussions4.1. Ice Cloud Microphysical Properties of DCSs During MC3E

To demonstrate the capability of the retrieval algorithm and its potential applications, we first present 4-Dradar reflectivity and retrieved ice cloud microphysical properties for the DCS sampled on 20 May 2011 dur-ing MC3E as an example. Early in the morning of 20 May 2011, an intense southwest-to-northeast orientedsquall line moved over the SGP and was extensively sampled by the ground-based instruments. Shortlythereafter, the UND Citation II sampled the SR and AC regions of the DCS near the ARM SGP site. This typicalDCS case represents one of the best examples of the coordinated sampling strategy obtained during MC3E[Tao et al., 2013; Fan et al., 2015].

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The instantaneously (10:15 UTC and 14:15 UTC 20 May 2011) observed NEXRAD Ze and retrieved IWC and Dm

over a large domain at the levels of 6 km and 8 km for the 20 May case during MC3E are presented inFigure 4. The intense southwest-to-northeast oriented squall line is clearly shown in Figures 4a and 4b.The retrieved IWC and Dm values presented in Figures 4c–4f show different cloud microphysical structuresboth horizontally and vertically, as well as their evolution with time. The large ice particles were initiallylofted by convective cores within the linear convective structure and then fell to lower altitudes.Therefore, large particles and IWC, corresponding to higher Ze, are mainly located at lower levels as illu-strated in Figure 4. From 10:15 to 14:15 UTC, the DCS moved northeastward and a large anvil region haddeveloped by 14:15 UTC (green and blue color regions shown in Figure 4b at 8 km). These cloud retrievalscan be combined with model simulations to better understand cloud physics and evaluate/improvesatellite-based cloud microphysical property retrievals.

To evaluate our retrieval algorithms, the vertical distributions of retrieved IWC values are first compared withthose retrieved using the H06 method and the CRM simulations. Note that only IWC values in the SR andACthick regions of the DCS (green and blue regions in Figures 5a, 5c, and 5e) are used for analysis. For theretrievals from H06 and this study, the SR and ACthick regions are identified following the methodology ofFeng et al. [2011]. For CRM simulations, the SR and ACthick regions are identified by vertical motion less than2m s�1, total water content greater than 10�6 kg kg�1, and graupel water content less than 10�3 kg kg�1

[Fan et al., 2015].

As mentioned above, H06 provides a method to retrieve IWC based on S-band radar reflectivity Ze and cloudtemperature T as follows:

log10 IWC=IWC0ð Þ ¼ 0:06 Ze=Ze0ð Þ � 0:02 T=T0ð Þ � 1:7; (10)

where the IWC0 is 1 gm�3, Ze0 is 1 dBZ, and T is 1°C. This relationship was derived from C-130 in situ measured

ice cloud properties in the European Cloud Radiation Experiment (EUCREX). Ze and IWC values measured

Figure 4. Instantaneously (a) observed NEXRAD Ze, (c) retrieved IWC, and (e) Dm over a large domain at levels of 6 km and8 km at 10:15 UTC 20 May 2011. (b, d, and f) Same as in Figures 4a, 4c, and 4e except at 14:15 UTC 20 May 2011 (x axis:longitude [deg], y axis: latitude [deg], and z axis: height).

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Figure 5. The classified three DCS components: convective core (CC), stratiform regions (SRs), and thick anvil clouds (ACthick) using the methodology of Feng et al.[2011] at (a) 10:00 UTC, (c) 11:00 UTC, and (e) 12:00 UTC on 20 May 2011 during MC3E. Retrieved IWC from this study (blue lines with error bars), Hogan et al. [2006](H06) method (green lines with error bars), and modeled IWC (red lines with error bars) using cloud-resolving model (CRM) in SR and ACthick regions over largedomain (shown in Figures 5a, 5c, and 5e at (b) 10:00 UTC, (d) 11:00 UTC, and (f) 12:00 UTC on 20 May 2011).

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during EUCREX ranged from�40 dBZ to 20 dBZ and 10�4 gm�3 to 100 gm�3, respectively, which have largeoverlaps with the ranges of Ze (3 dBZ~42 dBZ) and IWC (10�2 gm�3~3.3 gm�3) during MC3E. H06 has beenapplied to 3GHz scanning radar data to retrieve IWC for precipitation clouds in the United Kingdom and eval-uate the simulations from the operational mesoscale version of the Met Office forecast model. Moreover,Matrosov [2015] suggested that the quantitative information on IWC of precipitation systems can generallybe obtained from operational WSR-88D measurements using H06. Therefore, it is possible to compare theIWC values retrieved from H06 and this study. Although both retrievals are highly dependent on radarreflectivity Ze, H06 also depends on cloud temperature. In H06, the temperature arises because N0 dependson the temperature. However, our IWC retrieval is independent of N0 (equations (5) and (9)), which resultsin the independence of temperature. The IWC values retrieved from both H06 and this study decrease withheight (Figures 5b, 5d, and 5f). Both IWC retrievals are in agreement within 1 standard deviation at each level;however, the H06-retrieved IWC values are approximately 0.3 gm�3 larger than those from this studythroughout the ice cloud layer. The “overestimation” of IWC from H06 was also found in Matrosov [2015],where the integrated H06 IWC retrievals (IWPs) were on average 15–25% higher than IWP values retrievedfrom high-resolution vertically pointing satellite observations.

Formodel simulations, since the simulatedDCS is delayed by roughly 4 h and shifted by about 0.5° to the northand west for 20 May 2011 case, the analysis is shifted accordingly in location and time [Fan et al., 2015].Vertically, the retrieved and CRM-simulated IWC values are averaged according to gridded radar verticalresolution (1 km). The CRM-simulated IWC values increase and then decrease with height, whereas the radar-retrieved IWC values generally decrease with height. The different criteria used to select SR and AC regions ofDCS may result in the different trends of IWC with height between model and radar retrievals. Note that wearenot aiming toevaluatewhich IWC retrieval or simulationmethod is thebest in this section.However,wefindthat each retrieved or simulatedmean IWC values fall within 1 standard deviation of the other two.

Figure 6 shows the profiles of aircraft in situmeasured and radar-retrieved IWC andDm values averaged duringfourflightlegperiodson20May2011.TheicecloudmicrophysicalpropertiesretrievedfromNEXRADradarreflec-tivityarecollocatedwithaircraftflight tracks in spaceandtimeduring fouraircraft ascent/descentflight leg timeperiods (Leg 1: 13:52–14:17UTC, Leg 2: 14:17–14:56UTC, Leg3: 15:56–16:11UTC, and Leg 4: 16:11–16:25UTC inFigure 1e) on 20 May 2011. The retrieved IWC and Dm values are averaged according to NEXRAD vertical reso-lution (1 km), while the aircraft in situ measured microphysical properties are averaged by 1min intervals. Themean-retrieved and aircraft in situ measured IWC values decrease from ~0.7 gm�3 at 5 km to ~0.2 gm�3 to8 km, and the Dm values also decrease from ~2mm to ~0.5mm at the same levels in Legs 1 and 2.

In general, the aircraft in situ measured IWC values are within 1 standard deviation of the radar-retrieved IWCvalues at each level, except large differences that occur at lower levels (5–5.5 km, with temperatures in therange of �8°C to �13°C) as shown in Figures 6a and 6b. The supercooled liquid water at lower levels (abovethe radar melting/bright band at ~4 km) may be attributed to large radar reflectivity measurements andthereafter result in large IWC retrievals, while the supercooled liquid water was excluded in aircraft-measuredIWC values through the multisensor detection as discussed inW15. Even though there are large reflectivitiesat lower levels, the Dm values do not show a drastic increase with decreasing height as radar-retrieved IWCvertical profiles (Figures 6a and 6b and 6e and 6f) due to the radar-retrieved Dm being less sensitive to Zecompared to the sensitivity of IWC to Ze (Table A1).

The radar-retrieved and aircraft-measured IWC values in Legs 3 and 4 are smaller than those in Legs 1 and 2because the aircraft flew in the SR regions of the DCS during Legs 1 and 2 and in the anvil clouds of the DCSduring Legs 3 and 4 (Figures 1e and 5a in W15). In Legs 3 and 4, the vertical variations of aircraft-measuredIWC are small, while the aircraft-measured Dm values are much larger at lower levels than those at upperlevels. The Dm values are determined by both IWC values and the mass distribution. With nearly the sameIWC, the mass distributions with steeper slopes and larger intercepts observed at upper levels will result insmall Dm values, whereas large Dm values are deduced at lower levels, where the slopes of mass distributionsare flat and intercepts are small (as demonstrated by aircraft in situ measurements in Figure 6 of W15). Theradar retrievals are smaller than the aircraft in situ measured Dm values at 5 km in Legs 3 and 4, which isdue to smaller NEXRAD reflectivities at 5 km. The radar reflectivity is also determined by mass/size distribu-tion (both slope and intercept): a flat slope increases the radar reflectivity, while a small intercept decreasesthe radar reflectivity. Thus, similar to the vertical distribution of IWC, the radar reflectivity will not always

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follow the large vertical variation of Dm: the aircraft in situ measured Dm values at 5 km are much larger thanthose measured at 6 km, while the observed radar reflectivities at 5 km are almost the same and even smallerthan the radar reflectivities at 6 km.

The statistical results from six selected cases during MC3E are listed in Table 3, where the aircraft in situ mea-sured IWC and Dm are 0.47 ± 0.29 gm�3 and 2.02 ± 1.3mm, while the mean values of retrievals have positivebias of 0.19 gm�3 (40%) and negative bias of 0.41mm (20%). Note that the temporal resolution is 1min inthis study, while it is 5 s in W15; thus, the averaged aircraft-measured IWC and Dm values listed in Table 3are not exactly the same as those in Table 6 of W15.

Figures 5 and 6 have demonstrated that the ice cloud microphysical properties of DCSs retrieved from ournew algorithms agree with those retrieved from H06, simulated from CRM, and measured from aircraft

Table 3. Means and Standard Deviations of the Aircraft Height, In Situ Measurements and Collocated NEXRAD Reflectivity Measurements, and Retrievals Along theAircraft Flight Track During MC3E and BAMEX

Flight Height (km) Flight Temperature (°C) In Situ IWC (gm�3) In Situ Dm (mm) Ze (dBZ) Retrieved IWC (gm�3) Retrieved Dm (mm)

MC3E 5.50 ± 1.58 �13.12 ± 8.82 0.47 ± 0.29 2.02 ± 1.30 18.91 ± 6.93 0.66 ± 0.65 1.61 ± 0.50BAMEX 4.32 ± 0.50 �4.24 ± 2.50 1.25 ± 0.89 1.77 ± 0.75 27.26 ± 6.10 1.52 ± 1.02 2.08 ± 0.34

Figure 6. The (a–d) IWC and (e–h) Dm profiles retrieved from this study (blue lines with error bars) andmeasured by aircraftat four different ascending/descending flight legs as shown in Figure 1e (Leg 1: 13:52–14:17 UTC, Leg 2: 14:17–14:56 UTC,Leg 3:15:56–16:11 UTC, and Leg 4: 16:11–16:25 UTC) during 20 May 2011.

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generally. However, the empirical relationships used in this study were derived from the aircraft in situ mea-surements during MC3E, which may have forced a close agreement between the retrievals and aircraft in situmeasurements. To better evaluate the newly developed retrieval algorithms and investigate their suitabilityfor additional DCSs, we employ independent aircraft observations from the 2003 BAMEX field experiment.

4.2. Validation of the New Algorithms Using the Aircraft in Situ Data During BAMEX

Previous studies [Mace et al., 2002; Dong et al., 1998; Dong and Mace, 2003; Deng and Mace, 2006] havedemonstrated that aircraft in situ measurements provide excellent cloud microphysical properties to evalu-ate ground-based retrievals despite their limited spatial and temporal converge. In this study, aircraft in situdata are temporally averaged to 1min resolution to match the corresponding radar retrievals during BAMEX.Figures 7a and 7c show the collocated aircraft in situ measured and the radar-retrieved IWC and Dm valuesfrom eight flights during BAMEX. A total of 63, 1min collocated aircraft and radar samples are used in thecomparisons. The averages of radar-retrieved and aircraft in situ measured IWC values are 1.52 gm�3 and1.25 gm�3, respectively, with a correlation of 0.55. The scatterplot in Figure 7b shows that most of theretrieved and in situ measured IWC values are somewhat correlated except for a few outliers. The averagesof radar-retrieved and aircraft in situ measured Dm values are 2.08mm and 1.77mm, respectively. The scat-terplot in Figure 7d shows that the radar-retrieved and aircraft in situ measured Dm values agree with eachother for Dm> 1.5mm, but the retrieved Dm values are nearly constant and larger than aircraft in situmeasurements for Dm< 1.5mm. Both the retrieved IWC and Dm values increase with radar reflectivity Ze(Figure 7). The differences between radar retrievals and aircraft in situ measurements are analyzed from three

Figure 7. The 1min averages of aircraft in situ measured (a) IWC (black dots) with corresponding radar-retrieved IWC (blue dots) at the same aircraft altitudes andlocations for eight selected flights during BAMEX. (b) Scatterplot of radar-retrieved IWC versus aircraft in situ measured IWC. (c and d) Same as in Figures 7a and 7bexcept for Dm.

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aspects: (1) the uncertainties of radar retrievals, (2) the uncertainties of aircraft in situ measured IWC and Dm,and (3) the mismatch in sampling volumes between radar and aircraft sensors.

The retrieval uncertainties were estimated in Appendix B. It was found that the uncertainties from empiricalrelationships (μ-Ze, λ-Ze, and m(D)) dominate the retrieval uncertainties. For the 63 samples collected duringBAMEX, the derived a values range from 1.81 × 10�3 g cm�1.4 to 7.61 × 10�3 g cm�2.2, and b range from 1.4 to2.2. In addition, the λ values during MC3E and BAMEX are different, where the λ values observed during MC3Erange from ~0 cm�1 to 90 cm�1 (Figures 9 and 10 of Wang et al. [2015]), while the λ values vary in a rangefrom ~0 cm�1 to ~23 cm�1 during BAMEX [McFarquhar et al., 2007a]. The differences in m(D) relationshipsand λ between MC3E and BAMEX may result in discrepancies for the selected BAMEX cases when the empiri-cal relationships derived from MC3E are applied to the BAMEX cases. To investigate the larger differencesbetween measured and retrieved Dm, we calculated the λ-Ze relationship during BAMEX (figure is not shown)and used the λ-Ze relationship during BAMEX as inputs in our Dm retrieval; however, we did not see significantimprovement. Physically, Dm is a property representing the ice particle size, even if Dm is not equal to the dia-

meter of ice particle D. Ze is correlated to the fourth (or 4.2) power of ice diameter, which means D or Dm∝ffiffiffiffiffiZe

4:2p

, while IWC is proportional toffiffiffiffiffiZe

p. The retrieved Dm is less sensitive to Ze than IWC is to Ze. Thus, small

variation of retrieved Dm occurs over a broad range of reflectivities in Figure 7c and leads to larger differencesbetween measured and retrieved Dm. The retrieved IWC and Dm values increase with radar reflectivity Ze;however, since the retrieval uncertainties are dominated by ice mass and particle size assumptions, theyare almost independent of Ze. Most of (more than 85%) the aircraft in situ measured IWC and Dm values fallwithin the estimated uncertainties of radar retrievals (~1.20 gm�3 and ~1.00mm). During BAMEX, the 2DCprobe was used to measure ice particles with D< 1.2mm and the two-dimensional precipitation probe(2DP) for 1.2<D< 7mm. A fitted particle size distribution based on 2DC and 2DP measurements was extra-polated to estimate PSDs above 7mm (see more details in Appendix A of McFarquhar et al. [2007a]).Moreover, them(D) relationships used to calculate IWC andDmwere derived fromNOAA P-3 radar reflectivity.Tuning the m(D) coefficients a and b against independent radar reflectivity measurements significantlyreduced the uncertainty in computing mass concentration by avoiding assumptions about which ice shapeor mixture of shapes should be applied to the PSDs. However, radar reflectivity is dominated by contributionsfrom larger particles, while IWC is more dependent on small ones. Uncertainties likely exist when applying them(D) relationships derived from radar reflectivity to calculate IWC for the small particles (more details inAppendix B of McFarquhar et al. [2007a]). In addition to the uncertainties from extrapolated PSD and radarreflectivity-derived m(D) relationships, different regions of storms sampled by the aircraft will also result inthe variations of microphysical properties [Smith et al., 2009].

Moreover, the mismatches in time, space, and sampling volumes between radar and aircraft sensors cannotbe ignored because the three-dimensional gradients in wind speed and direction and the associated disper-sion of ice particles may result in sampling different parts of clouds from ground-based radar and aircraft[Dong et al., 1998; Heymsfield et al., 2002b]. It is clear that the aircraft-measured/calculated IWC is extremelyhigh at 29 dBZ, which is likely caused by large sample volume difference between NEXRAD andaircraft sensor.

Note that the λ-Ze and μ-Ze relationships used in the retrieval were derived based on a database with radarreflectivities ranging from about 3 dBZ to 38 dBZ during MC3E, and the samples with Ze greater than35 dBZ are limited (sample number less than 10). Thus, larger differences were shown when Ze> 35 dBZ thanthose for Ze< 35 dBZ in Figure 7a. Uncertainties in radar retrievals are quantitatively investigated and demon-strated in Figure 8 regarding the aircraft in situ measurements as “ground truth.” The fractional error is theratio of the difference between the retrieval and the in situ measurement to the in situ measurement. Themedian error for IWC retrieval is 60%, suggesting that 32, 1min radar-retrieved IWC values agree with aircraftin situ measurements within 60%. The 90th percentile corresponds to a 160% fraction error; that is, there are6 (10% of total 63 samples) retrievals with uncertainties exceeding 160%. The median error for Dm (25%) issmaller than its IWC counterpart, but ~20% of samples have uncertainties of 100%, which is caused by theDm retrieval discrepancy for smaller particles. Although the retrieval algorithms cannot capture the exact var-iations of observed IWC and Dm, the mean differences between radar-retrieved and aircraft in situ measuredIWC and Dm values are small. These comparisons also illustrate that the newly developed retrieval algorithmsusing empirical relationships derived from the aircraft in situ measurements at higher level of DCS with lower

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Ze values during MC3E can be applied to DCS ice cloud even at lower levels with larger Ze values such as theconditions in BAMEX. The averaged IWC and Dm values during MC3E and BAMEX have demonstrated thatthere are significant differences between ice microphysical properties of DCSs and single-layered cirrusclouds. The IWC and Dm values for DCSs during MC3E and BAMEX are 1~2 orders of magnitude larger thanthose in midlatitude cirrus cloud (~0.01 gm�3 for IWC and 0.2–0.3mm for Dm [Mace et al., 2002]).

5. Summary

This study presents newly developed algorithms for retrieving ice cloud microphysical properties for the stra-tiform and anvil regions of DCSs using NEXRAD reflectivity and empirical relationships from aircraft in situmeasurements. A typical DCS case during the 2011 MC3E field campaign (20 May 2011) is selected as anexample to demonstrate our 4-D retrieval results. The vertical distributions of retrieved IWC values are com-pared with those retrieved from the H06method and simulated by a CRM over the SR and ACthick regions ofDCSs. In general, the retrieved and simulated mean IWC values fall within 1 standard derivation of the othertwo. The retrieved IWC and Dm are also compared with the aircraft in situ measurements. The statisticalresults from six selected cases during MC3E show that the aircraft in situ measured IWC and Dm are 0.47± 0.29 gm�3 and 2.02 ± 1.3mm, while the mean values of retrievals have a positive bias of 0.19 gm�3

(40%) and negative bias of 0.41mm (20%), respectively.

To fully evaluate the retrieval algorithms, IWC and Dm are retrieved for other DCS cases observed during the2003 BAMEX field campaign using NEXRAD reflectivity and compared with independent aircraft in situ mea-sured IWC and Dm. A total of 63, 1min collocated aircraft and radar samples are collected for comparisons,and the averages of radar-retrieved and aircraft in situ measured IWC values are 1.52 gm�3 and1.25 gm�3, respectively, with a correlation of 0.55, and their averaged Dm values are 2.08 and 1.77mm.Although the retrieval of Dm is not very sensitivity to Ze and has deficiency in retrieving smaller Dm values,it can still be used to give a crude estimation of mean Dm values in the convective clouds. Median errorsof ~60% and ~25% for IWC and Dm retrievals, respectively, are found for the BAMEX cases. In general, thesecomparisons have shown that the new retrieval algorithms can be applied to additional midlatitude conti-nental DCSs. These 4-D retrievals can be used as a valuable data source to evaluate and improve satellite-retrieved ice cloud microphysical properties of DCSs.

Although these retrievals are promising, improvements are possible using higher-resolution, composite-gridded NEXRAD products (when available) or data from higher-resolution scanning S-band radars. Recentdual-polarization upgrades to the NEXRAD WSR-88D network may lead to improvements in the radar retrie-vals since they provide a wealth of additional microphysical information (size, shape, concentration, etc.).These upgraded radar measurements can improve the retrieval accuracy by restricting the selection of icemodels, which is the dominate source of retrieval uncertainty. In addition, the dual-polarization radar can

Figure 8. Cumulative error frequencies for (a) IWC and (b) Dm. The fractional error is the absolute value of the differencebetween the retrievals and the aircraft in situ measurements normalized by the aircraft in situ measurements. A pointon either curve indicates the fraction of all samples (shown on the ordinate) with error less than the amount on theabscissa. The 0.5 (red lines) and 0.9 (blue lines) cumulative error frequencies correspond to the median fractional error and90th fractional error percentile, respectively.

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be used to better separate the predominantly ice and liquid layers within DCSs and then to improve the per-formance of the retrieval algorithm. Moreover, little or nomicrophysical observations exist within the convec-tive cores of DCSs sampled by the research aircraft during MC3E or BAMEX. Future improvements to thealgorithm are likely required for its application to CC regions of DCSs since the retrieved microphysical prop-erties may have larger uncertainties than those in SR and ACthick regions, owing to larger variability in the size,shape, and types of hydrometers in the convective core.

Appendix A: Sensitivity StudiesTo evaluate the utility of these algorithms, several sources of uncertainty are considered. In this appendix, wewill present the sensitivities of the retrieved ice cloud microphysical properties (IWC and Dm) with respect tothe uncertainties from input variables (Ze), empirical relationships (μ-Ze, λ-Ze, andm(D) relationships), and thevalidity of the assumptions used in the retrieval (the assumed value of maximum and minimum diametersDmax and Dmin).

A1. Sensitivity to NEXRAD Reflectivity Ze Uncertainty

Since the 4-D composite-gridded NEXRAD reflectivity is merged from three individual radar observations,uncertainty of the composite reflectivity and its impact on the ice cloud property retrievals need to be eval-uated. In this study, the NEXRAD reflectivities are compared with the NOAA S-band vertical pointing radarreflectivities in the ice layer of DCSs (above 5 km) over the ARM SGP Central Facility to investigate the uncer-tainty of the composite-gridded NEXRAD reflectivity. The NEXRAD reflectivities are on average ~3.0 dB lowerthan the NOAA S-band radar reflectivities with a standard deviation of ~3.0 dB for their reflectivity differ-ences. That is, the uncertainty of NEXRAD reflectivity can range from 0 to 6.0 dB if the NOAA S-band radarreflectivity is considered as a “best estimate.” As listed in Table A1, with an uncertainty of 3 dB in NEXRADreflectivity, the retrieved IWC values vary ~50% and increase to ~70% for a 6.0 dB uncertainty. The Dm retrie-val algorithm is less sensitive to Ze uncertainty than IWC retrieval algorithm, where the retrieved Dm valuesvary less than 10% with an uncertainty of 3.0 dB in NEXRAD reflectivity and on average, increase to ~40%for 6 dB uncertainty.

A2. Sensitivity to the Uncertainties of μ-Ze and λ-Ze Empirical Relationships

The uncertainty of λ (μ) is estimated by calculating the differences between the λ (μ) values derived from λ-Ze(μ-Ze) equations that were fit to the aircraft in situ measured PSDs and NEXRAD reflectivity Ze during MC3E inW15. In reality, there is a strong covariance between λ and μ [McFarquhar et al., 2015;W15]. Thus, the mutualdependencies of λ and μ should be considered, and the influences of mutual dependence on retrievals arepresented in Table A2. For example, 17 pairs of fitted λ and μ at 8 dBZ during MC3E were applied in equations(5) and (9) to retrieve IWC and Dm with mean values of 0.27 gm�3 and 1.16mm, respectively. The differencesbetween these new means and the retrievals using λ-Ze (μ-Ze) equations are 10.29% and 81.53%.

The sensitivity studies discussed above are for estimating the uncertainties in the μ-Ze and λ-Ze empirical rela-tionships, and these uncertainties come primarily from the parameterization/fitting based on aircraft derivedλ (μ) values and corresponding Ze values during MC3E. For other DCS events, the μ-Ze and λ-Ze empirical rela-tionships may be different, which implies that the coefficients in μ-Ze and λ-Zemay be different. Thus, the sen-sitivities of retrieved IWC and Dm on the μ-Ze and λ-Ze empirical relationship coefficients (aλ, bλ, aμ, bμ, and cμ)are analyzed in Tables A3 and A4. The sensitivity studies are conducted by changing one of the five

Table A1. Sensitivities of the Retrieved IWC (gm�3) and Dm (mm) on the Expected Errors (±6.0 dB and ±3.0 dB) in Radar Reflectivity Observations (Ze)

Ze (dBZ) IWC(Ze �6.0 dB)

IWC(Ze �3.0 dB)

IWC(Ze)

IWC(Ze +3.0 dB)

IWC(Ze +6.0 dB)

Dm(Ze �6.0 dB)

Dm(Ze �3 dB)

Dm(Ze)

Dm(Ze +3 dB)

Dm(Ze +6.0 dB)

Mean Mean (%) Mean (%) Mean Mean (%) Mean (%) Mean (%) Mean (%) Mean Mean (%) Mean (%)

8 0.08 (�67.46) 0.14 (�41.34) 0.24 0.39 (60.98) 0.19 (�22.33) 0.69 (6.87) 0.66 (3.11) 0.64 0.63 (�2.25) 1.64 (155.56)16 0.34 (27.32) 0.16 (�39.86) 0.26 0.42 (60.01) 0.65 (�146.05) 0.63 (�62.10) 1.63 (�2.20) 1.67 1.72 (3.10) 1.79 (7.36)24 0.36 (57.16) 0.56 (�33.24) 0.85 1.22 (44.37) 1.71 (102.13) 1.70 (�8.17) 1.76 (�4.72) 1.85 1.97 (6.46) 2.14 (15.38)

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coefficients ±20% while keeping other four coefficients constant and then investigating the change ofretrieved IWC and Dm values. The retrieved IWC values are correlated to aλ, bλ, and bμ while inversely corre-lated to aμ and cμ. Retrieved IWC is more sensitive to bλ and bμ than other coefficients. The retrieved Dm

values are inversely correlated to aλ, bλ, and bμ but correlated to aμ and cμ. Retrieved Dm is most sensitiveto bμ among all the coefficients. Note that no monotonic trend is found for the sensitivities of IWC and Dm

to the coefficients with increasing Ze.

A3. Sensitivities to the Selection of Ice Mass-Dimensional Relationships

Accurate retrieval of the ice cloud microphysical properties of a DCS using different m(D) relationships hasbeen a major challenge. In this sensitivity study, three m(D) relationships m(D) = 3.65 × 10�3 g cm�2.1D2.1 inW15, m(D) = 3.28 × 10�3 g cm�2.25D2.25 in Wood et al. [2015], and m(D) = 6.0 × 10�3 g cm�2.1D2.1 inHeymsfield et al. [2013] are applied in the retrievals. The retrieved IWC values change from 3.83% to89.69% as listed in Table A5. In the Dm retrieval, the power b in the m(D) relationship affects the retrievalresults, and changing b from 2.25 to 2.1 results in ~15% increase in Dm.

A4. Sensitivity of Assumed Maximum and Minimum Diameters

Aircraft in situ measurements can be used to provide Dmax for each measured PSD. However, during theretrieval using radar measurements, it is impossible to know the exact Dmax. Thus, Dmax values need to beassumed during retrieval. In this study, the integration of Ze is performed from Dmin (90μm) to Dmax

(~3 cm in this study) instead of infinity. We select 3 cm as a threshold for the following two reasons: first,the 3 cm is assumed based on the upper limit of PSD in situmeasurements [W15] and second, this threshold isalso used inMatrosov [2011] to forward calculate Ze for optically thick ice clouds. Based on a mean Dmax valueof 0.88 cmmeasured by aircraft probes during MC3E, we use different Dmax values of 0.75, 1.0, 3.0, and 9.0 cmas the integral upper limits. The retrieved Dm is almost independent of the assumption of Dmax (see Table A6).The retrieved IWC values vary within 5% at lower Ze values (e.g., 8 dBZ or 16 dBZ), indicating that the retrievedIWC is also almost independent of the assumedDmax. However, at higher Ze values (e.g., 24 dBZ), which is corre-sponding to higher possibility of existence of larger particles, if smallerDmax values (e.g., 0.75 cm or 1 cm)were

Table A2. Sensitivities of Retrieved IWC (gm�3) and Dm (mm) on the Expected Errors in λ-Ze and μ-Ze Empirical Relationshipsa

Ze(dBZ)

λ Uncertainty(%)

μ Uncertainty(%)

IWC(λ, μ)

IWC(λ1, μ)

IWC(λ2, μ)

IWC(λ, μ1)

IWC(λ, μ2)

Dm(λ, μ)

Dm(λ1, μ)

Dm(λ2, μ)

Dm(λ, μ1)

Dm(λ, μ2)

Mean Mean Mean (%) Mean (%) Mean (%) Mean (%) Mean Mean(%)

Mean(%)

Mean (%) Mean (%)

8 53.22 79.08 0.24 0.57(133.32)

0.05(�78.77) 0.51(110.62)

0.13(�45.07)

0.64 0.40(�37.86)

1.42(120.74)

0.24(�63.29) 1.01(56.63)

16 37.80 100.00 0.26 0.51(95.14)

0.10(�62.90) 0.50(89.09)

0.16(�39.00)

1.67 1.20(�27.99)

2.70(62.13)

1.02 (�39.15) 2.30(37.86)

24 21.95 45.51 0.85 1.27(50.19)

0.51(�39.75)

2.31(173.35)

0.41(�51.04)

1.85 1.51(�18.70)

2.39(29.19)

0.39 (�78.85) 3.21(73.53)

aλ1 = λ × (1 + uncertainty), λ2 = λ × (1� uncertainty), μ1 = μ × (1 + uncertainty), μ2 = μ × (1� uncertainty). The μ values calculated are negative at 8 dBZ, 16 dBZ,and 24 dBZ, indicating that μ1 is smaller than μ and μ2 is greater than μ.

Table A3. Sensitivities of Retrieved IWC (gm�3) on the Coefficients in λ-Ze and μ-Ze Empirical Relationships

Ze(dBZ)

IWC IWC(aλ × 1.2)

IWC(aλ × 0.8)

IWC(bλ × 1.2)

IWC(bλ × 0.8)

IWC(aμ × 1.2)

IWC(aμ × 0.8)

IWC(bμ × 1.2)

IWC(bμ × 0.8)

IWC(cμ × 1.2)

IWC(cμ × 0.8)

Mean Mean Mean (%) Mean (%) Mean (%) Mean (%) Mean (%) Mean (%) Mean (%) Mean (%) Mean (%) Mean (%)

8 0.24 0.35 (44.32) 0.15(�36.50)

0.18(�25.63)

0.33 (34.13) 0.20(�19.04)

0.30 (25.52) 0.08(�65.16)

0.47(92.58)

0.37(51.37)

0.17(�30.53)

16 0.26 0.39 (46.03) 0.16(�37.08)

0.14(�45.40)

0.48(83.16)

0.21(�21.59)

0.35 (31.48) 0.13(�51.82)

0.48 (80.38) 0.39(49.60)

0.19(�28.84)

24 0.85 1.23 (45.20) 0.54 (�36.75)

0.35 (�58.85)

2.07(144.50)

0.71(�15.74)

1.02 (20.26) 0.59 (�30.37)

1.13 (33.39) 1.56(84.10)

0.52(�38.58)

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assumed, the IWC uncertainty can be up to 34%. The 90μm is assumed based on the lower limit of PSD in situmeasurements, and the retrieved IWC andDm are almost independent of the assumedDmin.

Note that the variations discussed above are estimated based on sensitivity studies rather than retrievaluncertainties. The uncertainties of ice cloud microphysical property retrievals will be estimated inAppendix B and evaluated by independent aircraft in situ measurements in section 4.2.

Appendix B: Estimation of Radar Retrieval UncertaintiesThe retrieval uncertainties were estimated with considering error propagations as

ΔIWCp ¼ ∂IWC∂P

�ΔP ¼ ∂IWC∂Ze

� Kp�ΔP� �

(B1)

and

ΔDmp ¼ ∂Dm

∂P�ΔP ¼ ∂Dm

∂Ze� Kp�ΔP� �

; (B2)

where the Jacobian matrix, Kp, is the sensitivity of the forward model (Ze) to the model parameters P (a, b, aλ,bλ, aμ, bμ, cμ, Dmax, and Dmin) and can be written as

Kp ¼ ∂Ze

∂p¼ ∂Ze

∂a∂Ze

∂b∂Ze

∂aλ∂Ze

∂bλ∂Ze

∂aμ∂Ze

∂bμ∂Ze

∂cμ∂Ze

∂Dmax

∂Ze

∂Dmin

: (B3)

Note that the retrievals are independent of N0; thus,∂Ze∂N0

is not included in equation (B3). The partial derivation

of Ze with respect to each of model parameters and the partial derivations of IWC and Dm with respect to Zeare estimated using centered finite differences based on MC3E data set. More specifically, Ze can be forwardcalculated with assumed m(D) and given N0, μ, and λ, which are derived from aircraft in situ measurementsaccording to equation (1). For example, two Ze values can be forward calculated with b changing to 0.9b

and 1.1b, where b is the exponent of m(D), and then ∂Ze∂b can be estimated using centered finite differences

by calculating the two Ze values difference over 0.42 (2 × 0.1 × b, where b=2.1). The estimated value of ∂Ze∂b

is ~�9.70 dB during MC3E; that is, if the natural variation of b is assumed to be 0.24 according to the b valueslisted in Table 3 ofWood et al. [2015], then the mean contribution to forward Ze calculation uncertainty due tothe sensitivity of b in the m(D) and due to the natural variability in b would be on the order of 2.33 dB

(�9.7 × 0.24). The estimated ∂IWC∂Ze is ~0.12 gm�3/dB, which implies that the retrieved IWC uncertainty from

the sensitivity/variability in b would be on the order of 0.3 gm�3.

The total retrieval uncertainties frommodel parameters P (a,b,aλ, bλ, aμ, bμ, cμ,Dmax, andDmin) are estimated as

UIWC ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiX

ΔIWCp� �2q

(B5)

Table A4. Sensitivities of Retrieved Dm (g m�3) on the Coefficients in λ-Ze and μ-Ze Empirical Relationships

Ze(dBZ)

Dm Dm(aλ × 1.2)

Dm(aλ × 0.8)

Dm(bλ × 1.2)

Dm(bλ × 0.8)

Dm(aμ × 1.2)

Dm(aμ × 0.8)

Dm(bμ × 1.2)

Dm(bμ × 0.8)

Dm(cμ × 1.2)

Dm(cμ × 0.8)

Mean Mean Mean (%) Mean (%) Mean (%) Mean (%) Mean (%) Mean (%) Mean (%) Mean (%) Mean (%) Mean (%)

8 0.64 0.53(�18.11)

0.82 (26.98) 0.75 (16.96) 0.55(�14.74)

0.76 (18.97) 0.52(�19.76)

1.34(108.48)

0.28(�56.00)

0.41(�35.75)

0.86 (33.30)

16 1.67 1.39(�16.93)

2.09 (25.36) 2.24 (34.32) 1.24(�25.70)

1.96 (17.57) 1.37(�17.80)

2.66 (59.26) 1.06(�36.49)

1.24(�25.63)

2.09 (25.13)

24 1.85 1.53(�17.28)

2.33 (25.88) 2.90 (56.72) 1.17(�36.78)

2.15 (15.87) 1.55(�16.25)

2.49 (34.67) 1.39(�25.06)

0.90(�51.14)

2.74 (47.84)

Table A5. Sensitivities of Retrieved IWC (gm�3) and Dm (mm) on Different Mass-Dimensional Relationships

Ze (dBZ) Mean IWC (W15) Mean IWC (H13) Mean (%) IWC (Wood15) Mean (%) Dm (W15) Mean Dm (Wood15) Mean (%)

8 0.24 0.28 (13.88) 0.32 (31.93) 0.64 0.71 (10.20)16 0.26 0.42 (58.93) 0.31 (17.24) 1.67 1.79 (7.57)24 0.85 1.60 (89.69) 0.88 (3.83) 1.85 2.12 (14.58)

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TIAN ET AL. CONVECTIVE CLOUD MICROPHYSICAL RETRIEVAL 10,836

and

UDm ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiX

ΔDmp

� �2q: (B6)

The total retrieval uncertainties frommodel parameters are estimated usingMC3E data set, and the frequencydistributionsof these total retrievaluncertaintiesare shown inFigureB1.Themodevaluesof retrievaluncertain-ties for IWCandDm are~1.20 gm�3 and~1.0mm,while themedianvalues are larger (3.02 gm�3 and1.45mm).

The retrieval uncertainties comemainly fromuncertainties in the forwardmodel (which relates to uncertaintiesof model parameters) as well as the uncertainties of radar reflectivity [Zhang andMace, 2006; Zhao et al., 2010;Deng et al., 2010; Hammonds et al., 2014;Wood et al., 2015]. It was found that the forward model uncertainties

(>15 dB, estimated usingffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP

Kp�ΔP� �2q

) are much larger than the reflectivity measurement uncertainties

(<6 dB). In addition, the uncertainties of ice mass and particle size distribution dominate the forward modeluncertainty over the uncertainties of assumed Dmin and Dmax values, which is consistent with the results pre-sented inAppendixA. That is, the forwardmodel uncertainties dominate the retrieval uncertainty, andassump-tions regarding ice mass and size distribution are critical to the accuracy of the retrievals [Deng et al., 2010].

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Table A6. Sensitivities of Retrieved IWC (gm�3) on Different Maximum Diameters (0.75 cm, 1.0 cm, 3.0 cm, and 9.0 cm) Assumed in the Retrievals

Ze (dBZ) IWC (0.75 cm) IWC (1.0 cm) IWC (3.0 cm) IWC (9.0 cm) Dm (0.75 cm) Dm (1.0 cm) Dm (3.0 cm) Dm (9.0 cm)

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AcknowledgmentsThe aircraft in situ data were obtainedfrom the Atmospheric RadiationMeasurement (ARM) Program spon-sored by the U.S. Department of Energy(DOE) Office of Energy Research, Officeof Health and Environmental Research,Environmental Sciences Division. Thisstudy was primarily supported by DOEASR project at the University of NorthDakota with award DESC0008468, theNASA CERES project at University ofNorth Dakota project under grantNNX14AP84G, and by the NationalScience Foundation under grant AGS-1359098 to the University of Illinois.Special thanks to Michael Jensen, PI ofMC3E; to Guosheng Liu; Gang Hong;and Holly Nowell who processed thebackscattering database using DDAmethod in W15 and to Christopher R.Williams who shared the NOAA verticalpointing S-band radar data at ftp://gpm.nsstc.nasa.gov/gpm_validation/mc3e/profiler/sband_products/. The aircraft-measured cloud microphysical proper-ties during BAMEX were downloadedfrom http://data.eol.ucar.edu/cgi-bin/codiac/fgr_form/id=85.120. The pro-cessed NEXRAD data, ice cloud micro-physical properties through aircraft insitu measurements, and retrieved icecloud microphysical properties duringMC3E can be obtained from XiquanDong (dong@aero.und.edu).

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