Quarterly Journal of the Royal Meteorological Society

Q. J. R. Meteorol. Soc. 136: 382–399, January 2010 Part B

Improving a spectral bin microphysical scheme using TRMM
satellite observations
Xiaowen Li,a,b * Wei-Kuo Tao,b Toshihisa Matsui,a,b Chuntao Liuc and Hirohiko MasunagadaGoddard Earth Science and Technology Center, University of Maryland, Baltimore, Maryland, USA
b Laboratory for Atmospheres, NASA Goddard Space Flight Center, Greenbelt, Maryland, USAc Department of Meteorology, University of Utah, Salt Lake City, Utah, USAdHydrospheric Atmospheric Research Centre, Nagoya University, Nagoya, Japan*Correspondence to: Xiaowen Li, Code 613.1, NASA/GSFC, Greenbelt, MD 20770, USA. E-mail: xli@agnes.gsfc.nasa.gov

TRMM-observed mature-stage squall lines during late spring and early summer
in the central USA over a 9-year period are compiled and compared with a casesimulation by the Goddard Cumulus Ensemble (GCE) model with a spectral bin
microphysical scheme. During the quasi-steady state of the simulation, a forward
radiative transfer model calculates TRMM Precipitation Radar (PR) reflectivity
and 85 GHz brightness temperatures from simulated particle size distributions.
Comparisons between model and TRMM observations using radar Contoured
Frequency with Altitude Diagrams (CFADs) and 85 GHz brightness temperatureprobability density distributions are performed, in addition to CFADs from a surface
C-band radar for the same case. Radar CFADs comparisons reveal that the model
overestimates sizes of snow/aggregates in the stratiform region.
Three sets of sensitivity tests are carried out in order to improve the simulated
radar reflectivity profiles: increase of aggregates’ density and terminal fall velocity;changing temperature dependency of collection efficiency between ice-phaseparticles, particularly those of the plate-type; and adding a break-up scheme forlarge aggregates. While all three approaches mitigate the discrepancies, changing
collection efficiency produces the best match in magnitudes and characteristicsof radar CFADs. In addition, interactions between ice- and water-phase particles
also need to be adjusted in order to have good comparisons in both radar CFADs
and 85 GHz brightness temperature distributions. This study shows that long-term
satellite observations, especially those with multiple sensors, can be very useful inc 2010 Royal Meteorological Society
constraining model microphysics. Copyright 
Key Words:

cloud-resolving model; squall line; microphysics

Received 21 April 2009; Revised 18 November 2009; Accepted 30 November 2009; Published online in Wiley
InterScience 1 February 2010
Citation: Xiaowen L, Wei-Kuo T, Toshihisa M, Chuntao L, Hirohiko M, 2010. Improving a spectralbin microphysical scheme using TRMM satellite observations. Q. J. R. Meteorol. Soc. 136: 382–399.
DOI:10.1002/qj.569

1.

Introduction

schemes (e.g. Srivastava, 1967; Kessler, 1969; Cotton et al.,
1982; Lin et al., 1983; Rutledge and Hobbs, 1984) have
Proper representation of cloud and precipitation micro- been used in cloud and mesoscale modelling for decades.
physics is one of the major challenges in cloud modelling There are numerous studies validating and improving
and quantitative precipitation forecasting (e.g. Stoelinga bulk microphysical schemes (e.g. Tao and Simpson, 1989;
et al., 2003). Simple (one-moment) bulk microphysical McCumber et al., 1991; Meyers et al., 1992; Krueger et al.,c 2010 Royal Meteorological Society
Copyright Improving Spectral Bin Microphysics Using Trmm

1995; Reisner et al., 1998; Grabowski et al., 1999; Luo et al.,2003, 2008; Thompson et al., 2004; Straka and Mansell,
2005; Lang et al., 2007; Woods et al., 2007; Zeng et al., 2007).
In addition to showing cloud models’ large sensitivities
to various microphysical parameters and processes, thesestudies indicated many limitations that are inherent in thesimple bulk-type microphysical scheme.
With the advance of computer power, more sophisticatedmicrophysical schemes have been developed/implemented
in increasingly large modelling domains. These schemes
generally fall into two categories: multiple-moment bulk
schemes and spectral bin microphysical schemes. Multimoment bulk schemes represent the particle size distributions (PSDs) better than the simple bulk scheme by using twoor three, instead of only one, prognostic variables for eachhydrometeor species (e.g. Cotton et al., 1986; Murakami,
1990; Wang and Chang, 1993; Ferrier, 1994; Meyers et al.,
1997; Carrio and Nicolini, 2002; Chen and Liu, 2004; Morrison and Pinto, 2005; Milbrandt and Yau, 2005; Seifert and
Beheng, 2006; Thompson et al., 2008). However, they still
have to make crucial assumptions on cloud droplet activation, pre-defined PSDs, as well as sedimentations of various
particles. Spectral bin microphysical schemes use dozens,even hundreds of particle size bins to represent the actual size
spectra of Cloud Condensation Nuclei (CCN) as well as different hydrometeor particles (e.g. Clark, 1973; Soong, 1974;
Takahashi, 1975; Hall, 1980; Feingold et al., 1994; Khain andSednev, 1996; Reisin et al., 1996; Geresdi, 1998; Ovtchinnikov and Kogan, 2000; Hashino and Tripoli, 2007). Cloud
activation and PSD of various particles and their evolution
are explicitly calculated in a bin model, making it an indispensable tool for studying detailed dynamics/microphysics
interactions, such as aerosol indirect effects.
Unlike one-moment bulk microphysical schemes, whichhave gone through decades of validations for various cloudsystems, the newly developed/implemented multi-momentbulk schemes and bin schemes have been subjected to relatively less systematic validation studies. In addition to
traditional validation methods used for bulk microphysicalmodels, these sophisticated schemes offer more depth inutilizing the wealth of observational datasets available (e.g.
particle sizes and concentrations, ice-phase particle shapes,
densities). This paper is the continuation of our previous
studies (Li et al., 2009) in validating a state-of-the-art bin
microphysical scheme (Khain and Sednev, 1996; Khain et al.,2000) that has been implemented in the Goddard Cumulus
Ensemble (GCE) model (Tao and Simpson, 1993; Tao et al.,2003). In the previous study, surface observations of the
10–11 June 1985 squall line during the Preliminary Regional
Experiment for Storm-scale Operational and Research
Meteorology (PRE-STORM) field campaign were used tovalidate both a bulk and the bin microphysical scheme in the
GCE model. It was shown that the model simulations agreed
well with the observed storm structure and evolution, radarreflectivity patterns, wind fields, retrieved pressure and temperature perturbations, as well as heating profiles. This study
further includes nine years of Tropical Rainfall Measurement
Mission (TRMM) satellite data, in addition to some surface
radar observations during the PRE-STORM field campaign,
to validate and improve the model microphysics.
Several previous studies have used TRMM data forvalidating cloud models. For example, Zhou et al. (2007)
uses TRMM retrievals during the South China Sea
Monsoon Experiment (SCSMEX) to validate GCE modelc 2010 Royal Meteorological Society
Copyright 383

simulation. The TRMM Microwave Imager (TMI) observedbrightness temperatures have also been used in several
model validations (e.g. Wiedner et al., 2004; Lang et al.,2007; Li et al., 2008). Li et al. (2008) further included
TRMM Precipitation Radar (PR) 20 dBZ and 40 dBZ
maximum heights in their validation of a tropical oceanic
mesoscale convective system simulation. More recently,
Matsui et al. (2009) established a systematic radiancebased evaluation using multi-sensor satellite simulators
and TRMM PR, TMI, as well as the Visible and InfraRed
Scanner (VIRS) to validate long-term GCE simulations ofboth SCSMEX and Kwajalein Experiment (KWAJEX) field
campaigns. Masunaga et al. (2008) also used both TRMM
PR and CloudSat radar reflectivity to evaluate the macroand micro-properties of a global cloud-resolving model
simulation of the Madden–Julian Oscillation.
This study is the first in attempting radiance-basedmodel validation and improvement using a sophisticatedbin microphysical scheme. Compared to bulk scheme
validations, bin scheme validations offer both advantages
and new challenges. Because PSDs are explicitly calculated inbin models, one major uncertainty associated with the PSD
assumptions in either satellite retrieval or forward radiativetransfer calculation is eliminated. Improvements made inbin schemes will be based more on fundamentals, without
the need to adjust PSDs, especially for ice-phase particles
with many uncertainties. On the other hand, improving
bin schemes according to satellite observation requires clear
understanding of the myriad of interlacing microphysicalprocesses. It also inevitably involves uncertainties as bin
schemes have more degrees of freedom than available
observational constraints. Another issue is computational.
Bulk scheme models can potentially afford better match
between satellite and model data through long-term
simulations over large, three-dimensional (3D) domains. On
the other hand, our bin scheme simulation is a 2D, 12-hourperiod case-study which necessitates careful comparisons
between specific features, as discussed in detail in section 2.1.
The paper is organized as follows. The second section
briefly describes the PRE-STORM case, the GCE model withbin microphysical scheme, and the forward radiative transfer
calculations. The third section analyses and compares
TRMM and C-band surface radar data with each other,and with model simulations. Section 4 includes diagnostic
studies using the GCE model, the resultant improvementsin the bin microphysical scheme, and comparisons between
the improved model and observations. A summary anddiscussion are given in section 5.
2.

Descriptions

2.1.

PRE-STORM case

The PRE-STORM 10–11 June 1985 case is a well-studied
midlatitude continental squall-line case (e.g. Rutledge et al.,
1988; Johnson and Hamilton, 1988; Zhang et al., 1989; Gallus
and Johnson, 1991; Biggerstaff and Houze, 1993; Tao et al.,
1993, 1995, 1996; Braun and Houze, 1996). It is a typicalsquall system travelling from northwest to southeast duringlate spring and early summer in the central USA. Figure 1,
which is a schematic plot of the cross-section of this type ofsystem, depicts the main microphysical processes associatedwith particle formation and growth (adapted from Houze,1989). The ‘convective region’ shown in Figure 1 has a width
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Figure 1. Schematic plot of a typical squall line. Copied from Fig. 2 in Houze (1989).

type of linear structure can be realistically captured
with a computationally efficient 2D model as usedin this study (i.e. Weisman et al., 1988; Fovell andDailey, 1995; Parker and Johnson, 2004). However,
3D simulations are still required in order to simulate
asymmetrical development of squall lines, e.g. asquall line with right-flank supercells (Dudhia andMoncrieff, 1989). Furthermore, Cotton et al. (1995)
suggested that a 2D framework cannot simulate thecross-squall flow of mid-level air that is evident intheir 3D simulation.

of 20–30 km. The trailing ‘stratiform region’ can extend
to more than 100 km. Several reasons make this type ofprecipitation system ideal for evaluating our bin scheme
cloud-resolving model using TRMM satellite observations:• First of all, both the coverage and resolution of the
TRMM satellite are suitable for observing large squall
systems. The TMI conical scanning has a swath of878 km (after the satellite orbit boost in August 2001,
and slightly narrower before that), which is large
enough to capture a typical squall system within its
overpass. PR has a narrower swath of 247 km (after
the orbit boost), which is marginal for covering asquall system. But the 5 km footprint of TRMM
PR with 0.25 km vertical resolution offers excellent
sampling, especially in the homogeneous stratiform
region, which is the emphasis of this study.
• Secondly, squall lines are long-lived systems with aquasi-steady mature stage that lasts from several tomore than ten hours. The mature stage of a squall line
has very robust structures, which are exploited in thisstudy to expand the satellite dataset and provide good
statistics. In addition, the mature stage is well captured
by idealized cloud-resolving model simulations. In
this study, we compare only the mature stage of thesquall line, which takes out the many uncertainties
associated with an individual cloud’s life cycle, as
well as the impact of a ‘cold’ start (i.e. cool pool
initialization) in our simulation.
• Thirdly, the extensive, homogeneous stratiform
region offers an ideal test-bed for ice-phase microphysical processes. As shown in Figure 1, the icehydrometeors generated in the deep convection are
advected back to the stratiform region, where theyfurther grow by deposition, aggregation, and less frequently, by riming while falling through a deep layerof weak ascending motion of ∼10 cm/s. In our simulation, there is very little liquid water in the stratiform
region. Ice-phase particle growth in the stratiform
region involves exclusively deposition and aggregation/splintering. These provide very useful constraints
when improving the model ice-phase microphysics.
• Lastly, a squall line has a quasi-2D structure asshown in Figure 1. The general structure illustrated in
Figure 1 repeats itself along a line ranging from tens ofkilometres to hundreds of kilometres in length. Thisc 2010 Royal Meteorological Society
Copyright 

2.2.

Model description

The 2D anelastic version of the GCE model coupled withthe spectral bin microphysical scheme from the Hebrew
University Cloud Model (HUCM) are used in simulating
the PRE-STORM squall-line case. The model is initializedwith a single sounding taken ahead of the forming squallline. A low-level cool pool is applied for the first 10 minutes
to initialize convection (e.g. Tao et al., 1991; Trier et al.,1996). The horizontal resolution is 1 km with stretched,open lateral boundaries. No large-scale advection of water
vapour or heat is imposed in this case simulation. There are
33 stretched vertical levels with a resolution of 240 m at thelowest level and 1250 m at the top. The total integration
time is 12 hours with t = 6 s. The model achieves aquasi-steady state with cloud structure similar to Figure 1
after about 6 hours. Only the quasi-steady-state data (6 to12 hours in our simulation) are used in this study. For
detailed descriptions of storm evolution and structure, thereaders are referred to Li et al. (2009).
The HUCM bin microphysical scheme explicitly simulates
size spectra of seven hydrometeor types: cloud/rain,
three types of ice crystals (plate, column and dendrite),snow/aggregates, graupel, hail/frozen drops, as well as
Cloud Condensation Nuclei (CCN). There are 33 size bins
representing each species’ size spectrum. Both cloud andice nucleation, diffusional growth of water and ice phase,drop–drop, drop–ice, and ice–ice collision/coalescence, ice
multiplication, collisional break-up of raindrops, freezing,and melting are represented explicitly in this model. Detailsof the HUCM bin scheme can be found in Khain and Sednev(1996) and Khain et al. (2000, 2004).
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Improving Spectral Bin Microphysics Using Trmm

2.3.

Forward radiative transfer calculations

For comparing direct satellite observations with model
simulations, one needs to use a forward radiative transfer
model to calculate the observed satellite signals using
simulated hydrometeor profiles and size distributions.
The Goddard Satellite Data Simulation Unit (SDSU:
Matsui et al., 2009) is used in this study. The SDSU
simulates satellite-consistent radiances or backscattering
using GCE model output. Currently, there are simulators forpassive microwave, radar, passive visible–infrared, Lidar,
broadband short-wave and long-wave, as well as ISCCPlike (International Satellite Cloud Climatology Project)observations within the unit. Here we use the passive
microwave and radar simulators. The 85 GHz TMI
brightness temperatures (BTs) are simulated using deltaEddington two-stream radiative transfer with slant pathview (Kummerow, 1993; Olson and Kummerow, 1996).
The 14 GHz TRMM PR reflectivity is calculated according
to Masunaga and Kummerow (2005). A derivation of theradar equation is also given in detail in Masunaga andKummerow (2005). For both the passive microwave andactive radar simulator, the electromagnetic properties ofsimulated hydrometeor profiles are calculated via Mie theory(spherical assumption). The dielectric function of a melting
particle uses the Maxwell–Garnet formula (e.g. Bohren
and Battan, 1980). Simulated BTs and radar reflectivity are
convolved within the TRMM instruments’ instantaneous
field of view through a Gaussian beam pattern. TRMM PR
data used in this study are attenuation-corrected. Therefore
SDSU does not include attenuation in radar reflectivity
calculations. Surface emissivity for TMI simulation uses theaverage value within the same data box during August 2006
TRMM observations (Karbou, 2008). The upward pointing
surface C-band radar reflectivity is simulated using the sameradar simulator, but at the corresponding wavelength of
5.5 cm and surface operating mode.
3.

Model evaluation

3.1.

Data

Two sets of data are used for model evaluation: two timeframes of gridded ground-based C-band radar data during
the mature stage of the PRE-STORM experiment, and thenine years of TRMM satellite observations (1998–2006) of
the squall lines over southern central USA.
3.1.1. Surface radar
Figure 2 shows radar reflectivity measured by the C-bandradar at 01:39:00 and 03:44:59 UTC on 11 June 1985, during
the mature stage of the PRE-STORM squall line. Figure 2(a)catches the whole system with a bowed leading edge anda stratiform region extending more than 100 km in width.
Figure 2(b) shows only the stratiform region of the same
system more than two hours later. The leading edge is again
to the right of the system. The vertical cross-section along
the black line in Figure 2(a) is plotted in Figure 2(c), whichclosely resembles the schematic plot shown in Figure 1, as
well as the simulated radar reflectivity during the mature
stage, as shown in Figure 2(h). The Contoured Frequency
with Altitude Diagrams (CFADs: Yuter and Houze, 1995)
are used for quantitative comparisons between observations
c 2010 Royal Meteorological Society
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385

by radar and model simulations. The CFADs represent
frequency distributions at each height for the 3D radarobservations, as shown in Figure 2(e), (f) and (g). Figure 2(e)and (f) are for the stratiform and convective region in
Figure 2(a), respectively. The stratiform CFADs at both timeframes show similar features. Above the melting level, theradar reflectivity shows remarkable homogeneity. The vast
majority of the data points cluster within a narrow band of±3 dBZ, which decreases from about 25 dBZ right above
the melting band to10 dBZ at about 11 km. The CFADs
have more scatter below the melting band, but still show the
majority of data points between 25 to 35 dBZ, with a slight
trend of decreasing intensity with decreasing height. The
convective region CFADs, on the other hand, have muchwider scatter, about 20 dBZ, throughout different heights
as shown in Figure 2(f). Although CFADs in the convective
region can provide some qualitative information when used
for model validation, the uncertainty becomes much larger
compared with using stratiform CFADs. For this reason, weconcentrate on analysing radar CFADs for the stratiform
region only. Another reason for using only the stratiform
region is that TRMM PR has a marginal resolution in
detecting single convective cores, which when used, adds
another degree of uncertainty to model validation.
3.1.2.

TRMM data

The TRMM satellite carries a suite of sensors for rainfall
measurement. We use the two major quantitative rainfall
measure sensors: the microwave imager TMI, and the Kuband Precipitation Radar. As stated in section 1, only direct
measurements are used for model validation. For PR, we
use attenuation-corrected radar reflectivity. For TMI, we use
85 GHz Polarization Corrected Temperature (PCT) definedas PCT = (βTBH − TBV )/(β − 1), where β has a fixed valueof 0.45 according to Spencer et al. (1989), and TBH and
TBV are horizontally and vertically polarized brightness
temperatures. Other TRMM rainfall measurements areinvestigated, but they turn out to be either heavily
contaminated by surface emission (e.g. 37 GHz BT overland), or too noisy (e.g. the PR path-integrated attenuationin the stratiform region) to be used confidently for model
validation.
This study takes advantage of the University of Utah
TRMM precipitation feature database (Nesbitt et al., 2000;
Liu et al., 2008). The first step is to identify squall lines
similar to the PRE-STORM case at the same geographic
location around the same time over nine years of TRMM
measurements. Figure 3 shows our study region that is
enclosed by the dashed lines (90◦W–103◦ W, 31◦ N–39.5◦ N).
It encompasses the southern Great Plains and the central
plain that are between the Rocky Mountains and theAppalachians. Previous studies (e.g. Velasco and Fritsch,1987) show that this is the area where most of themesoscale convective complexes occur. Also, the locationof these mesoscale convective complexes tends to be overthe southern plains during late spring and moves up north inlate summer/early autumn. Our northern edge is confinedby TRMM TMI’s range to about 40◦ N. TRMM PR has anarrower range (up to 36◦ N) that is represented by the thinsolid line. The southern edge is chosen so that coastlines andlocal convection triggered by the coastal circulations can be
avoided. The shaded area in Figure 3 covers the PRE-STORM
squall-line track over its 9-hour development (2300 UTC 10
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Figure 2. C-band surface radar observations during PRE-STORM and comparison with model simulation. (a) Surface radar reflectivity at 01:39:00 UTC
11 June 1985; (b) Same as (a) except at 03:44:59 UTC; (c) radar reflectivity cross-section along the black line in (a); (d) radar reflectivity cross-section
along the black line in (b); (e) radar CFAD for the stratiform region in (a); (f) radar CFAD for the convective region in (a); (g) radar CFAD for the
stratiform region in (b); (h) radar reflectivity simulated by 2D GCE model at t = 12 hours. (Radar data courtesy of Robert A. Houze Jr and Jasmine
Cetrone at University of Washington, Seattle).

June to 0800 UTC 11 June 1985). All mesoscale convective
systems as defined in the University of Utah database duringlate spring and early summer (1 May–31 July) over the
9-year period are visually examined to identify squall lines.
Only TMI images are used for system identification becauseof their good coverage. Convection is defined when the
85 GHz PCT of a system is below 180 K. To qualify as asquall line, a continuous band of convection has to be atleast 100 km in length and has a length-to-width ratio ofat least 4. Among over 500 mesoscale convective systemcases in the database, 51 cases are identified as squall lines.
Since our study uses only the mature stage simulations witha significant stratiform region, we further require the total
width of the identified squall line to be at least 3 times thewidth of its convective line. Using these criteria, a total of
41 squall lines have a significant stratiform region. These
41 cases form the base of the TMI brightness temperatureevaluation.
Figure 4 shows three examples of TRMM-observed squalllines. They include two basic types: the symmetric (thefirst two columns) and the asymmetric (the third column)(Houze, et al., 1990). The symmetric system has an evenly
distributed convective line with new cells regenerating aheadof its leading edge. The stratiform region has its centrec 2010 Royal Meteorological Society
Copyright Figure 3. US map with dashed-line frame representing the TMI data range,
and the solid-line frame within it, the PR data range. The shaded area isthe propagation track of the PRE-STORM squall-line case over its 9-hour
evolution.

directly behind the convective line. The asymmetric system
has stronger, newly developed convection at one end (thesouthwest) and weaker, dissipating convection at the otherend. The centre of its stratiform region is also biased toward
the northeast – the weaker convection end. Among the
41 cases identified as mature-stage squall lines, 32 aresymmetric and 9 are asymmetric. The PRE-STORM case
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Improving Spectral Bin Microphysics Using Trmm

387

Figure 4. Three examples of TRMM-observed squall lines over the area described in Figure 3. Each column represents one case. The first row (a)–(c) shows
images of 85 GHz PCT with 40 dBZ (black lines) and 20 dBZ (grey line) surface radar reflectivity overlaid. The second row (d)–(f) is the corresponding
radar reflectivity cross-sections along the red lines in the first row. The third row (g)–(l) shows radar reflectivity CFADs for each case. The stratiform
CFADs are on the left-hand side and the convective CFADs are on the right-hand side. The fourth row (m)–(o) is the probability density distributionsof 85 GHz PCT, binned in 10 K intervals, for the whole system without distinguishing convective and stratiform.

shown in Figure 2(a) is a symmetric system. However, as
far as the cross-section of a squall is concerned, which ismost relevant to 2D model simulations, both types of squallline have the same structure as shown in Figure 1. This is
the reason that we include the 9 asymmetric systems in ourcomparison. PR stratiform CFADs show little differences
between the symmetric and asymmetric systems. The TMI
probability density distributions in asymmetric systems havea flatter tail at the high-BT end compared with symmetriccases (cf. Figure 4(m), (n) and (o)). But the difference does
not affect the ensemble of probability density functions usedin our comparison study.
The first two columns in Figure 4 are the same systemobserved at different times. Figure 4(a) and (b) are about
an hour and a half apart and demonstrate the steadydevelopment of a mature squall line. The first row in Figure 4
shows images of 85 GHz PCT with the 40 dBZ PR surfacec 2010 Royal Meteorological Society
Copyright reflectivity overlaid as black contours and the 20 dBZ as grey
contours. The radar has excellent coverage for these twocases. Radar reflectivity cross-sections along the red lines in
Figure 4(a), (b) and (c) are shown in the second row. One
can clearly see the resemblance between these radar images
and the C-band radar observation in Figure 2, as well as
the schematic plot in Figure 1. CFADs of radar reflectivity
are plotted in the third row, again separated by stratiform
and convective region. The stratiform region is defined asrain-type flag equal to 100 (stratiform identified by bothvertical profile and horizontal pattern) in TRMM version
6 product 2A23. All convective-certain flags (200, 210 and220) are used for convective CFADs plots. Since a squall line
has a very clear-cut separation between the convective andstratiform regions, CFADs plots are not sensitive to different
definitions of convective and stratiform types in either the
TRMM product or model separation methods. Similar to
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Figure 5. Comparisons between observations (upper row) and model simulations (lower row). (a) Surface C-band radar CFAD in stratiform region at
01:39:00 UTC 11 June 1985; (b) TRMM PR CFAD in stratiform region for 28 squall-line cases over 9 years; (c) TRMM TMI 85 GHz PCT probability
density distribution for 41 squall-line cases; (d) simulated C-band radar CFAD in stratiform region during the mature stage of the PRE-STORM
case-study; (e) same as (d) except for the TRMM PR frequency and field of view; (f) simulated TRMM TMI 85 GHz PCT probability density distribution
during the mature stage of the system.

surface C-band radar in Figure 2, stratiform CFADs in
Figure 4 show very narrow distributions and consistentfeatures for all three cases. In contrast, significantly morevariations are seen in convective CFADs. The probability
density distributions of 85 GHz PCT are plotted in the
fourth row of Figure 4(m), (n) and (o). The PCTs arebinned in 10 K intervals and the highest value is cut at
260 K to avoid excessive surface contamination. Since themicrowave imager does not provide enough information to
separate convective from stratiform regions, the plots are forthe whole system. Despite variations in detailed distributions
for each case, several characteristics show up consistently.
First, the vast majority of the data points lie above 200 K.
Even for a system as strong as the asymmetric case, only
less than 10% of data are below 200 K. Second, the PCT
distributions are not smooth, in that there is a large jumpin the distributions between 200 and 220 K. This is very
consistent behaviour for all the mature-stage squall lines inthis study, as will be shown in the next section.
The asymmetric case in Figure 4(c) also represents
a situation with limited PR coverage. Since PR has amuch narrower swath than TMI, only 28 out of the 41
identified mature squall lines have some radar coveragein the stratiform region and are used for compiling thestratiform radar reflectivity CFADs. Figure 4(c) represents
the borderline stratiform coverage. Any case with radar
coverage less than this is rejected. One can see that thestratiform CFADs in Figure 4(k) are blotchy comparedwith Figure 4(g) and (i) because of their limited data size,
although the main features remain consistent. The outlier
bands above 5 km in the stratiform CFAD plot are producedby the small rain area to the west of the main system, whichmight be remnants of earlier convection. The ‘hook’ at thesouth end of this squall line has the strongest convection;c 2010 Royal Meteorological Society
Copyright such hooks are often associated with strong surface winds
and tornados (e.g. Fujita, 1981; Weisman, 1993).
3.2.

Comparisons

Radar reflectivity CFADs comparisons among surface radar,
TRMM PR and simulated reflectivity are shown in Figure 5.
The lowest reflectivity is cut at 10 dBZ for the C-bandradar and 20 dBZ for PR according to their sensitivities. As
discussed in the previous section, only the stratiform region
radar data are used for model evaluations. Figure 5(a)is the radar reflectivity CFADs at 01:39:00 UTC 11 June
1985. Figure 5(d) is the simulated C-band radar reflectivity
during the mature stage of the simulation (6–12 hours) with
output every 5 minutes. All seven hydrometeor types in thebin model are included for the forward radiative transfer
calculation. Figure 5(b) is the composite of stratiform
reflectivity CFADs of all 28 identified cases with stratiform
PR coverage, and Figure 5(e) is the simulations using thesame hydrometeor outputs as in Figure 5(d), except at PR
frequency of 13.8 GHz.
Despite the fact that Figure 5(b) is the composite of
28 different cases over a 9-year period, it shows goodconsistency and the same features as a single squall line (cf.
Figure 4(g), (i) and (k)). This confirms the robust structurein the homogeneous stratiform region. For example, radarreflectivity remains below 30 dBZ above the melting level in
Figure 5(b), and decreases roughly linearly down to 20 dBZ
at around 9 km. C-band radar CFADs in Figure 5(a) show
similar features, but are slightly weaker than the TRMM
composite.
Model simulations obviously overestimate radar reflectivity compared with both surface C-band radar (Figure 5(d))
and PR (Figure 5(e)). Surface radar reflectivity is more than
10 dBZ higher at both frequencies. Above the melting level,
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Improving Spectral Bin Microphysics Using Trmm(a) hail

389(c) snow aggregates(b) graupel

Figure 6. Simulated PR reflectivity for single ice-phase species: (a) hail; (b) graupel; and (c) snow aggregates, at the end of the 12-hour simulation.

for ice-phase particles, radar reflectivity remains more than
10 dBZ higher at C-band. The differences between simulations and TRMM PR observations are about 5 dBZ. Between
4 km and 7 km, simulated radar reflectivity profiles stay moreor less vertical, indicating almost constant reflectivity in thisregion, in contrast to the linear increasing trend observedin both C-band and PR. Above 7 km, both Figure 5(d) and(e) have more rapid linear decrease, which ultimately leadto a reasonable radar reflectivity range at around 10 km
compared with observations.
The simulated 85 GHz TMI PCT compares reasonably
well with TRMM observations, as shown in Figure 5(c)and (f). Figure 5(c) is the composite of probability density
distributions for all 41 cases. As with single cases in Figure 4,
one finds a clear jump of frequency of occurrence at around
220 K. The simulation also shows a nice match of the jumpat around 220 K. However, its frequencies below 200 K PCT
have higher values than the observations. After the jump, thefrequencies taper down instead of increasing continuously
as in Figure 5(c). As a result, the mean simulated 85 GHz
PCT is about 11 K lower than the TRMM composite.
However, some of these differences can be attributed to the2D geometry used in the simulation, where there is only oneedge area (with relatively high BT) in the stratiform region,
compared with three in a realistic 3D situation. This can also
be seen from comparing Figure 4(o) to Figure 4(m) and (n).
In the asymmetric system in Figure 4(o), the edge area issmaller compared with the symmetric system in Figure 4(m)and (n), and thus the tapering off of the PCT distribution at
the high-value tail.
4.

Bin microphysical scheme improvements

4.1.

Diagnoses

Figure 5(d) and (e) indicate high concentrations of largeraindrops simulated by the model near the surface, which
produce more than 10 dBZ overestimation of surface
radar reflectivity on average. Since rainfall rates in thestratiform region are generally below 6 mm/h, the raindrop
collision/coalescence process plays a relatively small role inshaping its size distribution. The simulated large raindrops
mainly come from melted large ice-phase particles, as
indicated by large radar reflectivity above the melting level.
In order to identify the source(s) of large ice-phase particles,
Figure 6 shows simulated radar reflectivity of single ice-phase
species at t = 12 hours. It is readily seen that both hail andgraupel are confined mainly to the convective region and thetransitional zone immediately behind it. Snow aggregates are
by far the dominant species contributing to radar reflectivity
signals in the upper stratiform region. Pristine crystals are
not shown because they contribute very little to the total PR
signal, although they are still included when calculating thetotal simulated radar reflectivity.
The main source of stratiform ice-phase particles isthe detrainment from leading convection. These detrained
particles further grow by deposition and aggregation in
the stratiform region until they reach the melting level,as illustrated in Figure 1. Since growth by deposition islimited by the mean updraught, which compares well withobservations (Li et al., 2009), one concludes that growthby aggregation should be overestimated, especially at upper
levels. As shown in Figure 5(d) and (e), simulated radarreflectivity increases much faster with decreasing heightcompared with the corresponding observations until about
6 km. At that point, snow aggregates become so large that thedifferences of their fall velocities start diminishing because
the terminal fall velocity of snow aggregates approaches aconstant value as their sizes increase. This prevents further
increases of the mean particle size by aggregation. From
6 km to around 4 km, simulated radar reflectivity remains
roughly constant, which is not observed in either ground or
spaceborne radar.

The comparison between observations and model simulations in Figure 5 shows large discrepancies in radarreflectivity profiles. This clearly indicates the need for
improvements in model simulations. There are many uncertainties inherent in the cloud model simulations, ranging
from numerical errors to physical uncertainties. Since previous studies of the same case (Li et al., 2009) show goodcomparisons in model kinematics and dynamics, here wefocus on analysing uncertainties in the bin microphysicalscheme itself, which is most relevant and sensitive to the
TRMM satellite observations. Even within microphysics,
solutions are far from unique based on the limited constraints provided by observations. Our approach to this 4.2. Improvements
problem is that, with a clear physical understanding, we
will do the least possible amount of adjustment in pro- Growth rates of snow aggregates by collection are
cesses/parameters to improve the comparisons.
represented by the stochastic collection equation (e.g.
c 2010 Royal Meteorological Society
Copyright 

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390

X. Li et al.

Pruppacher and Klett, 1997) in the bin scheme:
mk =mi +mj

1
dnk
=
dt
2



∞
Kk−j,j nk−j nj dmj − nk0

Kkj nj dmj ,0where nk is the number concentration of particles withmass mk ; Kij is the collection kernel of two particles withmass mi and mj . Assuming a geometric sweep-out kernel:
Kij =


2 
π
D i + D j  v i − v j  Ec ,4

where Di and vi are the diameter and terminal fall velocityof an ice particle with mass mi . Ec is the collection efficiency,
which itself depends on temperature, humidity, shapes andsizes of various ice particles. There are many uncertainties
associated with each variable in Kij . For example, densities
of snow aggregates vary by a factor of more than 2 indifferent measurements (e.g. Mitchell, 1994; Brandes et al.,2007). Terminal fall velocity of various ice-phase particles
can be determined either by observations (e.g. Locatelliand Hobbs, 1974; Heymsfield, 2003; Brandes et al., 2008)
or numerical calculations (e.g. Böhm, 1989; Mitchell andHeymsfield, 2005) and the results also vary by several factors.
In addition, irregular ice particles tumble along their falling
path, with oscillating fall velocities.
Collection efficiency Ec is by far the most uncertain factor
in collection kernel Kij . While uncertainties in densities andterminal fall velocities are generally within several-fold, Ec
measurements vary by orders of magnitudes. Figure 7 shows
examples of both measurements and model specifications
for Ec (T). The grey boxes are values of Ec from various
laboratory experiments, summarized in Pruppacher and
Klett (1997), fig. 14–18. Note these experiments were donein the 1960s and 1970s and most of them used ice spheresas collectors. Temperatures in these experiments are also
relatively warm. Airborne image sensors were later used toderive Ec . Some studies used statistics of the images (e.g.
Kajikawa and Heymsfield, 1989), others used co-ordinatedflight paths and aggregation models (e.g. Passarelli, 1978;
Field and Heymsfield, 2003; Field et al., 2006). Even using
the same method, the measured Ec still vary by magnitudes
in some cases, as shown in Figure 7. Apparently more basic
research is needed to determine these collection efficiencies.
With such a wide range in Ec values, more sophisticatedmodels (two-moment, bin spectral) used in situ observations
to try to constrain it. Figure 7 lists some results ofthese models. Cotton et al. (1986) experimented with
Ec formulations using an exponential fit from laboratory
measurements by Hallgren and Hosler (1960) (dash-dottedline in Figure 7) and aircraft observations by Passarelli (1978)
in a cloud-resolving model and compared their results
to surface observations. Mitchell (1988) used comparisons
between his snow growth model and aircraft observations
and decided on Ec = 0.1 for all species when relative
humidity is below water saturation. When relative humidity
is above water saturation, Ec varied between 0.1 and 1
depending on temperature and shapes of particles. Again,
there is no consensus in model simulations.
There is observational evidence that Ec also depends on
relative humidity (e.g. Hosler et al., 1957), but very little
quantitative information is available. In our model, Ec varies
c 2010 Royal Meteorological Society
Copyright Figure 7. Ice particle collection efficiency vs. temperature. The grey boxes
indicate ranges of Pruppacher and Klett (1997)’s summary of laboratory
measurements. Boxes and lines with asterisks in/on them are derived fromaircraft measurements. Each box represents the ranges of one particularmeasurement and each asterisk represents the mean value. The lines are thecollection efficiencies used in various cloud models (either bin spectral or
two-moment) that specifically compared modelled ice particle sizes withobservations: the dashed line is the original curve used in the spectral bin
scheme in the GCE model; the solid line is the revised curve that improves
radar reflectivity comparison in experiment ‘Ec’; the dash-dot-dot-dot line
is used in experiment ‘graup’ where both radar reflectivity and 85 GHz
PCT compare well with observations. The dotted line (Ec = 0.1) and thedash-dotted line are from two other model simulations: one is Mitchell(1988), the other is Cotton et al. (1986).

linearly with relative humidity with respect to ice. Sensitivity
tests (not plotted) on Ec variations with relative humidity(RH) do not improve comparisons, therefore the original
formulation is retained. Future laboratory studies are needed
to resolve this issue. The temperature dependence of Ec in
our original scheme is plotted in Figure 7 as the dashedline. They are the combinations of fitting and extrapolationsof measurements (Khain and Sednev, 1996). The bump-up
of Ec between −17◦ C and −12◦ C represents the observedhigh aggregation level due to dendrite formations (e.g.
Ohtake, 1970; Passarelli, 1978). Note this Ec value has
been applied to aggregational growth of all ice species withdifferent shapes, which is a questionable assumption andneeds further study.
Previous discussions focus on source terms of largesnow aggregates. Alternatively, it is possible to add asink term in the aggregates’ growth equation. Since radarreflectivity is proportional to the sixth power of particle
diameter, very large snow aggregates dominate radar signals.
Assuming these large particles are unstable, they may breakup spontaneously or upon collision with other particles,
thus produce lower radar reflectivity. This process is notconsidered in the original bin microphysical scheme.
Many sensitivity tests are performed in order toreduce discrepancies between radar observations andmodel simulations. We present here three independent
approaches. Experiment ‘rho vt’ increases bulk densitiesof large snow aggregates and their terminal fall velocities
within their uncertainty ranges. Experiment ‘Ec’ reduces icephase particles’ collection kernel by modifying temperaturedependency on collection efficiency Ec . Experiment‘sbreakup’ adds a simple break-up scheme for large snow
aggregates to reduce their mass density.
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Improving Spectral Bin Microphysics Using Trmm

391

‘Ec’ improved all qualitative features in radar CFADs
comparisons. For example, radar reflectivity increases
linearly with decreasing height above the melting bandfor both radar frequencies. Radar reflectivity profiles havealso substantially lower values, with the mean dBZ now inline with observations.
4.2.3.

Figure 8. Bulk densities and terminal fall velocities of snow aggregatesused in the bin microphysical scheme. The radius along the x-axis is theequivalent drop radius of a melted particle. Bulk densities decrease with size
while terminal velocities increase with size. The solid lines are the values
used in the original bin scheme, while the dashed lines are the modified
values in sensitivity experiment ‘rho vt’.

4.2.1. Bulk density and terminal fall velocity
Several model simulations have been carried out where snow
aggregates’ densities and/or their fall velocities are increased.
Increasing snow bulk density reduces its collection crosssection. Increasing terminal fall velocities of large particles
removes them quickly from the upper levels in stratiform
region. Variations of snow aggregates’ density and terminal
fall velocity with their sizes in the original scheme areplotted in Figure 8 in solid lines. In experiment ‘rho vt’,the minimum density for aggregates is set at 0.2 g cm−3 ,in contrast to 0.03 g cm−3 in the original scheme (dashedline in Figure 8). This is more than doubling of aggregates’
bulk density for particles larger than about 0.6 mm. In themeantime, all particles’ terminal fall velocities are doubled,as also shown in Figure 8. The simulated radar reflectivity
and 85 GHz BT statistics are shown in Figure 9(a) (C-bandradar reflectivity CFADs), 9(b) (PR reflectivity CFADs),
and 9(c) (TMI 85 GHz PCT distributions). Comparing thefirst row of Figure 9 with plots in Figure 5, one finds that
although experiment ‘rho vt’ reduces radar reflectivity inthe stratiform region by several dB, it is still considerably
higher than observations, especially above the melting level.
The slopes of the increasing radar reflectivity with decreasingheights are similarly curved as in the control run, in contrast
to the observed linear slope in both surface and TRMM
radar.
4.2.2. Temperature dependency of Ec
Another set of sensitivity simulations are carried out
on Ec (T). Experiment ‘Ec’ represents our best matchamong many trials. Ec (T) used in this simulation isplotted as the solid line in Figure 7. When warmer than−6◦ C, the revised Ec (T) are in range with measurements.
However, Ec (T) have to be reduced drastically from their
original values at lower temperatures in order for the
stratiform region radar reflectivity to match observations.
The middle row in Figure 9 is the simulated C-band(9(d)) and PR (9(e)) reflectivity CFADs, and 85 GHz
PCT distributions (9(f)). Compared with the original
simulations shown in Figure 5(d) and (e), experimentc 2010 Royal Meteorological Society
Copyright Break-up of large snow aggregates

Experiment ‘sbreakup’ is one of our tests to add a sinkterm to the snow aggregate growth equation in order toreduce the simulated snow aggregate size. Break-ups oflarge pristine snow crystals have been widely observed,
but there are no quantitative measurements of how largesnow aggregates would break up, either spontaneously or
through collisions. In this experiment, a simple binary breakup procedure is added to the original bin microphysicalscheme. A constant probability is assigned to the largestof the particles, with its value decreasing with decreasing
particle sizes, down to zero at a certain size. Each break-up
event results in two smaller particles of equal mass. The lastrow in Figure 9 shows results from experiment ‘sbreakup’.
In this simulation, the probability of aggregates’ break-up
decreases linearly from 0.8 for particles with melted radiusof 3 mm down to 0 for particles with melted radius of
0.5 mm. There is no break-up for particles smaller than
0.5 mm.
Figure 9(g) and (h) show that adding a simple breakup scheme lowers radar reflectivity values, both at thesurface and above the melting level. The maximum radarreflectivity above the melting level is less than 30 dBZ for
both C-band and PR radar, consistent with observations
shown in Figure 5(a) and (b). However, experiment‘sbreakup’ cannot reproduce the linear slope of radar
CFADs shown in both observations and experiment ‘Ec’.
The high growth rate above 7 km results in a fast increaseof radar reflectivity along the particles’ falling paths. Only
after aggregates become large enough does the break-up
process kick in and keep the radar reflectivity value below
30 dBZ.
4.3.

New discrepancy in 85 GHz BT and its diagnosis

All three sensitivity experiments described in the previous
subsection more or less reduced mean snow aggregate size,
and therefore radar reflectivity in the stratiform region, as
shown in Figure 9. However, all of them have produced
decidedly worse comparisons in 85 GHz PCT distributions.
The distributions simulated in the control run (Figure 5(f))
compare well with TRMM statistics (Figure 5(c)). In thesensitivity simulations, however, the distinct jump around
220 K in the control experiment is completely missing(Figure 9(c), (f) and (i)). PCT distributions in Figure 9
increase rather smoothly to a weak peak at around 180 K.
The mean BT is also reduced from 213 K in the control run
down to 197–200 K, further away from the observed 224 K
mean. This is a common problem in ‘tuning’ a microphysicalscheme according to a single set of observations; one fixes
one thing by breaking another. It also shows the intricate
relationships between different microphysical processes andtheir interactions with dynamics. In this section, we try toisolate the reasons for these discrepancies and search for a
possible solution.
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X. Li et al.

Figure 9. Simulated results from three sensitivity simulations. (a) C-band radar CFADs for experiment ‘rho vt’; (b) TRMM PR CFADs for experiment‘rho vt’; (c) TMI 85 GHz PCT probability density distributions for experiment ‘rho vt’; (d) C-band radar CFADs for experiment ‘Ec’; (e) TRMM
PR CFADs for experiment ‘Ec’; (f) TMI 85 GHz PCT probability density distributions for experiment ‘Ec’; (g) C-band radar CFADs for experiment‘sbreakup’; (h) TRMM PR CFADs for experiment ‘sbreakup’; (i) TMI 85 GHz PCT probability density distributions for experiment ‘sbreakup’.

Unlike radar reflectivity at mid-level stratiform regions,where snow aggregates dominate the signal, a microwave
radiometer observes column integrations of emission andscattering of radiances by all hydrometeor species, in bothwater- and ice-phase. Different species contribute to the BT
signal in different ways depending on their phases, sizes,
shapes, densities and associated electromagnetic properties.
At 85 GHz over land, TMI observes BT depression over a
warm surface background. A higher amount of ice content ina column generally means lower BT. When BT is calculated
for individual species, their contributions are more or lesscomparable. Therefore, we focus our analyses on finding
the species that has the largest change in favour of lowering
85 GHz BT in experiment ‘Ec’, which turns out to be
graupel. Figure 10 is an example of instantaneous number
concentration and mass content of graupel in the control
run and experiment ‘Ec’, at t = 12 hours. After adjusting
Ec (T), graupel remains at slightly lower heights and its
total amount decreases. However, the most dramatic change
comes in its number concentrations. In the convective
core, graupel number concentration decreases from morethan 100 L−1 in the control run down to about 30 L−1
in experiment ‘Ec’. In the stratiform region, it decreases
from about 20 L−1 to about 10 L−1 . The resulting 20–30%
c 2010 Royal Meteorological Society
Copyright increase in the mean graupel size is the main reason for thedecrease of mean 85 GHz PCT, as well as the shifting of its
distribution. In addition, a large increase of ice crystals inboth amount and size contributes to the BT depression (cf.
Figure 11(a) and (b)), but to a lesser extent compared withgraupel.
4.4.

Further improvements of microphysical scheme

In order to improve the 85 GHz PCT comparisons,we need to understand the causes of increasing mean
graupel size, after the mean sizes of snow aggregatesare reduced. Figure 11 shows vertical profiles of varioushydrometeor species averaged over the mature stage for threedifferent simulations carried out in this study. Comparing
Figure 11(a) and 11(b) one finds that by reducing Ec (T) in
experiment ‘Ec’, a large amount of ice content is shifted fromsnow aggregates to pristine crystals, especially between 5 and
10 km. This shift affects graupel formation in two ways: First,
compared with large snow aggregates, small ice particles
interact less efficiently with supercooled cloud droplets inthe convective region to form graupel. As a result, fewer
graupel are formed in the convective region. This leaves more
supercooled water available for the Bergeron–Findeisen
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Improving Spectral Bin Microphysics Using Trmm

393

Figure 10. Instantaneous graupel number concentration in the control run (a) and experiment ‘Ec’ (b) at the end modelling time. The contour lines are
10, 20, 50, 100, 200 and 500 L−3 . Graupel mass contents at the same time are plotted in (c) for the control run and (d) for experiment ‘Ec’. The contour
lines are 0.1, 0.2, 0.5, 1, 2 and 5 g m−3 .

Figure 11. Mean vertical profiles of various hydrometeors during the mature stage of the simulated squall line for three experiments: (a) control run;(b) experiment ‘Ec’; and (c) experiment ‘graup’. Long dashed lines represent cloud water; solid lines represent rain water at lower heights and ice crystal
at upper heights; short dashed lines represent snow aggregates; dash-dot lines represent graupel; dash-dot-dot-dot lines represent hail; and the grey solidline represent plate-shaped ice crystals which is the dominant type among the three different pristine ice species.

process (the depositional growth of ice-phase particles atthe expenses of evaporation of water-phase particles). As aresult, mean sizes of both graupel and pristine ice becomelarger in experiment ‘Ec’ compared with the control run(cf. Figure 10). This leads to the reduction of the 85 GHz BT.
On the other hand, when the amount of snow aggregatesis reduced, the only sink term for graupel, i.e. its collection
by large snow aggregates to form snow particles, is reduced
as well. Thus fewer graupel stays longer with the system
without being removed in experiment ‘Ec’. These relatively
large graupel are detrained to the stratiform region, causingc 2010 Royal Meteorological Society
Copyright 

reduction and redistribution of 85 GHz BT as shown in
Figure 9(c).
In this section, we attempt to modify the bin scheme toform more, smaller graupel while keeping the size of snow
aggregates in check. Numerous sensitivity tests have been
carried out to study the interactions between water- andice-phase particles to form graupel. Again, there may be
multiple solutions to this problem. Similar to discussions
in section 4.2, we attempt to achieve the goal with theleast amount of modification based on physics. Experiment‘graup’ represents our best result under this philosophy.
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X. Li et al.

Figure 12. Same as Figure 9, except for experiment ‘graup’.

In our bin microphysical scheme, one of the uncertainties
in graupel formation comes from the subjective thresholds
where the end product of coalescence of ice- and waterphase particles is assigned. For example, in the bin scheme,
snow aggregates collecting cloud droplets may form either
graupel or snow. When cloud liquid content is larger than
1 g m−3 , the end product is graupel. When cloud liquid
content is less than 1 g m−3 , the end product can beeither aggregates or graupel depending on its size. The
threshold size is set at the 17th size bin (2.2 × 10−6 g) in
the original scheme where particles smaller than that size
remain as aggregates. As previously noted, these thresholds
are empirically based and subjective. Two thresholds havebeen modified in experiment ‘graup’. First, the size thresholdseparating aggregates from graupel as the end productof snow aggregates collecting cloud droplets is increased
from the 17th to the 22nd size bin (7.0 × 10−5 g). This
modification reduces formation of medium-size graupel
which fall slowly enough to affect the 85 GHz BT in thestratiform region. Graupel larger than 7.0 × 10−5 g generally
precipitate out quickly, thus have little impact on thestratiform BT. To increase graupel number concentration,
similar modification is also applied to ice crystal collecting
cloud droplets, in the direction of increasing small graupel
concentrations. When ice crystals collect cloud droplets,
smaller particles remain as crystals, while larger ones become
graupel. In experiment ‘graup’, the threshold is lowered fromthe 17th to the 13th size bin (1.4 × 10−7 g) so that more,
smaller graupel are generated. This dramatically reduces
the total amount of ice crystals between 5 and 10 km, as
shown in Figure 11(c). At the same time, there are more,
smaller graupel in experiment ‘graup’ competing for theavailable water vapour, which further reduces mean graupel
size. In experiment ‘graup’, both snow and graupel content
increase compared with experiment ‘Ec’, at the expense of
ice crystals. Meanwhile, both surface rainfall and squall-line
structure remain similar for all three simulations as indicatedin Figure 11. Note that in experiment ‘graup’, we are able toincrease the temperature dependency of Ec compared withexperiment ‘Ec’, as shown in the dash-dot-dot-dot line in
Figure 7. Here Ec is fixed at 0.01 from −20 down to −40◦ C.
Although they are still smaller than observations, this set of
Ec represents a large increase from experiment ‘Ec’, which
adjusts temperature dependency of Ec only.
Statistics for experiment ‘graup’ are shown in Figure 12,
in the same format and scale as in Figures 5 and 9.
Radar reflectivity CFADs in Figure 12(a) and (b) arevery similar to their counterparts in Figure 9(a) and (b).
There are slight reductions in radar reflectivity, about 1–2
dBZ, in experiment ‘graup’ compared with experimentc 2010 Royal Meteorological Society
Copyright ‘Ec’. The major improvement comes in the probability
density distribution in Figure 12(c). The unrealistic PCT
peak between 170 and 180 K in Figure 9(c) is removed
in experiment ‘graup’. The majority of the data points are
shifted back to above 200 K, more closely reflecting TRMM
statistics. The mean PCT increased 21 K to 218 K, again
a much better comparison with the observation. There
are still discrepancies in details. For example, the abrupt
increase of the distribution at around 220 K in Figure 5(c)is less prominent in Figure 12(c). However, given the many
uncertainties in various aspects in the modelling otherthan microphysics, results in experiment ‘graup’ represent a
major improvement in comparisons with long-term satellite
statistics.
5.

Summary and discussion

A squall line over the central southern USA (PRE-STORM,
10–11 June 1985) is simulated using the GCE modelwith a detailed spectral bin microphysical scheme. Aftercomparisons with published, surface-based observations
and retrievals (Li et al., 2009), the model results are further
compared with ground-based C-band radar as well as PR
reflectivity and TMI 85 GHz BT from the TRMM satellite.
This study is unique in two aspects: First, it uses longterm satellite observations of robust features in squall lines,
especially in the stratiform region, whereas most model
validations use the same case-study. Second, it evaluates
and improves a bin spectral microphysical scheme which
explicitly simulates particle size distributions. Instead ofcomparing direct model output with retrieved quantities
from observations (i.e. surface rainfall, column watercontents), a forward radiative transfer model (simulator)
is used to calculate satellite-observed signals using themodelled particle size distributions. In this approach, if
discrepancies occur, as they did, the reasons are readily
linked to model physics.
It is first established that the stratiform region insquall lines in the central USA during late spring andearly summer has very robust structures. Comparisons ofradar reflectivity CFADs and distributions of 85 GHz PCT
between all individual cases and composites over a 9-year
period of TRMM observation show very consistent features.
Surface C-band radar observations during the PRE-STORM
experiment provide further corroboration. Comparisons
between simulated radar CFADs and observations revealthat the model overestimates stratiform radar reflectivity
by about 10 dBZ for both C-band radar and TRMM PR.
Diagnostic study shows that simulated snow aggregates inthe stratiform region are too large.
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Improving Spectral Bin Microphysics Using Trmm

Three sets of independent sensitivity simulations are performed in this study to reduce simulated radar reflectivity
in the stratiform region. Experiment ‘rho vt’ increases bothsnow aggregates’ density and their fall velocity; experiment‘Ec’ reduces the temperature dependency of ice-phase particles’ collection efficiencies, especially at low temperatures;experiment ‘sbreakup’ adds a binary break-up scheme forlarge aggregates as a sink term in the snow aggregates’
growth equation. All these methods reduce simulated radarreflectivity. However, increasing the aggregates’ density andfall velocity is not able to reduce radar reflectivity enoughto match the observations. Adding the break-up process
for large aggregates results in better comparisons withabsolute values of radar reflectivity, but it fails to produce
the observed linear slope in radar CFADs. Experiment‘Ec’ has the best comparison with observations. However,this does not necessarily mean that experiment ‘Ec’ is theunique, or even a correct solution. It is quite possible that
all three factors contribute to a possible solution. However,in a situation where there are many uncertainties with few
constraints in the microphysics, our general guidance is tofind the most important physical process while keeping themodifications and discussions as simple as possible.
Further study shows that while PR comparison becomes
good in experiment ‘Ec’, the probability density distributions of the 85 GHz PCT, which agreed relatively well withthe observation in the original scheme, are now distorted,due to decreased sizes of snow aggregates. The fewer but
larger graupel simulated in experiment ‘Ec’ are responsible
for the excessive 85 GHz PCT depression. Another sensitivity
simulation, ‘graup’, further adjusts end products of ice crystals/snow aggregates collecting droplets in order to increase
the number concentration and reduce the size of graupel.
The improved simulations in experiment ‘graup’ compare
reasonably well with both PR and TMI observations.
Several notes need to be made on modifications of Ec (T)and graupel formation parameters in our sensitivity studies:First, the Ec (T) profile used in experiment ‘Ec’ is relatively
low and does not consider some well-observed phenomena
such as the increase of Ec at around −15◦ C. This is kept
for its simplicity and is fine in this particular case because
the overwhelming majority of pristine ice crystals simulated
in this case are of the plate type (cf. Figure 11(a)), whose
collection efficiencies may be low at cold temperatures.
This result should not be extrapolated to other systems
such as synoptic snow events where dendrites are abundant.
Furthermore, collection coefficient is only one of the many
uncertainties in calculating the collection kernel. Density,
terminal fall velocity, shape and orientation of ice-phaseparticles all contribute to variations of the collection kernel.
Future research is needed in order to separate and quantify
these different mechanisms. Meanwhile, two examples ofactual values of collection kernels Kij used in experiment‘graup’ are given in the appendix for reference.
Second, the 2D framework used in this study may
exacerbate the overestimation of aggregate sizes, too. Cotton
et al. (1995) suggested that the mid-level air in front of asquall system also contributes to the stratiform region,
especially near the transition zone. This air mass flows
around the leading convective cores. It may not bring as
many ice-phase particles as the air detrained directly fromthe leading convection. In a 2D framework, this crossline flow cannot be properly simulated. Our future 3D
case-studies will address these issues.
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Copyright 

395

Third, in the paradigm of dry aggregates–graupel–hailseparation, there are inevitable assumptions that separate
different species, as we have shown in experiment ‘graup’.
We are in the process of including an additional variable,
the rimed fraction in snow aggregates, in order to separate
dry aggregates and graupel more objectively. However,current discussions remain useful for many of the simple
microphysical schemes that do not consider rimed fraction
explicitly.
Our study shows that multi-sensor, long-term TRMM
observations can provide very useful constraints, and leadto significant improvements in model microphysics. The
spectral bin microphysical scheme used in this study also
allows for direct modifications of microphysical processes,
in contrast to bulk microphysical schemes where theassumed particle size distributions are almost always thefirst to be questioned. However, the complex microphysicalprocesses always have many more degrees of freedom
than useful constraints provided by observations. The
improvements presented in this paper are only one possible
solution. One can hope that using more independent
observations and in situ measurements will reduce someof the uncertainties discussed in this study. For example,
both TRMM satellite and surface C-band radar are designed
for precipitation measurements. They are not sensitive tothe many smaller, non-precipitating particles which areimportant constituents of cloud systems and contributesignificantly to global radiation budget through, for example,
formation of anvil clouds. Our future study will include
cloud radar, both surface-based and space-borne, and/or
higher-frequency passive microwave sensors (e.g. 183 GHz)
to further constrain small ice-phase particles simulated
in the cloud model. In addition, in situ measurements
will also be used to validate the simulated particle size
distributions. Only through combinations of laboratory
experiments, in situ measurements, remote sensing, as wellas numerical modelling at various scales can we advance ourunderstanding and representation of microphysics in clouds
and cloud systems.
Acknowledgements
The authors wish to thank A.P. Khain at the Hebrew
University of Jerusalem and an anonymous reviewer for
their constructive and detailed suggestions that led to
substantial improvements in this manuscript. We also
thank R.C. Srivastava at the University of Chicago for his
careful editing. Lin Tian, Bob Meneghini, and Bill Olson at
NASA/GSFC have offered many of their insights on radarand microwave radiation observations and theories. This
research is mainly supported by NASA headquarters andthe NASA TRMM Mission. The authors are grateful to R.
Kadar at NASA headquarters for his support in this research.
Acknowledgement is also made to NASA GSFC for computer
time used in this research.
Appendix.
Collection Kernel KIj Used in Sensitivity Test ‘Graup’
Table AI is for snow aggregates collecting plate crystals.
Table AII is for snow aggregates collecting themselves. The
unit is cm−3 g−1 s−1 . All values are at T = −10◦ C.
Q. J. R. Meteorol. Soc. 136: 382–399 (2010)

c 2010 Royal Meteorological Society
Copyright 

.035

.077

.158

.022

.050

.104

.000

.000

.017

.000

.000

.010

.000

.000

.007

.000

.000

.005

.000

.000

.003

.000

.000

.002

.000

.000

.001

.000

.000

.001

.000

.000

3.4
×10−11
1.3
×10−10
5.4
×10−10
2.1
×10−9
8.6
×10−9
3.4
×10−8
1.4
×10−7
5.5
×10−7
2.2
×10−6
8.8
×10−6
3.5
×10−5
1.4
×10−4
.56
×10−4
2.2
×10−3
9.0
×10−3
3.6
×10−2

1.3
×10−10

3.4
×10−11Mass(g)Q. J. R. Meteorol. Soc. 136: 382–399 (2010)

.266

.131

.060

.029

.013

.006

.002

.000

.000

.000

.000

.000

.000

.000

.000

.000

5.4
×10−10

.455

.227

.105

.051

.023

.010

.003

.001

.000

.000

.000

.000

.000

.000

.000

.000

2.1
×10−9

.781

.392

.183

.089

.040

.016

.004

.001

.000

.000

.000

.000

.000

.000

.000

.000

8.6
×10−9

1.36

.687

.329

.158

.065

.017

.004

.001

.000

.000

.000

.000

.000

.000

.000

.000

3.4
×10−8

2.35

1.20

.566

.261

.070

.019

.005

.001

.000

.000

.000

.000

.000

.000

.000

.000

1.4
×10−7

4.01

2.06

.945

.273

.075

.021

.006

.004

.000

.000

.000

.000

.000

.000

.000

.000

5.5
×10−7

6.48

3.32

.907

.264

.074

.021

.014

.000

.001

.002

.002

.002

.001

.001

.001

.000

2.2
×10−6

10.3

3.13

.849

.256

.074

.019

.001

.005

.008

.009

.009

.008

.005

.003

.002

.001

8.8
×10−6

9.60

2.87

.780

.243

.064

.004

.019

.030

.036

.039

.033

.020

.013

.008

.005

.003

3.5
×10−5

8.18

2.48

.644

.018

.000

.073

.111

.136

.150

.124

.078

.049

.030

.019

.012

.008

1.4
×10−4

7.71

2.45

.573

.082

.169

.309

.408

.476

.388

.252

.160

.100

.063

.039

.025

.016

5.6
×10−4

Table AI. Collection kernel Kij for snow aggregates collecting plates, in the unit of cm−3 g−1 s−1 , at −10◦ C, in sensitivity test ‘graup’.

9.57

3.43

.847

.044

.510

.906

1.20

1.05

.690

.452

.289

.182

.115

.072

.046

.030

2.2
×10−3

14.3

5.97

1.65

.000

1.44

2.57

2.56

1.81

1.21

.796

.511

.324

.205

.131

.084

.055

9.0
×10−3

24.7

12.0

3.61

0.28

4.19

5.65

4.45

3.18

2.13

1.41

.910

.581

.371

.239

.157

.105

3.6
×10−2

396
X. Li et al.

c 2010 Royal Meteorological Society
Copyright 

.014

.031

.063

.009

.020

.042

.000

.000

.007

.000

.000

.004

.000

.000

.003

.000

.000

.002

.000

.000

.001

.000

.000

.001

.000

.000

.000

.000

.000

.000

.000

.000

3.4
×10−11
1.3
×10−10
5.4
×10−10
2.1
×10−9
8.6
×10−9
3.4
×10−8
1.4
×10−7
5.5
×10−7
2.2
×10−6
8.8
×10−6
3.5
×10−5
1.4
×10−4
5.6
×10−4
2.2
×10−3
9.0
×10−3
3.6
×10−2

1.3
×10−10

3.4
×10−11Mass(g)Q. J. R. Meteorol. Soc. 136: 382–399 (2010)

.098

.048

.022

.011

.005

.002

.001

.000

.000

.000

.000

.000

.000

.000

.000

.000

5.4
×10−10

.153

.076

.035

.017

.008

.003

.001

.000

.000

.000

.000

.000

.000

.000

.000

.000

2.1
×10−9

.241

.121

.056

.027

.012

.005

.001

.000

.000

.000

.000

.000

.000

.000

.000

.000

8.6
×10−9

.381

.192

.090

.044

.020

.006

.001

.000

.000

.000

.000

.000

.000

.000

.000

.000

3.4
×10−8

.600

.303

.142

.070

.025

.007

.002

.000

.000

.000

.000

.000

.000

.000

.000

.000

1.4
×10−7

.934

.473

.221

.095

.025

.006

.002

.000

.000

.000

.000

.000

.000

.000

.000

.000

5.5
×10−7

1.48

.752

.322

.091

.023

.006

.001

.000

.000

.000

.000

.000

.000

.000

.000

.000

2.2
×10−6

2.31

1.12

.292

.081

.020

.004

.000

.001

.002

.002

.001

.001

.001

.001

.000

.000

8.8
×10−6

3.44

.993

.249

.069

.015

.000

.004

.006

.006

.007

.006

.005

.003

.002

.001

.001

3.5
×10−5

2.94

.837

.197

.048

.000

.015

.020

.023

.025

.025

.020

.012

.008

.005

.003

.002

1.4
×10−4

2.39

.672

.119

.000

.048

.069

.081

.091

.095

.070

.044

.027

.017

.011

.007

.004

5.6
×10−4

2.07

.558

.000

.119

.197

.249

.292

.322

.221

.142

.090

.056

.035

.022

.014

.009

2.2
×10−3

Table AII. Collection kernel Kij for snow aggregates collecting themselves, in the unit of cm−3 g−1 s−1 , at −10◦ C, in sensitivity test ‘graup’.

1.09

.000

.558

.672

.837

.993

1.12

.752

.473

.303

.192

.121

.076

.048

.031

.020

9.0
×10−3

.000

1.09

2.07

2.39

2.94

3.44

2.31

1.48

.934

.600

.381

.241

.153

.098

.063

.042

3.6
×10−2

Improving Spectral Bin Microphysics Using Trmm
397

398

X. Li et al.

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