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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 113, D17210, doi:10.1029/2008JD009986, 2008

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ArticleA joint satellite and global cloud-resolving model
analysis of a Madden-Julian Oscillation event: Modeldiagnosis
H. Masunaga,1 M. Satoh,2,3 and H. Miura3
Received 9 February 2008; revised 13 May 2008; accepted 8 July 2008; published 12 September 2008.

[1] In this study, a methodology to diagnose a global cloud-resolving model (GCRM) is

explored on the basis of a joint analysis with satellite measurements. The Madden-Julian
Oscillation experiment carried out with the Nonhydrostatic Icosahedral Atmospheric
Model (NICAM) is used as the test bed. The NICAM output is compared with TropicalRainfall Measuring Mission (TRMM) and CloudSat measurements in terms of composite
analysis, contoured frequency by altitude diagrams (CFADs), and the joint histogram ofcloud top and precipitation top heights. It is found in the composite diagram that the
GCRM reproduces a slow, eastward migration of a convective envelope well comparable
to the satellite measurement. The GCRM CFAD qualitatively reproduces TRMM andCloudSat CFADs, except that the GCRM tends to overly produce snow in deep
convection. The joint histograms reveal that, while the overproduction of snow is evident,
NICAM-simulated snow is incapable of producing 94-GHz radar echoes higher than
5 dBZ. This deficiency can be mitigated by a modification to microphysicalparameterization in the way that a proportion of small particles is enhanced in the snow
mass spectrum.
Citation: Masunaga, H., M. Satoh, and H. Miura (2008), A joint satellite and global cloud-resolving model analysis of a MaddenJulian Oscillation event: Model diagnosis, J. Geophys. Res., 113, D17210, doi:10.1029/2008JD009986.

1. Introduction[2] Efforts are underway to develop next-generation
GCMs with less or no dependence on subgrid-scale parameterizations. Multiscale modeling framework (MMF) or
superparameterization [Randall et al., 2003] is among thoseefforts, where a two-dimensional cloud-resolving model(CRM) is embedded in each GCM grid box so that thecomputational burden required for the explicit treatment of
cumulus-scale physics is reduced to a practical level.
Another strategy aimed at next-generation GCMs is to
directly expand the CRM coverage to the entire globe. A
global CRM (GCRM) is an ultimate form to simulate
cumulus convection across the whole planet. Although it
is extremely demanding in computational cost, GCRM
simulation is now feasible by use of cutting-edge supercomputers. Such recent progress in global atmosphericmodels with the explicit representation of convective clouds
has invoked a need for new metrics to diagnose modelsimulated clouds in comparison with satellite observations.

1
Hydrospheric Atmospheric Research Center, Nagoya University,
Nagoya, Japan.
2Center for Climate System Research, University of Tokyo, Tokyo,
Japan.
3
Frontier Research Center for Global Change, Japan Agency for
Marine-Earth Science and Technology, Yokohama, Japan.

Copyright 2008 by the American Geophysical Union.
0148-0227/08/2008JD009986$09.00[3] Outgoing longwave radiation (OLR) and surface rain
rate are widely used for interfacing simulated cloud andprecipitation with observations. These parameters per se,
however, are not necessarily optimal metrics. OLR does notdifferentiate deep convection from opaque cirrus, let alone
make detailed soundings of in-cloud structure. Surface rain
rate is not very informative either for profiling the nature ofclouds aloft. An alternative observational tool more suitable for studying the cloud internal structure in depth isspaceborne radars. Satoh et al. [2008b] examined GCRMsimulated precipitation statistics together with TropicalRainfall Measuring Mission (TRMM) Precipitation Radar(PR) observations. The statistics of vertical precipitation
profiles analyzed by Satoh et al. [2008b] provides acompelling example demonstrating that a satellite radar is
promising for evaluating GCRM simulations. Care must be
taken, however, when using precipitation rate derived fromsatellite measurements because it largely depends on externally determined parameters, such as the Z-R relation
coefficients, implemented in the retrieval algorithm. The
built-in assumptions are a source of uncertainties which
could introduce a nonnegligible statistical bias in the
retrieved product [e.g., Berg et al., 2006]. Precipitation rate,furthermore, is only remotely related to cloud microphysics,
so that precipitation rate is generally not practical for the
purpose of validating the microphysical model that may be
critical for the CRM performance.
[4] These limitations may be circumvented by using
directly observable parameters, instead of geophysicalD172101 of 11

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parameters such as precipitation rate, for the model evaluation. For example, observed radar reflectivity can be analyzed
together with the synthesized radar reflectivity that iscomputed from simulated hydrometeor profiles and theassociated meteorological variables. This approach, basedon a forward radiative-transfer model, is unaffected by theadditional uncertainties arising from an inversion model
required for satellite retrieval algorithms. Another benefitof exploiting forward models is that microphysical parameterizations are testable by repeating multiple radiativetransfer calculations with different microphysical setups.
[5] The present paper explores a methodology to analyze
the synthesized ‘‘observation’’ from GCRM outputs inconjunction with actual satellite measurements primarily
from the TRMM PR and CloudSat Cloud Profiling Radar(CPR). The test bed simulation analyzed in this study is a
recent GCRM experiment of an Madden-Julian Oscillation(MJO) event [Miura et al., 2007]. The MJO has been one of
the most appealing and challenging problems in tropicalmeteorology for decades since first documented by Madden
and Julian [1971, 1972]. Observational and theoreticalstudies to date have vastly enriched our knowledge on the
MJO, whereas further work has yet to be done for a bettermodel reproducibility of the MJO. Model intercomparison
studies [Slingo et al., 1996; Lin et al., 2006] revealed that amajority of general circulation models (GCMs) have difficulty in simulating the MJO with proper period and amplitude. A key problem arises partly (or mostly) from cumulus
parameterizations, which limit the model capability toflexibly represent interactions between cumulus convection
and large-scale dynamics. Compared to (typical) conventional GCMs, MMF simulations produce realistic eastward
movement of convective envelope reminiscent of the MJO[Grabowski, 2003; Randall et al., 2003]. Miura et al. [2007]
and Inoue et al. [2008] demonstrated that their GCRM
experiment yielded a migrating convective envelope and theaccompanied cloud clusters remarkably similar to the observed MJO. The aforementioned studies suggest that the
MJO offers an excellent benchmark to test the performanceof global atmospheric models.
[6] The present work is focused on a methodology toidentify potential model deficiencies by comparison withsatellite measurements. The thorough evaluation of NICAM
simulations is outside the scope of this paper. General issues
concerning the current model setups such as the influence ofcoarse grid spacing are investigated in separate studies. The
dependence on grid resolution was examined by Tomita etal. [2005] on the basis of a NICAM aqua-planet experiment.
The dynamic and thermodynamic structure of eastward
moving convective envelopes simulated with the NICAM
was analyzed in detail by Nasuno et al. [2008] for theaqua-planet experiment and by Miura et al. [2007] andT. Nasuno et al. (Multi-scale organization of convection in a
global numerical simulation of the December 2006 MJO
event using explicit moist processes, submitted to Journal of
the Meteorological Society of Japan, 2008) for the MJO
experiment. Continuous efforts are being made to evaluate
and improve the NICAM performance.
[7] The GCRM and satellite data sets employed in thiswork are described in section 2. The analysis results are

D17210

shown in section 3 and discussed in section 4. Conclusions
are summarized in section 5.

2. Model and Data
2.1. Global Cloud-Resolving Model[8] In this study, we further analyze the GCRM simulation of an MJO event conducted by Miura et al. [2007] with
the Nonhydrostatic Icosahedral Atmospheric Model(NICAM) [Satoh et al., 2008a]. The experiment spans amonth from 15 December 2006 to 15 January 2007, which
encompasses a major portion of an MJO episode. Thisparticular MJO event hit Malaysia in the middle Decemberof 2006, and caused a devastating flush flood. Three different
numerical experiments were performed with different horizontal resolutions of about 14 km, 7 km, and 3.5 km, thelast of which was applied to only a week-long period from25 December 2006. The 7-km resolution run is adopted
throughout the present study because it is considered to bebetter in accuracy than the 14-km run and longer in period
than the 3.5-km experiment. Although the characteristics ofindividual cloud systems are affected by the choice of grid
spacing, the general nature of convective response to alarge-scale forcing is reasonably simulated for all grid
resolutions tested with the NICAM [Tomita et al., 2005;
Miura et al., 2007]. Simulated snapshots throughout the
global tropics (20°S – 20°N) are sampled at every 6 hour inthis study.
[9] A forward radiative-transfer calculation is applied offline to the NICAM experiment for comparison with satellite
measurements. The 14- and 94-GHz radar reflectivities arecomputed with gaseous and hydrometeor attenuations taken
into account. The hydrometeor species considered in theradar measurement synthesis are rain, snow, cloud water,
and cloud ice in accordance with the bulk microphysicalmodel by Grabowski [1998], which is implemented in the
NICAM MJO experiment. A simplified model of melting
particles [Masunaga and Kummerow, 2005] is included aswell so that the radar bright band is reproduced. The backscattering and extinction coefficients are calculated for eachhydrometeor species assuming the Mie approximation. The
particle mass and size distribution of precipitating hydrometeors (rain and snow) assumed for the Mie calculation
exactly follow the definition by Grabowski [1998] except
where otherwise indicated. The dielectric constant for snow
is computed by the Maxwell-Garnett model of ice matrix
with air inclusions [Olson et al., 2001]. The cloud size
spectrum is approximated by a gamma distribution with afixed mode radius for liquid droplets and by the Heymsfield
and Platt [1984] parameterization for ice crystals.
2.2. Satellite Data
[10] The TRMM Level-1 PR reflectivity (1C21) andCloudSat Level-2 CPR reflectivity (2B-GEOPROF) data
sets are used in this study. The TRMM PR is a 14-GHz
radar with the horizontal resolution of 4.1 km at nadir andthe vertical resolution of 250 m. The CloudSat CPR,
operated at 94 GHz, has the spatial resolutions of 2 km
(cross-track) and 1 km (along-track) horizontally and 500 m
vertically. The minimum detectable echo is 19 dBZ for the
TRMM PR (after the orbital boost in August 2001) and28 dBZ for the CloudSat CPR. The difference in frequency

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D17210D17210Figure 1. The time-longitude section of deep storm coverage (see text for definition) for (left) TRMM
observation and (right) NICAM. The bandpass filtered MJO is contoured at every 2s by solid (dashed)line for positive (negative) anomalies with zero contour omitted.
and sensitivity between the PR and CPR enables us to study
different aspects of cloud and precipitation. The CloudSat
CPR detects a broad range of hydrometeor species including
nonprecipitating cloud droplets, drizzle, rain drops, andsnow. Radar echoes from thick clouds and heavy precipitation, however, suffer from severe hydrometeor attenuation.
The TRMM PR has a marginal sensitivity to snow and does
not detect cloud droplets and ice crystals at all. The reflectivity profiles measured by the PR, on the other hand, are lessattenuated than the CPR reflectivity. Infrared (10.8 mm)
brightness temperature from the TRMM Visible/Infrared
Scanner (VIRS) 1B01 product is also employed to supplement PR measurements following the manner proposed by
Masunaga et al. [2005].
[11] Observation by low Earth orbiting (LEO) satellites ishighly inhomogeneous in spatial and temporal sampling,
restricted by satellite orbits and the scan geometry of
sensors. No attempt, however, is made in the present study
to sample the GCRM simulation according to the TRMM
and CloudSat orbital swaths. Little benefit is expected fromdoing so, given that our interest lies not in the individual
matching of a simulated cloud with an observed but in theoverall statistics.

3. Analysis Results
3.1. Time-Longitude Section[12] Examined first is the time-longitude section of deepstorm coverage for observed and simulated clouds integrated
meridionally between 20°S and 20°N. Deep storm coverageis defined as the area fraction occupied by precipitating
clouds with PR echo-top heights higher than 4 km andinfrared brightness temperatures colder than 245 K. Thisdefinition is equivalent to the Deep Stratiform and Deep
Convective categories combined together according to theterminology introduced by Masunaga et al. [2005]. The
MJO is extracted by a space-time bandpass filter applied tothe time-longitude section of TRMM deep storm coverage.
The time period used for the bandpass filtering spans awhole year from April 2006 to March 2007. The MJO filter
is bound by 20 and 80 days in period and 1 and 7 in zonal
wave number [Masunaga et al., 2006]. The time-longitudesection of TRMM deep storm coverage is smoothed bymultiple passes of the 1-2-1 filter, aimed at removing
sampling noise in the TRMM observation. The identicalsmoothing is applied to the NICAM simulation as well,although not necessarily required for the high sampling rateof the model, in order to assure methodological consistency.
[13] The TRMM observation exhibits an eastward migration of convective envelope visually recognizable within thefiltered MJO (Figure 1). The NICAM simulation starts witha broad convective area extending across the whole eastern
hemisphere, which gradually settles down into a narrower
convective band by 26 December. In the remainder of theperiod the convective envelope appears to closely follow thefiltered MJO defined from the TRMM observation. Also
successfully simulated by the NICAM is the embedded
structure of cloud clusters moving to west [Nakazawa,
1988; Inoue et al., 2008]. Diurnally modulated convective

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D17210Figure 2. The number count of detected radar echo composited around the MJO convective peak for(a) CloudSat CPR, (b) NICAM synthesized 94-GHz reflectivity, (c) TRMM PR, and (d) NICAM
synthesized 14-GHz reflectivity. The detectability limit is given as 28 dBZ for CPR/94-GHz and 19 dBZ
for PR/14-GHz.
signals standing over Africa [e.g., Yang and Slingo, 2001]
can be seen as a striped structure around 30°E. These highfrequency variabilities are absent in the TRMM observation,
because of the low revisit frequency of TRMM satellite
overpasses. A large inconsistency between the observationand model simulation, however, lies in the magnitude of
deep storm coverage. Simulated clouds are larger in deepstorm coverage than observed clouds by almost an order ofmagnitude. This bias results from the excessive productionof snow in deep convective clouds simulated by the model
as will be confirmed later.
3.2. Composite Analysis[14] A composite analysis is performed with respect to a
spatially movable base point defined along the MJO ridge inthe time-longitude domain. The procedure is briefly discussed as follows (see Masunaga et al. [2006] for details).
A time series of the local spatial maxima of the filtered MJO
is first identified. The base point for the MJO wet phase isgiven by the local maxima that exceeds twice the standard
deviation (2s) of the filtered MJO anomaly. The local
maxima that occurred in the east of the dateline from 10
to 15 January (see Figure 1) are not included in the analysis
since this particular event appears not to be directly associated with the MJO episode of interest. The MJO dry phaseis defined in the same manner but using the local minima of
the filtered MJO.
[15] Figure 2 is the composite height-longitude structureof the MJO in terms of the number count of detected radar

echoes. The CloudSat CPR profile (Figure 2a) is doublepeaked in altitude at 12 km and 1 – 2 km, implying thepredominance of cirrus and shallow clouds. The zonal
distribution of detected CPR echo is loosely peaked around0°, or the MJO convective peak, and to its west. The clouddeck extending westward presumably corresponds to thestratiform anvil left behind the MJO convective peak [e.g.,Morita et al., 2006]. In the composite PR profile (Figure 2c),detected signals are confined in the lower half of thetroposphere. The absence of radar echo above the freezing
level, typically 4 – 5 km in height for tropical latitudes, is dueto the PR insensitivity to frozen hydrometeors [Masunaga etal., 2002]. A shallow-topped radar echo is observed at theleading edge of the MJO envelope or to the 20° east of the
MJO convective peak, while a thick precipitation layer
reminiscent of stratiform anvil is extended to the west.
Despite large contaminative noise, these composite features
are consistent with existing knowledge on the MJO structure [Lin and Johnson, 1996; Kiladis et al., 2005].
[16] The composited 94-GHz and 14-GHz radar profiles,
for comparison with the Cloud CPR and TRMM PR,
respectively, that are synthesized from the NICAM output
are plotted in Figures 2b and 2d. It is found that radar echo
detected above the freezing level is exaggerated comparedto the observations. This indicates that frozen precipitating
particles are excessively produced in the NICAM experiment. Nevertheless, the zonal amplitude modulation in thecomposite diagram is relatively well reproduced by the
NICAM. Given the fact that the synthesized radar profiles

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D17210Figure 3. TRMM PR CFADs constructed for (a) the MJO wet phase, (b) dry phase, and (c) the
difference between the two phases. (d – f) Same as Figures 3a – 3c but constructed from the NICAMsynthesized 14-GHz radar reflectivity. Contour is linearly spaced in an arbitrary unit. Negative contours
are dashed without shade in Figures 3c and 3f.
are composited with respect to the observed MJO convective peak, it would be fair to claim that the NICAM is
reasonably successful in capturing the eastward migration of
MJO convection.
3.3. Contoured Frequency by Altitude Diagram(CFAD)[17] The vertical structure of cloud and precipitation
varies systematically with zonal distance away from the
MJO convective peak (Figure 2). The resultant contrast
between the MJO wet (i.e., convectively active) phase anddry (inactive) phase may be used for a brief exercise to
examine the model reproducibility of convective clouds
associated with the MJO. To this end, the contoured
frequency by altitude diagrams (CFADs), or the probability
distribution of radar reflectivity at different altitudes, isconstructed separately for different phases of the MJO.
The MJO wet (dry) phase is defined as a domain where
the filtered MJO anomaly is larger than 2s (smaller than2s), which is indicated by the outermost solid (dashed)
contour in Figure 1.

[18] Figure 3 shows the TRMM PR CFAD and the
NICAM synthesized 14-GHz CFAD. The PR insensitivity
to frozen hydrometeors is evident here again (Figures 3aand 3b) as implied by an abrupt drop in reflectivity above
the freezing level. The freezing level is clearly highlighted
by the radar bright band. The differential CFAD between the
opposing MJO phases (Figure 3c) shows that the dry phase
dominates the wet phase for altitudes lower than 2 km andreflectivities lower than 30 dBZ while the relationshipreverses elsewhere. This dipolar structure confirms anincrease of shallow cumulus population and a decrease ofdeep convection in the MJO dry phase. The differential
CFAD constructed from the NICAM simulation, however,is tripolar (Figure 3f). An additional negative pole in theupper troposphere arises from a train of spurious convection
initially prevailing across the eastern hemisphere (Figure 1)
since this third pole almost disappears when the differential
CFAD is reconstructed with the first 10 days removed (notshown). Synthesized CFAD pattern for individual MJO
phases (Figures 3d and 3e) is spread out to higher altitudes
and higher reflectivity than the observed CFAD. Overall,

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D17210Figure 4. Same as Figure 3 but for the CloudSat CPR and the synthesized 94-GHz reflectivity.
tropical convection tends to be developed too deep in the
NICAM simulation.
[19] Figure 4 shows CPR/94-GHz CFADs. The observed
CFAD (Figures 4a – 4c) is characterized by an arc-likestructure that penetrates through the whole troposphere.
Radar reflectivity increases with decreasing altitude along
the upper branch of the arc, corresponding to the transition
from cloud ice to precipitation ice (which potentially
includes any of snow, graupel, and hail), until reflectivity
achieves its maximum around 15 dBZ at the melting layer.
Below the dBZ maximum, a jump in the water dielectric
constant occurring from ice to liquid phases accentuates thelower branch of the arc in the MJO wet phase (Figure 4a).
Strong rain attenuation makes radar reflectivity rapidly
decline toward the ground. In the dry phase (Figure 4b) a
majority of precipitation does not experience the cold rain
processes, so that the discontinuity caused by melting isfainter. A reduced productivity of precipitation ice also
accounts for the shrinkage of the upper branch in Figure 4bcompared to Figure 4a. Cirrus clouds lingering near the
tropopause, marked by the upper end of the arc, are present
regardless of the MJO phases.
[20] A similar arc-like structure is present in the NICAMsynthesized CFAD (Figures 4d – 4f), although the upper
branch is exaggerated because of, as already seen, overly

produced snow in deep convective clouds. Interestingly, thesynthesized 94-GHz radar echo appears to avoid entering a
rectangular domain sharply edged at 5 dBZ and 8 km. This
empty rectangle is obviously unrealistic, as no hint of suchdiscontinuity is found in the observed CFAD. It turns outthat the simulated properties of snow are to be questioned.
The vertical distribution of individual hydrometeor species(Figure 5) shows that rain and cloud water are trapped
below 8 km while cloud ice is isolated within a pair ofseparate layers near 6 km and the tropopause. Snow is the
only candidate that can explain the continuous vertical rise
extending above 8 km shown in Figures 4d– 4f. In Figure 5,
however, snow water content (or snow mixing ratio multiplied by dry air density) per se does not exhibit any apparent
feature that explains the sharp CFAD cutoff. This issue will
be discussed later in section 4.
3.4. Cloud and Precipitation Top Heights[21] Masunaga et al. [2005] and Masunaga andKummerow [2006] analyzed TRMM PR and VIRS
measurements to investigate a broad spectrum of tropicalprecipitating clouds from shallow cumulus to deep convection. They used TRMM PR echo-top height and VIRS
infrared brightness temperature as a proxy of precipitation
top height (PTH) and cloud top height (CTH), respectively.

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D17210Figure 5. The contoured frequency of hydrometeor water content for (from left to right) cloud ice,
snow, rain, and cloud water. Contour lines are logarithmically spaced. (top) MJO wet phase. (bottom)
MJO dry phase.
Another way to derive CTH and PTH was devised by
Stephens and Wood [2007], who defined two echo-top
heights with different dBZ thresholds applied to 94-GHz
radar reflectivity. Following these studies, joint histograms of
CTH and PTH are constructed individually from TRMM andCloudSat observations as well as the corresponding parameters synthesized from the NICAM. The definitions of PTH
and CTH in the present study are summarized in Table 1.
[22] Figures 6a and 6b indicate that the MJO wet phasewell contrasts with the dry phase in the TRMM CTH-PTH
histogram. The wet phase is characterized by cold cloud tops(or high CTHs) with high PR echo tops, while shallow
cumulus dominates in the dry phase. It is noted that theconspicuous vertical ridge at the freezing level is due to thejump in back-scattering coefficient associated with hydrometeor melting. The CloudSat CPR histogram (Figures 6c
and 6d) shows prevailing high clouds near the tropopause,
whereas an increase in shallow cloud population from the wetphase to the dry phase is also evident. A majority ofhistogram peaks fall in the upper triangle away from the
diagonal line, indicative of a significant gap between CTH
and PTH, particularly where PTH is higher than the freezing

level. The portions with CTH>PTH can be attributed either tothe absence of large ice particles detectable by the PR (CPR)
above the 19-dBZ (10-dBZ) threshold [Masunaga et al.,2005] or midlevel clouds such as cumulus congestus overlapped with cirrus clouds [Stephens and Wood, 2007].
[23] In the synthesized 14-GHz histogram from the
NICAM experiment (Figures 6e and 6f), the TRMM observation is reasonably reproduced except for the overproduction of very high PTHs (10 km or higher), which is readily
expected from Figures 2 and 3. Given the abundance ofsnow in simulated deep convective clouds, it is seemingly

Table 1. Definitions of Cloud Top Height and Precipitation Top
Heighta
TRMM
CloudSat

CTH

PTH

10.8-mm brightness temperature28-dBZ echo-top height

19-dBZ echo-top height
10-dBZ echo-top heightaCTH, cloud top height; PTH, precipitation top height. The definition ofecho-top height requires three consecutive layers with reflectivities higher
than a given threshold (except for the TRMM CTH).

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D17210D17210Figure 6. Joint histograms of precipitation top height (PTH, abscissa) and cloud top height (CTH,
ordinate): (a) TRMM PR and VIRS histogram for the MJO wet phase. (b) Same as Figure 6a but for the
MJO dry phase. (c) Same as Figure 6a but CloudSat CPR histogram. (d) Same as Figure 6b but CloudSat
CPR histogram. (e – h) Same as Figures 6a – 6d but synthesized from the NICAM simulation. The
histograms are shaded and contoured in linear spacing.
puzzling that the domain with PTHs higher than 8 km is
totally blanked out in the synthesized 94-GHz histogram(Figures 6g and 6h). This is indeed not surprising if one
recalls that 94-GHz echoes higher than 5 dBZ are missing
above 8 km in the NICAM simulation (Figure 4). The
question to be asked is therefore narrowed down to why
NICAM-simulated snow does not yield 95-GHz reflectivities higher than 5 dBZ. This problem will be addressed in
section 4 below.

4. Discussion[24] Discrepancies between actual and synthesized radarmeasurements can result from a variety of reasons thatinvolve both dynamical and microphysical factors. Radar
reflectivity depends not only on hydrometeor water content
but on particle size distribution (PSD). The sensitivity toparticle size is very high in the Rayleigh scattering regime,
where back-scattering coefficient, sb, increases with the 6th
power of particle size. In reality, the frequency of 94 GHz,or 3.2 mm in wavelength, is comparable to the size of large
snowflakes, so that the premise for the Rayleigh approximation breaks down. The sensitivity of back-scattering
coefficient to particle size declines as the Rayleigh scattering regime (sb / the 6th moment of PSD) gives way
ultimately to the geometrical optics limit (sb / the 2nd
moment). The rate of increase in 94-GHz radar reflectivity

Figure 7. The original and modified particle size distributions (PSDs) of snow assumed in radarreflectivity synthesis. (a) Snow mass spectrum (or mass-weighed PSD) for the original Grabowski
parameterization (solid line) and modified microphysics (dotted line). Snow water contents of 0.01, 0.1,
and 1 g/m3 are given for three curves from bottom to top. See text for details on the modification.
(b) Snow back-scattering coefficient at 94 GHz as a function of snow water content for the original andmodified microphysics.
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D17210Figure 8. Same as Figures (a) 4d, (b) 4e, and (c) 4f but for the modified snow mass spectrum.

for increasing snow water content therefore tapers off when
an appreciable amount of millimeter-size snowflakes arepresent.
[25] Figure 7a shows the snow mass spectrum for different water contents (solid lines). For the largest water content
depicted (1 g/m3), a substantial fraction of snowflakes haveparticle diameters larger than the 3.2-mm wavelength of
CPR echo. Accordingly, the back-scattering coefficient at
94 GHz is highly insensitive to snow water content for awide range from 0.5 to 3 g/m3 (Figure 7b). It is speculated
that this nonlinearity may be a cause for the sharp cutoff inthe synthesized 94-GHz CFAD (Figures 4d– 4f). (Note thatsb is drawn in logarithmic scale in Figure 7b so as to be
proportional to radar reflectivity in dBZ.)[26] The impact of the non-Rayleigh effect on radar echo
is examined through a quick comparison with an additionaldBZ synthesis based on modified snow microphysics. In theoriginal Grabowski [1998] parameterization, the mass of asnowflake, m [kg], having the diameter, D [m], is assumed
to bemðDÞ ¼ aDb ;ð1Þ

where a = 2.5  102 and b = 2. A modified snow mass
spectrum is defined as a = 5  104 and b = 1 with theparticle size distribution, N(D), same as the original. The
resultant change to the snow mass spectrum, m(D)N(D),and back-scattering coefficient is shown by dotted line in
Figure 7. Large snowflakes that were present in theoriginal microphysics are replaced by many small snowflakes in the modified mass spectrum. Little fraction ofsnow has diameters larger than 3 mm even for a snow watercontent as large as 1 g/m3. Figure 7b shows that themodified sb decreases (increases) from the original sb for agiven snow water content smaller (larger) than 0.2 g/m3.
This turnover in sb as a function of snow water content may
be explained as follows. Below the turnover point, theoriginal and modified mass spectra both lie in the Rayleighscattering regime. Once the original mass spectrum expands
beyond the Rayleigh scattering regime, however, theoriginal sb starts losing the sensitivity to particle size while

the modified sb stays in the Rayleigh regime. As a result,the modified mass spectrum, constituted of abundant small
snowflakes, is capable of producing a larger sb than theoriginal mass spectrum, which consists of large but fewer
snowflakes, when compared for a fixed snow water content.
[27] Figure 8 illustrates the 94-GHz CFAD synthesizedfrom the same NICAM output as in Figures 4d– 4f but using
the modified snow mass spectrum. The 5-dBZ cutoff above
8 km in Figure 4 is smeared out in Figure 8, supporting the
hypothesis that the non-Rayleigh effect is responsible forthe problem. Correspondingly, the domain with PTHs >8 km in the synthesized 94-GHz histogram which was
found blank (Figures 6g and 6h) now contains the fullof signals (Figures 9c and 9d). For the 14-GHz histogram,in contrast, the modification to snow microphysics does notincrease the frequency of occurrence above 8 km but evenreduces it (compare Figures 9a and 9b with Figures 6e and6f). This does not contradict the theoretical expectation,
given that neither the original nor modified microphysics
suffers from the non-Rayleigh effect at the frequency of
14 GHz.
[28] Overall, reformulating the snow mass spectrum withan enhanced proportion of small snowflakes is successful inmitigating the disagreement between the simulation andobservations. The modified mass spectrum, however, is still
far from the best tuned microphysical model. The arc-likestructure present in the original 94-GHz CFAD is destroyedby the modification at the expense of the elimination of theartificial dBZ cutoff. Some optimization technique must be
developed for obtaining a desirable level of consistency
with the observation. Moreover, some key processes are
ignored in the present work. The modified dBZ synthesis
shown in Figures 8 and 9 does not include the impact on
cloud dynamics resulting from the imposed microphysicalchange. Although it is beyond the scope of this paper tocarry out an additional NICAM experiment with modified
microphysics, the expected outcome is worth speculating.
The result above indicates that the current microphysicalmodel is parameterized to assign an excessive amount oflarge snowflakes to a given snow water content. This
deficiency could be mitigated by updating the microphysical9 of 11

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D17210Figure 9. Same as Figures (a) 6e, (b) 6f, (c) 6g, and (d) 6h but for the modified snow mass spectrum.
scheme in some different manners. For instance, changing
the coefficients a and/or b in equation (1) as done in thepresent paper is a simple way to adjust the snowflake size.
The smaller snowflakes are, the longer they would stay aloft
as the result of a reduced precipitation rate. Snowflakes thus
could be advected further away before eventually precipitating out. As such, snow would be diffused over a broad
area beyond where formed. This is a favorable change, since
we have seen that a main issue of the current NICAM
simulation is the overproduction of snow. Another possible
solution is to introduce graupel, which is absent in the
Grabowski [1998] parameterization, into the microphysicalmodel. Graupel is less susceptible to the non-Rayleigheffect than snow since graupel has a higher particle density
and is therefore smaller in mean particle size for a given
mixing ratio.
[29] No microphysical scheme other than the Grabowski[1998] parameterization has been installed for the 2006/
2007 MJO experiment studied here. On the other hand, newmicrophysical schemes are being developed for the NICAM
and were tested for their performance by Tomita [2008].
Tomita [2008] found that the amount of ice condensate
significantly decreases when graupel is included because
graupel precipitates out more quickly than snow. A very
recent NICAM experiment to simulate a boreal summer
MJO event was performed with both the Grabowski [1998]
microphysical model and an updated scheme with graupel
included (K. Oouchi, private communication, 2008). Whilechanges to the microphysical scheme effect the structure ofindividual clouds, the eastward migration of an large-scaleenvelope of convective clouds was successfully simulatedwith the NICAM regardless of microphysical schemes
implemented.
[30] Radiative transfer calculations for the dBZ synthesis
rely on the Mie approximation, where hydrometeors are
assumed to be spherical. The Mie approximation is justifiable
for liquid particles, whereas ice crystals and snowflakes arehighly anisotropic in shape. Equation (1) not only controls
the hydrometeor mass spectrum but also regulates theparticle morphology depending on the parameter b. A
snowflake may be considered to be two dimensional (platelike) for b = 2 and one dimensional (needlelike) for b = 1.
Our radiative transfer scheme is currently not designed toaccount for the morphologic effect on the back-scatteringand extinction coefficients. In reality, frozen hydrometeors
are so complicated in crystal structure that the exact
modeling of their radiative properties is practically impossible. A simplified but reasonably realistic parameterizationof the radiative properties will be required for a better
treatment of cloud ice and snow in the dBZ synthesis.

5. Conclusions[31] Cloud and precipitation properties simulated by a
GCRM are analyzed jointly with satellite measurements.
The GCRM simulation used in this study is provided by the
NICAM. The study period is the 32-day sequence startingfrom 15 December 2006, which contains a major portion of
an Madden-Julian Oscillation event. Radiative transfer
calculations are applied to the NICAM output to synthesize
virtual observations for comparison with TRMM andCloudSat measurements. Analysis with the composite diagram supports the conclusion of Miura et al. [2007] that the
GCRM reproduces a slow, eastward migration of a convective envelope well comparable to the satellite measurement.
CFADs are constructed separately for the wet and dryphases of the MJO, which are isolated out by bandpass
filtering. In the TRMM PR CFAD, a contrast between the
wet and dry phases is clearly marked by the predominanceof deep (shallow) precipitation in the wet (dry) phase. The
CloudSat CPR CFAD confirms this contrast but also indicates the prevalence of cirrus clouds independently of the
MJO phases. The GCRM CFAD qualitatively reproduces
the TRMM and CloudSat CFADs, except that the GCRM
tends to overly produce snow in deep convection particularly in the MJO dry phase. The joint histograms of cloud
top and precipitation top are created individually from
TRMM and CloudSat measurements. The synthesized
TRMM histogram again indicates that snow is excessively
produced in simulated deep convective clouds, while thesynthesized 94-GHz histogram lacks radar echoes above
8 km in altitude. The latter is found to arise from the nonRayleigh scattering effect that the 94-GHz back-scattering
coefficient loses the sensitivity to an increase in snow watercontent when mean particle size is comparable to thewavelength of radar echo. A modification to microphysicalparameterization by redefining the snow mass spectrumwith an enhanced proportion of smaller particles turns out
to offset the model bias.
[32] The current paper is not intended to provide thecomplete list of remedies against the deficiencies inherent in
the particular model. Instead, this work is aimed at sketching out a general methodology to diagnose the simulated
cloud and precipitation properties in comparison with satellite measurements. The methodology is directly applicable toa variety of cloud models including the MMF as well as
GCRM. T. Matsui et al. (Evaluation of long-term cloud-10 of 11

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resolving model simulations using satellite radiance observations and multi-frequency satellite simulators, submitted to
Journal of Atmospheric and Oceanic Technology, 2008)
demonstrates a recent effort to assess the performance of
their CRM on the basis of a similar analysis technique to thepresent method. An intriguing implication of the present
findings is that combined use of the TRMM PR and CloudSat
CPR has the potential to evaluate not only macrophysicalvariables such as snow water content but the microphysicalparameterizations of cloud models.
[33] Acknowledgments. The authors acknowledge the work of the
NICAM development group, NASA CloudSat project, and the NASA andJAXA TRMM project teams. The data used in this work were madeavailable by their dedicated efforts. This study is partly supported by the
Virtual Laboratory for the Earth’s Climate Diagnostics.

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H. Masunaga, Hydrospheric Atmospheric Research Center, Nagoya
University, F3-1(200) Furocho Chikusa-ku, Nagoya 464-8601, Japan.
(masunaga@hyarc.nagoya-u.ac.jp)
H. Miura, Frontier Research Center for Global Change, Japan Agency for
Marine-Earth Science and Technology, 3173-25 Showamachi, Kanazawa-ku,
Yokohama, Kanagawa 236-0001, Japan. (miurah@jamstec.go.jp)
M. Satoh, Center for Climate System Research, University of Tokyo, 5-1-5
Kashiwanoha, Kashiwa, Tokyo, Chiba 277-8568, Japan. (satoh@ccsr.
u-tokyo.ac.jp)

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