November
Journalof the2008
Meteorological Society of Japan, Vol. T.
86A,
SATO
pp. 17−31,
et al. 2008

Resolution Dependency of the Diurnal Cycle of Convective Clouds
over the Tibetan Plateau in a Mesoscale Model
Tomonori SATO
Center for Climate System Research, University of Tokyo, Kashiwa, Japan

Takao YOSHIKANE
Frontier Research Center for Global Change, Japan Agency for Marine-Earth Science and Technology,
Yokohama, Japan

Masaki SATOH
Center for Climate System Research, University of Tokyo, Kashiwa, Japan
Frontier Research Center for Global Change, Japan Agency for Marine-Earth Science and Technology,
Yokohama, Japan

Hiroaki MIURA
Frontier Research Center for Global Change, Japan Agency for Marine-Earth Science and Technology,
Yokohama, Japanand
Hatsuki FUJINAMI
Hydrospheric Atmospheric Research Center, Nagoya University, Nagoya, Japan(Manuscript received 31 July 2007, in final form 29 February 2008 )Abstract
Sensitivity of precipitation diurnal cycle to the horizontal grid spacing was investigated using a mesoscale model without cumulus parameterization. Four numerical experiments with changing horizontal
resolution are performed over one month with NCEP reanalysis boundary forcing. The studied range ofgrid spacing is from 3.5 km to 28 km which has been known as the intermediate scale to simulate mesoscale systems with/without cumulus parameterization. The target area is the Tibetan Plateau where pronounced diurnal cycle of convective systems is observed during the spring season.
Lower resolution runs (14 and 28 km grid) show delayed formation and delayed mature stage of the
cumulus convection in comparison to satellite observations. On the other hand, higher resolution runs (3.5
and 7 km grid) reproduce the proper development of the clouds after local noon which is consistent withobservations. The total hydrometeor content and rainfall rate increase with grid size. Such systematic
relationship of resolution dependencies are confirmed even in the monthly mean diurnal cycle, althoughmost of previous studies examined only short periods. These results suggest that finer resolution at lessthan 7 kilometer is necessary to simulate realistic phase of the precipitation diurnal cycle over the Tibetan Plateau.
The mechanism that is responsible for the resolution dependency is discussed. We suggest that the

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daytime convection which initially occurs due to unstable stratification over the Tibetan Plateau in spring
tends to have a horizontal scale smaller than that is resolvable by the coarse resolution runs. The delayed
cloud formation induces larger downward shortwave radiation, which increases surface fluxes and results
in too strong rainfall in the coarser resolution runs.

1. Introduction
The diurnal cycle of precipitation is a pronounced feature (e.g., Dai 2001) that has a large
contribution to the total precipitation variability
over the low and middle latitude regions. Latentheating released in the precipitation system is one
important energy source that drives the circulationin the troposphere. Thus, the diurnal cycle of precipitation is also an inevitable aspect of the climate
system (Neale and Slingo 2003; Dai and Trenberth2004). The conventional General Circulation
Models (GCMs), which have horizontal resolution in the order of 100 kilometers, use cumulus
parameterizations (such as Arakawa and Schubert
1974; Kuo 1974) to deal with the cumulus convection whose horizontal scale is smaller than the gridsize. Recently, many studies have pointed out difficulties to simulate the phase of the precipitation
diurnal cycle in the GCMs with cumulus parameterization (Dai 2006; Collier and Bowman 2004).
Dai (2006) showed that the phase of the diurnal
cycle over land is still different (too early) from theobserved one in the latest generation of GCMs.
In order to reduce the uncertainties resulting
from cumulus parameterization, sophisticatedtreatment of convection in GCMs have been developed by some groups. Grabowski (2001) and
Khairoutdinov and Randall (2001) proposed the
MMF (Multi-scale Modeling Framework) in whicha Cloud-Resolving Model (CRM) is used to replace
the parameterization in a coarse resolution GCM.
The Nonhydrostatic ICosahedral Atmospheric
Model (NICAM) has been developed by Frontier
Research Center for Global Change (FRCGC)
and Center for Climate System Research (CCSR),
University of Tokyo (Tomita and Satoh 2004;
Satoh et al. 2007). With a few kilometers meshinterval over the globe, NICAM is intended to resolve mesoscale circulations associated with deep
convection by calculating explicit cloud physics
Corresponding author: Tomonori Sato, Center for
Climate System Research, University of Tokyo, 5-1-5
Kashiwanoha, Kashiwa, 277-8568, Japan
E-mail: t_sato@ccsr.u-tokyo.ac.jp©2008, Meteorological Society of Japan

instead of cumulus parameterizations. The NICAM
performed one month simulation at 3.5 km meshgrid without cumulus parameterization (Tomita
et al. 2005; Miura et al. 2005). So far, simulationsof typhoon development (Miura et al. 2007a) andpropagation of the Madden-Julian oscillation (Miuraet al. 2007b) were succeeded in the NICAM withrealistic land-ocean distribution. Although numerical experiments using NICAM are carried out
mainly by the Earth Simulator, high resolution
experiments, like 3.5 km mesh run, are still hardin respect of the computational cost. Therefore,coarser resolution runs are simultaneously carriedout for test runs related to the model development.
Molinari and Dudek (1992) summarized theideal grid size in case with/without cumulus parameterization in numerical models. Since thecumulus parameterization generally considers agroup of cumulus convections in a grid box, grid
spacing larger than approximately 20−30 km isdesired when one uses the cumulus parameterization in GCMs. On the other hand, cloud-resolving
or cloud-system-resolving model should be runwith grid size smaller than a few kilometers inorder to secure enough grid points within a cloudsystem. Therefore, our knowledge on the behaviors of numerical models whose horizontal gridsize is between a few kilometers and 20 km arevery much limited.
Generally, the mesoscale models, which covera certain area of interest by giving a boundary
forcing data, are easy to apply for cloud resolving
simulations because of its lower computationalcost. Many studies have already focused on thesensitivity of the simulated results to horizontal
grid spacing. The previous studies investigated ina broad spectral range of the horizontal grid size
from the order of 1 m up to the order of 10 km (e.g.,
Stevens et al. 2002; Weisman et al. 1997; Bryan
et al. 2003; Murata et al. 2003; Nagasawa et al.
2006). Some of the studies show that the characteristics (such as maximum intensity and life time) of
the simulated mesoscale convective systems varywith the horizontal grid size even without a cumulus parameterization in the mesoscale model (Weisman et al. 1997; Petch et al. 2002). Weisman et al.

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(1997) showed that the lifetime of the convective
storm tends to be long and the intensity becomesstronger as grid size of the mesoscale model increases. However, the integration period in theseexperiments were generally very short, such as
several days or even a few hours, because they
were interested in mesoscale phenomena. Further­more, since they were motivated to examine thedynamical frame and physical schemes in themodel, sensitivity of grid size was investigatedunder somewhat unrealistic conditions, such as
those done by two-dimensional models or thosedescribing the convective systems which are initialized by the artificial warm bubble in the model.
Petch et al. (2002) examined the sensitivity tohorizontal resolution in a viewpoint of precipitation
diurnal cycle, and found that the diurnal maximum
occurs earlier as the horizontal resolution becomes
higher. However, they also carried out only fora few days of integration by a two-dimensionalmodel. Thus, there is a need to study the resolution dependency of the precipitation diurnal cycle
under more realistic atmospheric conditions. Satoet al. (2007) showed using NICAM experimentsthat the diurnal cycle of convective activities over
the Tibetan Plateau tends to be closer to observations as the grid interval becomes smaller. Unfortunately, the period of the analysis was only sevendays due to huge computational cost, which may
be not enough to describe the resolution dependency under the realistic conditions owing to thelarge variability in atmospheric processes.
In this study, we investigate the detailed feature of resolution dependency from the four onemonth experiments changing the grid interval in amesoscale model. The studied range of horizontal
grid size is from 3.5 km to 28 km which has been
known as the intermediate scale to either use or
Table 1.

not use a cumulus parameterization. Implicationsof this study will be useful to evaluate the diurnal
cycle of precipitation simulated in the CRMs whichhave the horizontal resolution of this range.

2. Model simulations and obser vationaldata
2.1 Model simulations
The simulated region is the Tibetan Plateau
which was already studied by Sato et al. (2007)
using the NICAM data. The Tibetan Plateau wasselected because of its large influences on thecontinental to global-scale climate (e.g., Hahn
and Manabe 1975; Wu and Zhang 1998; Sato andKimura 2005, 2007; Liu et al. 2007). The studied period is April of 2004 over which Miura et al. (2007a)performed the realistic global simulation. Over the
Tibetan Plateau the diurnal cycle of convective systems becomes pronounced in April (Fujinami andYasunari 2001).
The Weather Research and Forecasting (WRF)model (Skamarock et al. 2005), which was developed by the collaboration study among the National Center for Atmospheric Research (NCAR), theNational Oceanic and Atmospheric Administration
the National Centers for Environmental Prediction (NCEP), the Forecast Systems Laboratory(FSL), the Air Force Weather Agency (AFWA), theNaval Research Laboratory, Oklahoma University,and the Federal Aviation Administration (FAA).
The detail configuration of the model is shown in
Table 1. The WRF Single-Moment 6-class (WSM6)
scheme, which is one of the available microphysics
schemes, was used as the precipitation formation
process in the experiments. A summary of the experimental setup is given in Table 2. In all experiments, the NCEP final analysis data on one-degree
grid every 6 hours was used as the initial and theOutline of the model.

Weather Research and Forecasting (WRF) modeling system Ver. 2.2
Dynamical Features
Compressible, nonhydrostatic Euler equations.
Terrain-following hydrostatic-pressure vertical coordinate
Physical Features
Microphysics
Boundary layer parameterization
Land-surface modelLongwave radiation
Shortwave radiation

19

WRF Single-Moment 6-class (WSM6)
Mellor-Yamada-Janjic TKE scheme (Janjic 2002)
Noah land-surface model (Chen and Dudhia 2001)
Rapid Radiative Transfer Model (RRTM) (Mlawer et al. 1997)
Dudhia scheme (Dudhia 1989)

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Table 2. Experimental setup of the model. Numerical
domains are shown in Fig. 1.
Calculation condition
Surface and lateralboundary
Vegetation
Simulation term

NCEP final analysis (one degree
grid, every 6 hours)
USGS 30 sec dataset in 1992
Started at 0 UTC 1 April, ended
at 18 UTC 30 April 2004
Lambert conformal
90°E, 33°N

Map projection
Center point of
domainNumber of Vertical 31
layerlateral boundary atmospheric conditions and theinitial soil condition. The simulation started at 0
UTC 1 April 2004 and ended at 18 UTC 30 April
2004.
The numerical experiments are listed in Table 3.
We conducted four experiments with the grid spacing of 3.5 km, 7 km, 14 km, and 28 km (hereinafterG3.5, G7, G14, and G28 runs, respectively), fromwhich 3-hourly outputs were analyzed. The G3.5
and G7 runs applied the nesting technique in the
14 km-mesh and 28 km-mesh of the coarse meshdomains, respectively. The G14 and G28 runs are
conducted without nesting domain. All numericalexperiments were carried out without cumulus
parameterization. Figure 1 shows the calculation
domains and topography over the studied area.
Figure 2 shows the cross sections of the topography along 87.5°E, which indicates that topographic
complexities are quite different among the sensitivity experiments.
In order to evaluate the model results quantitatively and to compare them to the satellite observations, a radiative transfer model, which wasdeveloped at Japan Meteorological Agency, wasVol. 86A

used (Owada 2006). The radiative transfer model
estimates the brightness temperature corresponding to the sensors boarded on the Geostationary
Meteorological Satellite (GMS) using the three-dimensional structures of microphysical parametersand meteorological elements in the model.
2.2 Satellite data
Hourly observations provided by the geostationary satellite are quite useful to evaluate the diurnal
cycle of convective activities in the model (e.g.,Slingo et al. 2004; Sato et al. 2007). In this study, weused the statistics from infrared channel of GMS5,
resolution of which is about 17 km over central
Tibetan Plateau, to compare with one-month mean
characteristics of the model results in Section 3.2.
However, since the GMS5 was not in operation in
April 2004, we also used the Geostationary Operational Environmental Satellite (GOES) 9 data toshow one typical event of the diurnal cycle in Section 3.1. Since the resolution of GOES9 is approximately 50 km over central Tibetan Plateau, we justbriefly describe the diurnal cycle of cloud activity.

3. Result
3.1 The diurnal cycle in 4 April 2004
Firstly, we compare the diurnal cycle of cloud
activity between that observed by GOES9 andthat simulated by the four sensitivity experiments.
The target day is the 4th April in 2004 when pronounced developments of the convective systems
were observed in the daytime. The environmental
condition was very similar to the typical patternrepresenting the active phase of the diurnal cycleof convection which was shown in Fujinami andYasunari (2001). The subtropical jet in the upper
troposphere was splitting to the north and southof the Tibetan Plateau, and wind velocity over the
Tibetan Plateau became very weak. Relatively cold
air with 230 K extended over the plateau in the 300

Table 3. List of sensitivity experiments. Sizes of the numerical domains are shown in
Fig. 1. Results from shaded parts were used for analysis.

Nesting
Coarse mesh grid spacing(grid number)Fine mesh grid spacing(grid number)

G28

G14

G7

G3.5

Off

Off

On

On

28 km
(120 × 90)

14 km(240 × 180)

28 km
(120 × 90)

14 km(240 × 180)

7 km
(401 × 273)

3.5 km(797 × 541)

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21

Fig. 1. Topography (m) in the numerical domain. Thin solid line indicates the area of the nested domain for G7 and G3.5 runs. Thick solid line indicates the area of the Tibetan Plateau used in Figs. 6, 7,
and 8.

Fig. 2. Cross sections of the model topo­
graphy (m) along 87.5°E.

hPa level (not shown). Those conditions seem tobe favorable for convective systems to develop as
the surface temperature rises during the daytime.
The diurnal variation of brightness temperatureobserved by GOES9 is shown in Fig. 3. Clouds
sparsely existed in the morning except for somehigh level clouds. At 12 LT (Local Time; LT = UTC+ 6), many small clouds are formed in the central
and western Tibetan Plateau. At the same timebrightness temperature of the larger cloud systems
over the eastern plateau decreases, indicating thedevelopment of high clouds. Cloud systems weredeveloping at 15 LT, and high clouds completely
cover the whole area of the plateau by 18 LT. Afterthe sunset some high clouds remain, but, theircloud top heights were decreasing by 22 LT. As aresult, nearly half of the region can be recognized
as cloud free areas. At 24 LT, clouds were further
decayed and higher brightness temperatures,
which denote the land surface, can be seen fromthe satellite over large areas of the plateau.
Figure 4 depicts the diurnal cycle of verticallyintegrated hydrometeors in the four WRF experiments for 4 April 2004. Values in G3.5, G7, andG14 are horizontally averaged at G28 grid points.
In each run, the model simulates clouds over eastern plateau in the morning (noted as A in Fig. 4).
The difference among the runs is pronounced at
12 LT. In G3.5 and G7 runs, numerous small-scale
clouds appear over the central and western plateau(noted as B in Fig. 4) whereas there are few suchclouds in the G14 and G28 runs. Cloud formationin the G14 run is more concentrated in the southwestern part of the plateau. In the G28 run, clouds

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Fig. 3. Brightness temperature (K) around the Tibetan Plateau in 4 April 2004 observed by GOES9.
Each panel covers 75−105°E, 25−42°N. (a) 06 LT, (b) 09 LT, (c) 12 LT, (d) 15 LT, (e) 18 LT, (f) 22 LT,
and (g) 24 LT. Data was not available for 21 LT.

over western plateau are absent, although they
are actually observed by the satellite and simulated in the G3.5 and G7 runs. On the other hand,the development of the observed clouds over theeastern plateau (cloud system A) is evident in all
the experiments. The cloud system A indicatesthe development at 12 LT as well as the cloud system B. The generations of the clouds in region B
are found in both G14 and G28 runs at 15 LT. It
is notable that the hydrometeor content becomeslarger as the grid size increases. At 18 LT clouds inregion B begin to decay, and the number of clouds

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Fig. 4. Diurnal change of vertically integrated condensed water (kg m−2) around the Tibetan Plateau
in 4 April 2004 simulated by four sensitivity experiments. Figures are drawn over 75−105°E 25−42°N.
Solid lines indicate the 3000 m topography. Values in G3.5, G7, and G14 are horizontally averaged at
G28 grid points.

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Journal of the Meteorological Society of Japandecreases. Most of the small clouds decease until
21 LT in central and western plateau, which agrees
with the satellite observations. At midnight, thesmall clouds completely disappear over the Tibetan
Plateau. The WRF simulations capture well the diurnal cycle of the cloud patterns for this particularday, which seems to be representative of the typical diurnal cycle over this region.
A latitude-height cross section of the mixing ratioof the condensed water is shown in Fig. 5, in which
the variables in G3.5, G7, and G14 are averaged fordrawing the figures with the same grid point with
G28. Marked difference in the vertical structure
also appears at 12 LT. The deep convection existing
to the whole troposphere is seen in the G3.5 run.
The height of the convection in the G7 run is similar to that in the G3.5 run, but the number of theconvection towers is smaller. On the other hand,the number of convective clouds is very small inboth G14 and G28 runs. At 15 LT, many cloud systems are still present in the G3.5 run. The numberof deep convective clouds is greatly increased in
G7, G14, and G28 runs compared with those at 12
LT. The horizontal scale of each convective systemis larger in G28 run, characterized by the distributed cores, than those in the G3.5 and G7 runs.
These results clearly indicate that the formation time of the cumulus clouds is quite different
even in the realistic simulation over complex ter-Vol. 86A

rain owing to the choice of the grid size in themodel. Cloud formations in the G14 and G28 runs
are about three-hour later than those in the G3.5
and G7 runs. Monthly mean characteristics of thecloud and precipitation diurnal cycle are describedin the next section followed by discussions on
the simulated differences in the cloud features in
Section 4.
3.2 Monthly average view
Diurnal variations of clouds over western andcentral plateau shown in Section 3.1 are very similar to those in the monthly mean cloud characteristics in terms of the cloud distribution. Thus, here
we mainly focus on the cloud statistics, especiallythe diurnal cycle of area-averaged monthly-mean
clouds and precipitation properties for April 2004.
Figure 6 shows the monthly mean diurnal variation of hydrometeor content over the Tibetan
Plateau (see Fig. 1) simulated by the model. In
G3.5 and G7 runs, total hydrometeor rapidly increases after 9 LT while the increases come laterin G14 and G28 runs. The daily maximum hydrometeor contents occur at 15 LT in all runs. The
amount decreases after 15 LT in all runs, with G28
decreasing at a slower pace. Consequently, cloud
mixing ratio remains largest after sunset in the
G28 run.
Diurnal variations of monthly mean precipitation

Fig. 5. Diurnal change of the vertical cross section of cloud mixing ratio along 87.5°E in 4 April 2004
simulated by four sensitivity experiments. Contour intervals are 5 × 10−3 [kg/kg]. Values are horizontally averaged in G3.5, G7, and G14 for drawing the figures with the same grid interval with G28.

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T. SATO et al.

Fig. 6. Monthly-mean diurnal variations ofvertically-integrated total hydrometeor
content over the Tibetan Plateau (seeFig. 1).

Fig. 7. Same as Fig. 6 but for precipitation. Observed estimations in April 2004
based on TRMM 3B42 product are also
drawn as triangles.

(Fig. 7) show very similar characteristics to thehydrometeor content. The area-mean precipitation
is lower in G28 and G14 runs than in G3.5 and G7
runs at 12 LT. In G3.5 and G7 runs, precipitation
starts during 9−12 LT. To the contrary, this relationship is opposite at 18 LT, in which the rainfall
amount is largest in G28 run and smallest in G3.5
run, suggesting that the nighttime precipitation is
also sensitive to the grid size. The diurnal maximum occurs around 18 LT in G28, G14, and G7
runs while precipitation rates at 15 LT and 18 LT
are almost the same in G3.5 run. The daily total
precipitation is largest in G28 run, and decreases
with smaller grid-size, indicating very systematic
relationship to the model resolution. In comparison to the satellite estimation based on the TRMM
3B42 product, the model tends to overestimate
the rainfall over the Tibetan Plateau, although the
3B42 product also contains uncertainties when it
uses the infrared channel observation to estimate
rainfall. The TRMM 3B42 data was also reported
to show later maximum than that of the surface observation (Dai et al. 2007). The rainfall intensity in
3B42 dataset seems to be stronger in comparison
to the seasonal mean values based on TRMM PR
observation (Hirose and Nakamura 2005) although
the analyzed area slightly differs from that in thecurrent study. The simulated diurnal cycle is ingood agreement to the observed one.
Figure 8 shows the diurnal variations of probability density (PD) of brightness temperature forsatellite observations and the WRF simulations.
The statistical analysis was performed only for
the Tibetan Plateau as shown in Fig. 1. Brightness
temperatures in the WRF simulations were com-puted using a radiation transfer model (see Section
2.1). The daily mean PD from five-year statisticsof the GMS observations shows sharp maximum
at 265 K indicating the surface temperature of theplateau (Fig. 8a). The PD at 18 LT has two peaks
around 230 K and 270 K. Similar pattern of diurnal
cycle are reproduced in all sensitivity runs. At 18
LT, the PD tends to show lower value around 230
K and higher value around 270 K in comparison to
the GMS observation (Figs. 8b, c). These results
indicate that in the afternoon the cloud cover is
too small even in G3.5 run. Diurnal changes of PD
show good resembling to the observations. After
18 LT, the signals indicating high-level clouds are
decreased, and very high density appears around265−270 K throughout the night corresponding to
the surface temperature in the cloud free areas.
The G3.5 run well captures the observed cloudformation in the afternoon, although the PD (i.e.,
cloud frequency and cloud cover) is still low. Disappearance of the high clouds is also in good agreement with the observation. On the other hand, theformation time of the clouds is too late in G28 run,
resulting in a diurnal peak of PD around 230 K at
18 LT. Additionally, the disappearance of the highclouds is also delayed in the G28 run, which results in absorbing the longwave radiation from theground surface during the night.

4. Discussions
4.1 Factors responsible for the resolution dependency
We investigated the sensitivity of the precipitation diurnal cycle over the complex terrain bychanging model resolution. The results indicatethat the phase and the amplitude of diurnal cycle

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Fig. 8. Diurnal variations of the probability density of brightness temperature over the Tibetan Plateau(see Fig. 1). (a) GMS5 observation in April during 1998−2002. (b) G3.5. (c) G28.

are strongly dependent on grid size of the model.
In this subsection, the resolution dependencies
revealed in Section 3 are discussed in association
with the controlling physical processes.
Representation of the model topography (cf.,Fig. 2) may be a significant factor which causes thedifferent behaviors of convective systems because
in summer monsoon season mountain-valley circulation plays an important role controlling diurnal
cycle of rainfall and clouds (Kuwagawa et al. 2001;
Kurosaki and Kimura 2002). Figure 9 shows thediurnal variations of low-level wind convergencealong 87.5°E. The magnitude of the convergencein each experiment clearly shows close relationship to the model resolution indicating stronger
convergence/divergence as grid interval decreases. In G3.5 and G7 daytime convergences over the
Himalaya around 27.5°N and southern plateau

around 30°N is evident while they are very weakin G14 and absent in G28. Over the plateau (30−37°N) daytime-nighttime alternation of the convergence and divergence is very dominant in G3.5
corresponding to the topography whereas it isvery weak in G28. From these aspects, topographic
contrast in the plateau seems to be an importantfactor to form the convergence pattern in lower
atmosphere. However, as we showed in Fig. 4 andFig. 5, diurnal change of clouds is evident in G28 inspite of the smooth topography and the weak lowlevel convergence. Thus, the topographic effect is
not always a necessary factor to initiate clouds or
to cause phase difference of the diurnal cycle.
The daytime convection cells over the Tibetan
Plateau consist of tall cumulus-type clouds whose
top reaches at tropopause as seen in Fig. 5. The
lifetime of each cloud system is not very long sinceNovember 2008

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27

Fig. 9. Monthly-mean diurnal variations of convergence (10−5 sec−1) at 10 m level along 87.5°E in (a)G3.5, (b) G7, (c) G14, and (d) G28 runs. Positive values indicate divergence. Values in G3.5, G7, andG14 are averaged to have the same grid spacing with G28. Topographies along the cross section are
shown below.

it generates around noon and disappears after sunset. Fujinami and Yasunari (2001) indicated thatthe formation of spring season convection occurs
as a result of unstable stratification due to boththe upper cold air and the daytime surface heatingwhen environmental wind is not strong. According
to the Bènard-Rayleigh convection theory, criticalhorizontal wavelength of the convection (kc) canbe expressed as kc = π / 2 ≈ 2.22. Over the Tibetan
Plateau if we simply assume the depth of convection (H) be 5-6 km, the convection which is firstly
initiated by the vertical potential temperature gradient will have the horizontal scale of H × kc ≈ 11
−13 km. Therefore, G14, G28, and G7 do not havesufficient resolution to simulate the convection that
initially occurs after the Rayleigh number exceeds
its critical value (Rc). As the unstable stratification
becomes stronger, vertical convection which haslarger horizontal scale can be developed. Therefore, relatively lower resolution runs are capable ofresolving the convection at this moment, although
its intensity may be too strong due to the increased
instability. The resultant convection causes stronger precipitation with its phase delayed in thecoarser resolution run. One has to note that thetheoretical approach should be limited to the quali-

tative comparison because of its assumptions for
simplicity, thus, we cannot directly apply it to therealistic cases of convective initialization. Additionally, we cannot quantitatively compare the critical
Rayleigh numbers derived from the theory and thenumerical experiments. The theoretical evaluationis very useful as long as to show the qualitative relationship of the resolvable convection sizes in eachexperiment against the realistic convection sizes.
It is very clear that a finer resolution run leads
to early maximum of convection while a coarser
resolution run leads to the late maximum withstrong intensity. In the past study effective upward
moisture transport was suggested to be importantfor initiation of the deep convection (Petch et al.
2002; Shinoda and Uyeda 2002). In the current
study, efficiency of the vertical moisture transport
by the grid-scale and subgrid-scale vertical motion
is one of the important processes which may cause
the phase difference. In the spring season over the
Tibetan Plateau, however, the atmosphere contains
very little moisture, and the unstable stratificationof the atmosphere becomes dominant while convective instability becomes significant in monsoon
season (Fujinami and Yasunari 2001).
In G3.5 cloud formation clearly takes place along

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Journal of the Meteorological Society of Japanthe mountain range (Fig. 5). Over the mountainarea the height of vertical convection is lower due
to the elevated surface than that potentially occurs
over the valley. Thus, the Rayleigh number exceeds its critical value (Rc) with relatively weakersurface heating. Therefore, the convective clouds
are likely to occur over the mountain than thoseover the valley. Clouds generate frequently overthe mountain even without the horizontal moisturetransport by the mountain-valley circulation, whichis totally different from that known in the summer
season (Kuwagata et al. 2001).
The delayed cloud formation conducts to thedifference of surface energy budget in coarse
resolution runs. Around local noon surface heat
flux in G28 becomes larger than other experiments
because, owing to the delayed cloud formation, thedownward shortwave radiation is higher without
any interception by the clouds. Therefore, if daytime convection occurs in G28, it is more intensethan other runs according to the larger sensible
heat flux.
The heavier rainfall in G28 induces high soil
moisture content. Relatively larger evaporation in
G28 tends to produce further delay of convection
start in the next day. This is the positive feedback
by the land surface processes indicating that acoarse resolution causes strong intensity anddelayed diurnal cycle of rainfall. In other word,
coarse resolution experiments tend to overestimate the water cycle, which implies the necessity
to adopt proper grid size to study the water cycle.
Our results indicate that the different grid size
causes the differences of land-atmosphere interaction which also complicatedly responses to thediurnal cycle through the feedback mechanisms. In

Vol. 86A

our experiments, initial conditions of soil moisture
are the same among the experiments. Therefore,
the differences in intensity and phase originally occur due to the limitation of resolvable convection
size followed by the feedback mechanisms whichfurther enhances the differences.
The results from sensitivity experiments indicatethat the diurnal cycle of convective activity is quitesensitive to horizontal resolution of the model inspite of the longer-term integration. The resolution dependencies are enough to modulate clouds
statistics including diurnal phase, amplitude, andfrequencies, which likely to modulate the radiativebalance and the hydrological cycles.
4.2 Implications to the global CRMs
As we have mentioned, horizontal grid size
should be properly determined to simulate precipitation by cumulus and microphysics parameterizations. Since the cumulus parameterization usuallyassumes a group of cumulus in a model grid box,
the grid size is desired to be larger than 20−30 km.
On the other hand, in order to simulate precipitation systems without cumulus parameterization,
the grid size should be at least smaller than a few
kilometers. Our study ranges the grid size among
them (3.5−28 km) which also covers the theorybased estimation of the horizontal scale of the
Bènard convection.
Conventional GCMs using cumulus parameterization exhibit too early and heavy precipitation
over land (Dai 2006). Arakawa and Kitoh (2005)
suggested that the phase of the precipitation diurnal cycle becomes later (closer to observations)by the improved representation of topography ina 20 km-mesh GCM than that in a low-resolution

Fig. 10. Illustration showing the phase of precipitation diurnal cycle over land from different models
and observation.

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T. SATO et al.

GCM (cf., Fig. 10). However, use of the cumulus
parameterization in GCMs with grid interval lessthan 20−30 km may be out of target according to
its physical concept behind. Thus, new generation
general circulation model like NICAM is necessary
in the future covering the globe without cumulus
parameterization. As we have indicated, a Global
Cloud Resolving Model (GCRM) is ought to do
longer-term (one month or longer) simulation witha low-resolution mode which does not have enoughresolution to explicitly resolve clouds. From theperspectives of previous studies and the current
study, a low resolution GCRM would exhibit a later
maximum of the diurnal cycle compared to thatobserved (Fig. 10). However, the diurnal cycle in
GCRM is expected to be closer to the observation
as we increase the horizontal resolution supported
by increasing computer power, even though somediscrepancies are currently recognized in lowresolution GCRM (Inoue et al. 2008).
Controlling physical processes and propagating
mechanisms of the diurnal cycle of convective systems differ from region to region and/or season toseason. Here we have shown one example of thediurnal cycle mainly excited by strongly unstablestratification. Further studies are necessary toinvestigate the relationship between model resolution and the simulated diurnal cycle under different environmental conditions such as in monsoon
season or over tropical regions where the diurnal
cycle of convection is more strongly affected by
the behavior of atmospheric moisture.

5. Conclusion
In this study, we have investigated the sensitivity of the diurnal cycle of clouds and precipitation
to the horizontal grid size of a mesoscale model.
Four numerical experiments with changing horizontal resolution were performed for April 2004
with NCEP reanalysis boundary forcing. The gridsize ranges from 3.5 km to 28 km which has been
known as the intermediate scale for simulating
meso­scale systems with/without cumulus para­
meterization. All numerical experiments were conducted without cumulus parameterization. The target area is the Tibetan Plateau where pronounced
diurnal cycles of convective systems are observed
during the spring season.
Lower resolution runs (14−28 km grid) tend
to show delayed formations and delayed mature
stages of the cumulus convection in comparison
to the satellite observations. On the other hand,higher resolution runs (3.5−7 km grid) reproduce
the proper development of the clouds after 12 LT
that is consistent to the observations. The totalhydro­meteor content and rainfall rate increase withthe grid size. As a result, the rainfall amount tends
to be too large compared to the observation in caseof coarse resolution runs. Such systematic relationship of resolution dependency is also confirmed in
the monthly averaged state. These results provide
useful information on the simulation of the precipitation diurnal cycle by regional and global models
that do not secure sufficient resolution for explicitly resolving the cloud systems. Additionally, afiner resolution at ≤ 7 km appears to be necessary
to obtain realistic phase of the precipitation diurnal
cycle over the Tibetan Plateau.
According to the theoretical consideration, initialconvection that is caused by unstable stratification
has the horizontal scale smaller than the coarser
model (G28) resolution. Hence, it is not resolvable by the G28 run. The G3.5 run can somehow
resolve the convection initially occurred by thesurface heating, which consequently conducts toproper simulation of the convection start. As vertical profile becomes more unstable, the verticalconvection which has larger horizontal scale canbe developed. Therefore, relatively lower resolution runs are capable of resolving the convection
at this moment, although its intensity may be
too strong because of the larger surface fluxes.
Numerical experiments further indicate that thecoarser resolution run tends to overestimate thewater cycle between land and atmosphere.

Acknowledgements
We acknowledge F. Kimura, W. Yanase, M. Hara,and S. Yokoi for their useful comments and discussions. Constructive comments and suggestions by
two anonymous reviewers were extremely helpful
to improve the manuscript. Radiative transfer codeto evaluate brightness temperature was provided
by H. Owada in Japan meteorological agency. One
of us (T.S) was supported by Japan Society for the
Promotion of Science (JSPS) as a research fellow.
The GMS and GOES data were obtained by Kochi
University. This study was financially supported
by Grant-in Aid for Scientific Research (20840013)
by MEXT and by CREST (Core Research for Evolutional Science and Technology) program of JST(Japan Science and Technology Agency).

30

Journal of the Meteorological Society of Japan

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