GEOPHYSICAL RESEARCH LETTERS, VOL. 40, 1–5, doi:10.1002/grl.50944, 2013

Deep moist atmospheric convection in a subkilometer global simulation
Yoshiaki Miyamoto,1 Yoshiyuki Kajikawa,1 Ryuji Yoshida,1 Tsuyoshi Yamaura,1Hisashi Yashiro,1,2 and Hirofumi Tomita1,2Received 19 July 2013; revised 6 September 2013; accepted 6 September 2013.

called cumulus parameterization [Arakawa, 2004 and references therein]. Recent advances in computer power and development of a new type of model to solve ﬂuid motions on asphere have made it possible to conduct global simulations without cumulus parameterizations [Tomita andSatoh, 2004; Satoh et al., 2008]. Previous studies demonstrated that cloudy atmospheric disturbances can be simulated accurately using such a global model [Miura et al.,2007; Sato et al., 2009; Fudeyasu et al., 2010a; 2010b;
Nasuno and Satoh, 2011; Kinter et al., 2013].
[4] However, their grid spacings (several kilometers) arestill coarser than or comparable to the observed convection
scale. It is essentially desired to conduct the simulations withresolution higher than the observed convection scale.
Furthermore, although the resolution of several kilometers
will be widely used for global simulations in the near future,
the resolution dependencies of convections simulated in
global models are not yet clear. Previous numerical studies
using a limited numerical domain, but without parameterization, have demonstrated the resolution dependence of
convection features [Weisman et al., 1997; Bryan andFritsch, 2002; Petch et al., 2002; Bryan et al., 2003].
[5] The scope of this study is to elucidate statistical featuresof convection in a global model and their resolution dependence, by conducting a series of high-resolution global simulations with resolution as ﬁne as subkilometer that is ﬁner
than the convection scale. Section 2 introduces the simulation
design and the methodology to detect convection in thesimulated results. Results and interpretations are presented in
section 3. The concluding remarks are described in section 4.

[1] Deep moist atmospheric convection is a key element of
the weather and climate system for transporting mass,
momentum, and thermal energy. It has been challenging tosimulate convection realistically in global atmosphericmodels because of the large gap in spatial scales between
convection (100 km) and global motions (104 km). We
conducted the ﬁrst ever subkilometer global simulation anddescribed the features of convection. Through a series ofgrid-reﬁnement resolution testing, we found that anessential change for convection statistics occurred around 2km grid spacing. The convection structure, number ofconvective cells, and distance to the nearest convective cell
dramatically changed at this resolution. The convection
core was resolved using multiple grids in simulations withgrid spacings less than 2.0 km. Citation: Miyamoto, Y.,
Y. Kajikawa, R. Yoshida, T. Yamaura, H. Yashiro, and H. Tomita(2013), Deep moist atmospheric convection in a subkilometer
global simulation, Geophys. Res. Lett., 40, doi:10.1002/grl.50944.

1. Introduction[2] Deep moist convection plays an important role intransporting energy in the troposphere. The temporal and spatial scales of the convection are 30 min–1 h and 1–10 km, respectively [Emanuel, 1994; Houze, 1994]. Convection also
contributes to energy transport from equatorial regions to polar
regions through meridional circulations. Furthermore, convection is an element of cloudy atmospheric disturbances withhorizontal scales from 102 to 103 km, which are the main causeof natural disasters. Therefore, modeling of convection is important for disaster prevention and daily/long-range forecasts,
as well as for understanding of atmospheric phenomena.
[3] Convection is a main cause of uncertainties in current
global atmospheric models [Stevens and Bony, 2013].
Convection has been impractical for global models tosimulate because of the large gap between the scales of theconvection patterns (100 km) and the global circulation trends(104 km). Classically, convection has been parameterizedusing atmospheric models whose horizontal resolution ranges
from 101 to 102 km . Effects of convection, such as the verticaltransport of heat and moisture, have been parameterized using
dynamic and thermodynamic quantities allocated on grids, so-

2. Experimental Settings and Deﬁnition of
Deep Convection[6] We conducted a subkilometer global simulation as acontrol and four additional simulations involving various resolutions using a Nonhydrostatic Icosahedral Atmpospheric
Model [NICAM; Tomita and Satoh, 2004; Satoh et al.,2008] on the K computer, one of the fastest supercomputersworldwide. The horizontal model grid spacing (Δ) was
0.87 km in the control simulation, and was set at 1.7, 3.5,
7.0, and 14 km in additional simulations. Hereafter, thesimulations are simply referred to as Δ0.87, Δ1.7,…, Δ14.
The number of vertical layers was 94 and the grid interval
gradually expanded with height. The height of the lowest
level was 36 m, and the averaged resolutions below 1000 m
and in the troposphere were respectively about 80 m and
250 m. The effects of shortwave and longwave radiation
were parameterized by the Sekiguchi and Nakajima’s[2009] scheme. The boundary layer turbulence was solvedby the Mellor-Yamada-type model [Nakanishi and Niino,
2004; Noda et al., 2010], and the surface ﬂuxes were
calculated by the scheme proposed by Louis [1979]. The

Additional supporting information may be found in the online version ofthis article.
1
RIKEN Advanced Institute for Computational Science, Kobe, Japan.
2
Research Institute for Global Change, Japan Agency for Marine-Earth
Science and Technology, Yokohama, Japan.
Corresponding author: Y. Miyamoto, RIKEN Advanced Institute for
Computational Science, 7-1-26, Minatojima-minamimachi, Chuo-ku,
Kobe, Hyogo, 650-0047, Japan. (ymiyamoto@riken.jp)©2013. American Geophysical Union. All Rights Reserved.
0094-8276/13/10.1002/grl.50944

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MIYAMOTO ET AL.: CONVECTION IN A SUB-KM GLOBAL SIMULATION

Figure 1. (top) Horizontal view of the total mixing ratio of condensed water contents in Δ0.87, (bottom left) close-up viewof the northwestern Paciﬁc, (bottom middle) a further close-up view for a cloud cluster, and (bottom right) an extreme closeup of an active convection region. The pink color indicates the hydrometeor density larger than 2 g kg 1. Topography andbathymetry are Blue Marble (August) by Reto Stöckli, NASA Earth Observatory.
microphysical processes were solved by a single-moment
ice-resolving scheme [Tomita, 2008]. Cumulus parameterizations were not used in any of the simulations. The initialcondition in each simulation was constructed using theresults of a one-step coarser resolution after a 3 day integration started from 2012082200 UTC. For example, an initialcondition of Δ3.5 was obtained from the 3 day integration
results of Δ7.0. The simulation periods were 12 h, i.e., from2012082500 UTC to 2012082512 UTC. The initial conditions were obtained from the linearly interpolated data fromthe National Center for Atmospheric Research’s ﬁnal
analysis [Kalnay et al., 1996].
[7] To analyze convection features in this study, wedeﬁned “convective grids” in the simulation as the grid
satisﬁes the following criteria of deep convection in the cloudseparation scheme of ISCCP [Rossow and Schiffer, 1999]:
optical thickness (> 35) and cloud top pressure (< 400 hPa).
Then, “convection core” was deﬁned as the grid at which
the vertical velocity averaged (> 0 m/s) in the troposphere
was greater than that in all neighboring grids. The
advantage of this diagnosis using the local peak ofvertical velocity is to remove threshold dependence ofdetected convection.

3. Results and Discussion[8] Figure 1 presents our simulated cloud ﬁeld in Δ0.87.
The global cloud distributions are simulated: cloud clusters
in the tropics, two tropical cyclones in the northwestern
Paciﬁc, and midlatitudinal disturbances. The extended panel
for the northwestern Paciﬁc displays the organized mesoscaledisturbances: cloud clusters and tropical cyclones. A closer
view shows the organized structure of the cloud clusters
and the detailed structure of the cyclone: an eye, circular
clouds around the eye, and spiral rainbands. The extreme
close-up view shows the number of individual deep convective cells. In short, Δ0.87 simulated these multiscale cloudy
convective phenomena ranging from 100 to 104 km in asingle simulation.
[9] Figure 2a displays the locations of convection cores
detected in the Δ0.87 results based on the above algorithm,
along with the simulated outgoing longwave radiation(OLR). The convection cores were reasonably detectedaround low-OLR regions with high cloud top altitudes (e.g.,
low-latitude regions in the western Paciﬁc or midlatitude
cyclonic regions). The latitudinal distribution of the numberof convection cores (Figure 2b) revealed a strong peak in the2

MIYAMOTO ET AL.: CONVECTION IN A SUB-KM GLOBAL SIMULATION

Figure 2. (a) Horizontal distribution of the extracted convection core in Δ0.87 (yellow) superimposing the OLR. (b)Latitudinal proﬁle of the number of extracted convective cells. (c) Radius-height cross section of composites: vertical velocity(shaded), total condensed water density (blue contour, CI = 0.6 g m 3), and potential temperature deviation from the areal
average within the 150 km radius (red, CI = 0.07 K). The center (x = 0) corresponds to the convection core grid.
[10] Figure 3 depicts the radius-height cross sections forthe composites of w for convection detected in the different
resolution simulations. Note that the horizontal axis shows
the grid number in each model simulation. Since the resolution in a panel is twice as large (small) as the right (left),the actual distance is twice as long (short) as the right (left)
as well. The overall structure of w is qualitatively consistentamong the simulations, but a clear difference appears
between Δ1.7 and Δ3.5. When the grid spacing is higher than
3.5 km (Δ1.7 or Δ0.87), w is strong at the center grid and insurrounding grids. In contrast, when the grid spacing is equal
to or lower than 3.5 km (i.e., Δ14–Δ3.5), a strong w appears
only at the center grid. Furthermore, the magnitude of w increases with the resolution in Δ1.7 and Δ0.87, but it does
not signiﬁcantly depend on the resolution in Δ14–Δ3.5.
These results strongly suggest that the convection in Δ1.7
and Δ0.87 is resolved by multiple grid points. In contrast,
the convection in Δ14–Δ3.5 is mainly expressed by one grid,because the resolution is too low compared to the realistic
horizontal scale of convection. Once the convection is
resolved by multiple grids, a higher resolution would resultin a larger simulated variability of physical quantities in theintertropical convergence zone. The number greatly decreasedin subtropical regions, and small peaks appeared at midlatitudes. Figure 2c displays the composite structure of thedetected convection. The composite is the ensemble averageof a radius-height cross section centered at the core grid foreach convective cell. The vertical velocity (w) is strongest at
the center and decays with radius. The water content is greaterthan 0.6 g m 3 in the 2 km radius, and high potential temperature deviations (i.e., positive buoyancy) appear around thestrong w regions. The convection features in Δ0.87 qualitatively capture the observed structure [Byers and Braham,
1948; Malkus, 1952; Emanuel, 1994; Houze, 1994], whereas
w is weaker than expected from the previous observations[e.g., LeMone and Zipser, 1980]. The smallness of w resultsfrom the signiﬁcant variability of the detected convection.
Since the deﬁnition of deep convection in this study does
not involve clear thresholds, the present method of detecting
convection detects weak convective cells as well. Practically,
Δ0.87 is computationally too expensive, and lower resolutions will be necessary in conventional global simulations.
Therefore, we examined the necessary resolution to resolve
the convection.

Figure 3. Radius-height cross sections for composites of vertical velocity w for all detected convections in each simulation.
The horizontal axis is the number of horizontal grids.
3

MIYAMOTO ET AL.: CONVECTION IN A SUB-KM GLOBAL SIMULATION(a) number of convection(b) distance between convection

frequency/total number

0.25

5

number

10

4

10

3

10

0.8

1.7

3.5

7

0.2

0.15

0.1

0.05

0

14

Δ14.0
Δ7.0
Δ3.5
Δ1.7
Δ0.8

0

Δ (km)

4

5

10

number of grid

Figure 4. Resolution dependencies of convective features: (a) number of convective features and (b) grid distance to thenearest convective feature. The thin dashed line in (Figure 4a) indicates a log Δ4 crossing at the point of Δ14 as a reference.
convection and also more localized strong upward motion.
Indeed, the variance of w in each simulation increased withthe resolution (Figure S1 in the supporting information).
The increase in the variance of vertical velocity with theresolution may result from the increase in the number ofdetected convection. From their grid-reﬁnement experiments using a regional model, Donner et al. [1999]
reported that the vertical velocity ﬁelds changed aroundthe 2 km resolution.
[11] Since the convection starts to be resolved by morethan one grid point beyond 3.5 km resolution, convection
number is also changed between Δ3.5 and Δ1.7 (Figure 4a).
The rate of increase in number with resolution decreased
from Δ3.5 to Δ1.7. Speciﬁcally, while the numbers appear
along the reference line ( logΔ4 line) from Δ14 to Δ3.5,
the number departs from the logΔ4 line in Δ1.7. If asimulation with a doubled resolution simply represents theinterpolated result of the original resolution, the number
should be four times larger than the original. However, theincrease must stop at some resolution, because the convection has a ﬁnite spatial scale, and the number of convective
cores is ﬁnite. Although no clear numerical convergenceappeared in the number of convective cells, the features of
convection did change between the grid spacings of 3.5
and 1.7 km.
[12] Figure 4b shows the histograms of distance from a
convection core to the nearest core. The peak frequency in
Δ14–Δ3.5 is four grids, and the distance becomes larger thanfour grids in Δ1.7 and Δ0.87. The actual lengths of “fourtimes the grid spacing” in Δ14, Δ7.0, and Δ3.5 are 56, 28,
and 14 km, respectively, although the peaks are located at
the same grid number. Thus, the distance between theconvection is determined not physically but numerically in
Δ14–Δ3.5. This model-induced limitation may be closely
related to the model effective resolution [Skamarock,2004], or the minimum scale resolved by the discretizedmodel. This depends on the numerical discretizing method.
Hence, the minimum resolvable scales in terms of theconvection distance in Δ14–Δ3.5 are likely too coarse for a
realistic convection distance. As the grid spacing decreases
to 1.7 km, the realistic distance appears to be larger than theeffective resolution.

4. Concluding Remarks[13] The global subkilometer simulation simulated cloudy
phenomena from 100 to 104 km spatial scales, including theconvection. The features of the simulated convection signiﬁcantly changed between the 3.5 km and 1.7 km resolutions;the convection was resolved by multiple grid points, theincreasing rate of number with the resolution decreased, andthe grid number between the convection increased. These features had still not reached the clear convergence in the present
simulations. It implies that further high resolution and/or sophisticated physical parameterizations for entrainment at thecloud boundary [Bryan et al., 2003] are necessary to achieve
the convergence. Our results illustrated the potential effectsof simulations with resolutions less than 2–3 km on simulated
global weather/climate. The simulations advance the understanding of atmospheric circulation and provide new insights
into cumulus parameterization in conventional global models.
[14] Acknowledgments. The authors would like to thank H. Miura, S.
Iga, S. Nishizawa, M. Satoh, our colleagues, and two anonymous reviewers
for fruitful discussions. This study has been conducted as a collaborative
study between RIKEN and MEXT Strategic Programs for Innovative
Research (SPIRE). The simulations were performed using the K computerat the RIKEN Advanced Institute for Computer Science.
[15] The Editor thanks two anonymous reviewers for their assistance inevaluating this paper.

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