Kajikawa et al. Progress in Earth and Planetary Science (2016) 3:16
DOI 10.1186/s40645-016-0094-5

Progress in Earth andPlanetary Science

RESEARCH ARTICLE

Open AccessResolution dependence of deep
convections in a global simulation fromover 10-kilometer to sub-kilometer grid
spacing
Yoshiyuki Kajikawa1*, Yoshiaki Miyamoto1, Ryuji Yoshida1, Tsuyoshi Yamaura1, Hisashi Yashiro1
and Hirofumi Tomita1,2

Abstract
The success of sub-kilometer global atmospheric simulation opens the door for resolving deep convections, which
are fundamental elements of cloudy disturbances that drive global circulation. A previous study found that theessential change in the simulated convection properties occurred at a grid spacing of about 2 km as a global
mean. In grid-refinement experiments, we conducted further comprehensive analysis of the global-mean state andthe characteristics of deep convection, to clarify the difference of the essential change by location andenvironment. We found that the essential change in convection properties was different in the location andenvironment for each cloudy disturbance. The convections over the tropics show larger resolution dependence
than convections over mid-latitudes, whereas no significant difference was found in convections over land or
ocean. Furthermore, convections over cloudy disturbances [(i.e., Madden-Julian oscillation (MJO), tropical cyclones(TCs)] show essential change of convection properties at about 1 km grid spacing, suggesting resolution
dependence. As a result, convections not categorized as cloudy disturbances make a large contribution to theglobal-mean convection properties. This implies that convections in disturbances are largely affected organization
processes and hence have more horizontal resolution dependence. In contrast, other categorized convections thatare not involved in major cloudy disturbances show the essential change at about 2 km grid spacing. This affects
the latitude difference of the resolution dependence of convection properties and hence the zonal-mean outgoing
longwave radiation (OLR). Despite the diversity of convection properties, most convections are resolved at less than
1 km grid spacing. In the future, longer integration of global atmosphere, to 0.87 km grid spacing, will stimulatesignificant discussion about the interaction between the convections and cloudy disturbances.
Keywords: Deep convection, High resolution, Global simulation, NICAM, Cloudy disturbance, Resolution
dependence

Background
The rapid increase of computer capabilities has enabled
meteorological and climatological researchers to increase
horizontal and vertical resolutions in the numericalmodel (Simmons et al. 1989; Mizuta et al. 2006; Saito etal. 2006; Kodama et al. 2015). The demand for highresolution simulation not only from regional-model* Correspondence: ykaji@riken.jp
1
RIKEN Advanced Institute for Computational Science, 7-1-26
Minatojima-minami-machi, Chuo-ku, Kobe, Hyogo 650-0047, Japan
Full list of author information is available at the end of the article

researchers but also from global-model researchers has
become intense. In the atmospheric general circulation
model (AGCM), one of the key issues is to explicitly resolve deep convection for the following reasons.
Deep convection is a minimum element for theorganization of cloud systems, including cloudy disturbances, and plays an essential role in driving the atmosphere, through the transportation of energy in the
troposphere from the tropics to the polar region (Webster
1972; Gill 1982; Emanuel and Raymond 1993). Cloudy disturbances are sometimes associated with natural disasters© 2016 Kajikawa et al. Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0
International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, andreproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to
the Creative Commons license, and indicate if changes were made.

Kajikawa et al. Progress in Earth and Planetary Science (2016) 3:16

because of related heavy rainfall; hence, it is important toenrich our understanding of the processes and mechanisms of cloudy disturbances. One of the important
processes that characterize cloudy disturbances is theinteraction between deep convection and cloudy disturbances through the hierarchical structure of cloud clusterand super cloud cluster (SCC). SCC is the eastwardmoving convection area near the equator with a horizontal scale of 2000–4000 km (Nakazawa 1988; Mapes andHouze 1993). However, it has been difficult to obtain observational data that is spatiotemporal enough to examinethat process (Stephens et al. 2010; Mrowiec et al. 2012).
Numerical simulations have been used to compensate thedeficiency and gaps in observational data. The ability to
express deep convection, with its effect on larger-scale
phenomenon, is crucial for better simulating global circulation and associated organizations of cloud systems anddisturbances.
However, because there is a large gap in spatiotemporalscale between convection on the order of 100–101 km andcloudy disturbances on the order of 103 km, it has beenchallenging to globally simulate both phenomena andcomprehensively discuss their interaction. In previous decades, due to the low horizontal resolution of the model,
clouds have been expressed as parameterization. Various
types of cumulus parameterization were established andhave been used in the AGCM [e.g., (Arakawa andSchubert 1974; Kain and Fritsch 1990; Yoshimura et al.
2015)]. The variety of these parameterizations has beena source of uncertainties in model results.
It is impossible for a conventional GCM to represent
the hierarchy of cloud organization from elemental convective clouds. Thus, comprehensive understanding, including the impact of organized clouds on generalcirculation, was not realistic. The new Nonhydrostatic
Icosahedral Atmospheric Model (NICAM) (Tomita andSatoh 2004; Satoh et al. 2008; Satoh et al. 2014) is designed to conduct global simulation without cumulus
parameterization. Previous studies have shown the usefulness of the global nonhydrostatic model without cumulus
parameterization for large-scale organized convective
systems and disturbances, such as tropical cyclones(Fudeyasu et al. 2008; Yamaura et al. 2013; Miyamoto etal. 2014; Nakano et al. 2015), the Madden-Julian oscillation (MJO) (Miura et al. 2007; Miyakawa et al. 2014), andmonsoon onset (Kajikawa et al. 2015). However, in theearly 2010s, the horizontal grid spacing with 3.5 km waslimited. Although this resolution was the best possible inthose days for qualitatively acceptable results for the cloud
disturbance expression, the impact of higher resolution onmodel results was expected for the interaction between
different spatiotemporal scale phenomena.
Because of these considerations, Miyamoto et al.
(2013) (hereafter MY13) successfully conducted thePage 2 of 14

first-ever global atmosphere simulations with subkilometer grid spacing. They further stepped forward
to resolve the convection for the entire Earth.
Through a set of grid-refinement experiments fromover 10 km to sub-kilometer, they found that thesimulated convection core averaging over the globe
is expressed not by a single grid point but by multiple grid points in the sub-kilometer grid-spacing
simulation. They also showed that the expression of
convection core was drastically changed between 3.5
and 1.7 km grid spacing. Furthermore, Miyamoto etal. (2015) (hereafter MY15) conducted detailed analysis for convections simulated in the finest grid spacing. They explained that the statistical properties ofdeep convection are significantly different in various
cloudy disturbances, such as MJOs or tropical cyclones (TCs).
In short, we have been in a transition stage of improving the representation of cloud processes, including the feedbacks, with computer resources (Randall
et al. 2003), and deep convection is one of the important components of climate modeling (Stevens andBony 2013). The success of sub-kilometer global atmospheric simulation in MY13 and MY15 opens thedoor to the next stage of global research for deep
convection and the cloudy disturbances that arise
from its organization, by truly resolving the deep
convection.
However, several issues remain. The primary issue isthe dependence of the essential change of convection
properties on the location and environment of the grid
spacing under consideration. MY13 showed the change
in the sense of global mean and the subsequent paper,and MY15 clarified the different convection aspects between the main cloud disturbances under the highest
resolution simulation only. MY13 did not discuss thedependence on the cloud disturbance, while MY15 did
not discuss the dependence on the resolution. In thisstudy, we investigate the primary issue more comprehensively, considering both MY13 and MY15. The specific question is as follows: In what area does
convection make the larger contribution to the resolution dependence of detected convection properties
averaging over the globe as shown in MY13? Anotherimportant question is as follows: What environmental
condition is effective in producing the diversity of convection properties, i.e., what is the resolution relationship between the number of deep convections, areas ofdeep convection, vertical mass flux outgoing longwave
radiation (OLR), and precipitation? In this paper, we
perform comprehensive analysis to address these questions and resolve the issues by describing an overview
of sub-kilometer global simulation with a set of gridrefinement experiments.

Kajikawa et al. Progress in Earth and Planetary Science (2016) 3:16

Methods
We used a set of global atmospheric simulation resultsof a grid-refinement experiment. The simulation was
conducted using NICAM. The number of vertical layers
was 94, and the grid interval gradually expanded withheight. The height of the lowest level was 36 m, and theaverage resolutions in the boundary layer and in the
troposphere were about 80 and 250 m, respectively. The
height of the top of the atmosphere was 39,291 m. The
detailed description of the dynamical core is summarizedin Tomita and Satoh (2004). Physical processes such asradiation process, microphysical process, boundary-layer
turbulence, and surface flux were solved using theparameterizations of Sekiguchi and Nakajima (2008),
Tomita (2008), Noda et al. (2010), and Louis (1979). Cumulus parameterization was not used in any experiment.
The horizontal grid spacing in the series of experiments
was set at 0.87, 1.7, 3.5, 7.0, and 14 km. Hereafter, thesimulations are referred to (as in MY13) as Δx, where x
is one of the horizontal grid-spacing values. For example, grid spacing for 0.87 km is Δ0.87. In addition, weused 20,480 nodes as the maximum for conducting
Δ0.87. The detailed computational performance is described in the Appendix.
The initial conditions and integration of each experiment are illustrated in Fig. 1. The initial conditions ineach experiment were constructed using the results of aone-step coarser resolution after a 3 day integration,
beginning 2012082200UTC, except for Δ0.87, which was
initialized with the two-step coarser resolution of Δ3.5,
as shown. This integration was initialized by linearlyFig. 1 Illustration of the initial condition in each experiment

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interpolated data from the final analysis of the National
Center for Atmospheric Research (Kalnay et al. 1996).
For example, the initial condition of Δ14 was obtained
from the 3 day integration of Δ28. The simulation period
was 12 h, from 2012082500UTC to 2012082512UTC. We
used the data at 2012082512UTC in each experiment for
the following analysis.
To define the convection in the simulation and validate such data for our analysis, we applied the following
method to extract the convection in the simulated results, as in MY13. First, we defined the convective grids
by optical thickness (>35) and cloud top pressure(<400 hPa) based on the cloud categorization scheme of
the International Satellite Cloud Climatology Project(ISCCP) (Rossow and Schiffer 1999). Then, we could detect the convection core in the convective grids as thegrid at which the vertical velocity averaged in the troposphere is greater than that in all neighboring grids. Thisdiagnosis, using the local peak of vertical velocity, enables us to avoid the controversial discussion on thethreshold dependences of detected convections. Figure 2
shows the time series of the number of convective grid
points in each simulation, which was not shown in
MY13. The number of convective grid points is sensitive
to the initial adjustment, abruptly increasing at the
beginning of the integration. A 3 day integration of theobservational data seems to be long enough for thenumber of deep convections to become almost
constant. Twelve-hour simulations initialized by thesimulation results of a one-step coarser resolution are
also long enough to obtain a constant number of deep

Kajikawa et al. Progress in Earth and Planetary Science (2016) 3:16

Page 4 of 14abFig. 2 a Time series of the convective grid numbers in each experiment. b Close-up view of (a) around 3 days

convections. Hence, the spin-up can be ignored in thedata snapshot that was used.
Since we focus on the resolution dependence of theconvection properties in each cloudy disturbance, we
extracted the area of MJOs, TCs, mid-latitudinal low disturbances (MDL), and fronts (FRT), as in MY15. Although the method is the same as that used in MY15,
we review it here to aid the following discussion. The
MJO area is defined as the grid where the reconstructed
OLR with first and second modes of boreal summer
intraseasonal oscillation index (Kikuchi et al. 2012) was
less than −10 W m−2. To extract the TCs, we applied theMiyamoto et al. (2014) methodology and defined thearea inside the 600 km radius from the center as the TC
area. To detect the MDL centers and FRT, we first reconstructed the simulation data with coarsened 2.5° ×
2.5° grid resolution. Then, we picked the MDL centers
as grids at which the SLP was 5 hPa less than the areal
average in the 10° radius. Finally, the MDL area wasdefined as inside of 1000 km from the MDL center. To
extract the FRT region, we first applied the thermal
frontal locator (Renard and Clarke 1965). This represented a third-order differential of the equivalent potential temperature at the 1500 m level in the horizontal
direction. We detected the grid where the thermal
frontal locator was >10–13 in the 2.5° × 2.5° data as a potential FRT grid. If the FRT grids lined up continuouslywith maximum distance greater than 10°, we defined thearea as the FRT line. Finally, the FRT area was definedas the area inside the 200 km distance from the FRTline. In this study, we merge the MDL and FRT areas as
the mid-latitude disturbance (MLD) area.

Figure 3 shows the horizontal distribution of theclouds in Δ14, Δ3.5, and Δ0.87, with the close-up region
over the western North Pacific in the same experiment.
The large-scale structure of the clouds, including cloudclusters, tropical cyclones, and mid-latitude disturbances, is almost unchanged among the grid-refinement
experiments. The convection reasonably represents theglobal aspect in higher resolution. By comparison,among three simulations focusing on the specific area
(Fig. 3d–f ), it is remarkable that the Δ0.87 provides amore detailed description of the smaller-scale cloud
structure. These available datasets from the gridrefinement experiments enabled us to statistically investigate the resolution dependence of the convection
properties.

Results and discussion
Resolution dependence in the global field

Before we discuss the characteristics of deep convection,
we need to confirm the consistency of the backgroundenvironment for the simulated convections among thedifferent grid-spacing simulations. Figure 4 shows theglobal mean of OLR, precipitation, zonal velocity, andvertical mass flux in all of the simulation results, with
their global standard deviations. Global-mean OLR
slightly increases on finer-resolution simulation. However, no meteorological variables showed significant
change; they were almost constant among the different
grid-spacing simulations. It is of interest that the global
standard deviation of precipitation and vertical mass flux
had a decreasing trend from Δ14 to Δ3.5 and that thistrend is not clear in Δ1.7 and Δ0.87. On the other hand,

Kajikawa et al. Progress in Earth and Planetary Science (2016) 3:16

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Fig. 3 Global view of cloud distribution simulated by (a) Δ14 km, (b) Δ3.5 km, and (c) Δ0.87 km (d–f) focusing over the western North Pacificregion of (a–c)

the standard deviation of zonal wind does not showsuch a trend. When compared to existing observation
data, the global-mean OLR in the simulations isaround 240–250 W m−2, which is relatively larger thanthe observed OLR at around 235 W m−2, [obtained
from daily-mean-interpolated OLR data from the
National Oceanic and Atmospheric Association satellite (Liebmann and Smith 1996)]. The global-mean precipitation of around 0.15 mm h−1 was relatively larger
than the daily-mean precipitation on August 25, 2012[provided by the Global Precipitation Climatology Project(Adler et al. 2003) (around 0.109)]. Since these variables inFig. 4 are based not on a specific time average but on asnapshot, slight differences are conceivable. The potential
reason for no significant change is that the integration
time of each simulation was 3.5 days in total, which is notenough time to respond to the interactions among
different-scale atmospheric phenomena.
Figure 5 shows the zonal-mean OLR and the numberof detected convections in each simulation. Zonal-mean

OLR has variability among the horizontal grid spacing.
This variability is large over the mid-high latitudes (especially 30 N–90 N) and small over the tropics and arid
regions (30 S–10 S) in the southern hemisphere (Fig. 5a).
Since we used snapshot data for this analysis, the location of the simulated convection and cloudy disturbances is different in each simulation, especially thesynoptic disturbances over the mid-high latitudes, whichcauses the relatively large variability. Overall, zonalmean OLR in Δ0.87 is higher than in other resolution
experiments, especially over the mid-high latitudes.
Zonal-mean OLR in each simulation is consistent withobservation, except for the area between 30 S and 10 S.
The OLR in the simulation is about 30 W m−2 larger
than observations in the peak. This strongly affects the
positive bias of the global-mean OLR in Fig. 4a.
How is the relatively larger OLR in Δ0.87 and Δ1.7
produced? MY13 pointed out that convection is resolved
in simulations with finer than 2 km grid spacing. This islinked with the OLR difference. However, we also need

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a

b

c

d

Fig. 4 Resolution dependencies of global-mean (a) OLR, (b) precipitation, (c) zonal wind speed at 5 km, and (d) vertical mass fluxabFig. 5 Resolution dependencies of zonal-mean (a) OLR and (b) the
number of detected convection coresto investigate the resolution dependence of the otherclouds in the simulation. Figure 6 shows the area of each
ISCCP cloud type over the globe, defined by cloud top
pressure and cloud optical thickness (Rossow and Schiffer
1999), in the grid-refinement experiments. The area of
deep convection that we focused on in this study isabruptly decreased between Δ3.5 and Δ1.7, whereas thearea of clear sky is increased with the same grid-spacingchange. This suggests that the simulations in Δ1.7 andΔ0.87 express the proper size of the convection core withthe multiple grid points and distinguish the non-cloudysky around the convection as well. It is of interest that theareas of cirrus also increased from Δ14 and Δ0.87, implying that the simulations with higher spatial resolution arereasonably able to express the anvil associated with deep
convections. According to the resolution dependence ofthe cloud area, increasing the zonal-mean OLR over the
mid-high latitudes in the finer-resolution simulation canbe explained by the increase of the area of clear sky. On
the other hand, in the tropics, the zonal-mean OLR may
be canceled out between the increased area of clear sky
and that of cirrus with deeper convection. Further analysis
is needed to quantitatively discuss the cause of resolution
dependence in the other types of clouds.
The area of low cloud (e.g., stratocumulus) gradually
decreases with higher resolution, especially from Δ14
and Δ3.5. Two possible reasons of this low-cloud trend
are suggested. The low-cloud cells are likely to be resolved with finer resolution as well as deep convection,
decreasing the low-cloud area and increasing the clearsky area. The upward motion in the low-cloud core may

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Fig. 6 Resolution dependence of total area of clear sky, deep convection, cirrostratus, cirrus, middle cloud, and low cloud, averaged over the globe

be accelerated with resolving the convection core. The
faster upward motion in this model provides faster conversion from cloud to rain (Tomita 2008; Sato et al.
2015). This would reflect the decrease of the low-cloudarea. On the other hand, drastically increasing the horizontal and vertical resolutions with the large-eddy simulation (LES) technique gives better representation ofstratocumulus (e.g., Sato et al. 2015). Their results andour results suggest that some parameterization or tuningof microphysics is still needed in the current global
modeling stage.
The area of deep convection over the globe has significantly decreased, between Δ3.5 and Δ1.7, which is consistent with the change of the convection number andthe distance to the nearest convection core, as pointed
out in MY13. The active convection is often accompanied by rainfall. In Fig. 7, we examine the resolution dependence of the precipitation rate at the grid of theconvection core and show the frequency of the precipitation. The vertical axis denotes the logarithmic axis of
the frequency. The precipitation over the convection
core in Δ14, Δ7.0, and Δ3.5 is confined to less than
20 mm h−1. Strong precipitation is shown in Δ1.7

(around 50 mm h−1) and Δ0.87 (more than 100 mm h−1).
The ratio of strong precipitation, which is in excess of
20 mm h−1, is drastically increased from Δ3.5 to Δ1.7.
This is consistent with the idea that convection is
resolved using multiple grid points in simulations andenhancement of the upward motion with the gridFig. 7 Probability function of precipitation at the grid of the simulated
convection core at each horizontal resolution

Kajikawa et al. Progress in Earth and Planetary Science (2016) 3:16

spacing of less than 2 km. The global-mean precipitation is almost constant in the different grid-spacing
simulations. In the case of grid spacing of more than
2 km, convection with rainfall is described as one gridfor the larger area, and then, the rainfall intensity isrelatively weak. In contrast, in the case of grid spacingof less than 2 km, the enhancement of the upward motion provides strong precipitation at the convection
core grid. In addition, we suggest the two effects of (1)resolving the convection with multiple grid points and(2) enhancement of the convection activity over thetropics. Since the former induce the increasing of thearea of clear sky and OLR and the latter induce the decrease of OLR, the OLR over the tropics tends to beless variable among the simulations due to the balance ofthe two effects (Fig. 5a). We also speculated that the decreasing trend in the standard deviation of global-mean
precipitation between Δ14 and Δ3.5 is linked to the decrease of total cloud area and the increase of the sample
grid number, whereas this trend would be canceled out by
the increasing heavy rainfall in Δ1.7 and Δ0.87.
In short, we confirm the diversity of the resolution dependence of OLR in the latitude and area of each cloudtype among the grid-refinement simulations, although
the global mean is consistent among the simulations.
We also found that the convection resolved by multiple
grid points in Δ1.7 and Δ0.87 was accompanied bystronger rainfall.
Resolution dependence on convection properties

First, we briefly introduce the results in MY13 anddescribe the resolution dependence of the simulated
convection properties averaging over the globe. MY13
found that the convection core is resolved with multiple
grid points when the horizontal grid space is less thananumber of convection

frequency/total number

5

number

2 km. Figure 8 shows the resolution dependence of (a)the number of convections and (b) grid distance to thenearest convection core over the globe. The number ofconvection core in Δ3.5 and Δ7.0 is about four times larger than the number in Δ7.0 and Δ14; hence, those areshown on the logΔ4 line starting from the number in
Δ14 (dashed line in Fig. 8a). This indicates that the simulated convection in double resolution is simply an interpolated result of the original. However, the rate ofincrease in the number of convection core is decreased
from Δ3.5 to Δ1.7. In other words, the number tends todistance from the logΔ4 line in Δ1.7. If the number ofthe simulated convection core reaches the appropriate
value, it is constant regardless of the grid spacing. Clear
convergence was not confirmed even in Δ0.87; however,
the increase rate of the convection is changed between
the grid spacing of 3.5 and 1.7 km.
The resolution dependence in the histogram of theminimum distance between convection cores is alsochanged between Δ3.5 and Δ1.7 (Fig. 8b). The peak offrequency in Δ14, Δ7.0, and Δ3.5 appears in four grind
points, whereas that in Δ1.7 and Δ0.87 is larger thanfour. Since the actual length of four grid points is different in each experiment, we suggest that the simulated
convection distance in coarser resolution experiments isdetermined not physically but numerically; it may depend on the numerical discretization method. Hence, we
speculated that the realistic distance between convection
cores appears to be larger than the effective resolutionin Δ1.7 and Δ0.87.
To investigate the horizontal diversity of the above
features as a global mean, we have further analyzed theresolution dependence of the simulated convection
properties, considering the perspective of the land-oceandifference (4.1), the latitude difference (4.2), and the

b

10

4

10

3

10

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0.8

1.7

3.5
Δ (km)

7

14

distance between convection
0.25

Δ14.0
Δ7.0
Δ3.5
Δ1.7
Δ0.8

0.2
0.15
0.1
0.05
0
0

4 5
number of grid10

Fig. 8 Resolution dependencies of convective features: a the number of convections and (b) grid distance to the nearest convective feature.
The thin dashed line in (a) indicates a log Δ4 crossing at the point of Δ14 as a reference (Miyamoto et al 2013)

Kajikawa et al. Progress in Earth and Planetary Science (2016) 3:16

difference in cloudy disturbances (4.3), and we pickedup the convections over the other specific region (4.4) inthe following sections.

Land and ocean difference

Different surface conditions are one of the potential
factors for characterizing convection. We investigatedconvection properties over land and ocean separately.
Figure 9 shows the number of convections and grid distance to the nearest convection core in each experimentas similar as Fig. 8 with vertical velocity of compositedconvections based on the detected convection cores in
Δ0.87 over land and ocean, respectively. The number ofconvections over ocean is larger than those over landbecause many deep convection cores are found over thetropical ocean. The number of convections drasticallychanges between Δ3.5 and Δ1.7, over both land andocean. The grid distance between convections alsochanges at around the 2 km grid spacing; the peak offrequency tends to be larger from four grids. This isconsistent with the global mean (Fig. 8). The verticalvelocity of the convection core is slightly larger in theconvection over land than that over ocean. In addition, aPage 9 of 14

decrease of the increasing rate of the convection number
occurred in the simulation of Δ3.5 over land. However,both convection properties over land and ocean are very
consistent with the global-mean feature (Fig. 8), and in aqualitative sense, little significant difference in the convection feature over land and over ocean is found in thisstudy.

Latitudinal difference

The location of the convection, especially in latitude,
should be connected to the thermal condition affecting
the property of convection. To examine the latitudedifference of convection properties and its resolution
dependence, we divided the convection over the globe
into four groups based on the gaps in its zonal-mean
distribution (Fig. 5): (1) 70 S–30 S, (2) 15 S–15 N, (3) 15
N–30 N, and (4) 30 N–70 N. Figure 10 shows thechange in the number of detected convections and grid
distance to the nearest convection core with the horizontal grid space in each region. Significant difference
between the tropics and the mid-latitude region is found.
The increasing rate of the convection number in the
mid-latitude begins to decrease between Δ3.5 and Δ1.7.

a

b

c

d

e

f

Fig. 9 Resolution dependence of (a) the number of convections and (b) grid distance to the nearest convection core detected over land. The
thin dashed line in (a) denotes a log Δ4 based on the value of Δ14 as a reference. c Radius-height cross section for composites of vertical velocity(w: shaded) and velocity vector of radial and vertical velocity (vector) for the simulated convection core detected over ocean in Δ0.87. The white
contour denotes 0.3 and 0.6 ms−1, and the black contour indicates the mixing ratio of hydrometeors weighted by air density with an interval of
0.5 g m−3. d–f The same as (a–c) but for the convection detected over land

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a

b

c

d

e

f

g

h

Fig. 10 Resolution dependence of (a) the number of convections and (e) grid distance to the nearest convection core detected over thelatitudinal area between 70 S and 30 S. Figure structure is the same as Fig. 8. The same as (a) and (e) but for the area between 15 S and 15 N(b, f); 15 N and 30 N (c, g); and 30 N and 70 N (d, h)

On the other hand, the convection number over the tropics tends to converge between Δ0.87 and Δ1.7.
The grid distance between convection cores also shows
the difference between the mid-latitude and the tropics. The
distance of the mid-latitude convection becomes larger thanfour grids in Δ1.7 and Δ0.87. Interestingly, the distance tothe mid-latitude convection in the coarse resolution has another peak around one grid. This indicates the convections
occur close to one another. When the convection core is
resolved with multiple grid points in Δ1.7 and Δ0.87, thenumber of convections with one grid distance is dramaticallydecreased and the number of convections with larger grid
distance is increased as well. This also supports that convections in the mid-latitudes are resolved and have a realistic
distance to the nearest convection cores in the simulation ofless than 2 km. In contrast, the grid distance between convections over the tropics is distributed widely, with the peakat four to five grids. Since the increasing ratio of the convection number does not change significantly around Δ1.7 andΔ3.5, the grid distance also does not change drastically.
However, the distance becomes larger than four grid points
in Δ0.87. Meanwhile, the change of grid distance between
convection cores can be seen from Δ1.7 to Δ0.87 in thewhole area. It also supports that most of the convections
would be resolved with multiple grid points in Δ0.87. In
short, the resolution dependence of the convection showsdifferent trends in the tropics and the mid-latitude area.

Different cloudy disturbances

MY15 showed the diversity of convection properties invarious disturbances in Δ0.87. In this study, we investigated the resolution dependence of the convection number in cloudy disturbances: MJO, TC, and mid-latitude
disturbances, as in MY15. Each disturbance region isshown in Fig. 11. In this study, we also add the categoryof “other,” which is defined as all convections that are
not located in any of the above cloudy disturbances.
Figure 12 shows the resolution dependence of the number of detected convections in each cloudy disturbance,“other,” and global accumulation. The global accumulation is the same as in Fig. 8. The trend of the number ofconvections does not converge at about 2 km except forthe convections categorized as “other” in this study. The
number of convections in each cloudy disturbance in
Δ0.87 is about 104, while those categorized as “other” isabout 105, which is similar to the global accumulation.
Therefore, the convection categorized as “other” makesa large contribution to the global aspects, while thecontribution of the convection in the cloudy disturbanceto the global aspect is limited. The difference in theconvection numbers between global accumulation andeach cloudy disturbance clearly shows that the convergent trend is weaker in MJO and TC. This would affectthe latitudinal difference in the “Latitudinal difference”
section. It is important that the trend of the convection

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Fig. 11 a Horizontal distribution of the extracted convection core in Δ0.87 (yellow) and the defined area of MJO (red), TC (blue), MDL (green), and
FRT (magenta) disturbances, respectively. b Latitudinal profile of the number of the extracted convective grid points in each disturbance in Δ0.87(Miyamoto et al., 2015)

number in the organized cloudy disturbance has lessconvergence around 2 km but tends to converge from
Δ1.7 to Δ0.87 at least. This supports that most of theorganized convection in the tropics would be resolvedin Δ0.87.
Specific area

We also checked the convection properties and resolution
dependence in the specific area where the convection isabactive. We selected the three regions: (1) mid-Pacific (150
E–150 W, 15 S–15 N), (2) Maritime Continent (90 E–150
E, 15 S–10 N), and (3) Tibetan Plateau (70 E–100 E, 20
N–35 N), based on the lower OLR in the surrounding
areas and the large number of detected convections (about104) (see Fig. 11). These three areas can be categorized as
the tropics or Asian monsoon region. The essentialchange of the convection properties starts between Δ1.7
and Δ0.87 over the mid-Pacific and Maritime Continent

c

f
d

e

Fig. 12 Resolution dependence of the number of detected convections in (a) the globe, (b) other, (c) MJO, (d) TC, (e) MLD (MDL and FRT), and(f) difference from globe after notarizing based on the convection number of Δ14 in each disturbance. The thin dashed line in (a–e) denotes alog Δ4 based on the value of each Δ14 as a referenceKajikawa et al. Progress in Earth and Planetary Science (2016) 3:16

(Fig. 13). The number of the convection distances around
one to two grids is also drastically decreased between Δ3.5
and Δ1.7. On the other hand, the convections over the
Tibetan Plateau do not show a significant convergent
trend for the number of convections. Since the convections over the Tibetan Plateau and mid-Pacific seem to bein the organized cloud system (Fig. 11), it is implied thatconvections forced by large-scale disturbances tend tohave a less significant change of properties, even in Δ1.7.
Although the detailed cloud system over the mid-Pacificand Tibetan Plateau is not determined in this study, environmental conditions over those areas should be explained
for a better understanding of the resolution dependence ofthe convection.

Conclusions
We comprehensively investigated the simulated convection properties and global-mean field by focusing on
their resolution dependence, based on grid-refinement
experiments from 14 to 0.87 km grid spacing by using
NICAM. The convergence trend for the number of convections is confirmed to occur between Δ3.5 and Δ1.7
(Miyamoto et al. 2013). The global mean of vertical massflux, precipitation, and zonal wind at 5 km are conservedin different resolution simulations (Fig. 4). Global-mean
OLR is slightly increased in Δ1.7 and Δ0.87, and thistrend is more remarkable over the mid-latitude area
(Fig. 5). Global-mean precipitation has no resolution
dependence, while the precipitation intensity associatedwith deep convection becomes higher in increasing resolutions (Fig. 7). Interestingly, the ratio of the cloud type

Page 12 of 14

over the globe is different between simulations. The areaof low and middle clouds is also decreased with increasing the resolution as well as deep convection, and thoseof clear sky are increased particularly in Δ1.7 and Δ0.87(Fig. 6). These differences reflect the resolution dependence of zonal-mean OLR (Fig. 5).
MY13 pointed out that the essential change of thenumber of convection cores and distance to the nearest
convective core occurred around the 2 km grid spacing
as a global mean (Fig. 8). We further investigated theresolution dependence of the simulated convection fromthe wider and more various perspectives than MY13.
We found that the results in MY13 were different
between latitudinal regions and cloudy disturbances(Figs. 10 and 12), although the trend of the convection
number and grid distance between convection cores is
not significantly different between over land and ocean(Fig. 9). The convergence trend for the number of convections in the mid-latitude area is more predominant
than that in the tropics (Fig. 10). The essential change ofthe convection properties around the 2 km grid spacing
is not clear, even in Δ1.7, for the convections in thecloudy disturbances categorized by MY15. In contrast,
the convection properties that are not detected in the
categorized cloudy disturbance change drastically between
Δ3.5 and Δ1.7, which is similar to global accumulations(Fig. 12). Moreover, the convections in the cloud cluster
over the mid-Pacific and Maritime Continent show asimilar trend of convections in MJO and TC (Fig. 13).
In this study, we showed the diversity of the resolution
dependency of the simulated convection properties.

a

b

c

d

e

f

Fig. 13 Resolution dependence of (a) the number of convections over the mid-Pacific. b The same as (a) but for over the Maritime Continent. c
The same as (a) but for over the Tibetan area. d–f Grid distance to the nearest convection core detected. The same area as (a–c)

Kajikawa et al. Progress in Earth and Planetary Science (2016) 3:16

Convections over the mid-latitudes and convections detected other than in the cloudy disturbances show theessential change of properties more clearly around the
2 km grid spacing, largely contributing the global mean.
We speculate that this difference is related to thestrength of forcing under the tropical cloudy disturbance. In fact, larger CAPE in the MJO area and larger
low-level convergence in the TC area are confirmed in
MY15. It is also speculated that the convection naturally
arises as many as possible in such area under the strong
forcing. Therefore, the convections are tightly packed in
the cloudy disturbance, the size of convection core isrelatively smaller than other categorized convections,and the convection core is not resolved by multiple grid
points, even in Δ1.7. In contrast, where the environmental atmosphere allows convection to occur freely, thesimulated convection, likely the isolated convective
cloud, is relatively larger than that in tropical cloudy
disturbances and it can be resolved by multiple grid
points in Δ1.7 and Δ0.87. Since this difference in therelationship between cloudy disturbances appears to notlink with the surface condition, it does not affect theconvection property difference between convection overland and ocean.
We found a difference in resolution dependency inthe simulated convection property. It is important thatthe convections, even in cloudy disturbances, show aconvergent trend for the number and are resolved notby a single grid but by multiple grid points between
Δ1.7 and Δ0.87, at least, despite the existence of theabove difference. This is a noteworthy aspect for a

Page 13 of 14series of grid-refinement experiments. It recalls the further high spatial resolution for better simulations oftropical convections. This would bring a better understanding of tropical cloudy disturbances, based on thehierarchical structure of convections. Hence, longer
time integration of the global atmosphere in the
0.87 km grid spacing in the future will provide significant discussion about the interaction between convections and cloudy disturbances.

Appendix
In the highest resolution run of Δ0.87, we achieved thegreatest computational performance for weak scaling on
the K computer. Figure 14 from Terai et al. (2014)shows a computational performance and scalability of
NICAM on the K computer. At this scaling test, we
increased the number of grids while increasing thenumber of nodes. We achieved 10 % of the peak performance using five nodes (40 cores) with 56 km ofhorizontal grid spacing. The performance was maintained to 8 % with 81,920 nodes (655,360 cores) and
0.44 km of horizontal grid spacing. Elapsed time perstep was increased ~15 % from 80 nodes (Δ14 run) to
20,480 nodes (Δ0.87 run) due to the imbalance of thenumber of computations. This load imbalance is mainly
related to computation in cloud microphysics and thespatial inhomogeneity of cloud distribution. In thisstudy, the run of Δ0.87 with 20,480 nodes was conducted as the highest resolution of the production run,by taking the total computational time and resources
into account.

Fig. 14 Elapsed time and peak performance ratio in weak scaling (Terai et al. 2014)

Kajikawa et al. Progress in Earth and Planetary Science (2016) 3:16

Acknowledgements
The authors are grateful to the editor of the Progress in Earth and Planetary
Science and anonymous reviewers. Special thanks are due to Drs. S.
Nishizawa Y. Sato, and S. Iga in the RIKEN Advanced Institute for Computer
Science (AICS) for the valuable comments. The simulations were performed
using the K computer at the RIKEN AICS under the supported by Strategic
Programs for Innovative Research (SPIRE) Field 3 (Projection of Planet Earth
Variations for Mitigating Natural Disasters).
Authors’ contributions
YK conceived the idea, organized this study, and wrote the manuscript. YM
carried out the simulations, analyzed the simulated results, and collaborated
with YK to draft the manuscript. RY and TY supported to conduct thesimulation and analysis with arranging the necessary environment on the
K computer. HY led the implementation of NICAM on the K computer.
HT coordinated the project and collaborated with YK in the construction of themanuscript. All co-authors provided guidance for the analysis and commented
on the manuscript. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
Author details
1
RIKEN Advanced Institute for Computational Science, 7-1-26
Minatojima-minami-machi, Chuo-ku, Kobe, Hyogo 650-0047, Japan. 2Japan
Agency for Marine-Earth Science and Technology, 2-15, Natsushima-cho,
Yokosuka, Kanagawa 237-0061, Japan.
Received: 3 December 2015 Accepted: 11 May 2016

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