Resolution dependence of deep convections in a global simulation from over 10-kilometer to sub-kilometer grid spacing
© Kajikawa et al. 2016
Received: 3 December 2015
Accepted: 11 May 2016
Published: 6 June 2016
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 the essential 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 and the characteristics of deep convection, to clarify the difference of the essential change by location and environment. We found that the essential change in convection properties was different in the location and environment 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 the global-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 that are 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 stimulate significant discussion about the interaction between the convections and cloudy disturbances.
The rapid increase of computer capabilities has enabled meteorological and climatological researchers to increase horizontal and vertical resolutions in the numerical model (Simmons et al. 1989; Mizuta et al. 2006; Saito et al. 2006; Kodama et al. 2015). The demand for high-resolution simulation not only from regional-model 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 the organization 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 because of related heavy rainfall; hence, it is important to enrich our understanding of the processes and mechanisms of cloudy disturbances. One of the important processes that characterize cloudy disturbances is the interaction between deep convection and cloudy disturbances through the hierarchical structure of cloud cluster and super cloud cluster (SCC). SCC is the eastward-moving convection area near the equator with a horizontal scale of 2000–4000 km (Nakazawa 1988; Mapes and Houze 1993). However, it has been difficult to obtain observational data that is spatiotemporal enough to examine that process (Stephens et al. 2010; Mrowiec et al. 2012). Numerical simulations have been used to compensate the deficiency 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 and disturbances.
However, because there is a large gap in spatiotemporal scale between convection on the order of 100–101 km and cloudy disturbances on the order of 103 km, it has been challenging to globally simulate both phenomena and comprehensively 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 and have been used in the AGCM [e.g., (Arakawa and Schubert 1974; Kain and Fritsch 1990; Yoshimura et al. 2015)]. The variety of these parameterizations has been a 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 general circulation, was not realistic. The new Nonhydrostatic Icosahedral Atmospheric Model (NICAM) (Tomita and Satoh 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 et al. 2014; Nakano et al. 2015), the Madden-Julian oscillation (MJO) (Miura et al. 2007; Miyakawa et al. 2014), and monsoon onset (Kajikawa et al. 2015). However, in the early 2010s, the horizontal grid spacing with 3.5 km was limited. Although this resolution was the best possible in those days for qualitatively acceptable results for the cloud disturbance expression, the impact of higher resolution on model results was expected for the interaction between different spatiotemporal scale phenomena.
Because of these considerations, Miyamoto et al. (2013) (hereafter MY13) successfully conducted the first-ever global atmosphere simulations with sub-kilometer grid spacing. They further stepped forward to resolve the convection for the entire Earth. Through a set of grid-refinement experiments from over 10 km to sub-kilometer, they found that the simulated 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 et al. (2015) (hereafter MY15) conducted detailed analysis for convections simulated in the finest grid spacing. They explained that the statistical properties of deep 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 and Bony 2013). The success of sub-kilometer global atmospheric simulation in MY13 and MY15 opens the door 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 is the 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 the dependence on the cloud disturbance, while MY15 did not discuss the dependence on the resolution. In this study, 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? Another important 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 of deep 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 grid-refinement experiments.
We used a set of global atmospheric simulation results of a grid-refinement experiment. The simulation was conducted using NICAM. 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 average 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 summarized in Tomita and Satoh (2004). Physical processes such as radiation process, microphysical process, boundary-layer turbulence, and surface flux were solved using the parameterizations 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, the simulations 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, we used 20,480 nodes as the maximum for conducting Δ0.87. The detailed computational performance is described in the Appendix.
Since we focus on the resolution dependence of the convection 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 the Miyamoto et al. (2014) methodology and defined the area 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 was defined 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 continuously with maximum distance greater than 10°, we defined the area as the FRT line. Finally, the FRT area was defined as the area inside the 200 km distance from the FRT line. In this study, we merge the MDL and FRT areas as the mid-latitude disturbance (MLD) area.
Results and discussion
Resolution dependence in the global field
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 clear-sky area. The upward motion in the low-cloud core may 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-cloud area. On the other hand, drastically increasing the horizontal and vertical resolutions with the large-eddy simulation (LES) technique gives better representation of stratocumulus (e.g., Sato et al. 2015). Their results and our results suggest that some parameterization or tuning of microphysics is still needed in the current global modeling stage.
In short, we confirm the diversity of the resolution dependence of OLR in the latitude and area of each cloud type 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 by stronger rainfall.
Resolution dependence on convection properties
The resolution dependence in the histogram of the minimum distance between convection cores is also changed between Δ3.5 and Δ1.7 (Fig. 8b). The peak of frequency in Δ14, Δ7.0, and Δ3.5 appears in four grind points, whereas that in Δ1.7 and Δ0.87 is larger than four. Since the actual length of four grid points is different in each experiment, we suggest that the simulated convection distance in coarser resolution experiments is determined 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 resolution in Δ1.7 and Δ0.87.
To investigate the horizontal diversity of the above features as a global mean, we have further analyzed the resolution dependence of the simulated convection properties, considering the perspective of the land-ocean difference (4.1), the latitude difference (4.2), and the difference in cloudy disturbances (4.3), and we picked up the convections over the other specific region (4.4) in the following sections.
Land and ocean difference
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 than four grids in Δ1.7 and Δ0.87. Interestingly, the distance to the 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, the number of convections with one grid distance is dramatically decreased 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 of less than 2 km. In contrast, the grid distance between convections over the tropics is distributed widely, with the peak at four to five grids. Since the increasing ratio of the convection number does not change significantly around Δ1.7 and Δ3.5, 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 the whole 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 shows different trends in the tropics and the mid-latitude area.
Different cloudy disturbances
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 mass flux, precipitation, and zonal wind at 5 km are conserved in different resolution simulations (Fig. 4). Global-mean OLR is slightly increased in Δ1.7 and Δ0.87, and this trend is more remarkable over the mid-latitude area (Fig. 5). Global-mean precipitation has no resolution dependence, while the precipitation intensity associated with deep convection becomes higher in increasing resolutions (Fig. 7). Interestingly, the ratio of the cloud type over the globe is different between simulations. The area of low and middle clouds is also decreased with increasing the resolution as well as deep convection, and those of 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 the number 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 the resolution dependence of the simulated convection from the 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 of the convection properties around the 2 km grid spacing is not clear, even in Δ1.7, for the convections in the cloudy 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 a similar 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. Convections over the mid-latitudes and convections detected other than in the cloudy disturbances show the essential change of properties more clearly around the 2 km grid spacing, largely contributing the global mean. We speculate that this difference is related to the strength 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 is relatively 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, the simulated 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 the relationship between cloudy disturbances appears to not link with the surface condition, it does not affect the convection property difference between convection over land and ocean.
We found a difference in resolution dependency in the simulated convection property. It is important that the convections, even in cloudy disturbances, show a convergent trend for the number and are resolved not by a single grid but by multiple grid points between Δ1.7 and Δ0.87, at least, despite the existence of the above difference. This is a noteworthy aspect for a series of grid-refinement experiments. It recalls the further high spatial resolution for better simulations of tropical convections. This would bring a better understanding of tropical cloudy disturbances, based on the hierarchical 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.
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).
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 the simulation 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 the manuscript. All co-authors provided guidance for the analysis and commented on the manuscript. All authors read and approved the final manuscript.
The authors declare that they have no competing interests.
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