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    Comparison of surface precipitation (mm day−1) in (a) TRMM 3B42, (b) R7, and (c) R14. Data are averaged over June–August 2004. Simulation data were linearly interpolated in space from the original resolutions (i.e., 14 and 7 km) to 1° data.

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    Comparison of observed and modeled frequency (%) for the daily precipitation rate over (a) land and (b) ocean in the tropics (±10° of latitude) from 1 Jun 2004 to 31 Aug 2004. Figure is constructed with the same horizontal resolution in all cases (1°).

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    Temporal changes in surface precipitation (mm day−1) over (a) ocean and (b) land in the tropics (±10° of latitude). Lines with + symbols represents data from TRMM 3B42. Lines with circles and squares represent data from R14 and R7, respectively.

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    Spatial distribution of periods during which the maximum precipitation occurs in (a) TRMM 3B42, (b) R7, and (c) R14.

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    Time–height plot of (a) moist static energy (solid contours; kJ kg−1) and deviation from the daily mean (colors), and (b) vertical velocity (solid contours; m s−1) and deviation from the daily mean (colors) over land in the tropics (±10° of latitude). Contour intervals are (a) 2000 kJ kg−1 and (b) 0.02 m s−1. Note that the data over land are also drawn near the ground, reflecting the result over low topographical regions (e.g., the Amazon basin).

  • View in gallery

    As in Fig. 5, but over ocean. Contour intervals are (a) 500 kJ kg−1 and (b) 0.02 m s−1, respectively.

  • View in gallery

    Temporal changes in (a) CAPE (J kg−1) and (b) CIN (J kg−1) over land in the tropics. Solid and dashed lines (drawn at an interval of 1 h) show the results of R7 and R14, respectively. Dotted lines with open circles and + symbols show the results of JRA-25 and NCEP reanalysis data, respectively. (c),(d) As in (a),(b), but over ocean. For (a),(b),(d), the vertical axes of JRA-25 and NCEP reanalysis data are shown on the right-hand side. Note that CAPE and CIN are computed by lifting an air parcel at the 950-hPa height.

  • View in gallery

    Temporal changes in the modeled tropical atmosphere. Color shadings show the sum of cloud water and cloud ice mixing ratios (mg kg−1) over land in (a) R7 and (b) R14. (c) Difference of R7 from R14. (d)–(f) As in (a)–(c), but for the result over ocean.

  • View in gallery

    Example of the horizontal distribution of precipitating areas at 0000–0130 UTC 6 Jun 2004. (a) Surface precipitation in the tropics, and (b) enlargement of the region outlined by the rectangle in (a). Shading indicates precipitating areas, and dots in (b) indicate grid points identified as precipitating areas.

  • View in gallery

    Temporal changes (mm h−1 km−1) in the size distribution of precipitating areas over the tropics. Data are shown for (a) R7 and (b) R14. Histograms were constructed by sampling the data at radii intervals of 50 km. (c),(d) As in (a), (b), but over ocean.

  • View in gallery

    Temporal changes in the percent cloud coverage in R7 for the TC region for clouds with tops lying within 1°C intervals. Size categories of clusters are (a) small, (b) medium, (c) large, and (d) giant, with a contour interval of 0.5%. See the text for further details.

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    Percentage contribution to surface precipitation and cloud mass flux at 2 km AGL of precipitating areas over the tropics with different radii. Results of surface precipitation over (a) land and (b) ocean. Solid and dashed bars show the results of R7 and R14, respectively. (c),(d) As in (a),(b), but for the results of cloud mass flux at 2 km AGL.

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Quantitative Assessment of Diurnal Variation of Tropical Convection Simulated by a Global Nonhydrostatic Model without Cumulus Parameterization

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  • 1 Research Institute for Global Change, Japan Agency for Marine-Earth Science and Technology, Kanagawa, Japan
  • 2 Research Institute for Global Change, Japan Agency for Marine-Earth Science and Technology, Kanagawa, and Atmosphere and Ocean Research Institute, The University of Tokyo, Chiba, Japan
  • 3 Research Institute for Global Change, Japan Agency for Marine-Earth Science and Technology, Kanagawa, and Advanced Institute for Computational Science, RIKEN, Hyogo, Japan
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Abstract

This study investigated the resolution dependence of diurnal variation in tropical convective systems represented by a global nonhydrostatic model without cumulus parameterization. This paper describes the detailed characteristics of diurnal variation in surface precipitation based on three-dimensional data, with the aim of explicitly clarifying the mechanism that underlies the variation. The study particularly focused on the evolution in the size of the precipitation area for deep convective systems with an analysis of the vertical structure of thermodynamic fields. This analysis compares the results of simulations with horizontal grid sizes of 14 and 7 km (R14 and R7, respectively). Over land, the phase delay of diurnal variations in R7 is about 3 h less than that in R14. R7 produces a pronounced diurnal variation in the size distributions of precipitating area(s), especially for areas with a radius of 0–100 km; this characteristic is not found for R14. Such areas actively evolve between noon and evening, leading to the smooth development of larger-scale precipitating areas having a radius of 100–150 km. The maximum surface precipitation in R7 over land occurs at around 2000 local time throughout the tropics, approximately 2 h prior to the development of nighttime deep convection. Deep convective regimes are important as agents of vertical heat transport in the tropics. The present results suggest that precipitating areas with a radius <100 km make a strong contribution to the total amount of precipitation and to mass transport.

Corresponding author address: Akira T. Noda, Research Institute for Global Change, Japan Agency for Marine-Earth Science and Technology, 3173-25 Showamachi, Kanazawa-ku, Yokohama City, Kanagawa 236-0001, Japan. E-mail: a_noda@jamstec.go.jp

Abstract

This study investigated the resolution dependence of diurnal variation in tropical convective systems represented by a global nonhydrostatic model without cumulus parameterization. This paper describes the detailed characteristics of diurnal variation in surface precipitation based on three-dimensional data, with the aim of explicitly clarifying the mechanism that underlies the variation. The study particularly focused on the evolution in the size of the precipitation area for deep convective systems with an analysis of the vertical structure of thermodynamic fields. This analysis compares the results of simulations with horizontal grid sizes of 14 and 7 km (R14 and R7, respectively). Over land, the phase delay of diurnal variations in R7 is about 3 h less than that in R14. R7 produces a pronounced diurnal variation in the size distributions of precipitating area(s), especially for areas with a radius of 0–100 km; this characteristic is not found for R14. Such areas actively evolve between noon and evening, leading to the smooth development of larger-scale precipitating areas having a radius of 100–150 km. The maximum surface precipitation in R7 over land occurs at around 2000 local time throughout the tropics, approximately 2 h prior to the development of nighttime deep convection. Deep convective regimes are important as agents of vertical heat transport in the tropics. The present results suggest that precipitating areas with a radius <100 km make a strong contribution to the total amount of precipitation and to mass transport.

Corresponding author address: Akira T. Noda, Research Institute for Global Change, Japan Agency for Marine-Earth Science and Technology, 3173-25 Showamachi, Kanazawa-ku, Yokohama City, Kanagawa 236-0001, Japan. E-mail: a_noda@jamstec.go.jp

1. Introduction

Cumulus convection in the tropics, which has important contributions to general circulation on earth, is known to have a clear diurnal cycle over both land and ocean. The success of past studies involving earth-observation satellites and in situ observations has led to an improved understanding of the characteristics of tropical precipitation (e.g., Brier and Simpson 1969; McGarry and Reed 1978; McBride and Gray 1980; Houze 1989; Nitta and Sekine 1994; Sui et al. 1997). Although differences in satellite sensors may give rise to uncertainty regarding the comparability of their data in these various studies (Kikuchi and Wang 2008), the picture of the gross behavior of tropical convection is that surface precipitation intensifies at around sunrise and evening, whereas it weakens at around noon and midnight over oceanic regions. For land regions, surface precipitation strengthens after noon and weakens by sunrise.

It is well known that tropical precipitation has markedly different characteristics between land and oceanic regions: tropical precipitation over land accompanies a significant diurnal variation of the depth of the boundary layer (BL), which may also give rise to heavy precipitation in the late afternoon. Researchers have constructed numerical models, including general circulation models (GCMs), to investigate the detailed mechanisms that drive such surface precipitation; however, even state-of-the-art GCMs have difficulty in reproducing the behavior of such diurnal changes (e.g., Lee et al. 2007; Hara et al. 2009). One cause of this difficulty is uncertainties related to cumulus parameterization. In fact, Takayabu and Kimoto (2008) indicated that a parameter of the cumulus parameterization, which controls the initiation of convection in the Arakawa–Schubert-type scheme, strongly modulates diurnal changes in global-scale precipitation.

An alternative approach is to use a global nonhydrostatic model without cumulus parameterization and to drastically increase the horizontal resolution to a few kilometers. This type of model explicitly computes the heat and momentum transport by deep convection with minimal ambiguity. Attempts to conduct numerical simulations using such high-resolution GCMs are somewhat primitive, and the finest horizontal grid size employed to date is 3.5 km (Tomita et al. 2005; Miura et al. 2007); however, much more resolution (e.g., <100 m) is required to resolve the detailed behavior of individual deep convections (e.g., Bryan et al. 2003; Grabowski et al. 2006; Pauluis and Garner 2006; Petch 2006). Given the limitations of computational resources, it will be decades before it is possible to perform a global simulation by sufficiently resolving convective processes; consequently, it is necessary to investigate how deep convective systems behave in GCMs with a resolution of a few kilometers. It is expected that climate modelers will start to develop more reliable parameterization schemes of shallow and deep convection for use in O(10 km)-resolution GCMs, and it is important to know how the results would change if cumulus parameterization is switched off. This motivates us to study the extent to which a nonhydrostatic GCM can reproduce cloud activity, including precipitating processes, at the global scale using a model resolution of around 10 km.

Several studies have examined the global characteristics of clouds and precipitating systems by using data simulated by a global nonhydrostatic model; that is, the Nonhydrostatic Icosahedral Atmospheric Model (NICAM; Tomita and Satoh 2004; Satoh et al. 2008). Sato et al. (2009, hereafter S09) examined the characteristics of surface precipitation using horizontal mesh sizes of 14, 7, and 3.5 km of NICAM simulations, and showed that diurnal changes become more realistic with finer horizontal grid size. Their results highlight the benefits of using a nonhydrostatic GCM with a resolution of a few kilometers to clarify the complex behavior of tropical cumulus convection.

We recently performed season-long experiments with horizontal grid sizes of 7 and 14 km (R7 and R14, respectively) over the global domain to investigate the characteristics of climatological clouds along with specific events, such as the Indian monsoon and the development of tropical cyclones (Oouchi et al. 2009a,b; Noda et al. 2010; Yamada et al. 2010). An advantage of the present dataset, compared with those used in previous works (e.g., Inoue et al. 2008; S09), is its high temporal resolution. This enables us to explore the characteristics of surface precipitation, which is strongly related to diurnal variations in thermodynamic structures within the atmosphere.

Recent advances in computational resources have enabled the use of GCMs with an O(10 km) grid size. The importance of models with this resolution has increased over the past decade. For example, the European Centre for Medium-Range Weather Forecasts recently began operational forecasting with a 16-km-mesh GCM (Riddaway 2010), enabling more detailed weather predictions. Based on research that employs NICAM, as outlined above, we consider that a 14-km-mesh model is an important tool with which to assess the gross behavior of convective systems, and it has advantages in, for example, sensitivity studies of physical parameters, for which 3.5- and 7-km-mesh models encounter difficulties in performing month-long integrations due to limitations on computational resources. Although models with O(10 km) mesh or coarser are barely able to resolve individual clouds explicitly (e.g., Grabowski et al. 2006; Pauluis and Garner 2006; Petch 2006), several studies have reported that the 7-km- and 14-km-mesh models perform reasonably well in reproducing tropical convective systems, including the spontaneous onset of an MJO event and the genesis of tropical cyclones (e.g., Miura et al. 2009; Yanase et al. 2010). In such a situation, it is important for climate modelers who employ high-resolution GCMs to understand the peculiarities of numerical models with grid sizes of O(10 km) and O(1 km) in simulated convective systems.

The objective of this study is to clarify the differences in the characteristics of tropical precipitation observed in the 7- and 14-km-mesh models and to explain the cause of the resolution dependence via an analysis of tropical stratification and the resultant diurnally varying precipitating areas, which are not investigated in S09. It would also be important to assess the capability of a 3.5-km-mesh model in this regard; however, long-term integration of such a model would require greater resources than are currently available, meaning that this task is assigned to a future study.

2. Model description and evaluation

The nonhydrostatic GCM used in the present study is NICAM (Tomita and Satoh 2004; Satoh et al. 2008). We investigate the datasets of two global cloud-system-resolving simulations: one with a horizontal grid size of 14 km and another with a grid size of 7 km. Computational conditions for R14 and R7 are the same except for their horizontal grid sizes. We briefly describe the model used for the experiments; for details, see Noda et al. (2010). The vertical grid size increases from 80 m at the lowest grid to 3 km at the model top of 38 km above ground level (AGL). The bottom boundary over land is computed by a bucket-type model, while that over ocean is given by linearly interpolating weekly Reynolds sea surface temperature data (Reynolds and Smith 1994). Cloud microphysics and turbulent mixing processes are computed based on Grabowski et al. (1998) and level 2 of the Mellor–Yamada–Nakanishi–Niino (MYNN) model (Nakanishi and Niino 2006; Nakanishi and Niino 2009; Noda et al. 2010), respectively. National Centers for Environmental Prediction (NCEP) global analysis data at 0000 UTC 1 June 2004 are given for the initial state, and the time integration is performed over 3 months without a nudging scheme. We use the Tropical Rainfall Measuring Mission (TRMM) 3B42 dataset during this period for model verification. We also compare the results with the Global Precipitation Climatology Project (GPCP) version 2 data (Adler et al. 2003) to assess the global characteristics of the modeled surface precipitation (section 3a).

3. Results

a. General characteristics of modeled precipitation

Prior to examining the observed and modeled characteristics of diurnal precipitation, we compare their temporal mean values in Fig. 1. Both R7 and R14 perform well in simulating the spatial characteristics, such as regions of intense precipitation over the intertropical convergence zone (ITCZ), including the African continent and the South Pacific convergence zone (SPCZ); however, the models overestimate precipitation over the Indian Ocean, among other areas, and underestimate precipitation over India, Southeast Asia, and central South America. The excessive surface precipitation is less pronounced in R7 for areas such as the Indian Ocean, SPCZ, and ITCZ of the Atlantic Ocean. Overall, R14 and R7 show similar positive biases in surface precipitation averaged over the longitudes of the ITCZ; the values are up to approximately 3 mm day−1 higher than the 3B42 result. This finding is consistent with the results of Oouchi et al. (2009b) and S09.

Fig. 1.
Fig. 1.

Comparison of surface precipitation (mm day−1) in (a) TRMM 3B42, (b) R7, and (c) R14. Data are averaged over June–August 2004. Simulation data were linearly interpolated in space from the original resolutions (i.e., 14 and 7 km) to 1° data.

Citation: Journal of Climate 25, 14; 10.1175/JCLI-D-11-00295.1

The excessive precipitation over the Indian Ocean in R7 and R14 is also seen in the results of a coupled circulation model [Climate Model version 3 (CM3)] and its atmospheric component [Atmosphere Model version 3 (AM3)] developed by the Geophysical Fluid Dynamics Laboratory (Fig. 25 in Donner et al. 2011). A similar bias has been reported for the Community Climate System Model, version 4 (CCSM4) developed by the National Center for Atmospheric Research (Fig. 5 in Gent et al. 2011). These models suffer from the problem of the so-called double ITCZ, as do R7 and R14.

Tables 1–3 provide a summary statistical comparison of modeled and observed surface precipitation. We also compare the model results with global precipitation data by GPCP. All of the values are compared after interpolating the data into the same spatial and time scales (1° and monthly mean, respectively). For the area 40°S–40°N (see Fig. 1), 3B42 shows an average precipitation rate of 2.6 mm day−1 over 3 months, while GPCP, R7, and R14 yield values of 2.7–2.9, 3.2–3.6, and 3.3–3.9 mm day−1, respectively. The modeled precipitation rate is higher in the first month of the simulation, decreasing thereafter. A comparison of the modeled and observed precipitation rate, based on the root-mean-square error (RMSE) shows that the modeled value of RMSE is especially large during the first month (June), decreasing slightly thereafter. Correlation coefficients among the outputs of the various models are 0.4 or less for most of the present results.

Table 1.

Monthly surface precipitation (mm day−1) averaged over the 40°S–40°N domain.

Table 1.
Table 2.

RMSE (mm day−1) and correlation coefficients (Corr) in comparisons of the present model data with TRMM 3B42 and GPCP data. Data are compared over the 40°S–40°N domain.

Table 2.
Table 3.

As in Table 2, but in comparison with GPCP data. Data are compared over the global domain.

Table 3.

For the global comparison, the average precipitation rate in GPCP is 2.2–2.3 mm day−1 and the modeled rate is 2.7–2.9 mm day−1. The RMSE values of the modeled precipitation are slightly smaller than those over the 40°S–40°N region. The correlation coefficient between modeled and observed results is approximately 0.4, and there is no marked difference about the monthly correlation coefficients during the months simulated.

A comparison with recent climate models indicates that for R7 and R14, the absolute error over the globe in the present period is ∼0.6 mm day−1, which is approximately twice that for CCSM4, AM3, and CM3. RMSEs over the global domain in R7 and R14 are 3.0 and 2.3 mm day−1, respectively; these values are twice as large as those in CCSM4 and AM3. The correlation coefficient between observation and R7 or R14 is half that in AM3 and CM3; consequently, efforts are needed to improve the modeled behavior of climatological precipitation.

Figure 2 compares the observed and modeled frequency of occurrence against a gridcell precipitation rate over land and over oceanic regions in the tropics. Over land, the model tends to overestimate the frequency of occurrence in the ranges of intense and weak precipitation, and it tends to underestimate the frequency of occurrence of moderate precipitation (e.g., 0.1–1.0 mm h−1). The errors observed in R14 are somewhat reduced in R7. Although the modeled bias over ocean shows characteristics that are basically similar to those over land, the result over ocean for precipitation of 0.1–1.0 mm h−1 is closer to that observed, although the error for intense and weak precipitation is greater than that over land.

Fig. 2.
Fig. 2.

Comparison of observed and modeled frequency (%) for the daily precipitation rate over (a) land and (b) ocean in the tropics (±10° of latitude) from 1 Jun 2004 to 31 Aug 2004. Figure is constructed with the same horizontal resolution in all cases (1°).

Citation: Journal of Climate 25, 14; 10.1175/JCLI-D-11-00295.1

Figure 3 shows diurnal variations in surface precipitation within the tropics (10°S–10°N). Over ocean (Fig. 3a), 3B42 data show maximum and minimum values at 0300–0600 and 1800–2100 local time (LT), respectively. The diurnal variation in surface precipitation in R7 is similar to that in R14, and both models perform well in reproducing its phase, although the overestimation of mean values is an important issue that requires improvement (Fig. 1).

Fig. 3.
Fig. 3.

Temporal changes in surface precipitation (mm day−1) over (a) ocean and (b) land in the tropics (±10° of latitude). Lines with + symbols represents data from TRMM 3B42. Lines with circles and squares represent data from R14 and R7, respectively.

Citation: Journal of Climate 25, 14; 10.1175/JCLI-D-11-00295.1

Over land (Fig. 3b), both models show a delay in the phase of diurnal variations. R14 shows maximum and minimum values at 2100–2400 and 1200–1500 LT, respectively, which are about 6 h later than those in the 3B42 result. R7 shows a phase delay of about 3 h. Previous studies using idealized simulations also reported a similar issue of the delay in the development of continental convection in the case of reduced horizontal resolution (e.g., Grabowski et al. 2006). The resolution dependence is more prominent over land than over ocean. The reasons for these resolution-related differences over land and ocean are explored in section 3c. Figure 3b also shows an interesting feature, in that the phase in R7 from 2400 to 1200 LT is similar to that in R14; in contrast to the precipitation maximum, the difference in resolution has relatively little effect on the phase delay of the minimum. The reason for this similarity in phase change between the two resolutions is discussed below.

Figure 4 compares the horizontal distribution of the periods in which maximum precipitation occurs at each grid point. For the 3B42 result over ocean (Fig. 4a), the precipitation is intensified before dawn; the modeled results show similar features in this regard (as indicated by the green and orange colors in the figure; see also Fig. 1a). Several systematic differences are apparent between the datasets, such as the region off the coast of Peru, where the maximum modeled precipitation is delayed by 3 h relative to 3B42, although this makes only a small contribution to the total amount of tropical precipitation (Fig. 1a). The departures from observed values may reflect the difficulty encountered in simulating detailed local circulations. The reasons for these discrepancies should be investigated in a future study. Note that striped patterns appear at latitudes higher than 20°S, presumably representing less meaningful modes compared with the dominant lower-frequency modes due to baroclinic instability waves. Similar patterns were reported by S09.

Fig. 4.
Fig. 4.

Spatial distribution of periods during which the maximum precipitation occurs in (a) TRMM 3B42, (b) R7, and (c) R14.

Citation: Journal of Climate 25, 14; 10.1175/JCLI-D-11-00295.1

Many previous studies have reported a variety of precipitating events caused by diurnal variations related to land–sea breezes, local circulations oscillated by gravity waves, or migrating precipitating systems influenced by terrain (e.g., Houze et al. 1981; Nitta and Sekine 1994; Yang and Slingo 2001; Wang et al. 2007; Takayabu and Kimoto 2008). Although these are important elements in understanding the variability in precipitating systems, we attribute the phase delay of 3–6 h in diurnal variations of surface precipitation over land (Fig. 3b) to a systematic bias that arises over continents, such as over the African continent and South America, rather than to uncertainties related to local circulation.

b. Temporal structures of the modeled atmosphere

The previous section showed that the resolution dependence of diurnal variations in surface precipitation is apparent mainly over land, and that the magnitude of the dependence is smaller over ocean. This observation highlights the fact that the mechanisms controlling diurnal cycles in precipitation are markedly different between land and ocean, and that the influence of horizontal resolution is greater over land.

We first examine the controlling mechanism of the modeled diurnal precipitation, based on the R7 data (an analysis of the R14 data yielded similar results and is therefore not presented here). The detailed mechanisms that drive the resolution dependence in R7 and R14 are considered in section 3c. Figures 5 and 6 show time–height plots of moist static stability (hs) and vertical velocity over land and ocean, respectively. The term “anomaly” indicates the residual from the temporal mean at each height.

Fig. 5.
Fig. 5.

Time–height plot of (a) moist static energy (solid contours; kJ kg−1) and deviation from the daily mean (colors), and (b) vertical velocity (solid contours; m s−1) and deviation from the daily mean (colors) over land in the tropics (±10° of latitude). Contour intervals are (a) 2000 kJ kg−1 and (b) 0.02 m s−1. Note that the data over land are also drawn near the ground, reflecting the result over low topographical regions (e.g., the Amazon basin).

Citation: Journal of Climate 25, 14; 10.1175/JCLI-D-11-00295.1

Fig. 6.
Fig. 6.

As in Fig. 5, but over ocean. Contour intervals are (a) 500 kJ kg−1 and (b) 0.02 m s−1, respectively.

Citation: Journal of Climate 25, 14; 10.1175/JCLI-D-11-00295.1

Over land, the anomaly of hs (Fig. 5a) turns to positive during the period 0700–1100 LT, due to the development of a convective BL by solar insolation. This vertical mixing occurs mainly via subgrid-scale (SGS) turbulence (parameterization) and is large at the boundary beneath 2 km AGL, the layer near the BL top. After 1700 LT, the anomaly of vertical velocity (Fig. 5b) develops vertically, eventually showing strong positive values (>0.06 m s−1) after 1800 LT, indicating the development of nighttime deep convection. These results show that vertical transport of moist air in the BL to the layer around the BL top is a key factor in the subsequent intense convection over land.

It is well recognized that the daytime heat supply from a BL to a free atmosphere is strongly linked to evening deep convection and consequent surface precipitation (e.g., Yang and Slingo 2001; Lee et al. 2007). An interesting piece of evidence in this regard, as obtained from the present results, is that the maximum surface precipitation over land occurs at 1800–2100 LT (Fig. 3b), when vertical vapor transport in the BL is at a maximum (represented by the anomaly of increasing hs vertically with time; Fig. 5a).

Over ocean, the anomaly of hs (Fig. 6a) in the free atmosphere shows clear diurnal signals as a result of daytime radiative heating and nighttime cooling. The diurnal variations in hs (Fig. 6a) are much weaker than those over land. The stability changes that occur in the free atmosphere over ocean are in good agreement with diurnal surface precipitation in this region. The picture presented above is consistent with the results of conventional GCM studies (e.g., Randall et al. 1991; Lee et al. 2007), and it presumably indicates the robustness of the fundamental mechanisms that drive modeled diurnal variations in tropical precipitation. The anomaly of vertical velocity over ocean (Fig. 6b) below 2 km AGL shows a phase change similar to that of diurnal variations in surface precipitation (Fig. 3b); that is, the period showing an updraft motion in early morning (downdraft motion) corresponds to the period of maximum (minimum) precipitation.

To explore the reason for the similarity in the diurnal precipitation of R7 and R14 observed during late evening and at 1200 LT, we compare the more detailed diurnal variation of convective available potential energy (CAPE) and convective inhibition (CIN) values in Fig. 7. Over land in R7 (Fig. 7a), their amplitudes gradually increase after sunrise but start to decay at 1700 LT, showing a delay of 5 h relative to the maximum surface temperature (∼1200 LT; not shown). The peak time in R14 is approximately 1 h later than that in R7. A systematic difference in the amplitudes is evident after the peak time. Because the vertical transport of vapor from the BL air to the bottom of the free atmosphere in R7 occurs more actively than in R14, the air of the lower BL during evening in R14 is more humid than that in R7. Consequently, the amplitudes of CAPE and CIN in R14 are larger than those in R7 during much of the day (Figs. 7a and 7b). From morning to noon, when the active deep convective motion gradually weakens (Fig. 5b), the temporal changes in CIN values become comparable in R7 and R14. Once the convective motion consumes atmospheric instability, which occurs due to the previous solar incident, the diurnal variation in precipitation shows similar characteristics in R7 and R14 (Fig. 3b).

Fig. 7.
Fig. 7.

Temporal changes in (a) CAPE (J kg−1) and (b) CIN (J kg−1) over land in the tropics. Solid and dashed lines (drawn at an interval of 1 h) show the results of R7 and R14, respectively. Dotted lines with open circles and + symbols show the results of JRA-25 and NCEP reanalysis data, respectively. (c),(d) As in (a),(b), but over ocean. For (a),(b),(d), the vertical axes of JRA-25 and NCEP reanalysis data are shown on the right-hand side. Note that CAPE and CIN are computed by lifting an air parcel at the 950-hPa height.

Citation: Journal of Climate 25, 14; 10.1175/JCLI-D-11-00295.1

Over ocean, the CAPE values in R14 are higher than those in R7 throughout the day (Fig. 7c), probably reflecting higher humidity in the lower atmosphere; however, the difference in amplitude at each time bin is almost constant at ∼20 J K−1, in contrast to the time dependence seen in the result over land. The resolution dependence of the CIN values over ocean is much weaker than that over land (Fig. 7d).

For reference, we also compared the reanalysis 6-hourly data provided by the Japanese 25-year Reanalysis (JRA-25) and NCEP. Over land, the phase of CAPE is similar to those in reanalysis data. Mean values of CAPE and CIN in modeled data are, however, much smaller than those in the reanalysis data, because the modeled lower atmosphere has less vapor and higher temperature in the tropics (not shown). The minimum peak of CIN occurs about 6 h later than in the reanalysis data, because the temperature in the lower atmosphere tends to rise earlier (not shown). Over ocean, the magnitude and phase of CAPE are well simulated. However, the phases of CAPE and CIN are almost reversed, due to the larger amplitudes of the temperature change in the upper part of the boundary layer to the lower part of the free atmosphere (not shown).

To further assess the relation between BL processes and the development of subsequent deep convection, Fig. 8 compares the diurnal variations of the sum of cloud water and cloud ice mixing ratios. The BL cloud in R7 starts to develop actively at 1 km AGL after 1000 LT. The cloud-top height (represented in Fig. 8 by the color shading corresponding to 20 mg kg−1) then develops up to 3 km AGL by 1600 LT. The figure also shows that the cloudy region with values >20 mg kg−1 continuously evolves until nighttime (Fig. 6b). The value in R7 above 2 km AGL is larger than the anomaly of the R7 result from the R14 result, implying greater vertical vapor supply to the layer near the cloud-top height; consequently, the region around the upper half of the BL (∼1.5 km AGL) becomes drier, especially during the evening in R7.

Fig. 8.
Fig. 8.

Temporal changes in the modeled tropical atmosphere. Color shadings show the sum of cloud water and cloud ice mixing ratios (mg kg−1) over land in (a) R7 and (b) R14. (c) Difference of R7 from R14. (d)–(f) As in (a)–(c), but for the result over ocean.

Citation: Journal of Climate 25, 14; 10.1175/JCLI-D-11-00295.1

Note that the amplitude of low-level cloud, with a cloud top at ∼3 km, has much higher values than that of higher-level cloud compared with previous studies (e.g., Fig. 2 in Petch 2006), possibly reflecting the different environments analyzed and the humid bias in the lower atmosphere of the present model (Noda et al. 2010). Over ocean, R7 tends to have less cloud than R14; however, the resolution dependence of cloud evolution in the vertical direction is small compared with the result over land.

c. Size changes of precipitating areas

Figure 3 shows a distinguishable dependency of surface precipitation on horizontal resolution (in comparing R7 and R14), especially over land, and R7 shows an improvement (relative to R14) in the phase delay of maximum surface precipitation over land. In this section, we examine diurnal variations in the sizes of precipitating areas with the aim of understanding why R7 yields better results than R14.

Here, a precipitating area is defined as spatially continuous grid points, the number of which is >2, with surface precipitation of >0.5 mm day−1 to exclude as much numerical noise as possible. The sizes of areas are compared in terms of the equivalent radius (r) of a circle. For example, a 2-grid area in R14 corresponds to r = 11.2 km; the minimum area size is then less than the actual grid size (14 km). As shown below, we discuss the roles of areas up to 1000 km in radius, which are clearly much larger than isolated convective clouds in the real atmosphere [O(10 km) or less]. Thus, we can naturally interpret the precipitating areas as precipitating systems rather than single convective clouds, although we refer them to as “areas” for convenience.

Figure 9 shows an example of precipitating areas detected in the Indian Ocean. The area-detection algorithm performed well in capturing precipitating areas (areas of dotted grid points) in the area outlined by the rectangle in Fig. 9a. Figure 10 shows the size distributions of precipitating areas. For R7 over land, small precipitating areas (<100 km) gradually develop after sunrise, reaching a maximum value by 2100 LT. Subsequently, the contribution of these areas decreases, and that of areas with a radius of 0–50 km decreases by 0600 LT (Fig. 10a). The change in the size distributions from 1400 to 0600 LT reflects the nighttime evolution of deep convective clouds (cf. Fig. 6b). Clear diurnal signals are also evident in R14 (Fig. 10b); however, the temporal changes apparent in the histogram are relatively monotonic: the maximum range of area sizes in R14 always occurs at an area size of 50–200 km, whereas that in R7 varies over time. Consequently, the diurnal variations are weaker in R14, depending on area size. A comparison of the size distributions of precipitating areas in R7 and R14 over ocean (Figs. 10c and 10d) shows relatively small differences in their diurnal variations; even in R7, the maximum range of area sizes throughout the day is 0–100 km.

Fig. 9.
Fig. 9.

Example of the horizontal distribution of precipitating areas at 0000–0130 UTC 6 Jun 2004. (a) Surface precipitation in the tropics, and (b) enlargement of the region outlined by the rectangle in (a). Shading indicates precipitating areas, and dots in (b) indicate grid points identified as precipitating areas.

Citation: Journal of Climate 25, 14; 10.1175/JCLI-D-11-00295.1

Fig. 10.
Fig. 10.

Temporal changes (mm h−1 km−1) in the size distribution of precipitating areas over the tropics. Data are shown for (a) R7 and (b) R14. Histograms were constructed by sampling the data at radii intervals of 50 km. (c),(d) As in (a), (b), but over ocean.

Citation: Journal of Climate 25, 14; 10.1175/JCLI-D-11-00295.1

Mapes and Houze (1993, hereafter MH93) examined diurnal variations in tropical high-cloud clusters based on infrared data of the Geostationary Meteorological Satellite (GMS). The spatial resolution of their GMS data is about 9 km, which is close to that of the modeled data. We compared their findings with the present results to gain a further understanding of the modeled precipitating systems, based on the classification of cluster sizes given by MH93: small (<40 000 km2), medium (up to 250 000 km2), large (up to 640 000 km2) and giant (>640 000 km2).

Figure 11 shows diurnal variations in areal coverage (%) of the various cluster sizes for the region of the Tropical Ocean and Global Atmosphere Coupled Ocean–Atmosphere Response Experiment [TOGA COARE (TC)] field experiment (5°S–5°N, 120°E–160°W). In compiling the figure, we only considered grids for which outgoing longwave radiation is less than 136 W m−2, as this corresponds to a threshold-equivalent blackbody temperature (TBB) of −38°C (Inoue et al. 2008). For example, Fig. 11a (for small clusters) shows values of 1% and 0% at −60° and −85°C, respectively, at 0000 LT; thus, the frequency of occurrence of small clusters is 0.5% in the 25°C interval at 0000 LT. Although the TBB analyzed by MH93 does not directly correspond to the equivalent TBB, due to the upwelling radiation of vapor, we believe that the analyzed altitudes are sufficiently high to provide a valid comparison.

Fig. 11.
Fig. 11.

Temporal changes in the percent cloud coverage in R7 for the TC region for clouds with tops lying within 1°C intervals. Size categories of clusters are (a) small, (b) medium, (c) large, and (d) giant, with a contour interval of 0.5%. See the text for further details.

Citation: Journal of Climate 25, 14; 10.1175/JCLI-D-11-00295.1

For small clusters (Fig. 11a), especially large values, appear at 2000–0500 LT, decreasing in the early morning. Compared with the results of MH93 (see their Fig. 11), the modeled peak is delayed by ∼4 h. In Fig. 11a, the region showing marked diurnal variations is found below the −30°C altitude, and the coverage of the high-cloud region (approximately −70°C) decreases from early morning to afternoon. These modeled characteristics are in agreement with the results of MH93.

For medium-sized clusters (Fig. 11b), peak coverage appears below the −50°C altitude at 2000 LT, which is similar to the result reported by MH93. MH93 also reported that the occurrence frequency of cloudy regions decreases at around the −60°C altitude after 1600 LT. The modeled results of the present study show similar characteristics, except that the decrease begins after 1700 LT—1 h later than that reported by MH93.

For the coverage of large and giant clusters (Figs. 11c and 11d, respectively), the result in MH93 shows peak values in layers higher than the −70°C altitude at around 1600 LT. The modeled values of areal coverage show an increase in lower layers after 1800 LT. A notable difference between the MH93 result and ours is that modeled values show peaks at around the −70°C altitude, which differs from observations.

MH93 performed a similar analysis of the coverage of small to giant clusters for other specific regions (the Maritime Continent, Indian Ocean, and western Pacific). They reported that, compared with the result in the TC region, the coverage of giant clusters showed a greater increase in the layer between the −50° to −70°C altitudes from early morning to afternoon. The modeled result of the present study (not shown) shows a similar increase in cloud coverage, although lacking structures with clear peaks when compared with the results of MH93.

Overall, the modeled result shows clear diurnal variations in the extent of cloudy regions, comparable to observations; however, it also shows a phase delay as was also found for surface precipitation (Fig. 3). Of note, the magnitude of the modeled variations is 2–3 times larger than those observed. In addition to model biases, this discrepancy may reflect the fact that the MH93 analyses were based on the TBB of the GMS infrared channel, whereas the present analyses were based on outgoing longwave radiation [as also discussed by Inoue et al. (2008)]. An additional factor may be differences in the analysis period—we considered the boreal summer of 2004, whereas MH93 examined the boreal winter of 1986–89. To improve our understanding of cloud behavior based on a more detailed comparison of cloud properties, we are currently investigating the use of sophisticated satellite simulators, including the signals of active sensors (e.g., Chepfer et al. 2010).

To further understand the role of small precipitating areas in controlling tropical precipitation and mass transport by cumulus convection in the tropics, Fig. 12 shows the size distributions of 3-month means of surface precipitation along with the cloud mass flux at 2 km AGL—the height around which heat exchange between the BL and the free atmosphere is active after noon (Fig. 4). Here, we define the cloud mass flux (M, kg m−2 s−1) by the following commonly used formulation: , where (kg m−3) is the air density of a basic field, which is defined here by the average over the tropics during June–August 2004; and (m s−1) are a fractional area against the computed domain (i.e., tropics) with precipitation of each cloud and the mean updraft in the area, respectively. A precipitating area is defined as grid points with a rainwater mixing ratio of >5.8 × 10−3 g kg−1, which corresponds to a precipitation flux of >0.5 mm day−1 at a fall speed of 1 m s−1 for a rain droplet with an air density of 1 kg m−3.

Fig. 12.
Fig. 12.

Percentage contribution to surface precipitation and cloud mass flux at 2 km AGL of precipitating areas over the tropics with different radii. Results of surface precipitation over (a) land and (b) ocean. Solid and dashed bars show the results of R7 and R14, respectively. (c),(d) As in (a),(b), but for the results of cloud mass flux at 2 km AGL.

Citation: Journal of Climate 25, 14; 10.1175/JCLI-D-11-00295.1

The frequency occurrence of the size distribution of surface precipitation over land in R7 (solid bars in Fig. 12a) shows that areas with radii of 0–100 km contribute most to surface precipitation, with a gradual decrease with increasing radius. For R14 (dashed bars in Fig. 12a), larger contributions are made by areas with radii of >50 km. Similar characteristics of surface precipitation are seen over ocean (Fig. 9b), although with larger amplitudes than those over land.

The frequency occurrence of the size distribution of cloud mass flux in R7 over land (solid bars in Fig. 12c) shows large values for radii of 0–100 km, similar to the result for surface precipitation (Fig. 12a). This finding reflects the large extent of cloudy regions, even though the number of areas shows a marked decrease with increasing radii (not shown). For R14 (dashed bars in Fig. 12c), larger areas (radii > 100 km) make a greater contribution to the total cloud mass flux over the tropics compared with the results for R7. Over ocean (Fig. 12d), small areas in R7 and R14 contribute to the total cloud mass flux, even though their contribution to diurnal variations in precipitation is insignificant compared with those over land (Figs. 10a and 10c). We conclude that the role of small precipitating areas is more important in R7 than in R14, in terms of determining the total amount of surface precipitation and mass transport by cumulus convection near the BL top.

4. Discussion

Above, we showed the importance of pre-moistening near the BL top from noon to early evening, especially over land regions, which helps the subsequent evolution of deep convection during the night. The parameterization of BL processes is therefore important because with the current state of computational resources, it is difficult to resolve BL eddies, which should apparently be modeled implicitly. In this regard, the present results may be somewhat overestimated because the present scheme (MYNN) is constructed based primarily on simple thermal structures of BLs, including the diurnal evolution of a well-mixed layer, meaning that the scheme may underestimate heat transport due to shallow convection less than 100 m in scale, which leads to wet and dry biases in a BL and in a lower troposphere, respectively, as pointed out by Pauluis and Garner (2006). Noda et al. (2010) addressed this issue by suggesting that the present turbulent scheme should incorporate the interaction between resolvable and SGS motions. Previous numerical studies that are conducted based on field observations also show the importance of such small-scale clouds and turbulent processes for simulating tropical convective systems (e.g., Grabowski et al. 1998; Xu and Randall 1996; Donner et al. 1999; Wu et al. 2007). For improving a GCM (or at least every so-called cloud-resolving model with a horizontal grid size >100 m), numerical modelers need to consider a trial installation of a parameterization scheme of shallow convection developed based on state-of-the-art knowledge (e.g., Bretherton et al. 2004; Bretherton and Park 2009). This is along with further efforts to improve the model by introducing all the relevant processes regarding turbulence, clouds, and radiation so as to more realistically consider the interactions among these processes into models with such resolution.

Regarding the dependency on horizontal resolution of diurnal precipitation, the present results show that use of a grid size <10 km (i.e., R7) improves the phase of diurnal precipitation over land compared with a grid size >10 km (R14), although R7 still suffers from a phase delay of approximately 3 h. Nevertheless, we believe that this result indicates the superiority of higher-resolution models in, among other tasks, simulating diurnal variations in precipitation over land. An improvement in simulating diurnal variations in small-sized precipitating areas (section 3c) is likely to be attained in higher-resolution models by at least coarser than approximately 1 km, for which turbulent eddies in a BL occur entirely at a subgrid scale; thus, we can expect similar responses for resolvable convection. In this respect, we consider that the present results (i.e., the differences between R14 and R7 in terms of the size distributions of precipitating areas and resultant vertical mass transport by cumulus convection) are adequate for application to such high-resolution models.

Although many studies have investigated the dependence on horizontal resolution of modelling convection and well-organized convective systems, it is important to realize the difficulties encountered in gaining a comprehensive understanding of this dependence, even in the case of idealized simulations (e.g., Bryan et al. 2003; Noda and Niino 2003). To resolve this issue, it is necessary for model developers to keep exchanging state-of-the-art information obtained by idealized simulations, which can be conducted with much higher model resolutions.

5. Summary and conclusions

Sato et al. (2009, hereafter S09) investigated diurnal variations in tropical surface precipitation obtained by global cloud-resolving simulations in the boreal winter season of 2006/07 and showed the strong dependence of such variations on horizontal resolution, especially over land. For the difference of the resolution dependence of surface precipitation during the periods analyzed, we conclude that the diurnal variation over ocean shows a result that is basically similar to that for the boreal winter season in 2006/07. A notable difference between the two periods is that the daily mean of surface precipitation in the present period over ocean is about 1.4 mm day−1 (Fig. 3) less than that in the boreal winter season, when the surface precipitation in the tropical Southern Hemisphere is climatologically smaller.

In contrast to the result over ocean, we note a slight difference between the two periods over land; the relative magnitude of precipitation at 1200–1500 LT (immediately before the maximum at 1500–1800 LT) is smaller than the boreal winter in 2006/07 (Figs. 3b and 5 in S09). For example, for the June–August period in 2004, the amount of diurnal precipitation shows a gradual increase after 0600–0900 LT. For the December–January period in 2006/07, however, precipitation shows a rapid increase after 0900–1200 LT. We suspect that this discrepancy between the two periods reflects the fact that the southern Amazon receives greater surface heating in the boreal winter.

We qualitatively assessed the mechanisms of the diurnal surface precipitation based on detailed three-dimensional data (which was not explored in S09), using global 14- and 7-km-mesh models (R14 and R7, respectively). We also provided an explanation of why the phase delay of the minimum surface precipitation over land does not improve with finer resolution in contrast to the maximum.

Many studies have investigated diurnal variations in convection over land (e.g., Grabowski et al. 2006; Petch 2006), although generally in an idealized environment, meaning that it is difficult to evaluate the extent to which their conclusions are significant in the real world. Even though one may say “over land” indiscriminately, it is necessary to also consider geographical features (e.g., coastal regions vs inland regions) and details of the topography. This paper examined details of diurnal variations in precipitation over the tropics based on global nonhydrostatic simulations that comprehensively considered the ambiguity arising from the inhomogeneity of geography and topography as much as possible. The main conclusions, based on the simulation data, justify and/or strengthen the assertion given by the previous case studies.

The diurnal variations in tropical precipitation produced by R7 and R14 are in agreement with those reported by S09, despite that the analysis period differs between the two studies. For land regions, the phase of the diurnal cycle in R14 is delayed by approximately 6 h compared with TRMM 3B42 data. R7 shows a smaller phase delay of about 3 h. Over oceanic regions, both R7 and R14 show diurnal variations similar to the 3B42 result. The phase delay of precipitation over land is derived primarily from a systematic bias rather than from a lack of local circulation (Fig. 4).

To clarify the mechanisms that produce the resolution dependence in the phase of diurnal precipitation for R14 and R7, especially over land regions, we examined diurnal variations in the size distribution of precipitating areas. The most remarkable difference between R7 and R14 is found in the behavior of small-sized areas (radius < 100 km). The number of such areas shows a gradual increase after noon, and they evolve to become larger-scale areas (i.e., deep convective clouds). Of note, the distribution of the size of areas of surface precipitation in R7 over land show a change across 1200 LT; the contribution to total precipitation of small precipitating areas shows an increase until 2400 LT, after which time it is not observed in R14.

For oceanic regions, only minor differences are seen between R7 and R14 because the diurnal cycle of precipitation is likely to be controlled by the diurnal cycle of radiative heating–cooling in the troposphere, that is, changes in atmospheric stability, which are determined primarily by the thermal structure of the atmosphere. Thus, the amount of radiative heating–cooling is only weakly dependent on horizontal resolution in the case of minor differences in the distributions of cloud layers between R7 and R14. The present results explain why we observe clear differences over land, but not over ocean, between these models with contrasting resolutions.

An analysis of the size distribution of total precipitation and cloud mass flux at 2 km AGL indicates that the contributions of small precipitating areas to these values in R7 are larger than those in R14. In addition, the present results indicate that differences in the size distributions not only occur for areas with radii similar to the grid sizes but also for areas with much larger radii. Over land (ocean), the total amount of surface precipitation in R14 is greater than that in R7 for areas with radii of up to 400 km (200 km). In addition, over land (ocean), the cloud mass flux in R7 is greater than that in R14 for area radii up 800 km (600 km); the trend is reversed for larger radii. These results emphasize the need to take special care in using a grid size of O(10 km) because the resultant organization of cumulus convection may differ markedly from that in models with a grid size of O(1 km).

There remain several issues to resolve if we are to achieve a comprehensive understanding of the behavior of precipitating systems in nonhydrostatic GCM studies. An additional study is required to examine air–sea interaction, as emphasized by Chen and Houze (1997), who noted the importance of diurnal variations at and near the ocean surface. A practical approach in this regard is to introduce an oceanic mixed-layer model and to investigate its influence on cumulus convection. Another interesting issue for a nonhydrostatic GCM study is local precipitating systems affected by spatial inhomogeneity (e.g., topography), and to clarify the dependence of their diurnal variations on model resolution. Such efforts would increase the reliability of simulated results by nonhydrostatic GCMs.

Acknowledgments

We appreciate Prof. Taro Matsuno of the Japan Agency for Marine-Earth Science and Technology, Dr. Toshiro Inoue of the Atmosphere and Ocean Research Institute, the University of Tokyo, and Drs. Sin-ichi Iga and Tatsuya Seiki of the Advanced Institute for Computational Science, RIKEN for their valuable discussions about this research. We also thank two anonymous reviewers for their constructive and thoughtful comments. This work is partly supported by the Innovation Program of Climate Projection for the 21st Century of the Ministry of Education, Culture, Sports, Science and Technology (MEXT). The simulations of this study were performed using the Earth Simulator.

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