1. Introduction
Clouds are a major controlling factor in the atmospheric energy budget through both infrared and visible radiation. High-altitude clouds associated with deep convection and/or anvil clouds, which prevail in large domains in the tropics near the tropopause layer, are of primary importance in the radiation budget of the atmosphere. A great deal of effort is expended in the current development of climate models to improve the properties of high clouds in the tropics. Statistics on high-cloud areas are directly related to the atmospheric energy budget, and an understanding of their behavior is important if we are to improve climate models.
Observational facts on the coverage of anvil clouds in the tropics are well known through geostationary satellite images. Mapes and House (1993) analyzed statistics on cloud areas using infrared images taken by a geostationary satellite. They used the threshold values of equivalent blackbody temperature (TBB), 198, 208, and 235 K, and obtained histograms of cloud areas defined by the respective threshold values. The results show that the major fraction of cloud areas is explained by large clouds. For example, the number of clouds larger than 50 000 km2 defined by TBB = 208 K is just 1%, but the sum of the areas of these clouds is as much as 40% of the total area.
Deep convection, which is the source of anvil clouds aloft, is not resolved in current atmospheric general circulation models (GCMs) because of the coarse resolution and is represented by cumulus parameterization. On the other hand, anvil clouds—whose scale is sometimes wider than the typical resolvable scale of GCMs—are represented by stratiform cloud schemes or large-scale condensation. This artificial separation of treatments of deep convection and anvil clouds might cause inconsistency, which is absent in reality where both are inseparable.
Cloud-resolving models (CRMs), or cloud system–resolving models, which have a grid size of a few kilometers, are used to directly calculate the mesoscale circulations associated with deep convection. Although recent studies show that much higher resolution is required to really resolve deep clouds (Bryan et al. 2003; Deng and Stauffer 2006), we use the term CRMs to refer to numerical models that explicitly calculate deep convective circulations using a cloud microphysics scheme. CRMs can simultaneously produce deep convection and anvil clouds. Instead of the cloud parameterization of GCMs, the behaviors of anvil clouds are sensitive to the cloud microphysics schemes used in CRMs (e.g., Redelsperger et al. 2000; Tao et al. 2003; Grabowski 2003). In recent years, CRMs have been extended to cover the entire domain of the earth as a result of the increased power of computational abilities; these are called global cloud-resolving models (GCRMs). GCRMs directly calculate deep convective circulations without the need to use cumulus parameterization. In GCRMs, the interactions between resolved clouds and radiation are explicitly calculated.
Miura et al. (2007) performed global cloud-resolving simulations using the Nonhydrostatic Icosahedral Atmospheric Model (NICAM; Tomita and Satoh 2004; Satoh et al. 2008) and reproduced a Madden–Julian oscillation (MJO) event, using grid sizes of 3.5, 7, and 14 km. Because the grid sizes of the experiments were almost comparable to the pixel size of geostationary satellite images, the cloud properties of the simulations can be analyzed by means of the same method used by Mapes and House (1993). Inoue et al. (2008) used the simulated outgoing longwave radiation (OLR) of Miura et al. (2007) and examined statistics on high-cloud areas in the western Pacific by comparing them with data from the MTSAT-1R geostationary satellite. The result shows that the statistics on high-cloud areas are very close to that of MTSAT-1R observations and that the diurnal variations of high-cloud covers also are clearly reproduced.
On the other hand, the high-cloud covers of GCRMs are sensitive to details of the cloud microphysics scheme, as are other CRMs. Iga et al. (2007) performed a perpetual July experiment using NICAM and showed that OLR is dependent on parameters of the fall speed of snow; as the snowfall speed slows, the latitudinal profile of OLR uniformly decreases. A similar dependency also is seen in other CRMs and GCMs, in which the radiation budget is sensitive to the fall speed of cloud ice (Wu et al. 1999; Jakob 2002). Sometimes the fall speeds of snow and cloud ice are chosen so that the average OLR becomes closer to the observed value. However, even though the average value of OLR is improved, it is not known how statistics on high-cloud areas will change.
As mentioned above, high-cloud properties of CRMs and GCRMs are sensitive to details of cloud microphysics schemes. We need to comprehensively understand how clouds in models respond to the choices of parameters used in cloud microphysics schemes. We focus on the relationships between high-cloud areas and cloud microphysics parameters and on their impacts on OLR.
Although our final goal is an improvement of cloud properties for more realistic experiments with CRMs and GCRMs, it is almost impossible to run wide-area experiments for a wide range of parameter sets using current computer resources. Thus, we define a smaller-area CRM experiment, in which a single deep convection revolves effectively, to discuss the dependency of areas of high clouds on cloud microphysics parameters. Our experiments are categorized into widely used radiative–convective experiments (Nakajima and Matsuno 1988; Held et al. 1993; Sui et al. 1994; Grabowski et al. 1996; Tompkins and Craig 1998; Bretherton et al. 2005; etc). Although radiative–convective equilibrium experiments are highly idealized under an “everywhere tropics” condition, they also can be used to evaluate interactions between clouds and radiation, total performance of physics schemes, and intercomparisons of different models.
In this study, we explore parameter dependencies using a single-moment bulk cloud microphysics scheme (SMB), in which the mixing ratios, or mass concentrations, of hydrometeors are prognostic variables. The importance of the SMB is still acknowledged by the community because our limited computer resources are not adequate for wide-area CRMs, although double-moment bulk microphysics schemes (DMBs), in which mixing ratios and number concentrations of hydrometeors are prognostic variables, are more attractive (Murakami 1990; Ferrier 1994; Meyers et al. 1997; Reisner et al. 1998; Seifert and Beheng 2001, 2006; Phillips et al. 2007; Morrison and Gettelman 2008). The current study is important in gaining an understanding of the relation between SMB and DMB, as we will argue that the number concentrations of snow and graupel play important roles in sections 3 and 4.
In section 2, we describe the model used in this study and explain the experimental setups and the analysis method. In section 3, we show resolution dependencies to aid understanding of the overall characteristics of high clouds and identify which processes and parameters are important for high-cloud cover. In section 4, we study sensitivities on parameters related to high-cloud cover. Discussions on related topics follow in section 5, and a summary is given in section 6.
2. Model and experimental design
a. Model setting
We use NICAM (Tomita and Satoh 2004; Satoh et al. 2008) and perform radiative–convective equilibrium experiments under the condition of a uniform sea surface temperature (SST). NICAM is a spherical model based on icosahedral grids and its governing equations are nonhydrostatic. Tomita et al. (2005) and Miura et al. (2007) performed global cloud-resolving simulations using NICAM with a grid interval of approximately 3.5 km. We reduce the radius of the model earth to achieve an “everywhere tropics” condition, setting the radius at approximately 200 km, which is 
Despite the spherical geometry, the model planet has no rotation. Solar insolation is horizontally uniform, set at the equinox value on the equator, and it has diurnal cycles. The SST is also horizontally uniform (300 K). The initial state has a constant temperature lapse rate at a given height and no humidity. Giving a random perturbation of amplitude of 0.5 K to the initial field, we integrate the model for 90 days. We mainly use the last 30 days of this period for cloud analysis.
The cloud microphysics scheme is the NICAM single-moment water 6 class scheme (NSW6; Tomita 2008). The radiation scheme is MSTRNX (Nakajima et al. 2000; Sekiguchi and Nakajima 2008). In the radiation scheme, we take all the liquid and solid hydrometeors into account. Cloud categories are classified into liquid and ice phases, and the effective radius of liquid (cloud water and rain) is assumed to be 8 μm whereas that of ice (cloud ice, snow, and graupel) is assumed to be 40 μm, both of which are independently given from the cloud microphysics scheme. Because we are focusing on the relation between high-cloud areas and cloud microphysics scheme, we do not debate the effects of cloud radius on radiation, although it is an important issue in cloud and radiation interaction. The parameterization of surface process follows Louis (1979), and the boundary layer process is level 2 of the MYNN scheme (Mellor and Yamada 1974; Nakanishi and Niino 2004). We call the radiation code every 10 min; all other processes are calculated at every time step. The time increments are 7.5, 15, and 30 s for 3.5-, 7-, and 14-km grid experiments, respectively. The height–coordinate system is used in the vertical, and the number of vertical levels is 54, with finer resolutions near the surface as described in Tomita et al. (2005).
Because of the small domain of the radius (∼200 km), cloud areas tend to aggregate at one location. Figure 1 shows an example of simulated clouds over one hemisphere. High clouds, or anvil clouds—associated with deep convection—cover one hemisphere; the other hemisphere is a clear region with higher OLR values. Although circulation patterns evolve over time and the location of clouds is not stationary, cloud-populated areas are concentrated in one location. That is, a single-cloud system is produced over the domain at all times in the simulations. This single-cloud state is probably related to the self-aggregation discussed by Bretherton et al. (2005), but our experiments are different because diurnal cycles are considered here. We will not discuss the transition of self-aggregation from random clouds to a single cloud in this study.
We will statistically analyze areas of high clouds. Following Mapes and House (1993) and Inoue et al. (2008), we use the values of the OLR to define high clouds. One-hour-interval snapshot data for 30 days are used to count the areas and numbers of clouds. We first interpolate data into latitude–longitude grid points from the original icosahedral grid points and then count areas of high clouds by means of an enclosed contour of threshold values of the OLR, 180 and 230 W m−2. The higher value corresponds to anvil clouds; the lower one corresponds to cores of deep convection. We chose these values so that the cumulative percentages of cloud areas almost correspond to those of observations. Note that Inoue et al. (2008) used threshold values of 90 and 210 W m−2. Because our experiments are within a small domain without large-scale forcing, deep convection is not so strong that the lower threshold becomes much higher than that used by Inoue et al. (2008).
b. Sensitivity experiments
Table 1 shows a list of the experiments conducted in this study. First, we examine the resolution dependency of cloud properties in section 3, using 3.5-, 7-, and 14-km grid interval experiments. We call these experiments dx3.5km, dx7km, and dx14km, respectively. They are intended to provide an understanding of the overall characteristics of high clouds in these kinds of experiments. Although we will see many quantitative differences among the three experiments, we will show that dx14km is still useful for discussing variations of high-cloud areas. Thus, we will call dx14km the control experiment (CTRL) and perform sensitivity experiments using a 14-km grid interval by comparing them with CTRL in section 4.
Experiment WF is intended to compare the results obtained from the idealized small planet experiments with those seen in observations in which a large-scale circulation coexists with deep convective circulations. Because the domain size of the current experiments is almost comparable to the size of typical cloud clusters in the tropics (Mapes and House 1993), it is more reasonable to introduce “large-scale forcing” to the whole area of the domain to make a comparison with observations. To this end, we apply a horizontally uniform upward motion, following Sui et al. (2008). The applied vertical motion is zero at the ground, reaches a maximum value of about 1.5 cm s−1 at an altitude of 11 km, and comes back to zero at about 16 km.
We also study the sensitivity to the snow density ρs in experiments ρsx0.5 and ρsx2. Although interesting results were obtained, we only tabulate the results and will not examine them in detail in the following sections.
We complementarily perform additional sets of sensitivity experiments with different resolutions and domain size. One set is an extension of dx7km, using a 7-km grid and the same radius r = 200 km, and is called dx7km_r200km. The other set uses a 14-km grid and the wider domain r = 400 km and is called dx14km_r400km. Table 1 also shows the additional experiments of these two sets. The results of these experiments will be referred to in section 4a.
3. Dependency on resolution
First, we show a dependency on horizontal resolution for dx3.5km, dx7km, and dx14km. Although dx3.5km can be categorized as a CRM-experiment, dx14km is too coarse to resolve deep convective cores in general. However, global cloud-resolving simulations by NICAM show that large-scale organization of tropical clouds behaves similarly for three experiments with grid sizes of approximately 3.5, 7, and 14 km (Tomita et al. 2005; Miura et al. 2007; Nasuno et al. 2009). Although Inoue et al. (2008) shows a quantitative difference of statistics of high-cloud areas between the 3.5- and 7-km grid experiments by Miura et al. (2007), the diurnal variability has a similar phase, irrespective of resolutions. Thus, it is still valuable to examine how high clouds behave in a coarse-resolution experiment in dx14km.
Figure 2 shows the time sequences of domain-averaged mass-weighted temperature and precipitable water. All the experiments show that they reach almost statistically equilibrium values after 20 days integration from the initial state. Both quantities have time variations of several tens of days. Although the temperature of dx14km tends to be lower than that of dx3.5km and dx7km, precipitable water does not show a clear resolution dependency. Figure 3 shows the time- and domain-averaged vertical profiles of water species. Cloud ice (qi) and snow (qs) exist mainly in the upper troposphere and contribute to high clouds. Their amounts are closely related to the OLR. As the resolution becomes finer, qi, qs, and graupel (qg) become more abundant, whereas cloud water (qc) becomes less abundant. Note that qc has two peaks: around the top of the boundary layer at about 1 km and at the melting level around 5 km. Reflecting the opposite dependency of qg and qc, rain (qr) increases above an altitude of 2 km and decreases below it.
Diurnal variations of vertical profiles of five categories of hydrometeors for dx3.5km and dx14km are shown in Fig. 4. This shows the time- and domain-averaged values in the time–height cross section. Although these five categories have a clear resolution dependency in amplitude as shown by Fig. 3, they have similar diurnal variations irrespective of resolution. The four categories (qi, qs, qg, and qr) have two peaks in time. Although the first peak of qg and qr is stronger than the second one, the two peaks of qi and qs are almost comparable. The coarser-resolution model tends to accumulate cloud water around the top of the boundary layer and causes a delay in the onset of deep convection. In dx3.5km, qr is at its maximum before dawn and has a second high at about 11 h, whereas the maxima of dx14km are at 6–8 h and 13–14 h. The diurnal variation of precipitation is similar to that of the equatorial region of the aquaplanet experiments by NICAM (Tomita et al. 2005) and is also consistent with the analysis of Sui et al. (1997). Figure 5 shows the statistical analysis of high clouds defined by the two threshold values of the OLR. Normalized frequencies of cloud areas are shown in Figs. 5a,b, and the cumulative percentages of cloud size are shown in Figs. 5c,d. The threshold value of 230 W m−2 is used to define anvil clouds, and the smaller value of 180 W m−2 corresponds to the core of deep convection as shown by Fig. 1. The higher clouds defined by 180 W m−2 shows a clear resolution dependency; as the resolution becomes finer, the fraction of smaller clouds increases (Figs. 5b,d). In contrast, the frequencies of anvil clouds defined by 230 W m−2 have a maximum at around 30 000 km2 in dx3.5km and dx7km whereas the frequency of dx14km has its maximum in a broader region, 10 000–20 000 km2. That is, smaller anvil clouds are more frequent in dx14km compared to dx7km and dx3.5km. The cumulative percentages of anvil clouds smaller than 5000 km2 are almost the same irrespective of resolution (Fig. 5c). As the resolution becomes finer, larger anvil clouds contribute more to total cloud areas. As for the higher clouds (180 W m−2; Fig. 5d), smaller clouds cover more areas as the resolution becomes finer.
Figure 6 shows diurnal variations of surface precipitation and total high-cloud areas defined by the OLR thresholds. Consistent with Fig. 5, the total area has a resolution dependency; as the resolution becomes coarser, the total area becomes smaller, irrespective of the thresholds (see also Table 3). However, the resolution dependency becomes smaller around the maximum values of anvil clouds defined by 230 W m−2. In addition, the phases of the diurnal variations are very similar in all three cases. They become minima around midnight 0 h and reach maximum at about 15 h. The maximum of high-cloud areas reflects the maxima of qi and qs at an altitude of about 11 km (Fig. 4). In contrast, Fig. 6 shows that the diurnal phase of surface precipitation has a clear resolution dependency as consistent with Fig. 4. Overall, diurnal variations of precipitation and high-cloud covers are almost out of phase; and this phase lag is consistent with the diagnosis by Fu et al. (1990).
As shown above, the vertical profiles of hydrometeors, the histograms of high-cloud areas, and the magnitude of vertical velocity have a clear resolution dependency, not surprisingly. However, there are the common characteristics of diurnal variations of cloud ice, snow, and high-cloud covers. The above results motivate us to use the 14-km grid interval model for sensitivity studies in the following section. At least, we can argue about the relative importance of factors controlling high clouds, although we must remark that it is dangerous to jump to quantitative conclusions.
4. Sensitivity experiments
a. Summary of results
Before giving a detailed analysis of each experiment, we summarize the results from the sensitivity study in Tables 3 –5. The high-cloud cover analysis is shown in Table 3, and Table 4 shows the radiative fluxes and cloud radiative forcing at the top of the atmosphere and the radiative energy budget. The column-integrated ice categories and the surface precipitation are summarized in Table 5. We define γ as the ratio of the column-integrated graupel to the column total ice. These tables also contain the resolution dependencies among dx3.5km, dx7km, and dx14km (CTRL) described in section 3.
In Table 3, it is confirmed that both the numbers and average fractions of high clouds increase as the resolution becomes finer, regardless of the thresholds, although it is noted that the largest cloud fractions behave differently. However, longwave radiative fluxes (LW) and their cloud forcing do not show a clear dependency in Table 4. Shortwave reflective flux (SW) increases in the case of dx14km because there is more low-level cloud cover, as implied by the cloud water in Fig. 3. Although our original motivation is to study the energy budget, especially OLR (LW), related to high clouds, cloud fractions have a clearer dependency than radiative fluxes in these cases. Thus, we proceed using the results from the analysis of cloud size (Table 3). Note that the OLR fluctuates with about 10-day periods, so the time-mean OLR over the 30 days is not a good proxy of the experiment. Table 5 confirms the resolution dependency of the amount of ice categories shown by Fig. 3. The surface precipitation does not show a clear resolution dependency.
The average cloud fraction is related to the sum of cloud ice and snow. The relation is clearly seen by using γ. Figure 7 shows that as γ increases, the averaged cloud fraction defined by the two thresholds generally decreases. In this figure, the results from the additional experiments for dx7km_r200km and dx14km_r400km are also compiled. This dependency is robust regardless of the resolution and the domain size and will be examined in the sensitivity experiments.
In the following subsections, we will show the sensitivities on cloud microphysics parameters. The result from large-scale forcing (WF) is just mentioned here. When large-scale forcing is applied, the number of high clouds decreases and average cloud fraction increases (Table 3). The vertical profiles of the hydrometeors show an increase in cloud ice, reflecting the change in high-cloud areas, but the change in snow is small in this case (not shown). We need to take this effect into account when the results of the single-cloud experiment are to be applied to more realistic cases.
b. Dependency on fall speeds of snow and cloud ice
Consistent with other studies (Wu et al. 1999; Jakob 2002; Iga et al. 2007), the impacts of the fall speed of snow (Csx05, Csx2) and cloud ice (VTi0) show clear dependencies. If the fall speeds are reduced, the high-cloud fraction increases and LW decreases (Tables 3 and 4).
The dependency on cs is shown in Figs. 8 and 9. As the fall speed of snow becomes smaller (Csx0.5), larger clouds are more frequent for both thresholds. The cumulative percentage of anvil clouds (230 W m−2) smaller than 10 000 km2 is reduced to 18% in Csx0.5 from 43% in Csx2, whereas that of higher clouds (180 W m−2) is reduced to 30% in Csx0.5 from 60% in Csx2 (not shown).
We confirm from Fig. 9 that the amount of snow increases as the snowfall speed slows. At the same time, the amount of cloud ice increases (Table 5). This is interpreted as follows: Because the accretion rate of cloud ice by snow (PSACI) is proportional to cs, PSACI becomes smaller if cs is reduced, resulting in an increase in cloud ice. This in turn enhances the effects of PSAUT and PSFI and causes an increase in snow.
The effect of cs shown above is similar to the study by Iga et al. (2007). However, quantitatively, the change in OLR is different. Figure 3 of Iga et al. (2007) shows that the reduction of OLR is about 15 W m−2 in the equatorial zone if cs is changed from 4 to 3, whereas in our cases the reduction is about 2.2 W m−2 from CTRL (cs = 4.8) to Csx0.5 (cs = 2.4). One of the differences is ascribed to the different cloud microphysics schemes. We are using NSW6, whereas Iga et al. (2007) uses Grabowski (1998), which enhances the effect of snow as shown by Tomita (2008). Of course, the different geometry between the small planet and the full global model may be the cause of the difference. The large-scale circulation naturally introduced in a GCRM will change the impact, as confirmed by the sensitivity experiment of WF (Table 3).
The effect of the fall speed of cloud ice also is prominent (VTi0). The average high-cloud fraction is greatly increased compared to CTRL (Table 3), and LW is decreased (Table 4). The normalized frequencies of high-cloud areas are flattened for both thresholds (Fig. 10). In VTi0, the frequency of large clouds is much higher than in CTRL. The cumulative percentage of anvil clouds (230 W m−2) smaller than 10 000 km2 is 9.6% in VTi0, and that of higher clouds (180 W m−2) is 22% in VTi0 (not shown).
As expected, the vertical profiles of cloud ice show a drastic increase in higher levels, around 12 km, in VTi0 (Fig. 11). Because cloud ice does not fall, it prevails in the upper layer. The increase in cloud ice causes an increase in snow through PSACI and PSAUT. This effect on snow is confined in altitudes where cloud ice actually increases above 11 km. In contrast, the supply of cloud ice to graupel is reduced, resulting in a reduction of graupel and rain lower down (see also Table 5).
c. Dependency on intercept parameters of graupel and snow
We next consider the dependencies of N0s, N0g, and ρs. Table 3 shows that N0s and N0g have opposite dependencies on the high-cloud fraction. That is, as N0s increases, the cloud fraction becomes larger, whereas as N0g increases, the cloud fraction becomes smaller. The radiative fluxes do not show appreciable difference in Table 4. The high-cloud areas show the behavior of high clouds more appropriately than the OLR in these cases.
The normalized frequencies of high-cloud areas for different values of N0g are shown in Fig. 12. As N0g decreases, larger clouds become more frequent, in general. The dependence is clearer for anvil clouds (230 W m−2) than higher clouds (180 W m−2). For CTRL, half of the total anvil cloud area is attributed to clouds larger than 15 000 km2, whereas half is attributed to clouds larger than 22 000 km2 for N0gx0.5 (not shown).
The dependency of the vertical profiles of the ice categories is shown in Fig. 13, and that of the mean values of the conversion terms of cloud microphysics is shown in Fig. 14. First, we see that the amount of graupel increases as N0g increases. This is because of the increase of the accretion rate of cloud water by graupel PGACW through N0g and hence the increase of its collision cross section (Fig. 14). On the other hand, the amount of cloud water in higher levels decreases because of the increase of PGACW, and this results in suppression of production of snow through PSACW. Thus, the amount of snow decreases as N0g increases (Table 5). This result is consistent with Gilmore et al. (2004).
The contrasting features are seen by the dependency on N0s. Figure 15 shows that larger clouds become more frequent as N0s increases, but the impact is not so large as in the case of N0g (Table 3). In the case of N0sx2, one third of the total area of anvil clouds (230 W m−2) consists of clouds larger than 12 000 km2, whereas it consists of clouds larger than 10 000 km2 in the case of CTRL (not shown). Figure 16 shows that the amount of snow actually increases as N0s increases because of the similar mechanism in the case of N0g. As N0s increases, both PSACW and PSACI increase, and the latter causes a reduction of cloud ice at an altitude of about 11 km (Fig. 14).
The effect of N0s is further investigated by introducing temperature dependency on N0s (N0sT). Here N0s varies by a factor of 100 in the range 0°–40°C, as given by Eq. (6). Although N0s increases in the upper layer in this case, the high-cloud fraction behaves differently from N0sx2. The average cloud fraction of N0sT is smaller than that of CTRL, whereas the average cloud fraction of N0sx2 is larger than that of CTRL (Table 3). The small change in high-cloud areas is partly explained by Table 5. In the case of N0sT, although the amount of snow is greatly increased, the amount of cloud ice is drastically reduced. That is, the increase in snow is compensated for by the decrease in cloud ice due to PSACI, and the frequency distribution of high-cloud areas remains almost the same (not shown).
5. Discussion
Of the many sensitivity studies, we particularly focus on the effects of the intercept parameters of snow and graupel, N0s and N0g, because they have opposite effects on high-cloud fractions (Table 3). In general, more graupel means more efficiency in precipitation and a faster reduction of atmospheric water content, because graupel has a faster fall speed than snow and cloud ice. That is, “precipitation efficiency” is enhanced by graupel. This mechanism is proposed by Tompkins and Craig (1999).
For high clouds where the ice phase mainly exists, we need to consider graupel, snow, and cloud ice in NSW6. We already see that the ratio γ is clearly related to the high-cloud fraction in Fig. 7. The ratio γ is further related to the precipitation, in general (Table 5). Figure 17 shows that the relation between γ and precipitation can be clearly seen for the cases Csx05, Csx2, and VTi0. For other cases, the relation is less clear because the integration time is not sufficient to detect small differences of statistical equilibrium states of the precipitation. Figure 17 also shows the relation between γ and OLR. Although the dependency is not as clear as the cloud fraction shown by Fig. 7, we generally say that both the rain and the OLR increase with γ.
The sensitivity experiments of N0s and N0g in section 4c show the opposite impact on the high-cloud fraction. This stems from the fact that snow and graupel compete with each other in capturing cloud water. Generally speaking, under the constraint of the same cloud production rate, more graupel means less snow, and more snow means less graupel. Thus, more graupel leads to reduction of high-cloud fraction through enhancement of the precipitation efficiency.
Although the precipitation efficiency may be defined differently (Rennó et al. 1994; Held and Soden 2000; Del Genio and Kovari 2002; Sui et al. 2005), it is suitable to use the ratio of surface precipitation P to the total condensation rate of cloud water C to discuss high-cloud amounts: η = P/C. As η increases, a greater portion of condensed water is released from the atmosphere as rain, and less cloud remains in the atmosphere. We may say that anvil clouds in the upper layer mainly consist of the portion of (1 − η) within this framework of the experiments. Water categories that have faster fall speed contribute to an increase in η. In NSW6, if rain or graupel increases, η increases; if cloud water, cloud ice, or snow increases, η decreases.
The high-cloud fraction also is related to the circulations. One example is shown in Fig. 18, which shows the dependency of the probability distribution functions (PDFs) of vertical velocity w at an altitude of 6 km for Csx0.5, Csx2, and VTi0. Notice that strong downdrafts coexist near updraft cores of deep convective circulations in these experiments. Hence, higher absolute values of w occur near the cores of deep convection, whereas values near zero occur in slow subsidence regions off the cores. If the probability around w = 0 is higher, deep convective circulation is slower. Figure 18 shows that as the fall speed of snow or cloud ice slows, the circulation becomes weaker. We already noted that as the fall speed of snow or cloud ice decreases, the high-cloud fraction increases (Table 3). Therefore, this indicates a relation between the high-cloud fraction and the circulation; as the high-cloud fraction increases, the circulation becomes weaker.
This relation is explained by the energy budget as shown by Table 4. As the fall speed of snow or cloud ice decreases, LW (or OLR) and the total radiative cooling (QRAD) become smaller. This means a reduction of latent heat release by condensation, hence a decrease in precipitation at the surface. Thus, as the high-cloud fraction increases, radiative cooling in the free atmosphere in the subsidence region decreases, and this results in a weakening of subsidence motion.
Although these results are only from single-cloud experiments, we may consider a response to the real atmospheric general circulation by this mechanism. If the high-cloud fraction is altered by changes in some external parameters, high-cloud areas from the tropics to the subtropics will be changed. Associated with a change in radiative cooling in the subtropics, the strength of the Hadley circulation might be weakened (Satoh 1994). We may interpret a response of atmospheric circulation to global warming in terms of the relation between circulation and high-cloud cover, a different view from that given by the hydrostatic cycle (Held and Soden 2006). Although it is known that the ambiguity of the climate sensitivity of current climate models is larger for low clouds (Bony and Dufresne 2005), ambiguity due to high clouds is not completely resolved. For example, the climate sensitivity test using NICAM by Y. Tsushima, S. Lga, H. Tomita, and M. Satoh (2008, unpublished manuscript) and Collins and Satoh (2009) shows that high clouds might increase in a warmer climate. If the above mechanism works in their experiments, the strength of the Hadley circulation would change in accordance with high-cloud covers.
6. Summary
We studied the sensitivities of statistical behavior of high clouds to parameters of cloud microphysics by performing direct calculations of radiative–convective experiments. We used the Nonhydrostatic Icosahedral Atmospheric Model (NICAM) under an “everywhere tropics” condition by reducing the planetary radius to r = 200 km. Because the domain size is small, only a single deep convective cloud effectively emerges, so that the current experiments can be called “single-cloud experiments.” Although the experiments are highly idealized, they offer an advantage in that we can isolate the response of anvil clouds to parameter changes in cloud microphysics. Of course, other factors such as environmental conditions (large-scale forcing, vertical shear, etc.) may affect high-cloud covers, but we do not discuss these effects in detail in this study except for large-scale forcing (WF). High clouds are defined by the threshold values of the OLR, and statistical behavior of high clouds is analyzed by counting the areas of each high cloud. We use a comprehensive six-category cloud microphysics scheme (NSW6; Tomita 2008) to study the sensitivity.
To ascertain the overall characteristics of high clouds in the model, we first examined resolution dependency for grid intervals of approximately 3.5, 7, and 14 km. The results show that the average high-cloud fraction and the amounts of hydrometeors quantitatively depend on resolution. However, diurnal variations of high-cloud covers and the amounts of snow and cloud ice are similar irrespective of resolution. Following these results, we use the subsequent sensitivity experiments with a 14-km grid interval.
High-cloud covers are closely related to the amount of snow and cloud ice. The analysis of the conversion terms of cloud microphysics of the control experiment (CTRL, i.e., dx14km) showed that the intercept parameters of snow and graupel, N0s and N0g, are related to the major conversion terms for snow and cloud ice. We also study the impacts of the fall speeds of snow and cloud ice because they are frequently invoked for sensitivity studies with cloud and climate models (Wu et al. 1999; Jakob 2002; Iga et al. 2007).
Consistent with previous studies, we find that as the fall speed of snow or cloud ice decreases, high-cloud covers increase (Csx0.5, Csx2, Vti0). The change in the speed of snowfall by coefficient cs shows that the decrease in OLR is much smaller than that obtained by Iga et al. (2007). We also show the effect of large-scale forcing by introducing an average upward motion in the entire domain (WF). The experiment shows that the high-cloud fraction increases under the condition of a large-scale updraft.
The sensitivity experiments of N0s and N0g show the opposite effect on the high-cloud fraction (N0sx0.5, N0sx2, N0gx0.5, N0gx2). As N0g increases, the amount of graupel increases because of the enhancement of accretion of cloud water by graupel, and the amount of snow decreases because the supply of cloud water is reduced. On the other hand, as N0s increases, the amount of snow increases because of the enhancement of accretion of cloud water and cloud ice by snow. The impact on high-cloud fraction is not as large as in the case of N0g. Furthermore, if temperature dependency on N0s is introduced following Hong et al. (2004), the high-cloud fraction remains almost the same because the increase of snow is compensated for by the decrease of cloud ice.
One of the points of this study is to show the effects of the number concentration of ice particles on the high-cloud covers through collision among different categories of cloud particles. In particular, high-cloud covers are related to the precipitation efficiency, which is controlled by the relative ratio of the production rates of snow and graupel. If more graupel is produced, the precipitation efficiency increases, and the high-cloud covers decreases.
Although this study is specific to a highly idealized setup with a particular cloud microphysics scheme and a numerical model, the results will give an insight into the use of a double-moment bulk cloud microphysics scheme (DMB) for prospective cloud microphysics schemes in the near future. Because the effective radius of cloud particles can be retrieved by remote sensing (Nakajima and King 1990; Nakajima and Nakajima 1995), some aspects of DMB can be evaluated by observation. The results of this study can also be used to understand or improve global cloud-resolving simulations that currently require extremely high computational costs. In fact, sensitivity to cs has a similar effect in this study and in Iga et al. (2007). The relative importance of cloud microphysics parameters on high clouds can be evaluated by single-cloud experiments. Of course, more studies are needed to understand the importance of other effects such as environmental conditions.
Acknowledgments
The authors wish to thank Toshiro Inoue, Hirofumi Tomita, Yoko Tsushima, and Shinichi Iga. We also wish to thank two anonymous reviewers. This study is supported by JST/CREST. SR11000 at the University of Tokyo and SX9 at NIES were used for simulations.
REFERENCES
Bony, S., and J-L. Dufresne, 2005: Marine boundary layer clouds at the heart of tropical cloud feedback uncertainties in climate models. Geophys. Res. Lett., 32 , L20806. doi:10.1029/2005GL023851.
Bretherton, C. S., P. Blossey, and M. Khairoutdinov, 2005: An energy-balance analysis of deep convective self-aggregation above uniform SST. J. Atmos. Sci., 62 , 4273–4292.
Bryan, G. H., J. C. Wyngaard, and J. M. Fritsch, 2003: Resolution requirements for the simulation of deep moist convection. Mon. Wea. Rev., 131 , 2394–2416.
Chen, S-H., and W-Y. Sun, 2002: A one-dimensional time-dependent cloud model. J. Meteor. Soc. Japan, 80 , 99–118.
Collins, W. D., and M. Satoh, 2009: Simulating global clouds, past, present, and future. Clouds in the Perturbed Climate System: Their Relationship to Energy Balance, Atmospheric Dynamics, and Precipitation, Vol. 2, J. Heintzenberg and R. J. Charlson, Eds., MIT Press, 469–486.
Del Genio, A. D., and W. Kovari, 2002: Climatic properties of tropical precipitating convection under varying environmental conditions. J. Climate, 15 , 2597–2615.
Deng, A., and D. R. Stauffer, 2006: On improving 4-km mesoscale model simulations. J. Appl. Meteor. Climatol., 45 , 361–381.
Federer, B., and A. Waldvogel, 1975: Hail and raindrop size distributions from a Swiss multicell storm. J. Appl. Meteor., 14 , 91–97.
Ferrier, B. S., 1994: A double-moment multiple-phase four-class bulk ice scheme. Part I: Description. J. Atmos. Sci., 51 , 249–280.
Field, P. R., R. J. Hogan, P. R. A. Brown, A. J. Illingworth, T. W. Choularton, and R. J. Cotton, 2005: Parametrization of ice-particle size distributions for mid-latitude stratiform cloud. Quart. J. Roy. Meteor. Soc., 131 , 1997–2017.
Fu, R., A. D. Del Genio, and W. B. Rossow, 1990: Behavior of deep convective clouds in the tropical Pacific deduced from ISCCP radiances. J. Climate, 3 , 1129–1152.
Gilmore, M. S., J. M. Straka, and E. N. Rasmussen, 2004: Precipitation uncertainty due to variations in precipitation particle parameters within a simple microphysics scheme. Mon. Wea. Rev., 132 , 2610–2627.
Grabowski, W. W., 1998: Toward cloud resolving modeling of large-scale tropical circulation: A simple cloud microphysics parameterization. J. Atmos. Sci., 55 , 3283–3298.
Grabowski, W. W., 2003: Impact of ice microphysics on multiscale organization of tropical convection in two-dimensional cloud-resolving simulations. Quart. J. Roy. Meteor. Soc., 129 , 67–81.
Grabowski, W. W., M. W. Moncrieff, and J. T. Kiehl, 1996: Long-term behavior of precipitating tropical cloud systems: A numerical study. Quart. J. Roy. Meteor. Soc., 122 , 1019–1042.
Gunn, K. L. S., and J. S. Marshall, 1958: The distribution with size of aggregate snowflakes. J. Meteor., 15 , 452–461.
Held, I. M., and B. J. Soden, 2000: Water vapor feedback and global warming. Annu. Rev. Energy Environ., 25 , 441–475.
Held, I. M., and B. J. Soden, 2006: Robust responses of the hydrological cycle to global warming. J. Climate, 19 , 5686–5699.
Held, I. M., R. S. Hemler, and V. Ramaswamy, 1993: Radiative–convective equilibrium with explicit two-dimensional moist convection. J. Atmos. Sci., 50 , 3909–3927.
Heymsfield, A. J., and L. J. Donner, 1990: A scheme for parameterizing ice-cloud water content in general circulation models. J. Atmos. Sci., 47 , 1865–1877.
Hong, S-Y., J. Dudhia, and S-H. Chen, 2004: A revised approach to ice microphysical processes for the bulk parameterization of clouds and precipitation. Mon. Wea. Rev., 132 , 103–120.
Houze, R. A., P. V. Hobbs, P. H. Herzegh, and D. B. Parsons, 1979: Size distributions of precipitation particles in frontal clouds. J. Atmos. Sci., 36 , 156–162.
Iga, S., H. Tomita, Y. Tsushima, and M. Satoh, 2007: Climatology of a nonhydrostatic global model with explicit cloud processes. Geophys. Res. Lett., 34 , L22814. doi:10.1029/2007GL031048.
Inoue, T., M. Satoh, H. Miura, and B. Mapes, 2008: Characteristics of cloud size of deep convection simulated by a global cloud resolving model over the western tropical Pacific. J. Meteor. Soc. Japan, 86A , 1–15.
Jakob, C., 2002: Ice clouds in numerical weather prediction models. Cirrus, D. K. Lynch et al., Eds., Oxford University Press, 327–345.
Kuang, Z., P. N. Blossey, and C. S. Bretherton, 2005: A new approach for 3D cloud-resolving simulations of large-scale atmospheric circulation. Geophys. Res. Lett., 32 , L02809. doi:10.1029/2004GL021024.
Lin, Y-L., R. D. Farley, and H. D. Orville, 1983: Bulk parameterization of the snow field in a cloud model. J. Climate Appl. Meteor., 22 , 1065–1092.
Locatelli, J. D., and P. V. Hobbs, 1974: Fall speeds and masses of solid precipitation particles. J. Geophys. Res., 79 , 2185–2197.
Louis, J., 1979: A parametric model of vertical eddy fluxes in the atmosphere. Bound.-Layer Meteor., 17 , 187–202.
Mapes, B. E., and J. R. A. House, 1993: Cloud clusters and superclusters over the oceanic warm pool. Mon. Wea. Rev., 121 , 1398–1416.
Mellor, G. L., and T. Yamada, 1974: A hierarch of turbulence closure models for planetary boundary layers. J. Atmos. Sci., 31 , 1791–1806.
Meyers, M. P., R. L. Walko, J. Y. Harrington, and W. R. Cotton, 1997: New RAMS cloud microphysics parameterization. Part II: The two-moment scheme. Atmos. Res., 45 , 3–39.
Miura, H., M. Satoh, T. Nasuno, A. T. Noda, and K. Oouchi, 2007: A Madden–Julian oscillation event realistically simulated by a global cloud-resolving model. Science, 318 , 1763–1765.
Morrison, H., and A. Gettelman, 2008: A new two-moment bulk stratiform cloud microphysics scheme in the Community Atmosphere Model (CAM3), version 3. Part I: Description and numerical tests. J. Climate, 21 , 3642–3659.
Murakami, M., 1990: Numerical modeling of dynamical and microphysical evolution of an isolated convective cloud—The 19 July 1981 CCOPE cloud. J. Meteor. Soc. Japan, 68 , 107–128.
Nakajima, K., and T. Matsuno, 1988: Numerical experiments concerning the origin of cloud clusters in the tropical atmosphere. J. Meteor. Soc. Japan, 66 , 309–329.
Nakajima, T., and M. D. King, 1990: Determination of the optical thickness and effective particle radius of clouds from reflected solar radiation measurements. Part I: Theory. J. Atmos. Sci., 47 , 1878–1893.
Nakajima, T., M. Tsukamoto, Y. Tsushima, A. Numaguti, and T. Kimura, 2000: Modeling of the radiative process in an atmospheric general circulation model. Appl. Opt., 39 , 4869–4878.
Nakajima, T. Y., and T. Nakajima, 1995: Wide-area determination of cloud microphysical properties from NOAA/AVHRR measurements for FIRE and ASTEX regions. J. Atmos. Sci., 52 , 4043–4059.
Nakanishi, M., and H. Niino, 2004: An improved Mellor–Yamada level-3 model with condensation physics: Its design and verification. Bound.-Layer Meteor., 112 , 1–31.
Nasuno, T., H. Miura, M. Satoh, A. T. Noda, and K. Oouchi, 2009: Multi-scale organization of convection in a global numerical simulation of the December 2006 MJO event using explicit moist processes. J. Meteor. Soc. Japan, 87 , 335–345.
Phillips, V. T. J., L. J. Donner, and S. T. Garner, 2007: Nucleation processes in deep convection simulated by a cloud-system-resolving model with double-moment bulk microphysics. J. Atmos. Sci., 64 , 738–761.
Redelsperger, J-L., and Coauthors, 2000: A GCSS model intercomparison for a tropical squall line observed during TOGA-COARE I: Cloud-resolving model. Quart. J. Roy. Meteor. Soc., 126 , 823–863.
Reisner, J., R. M. Rasmussen, and R. T. Bruintjes, 1998: Explicit forecasting of supercooled liquid water in winter storms using the MM5 mesoscale model. Quart. J. Roy. Meteor. Soc., 124 , 1071–1107.
Rennó, N. O., K. A. Emanuel, and P. H. Stone, 1994: Radiative–convective model with an explicit hydrologic cycle. 1. Formulation and sensitivity to model parameters. J. Geophys. Res., 99 , 14429–14441.
Rutledge, S. A., and P. V. Hobbs, 1984: The mesoscale and microscale structure and organization of clouds and precipitation in midlatitude cyclones. XII: A diagnostic modeling study of precipitation development in narrow cold-frontal rainbands. J. Atmos. Sci., 41 , 2949–2972.
Satoh, M., 1994: Hadley circulations in radiative–convective equilibrium in an axially symmetric atmosphere. J. Atmos. Sci., 51 , 1947–1968.
Satoh, M., T. Matsuno, H. Tomita, H. Miura, T. Nasuno, and S. Iga, 2008: Nonhydrostatic Icosahedral Atmospheric Model (NICAM) for global cloud resolving simulations. J. Comput. Phys., 227 , 3486–3514.
Seifert, A., and K. D. Beheng, 2001: A double-moment parameterization for simulating autoconversion, accretion, and self-collection. Atmos. Res., 59–60 , 265–281.
Seifert, A., and K. D. Beheng, 2006: A two-moment cloud microphysics parameterization for mixed-phase clouds. Part 1: Model description. Meteor. Atmos. Phys., 92 , 45–66.
Seifert, A., and S. Crewell, 2008: A revised microphysical parameterization for operational numerical weather prediction using the COSMO model. Extended Abstracts, 15th Int. Conf. on Clouds and Precipitation, Cancun, Mexico, ICCP, P6.3. [Available online at http://cabernet.atmosfcu.unam.mx/ICCP-2008/abstracts/Program_on_line/Poster_06/SeifertAxel_P6-3_extended.pdf].
Sekiguchi, M., and T. Nakajima, 2008: A k-distribution-based radiation code and its computational optimization for an atmospheric general circulation model. J. Quant. Spectrosc. Radiat. Transfer, 109 , 2779–2793.
Shige, S., Y. Takayabu, W-K. Tao, and D. E. Johnson, 2004: Spectral retrieval of latent heating profiles from TRMM PR data. Part I: Development of a model-based algorithm. J. Appl. Meteor., 43 , 1095–1113.
Smolarkiewicz, P. K., V. Grubisic, L. G. Margolin, and A. A. Wyszogrodzki, 1999: Forward-in-time differencing for fluids: Non-hydrostatic modeling of fluid motions on a sphere. Proc. 1988 ECMWF Seminar on Recent Developments in Numerical Methods for Atmospheric Modelling, Reading, United Kingdom, ECMWF, 21–43.
Sui, C-H., K-M. Lau, W. K. Tao, and J. Simpson, 1994: The tropical water and energy cycles in a cumulus ensemble model. Part I: Equilibrium climate. J. Atmos. Sci., 51 , 711–728.
Sui, C-H., K-M. Lau, Y. N. Takayabu, and D. A. Short, 1997: Diurnal variations in tropical oceanic cumulus convection during TOGA COARE. J. Atmos. Sci., 54 , 639–655.
Sui, C-H., X. Li, M-J. Yang, and H-L. Huang, 2005: Estimation of oceanic precipitation efficiency in cloud models. J. Atmos. Sci., 62 , 4358–4370.
Sui, C-H., X. Li, C-H. Ho, and K-M. Lau, 2008: Effects of radiative cooling on the tropical convective response to sea surface temperature: 2D large domain cumulus ensemble simulations. J. Geophys. Res., 113 , D08116. doi:10.1029/2007JD008557.
Tanaka, K. K., T. Yamamoto, S. Watanabe, and K. Nakajima, 2008: Analytic model of upper tropospheric clouds in tropical Hadley cell. Earth Planets Space, 60 , 219–228.
Tao, W. K., and Coauthors, 2003: Micro-physics, radiation and surface processes in the Goddard cumulus ensemble (GCE) model. Meteor. Atmos. Phys., 82 , 97–137.
Tomita, H., 2008: New microphysical schemes with five and six categories by diagnostic generation of cloud ice. J. Meteor. Soc. Japan, 86A , 121–142.
Tomita, H., and M. Satoh, 2004: A new dynamical framework of nonhydrostatic global model using the icosahedral grid. Fluid Dyn. Res., 34 , 357–400.
Tomita, H., H. Miura, S. Iga, T. Nasuno, and M. Satoh, 2005: A global cloud-resolving simulation: Preliminary results from an aqua planet experiment. Geophys. Res. Lett., 32 , L08805. doi:10.1029/2005GL022459.
Tompkins, A. M., and G. C. Craig, 1998: Radiative–convective equilibrium in a three-dimensional cloud-ensemble model. Quart. J. Roy. Meteor. Soc., 124 , 2073–2097.
Tompkins, A. M., and G. C. Craig, 1999: Sensitivity of tropical convection to sea surface temperature in the absence of large-scale flow. J. Climate, 12 , 462–476.
van den Heever, S. C., and W. R. Cotton, 2004: The impact of hail size on simulated supercell storms. J. Atmos. Sci., 61 , 1596–1609.
Wu, X., W. D. Hall, W. W. Grabowski, M. W. Moncrieff, W. D. Collins, and J. T. Kiehl, 1999: Long-term behavior of cloud systems in TOGA COARE and their interactions with radiative and surface processes. Part II: Effects of ice microphysics on cloud–radiation interaction. J. Atmos. Sci., 56 , 3177–3195.
APPENDIX
Summary of NSW6: The NICAM Single-Moment Water 6 Scheme
NSW6 is described in Tomita (2008) and is based on a scheme by Lin et al. (1983). It has six categories of water species: prognostic variables are mass concentrations of water vapor, cloud ice, rain, cloud ice, snow, and graupel. One advantage of NSW6 is its computational efficiency. NSW6 simplifies the ice-generation process by using saturation adjustment and omits the effect of the wetness of graupel. NSW6 is similar to the Purdue–Lin scheme (Chen and Sun 2002) in that both use the saturation adjustment for ice generation process. The conversion diagram of NSW6 is shown in Fig. A1, and a description of symbols is given in Table A1.
An example of cloud distribution simulated by a single-cloud experiment with a 7-km-grid small planet (radius = 200 km) model. Colors show OLR in W m−2. Only one hemisphere is depicted. The two dashed contours indicate 180 (outer) and 230 (inner) W m−2, which are used for thresholds of deep clouds and anvil clouds, respectively.
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
An example of cloud distribution simulated by a single-cloud experiment with a 7-km-grid small planet (radius = 200 km) model. Colors show OLR in W m−2. Only one hemisphere is depicted. The two dashed contours indicate 180 (outer) and 230 (inner) W m−2, which are used for thresholds of deep clouds and anvil clouds, respectively.
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
An example of cloud distribution simulated by a single-cloud experiment with a 7-km-grid small planet (radius = 200 km) model. Colors show OLR in W m−2. Only one hemisphere is depicted. The two dashed contours indicate 180 (outer) and 230 (inner) W m−2, which are used for thresholds of deep clouds and anvil clouds, respectively.
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
Time sequences of (a) mass-weighted mean temperature and (b) precipitable water averaged over the domain, showing dependency on grid intervals: dx14km (solid), dx7km (dashed), and dx3.5km (dotted). Horizontal axis is time in days.
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
Time sequences of (a) mass-weighted mean temperature and (b) precipitable water averaged over the domain, showing dependency on grid intervals: dx14km (solid), dx7km (dashed), and dx3.5km (dotted). Horizontal axis is time in days.
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
Time sequences of (a) mass-weighted mean temperature and (b) precipitable water averaged over the domain, showing dependency on grid intervals: dx14km (solid), dx7km (dashed), and dx3.5km (dotted). Horizontal axis is time in days.
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
Time- and domain-averaged vertical profiles of water categories showing resolution dependency: (a) water vapor, qv; (b) cloud water, qc; (c) rain, qr; (d) cloud ice, qi; (e) snow, qs; and (f) graupel, qg; for dx14km (solid), dx7km (dashed), and dx3.5km (dotted). Vertical axis is height (km).
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
Time- and domain-averaged vertical profiles of water categories showing resolution dependency: (a) water vapor, qv; (b) cloud water, qc; (c) rain, qr; (d) cloud ice, qi; (e) snow, qs; and (f) graupel, qg; for dx14km (solid), dx7km (dashed), and dx3.5km (dotted). Vertical axis is height (km).
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
Time- and domain-averaged vertical profiles of water categories showing resolution dependency: (a) water vapor, qv; (b) cloud water, qc; (c) rain, qr; (d) cloud ice, qi; (e) snow, qs; and (f) graupel, qg; for dx14km (solid), dx7km (dashed), and dx3.5km (dotted). Vertical axis is height (km).
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
Diurnal variation of domain-averaged vertical profiles of cloud water (qc), cloud ice (qi), snow (qs), graupel (qg), and rain (qr) for (top five panels) dx3.5km and (bottom five panels) dx14km. Unit is 10−3 g kg−1.
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
Diurnal variation of domain-averaged vertical profiles of cloud water (qc), cloud ice (qi), snow (qs), graupel (qg), and rain (qr) for (top five panels) dx3.5km and (bottom five panels) dx14km. Unit is 10−3 g kg−1.
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
Diurnal variation of domain-averaged vertical profiles of cloud water (qc), cloud ice (qi), snow (qs), graupel (qg), and rain (qr) for (top five panels) dx3.5km and (bottom five panels) dx14km. Unit is 10−3 g kg−1.
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
(a),(b) Histograms and (c),(d) cumulative percentages of cloud size defined by threshold values of OLR, (a),(c) 230 and (b),(d) 180 W m−2, for dx14km (red), dx7km (green), dx3.5km (blue).
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
(a),(b) Histograms and (c),(d) cumulative percentages of cloud size defined by threshold values of OLR, (a),(c) 230 and (b),(d) 180 W m−2, for dx14km (red), dx7km (green), dx3.5km (blue).
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
(a),(b) Histograms and (c),(d) cumulative percentages of cloud size defined by threshold values of OLR, (a),(c) 230 and (b),(d) 180 W m−2, for dx14km (red), dx7km (green), dx3.5km (blue).
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
Diurnal variations of (a) domain-averaged surface precipitation and (b),(c) total cloud area defined by threshold values of OLR = (b) 230 and (c) 180 W m−2 for dx14km (solid), dx7km (dashed), and dx3.5km (dotted).
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
Diurnal variations of (a) domain-averaged surface precipitation and (b),(c) total cloud area defined by threshold values of OLR = (b) 230 and (c) 180 W m−2 for dx14km (solid), dx7km (dashed), and dx3.5km (dotted).
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
Diurnal variations of (a) domain-averaged surface precipitation and (b),(c) total cloud area defined by threshold values of OLR = (b) 230 and (c) 180 W m−2 for dx14km (solid), dx7km (dashed), and dx3.5km (dotted).
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
The relation between γ and the cloud fraction defined by two thresholds: OLR = 230 (black) and 180 W m−2 (red). The horizontal axis γ is the ratio of the column-integrated graupel (qg) to the column ice (qi + qs + qg). Crosses indicate 14-km grid experiments with r = 200 km from Tables 3 and 5; circles, dx7km_r200km; and triangles, dx14km_r400km.
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
The relation between γ and the cloud fraction defined by two thresholds: OLR = 230 (black) and 180 W m−2 (red). The horizontal axis γ is the ratio of the column-integrated graupel (qg) to the column ice (qi + qs + qg). Crosses indicate 14-km grid experiments with r = 200 km from Tables 3 and 5; circles, dx7km_r200km; and triangles, dx14km_r400km.
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
The relation between γ and the cloud fraction defined by two thresholds: OLR = 230 (black) and 180 W m−2 (red). The horizontal axis γ is the ratio of the column-integrated graupel (qg) to the column ice (qi + qs + qg). Crosses indicate 14-km grid experiments with r = 200 km from Tables 3 and 5; circles, dx7km_r200km; and triangles, dx14km_r400km.
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
Histograms of cloud size defined by threshold values of OLR, (a) 230 and (b) 180 W m−2, for dependency on the coefficient of snowfall speed cs: CTRL (red), Csx0.5 (green), and Csx2 (blue).
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
Histograms of cloud size defined by threshold values of OLR, (a) 230 and (b) 180 W m−2, for dependency on the coefficient of snowfall speed cs: CTRL (red), Csx0.5 (green), and Csx2 (blue).
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
Histograms of cloud size defined by threshold values of OLR, (a) 230 and (b) 180 W m−2, for dependency on the coefficient of snowfall speed cs: CTRL (red), Csx0.5 (green), and Csx2 (blue).
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
Time- and domain-averaged vertical profiles of ice phases showing dependency on the coefficient of snowfall speed cs: (a) cloud ice, qi; (b) snow, qs; and (c) graupel, qg; for CTRL (solid), Csx0.5 (dashed), and Csx2 (dotted). Vertical axis is height (km).
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
Time- and domain-averaged vertical profiles of ice phases showing dependency on the coefficient of snowfall speed cs: (a) cloud ice, qi; (b) snow, qs; and (c) graupel, qg; for CTRL (solid), Csx0.5 (dashed), and Csx2 (dotted). Vertical axis is height (km).
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
Time- and domain-averaged vertical profiles of ice phases showing dependency on the coefficient of snowfall speed cs: (a) cloud ice, qi; (b) snow, qs; and (c) graupel, qg; for CTRL (solid), Csx0.5 (dashed), and Csx2 (dotted). Vertical axis is height (km).
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
As in Fig. 8, but for dependency on cloud-ice fall speed; CTRL (solid) and VTi0 (dashed).
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
As in Fig. 8, but for dependency on cloud-ice fall speed; CTRL (solid) and VTi0 (dashed).
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
As in Fig. 8, but for dependency on cloud-ice fall speed; CTRL (solid) and VTi0 (dashed).
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
As in Fig. 9, but for dependency on cloud-ice fall speed; CTRL (solid) and VTi0 (dashed).
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
As in Fig. 9, but for dependency on cloud-ice fall speed; CTRL (solid) and VTi0 (dashed).
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
As in Fig. 9, but for dependency on cloud-ice fall speed; CTRL (solid) and VTi0 (dashed).
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
As in Fig. 8, but for dependency on N0g; CTRL (red), N0gx0.5 (green), and N0gx2 (blue).
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
As in Fig. 8, but for dependency on N0g; CTRL (red), N0gx0.5 (green), and N0gx2 (blue).
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
As in Fig. 8, but for dependency on N0g; CTRL (red), N0gx0.5 (green), and N0gx2 (blue).
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
As in Fig. 9, but for dependency on N0g; CTRL (solid), N0gx0.5 (dashed), and N0gx2 (dotted).
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
As in Fig. 9, but for dependency on N0g; CTRL (solid), N0gx0.5 (dashed), and N0gx2 (dotted).
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
As in Fig. 9, but for dependency on N0g; CTRL (solid), N0gx0.5 (dashed), and N0gx2 (dotted).
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
Column-integrated and domain-averaged values of transformation terms of cloud microphysics, showing dependency on N0g, N0s, and ρs. The unit is 10−6 kg kg−1 s−1.
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
Column-integrated and domain-averaged values of transformation terms of cloud microphysics, showing dependency on N0g, N0s, and ρs. The unit is 10−6 kg kg−1 s−1.
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
Column-integrated and domain-averaged values of transformation terms of cloud microphysics, showing dependency on N0g, N0s, and ρs. The unit is 10−6 kg kg−1 s−1.
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
As in Fig. 8, but for dependency on N0s; CTRL (red), N0sx0.5 (green), and N0sx2 (blue).
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
As in Fig. 8, but for dependency on N0s; CTRL (red), N0sx0.5 (green), and N0sx2 (blue).
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
As in Fig. 8, but for dependency on N0s; CTRL (red), N0sx0.5 (green), and N0sx2 (blue).
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
As in Fig. 9, but for dependency on N0s; CTRL (solid), N0sx0.5 (dashed), and N0sx2 (dotted).
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
As in Fig. 9, but for dependency on N0s; CTRL (solid), N0sx0.5 (dashed), and N0sx2 (dotted).
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
As in Fig. 9, but for dependency on N0s; CTRL (solid), N0sx0.5 (dashed), and N0sx2 (dotted).
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
(a) The relation between γ and the precipitation; (b) the relation between γ and OLR. The unit of the precipitation is 10−5 kg m−2 s−1 and the unit of the OLR is W m−2. Black squares indicate CTL, Csx0.5, Csx2, and VTi0; crosses indicate the rest of the cases.
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
(a) The relation between γ and the precipitation; (b) the relation between γ and OLR. The unit of the precipitation is 10−5 kg m−2 s−1 and the unit of the OLR is W m−2. Black squares indicate CTL, Csx0.5, Csx2, and VTi0; crosses indicate the rest of the cases.
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
(a) The relation between γ and the precipitation; (b) the relation between γ and OLR. The unit of the precipitation is 10−5 kg m−2 s−1 and the unit of the OLR is W m−2. Black squares indicate CTL, Csx0.5, Csx2, and VTi0; crosses indicate the rest of the cases.
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
PDFs of vertical velocity (w) at altitude z = 6 km for dependency on the coefficient of snowfall speed cs and cloud-ice fall speed; CTRL (solid), Csx0.5 (dashed), Csx2 (dotted), and VTi0 (dashed–dotted).
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
PDFs of vertical velocity (w) at altitude z = 6 km for dependency on the coefficient of snowfall speed cs and cloud-ice fall speed; CTRL (solid), Csx0.5 (dashed), Csx2 (dotted), and VTi0 (dashed–dotted).
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
PDFs of vertical velocity (w) at altitude z = 6 km for dependency on the coefficient of snowfall speed cs and cloud-ice fall speed; CTRL (solid), Csx0.5 (dashed), Csx2 (dotted), and VTi0 (dashed–dotted).
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
Fig. A1. Conversion diagram of NSW6.
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
Fig. A1. Conversion diagram of NSW6.
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
Fig. A1. Conversion diagram of NSW6.
Citation: Journal of the Atmospheric Sciences 66, 9; 10.1175/2009JAS2948.1
Summary of experiments; dx7km_r200km and dx14km_r400km denote experiments with 7-km grid and r = 200 km and with 14-km grid and r = 400 km, respectively.
Vertically integrated, time- and domain-averaged values of transformation terms of cloud microphysics for CTRL.
Summary of cloud statistics, showing number of cloud samples enclosed by the threshold values of OLR (230 or 180 W m−2), largest cloud fraction (%) during analysis, and averaged total cloud fraction (%).
Summary of results of radiative flux at the top of the atmosphere (TOA) and the radiative energy budget. The radiative fluxes at TOA are LW [upward longwave radiation flux (OLR)], SW (upward reflective shortwave radiation flux), CLW (LW cloud forcing), and CSW (SW cloud forcing). The radiative energy budget is represented by the difference of the radiative fluxes between TOA and the surface: QLW (the divergence of longwave radiation flux), QSW (the convergence of shortwave radiation flux), and QRAD (the total radiative cooling in the air column). Unit is W m−2.
Summary of results of column integrated ice categories of hydrometeors and the surface precipitation. The column-integrated values are qi (cloud ice), qs (snow), and qg (graupel); γ is the ratio of qg to the total ice (qi + qs + qg).
Table A1. Symbols used in the conversion diagram for NSW6.
