Effects of Ice Microphysics on Tropical Radiative–Convective–Oceanic Quasi-Equilibrium States

1. Introduction

Tropical climate is essentially controlled by multiscale nonlinear interactions among the large-scale dynamics, radiative transfer, cloud dynamics, microphysics, surface processes, and turbulence. Clouds and water vapor are two quantities intrinsic to the climate system, but are sources of great uncertainty. Convection and cloud microphysics affect the coupling of radiative, dynamic, hydrologic, and oceanic processes through the release of latent heat; evaporation; the redistribution of heat and momentum; the reflection, absorption, and emission of radiation; precipitation; and the modification of surface radiative and heat fluxes.

The impact of cloud microphysics on equilibrium climate states is difficult to quantify from observations alone because of the complicated relationship among physical processes and the need to measure various properties on both small and large temporal and spatial scales. For example, observational analyses by Ramanathan and Collins (1991) and Fu et al. (1992) showed different relationships between cirrus clouds and sea surface temperatures (SSTs). The former found that cirrus clouds have negative feedback on SSTs, while the latter suggested that the changes in cloud radiative properties are influenced by the large-scale atmospheric circulation, which is more related to the pattern of SSTs, instead of magnitude of SSTs.

General circulation models (GCMs) have been used to study the effects of convection and cloud feedback processes on the simulated equilibrium climate (e.g., Wetherald and Manabe 1988; Mitchell et al. 1989; Cess et al. 1989; Randall et al. 1989; Senior and Mitchell 1993). It is shown that the model climate and climate change due to the imposed forcing, such as a doubling of atmospheric CO₂ concentration, and SST perturbations are sensitive to the parameterizations of convection and clouds.

The effects of cloud ice particle sizes and types on cloud and water vapor feedback have been suggested by several previous studies. Twomey et al. (1984) found that the increasing cloud drop concentration induced by increased pollution has a large impact on global climate and is comparable to the effect induced by the increased carbon dioxide. Sun and Lindzen (1993) demonstrated that precipitating upper-level clouds strongly affect the tropospheric relative humidity and suggested that water vapor and clouds should be treated consistently in climate studies. Emanuel and Pierrehumbert (1996) illustrated that climate is sensitive to poorly known microphysical and dynamical processes in a one-dimensional radiative–convective model.

Prognostic cloud microphysics, as used in cloud-resolving models (CRMs) and mesoscale models, has been increasingly modified to improve the simulation of clouds in GCMs (e.g., Sundqvist 1993; Del Genio et al. 1996; Fowler et al. 1996; Rasch and Kristjánsson 1998). Recently, a sensitivity study (see references in Heymsfield and Iaquinta 2000) showed that changes in the ice crystal sedimentation rate have significant impacts on the global mean radiative flux divergence in the European Centre for Medium-Range Weather Forecasts (ECMWF) model. Difficulties arise because of the large difference in temporal and spatial scales between large-scale dynamical and cloud microphysical processes. Also, moist convection has to be parameterized in GCMs, which introduces another uncertainty that further complicates the quantification of cloud effects on climate.

Cloud-resolving models contain most of the physical processes that are thought to be important to climate, and can quantitatively investigate the relationship between cloud microphysics and tropical climate. By definition, CRMs resolve convective dynamics and, with modern computers, can explicitly simulate cloud systems on spatial scales up to thousands of kilometers, and for month-long periods. The CRM approach has been successfully used to quantify the convective–radiative responses to the sea surface temperature variation, large-scale dynamics, surface fluxes and cloud microphysics (e.g., Held et al. 1993; Lau et al. 1993; Sui et al. 1994; Fu et al. 1995; Krueger et al. 1995; Grabowski et al. 1996a; Wu et al. 1999; Wu and Moncrieff 1999; Grabowski et al. 1999; Tao et al. 1999; Li et al. 1999; Tompkins and Craig 1999; Grabowski 2000, hereafter G2000). Fundamental mechanisms affecting complicated relationships among processes can be explored in a controlled experimental setting. Wu and Moncrieff (1999) showed that SST variation has a large impact on the water vapor field under a given large-scale dynamic state, while a change of large-scale dynamics has a large effect on the cloud condensate field under a constant SST.

In all long-term CRM equilibrium simulations except Grabowski (2000), who applied a simple surface energy budget equation (e.g., Wu et al. 1998) for a shallow isothermal layer of water to calculate the SST for each column of a CRM, SSTs were kept constant and the SST feedback therefore has no impact on the radiative–convective equilibrium state. Recently, Li et al. (2000) coupled their CRM with ocean mixed-layer models to study the impacts of atmospheric precipitation on the ocean mixed-layer temperature and salinity using a 7-day evolving large-scale forcing from the Tropical Ocean Global Atmosphere (TOGA) Coupled Ocean–Atmosphere Response Experiment (COARE). Herein, the SST feedback is included by coupling the CRM with a one-dimensional ocean model, for the first time realizing a radiative–convective–oceanic quasi-equilibrium state with a CRM. The effects of cloud systems on the equilibrium state are investigated by analyzing 40-day simulations with different ice microphysics. The idealized cloud-resolving equilibrium simulations are providing some insights on the physical processes through which the ice microphysics affect the quasi-equilibrium state and what “the climate” will look like if the different ice physics are used. We find that changes in sedimentation flux of ice particles and ice water content have profound impacts on both the atmospheric and oceanic quasi-equilibrium states. The quasi-equilibrium state associated with smaller ice water content features a warmer and moister atmosphere, smaller SST, weaker convection and larger cloud amount than that associated with larger ice water content.

Section 2 describes the cloud-resolving model, 1D ocean model, variation of ice microphysics, and experimental design. Section 3 analyzes thermodynamic properties, cloud and radiative properties, and the top-of-atmosphere and surface energy budgets from two coupled CRM–ocean simulations. Section 4 compares two coupled simulations with two fixed-SST simulations to illustrate the effects of SST feedback on the water vapor, cloud, and radiation variations induced by changing the ice microphysics. The paper concludes in section 5 with a summary and discussion.

2. Cloud-resolving model, 1D ocean model, ice microphysics, and experimental design

The cloud-resolving model is described in Wu and Moncrieff (1999). The dynamical core is a two-dimensional version of the Clark–Hall cloud-scale model (Clark et al. 1996). Radiative processes are parameterized by the National Center for Atmospheric Research (NCAR) Community Climate Model radiation scheme (Kiehl et al. 1994), modified to distinguish between the radiative properties of liquid and ice cloud particles. The cloud microphysics are parameterized by a Kessler (1969) bulk warm rain parameterization and a Koenig and Murray (1976) bulk ice parameterization. The subgrid-scale mixing is parameterized using the first-order eddy diffusion method of Smagorinsky (1963). The surface fluxes of sensible and latent heat are calculated using a simplified version of the surface flux algorithm (Fairall et al. 1996; Wu et al. 1998, 1999) that is based on measurements made during TOGA COARE.

The x axis of the CRM is aligned east–west with a 600-km-long by 40-km-deep x–z domain. The horizontal resolution is 2 km. A stretched grid in the vertical with 52 levels (100-m spacing at the surface, increasing to 1500-m spacing at the model top) is used, requiring a time step of 15 s. Radiation calculations are performed every 150 s. Free-slip, rigid bottom, and top boundary conditions are applied, together with a gravity wave absorber in the uppermost 14 km of the domain. Cyclic lateral boundary conditions are used.

The 1D ocean model is from Large et al. (1994), which uses a nonlocal K-profile parameterization to represent the vertical mixing in the oceanic surface boundary layer. The oceanic boundary layer depth is determined by a stability condition on a bulk Richardson number that depends on the surface forcing, oceanic buoyancy, and velocity profiles. The vertical mixing in the interior is due to shear instability, internal waves, and double diffusion. The horizontal and vertical advection for the temperature and salinity are not included in the simulations. The 1D model has a depth of 200 m with 0.5-m resolution and a time step of 900 s. The reader is referred to Large et al. (1994) for a detailed description of the model physics. The 1D ocean model can reproduce the long-term trend and diurnal variation of observed SST over the TOGA COARE region using the observed and CRM-produced surface energy budgets (Anderson et al. 1996; Sui et al. 1998; Li et al. 1998; Wu and Moncrieff 2001).

The procedures that couple the CRM with the 1D ocean model are as follows. First, the CRM is run for 3 h with an initial SST of 29.37°C. The surface longwave and shortwave fluxes, latent and sensible heat fluxes, and wind stresses are calculated at each surface grid point (a total of 300 points). Second, the surface heat fluxes and wind stresses averaged over the whole domain of CRM are used to force the ocean model for three hours. The SST produced by the ocean model is then used for the next 3-h simulation of the CRM. This is an intermediate step before fully coupling the CRM and the ocean model.

Four 40-day simulations are presented: two with the coupled CRM-ocean model (T0C and M2C) and two with the fixed SST (T0 and M2). The large-scale forcing is specified by a 39-day (5 December 1992 to 12 January 1993) mean of the large-scale horizontal and vertical temperature and moisture advection over the Intensive Flux Array (IFA) of TOGA COARE (Lin and Johnson 1996; Figs. 1a and 1b). The 39-day mean SST of 29.37°C was calculated from four buoy datasets inside the IFA. The domain-averaged horizontal velocities are constrained to follow the 39-day mean values (Fig. 1c), which is a simple way to represent the control of the cloud-scale properties by the large-scale dynamics (Grabowski et al. 1996b; Wu et al. 1998). The initial atmospheric temperature and moisture profiles are the 39-day means over the IFA. The initial oceanic temperature and salinity profiles are the annual means from TOGA–Thermal Array for the Ocean (TAO) observations (Large and Gent 1999). The simulations start without any clouds in the domain.

Two different variations of the ice microphysical parameterization are used for investigating the effects of clouds on the radiative–convective–oceanic equilibrium state. Extreme changes in the representation of ice fall speed are applied in the idealized long-term simulation. This strategy has been used by other studies such as Grabowski et al. (1999) and G2000. In the original microphysics scheme of Koenig and Murray (1976), it is assumed that a given ice category falls with the velocity defined as a terminal velocity of an ice particle of the averaged mass. The averaged mass is defined as the ratio between the ice mixing ratio and ice number concentration. The particle size-velocity relationship is based upon water droplet formulas with ice particle correction factors ranging from 0.2 to 0.8, depending on ambient temperature and mean mass. Wu et al. (1999) showed that the modification of ice particle correction factors can significantly affect the simulation of cloud and radiative properties during TOGA COARE. In T0C and T0, a constant correction factor for all ice particles of 0.8 is used as in Wu et al. (1999), which is representative of high density particles such as ice pellets, frozen droplets, and graupel. In M2C and M2, the correction factor is 0.2 and the ice fall speed is representative of low density particles such as dendritic snowflakes and small pristine ice particles. The larger correction factor results in the larger ice fall speed and a different relationship between the ice fall speed and the ice water mixing ratio (Figs. 2a and 2b).

3. Effect of ice microphysics on the radiative–convective–oceanic quasi-equilibrium state

Figures 3 and 4 show the 40-day evolution of density-weighted temperature, precipitable water, SST, and oceanic boundary layer depth for T0C and M2C, respectively. The two coupled CRM–ocean simulations demonstrate distinct quasi-equilibrium states for both atmospheric and oceanic processes after about 20 days of integration. T0C produces a cold and dry atmospheric quasi-equilibrium state and warm SST with a large diurnal variation and shallower ocean mixed layer, while M2C produces a warm and moist atmospheric state and cold SST with a small diurnal variation and deep mixed layer. The radiative–convective–oceanic quasi-equilibrium state allows an in-depth analysis of how single processes such as radiative, cloud-scale and oceanic processes respond to the variation of ice microphysics. Table 1 summarizes various properties averaged over the last 10 days of simulations for T0C and M2C. The standard deviations for the 10-day daily mean and domain-averaged T0C data are also shown to measure the significance of the differences between two simulations. The difference between T0C and M2C are larger than the standard deviation of all properties in T0C, suggesting that the ice microphysics has important effects on the simulated atmospheric and oceanic quasi-equilibrium states. The mean atmospheric temperature and precipitable water in M2C are 2 K and 10.1 kg m⁻² larger than those in T0C. However, the mean SST and mixed layer depth in M2C is 0.67 K colder and 33 m deeper than those in T0C, respectively. The equilibrium SST of 29.38°C obtained in T0C is very close to the 39-day mean SST of 29.37°C from observations.

The warmer and moister quasi-equilibrium state associated with the smaller ice fall speed largely results from the cloud–radiation interaction. M2C produces more clouds than T0C. The vertically integrated ice and liquid water paths in M2C are 0.271 kg m⁻² and 0.184 kg m⁻² compared to 0.113 kg m⁻² and 0.127 kg m⁻² in T0C, respectively. The increase of ice water content is more than that of liquid water content from T0C to M2C as also shown in Fig. 5. The 10-day mean vertical profiles of cloud fraction (Fig. 6) show that M2C produces much more extensive cloudiness than T0C throughout the troposphere, especially above the freezing level (about 5 km). In the calculation of cloud fraction, a gridbox is defined to be cloudy if the sum of liquid and ice water exceeds 0.02 kg m⁻² at a given height. Increased cloud amount in M2C results in smaller outgoing longwave radiation (OLR) and larger albedo. The probability distribution of hourly OLR (Fig. 7) shows that smaller OLR (associated with higher ice clouds) is dominant for M2C, while T0C has a more uniformly distributed OLR.

The different cloud fields correspond to very different profiles of radiative tendency shown in Fig. 8. M2C has less longwave radiative cooling than T0C below 14 km and vice versa above (Fig. 8b). The shortwave radiative heating is larger for M2C than T0C above 9 km and vice versa below (Fig. 8a). The net radiative tendency (longwave plus shortwave) shows that T0C has larger cooling rate than M2C below 14 km and vice versa above (Fig. 8c). The vertically integrated radiative cooling is −54.8 W m⁻² in T0C compared to −7.7 W m⁻² in M2C. To quantify the role of temperature, water vapor, and cloud condensate fields in the total radiative tendency, the vertical profiles of radiative tendency over the clear sky are shown in Fig. 9. The temperature and moisture differences between M2C and T0C contribute to the differences of total radiative tendency in the upper troposphere, but the impact is relatively small compared to the cloud effects (the differences between Fig. 8 and Fig. 9).

Figure 10 shows the temperature and moisture profiles averaged over the last 10 days of the T0C and M2C simulations. Corresponding to the radiative heating profiles shown in Fig. 8c, the temperature is warmer in M2C than in T0C below 16 km and vice versa above (Fig. 10a). T0C has larger middle and lower tropospheric instability than M2C, while M2C has larger upper tropospheric instability than T0C. Consequently, T0C produces stronger cloud mass flux in the middle and lower troposphere and weaker cloud mass flux in the upper troposphere (Fig. 11). Strong convection in T0C produces larger net condensation (215.3 W m⁻²) and precipitation (211.7 W m⁻²) than in M2C (172.0 W m⁻² and 169.2 W m⁻², respectively). Under the quasi-equilibrium atmospheric state, the sum of precipitation and surface sensible heat flux (221.9 W m⁻² in T0C and 173.2 W m⁻² in M2C) are almost balanced by the sum of the large-scale advective cooling and radiative cooling (223.7 W m⁻² in T0C and 176.6 W m⁻² in M2C), and the sources of precipitation are from the large-scale moisture advection and surface latent heat flux. Table 1 also shows that the colder (warmer) SST in M2C (T0C) is, the weaker (stronger) precipitation, which is consistent with satellite observations (Gill and Rasmusson 1983). Because of stronger convection and more intense precipitation, T0C has a smaller water vapor mixing ratio than M2C (Fig. 10b). Figure 10c shows that the relative humidity is smaller in T0C than in M2C throughout the troposphere.

Ice microphysics affects the radiative fluxes at the top of atmosphere (Table 1). The cloud radiative forcing is defined in the usual way as the difference between the total radiative forcing and the radiative forcing corresponding to clear-sky conditions. The clear-sky radiative flux is obtained from offline calculations of the radiative transfer model by setting the cloud condensate fields to zero (Wu and Moncrieff 2001). The clear-sky flux is thereby more precisely defined than the method used in Wu and Moncrieff (1999) and Wu et al. (1998, 1999). The total greenhouse effect (G) is much larger in M2C than in T0C, but the clear-sky portion of the greenhouse effect (G_a) is about the same for M2C and T0C. The colder upper-tropospheric temperature and SST in M2C allow the smaller longwave radiation emitted to space by the clear sky (F_c) and the ocean surface (E) compared to T0C, respectively. The enhancement of total greenhouse effect in M2C is contributed mainly by the cloud portion of the greenhouse effect. Larger cloud amount leads to larger greenhouse effect in M2C than in T0C. There are 60.4 W m⁻² more cloud longwave forcing and 82.0 W m⁻² more cloud shortwave forcing in M2C than in T0C. The resulting net radiative flux at the top of the atmosphere is smaller in M2C (55.0 W m⁻²) than in T0C (74.3 W m⁻²).

The impact of ice microphysics on temperature and moisture fields, convection, and clouds also results in a very different surface energy budget. The 10-day (31–40 days) daily mean net surface shortwave flux Q_SW in M2C is smaller than that in T0C by 88.0 W m⁻². Larger cloud amount in M2C leads to a larger shortwave cloud forcing (Q^cld_SW), and consequently the smaller Q_SW than T0C. The diurnal variation of net surface shortwave flux in M2C is also smaller than that in T0C (not shown). The smaller solar flux into the surface results in the smaller variation during the day and night, which explains the smaller diurnal variation of SSTs in M2C than in T0C. The net surface longwave flux Q_LW in M2C is smaller than that in T0C by 17.6 W m⁻². Larger water vapor and smaller SST in M2C result in smaller net surface clear-sky longwave flux (Q^clr_LW), and larger cloud amount in M2C produces larger surface longwave cloud forcing (Q^cld_LW), which consequently leads to smaller Q_LW in M2C than T0C. The ocean heat loss by the latent and sensible heat fluxes is smaller in M2C (−53.9 W m⁻² and −4.1 W m⁻²) than that in T0C (−89.6 W m⁻² and −10.2 W m⁻²), which is consistent with the weaker convection in M2C than in T0C. The net surface heat flux in M2C is close to zero, while T0C has more than 25 W m⁻² net heat flux. The smaller net surface flux and weaker precipitation in M2C yield the deeper mixed layer and the colder SST in M2C than in T0C. This is consistent with the observational and 1D ocean model study of Anderson et al. (1996) that demonstrated decreased precipitation producing a deeper mixed layer. The smaller net surface flux and weaker precipitation (fresh water) in M2C lead to smaller buoyancy flux at the ocean surface, more unstable mixed layer, larger convective mixing, and then deeper mixed layer in M2C than in T0C. The larger upper oceanic mixing that entrains deep colder water into the surface layer in M2C yields the colder SST in M2C than in T0C.

The above analysis demonstrates that the variation of ice microphysics has a huge impact on radiative–convective–oceanic quasi-equilibrium state through the cloud–radiation interaction. The simulation with the smaller ice fall speed reaches a quasi-equilibrium state featured by a warmer and moister atmosphere but colder SST, and a larger cloud amount but weaker convection. On the other hand, the simulation with the larger ice fall speed achieves a quasi-equilibrium state featured by a colder and drier atmosphere but warmer SST, and a smaller cloud amount but stronger convection.

4. Effect of SST feedback on quasi-equilibrium state

In the coupled CRM–ocean system, the change of ice microphysics has significant effects on the atmospheric and oceanic equilibrium state. Does the SST feedback amplify or reduce the temperature, water vapor, cloud, and radiation variations induced by the change of ice microphysics in the coupled simulation? To quantify the role played by the SST feedback, two 40-day simulations with the fixed SST of 29.37°C (T0 and M2) are presented in this section and the differences between M2 and T0 are compared with those between M2C and T0C.

Table 2 lists various properties averaged over the last 10 days of simulations for T0 and M2. The two uncoupled simulations show similar features presented in the coupled simulations (T0C and M2C), that is, marked effects of ice microphysics on the atmospheric quasi-equilibrium state, convection, cloud, and radiative properties. The differences of mean atmospheric temperature and precipitable water between M2 and T0 are 2.7 K and 12.4 kg m⁻², respectively, which are slightly larger than the differences between M2C and T0C (2.0 K and 10.1 kg m⁻²). The differences between M2–T0 and M2C–T0C are larger than the standard deviations of either T0 or T0C, because the SST in M2 (29.37°C) is warmer than the mean SST in M2C (28.71°C), while the SSTs are about the same for T0 and T0C. Consequently, M2 is warmer and moister than M2C, which is consistent with the result presented in Wu and Moncrieff (1999). Therefore, the water vapor variation associated with the change of ice microphysics is somewhat reduced by the SST feedback in the coupled simulations.

In contrast, the differences of convection, precipitation, surface heat fluxes, cloud, and radiative properties between M2 and T0 (Table 2) are slightly smaller than those between M2C and T0C (Table 1). For example, the differences between M2C–T0C and M2–T0 are 0.022 and 0.023 kg m⁻² in liquid and ice water paths, respectively, which are larger than the standard deviation of either T0 (0.008 and 0.003 kg m⁻²) or T0C (0.008 and 0.007 kg m⁻²). The difference of radiative tendency between M2C–T0C and M2–T0 is 5.2 W m⁻², that is larger than the standard deviation of either T0 (2.6 W m⁻²) or T0C (4.7 W m⁻²). The difference of cloud shortwave forcing at the top of the atmosphere (C_s) between M2–T0 and M2C–T0C is 11.9 W m⁻²; that is larger than the standard deviation of either T0 (7.9 W m⁻²) or T0C (7.3 W m⁻²). Finally, the difference of net shortwave flux at the surface (Q_SW) between M2–T0 and M2C–T0C is 13.0 W m⁻²; that is larger than the standard deviation of either T0 (8.6 W m⁻²) or T0C (7.7 W m⁻²). These results show that the cloud and radiation variations induced by the change of ice microphysics is enhanced by the SST feedback in the coupled simulations.

5. Summary and discussion

The uncertainty associated with the parameterization of subgrid-scale physical processes in GCMs presents a major problem for understanding the mechanism of climate feedback and the effects of water vapor, convection, cloud, and radiation processes on the tropical climate (e.g., Cess et al. 1989; Chahine 1992; Browning 1994). To address this uncertainty, the cloud-resolving modelling approach, which treats cloud dynamics explicitly, has been increasingly used to study the relationships among key physical parameters and processes. In this paper, we extend the idealized simulation of Wu and Moncrieff (1999) to investigate the effects of ice microphysics on the mean state of the tropical atmosphere and ocean by coupling the CRM with the 1D ocean model.

We find that the change of ice microphysics leads to two markedly different radiative tendency profiles (Q_R) that result in two different radiative-convective-oceanic quasi-equilibrium states. The quasi-equilibrium state associated with the smaller ice fall speed features a warmer and moister atmosphere but colder SST, while the quasi-equilibrium state associated with the larger ice fall speed shows a colder and drier atmosphere but warmer SST. The simulation with the smaller ice fall speed produces more cloud but weaker convection and precipitation, while the simulation with the larger ice fall speed has less cloudiness but stronger convection. We also find that the temperature and water vapor variation due to the change of ice microphysics is reduced by the atmosphere–ocean interaction, while the cloud and radiation variation is amplified by the SST feedback in the coupled simulation.

Our findings differ from that of G2000 who showed that the cloud microphysics has a major impact on the ocean surface but rather minor impact on the mean state of the atmosphere. The difference between the two studies is evidently due to the absence of ocean dynamics in the simulation of SST in G2000. Without the balancing factor of cooling by the oceanic mixing, the SST in G2000 runs away as a result of the net surface heating. For the atmospheric part, two simulations of G2000 applied extreme changes in cloud (ice and liquid) and precipitation particle sizes, which are similar to the changes of the ice fall speed herein. The smaller the particles, the slower they fall (see Fig. 1 in G2000). However, for the oceanic part, G2000 used a simple surface energy budget equation with a shallow isothermal layer of water. Because of the lack of oceanic mixing and entrainment of the oceanic deep water, two simulations of G2000 produced very different and unrealistic SSTs: 37°C in the simulation assuming large particles and 33°C in the simulation assuming small particles.

The coupled CRM–1D ocean simulations presented here did not include the oceanic advection. Gent (1991) found that the annual mean net heating of the ocean surface in the area 140°–180°E, 10°S–10°N is between 0 and 20 W m⁻². Anderson et al. (1996) pointed out that during the most time of TOGA COARE period, the 1D oceanic budgets can be closed without the oceanic advection suggesting the dominance of local air–sea interactions in the maintenance of the warm pool. Sui et al. (1997, 1998) and Li et al. (1998) also noticed horizontal advection in the upper ocean within the TOGA COARE region is generally small during the intensive observation period (IOP), though it may not be negligible at times. The net surface heat fluxes averaged over the last 10 days (days 31–40) are 28.5 W m⁻² for T0C and −0.1 W m⁻² for M2C, respectively. The net heat flux into ocean in T0C may continue to heat the ocean until the net heat flux reaches zero. It will take longer time for the adjustment of the atmosphere and the ocean to reach the zero net surface heat flux in the T0C run. In an offline calculation, the surface forcing from the uncoupled run T0 is used to force the 1D ocean model. The 10-day mean SST (29.31°C) from uncoupled forcing is close to the coupled run T0C (29.38°C). The SST difference between coupled and uncoupled forcing is 0.07°C. In another two offline calculations, the surface forcing from the coupled run T0C and M2C are used to force the 1D ocean model that includes the advection of −28.5 W m⁻² throughout the entire column. The 10-day mean SST is 29.18°C for T0C forcing and 28.50°C for M2C focing, respectively. So the inclusion of −28.5 W m⁻² oceanic advection reduces the SST by 0.2°C for both T0C and M2C forcing. These suggest the sensitivity of the quasi-equilibrium state to the ice microphysics shown in the coupled CRM–1D ocean model run T0C and M2C may hold for runs using the ocean model with the advection. But it remains to be quantified. We will report the result when the fully coupled CRM–1D (2D or 3D) ocean model is completed.

The mean state of the atmosphere is warmer and moister in the simulation with the smaller particles than with the larger particles under the same SST. However, the simulation with the smaller particles produces much smaller SST than that with the larger particles, which will produce a colder and drier mean state (Wu and Moncrieff 1999). These competing effects result in the small difference of mean state of the atmosphere between two simulations of G2000. Since the difference between equilibrium SSTs of T0C (29.38°C) and M2C (28.71°C) is much smaller than that between two simulations of G2000, the effect of ice microphysics on the mean state of the atmosphere is not reduced by the SST feedback as much as in G2000.

Recall that the large sensitivity of equilibrium state to microphysical parameters is also found in 1D radiative–convective equilibrium simulations (Emanuel 1991). However, the cumulus parameterization was used to represent the cloud-scale processes in these 1D simulations. The coupled CRM–ocean simulations, which resolve the cloud dynamics and include the ocean dynamics, certainly have advantages over the 1D simulations. As presented in Wu and Moncrieff (1999) and herein, with a well-controlled experimental setting the coupled CRM–ocean model is able to explore the relationship between ice microphysics and components of the hydrological cycle. This will help understand the complexity of interactive processes in the real and virtual (GCM) worlds.

Finally, we note that comprehensive measurements of ice particles in the atmosphere are not yet available. It is clear that cloud-resolving simulations such as those we reported herein really call for more definitive measurements under different environmental conditions, not only to improve cloud microphysics parameterization (e.g., McFarquhar and Heymsfield 1996; Heymsfield and Iaquinta 2000), but also assure that existing parameterization are used in the best way possible (e.g., Wu et al. 1999).