Equilibrium States Simulated by Cloud-Resolving ... - AMS Journals

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JOURNAL OF THE ATMOSPHERIC SCIENCES

VOLUME 56

Equilibrium States Simulated by Cloud-Resolving Models W.-K. TAO, J. SIMPSON,

AND

C.-H. SUI

Laboratory for Atmospheres, NASA/Goddard Space Flight Center, Greenbelt, Maryland

C.-L. SHIE Laboratory for Atmospheres, NASA/Goddard Space Flight Center, Greenbelt, Maryland, and Science Systems and Applications Inc., Lanham, Maryland

B. ZHOU Laboratory for Atmospheres, NASA/Goddard Space Flight Center, Greenbelt, Maryland, and Universities Space Research Association, Columbia, Maryland

K. M. LAU Laboratory for Atmospheres, NASA/Goddard Space Flight Center, Greenbelt, Maryland

M. MONCRIEFF National Center for Atmospheric Research, Boulder, Colorado (Manuscript received 19 June 1998, in final form 9 October 1998) ABSTRACT Recently, several cloud-resolving models (CRMs) were used to study the tropical water and energy cycles and their role in the climate system. They are typically run for several weeks until modeled temperature and water vapor fields reach a quasi-equilibrium state. However, two CRMs produced different quasi-equilibrium states (warm and humid versus cold and dry) even though both used similar initial thermodynamic profiles, horizontal wind, prescribed large-scale vertical velocity, and fixed sea surface temperature. Sensitivity tests were designed to identify the major physical processes that determine the equilibrium states for the different CRM simulations. Differences in the CRM simulated quasi-equilibrium state can be attributed to how the atmospheric horizontal wind was treated throughout the integration. The model that had stronger surface wind produced a warmer and more humid thermodynamic equilibrium state. The physical processes responsible for determining the modeled equilibrium states can be identified by examining the differences in the modeled water vapor, temperature, and moist static energy budget between warm/humid and cold/dry states. One of the major physical processes responsible for the warmer and more humid equilibrium state is larger latent heat fluxes from the ocean (due to stronger surface wind). The moist static energy budget further indicates that the large-scale forcing in water vapor is another major physical process responsible for producing the warmer and more humid thermodynamic equilibrium state. The model results also indicated that the advective forcing in temperature (cooling) and water vapor (moistening) by the imposed large-scale vertical velocity was larger (smaller) for the warm and humid (cold and dry) equilibrium state. This is because the domain mean thermodynamic state is more unstable and has a stronger vertical gradient of water vapor for those experiments that produced a warmer and more humid climate. Specified minimum wind speed in the bulk aerodynamic formulas and initial soundings on the modeled thermodynamic equilibrium state are also discussed.

1. Introduction The highest science priority identified in the Global Change Research Program is the role of clouds in

Corresponding author address: Dr. Wei-Kuo Tao, Mesoscale Atmospheric Processes Branch, Code 912, NASA/GSFC, Greenbelt, MD 20771. E-mail: tao@agnes.gsfc.nasa.gov

q 1999 American Meteorological Society

climate and hydrological systems, which have been identified as being the most problematic issues facing global change studies. For this reason, the Global Energy and Water Cycle Experiment (GEWEX) formed the GEWEX Cloud System Study (GCSS) specifically for the purposes of studying such problems. Cloudresolving models (CRMs) were chosen as the primary approach (GEWEX Cloud System Science Team 1993). Progress in studying precipitating convective

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systems in GCSS is reported in Moncrieff et al. (1997). The cloud-resolving model (CRM) is an important and flexible tool for studying tropical convection and its interaction with the large-scale environment. It explicitly calculates cloud properties (e.g., transport processes and the diabatic heating due to microphysical processes associated with phase changes of water). CRMs can also explicitly treat cloud–radiation and air– sea interaction. As computational facilities improve, these models can progressively include more sophisticated ice processes and explicit interaction between clouds and radiation (Ferrier 1994; Meyers 1995; Tao et al. 1996) as well as address multiday simulations (Moncrieff et al. 1997; Grabowski et al. 1996; Xu and Randall 1996). The large-scale quantities required for multiday integrations (initial conditions, upper and lower boundary conditions, large-scale advective tendencies of potential temperature and water vapor, and horizontal winds) can be based on large-scale measurements made during field campaigns (Soong and Tao 1980; Moncrieff et al. 1997; Moncrieff and Tao 1998; and many others). In these simulations, clouds of different sizes/types in various stages of their life cycles occur. In addition, CRMs can use progressively larger horizontal domains (to allow for an ensemble of clouds) and be integrated for up to month-long periods. CRMs are laterally bounded. While various kinds of lateral boundary conditions can be defined, simple periodic (cyclic) conditions are relatively straightforward to make consistent with the large-scale forcing and give useful results provided the domains are sufficiently large (at least many hundreds of kilometers). Recent CRM studies on tropical water and energy cycles and their role in the climate system are summarized in Table 1.1 All of these CRM studies are similar in that ensembles of cumulus clouds are generated by ‘‘an imposed (or prescribed) forcing’’ and/or by sensible and latent heat fluxes from the ocean. A fixed sea surface temperature was always assumed. In addition, a cyclic lateral boundary condition was used so as to not allow extra heat and moisture into the domain other than the imposed forcing. The CRM-climate simulations are usually integrated for several days/weeks until modeled thermodynamic fields reach a quasi-equilibrium (or statistical equilibrium) state. Some of these modeling studies used a two-dimensional model and included ice processes in order to represent the stratiform cloud (or anvil) realistically. Islam et al. (1993), Robe and Emanuel (1996), and Tompkins and Craig (1998) applied three-dimensional CRMs and argued that the three-dimensional CRM can correctly represent the organization

1 No feedback from clouds to their embedded large-scale circulation is allowed in any of these long-term CRM integrations. Therefore, current CRMs may only be sufficient for the study of idealized climate.

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of cloud systems as well as interactions between clouds. However, the forcing imposed in these models is substantially different. For example, Nakajima and Matsuno (1988), Islam et al. (1993), and Robe and Emanuel (1996) used a fixed (time invariant) radiative cooling to drive convection. Cloud and radiation interaction was allowed in Held et al. (1993) and Tompkins and Craig (1998). In addition to the interactive cloud–radiative forcing, large-scale advective forcing in temperature and water vapor can be imposed, as suggested by Soong and Ogura (1980) and Soong and Tao (1980). There are two ways to implement large-scale advective forcing in a CRM. One is to specify the large-scale vertical velocity (derived from observations) in the model and compute the advective forcing in temperature and water vapor using the model mean vertical temperature and water vapor gradients [adopted by Sui et al. (1994) and Grabowski et al. (1996)]. This method allows more realistic explicit interaction between prescribed large-scale velocity and CRM generated temperature and water vapor fields. Second, the observed large-scale advective forcing can be held constant during the model integration [adopted by Randall et al. (1994) and Xu and Randall (1999)]. The second approach has the advantage of having a fixed large-scale forcing, and would make better comparisons with observations. Although CRMs are powerful tools for understanding the large-scale role of convection and its parameterization, the interactions among processes are highly nonlinear and difficult to understand. Numerical experiments from two different CRMs, Sui et al. (1994) and Grabowski et al. (1996), produced different quasi-equilibrium states even though both models contained interactive cloud–radiation processes and sea surface fluxes under similar large-scale influences. For example, Sui et al. (1994) used the Goddard Cumulus Ensemble (GCE) model and found that the simulated climate was cool and dry (relative to the initial thermodynamic state—the climatological state). On the other hand, Grabowski et al. (1996), using the Tripoli (1992) model, found that their modeled climate was warm and humid. The initial conditions of Sui et al. (1994) and Grabowski et al. (1996) were taken from the 1956 Marshall Islands Experiment in the central Pacific. However, there remain many differences between these two studies (see Table 2). For example, the mass-weighted relative humidity is almost 10% higher in Grabowski et al. (1996) than in Sui et al. (1994) (see Fig. 1). The convective available potential energy (CAPE) in Grabowski et al. (1996) is also larger than that of Sui et al. (1994). The microphysical processes, grid sizes, and domain sizes are also quite different. Another major difference is how the atmospheric horizontal wind is treated throughout the integration in these two CRMs. There are two major processes that affect the horizontal momentum in CRMs. The first is the vertical transport of momentum by cloud updrafts

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TABLE 1. Summary of previous cloud–radiation modeling studies. The general setup for each study is given along with some of the model characteristics and treatments used to parameterize the radiative effects. The case used in each study is also given.

Model Nakajima and Matsuno (1988) Islam et al. (1993) Held et al. (1993)

2D No ice 3D

2D 3 ice Sui et al. (1994); Lau et al. (1993); 2D Lau et al. (1994) 3 ice Randall et al. (1994) 2D 3 ice Grabowski et al. (1996) 2D 2 ice Robe and Emanuel (1996) 3D No ice Tompkins and Craig (1998) 3D 3 ice Xu and Randall (1999) 2D 3 ice

Domain (dx)

Large-scale forcing

512 km (1000 m) 60 3 60 km 2 (2000 m) 640 km (5000 m) 768 km (1500 m) 256 km (2000 m) 900 km (1000 m) 60 3 60 km 2 (2000 m) 100 3 100 km 2 (2000 m) 512 km (2000 m)

Integration time (days)

Case

Constant radiative cooling

2.5

East Atlantic

Constant radiative cooling

4

West Indies

Cloud-radiative forcing

42

Tropics

Large-scale velocity and radiative forcing Radiative forcing

52

West Pacific

100

East Atlantic

25

West Pacific

6–30

West Indies

Large-scale velocity and radiative forcing Constant radiative cooling Cloud-radiative forcing

70

Radiative–convective equilibrium

Constant forcing in T and Q V and radiative forcing

29

West Pacific and East Atlantic

and downdrafts. This process allows the horizontal mometum in the lower (middle and upper) troposphere to be brought upward (downward) by cloud updrafts to the middle and upper (lower) troposphere. This process is a downgradient transport (reduces the wind shear). The second is the convective-scale and mesoscale horizontal pressure gradient force. This pressure gradient force can generate convective-scale horizontal momentum, which may be transported vertically by clouds. This process has been demonstrated by LeMone (1983) using observational data, by Moncrieff (1981, 1992, 1995) using a theoretical approach, and by Soong and Tao (1984) and Tao and Soong (1986) in numerical experiments. Neither mechanism can maintain the imposed large-scale shear in 2D periodic domain simulations. However, the horizontal mometum can be relaxed to a specified value (e.g., maintain the imposed vertical shear and strength of horizontal mometum). This can be done either by considering the geostrophic control associated with the large-scale horizontal pressure gradient (i.e., Xu and Krueger 1991) or by adding

an extra nudging (relaxation) term in the horizontal momentum. The initial large-scale horizontal wind and its shear are maintained in Grabowski et al. (1996) by including geostrophic control, but they are mixed by the convective processes in Sui et al. (1994). To determine what physical processes contribute to the different CRM quasi-equilibrium states, we have performed more than 50 two-dimensional GCE model integrations focusing on the various model setups (i.e., microphysics, method of large-scale forcing, diurnal cycle, initial conditions, air–sea interaction, and mixing of horizontal wind by clouds). In this paper, we will only discuss 8 representative runs from among the 50 that produced 1) a warm/humid climate (as in Grabowski et al. 1996), 2) a climate that is close to Sui et al. (1994), and 3) a colder/drier climate than Sui et al. (1994). The water vapor, temperature, and moist static energy budgets will be examined to identify the major ‘‘physical processes’’ that determine different CRM climates.

TABLE 2. Summary of differences between model setups of Sui et al. (1994) and Grabowski et al. (1996). Sui et al. (1994) CAPE Mass-weighted relative humidity L x, L z Dx, Dz Model setup Advection scheme Cloud radiation Microphysics

1722 m 2 s22 51.9% 768 km, 21.5 km 1500 m, 300–1000 m Mean horizontal wind varies with time (by convective mixing) Second order in vertical and fourth order in horizontal No diurnal cycle Water/ice optical properties 2 water and 3 ice

Grabowski et al. (1996) 1969 m 2 s22 61.4% 900 km, 24 km 1000 m, 200–500 m Horizontal wind is nudging to its initial wind profile Positive definite advection Diurnal cycle Water optical properties 2 water and 4 ice

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FIG. 1. The sounding used to initialize the model in (a) Sui et al. (1994) and (b) Grabowski et al. (1996) (kindly provided by Dr. Grabowski).

2. Model setup and sensitivity experiments The CRM (GCE model) used in Sui et al. (1994) is used here. The simulated flow is nonhydrostatic and anelastic where the sound waves are eliminated. The cloud microphysics includes a parameterized Kesslertype two-category liquid water scheme (cloud water and rain) and a parameterized Lin et al. (1983) or Rutledge and Hobbs (1984) three-category ice-phase scheme (cloud ice, snow and hail/graupel). Shortwave (solar) and longwave (infrared) radiation parameterizations

(Chou and Arking 1980, 1984) as well as a subgridscale turbulence (one-and-a-half order) scheme are also included. Details of the model can be found in Tao and Simpson (1993). A second-order accurate advection scheme and a leapfrog time integration (kinetic energy semiconserving method) were used. A stretched vertical coordinate (height increments from 250 to 1150 m) with 31 grid points was used to maximize resolution in the lowest levels of the model. A total of 512 grid points was used

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TABLE 3. Setups for the eight experiments that were conducted for examining the physical processes that determine a warm/humid or cool/ dry climate. The vertical shear and strength of the imposed large-scale horizontal momentum cannot be maintained (unforced) in runs 1–4, but they can (forced) in runs 1W–4W.

Run 1 2 3 4 1W 2W 3W 4W

Sounding Sui et al. (1994) (GSFC) Grabowski et al. (1996) (NCAR) GSFC NCAR GSFC NCAR GSFC NCAR

in the horizontal with 1500-m resolution. Constant sea surface temperature and bulk aerodynamic formulas are used to compute the surface sensible heat flux and evaporation. To account for the gustiness effect in the boundary layer, Sui et al. (1994) assumed that the wind speed (V s ) in the bulk aerodynamic formulas was to be no less than 4 m s21 in computing surface fluxes. Details of the model setup and initial conditions can be found in Sui et al. (1994). Eight sensitivity experiments were performed to investigate the effects of convective mixing of horizontal momentum, specified minimum wind speed in the bulk aerodynamic formulas, and initial soundings on the modeled thermodynamic equilibrium state. Table 3 lists the major characteristics of these sensitivity tests. All eight experiments were integrated for 25 days. As noted, the density weighted relative humidity (RH) is higher in Grabowski et al. (1996) with the largest difference mostly above 400 mb and below 850 mb (Fig. 1). The initial conditions of Sui et al. (1994) and Grabowski et al. (1996) are used in runs 1 and 2, respectively. The objective of these two runs was to test whether the difference in upper relative humidity could cause different modeled climates. The sensitivity of the prescribed minimum wind speed in the bulk aerodynamic formulas upon the modeled climate will be examined. Instead of allowing no less than 4 m s21 (V s ) in computing surface fluxes, a smaller minimum wind speed (V s 5 1 m s21 ) is used in runs 3 and 4. Cloud organization is sensitive to the vertical shear of the environmental horizontal wind (i.e., Moncrieff 1981; Thorpe et al. 1982; Rotunno et al. 1988). Moncrieff (1981) showed that the structure of the convection and its associated transport is fundamentally different if the vertical shear of the horizontal wind and thermodynamic profiles are changed (measured by a convective Richardson number). Well-organized cloud systems usually generate strong surface (gust) winds and strong cold outflows that enhance the surface fluxes into the atmosphere (Wang et al. 1996). In addition, the stratiform cloud amount generated by organized convective systems is very different from that due to nonorganized

U Wind (function of time)

Minimum wind speed in surface flux calculation (ms21 )

Varying Varying Varying Varying Nudging Nudging Nudging Nudging

4 4 1 1 4 4 1 1

convective systems. This difference is expected to have an impact on cloud–radiation interaction. Runs 1W–4W are the same as runs 1–4, respectively, except that the u momentum is relaxed (nudged) to its initial value.2 A 10-h relaxation period is used. The objective of these four runs is to test whether the effect of convective organization could cause different modeled climates. 3. Results Figures 2a and 2b show the time series of the domainaveraged temperature and water vapor for the eight experiments listed in Table 3. Figure 3 is a scatterplot of domain-averaged water vapor versus temperature at 25 days of integration for all eight runs. The results from Sui et al. (1994) and Grabowski et al. (1996) are also shown in Figs. 2 and 3. Generally, three distinct climate/ thermodynamic regimes have been simulated in these eight runs.3 For example, runs 1W, 2W, 3W, and 4W produced a quasi-equilibrium state very similar to that of Grabowski et al. (1996); that is, the modeled temperature and water vapor in these four runs are above 261.5 K and 68 mm. On the other hand, in runs 3 and 4 the modeled temperature and water vapor are colder and less humid than 257 K and 48 mm. In the third regime, the modeled temperature and water vapor in runs 1 and 2 are centered at 259 K and 57 mm. The latter two regimes are much closer to that simulated by Sui et al. (1994) than by Grabowski et al. (1996). These sensitivity tests indicate that initial conditions (variations in CAPE and upper-tropospheric humidity) cannot change the modeled climate (warm/humid to cold/dry or vice versa). The prescribed minimum wind speed (V s )

2 Imposing a geostrophic balance of the horizontal wind has the same effect in terms of maintaining the imposed vertical shear and strength of the large-scale horizontal wind as nudging (relaxation) of the horizontal wind (K. Xu 1998, personal communication). 3 Runs 3 and 4 required a longer time (40 days) integration in order to reach their ‘‘quasi-equilibrium states.’’ The temperature and water vapor dropped another 1 K and 2 mm, respectively, over the additional 15 days of model integration.

FIG. 2. Time series of the vertically and horizontally averaged (a) mass-weighted temperature ^T & (K) and (b) water vapor ^rq y & (mm). ‘‘G’’ and ‘‘S’’ denote the modeled climates simulated from Grabowski et al. (1996) and Sui et al. (1994), respectively. The time series of mass-weighted temperature and water vapor for runs 1W and 2W resemble runs 3W and 4W. Only those from runs 3W and 4W are shown.

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TABLE 4. Water budgets of the eight runs. Net condensation is sum of condensation, deposition, evaporation, and sublimation of cloud. Large-scale forcing is the imposed large-scale advective effect on water vapor, and Lvd (qy ) is the local time change (over 25 days of integration) of water vapor. Units are in W m22 . Differences in the individual water budget terms for the pairs of runs with and without nudging of horizontal wind are also shown.

Run 1 2 3 4 1W 2W 3W 4W 1W 2W 3W 4W

Ly

2 2 2 2

1 2 3 4

Net Large-scale condensation forcing Latent heat d (Ly Qy )/dt in Ly Qy in Ly Qy fluxes 2502.4 2490.2 2458.5 2438.4 2545.3 2536.8 2547.0 2533.0 242.9 246.6 288.5 294.6

5.89 5.35 25.32 27.45 23.14 19.55 22.24 21.62 17.25 14.20 27.56 29.06

410.6 397.8 382.5 364.2 463.6 446.5 462.4 448.2 53.0 48.7 79.9 84.0

7 8

97.8 97.8 70.7 66.8 105.2 110.2 106.9 106.3 7.4 12.4 36.2 39.5

7 8

]q y ]q 5 2^Ly (c 2 e ) 1 L s (d 2 s )& 2 Ly w y ]t ]z 1 Ly E o

FIG. 3. Scatterplot of horizontal mass-weighted temperature vs water vapor after 25 days of integration from all eight runs. The result from Sui et al. (1994) after 25 days of integration is denoted as S while that of Grabowski et al. (1996) is denoted as G.

in the bulk aerodynamic formulas, however, can have a major impact upon the modeled climate for runs 1 and 2 and runs 3 and 4. An interesting feature in Fig. 3 is the almost linear relationship between domain-averaged temperature and water vapor. Additional two-dimensional GCE model integrations focusing on the various model setups (i.e., microphysics, method of large-scale forcing, diurnal cycle, initial conditions, air–sea interaction, and mixing of horizontal wind by clouds) have been performed. These additional sensitivity tests indicated that microphysics and its interaction with radiation as well as the diurnal cycle cannot basically alter the model-simulated equilibrium state from one regime (warm/humid) to another (cold/dry). But the microphysical processes and their interaction with radiation can still change the ‘‘magnitude’’ (i.e., warm to warmer or vice versa) of the modeled thermodynamic state. The vertical distribution of water vapor (as well as surface rainfall) can be quite different between runs with similar thermodynamic equilibrium states. Horizontal and vertical integration of the equation for water vapor (q y ), temperature, and moist static energy h (h 5 C p T 1 L y q y 1 gz) over the horizontal and from the surface to the top of the model domain yields

Cp

7 8

(1)

]T 5 ^Ly (c 2 e ) 1 L s (d 2 s ) 1 L f ( f 2 m )& ]t

7 u8

2 Cp p w

7 8

] ]z

1 ^Q R & 1 C p H s

71

]h ]u ]q ù ^L f ( f 2 m )& 2 w C p p 1 Ly y ]t ]z ]z 1 ^Q R & 1 C p H s 1 Ly E o ,

(2)

28 (3)

where c, e, d, s, f, and m are condensation, evaporation, deposition, sublimation, freezing, and melting of cloud, respectively; u is potential temperature and p 5 ( p/Poo ) R/C p is the nondimensional pressure, where p is the dimensional pressure and Poo the reference pressure taken to be 1000 mb, C p is the specific heat of dry air at constant pressure, and R is the gas constant for dry air; 2^w ]q y /]z & and 2^w ]u /]z & are the large-scale advective moistening and cooling forcing; w is the prescribed-imposed large-scale vertical velocity (constant with time); ]u /]z and ]q y /]z are model mean vertical temperature and water vapor gradients (varying with time); Q R is the radiative heating; and E o and H s are the latent and sensible heat fluxes from the ocean surface. The variables L y , L f , and L s are the latent heats of condensation, fusion, and sublimation. The physical processes responsible for determining the modeled equlibrium states can be identified by examining the budget differences between nudged (runs 1W–4W) and nonnudged runs (runs 1–4). Table 4 lists the water vapor budget. In all eight runs, the largest two terms in the water vapor budget are net

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TABLE 5. Temperature budgets of the eight runs. Net condensation is sum of condensation, deposition, evaporation, sublimation, freezing, and melting of cloud. Large-scale forcing is the imposed largescale advective effect on temperature, and d(CpT) is the local time change (over 25 days of integration) of temperature. Net radiative processes are shown in QR . Units are W m22 .

Run 1 2 3 4 1W 2W 3W 4W 1W 2W 3W 4W

2 2 2 2

1 2 3 4

Net conden- Large-scale sation forcing d(C pT)/dt in C pT in C pT 0.13 26.02 212.94 222.71 13.12 9.47 14.55 8.44 13.00 15.49 27.49 31.16

498.3 485.6 455.5 435.1 542.1 532.3 543.6 528.4 43.8 46.7 88.1 93.3

2421.9 2414.3 2400.1 2391.7 2454.3 2444.6 2452.5 2443.6 232.4 230.3 252.4 251.9

Net Q R

Sensible heat fluxes

297.18 297.61 283.53 281.00 292.97 297.69 295.17 294.87 4.2 20.1 211.6 213.9

20.71 20.16 15.66 14.71 18.79 19.21 19.09 18.72 21.92 20.95 3.43 4.01

condensation (drying) and imposed large-scale forcing (moistening). The dominance of these two terms, which are opposite in sign, is characteristic of the tropical atmosphere. In other words, the temporal changes in the mean state are small residuals of these two primary terms. This behavior is also seen in the temperature budget (Table 5). Soong and Tao (1980) performed experiments with different magnitudes of large-scale forcing and found that the larger the large-scale forcing (cooling/moistening), the larger the net condensation (heating/drying). They hypothesized that the CRM-simulated effect of convective processes may simply be a response to the ‘‘imposed large-scale forcing in temperature and water vapor.’’ Our results testing different magnititudes of large-scale forcing (not shown here) and those of others (Grabowski et al. 1996; Xu and Randall 1998) also indicated that CRM-simulated climate (warm/humid or cold/dry) is not very sensitive to the magnitude of the prescribed large-scale forcing. The simulated cloud structure and the surface wind are very different between these climate regimes. The simulated clouds are organized into squall lines having large stratiform regions and stratiform rain amounts in runs 1W–4W. On the other hand, the clouds simulated in runs 1–4 are typically less organized than those in runs 1W–4W. This is because the u momentum is well mixed (almost constant with height below the 250-mb level) after only 5 days of integration in runs 1–4 (Fig. 4). As aforementioned, this occurs because highly organized convective systems occur in strong to moderate shear, whereas random convection prevails in light wind shear. In addition, the surface wind in runs 1–4 is only about 1–2 m s21 after 5 days of integration (versus 7– 8 m s21 in runs 1W–4W). This is why the modeled climate as well as latent heat flux (shown later in the water budget) is sensitive to the prescribed minimum

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wind speed in the bulk aerodynamic formulas for runs 1–4, but not for runs 1W–4W. Although the latent heat flux is only 1⁄ 5 to 1⁄6 of the large-scale forcing in all eight runs, its role in determining model climate is quite important. Note that the runs that produced the more humid/drier climates are always associated with larger/smaller latent heat fluxes from the ocean. Also note that the latent heat flux (67– 110 W m22 ) is about the same magnitude as the summation (74–92 W m22 ) of net condensation and largescale forcing. Additionally, the differences in latent heat fluxes between runs 3 and 3W and runs 4 and 4W, respectively, are larger (about 9 W m22 ) than their corresponding differences in local time change of water vapor (Table 4). Only about 42% and 87% of the change in modeled water vapor can be attributed to the change in latent heat flux between runs 1 and 1W and runs 2 and 2W, respectively. The large-scale advective forcing of water vapor can also contribute to a change in modeled water vapor (from 13% to 58%).4 The physical processes that account for the differences between humid- and dry-modeled climate are therefore the latent heat flux and the large-scale forcing in moisture. However, the contribution from each process depends upon the initial sounding and the prescribed minimum wind speed (V s ) in the bulk aerodynamic formulas. Our results indicate that with a smaller prescribed minimum V s , the contribution from latent heat flux in determining modeled climate becomes larger. The sounding used by Sui et al. (1994) is drier aloft than in Grabowski et al. (1996), and it allows for greater large-scale forcing (moistening) of water vapor. Likewise, the largest two terms in the temperature budget (Table 5) are net condensation (heating) and imposed large-scale forcing (cooling). The local time change in temperature is also at least one to two orders of magnitude smaller than either net condensation or the large-scale forcing. The sensible heat flux (15–21 W m22 ) is about five times smaller than the latent heat flux and is about the same order of magnitude as the local time change in temperature (223–15 W m22 ). There is no clear relationship (compared to the moisture budget) between local time change in temperature and the sensible heat fluxes. The differences in sensible heat flux (from 21.9 to 4.0 W m22 ) between pairs of runs with and without nudging of horizontal winds is smaller than their corresponding differences in local time change of modeled temperature (from 13 to 31 W m22 ). The radiative cooling term is about 1⁄4 to 1⁄5 of the large-scale forcing in all eight runs and is not responsible for determining one modeled equilibrium temperature state or the other (see Table 5). The primary factor

4 By examining the evolution of various moisture budget terms, the latent heat flux is found to be the leading process during the early stages of integration in determining the differences in equilibrium states simulated between runs 1 and 1W and between runs 2 and 2W.

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FIG. 4. Time variation of the horizontally averaged U-momentum profile for (a) run 4 and (b) run 4W.

determining the equilibrium temperature is the balance between net condensation (heating) and large-scale forcing (cooling). A reduction in net condensation and largescale forcing leads to a more negative local time change in temperature. This again implies that convective organization affects the equilibrium temperature. Temperature and water vapor fields are closely related because evaporative cooling/latent heating is a source/ sink of moisture for the water vapor field. On the other hand, latent heat flux from the ocean surface provides water vapor for latent heating. The moist static energy budget (Table 6) yields additional information on the physical processes that shape the modeled equilibrium state. The largest two terms in the moist static energy budget are latent heat flux and net radiation. The microphysical processes in the moist static energy budget are melting (cooling) and freezing (heating) [Eq. (3)]. Large-scale forcing, sensible heat flux, and net microphysical processes are of the same order as the local

time change of moist static energy. The differences in the moist static budgets for each pair of runs with nudging and without nudging of large-scale horizontal wind comes from the differences in latent heat flux and in large-scale forcing. The difference in large-scale forcing is mainly from moisture, not temperature (see Tables 4 and 5). This implies that the two primary major physical processes responsible for determining the modeled quasi-equilibrium state are latent heat flux and large-scale forcing of water vapor; these are strongly affected by the organization of convection. Tables 4 and 5 show that the net condensation as well as the large-scale advective forcing of temperature and moisture are larger in the runs producing a warm/humid climate (runs 1W to 4W) than in the other two regimes (runs 1 and 2 and runs 3 and 4). Runs 1W to 4W simulate organized cloud systems and they also produced a stronger domain-mean vertical gradient of temperature and water vapor and consequently have more large-scale

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TABLE 6. Moist static energy budget of the eight runs. Net condensation is sum of condensation, deposition, evaporation, and sublimation of cloud. Large-scale forcing is the imposed large-scale advective effect on water vapor, and Lv d (qy ) is the local time change (over 25 days of integration) of water vapor. Units are in W m22 . Differences in the individual water budget terms for the pairs of runs with and without nudging of horizontal wind are also shown.

Run 1 2 3 4 1W 2W 3W 4W 1W 2W 3W 4W

2 2 2 2

1 2 3 4

Net Larged(C pT 1 condensa- scale Ly Q y ) tion forcing

Net Q R

24.13 24.60 23.02 23.29 23.20 24.53 23.43 24.54 0.93 0.07 20.41 21.25

297.18 297.61 283.53 281.00 292.97 297.69 295.17 294.87 4.21 20.08 211.64 213.87

6.01 20.67 218.26 230.16 36.26 29.03 36.79 30.06 30.24 29.69 55.05 60.22

211.31 216.50 217.64 227.54 9.27 1.94 9.92 4.66 20.58 18.44 27.56 32.20

Sensible Latent heat heat fluxes fluxes 20.71 20.16 15.66 14.71 18.79 19.21 19.09 18.72 21.92 20.95 3.43 4.01

97.81 97.81 70.72 66.83 105.2 110.2 106.9 106.3 7.4 12.4 36.2 39.5

advective forcing.5 However, this is true only if the modeled domain-mean lapse rate and water vapor gradient are allowed to interact with the imposed large-scale vertical velocity (i.e., the first of the two methods mentioned in the introduction). 4. Summary Two-dimensional long-term cloud-resolving simulations using the GCE model quantified the effects on the modeled thermodynamic state of various large-scale forcing setups, mixing of horizontal momentum by convection, specified minimum wind speed (V s ) in the bulk aerodynamic formulas, and initial soundings. Three distinct quasi-equilibrium thermodynamic regimes were identified. Sensitivity tests indicate that initial conditions (e.g., variations in CAPE and upper-tropospheric humidity) do not substantially alter the simulated climate state. However, the minimum wind speed (V s ) prescribed in the bulk aerodynamic formulas can have a major impact upon the modeled climate in the simulations where the wind field is not relaxed to the initial profile (i.e., weakly organized convection). The simulated quasi-equilibrium regime depends on whether or not the large-scale shear flow is maintained throughout the simulation, an issue closely related to the organization of convection. A warm and humid climate is associated with strong shear and surface wind because evaporation from the sea surface is a function of the convective regime and the surface wind variability. In reality, the ambient wind will be neither con-

5 CAPE is 1481 and 2119 m 2 s22 , respectively, for runs 3 and 3W after 25 days of integration.

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stant (as in Grabowski et al. 1996) nor mixed by convective processes (as in Sui et al. 1994). In other words, the ambient wind evolves due to the interaction of largescale and small-scale processes. This includes the indirect effect of heating on the momentum field, the direct convective momentum transport, and feedback between large and small scales. Feedback has not yet been examined in cloud-resolving models because it is not really tractable with present-day computers. The physical processes that determine the quasi-equilibrium thermodynamic state were evaluated in the water vapor, temperature, and moist static energy budgets. The runs that produced a more humid (drier) climate are always associated with larger (smaller) latent heat fluxes from the ocean and larger (smaller) large-scale forcing terms. As anticipated, the largest terms in the temperature and water vapor budgets are opposite in sign and are net condensation [heating (drying)] and large-scale forcing [cooling (moistening)]. The local time change in temperature and water vapor (warmer and more humid or colder and drier than their initial values) is at least one to two orders of magnitude smaller than the net condensation and large-scale forcing. Tests of different magnitudes of large-scale forcing (see Soong and Tao 1980; Grabowski et al. 1996; and Xu and Randall 1999) indicate that a bigger large-scale forcing (cooling/moistening) is reflected in a bigger net condensation (heating/drying). This result is consistent with the effect of convection simply being a response to the imposed large-scale forcing in temperature and water vapor. It may explain why CRM-simulated climate is not very sensitive to the prescribed large-scale forcing. Simulations that produced a more humid (drier) climate are always associated with larger (smaller) latent heat fluxes from the ocean. It is found that the advective forcing in temperature (cooling) and water vapor (moistening) by the imposed large-scale vertical velocity is larger (smaller) for the warm and humid (cold and dry) thermodynamic equilibrium state. For the most part, this is because the domain-mean thermodynamic profile is more unstable and has a stronger vertical gradient of water vapor for those experiments that produced a warmer and more humid equilibrium compared to the experiments that produced a colder and drier equilibrium. The moist static energy budget further indicates that smaller (larger) large-scale forcing leads to larger cooling (heating) in the local temporal change of temperature. Because the difference in large-scale forcing stems from moisture not temperature, the large-scale forcing in water vapor is another key process in realizing a warmer and more humid state. Cloud-resolving simulations are a path to the better understanding of the role of convection in climate that takes into account all pertinent physical processes. Because the parameterization of physical processes in the CRMs is imperfect, systematic studies of the interaction between clouds and radiation, between shallow and deep

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convection, and the effects of more complex microphysical parameterizations are necessary. Other aspects that need scrutiny are the effects of sea surface temperature and large-scale dynamics on the properties of cloud systems and their environmental effect (Wu and Moncrieff 1999, manuscript submitted to J. Atmos. Sci.). The effect of convective organization on the mean flow and its effects on surface fluxes are a fundamental aspect that has been little studied in the climate context (Moncrieff 1995). We quantified certain key aspects by analyzing eight experiments; further results will be reported in a future paper. In view of the major conclusion from this research concerning the relation of climate regime difference to surface fluxes, particularly those of water vapor, it is urged that near the interface direct measurements of these fluxes be made. The weakness of the bulk formulas is well known, particularly with lapse rates departing from dry adiabatic and under conditions of very low and very high wind speeds. While measurements made during the Tropical Ocean Global Atmosphere Coupled Ocean–Atmosphere Response Experiment are useful, further measurements need to be made in order to test the representativeness of these measurements in different environments. For example, comprehensively instrumented masts could be mounted on observation posts on small islands and Pacific atolls, such as Kwajalein Atoll and Willis Island, Australia, which also make rawinsondes and other observations. These observations could provide averages of w9q9 under varying conditions of light and heavy winds, clear skies, gust front outflows, and squall line and non-squall-line cloud organizations. Flux measurements can also be made from ships if great care is taken, or from instrumented aircraft, piloted or not, which can fly low enough to be within the constant flux layer depth of about 50 m. Acknowledgments. The authors thank Mr. S. Lang and Dr. B. Ferrier for reading the manuscript. Discussions with Drs. X. Wu (NCAR) and W. Grabowski (NCAR) and K.-M. Xu (CSU) during the earlier stages of this work are appreciated. We also thank three anonymous reviewers for their constructive comments that improved the clarity of the presentation in this paper. This work is supported by the NASA Headquarters Physical Climate Program, the NASA Tropical Rainfall Measuring Mission, and the Interdisciplinary Investigation of the Earth Observing System. These authors are grateful to Dr. R. Kakar for his support of this research. Acknowledgment is also made to NASA/Goddard Space Flight Center for computer time used in the research. NCAR is sponsered by the National Science Foundation. REFERENCES Chou, M.-D., and A. Arking, 1980: Computation of infrared cooling rates in the water vapor bands. J. Atmos. Sci., 37, 855–867.

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