Abstract

A series of long-term integrations using the two-dimensional Goddard Cumulus Ensemble (GCE) model were performed with various imposed environmental components. Vertical wind shear, minimum surface wind speed (only used for computing surface fluxes), and radiation are found to be the three major components that determine the quasi-equilibrium temperature and water vapor fields simulated in this study. The genesis of a warm/wet quasi-equilibrium state is mainly due to either strong vertical wind shear along with strong surface winds or large surface fluxes, while a colder/drier quasi-equilibrium state is due to weak (mixed wind) shear along with weak surface winds. Latent heat flux and net large-scale temperature forcing dominate the beginning stages of the simulated convective systems, then considerably weaken in the final stages leading to quasi-equilibrium states. Radiation is necessary in establishing the quasi-equilibrium states but is not crucial to the considerable variation between them.

A warmer/wetter thermodynamic state is found to produce more rainfall, as convective clouds are the leading source of rainfall over stratiform clouds even though they occupy much less area. Convective clouds are more likely to occur in the presence of strong surface winds (latent heat flux), while stratiform clouds (especially the well-organized type) are favored in conditions with strong wind shear (net large-scale forcing). The convective systems, which consist of distinct cloud types due to the variation in horizontal winds, are also found to propagate differently. Convective systems with mixed-wind shear generally propagate in the direction of shear, while systems with strong, multidirectional wind shear propagate in a more complex way. Cloud-scale eddies are found to transfer the heat and moisture vertically and assist in balancing the heat (Q1) and moisture (Q2) budgets and in reaching a quasi-equilibrium state. Atmospheric stability, CAPE, and mass fluxes are also investigated and compared between the various quasi-equilibrium states.

1. Introduction

Increasing attention has been given to cloud resolving models (CRMs) or cloud ensemble models (CEMs) in recent years for their ability to simulate the radiative–convective system, which plays a significant role in determining the regional heat and moisture budgets in the Tropics. The growing popularity of CRM usage can be credited to its inclusion of crucial and physical relatively realistic features such as explicit cloud-scale dynamics, sophisticated microphysical processes, and explicit cloud–radiation interaction (e.g., Islam et al. 1993; Held et al. 1993; and also Sui et al. 1994; Grabowski et al. 1996; Tao et al. 1999; hereafter S94, G96, and T99, respectively; and others—see discussion and Table 1 in T99).

Several recent CRM studies show that certain model setups are critically responsible for some common model responses. These include three major aspects: first, how the large-scale forcing is prescribed—time-invariant or time-varying observations or modeled large-scale advective forcing (e.g., Yamasaki 1975; Soong and Ogura 1980; Soong and Tao 1980; Tao and Soong 1986; Nakajima and Matsuno 1988; Lau et al. 1993; S94; G96; Xu and Randall 1996; T99; Li et al. 1999; Wu and Moncrieff 1999; Xu and Randall 1999); second, how the radiation is treated—a fixed one-way radiation input or a two-way cloud–radiation interaction (e.g., Islam et al. 1993; Held et al. 1993; Robe and Emanuel 1996); third, how and what type of large-scale horizontal winds are applied—a weak wind shear due to time-varying vertical mixing, a strong wind shear maintained by almost time-invariant nudging, or simply no basic zonal flow (e.g., Held et al. 1993; S94; G96; T99; Peng et al. 2001).

A few of the aforementioned research studies are briefly reviewed here. Employing interactive cloud–radiation processes and an assumed surface heat flux in balance with radiative cooling (i.e., no net heat allowed) in a three-dimensional cloud model, Islam et al. (1993) produced radiative–convective equilibrium states in the Tropics. Using a two-dimensional cloud model with interactive cloud–radiation processes, Held et al. (1993) found that the model-generated rainband propagated in the direction of the low-level zonal mean winds; however, the precipitation system became “localized” (limited within a small portion of the domain) as zonal mean winds were removed. In a study with a two-dimensional cloud–radiation model, Randall et al. (1994) reviewed the so-called radiative–convective oscillations mechanism that was prevalent in radiative–convective systems. Accordingly, a cycle of radiative destabilization (in general, radiation generated a cooling effect for the air aloft) succeeded by convective stabilization (convection, on the other hand, tended to dry the boundary layer as well as warm the air aloft) could form under the proper circumstances.

Using the two-dimensional Goddard Cumulus Ensemble (GCE) model with embedded time-variant large-scale forcing, Lau et al. (1993) performed a sensitivity study to investigate the impact of surface warming on the tropical water cycle. Their results showed that the ensemble (time- and domain-averaged) temperature and water vapor fields were enhanced as the prescribed sea surface temperature increased (i.e., surface warming). Concurrently, their study using explicit microphysics and cloud-scale radiation and dynamics also genuinely verified the features that were found in the general circulation model, which had been considered unreliable because of the use of cumulus parameterization. Wu and Moncrieff (1999) further quantified the impact of sea surface temperature as well as large-scale dynamics on a tropical convective system using a different two-dimensional CRM (Clark et al. 1996) with imposed time-invariant large-scale forcing. The variation of sea surface temperature was found to have a large (small) impact on the water vapor (cloud) feedback, while changes in the large-scale forcing had a different effect with a small (large) impact on the water vapor (cloud) feedback.

Two distinctive two-dimensional CRM simulations by S94 and G96, however, showed considerably different quasi-equilibrium states regardless of model similarity and initial sounding data used [e.g., the imposing of an observed mean (time-invariant) vertical velocity]. The former produced a colder/drier statistical quasi-equilibrium state than the latter. In an attempt to identify the plausible causes for such a drastic discrepancy between these two model results, T99 delved into the problem by performing a systematic series of numerical experiments simulating thermodynamic quasi-equilibrium states over a tropical ocean domain using the GCE model. In their findings, T99 suggested that the different treatment for horizontal wind shear applied in S94 (allowed vertical mixing by deep convection that swiftly and greatly weakened an otherwise strong initial horizontal wind shear) and G96 (permitted the strong initial wind shear to be maintained almost time-invariant by geostrophy) was one of the two main factors that produced these two greatly diverse quasi-equilibrium states. Surface fluxes, which were computed in the bulk aerodynamic formulas (minimum surface winds were imposed and used only for flux computation), were found to be the other crucial factor in determining the tropical quasi-equilibrium states.

Overall, T99 focused their general discussion on large-scale mechanisms and the associated physical processes that accounted for the occurrence of various modeled quasi-equilibrium states, while many specific and detailed characteristics such as the cloud organization, the precipitation features and system propagation, and the cloud-scale eddy transport involved in the vertical distribution of heat (temperature) and moisture (water vapor) were not discussed. As a continuation of the study by T99, this paper serves four major objectives. First, the general features and the specific characteristics of convective systems (such as system propagation, convective and stratiform rainfall) associated with various quasi-equilibrium states will be examined. Second, the major characteristics associated with the atmospheric states (such as stability and CAPE) will be investigated. The third objective is to present a detailed analysis on the vertical structure of the heat, moisture, and Q1 and Q2 budgets as well as cloud mass fluxes. The final objective in this paper is to present the budget analysis for stages both before and during the quasi-equilibrium states as well as for the entire period of integration.

The detailed model setup and the sensitivity experiments chosen for presentation are described in section 2. Section 3 presents the major findings and discussions on the modeled tropical quasi-equilibrium states, which is divided into three sections. The first section includes a presentation of general features for the various quasi-equilibrium states. The second presents a detailed discussion on the specific features and characteristics of the model simulations, while the third provides a detailed discussion (via vertical cross sections) on the physical processes associated with both the heat and moisture budgets. Thermodynamic budget analyses that examine the genesis and maintenance of quasi-equilibrium states as well as the horizontal wind structure effects (wind shear and surface wind speed effects) are presented in section 4. A summary is concluded in section 5.

2. Model

a. Model setup

The GCE model is an anelastic, nonhydrostatic model that has been broadly used to study cloud–radiation interaction, cloud–environment interaction, and air–sea interaction. The cloud microphysics include a Kessler two-category liquid water scheme (cloud water and rain) and a three-category ice microphysics scheme (cloud ice, snow, and hail/graupel). The model includes shortwave (solar) and longwave (infrared) radiative transfer processes, and a subgrid-scale turbulence (one-and-a-half order of turbulent kinetic energy) scheme. Details of the model can be found in Tao and Simpson (1993).

This model includes a stretched vertical coordinate of 31 grid points (with height increments from a 173-m resolution in the lower boundary layer to a 1057-m coarse resolution at the top) as well as a uniform horizontal coordinate with a cyclic boundary condition and a 1500-m resolution for a total of 512 grid points. A constant sea surface temperature of 28.18°C is prescribed for the entire bottom domain. A minimum surface wind speed (varying with various runs, see details in the following section) is imposed only in the bulk aerodynamic formulas to compute (obtain) surface fluxes during the model integration.

b. Experiment design

There are six major idealized numerical runs (integrated for 25 days reaching or near statistically quasi-equilibrium states) chosen for presentation in this paper (Table 1a). They involve various model setups pertaining to two major components: the vertical wind shear pattern and the minimum surface wind speed used for surface flux computation, which could be critical in determining the modeled quasi-equilibrium states. The naming convention for these runs is explained in the table captions. For example, for run 4M a minimum surface wind speed of 4 m s–1 (4) in the bulk formulas and a mixed-wind shear condition (M) are applied. The zonal wind profile is vertically well mixed with time by deep convection (as in S94) for the mixed-wind shear runs, while it is relaxed to its initial value (strong wind shear) in the counterpart runs with nudging (N, similar to G96). Three levels of minimum surface wind speed (1, 4, and 7 m s–1) are applied in order to examine the sensitivity of quasi-equilibrium states to surface fluxes. The 4 m s–1 minimum surface wind accounting for the gustiness wind effect (based on S94) is considered a realistic “control” value, while 1 m s–1 was first introduced in T99. Note that the strong wind shear runs in this paper (1N, 4N, and 7N in Table 1a) are also associated with strong surface winds, that is, 7–8 m s–1. Namely, the strong wind shear effect discussed later in this paper implicitly includes mechanisms of the pure wind shear and the surge of surface wind speed. In addition to examining the impact of surface fluxes, the new application of 7 m s–1 (which is within the strong surface wind speed range) in this study is also intended to isolate the pure wind shear effect (i.e., by minimizing the surge of surface wind speed, and hence its impact) due to nudging. Six additional runs (Table 1b) that have the same setup as before (Table 1a) except with fixed (time-invariant) surface wind speed prescribed in the bulk aerodynamic formulas are also performed to isolate the pure wind shear effect. This additional set of runs is only presented and discussed in section 4 for this specific purpose. All the runs presented in this study used the S94 soundings.

Table 1a. Minimum surface wind speed and wind shear characteristics for six (three pairs) major numerical experiments performed in this study. The two-letter naming convention identifies the two main parameters. For example, 1M denotes a 1 m s–1 min wind speed (1) and mixed-wind shear (M), respectively. Experiments presented here all used the S94 sounding

Table 1a. Minimum surface wind speed and wind shear characteristics for six (three pairs) major numerical experiments performed in this study. The two-letter naming convention identifies the two main parameters. For example, 1M denotes a 1 m s–1 min wind speed (1) and mixed-wind shear (M), respectively. Experiments presented here all used the S94 sounding
Table 1a. Minimum surface wind speed and wind shear characteristics for six (three pairs) major numerical experiments performed in this study. The two-letter naming convention identifies the two main parameters. For example, 1M denotes a 1 m s–1 min wind speed (1) and mixed-wind shear (M), respectively. Experiments presented here all used the S94 sounding

c. Budget equations

Horizontal integration (average) of the equations for potential temperature (θ), and water vapor (qυ) over the model horizontal domain yields

 
formula

where variables with an overbar are horizontal-mean quantities, and deviations from the means are denoted by a prime, while c, e, d, s, f, and m are condensation, evaporation, deposition, sublimation, freezing, and melting, respectively. The value T is temperature, and π = (p/P00)R/Cp is the nondimensional pressure, where p is the dimensional pressure and P00 the reference pressure taken to be 1000 mb; Cp is the specific heat of dry air at constant pressure, and R is the gas constant for dry air. Here, −w(∂θ/∂z) and −w(∂qυ/∂z) are the mean advection of potential temperature (cooling) and water vapor (moistening); w is the prescribed large-scale mean vertical velocity (constant with time); ∂θ/∂z and ∂qυ/∂z are model mean vertical potential temperature and water vapor gradients (varying with time); −(1/ρ)(∂/∂z)ρwθ and −(1/ρ)(∂/∂z)ρυ are the vertical eddy flux convergence (divergence) for potential temperature and water vapor, respectively. The value QR is the radiative heating containing solar and infrared radiation. The variables Lυ, Lf, and Ls are the latent heats of condensation, fusion, and sublimation, respectively. The mean advective cooling (moistening) applied in the model is integrated using a time-varying gradient of modeled temperature (water vapor), along with a constant observed large-scale vertical velocity (same as used in S94, G96, and T99). Note that the apparent heat source Q1 and the apparent moisture sink Q2 (e.g., Yanai et al. 1973) can be readily defined using Eqs. (1) and (2), respectively,

 
formula

3. Modeled tropical quasi-equilibrium states

In this section, general features of the quasi-equilibrium states of temperature and water vapor for the six major runs are first discussed. Then, several specific features, such as rainband propagation, rainfall properties, dry- and pseudoadiabatic stabilities, and CAPE associated with various quasi-equilibrium states in the radiative–convective system are presented. Finally, vertical distributions of the heat and moisture budgets, and mass fluxes are examined.

a. General features of modeled tropical quasi-equilibrium states

A scatterplot of domain-averaged water vapor versus temperature at their quasi-equilibrium states (25 days of integration) for the six major runs listed in Table 1a, along with the results of S94 (S) and G96 (G) is shown in Fig. 1. The mixed-wind shear runs 1M (the coldest/driest), 4M, 7M, and S fall on a line, whose warm/wet end is near G and the nudged runs 1N, 4N, and 7N. Based on various quasi-equilibrium states, the six major runs are hereafter referred to as warm/wet runs (1N, 4N, 7N, and 7M), mild/moist run (4M), and cold/dry run (1M) for discussion convenience. Two major characteristics can be generalized from Fig. 1. First, the strong wind shear and surface wind due to nudging have a prominent impact on quasi-equilibrium state variation for runs with lower minimum wind speeds. Variations in temperature and water vapor due to nudging increase with a decreasing minimum surface wind speed. The variations between the paired runs (1M, 1N) are substantially greater than those between (4M, 4N) and even more so between (7M, 7N). The significantly diminished impact occurred for runs (7M, 7N) using a minimum wind speed of 7 m s–1, which is near the magnitude of the surface wind speed found in the strong wind shear runs (i.e., 7–8 m s–1). The prominent nudging effect that accounts for a significant contribution to both temperature and water vapor comes by way of two primary processes: first, a greater “net large-scale forcing” process (i.e., the combined effect of mean advection and net condensation in temperature and moisture, respectively) due to the strong vertical wind shear, and second, greater surface fluxes due to a relative surge in surface wind speed from the wind shear. Later budget analyses will clearly show that the impact from nudging peaks for the 1 m s–1 runs when both processes genuinely contribute, whereas it greatly weakens for the 7 m s–1 runs when the contribution by surface fluxes becomes much weaker and only the effect of shear remains (see section 4).

Fig. 1.

Scatter diagram of domain-averaged water vapor vs temperature at the quasi-equilibrium states (after 25 days of integration) for the 6 major runs listed in Table 1a, along with results of S94 (S) and G96 (G)

Fig. 1.

Scatter diagram of domain-averaged water vapor vs temperature at the quasi-equilibrium states (after 25 days of integration) for the 6 major runs listed in Table 1a, along with results of S94 (S) and G96 (G)

Second, the imposed minimum surface wind for computing surface fluxes also plays a crucial role in determining the quasi-equilibrium state, particularly for runs with a mixed-wind shear where surface winds are very weak (about 1–2 m s–1, see Fig. 2 shown later). In Fig. 1, the three mixed-wind shear runs are spread over the thermodynamic chart, while the three strong wind shear runs all reside in the warm/wet (upper-right corner) region. For mixed-wind shear runs, a higher minimum surface wind produces a larger surface flux into the atmosphere, which accounts for a substantial variation in both temperature and moisture. On the other hand, the high surface wind speed found in all strong wind shear runs minimizes the impact of the minimum surface wind on quasi-equilibrium-state variation.

Fig. 2.

Two sets of 5-day averaged wind shear profiles for 4M and 4N: (dashed lines) initial 5 days; (solid lines) final 5 days

Fig. 2.

Two sets of 5-day averaged wind shear profiles for 4M and 4N: (dashed lines) initial 5 days; (solid lines) final 5 days

It can be concluded that a warm/wet quasi-equilibrium state is generated either due to strong vertical wind shear (from nudging) or/and strong surface fluxes (from strong surface winds), while a colder/drier state is generated attributed to a notably weakened wind shear (from vertical mixing) along with weak surface winds. Figure 2 shows the initial and final 5-day averaged wind shear profiles for a pair of runs 4M (mild/moist) with mixed-wind shear and 4N (warm/wet) with strong wind shear, respectively. Horizontal wind shear in 4M weakens considerably within the first 5–6 days and remains light and westerly at all levels except at the very top due to strong vertical mixing by deep convection. On the other hand in 4N, strong horizontal wind shear with easterly flow below and westerly aloft is maintained (almost time-invariant) due to nudging. Hereafter for those features that are qualitatively similar between the three paired of runs, only those from a single pair are to be presented [i.e., (4M, 4N)].

b. Specific characteristics of modeled tropical quasi-equilibrium states

1) Propagation of convective systems

The strong wind shear due to nudging favors the generation of well-organized cloud systems with large stratiform clouds. The induced surface wind surge also increases the amount of erect, yet nonprecipitating convective clouds (discussed later). On the other hand, surface fluxes (due to minimum surface wind) enhance erect precipitating convective clouds in the mixed-wind shear runs. The various cloud systems generated by the mixed-wind shear and strong wind shear runs also propagate differently. Most likely the diverse large-scale wind shear structures (e.g., in 4M and 4N) are the key elements. Surface rain-rate data for 4M and 4N are shown in a time–distance diagram for the final 5 days in Figs. 3a and 3b, respectively. Rainbands in 4M are mainly associated with sporadic precipitating clouds dominated by convective cells and unorganized stratiform clouds, and move eastward with an estimated phase speed slightly greater than 2 m s–1 (∼7.7 km h–1). The strong wind shear run 4N possesses a dramatically different rainband system and migration pattern. The much broader rainbands mainly associated with massive stratiform cloud clusters seem to form at certain favored locations and migrate eastward with a phase speed around 10.7 m s–1 (∼38.6 km h–1) before they dissipate, whereas the sparse and small rain spots relevant to the erect but relatively shallow convective cells propagate westward with a phase speed of about 8.7 m s–1 (∼31.4 km h–1).

Fig. 3.

Time–domain cross sections of surface rain rate (mm h–1) over the final 5 days for (a) 4M and (b) 4N

Fig. 3.

Time–domain cross sections of surface rain rate (mm h–1) over the final 5 days for (a) 4M and (b) 4N

The eastward (about 2 m s–1) propagating rainband systems (mainly the shallow and deep convective cells) in 4M are driven by a net light westerly mean advection due to light west winds at all levels (an average of 1.71 m s–1 and a surface value of 1.68 m s–1) except at the very top (see Fig. 2). In contrast, the more complex propagating systems in 4N are attributed to a more complicated wind shear due to nudging, which possesses strong easterly flow below 580 mb (around 5 km in height) and strong westerly above it (also see Fig. 2). With the rainband systems of 4N, the shallow convective clouds propagate westward mainly due to the easterlies prevailing in the lower atmosphere, while the eastward-moving well-organized stratiform clouds are determined by the westerlies aloft. The eastward-moving well-organized cloud system, however, dissipates after indefinite periods of time (usually a couple of hours). Shige and Satomura (2001) suggested that gravity waves (disturbances) excited by the mesoscale cloud line played a crucial role in the sequential generation of new convective bands to the west of an old eastward-moving convective band with a prescribed wind shear of west winds at low levels and strong easterlies aloft. Whether or not 4N resembles the case in Shige and Satomura (2001) in which gravity waves play a role in rainband propagation remains unclear and will be examined in a future study. Held et al. (1993) found that the direction of propagation of rainbands changed sign due to a change in sign in the direction of low-level mean zonal winds. Apparently, the large-scale zonal wind shear plays a crucial role in determining the formation as well as the migration of the radiative–convective system not only by its wind and vertical gradient intensity, but also by the wind direction, which veers with height.

Figure 4a shows erect convective clouds that develop in a mixed-wind shear environment (4M), while Fig. 4b displays a well-established stratiform cloud cluster prevailing in a strong wind shear scenario (4N). By tracing the wind vectors, circulation cells may be approximated for these two cases. In 4M, a relatively short clockwise-circulation cell (centered around 250–260 km and 700–750 mb) located east (ahead) of the major erect cloud plus a relatively tall counterclockwise-circulation cell (centered around 180–190 km and 450–500 mb) west of (behind) it, are primarily triggered by convergence associated with deep convection. On the other hand, in 4N, a horizontally elongated and vertically flattened “conceptual” circulation cell (centered around 300–310 km and 600–620 mb at the base of the anvil) can be roughly drawn within the well-organized cloud cluster and is mainly induced by the strong wind shear. Note that the regular stratiform clouds (the unorganized type partitioned out of the convective clouds) still dominate in coverage (to be discussed later) in the mixed-wind shear runs; however, the strong wind shear further enhances the stratiform cloud coverage by generating extensive well-organized stratiform clouds (Fig. 4b). Details for how the “stratiform” and “convective” clouds are defined (partitioned) can be found in Tao et al. 1993, and S94.

Fig. 4.

Instantaneous vertical cross sections of the total cloud field (g kg–1) for part of the domain (360 km out of a full domain of 768 km) for (a) 4M and (b) 4N near the end of the simulations (23 days and 6 h). Background wind vectors represent the total wind fields (zonal mean wind plus perturbation wind for both the zonal and vertical directions) scaled by the designated arrows (cm s–1) shown in the lower-left corner

Fig. 4.

Instantaneous vertical cross sections of the total cloud field (g kg–1) for part of the domain (360 km out of a full domain of 768 km) for (a) 4M and (b) 4N near the end of the simulations (23 days and 6 h). Background wind vectors represent the total wind fields (zonal mean wind plus perturbation wind for both the zonal and vertical directions) scaled by the designated arrows (cm s–1) shown in the lower-left corner

2) Characteristics of rainfall (convective and stratiform)

Time- and domain-averaged surface rainfall (mm day–1 grid–1), rainfall contribution by convective/stratiform clouds, and the respective convective/stratiform cloud area coverage for the six major runs are shown in Table 2. The first two-column results show that the warm/wet runs (1N, 4N, 7N, and 7M) generally produce larger rainfall than the colder/drier runs (4M and 1M), while the respective contributions by convective and stratiform clouds vary depending on the vertical structure of horizontal winds. Among warm/wet runs, those associated with strong wind shear (1N, 4N, and 7N) favor higher stratiform rainfall percentages (between 41% and 43%), while the sole mixed-wind shear run 7M favors less rainfall contribution by stratiform clouds (31%). Among mixed-wind shear runs (1M, 4M, and 7M), the contribution by convective (stratiform) clouds increases (decreases) with enhanced rainfall as the minimum surface wind increases. This enhanced contribution by convective cloud is, however, smaller between (4M, 7M) than between (1M, 4M), which is mainly due to the relative softening in the latent heat flux enhancement (see Table 7 shown later in section 4). It may further imply that, for runs with weak wind shear, the larger surface fluxes generate more convective clouds responsible for the increased rainfall, while for runs with strong wind shear, the enhancement in precipitation mainly comes from the (well organized) stratiform clouds. Overall, convective clouds (between 57% and 69%) dominate over stratiform clouds (between 31% and 43%) in rainfall contribution. Based on a series of earlier studies (e.g., Houze 1977; Cheng and Houze 1979; Gamache and Houze 1983), stratiform clouds were often found responsible for around 40% of precipitation in tropical convective systems.

Table 2. Time- (over 25 days of integration) and domain-averaged (over 512 grids) surface rainfall (mm day–1 grid–1), rainfall contribution by convective/stratiform clouds (%), and the respective convective/stratiform cloud area coverage (%) for the six major runs. Cloud area coverage is defined as the fraction of the cloud region (with or without precipitation) over the entire model domain

Table 2. Time- (over 25 days of integration) and domain-averaged (over 512 grids) surface rainfall (mm day–1 grid–1), rainfall contribution by convective/stratiform clouds (%), and the respective convective/stratiform cloud area coverage (%) for the six major runs. Cloud area coverage is defined as the fraction of the cloud region (with or without precipitation) over the entire model domain
Table 2. Time- (over 25 days of integration) and domain-averaged (over 512 grids) surface rainfall (mm day–1 grid–1), rainfall contribution by convective/stratiform clouds (%), and the respective convective/stratiform cloud area coverage (%) for the six major runs. Cloud area coverage is defined as the fraction of the cloud region (with or without precipitation) over the entire model domain

Table 7. Same as in Table 5 except for the 25 days of integration of the six major runs. Units are W m–2

Table 7. Same as in Table 5 except for the 25 days of integration of the six major runs. Units are W m–2
Table 7. Same as in Table 5 except for the 25 days of integration of the six major runs. Units are W m–2

The second two-column results in Table 2 show that the cloud area coverage for warm/wet runs with strong wind shear (1N, 4N, and 7N) is significantly larger in both stratiform and convective clouds than mixed-wind shear runs (1M, 4M, and 7M), particularly in stratiform clouds. The strong wind shear intensifies the total cloud area coverage by providing the convective system first with an environment favorable for the enhancement of mean advection in temperature and moisture that produces well-organized clouds, and second with a strong surface wind that strengthens the surface fluxes, which generates more convective clouds. On the other hand, for runs with low (mixed wind) wind shear, the enhancement in surface fluxes due to the increased minimum surface wind only tends to extend (reduce) the cloud coverage in convective (stratiform) clouds; however, the total cloud coverage remains unchanged. Nonetheless, an increase in total cloud coverage in warm/wet runs with strong wind shear does not guarantee a substantial increase in total rainfall production (compare 7N with 7M in Table 2). This feature will be further discussed later. Stratiform clouds are more extensive than convective clouds, particularly for the warm/wet runs with strong wind shear, even though they produce relatively less precipitation.

Rainfall histograms of rainfall amount and rainfall frequency for the six major runs are shown in Figs. 5a and 5b, respectively. Histograms shown here are the 25-day averages of instantaneous rain-rate histograms constructed with a 2 mm h–1 grid–1 bin. For example, a rain rate of 1 mm h–1 grid–1 represents a range of 0;nd2 mm h–1 grid–1 (but note that zero rain rate was excluded). The lightest rain rate of 1 mm h–1 grid–1 (i.e., 0–2 mm h–1 grid–1) dominates in both amount and frequency for the strong wind shear runs of warm/wet (1N, 4N, and 7N), while a rain rate of 3 mm h–1 grid–1 (i.e., 2–4 mm h–1 grid–1) accounts for the peak amount for the mixed-wind shear runs of warm/wet (7M) and mild/moist (4M). The cold/dry run with mixed-wind shear (1M), however, possesses a broader range (0–4 mm h–1 grid–1) of maximum rainfall amount. Overall, the strong wind shear runs dominate the mixed-wind shear runs in rainfall amounts in regions of rain rates less than 10 mm h–1 grid–1, while 4M and 7M of mixed-wind shear dominate the strong wind shear runs mainly in regions of high rain rates (also see a follow-up quantitative analysis in Table 3). In terms of rainfall frequency (Fig. 5b), the strong wind shear runs generally dominate the mixed wind shear runs for low rain rates, while the latter runs dominate the former runs for high rain rates (i.e., a rain rate of 3 mm h–1 grid–1 is the cutoff). Based on Fig. 5, a quantitative summary for two extreme rain-rate ranges—one of light rain rates (less than 4 mm h–1 grid–1) and the other of strong rain rates (at least 24 mm h–1 grid–1) is also presented (Table 3). Table 3 clearly reveals that the mixed-wind shear runs (particularly, 4M and 7M) dominate the strong wind shear runs in the strong rain-rate range for both amount and frequency, while the latter runs dominate the former ones for the light rain-rate range (as discussed above). For mixed-wind shear runs, the rainfall enhancement in the strong rain-rate range as well as an increased convective cloud coverage (Table 2) due to increased minimum wind speed suggest the additional convective clouds are accountable for the enhanced rainfall generated with higher rain rates. On the other hand for strong wind shear runs, the rainfall increasing in the light rain-rate range along with an increased stratiform cloud coverage (Table 2) with increased minimum surface wind speed imply that the enlarged stratiform cloud coverage due to strong wind shear is responsible for the increased rainfall generated by light-precipitating clouds.

Fig. 5.

(a) Rainfall amount, and (b) rainfall frequency (occurrence) histograms for the six major runs. The histograms are the averages of the instantaneous rain-rate histograms (collected every 18 min) over the entire integration period (25 days). The rainfall frequency is normalized by the total occurrence and expressed in %

Fig. 5.

(a) Rainfall amount, and (b) rainfall frequency (occurrence) histograms for the six major runs. The histograms are the averages of the instantaneous rain-rate histograms (collected every 18 min) over the entire integration period (25 days). The rainfall frequency is normalized by the total occurrence and expressed in %

Table 3. Time- and domain-averaged surface rainfall amount and frequency (Freq., %) distributions of the six major runs for two rain-rate ranges. The respective rainfall amounts listed in each range are shown with both their values (units in mm day–1 grid–1) and percentages (in %, normalized by the total time- and domain-averaged amounts from each run)

Table 3. Time- and domain-averaged surface rainfall amount and frequency (Freq., %) distributions of the six major runs for two rain-rate ranges. The respective rainfall amounts listed in each range are shown with both their values (units in mm day–1 grid–1) and percentages (in %, normalized by the total time- and domain-averaged amounts from each run)
Table 3. Time- and domain-averaged surface rainfall amount and frequency (Freq., %) distributions of the six major runs for two rain-rate ranges. The respective rainfall amounts listed in each range are shown with both their values (units in mm day–1 grid–1) and percentages (in %, normalized by the total time- and domain-averaged amounts from each run)

Precipitation efficiency for the six major runs has also been examined by defining the total precipitation efficiency as the ratio of the total rainfall to the total condensation (see details in Ferrier et al. 1996). The results show that total precipitation efficiencies range from 50% to 53% for mixed-wind shear runs to 41% to 42% for strong wind shear runs, which indicates that the upright convective clouds possess higher precipitation efficiencies than the well-organized tilted stratiform clouds. Apparently, the higher precipitation efficiency for convective clouds is crucial for their larger precipitation contribution. Our results qualitatively agree with the precipitation efficiencies found by Ferrier et al. (1996), that is, 40% to 50% for the upright convection runs (erect storms) and 20% to 35% for the upshear-tilt runs.

3) Dry- and pseudoadiabatic stabilities, and CAPE

Table 4 shows the final 5-day averaged surface relative humidity, lower-tropospheric (below the 4.3-km level) mass-weighted mean lapse rate of temperature, and equivalent potential temperature for the six major runs along with the respective CAPE and wet-bulb potential temperature θw at the end of the simulation time. Equivalent potential temperature θe (950 mb) is generally found to increase in the troposphere (about 15 to 17 km deep from cold/dry to warm/wet runs) in the warm/wet runs relative to the colder/drier runs, especially in the lower atmosphere below the freezing level (∼4 km near cloud base) and above the surface boundary layer. As a result, the warmer and more saturated lower atmosphere (also deeper) found in the warm/wet runs possesses a stronger vertical gradient of θe (decreasing with height) compared to the colder/drier runs with a relatively colder and drier lower atmosphere. On the other hand, the colder/drier runs posses a higher lapse rate of temperature than the warm/wet runs (especially the nudging runs). In contrast, the warm/wet runs reach a quasi-equilibrium state with a lower atmosphere that is more moist-unstable (pseudoadiabatic) as well as more static-stable (dry adiabatic) than the colder/drier runs. Apparently, moisture (from latent heat flux or mean advection) plays a crucial role in modifying the atmospheric stability. The opposing tendency between the temperature and equivalent potential temperature lapse rate, particularly among mixed-wind shear runs, also indicates the direct and important role surface fluxes play in determining the quasi-equilibrium system.

Table 4. Final 5-day averaged surface relative humidity (RH), lower-tropospheric (below the 4.3-km level) lapse rate of domain mean temperature (−∂T/∂z), and equivalent potential temperature (−∂θe/∂z) for the six major runs along with the respective CAPE and wet-bulb potential temperature θw at the end of the simulation time

Table 4. Final 5-day averaged surface relative humidity (RH), lower-tropospheric (below the 4.3-km level) lapse rate of domain mean temperature (−∂T/∂z), and equivalent potential temperature (−∂θe/∂z) for the six major runs along with the respective CAPE and wet-bulb potential temperature θw at the end of the simulation time
Table 4. Final 5-day averaged surface relative humidity (RH), lower-tropospheric (below the 4.3-km level) lapse rate of domain mean temperature (−∂T/∂z), and equivalent potential temperature (−∂θe/∂z) for the six major runs along with the respective CAPE and wet-bulb potential temperature θw at the end of the simulation time

The stability issue addressed here involves two perspectives: the moist adiabatic (pseudoadiabatic) and dry adiabatic, especially considering that the former is commonly referenced in areas of tropical convection. The current results show that a final warmer and more humid quasi-equilibrium state tends to equilibrate with a more moist-unstable lower atmosphere. Williams and Renno (1993) indicated that more than half of the area in the tropical belt is conditionally pseudoadiabatic unstable, even though the convective area is only a small fraction of the unstable area (which is also found in this study, see Table 2).

Additional thermodynamic quantities in the form of CAPE and θw in the surface layer are also studied based on the modeled “soundings” near the end of the simulation time. A moistened lower atmosphere is also apparent in the warm/wet runs based on the CAPE and θw in the surface layer shown in Table 4. Both CAPE and the surface θw are larger in the warm/wet runs than in the colder/drier runs, which again implies a positive correlation between a more (less) pseudoadiabatic unstable environment and the warm/wet (colder/drier) runs. Table 4 also indicates that CAPE changes only slowly with the increase of latent heat fluxes among the mixed-wind shear runs [e.g., (1M, 4M)] but is quite sensitive to the wind shear [e.g., (1M, 1N)]. Using the Goddard Institute for Space Studies (GISS) GCM, Ye et al. (1998) produced a linear relationship between CAPE and θw in the surface layer and suggested the CAPE change was mostly determined by moisture variations in the boundary layer over the tropical ocean. Our modeled CAPE–θw correlation is qualitatively similar to that of Ye et al. 1998 (see their Fig. 2), while the mild/moist run 4M seems to be the more realistic simulation for its being in the linear trend of Ye et al. (1998).

c. Heat, moisture, and cloud mass budgets

1) Heat (Q1) and moisture (Q2) budgets

Vertical profiles of individual time-mean (for the final 5 days representing the quasi-equilibrium state) and horizontally averaged temperature (water vapor) budget components are shown in Fig. 6a (Fig. 6c) for the mild/moist run 4M, and Fig. 6b (Fig. 6d) for the warm/wet run 4N. For the heat budget (Fig. 6a), the eddy heat flux term due to cloud-scale motion and subgrid turbulence is coupled with the net sum of the other forcing terms (mean advection, net condensation, and radiation). The two heating maxima in eddy heat convergence located near 4.8 and 12.6 km, respectively, correspond with different heat budget balances though. The former responds to the combined heat loss associated with stronger cooling by mean advection and a reduction in net condensational heating due to melting near the melting level (∼4–5 km) and the latter to the sole strong radiative cooling near the top of deep clouds. At high altitudes, where both the mean advection and cloud microphysical processes are no longer vital, the eddy transport becomes the prominent process that offsets the net radiation and maintains a balanced heat budget. The two regions with maximum net condensational heating above and below the melting level are partly offset by large eddy heat divergence. In the boundary layer, eddy heat divergence compensates most of a net heat surplus consisting of heating from surface sensible heat flux and evaporative cooling due to falling precipitation. The results suggest that cloud-scale eddies transfer heat from regions of surplus into regions of deficit by means of upward and downward convective motion. Note that the surface value of eddy heat flux convergence (EFCt) shown in the figure is actually a net heating by adding surface sensible heat flux (heating) to the lowest-level eddy heat divergence (cooling).

Fig. 6.

Vertical profiles of individual time-mean (for the final 5 days) components in the heat budget for (a) 4M, and (b) 4N. Net latent heating due to phase change of water, mean advection in temperature, net radiation, and eddy heat flux convergence are denoted as Ct, MAt, SwLw, and EFCt, respectively, in solid lines, while the sum of the first three components is denoted as Res by the dashed line; (c),(d) the same as in (a) and (b) except for the moisture budget. Net moisture condensation, mean advection in moisture, and eddy moisture flux convergence are denoted as Cq, MAq, and EFCq, respectively, in solid lines, while the sum of the first two components is denoted as Res by the dashed line; (e),(f) the same as in (a) and (b) except for the Q1 and Q2 budgets. Here, Q1 is denoted by a solid line and Q2 by a dashed line

Fig. 6.

Vertical profiles of individual time-mean (for the final 5 days) components in the heat budget for (a) 4M, and (b) 4N. Net latent heating due to phase change of water, mean advection in temperature, net radiation, and eddy heat flux convergence are denoted as Ct, MAt, SwLw, and EFCt, respectively, in solid lines, while the sum of the first three components is denoted as Res by the dashed line; (c),(d) the same as in (a) and (b) except for the moisture budget. Net moisture condensation, mean advection in moisture, and eddy moisture flux convergence are denoted as Cq, MAq, and EFCq, respectively, in solid lines, while the sum of the first two components is denoted as Res by the dashed line; (e),(f) the same as in (a) and (b) except for the Q1 and Q2 budgets. Here, Q1 is denoted by a solid line and Q2 by a dashed line

In 4N (Fig. 6b), both the heating due to net large-scale forcing and the cooling due to net radiation increase in both magnitude and vertical scale due to strong wind shear. However, the increase in temperature tendency (not shown) from 4M to 4N is mainly due to the enhanced net large-scale forcing process (most occurred below around 14 km). The eddy heat flux responds by expanding in the vertical with magnitudes slightly increased. Meanwhile, the region with a temperature tendency of cooling found in the upper atmosphere (above the top of deep clouds, not shown) shifts upward since the maximum eddy heat divergence occurs at higher levels where the longwave radiative heating peaks. This local radiative maximum is mainly attributed to strong longwave radiation emitted from the atmosphere below (deeper well-organized clouds with higher cloud ceilings), along with weak shortwave radiation.

Two layers of strong eddy moisture convergence are found around 4.2 km (4.8 km) and 9.2 km (9.6 km) for 4M in Fig. 6c (4N in Fig. 6d). These maxima in eddy moisture flux convergence offset a considerable portion of the net drying mainly due to microphysical processes involving vapor condensation and subsequent rain sedimentation in the lower atmosphere, and ice deposition/riming and sedimentation in the higher atmosphere. Similar to the heat budget, the grid-scale eddies play a similar role in vertically redistributing the water vapor field by transferring it from regions of surplus into regions of deficit. Some differences are, however, found between the heat and moisture budget distributions. Unlike the extensive vertical region of heat activity that goes beyond the cloud levels, the vertical region of moisture activity is primarily confined to cloud levels. Similar to the heat budget, the net large-scale forcing process intensifies the moisture contribution in both magnitude and vertical scale in 4N; however, the mean advection in moisture intensifies both above and below 4.5 km while the mean advection in temperature is only enhanced in the upper atmosphere (above 4.5 km).

The vertical distribution of the apparent heat source Q1 and moisture sink Q2 are shown in Figs. 6e,f (Q2 is defined positive for a moisture sink). Vertical distributions of the Q1 budget qualitatively resemble those of net condensation heating Ct (Figs. 6a,b) for both 4M and 4N due to its dominance over the eddy heat flux convergence/divergence and net radiation. Overall, the Q1 budget is enhanced by strong wind shear; however, the level of maximum Q1 is determined by the local maximum in eddy heat convergence in the lower atmosphere (around 4.8 km for 4M and 5.3 km for 4N), which overcomes strong cooling by mean advection and a heat loss in net condensation due to melting. On the other hand, a dual-peak distribution occurs in the Q2 budget as a considerable amount of moistening due to a maximum in eddy moisture convergence (around 4.2 km for 4M and 4.8 km for 4N) significantly compensates for a maximum drying in net condensation due to rain processes and forms a local minimum in drying. The strong wind shear raises the vertical level of maximum Q2 and intensifies the drying especially for the lower maximum. The eddy flux convergence/divergence terms reshape the vertical distribution for both Q1 and Q2 by cascading heat and moisture vertically. Eventually, vertical distributions of Q1 and Q2 resemble those of mean advection in temperature and moisture, respectively, as the quasi-equilibrium state is reached with negligible temperature and moisture tendency (see Figs. 6a–f).

2) Mass fluxes

The evolved circulation of various convective systems can be exhibited by the mass fluxes. The vertical profiles of horizontally averaged mass fluxes for 4M and 4N at their early (final) stage are shown in Figs. 7a,b. The two peaks of the imposed total mass fluxes around 8.9 and 2.5 km critically affect the level of peak mean advection in temperature (see Figs. 6a,b) and the lower-level peak in mean advection in moisture (see Figs. 6c,d). In general, positive net mass fluxes dominate in the convective cloud region, especially in the lower atmosphere, while positive/negative net mass fluxes prevail in the upper/lower atmosphere in the stratiform cloud region. However, positive net convective mass fluxes are stronger in the beginning stage, while net stratiform mass fluxes are enhanced (more positive aloft and less negative below) in the final stage. Though the total mass fluxes are time-invariant, the respective upward and downward fluxes do vary with time (not shown). Upward and downward fluxes are much larger in the first 5 days compared to the final 5 days, and both fluxes are enhanced in 4N. The stronger initial circulation may be caused by the spurious energy generated from a high surface air–sea temperature and moisture difference in the initial model system as well as in the spinup process.

Fig. 7.

Vertical profiles of horizontally averaged mass fluxes for the pair of runs 4M and 4N for (a) the initial 5 days, and (b) the final 5 days, where dashed lines with symbols specify various cloud areas (Con, Str, and Clr denote convective, stratiform, and cloud-free areas, respectively) for 4N, while the adjacent solid lines with symbols are for 4M. The total (upward and downward) horizontally averaged mass fluxes (denoted by solid line Tot) are identical for 4M and 4N since a time-invariant horizontally averaged vertical velocity field (all positive vertically) is prescribed in the model

Fig. 7.

Vertical profiles of horizontally averaged mass fluxes for the pair of runs 4M and 4N for (a) the initial 5 days, and (b) the final 5 days, where dashed lines with symbols specify various cloud areas (Con, Str, and Clr denote convective, stratiform, and cloud-free areas, respectively) for 4N, while the adjacent solid lines with symbols are for 4M. The total (upward and downward) horizontally averaged mass fluxes (denoted by solid line Tot) are identical for 4M and 4N since a time-invariant horizontally averaged vertical velocity field (all positive vertically) is prescribed in the model

The wind shear effect on the partitioned fluxes is more complex. In the early stage (Fig. 7a), the low-level peak negative net mass flux (below 2.2 km) in the stratiform cloud region is enhanced in 4N by strong wind shear, while positive net stratiform fluxes aloft (maximum near 9.3 km) are slightly weakened. For the convective region, the wind shear effect does not appear to alter net mass fluxes (all positive) but shifts the level of maximum flux downward. For the cloud-free area, the strong wind shear, however, reduces the intensity of negative net fluxes in 4N, which is a combined effect of weakened upward and downward fluxes (not shown). The respective upward and downward mass fluxes for both stratiform and convective cloud areas are strengthened in 4N, especially in the stratiform area (not shown). In the final stages, Fig. 7b shows that net mass fluxes weaken more in 4N than 4M for the stratiform, convective cloud and cloud-free areas, especially for the positive net fluxes in the lower levels of convective cloud areas. Actually, in stratiform cloud areas, the respective upward and downward mass fluxes in 4N remain strong toward the final stage due to the strong wind shear, while the respective fluxes in 4M become much weaker toward the end. In convective cloud areas, the wind shear effect moderately enhances the upward and downward mass fluxes, but the fluxes are much weaker in this final stage compared to the initial stage.

4. Thermodynamic budget analysis

The horizontally integrated budget Eqs. (1) and (2) listed in section 2c can be further vertically integrated for budget computations for heat and moisture over the entire model domain. The model-domain-integrated vertical eddy flux convergence/divergence terms for both potential temperature and water vapor, −〈(1/ρ)(∂/∂z) ρwθ〉 and −〈(1/ρ)(∂/∂z)ρυ 〉, respectively, (where angle brackets denote a vertical average) vanish over the entire domain, except for contributing to the respective surface sensible and latent heat fluxes (denoted as SHF and LHF, respectively, hereafter) from the ocean surface. Two major objectives are presented in this section through thermodynamic budget analysis. First, the physical processes that determine how the quasi-equilibrium states of temperature and water vapor are approached (beginning stage) and maintained (final stage) are examined in section 4a. Second, the associated physical processes accounting for the impact on the quasi-equilibrium states by various horizontal wind structures are discussed in section 4b.

a. Thermodynamic budget before and during quasi-equilibrium states

Tables 5 and 6 list the domain-averaged moist static energy for the initial and final 10 days of integration of the six major runs, respectively. In the beginning stage for the cold/dry run 1M, the strong net radiative cooling dominates over the heating from both net large-scale temperature forcing [more heating by Ct than cooling by mean advection in temperature (MAt)] and sensible heat flux leading to net cooling in temperature tendency, while the moistening from latent heat flux exceeds the drying from net large-scale moisture forcing [more drying by moisture condensation (Cq) than moistening by mean advection in moisture (MAq)] to produce net moistening (Table 5). Overall, in terms of moist static energy, the positive contribution from both latent and sensible heat fluxes tends to compensate for the strong net radiative cooling, while the net heating due to net large-scale temperature forcing fully balances the net cooling (drying) by net large-scale moisture forcing. In the final 10 days (Table 6), all of the components are reduced in magnitude compared to the initial stage, especially latent heat flux and net large-scale temperature forcing, which results in the very low moist static energy for 1M. The decrease in temperature and water vapor in 1M flattens out near the end of the simulation as a quasi-equilibrium state is reached.1 The strong reduction in latent heat flux due mainly to the greatly weakened wind speed weakens the convection, which reduces the net heating by microphysical processes, especially that by the freezing process (Ct is found reduced in magnitude 8 W m–2 more than Cq). Compared to the cold/dry run 1M, the mild/moist run 4M has a significant enhancement in latent heat flux (8.9 W m–2) and net large-scale temperature forcing (7.8 W m–2) over other physical processes in the beginning stage (Table 5). These two major processes, however, weaken in the final stage of 4M (Table 6). A reduced air–sea humidity difference (due to increased air humidity) along with the weak surface wind accounts for the weakened latent heat flux. Net large-scale moisture forcing, however, increases relatively (less drying) in the final stage as the reduction in drying due to Cq outweighs the reduction in moistening due to MAq.

Table 5. Moist static energy (CpdT + Lυdqυ) budget for the initial 10 days of integration of the six major runs. CpdT and Lυdqυ are the local time change of temperature and water vapor, respectively. SHF, LHF, and SwLw are sensible, latent heat flux, and net radiation, respectively. Here, Ct and MAt are the net latent heating due to phase change of water and mean advection in temperature, while Cq and MAq are the net moisture condensation and mean advection in water vapor, respectively. The summed values (within parentheses) in column Ct/MAt and MAq/Cq are considered “the net large-scale forcing in temperature and moisture,” respectively. Units are W m–2

Table 5. Moist static energy (CpdT + Lυdqυ) budget for the initial 10 days of integration of the six major runs. CpdT and Lυdqυ are the local time change of temperature and water vapor, respectively. SHF, LHF, and SwLw are sensible, latent heat flux, and net radiation, respectively. Here, Ct and MAt are the net latent heating due to phase change of water and mean advection in temperature, while Cq and MAq are the net moisture condensation and mean advection in water vapor, respectively. The summed values (within parentheses) in column Ct/MAt and MAq/Cq are considered “the net large-scale forcing in temperature and moisture,” respectively. Units are W m–2
Table 5. Moist static energy (CpdT + Lυdqυ) budget for the initial 10 days of integration of the six major runs. CpdT and Lυdqυ are the local time change of temperature and water vapor, respectively. SHF, LHF, and SwLw are sensible, latent heat flux, and net radiation, respectively. Here, Ct and MAt are the net latent heating due to phase change of water and mean advection in temperature, while Cq and MAq are the net moisture condensation and mean advection in water vapor, respectively. The summed values (within parentheses) in column Ct/MAt and MAq/Cq are considered “the net large-scale forcing in temperature and moisture,” respectively. Units are W m–2

Table 6. Same as in Table 5 except for the final 10 days of integration of the six major runs. Units are W m–2

Table 6. Same as in Table 5 except for the final 10 days of integration of the six major runs. Units are W m–2
Table 6. Same as in Table 5 except for the final 10 days of integration of the six major runs. Units are W m–2

Similarly, latent heat flux and net large-scale temperature forcing are also the two major physical processes that account for the variation between 4M and 7M in the initial stage (Table 5). Latent heat flux dominates the increase in water vapor while net condensation (Ct) dominates the temperature increase. In the final stage of 7M, latent heat flux weakens significantly, while net large-scale forcing in temperature/moisture decreases/increases considerably (compared to the beginning stage). Similar to 4M, net large-scale moisture forcing of 7M becomes more important in the moisture budget near the end as latent heat flux weakens. The three warm/wet runs with strong wind shear (1N, 4N, and 7N) do not behave exactly the same as 7M does. They all possess large heating by net large-scale temperature forcing in the beginning stage as 7M does. They, however, have a higher contribution to the moisture budget by net large-scale moisture forcing (larger MAq), but smaller latent heat flux than 7M. Moreover, the stronger net radiative cooling in 7M results in a relatively smaller temperature tendency than 1N, 4N, and 7N. The stronger cooling by net radiation in 7M may be due to the higher percentage of precipitating convective clouds occurring in 7M. On the other hand, for the moisture budget, a smaller moisture tendency in 7M than those in 1N, 4N, and 7N is mainly due to the less intensification of latent heat flux due to strong surface winds (7M) than that of net large-scale moisture forcing due to strong wind shear (1N, 4N, and 7N). In the final stage, net large-scale temperature forcing decreases (less heating by Ct than cooling by MAt) as well as latent heat flux, while net large-scale moisture forcing increases (more moistening by MAq than drying by Cq) for 1N, 4N, and 7N (Table 6). Compared to the strong wind shear runs, 7M has more heating by sensible heat flux, which compensates for most of the larger cooling by net radiation. It also has stronger moistening by latent heat flux balanced by a relatively stronger drying by net large-scale forcing in moisture.

b. Impact on thermodynamic budget due to various horizontal wind structures

Results discussed in the previous section reveal that various horizontal wind structures play a crucial role in determining the quasi-equilibrium states by both the wind shear and surface wind speed effects. These effects can be further examined by comparing the heat and moisture budgets for the 25-day integration (Table 7) as well as the initial and final 10-day periods between deliberately paired runs either with different wind shear patterns [e.g., (4M, 4N)] or with different surface wind speeds [e.g., (1M, 4M)]. A further discussion on the pure wind shear effect is also presented in this section.

In terms of the impact of strong wind shear on the heat budget, net large-scale temperature forcing (involving a large amount of condensational heating offset mostly by a comparable vertical advective cooling) is predominantly responsible for the temperature increase for runs with low surface wind speeds (i.e., from 1M to 1N, and 4M to 4N in Table 7). Sensible heat flux plays a minor positive role in the warming, while net radiation offsets it with stronger longwave radiative cooling. An overall expanded cloud system (broadening and deepening) due to strong wind shear generally enhances both longwave cooling and shortwave heating. The net radiative effect is negative since the shortwave heating is overpowered by the longwave cooling. Between 7M and 7N, the net radiation becomes the dominant process, while the net large-scale forcing remains a positive but much less crucial term. This net radiative gain due to strong wind shear with a high surface wind is attributed to more shortwave heating than longwave cooling throughout the entire integration. Based on analyses for various periods (the initial, final 10 day, and the entire 25 day), the net large-scale temperature forcing remains the dominant process accounting for the wind shear effect from the beginning to the end for runs with weaker surface winds, while the net radiation remains the dominant process in runs with strong surface wind.

The impact due to various surface wind speeds on the heat budget is found significant only between runs with mixed-wind shear, that is, (1M, 4M) and (4M, 7M) (Table 7). The net large-scale temperature forcing and sensible heat flux are the major and minor processes responsible for the increase in temperature tendency, while a net radiative cooling performs a negative effect. Accordingly, intensification in the net large-scale forcing is mainly due to the enhanced net condensation (Ct) originating from enlarged convective clouds, while the net radiative cooling comes primarily from a longwave radiative cooling, which is also a response to the extensive convective clouds. These two major physical processes (constructively and destructively), however, have a stronger impact in the final stage (Table 6) than in the initial stage (Table 5), which is consistent with a finding that the enhancement of convective clouds occurs more in the later stage than in the earlier stage.

In the moisture budget for the entire 25-day period, latent heat flux and net large-scale moisture forcing are the two dominant processes responsible for the increased moisture tendency due to strong wind shear (Table 7). Latent heat flux (positive) dominates net large-scale moisture forcing (negative) in the moisture increase for runs from 1M to 1N. Such a dominance by latent heat flux is mainly due to a great surge in surface wind speed by strong wind shear, even at the expense of a moderate loss in sea–air humidity difference. From 4M to 4N, latent heat flux weakens its (still positive) contribution due to a reduced surge in surface wind speed, while the contribution by net large-scale forcing in moisture is enhanced to be positive. From 7M to 7N, net large-scale forcing in moisture becomes the dominant process (positive) over the further weakened latent heat flux (negative). Overall, latent heat flux is the dominant process that accounts for the wind shear effect in runs with weaker surface winds, while net large-scale forcing dominates in runs with stronger surface winds when the pure wind shear effect prevails. Again, this is mainly because the surface wind speed surge due to strong wind shear flattens out as the prescribed minimum wind speed increases closer to those in the strong wind shear runs (about 7–8 m s–1).

Similar to its impact on the heat budget, the minimum surface wind effect on the moisture budget is significant only between runs with mixed-wind shear. Latent heat flux is the dominant process over net large-scale moisture forcing responsible for the variation of moisture tendency between the mixed-wind shear runs from the beginning period to the end. Apparently, embedded surface fluxes are necessary for a convective system to develop into a quasi-equilibrium state. Overall, the net large-scale forcing (in both temperature and moisture) and surface fluxes are crucially responsible for the discrepancy found in modeled quasi-equilibrium states, for example, that between S94 and G96. However, the role sensible heat flux plays in the heat budget is much less significant than what latent heat flux does in the moisture budget and so too in the thermodynamic quasi-equilibrium system.

To further confirm the concept that strong wind shear provides the convective system with two major mechanisms, mean advection (in temperature and moisture) and surface wind surge, six respective pilot runs with constant surface wind speed (for computing surface fluxes) were performed. The corresponding heat and moisture budgets for the 25-day integration are shown in Table 8. For the paired runs with low surface winds [i.e., (1Mc, 1Nc) and (4Mc, 4Nc)], both the sensible and latent heat flux decrease, while the net large-scale forcing in both temperature and moisture increase from the shear such that they resemble (7M, 7N) in major features instead of (1M, 1N) or (4M, 4N). Evidently, the pure effect of shear dominates the nudging when the surface wind speed surge vanishes with the treatment of constant surface wind speed. For example, comparing (1Mc, 1Nc) with (1M, 1N), the net large-scale moisture forcing (the former pair) replaces the latent heat flux (the latter pair) as the dominant process responsible for the moisture increase. As expected, the constant surface wind speed treatment has the least impact on the paired runs (7Mc, 7Nc) [i.e., the small variations found comparing (7Mc, 7Nc) in Table 8 with (7M, 7N) in Table 7], since (7M, 7N) has the least minimum surface wind surge effect. However, it seems that the dominant process—the net radiation/net large-scale moisture forcing in the heat/moisture budget—is slightly enhanced.

Table 8. Same as in Table 7 except for the six pilot runs with respective constant surface wind speed (for computing surface fluxes). Units are W m–2

Table 8. Same as in Table 7 except for the six pilot runs with respective constant surface wind speed (for computing surface fluxes). Units are W m–2
Table 8. Same as in Table 7 except for the six pilot runs with respective constant surface wind speed (for computing surface fluxes). Units are W m–2

5. Summary

The imposed vertical wind shear condition, minimum surface wind speed for computing surface fluxes, and radiation are the three major components that determine the quasi-equilibrium temperature and water vapor fields simulated in this paper. The imposed wind shear patterns and minimum wind speeds are particularly responsible for generating various quasi-equilibrium states as, for example, were found between S94 and G96. Conditions associated with strong wind shear (along with strong surface winds) or a large minimum wind speed tend to produce a warm/wet quasi-equilibrium state, while a mixed-wind shear and a small minimum wind speed create a colder/drier state. Radiation is necessary in establishing the aforementioned quasi-equilibrium states but is not crucial to the considerable variation between them.

Several specific characteristics of convective systems associated with various quasi-equilibrium states have been studied. In terms of cloud area coverage, latent heat flux plays a decisive role in extending erect convective clouds for mixed-wind shear runs. For strong wind shear runs (all warm/wet), both stratiform (well-organized type, particularly) and convective clouds expand their area coverage as minimum wind speed increases, though the former dominates the latter in area coverage. Strong wind shear provides cloud systems with two distinct effects: first, an environment favorable for the enhancement of mean advection in temperature and moisture that produces more well-organized clouds, and second, a strong surface wind that strengthens surface fluxes, which generate more convective clouds. A warmer/wetter run is found to produce a larger rainfall amount, as convective clouds are the leading source of rainfall over stratiform clouds. Strong wind shear runs are dominated by low rain rates (0–2 mm h–1) in both amount and frequency, while mixed-wind shear runs are dominated by slightly higher rain rates (2–4 mm h–1) in amount. However, the infrequent, high rain rates (e.g., no less than 24 mm h–1) together contribute a large amount of the rainfall. They are associated with the most intense convective clouds that have high precipitation efficiency.

Convective systems with mixed-wind shear (mainly shallow and deep convective cells) are driven by a net light-westerly mean advection. The more complex systems with strong wind shear move as follows: the shallow convective clouds propagate westward due to low-level easterly flow, while the well-organized stratiform clouds move eastward in response to the westerlies aloft. The large-scale zonal wind shear plays a crucial role in determining the formation as well as the migration of radiative–convective systems. Warm/wet runs of high CAPE reach a quasi-equilibrium state associated with a lower atmosphere that is more moist-unstable (pseudoadiabatic) and more static-stable (dry adiabatic) than that in the colder/drier runs of low CAPE. Moisture is believed to be the key factor in modifying the atmospheric stability. Cloud-scale eddies redistribute the heat and moisture vertically by means of upward and downward convective motions. They assist in balancing the heat (Q1) and moisture (Q2) budgets and in reaching a quasi-equilibrium state. A strong circulation (upward and downward fluxes) associated with strong wind shear provides sufficient vertical momentum for stronger mean advection in temperature and moisture.

The physical processes that account for the genesis and maintenance of quasi-equilibrium states as well as the effects from the associated horizontal wind structures have been examined based on thermodynamic budget analyses. For the cold/dry run (1M), in the beginning stage the positive contribution from both latent and sensible heat fluxes tends to compensate for the strong net radiative cooling, while the heating from net large-scale temperature forcing fully balances the cooling (drying) by net large-scale moisture forcing. In the final stage, all of the components weaken, especially latent heat flux and net large-scale temperature forcing, which leads to a quasi-equilibrium state. For the mild/moist run (4M), a significant enhancement in latent heat flux and net large-scale temperature forcing occurs in the beginning stage that eventually results in the substantial variations in both temperature and water vapor. The warm/wet runs with strong wind shear (1N, 4N, and 7N) behave differently from 7M. In the beginning stage, they all possess large heating by net large-scale temperature forcing as does 7M, but they have smaller net radiative cooling. They have a higher contribution to the moisture budget from net large-scale moisture forcing, but smaller latent heat flux than 7M. In the final stage of the strong wind shear runs, net large-scale temperature forcing decreases as well as latent heat flux, while net large-scale moisture forcing increases.

In determining the quasi-equilibrium state, the wind shear effect has a prominent impact on runs with lower minimum wind speeds, while the minimum surface wind effect is crucial for mixed-wind shear runs. Latent heat flux dominates the moisture budget associated with both a strong wind shear and a strong minimum wind speed effect, while net large-scale moisture forcing is most important when the pure effect of shear dominates the nudging [i.e., the surface wind speed surge significantly diminishes between runs (7M, 7N)]. Net large-scale forcing in temperature on the other hand is the primary process that determines the temperature equilibrium state associated with a strong wind shear or a strong minimum wind speed effect.

These simulations are based on a more idealized than realistic environment, several important features (claimed in the four major goals of this paper) have, however, been identified and presented. In this study, the modeled quasi-equilibrium state is found to be sensitive to two crucial components: sea surface fluxes (dependent on the prescribed minimum wind speed or the strong surface wind due to shear) and the cloud system organization (sensitive to the vertical wind shear). Improving the performance of our model simulations by better understanding the physical, dynamic, and microphysical processes involved in radiative–convective systems as well as carefully employing physically realistic data (e.g., reliable in situ observations) for the initial conditions and main forcing is our major goal for the future.

Table 1b. Same as Table 1a except with a fixed (time-invariant) surface wind speed imposed in the bulk aerodynamic formulas

Table 1b. Same as Table 1a except with a fixed (time-invariant) surface wind speed imposed in the bulk aerodynamic formulas
Table 1b. Same as Table 1a except with a fixed (time-invariant) surface wind speed imposed in the bulk aerodynamic formulas

Acknowledgments

The authors wish to thank the editor and three anonymous reviewers for their thoughtful and constructive comments that improved this paper. Special thanks also go to Mr. S. Lang for reading the manuscript and Dr. S. Shige for useful discussions. This study is supported by the NASA Headquarters Physical Climate Program and by the NASA TRMM project. The authors are also grateful to Dr. R. Kakar (NASA HQ) for his support of this research. Acknowledgment is also made to NASA Goddard Space Flight Center for computer time used in the research.

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Footnotes

Corresponding author address: Dr. Chung-Lin Shie, Mesoscale Atmospheric Process Branch, Code 912, NASA/GSFC, Greenbelt, MD 20771. Email: shie@agnes.gsfc.nasa.gov

1

A similar feature can be found in Run_3 in Fig. 2 of T99.