1. Introduction
In general, there are two broad scientific objectives when using cloud-resolving models (CRMs) or cloud ensemble models (CEMs) to study tropical convection. The first objective is to use them as physics-resolving models to understand the dynamic and microphysical processes associated with the tropical water and energy cycles and their role in the climate system (Soong and Ogura 1980; Tao and Soong 1986; Sui et al. 1994; Grabowski et al. 1996; and many others listed in Table 1 in Tao et al. 1999). The second approach is to use the CRMs to improve the representation of moist processes and their interaction with radiation in large-scale models [see Global Energy and Water Cycle Experiment (GEWEX) Cloud System Study (GCSS) plan (GEWEX Cloud System Science Team 1993)]. In order to improve the credibility of the CRMs and achieve the above goals, CRMs using identical initial conditions and large-scale influences need to produce very similar results.
Two CRMs produced different statistical equilibrium (SE) states [warm and humid in Grabowski et al. (1996) and cold and dry in Sui et al. (1994)] even though both used the same initial thermodynamic and wind conditions (1956 Marshall Islands data). Tao et al. (1999) have performed sensitivity tests to identify the major physical processes that determine the SE states for the different CRM simulations.1 They identified three very distinct SE states (see the three boxes shown in their Fig. 3). Based on differences in the water budget between these three SE states, Tao et al. (1999) concluded that “the warm and humid (cold and drier) climates are always associated with stronger (weaker) latent heat fluxes from the ocean and stronger (weaker) advective moistening.” In addition, Tao et al. (1999) found that the domain mean thermodynamic state is more unstable for those experiments that produced a warmer and more humid SE state.
Xu and Randall (1999), however, indicated that their simulated wet (warm and humid) SE states are thermally more stable in the lower troposphere (from the surface to 4–5 km in altitude). Xu and Randall (1999) also suggested that the large-scale horizontal advective effects on temperature and water vapor mixing ratio [ignored in Tao et al. (1999) and others] are needed when using CRMs to perform long-term integrations to study convective feedback under specified large-scale environments. In addition, they suggested that the dry and cold SE state simulated by Sui et al. (1994) was associated with enhanced precipitation but not enough surface evaporation. We find some problems with their interpretation of these three phenomena.
2. Comments
a. Large-scale forcing employed in the CRMs
Xu and Randall (1999) performed two numerical experiments, “cM” (the second approach) and “cW” (the first approach), to identify the importance of the large-scale horizontal advective effects on temperature and the water vapor mixing ratio in their simulated SE states. The cM experiment produced a thermodynamic SE state that was closer to a 3-month observed mean thermodynamic state than that of the cW experiment (see Fig. 1).3 Xu and Randall (1999) then used the relatively poor performance of the cW experiment to identify the important role of the large-scale horizontal advective effects upon their simulated SE states. As shown in (1) and (2), experiment cW is not the same as the experiment without large-scale horizontal advective effects. Xu and Randall (1999), however, never performed a numerical experiment without the large-scale horizontal advective effects on temperature and water vapor. They also did not separate the vertical and the horizontal components of the large-scale forcing to show the relative magnitude of the horizontal component to the total forcing (shown in their Fig. 2a). We feel that their results may be misleading and cannot be used to address the importance of large-scale horizontal advective effects on temperature and water vapor in their own or in other CRM studies.
Xu and Randall (1999) also criticized the model used by Sui et al. (1994) that does not have the ability to maintain the initial wind profile. As discussed in Tao et al. (1999), the Sui et al. (1994) model setup did not add any artificial terms (i.e., nudging or other) to the horizontal (u) momentum equation that would maintain the domain mean horizontal (u) momentum close to its initial value. Consequently, the horizontal momentum is simply mixed by convective transport processes in Sui et al. (1994) resulting in weak surface wind speeds and almost uniform horizontal flow through the whole troposphere after 4 days of model integration. We feel that the ideal design for future CRM simulations should allow both convective mixing and large-scale processes involving the horizontal momentum by allowing for the change in strength and vertical shear of horizontal momentum. This could be particularly important in any CRM simulation allowing time-varying large-scale vertical motion [i.e., experiments, vW, vhW, and vG-ns, in Xu and Randall (1999)].
b. Moisture budgets and physical processes determining the CRM simulated SE states
Tao et al. (1999) identified the physical processes responsible for determining the modeled equilibrium states by examining the budget differences between CRM simulated warm–humid and cold–dry SE states. They examined the energy budget from the beginning to the end of the simulation. This type of budget analysis is necessary in order to determine how the two simulated SE states were obtained even though both start with almost identical initial conditions. On the other hand, one can analyze the modeled energy budget during a subperiod when a specific SE state is achieved. This type of budget analysis can only be used to investigate what the energy budget or balance is during that specific SE state (i.e., what is the energy balance that may be needed or required to maintain a cold–dry or a warm–humid SE state). This type of budget study cannot be used to explain what causes the different SE states. Xu and Randall (1999) performed this type of budget analysis.
Table 1 lists the precipitable water and the difference between evaporation and precipitation in Sui et al. (1994), Grabowski et al. (1996), and three runs (cM, cW, and vW) in Xu and Randall (1999). Xu and Randall’s interpretation of the results of Sui et al. (1994),“The weaker surface wind cannot increase the surface evaporation enough to compensate for the enhanced precipitation so that less precipitable water remains in the column,” is justified in run cM being drier compared to either run cW or vW. However, their interpretation cannot apply to runs cW and vW. In addition, the difference between the surface evaporation and precipitation is very small (less than 5 W m−2) between Sui et al. (1994) and Grabowski et al. (1996) compared to the difference between runs cM and cW (31 W m−2) in Xu and Randall (1999). But, the difference in precipitable water between Sui et al. (1994) and Grabowski et al. (1996) is over 20 mm and is much bigger than the difference between runs cM and cW (about 6 mm).
Table 2 lists individual components of the water vapor budget simulated by Xu and Randall (1999) and Tao et al. (1999). The difference in precipitation between experiments cW and vW in Xu and Randall (1999) is very small. These two runs cannot be used to justify the hypothesis that the dry and cold SE state was caused by enhanced precipitation but not enough surface evaporation. The difference between experiments cW and cM is very large, but both surface evaporation and large-scale advective forcing in water vapor contribute equally to their difference in precipitation. Several noted differences between Tao et al. (1999) and Xu and Randall (1999) can be seen in Table 2. For example, the runs that produced the more humid (drier) SE states are always associated with larger (smaller) latent heat flux from the ocean, larger (smaller) net condensation, and larger (smaller) large-scale advective forcing in Tao et al. (1999). It implies that more surface latent heat fluxes and large-scale advective forcing in water vapor can lead to more net condensation and surface precipitation. In contrast, the relatively warm–humid SE state (experiment cW) in Xu and Randall (1999) is associated with less latent heat flux from the ocean, less net condensation, and less large-scale advective forcing than the relatively cold–dry SE state (experiment cM). It may be reasonable to assume that warm and humid states have more precipitation and more evaporation from the ocean. Observations are needed to verify these idealized climate simulations.
Also, note in Table 2 that the contribution of the large-scale advective forcing in water vapor to net condensation–surface precipitation ranges from 0.67 to 0.70 in Xu and Randall (1999) for their Marshall Island simulations. It is about 0.81 to 0.85 in Tao et al. (1999) and Sui et al. (1994). The Goddard Cumulus Ensemble (GCE) modeled precipitation processes have a stronger response to the large-scale advective forcing than the University of California, Los Angeles–Colorado State University (UCLA–CSU) CEM (Xu and Randall 1999). On the other hand, the surface latent heat fluxes only contribute to about 15%–21% of the total precipitation processes (net condensation–surface precipitation) in the GCE model compared to 30%–33% in the UCLA–CSU CEM. Two models, the GCE model and the UCLA–CSU CEM, behave very differently in terms of precipitation processes and their interaction with surface processes and the imposed large-scale advective forcing.
Tripoli’s (1992) cloud-resolving model used in Grabowski et al. (1996) also has a larger contribution from the large-scale forcing to the precipitation processes (81%) and a smaller ratio (19%) between surface latent heat fluxes and surface precipitation. Yanai et al. (1976) analyzed Marshall Islands 1956 data and found that the surface latent heat fluxes make up about 21.7% of the surface precipitation during disturbed periods (dominated by deep cumuli–Type 1 classification with 351 cases).5 The ratio between the latent heat fluxes and the surface precipitation increases to 37% for undisturbed convective periods (shallow cumuli–type 2 classification with 35 cases). The classification is based on observed large-scale vertical velocity (positive or upward for disturbed periods and negative or downward for undisturbed periods). The large-scale vertical velocity imposed within the CRMs is all upward and the modeled precipitation processes are quite active. We believe that the GCE model and Tripoli’s (1992) cloud-resolving model results perhaps are both in reasonable agreement with observations. We also believe that a more rigorous cloud-resolving model intercomparison (including offline detailed comparisons of selected physical processes) involving responses to different large-scale forcing and surface fluxes is needed in the future. A good quality controlled long-term observational dataset (i.e., Yanai et al. 1976) that can provide large-scale forcing and flux measurements is also required.
Another comment is that Xu and Randall (1999) performed several Global Atmospheric Research Program (GARP) Atlantic Tropical Experiment (GATE) simulations, and they indicated that the presence of vertical shear of the horizontal wind does not significantly change the simulated SE states, provided that the surface wind speeds are identical. These results are, somewhat, consistent with Tao et al. (1999) in that runs with stronger (weaker) surface winds produced more latent heat fluxes and warm and humid (cold and dry) SE states. However, we feel that their GATE simulations may be inappropriate because the observed precipitable water during GATE Phase III never reaches an equilibrium state [see Fig. 15 in Xu and Randall (1996)]. In addition, their GATE simulations did not employ observed large-scale advective forcing in temperature and water vapor.
c. Stability in CRM simulated equilibrium states
Figure 2a shows the relation between the surface relative humidity and the lower-tropospheric lapse rate (below the 4.7-km level) for a fixed sea surface temperature (28°C). The results show a negative correlation between surface relative humidity and the lower-troposheric lapse rate. The results in Fig. 2a show that warm–humid SE states are thermally more stable and cold–dry SE states are thermally more unstable in the lower troposphere in both Xu and Randall (1999) and Tao et al. (1999).
Figure 2b shows the relation between the surface relative humidity and the lapse rate for equivalent potential temperature [an indicator for convective available potential energy (CAPE)]. The results shown in Fig. 2b indicate that the thermodynamic state is more unstable (stable) for those experiments that produced a warmer and more humid (cold and dry) SE state. In addition, the domain column mean thermodynamic profile has a stronger vertical gradient of water vapor for those experiments that produced warmer and more humid SE states compared to the experiments that produced colder and drier SE states. This is why stronger large-scale forcing (the first approach) can lead to larger heating and moistening in the local temporal change of temperature and water vapor in Tao et al. (1999) (see Table 1). Our results also indicated that warmer and more humid SE states are associated with a larger CAPE (2000 to 2500 m2 s−2) compared to the colder and drier SE states (1300 to 1600 m2 s−2).
3. Summary
Xu and Randall (1999) performed sensitivity tests to improve the understanding of radiative–convective equilibrium in the Tropics using the UCLA–CSU CEM. We have three major comments on their three major conclusions:
Xu and Randall (1999) did not show solid evidence of the important role of large-scale horizontal advective forcing in temperature and water vapor on their simulated SE states. We believe that horizontal advective forcing is needed when a CEM is used for comparison with particular observations and for the purposes of the GCSS (to improve the understanding of moist processes in general circulation models and climate models).
Their interpretation of Sui et al.’s (1994) results that the dry and cold SE state is associated with enhanced precipitation but not enough surface evaporation can not be fully justified, because their own CEM simulations clearly indicated that both surface evaporation and large-scale advective forcing of water vapor contribute equally to the difference in precipitation. Also, their simulated warm–humid SE states are associated with less surface precipitation–net condensation, less large-scale advective forcing, and less latent heat fluxes from the ocean compared to the cold–dry SE states. By contrast, the warm–humid (cold–dry) SE states simulated by Tao et al. (1999) are characterized by more (less) surface precipitation, more (less) large-scale advective forcing, and more (less) surface fluxes. It may not be reasonable to have cold and dry states that are associated with more evaporation from the ocean and more precipitation. In addition, their CEM’s precipitation processes have a weaker response to the imposed large-scale advective forcing in water vapor but a larger contribution from surface latent heat fluxes to surface precipitation as compared to two other CEMs (Goddard Cumulus Ensemble model, and Tripoli 1992) even though all the models were initialized with the same 1956 data from the Marshall Islands. The GCE and Tripoli’s model results are in reasonable agreement with observations (Yanai et al. 1976).
Their warm–wet SE states are more stable than their corresponding cold–dry SE states in the lower troposphere. They only discussed the vertical stability (lapse rate) of a dry atmosphere. However, the warm–wet SE states are actually more unstable (lapse rate of equivalent potential temperature or wet-bulb potential temperature) in the lower troposphere than their corresponding cold–dry SE states. In addition, the warm–wet SE states are always associated with higher convective available potential energy than their corresponding cold–dry SE states.
In order to use the CRM as a physical process–resolving model to understand the dynamic and microphysical processes associated with tropical water and energy cycles and their role in the climate system, we need to use available observations to validate whether a warm and humid thermodynamic state (i.e., El Niño–Southern Oscillation) is associated with stronger large-scale advective forcing (i.e., large-scale moisture convergence) and larger surface fluxes from the oceans than its counterpart cold and dry state. We also need to use observations to address whether or not the CAPE is higher for a simulated warm–humid SE than that associated with a cold–dry SE. The design (i.e., time-variant large-scale forcing in temperature and water vapor, and horizontal momentum) of future CRMs for studying convective–radiative equilibrium in the Tropics needs to be addressed.
Acknowledgments
The authors thank Mr. S. Lang, Dr. B. Ferrier, and Dr. C.-H. Sui for reading the manuscript. We also thank Drs. R. Adler and W. Lau for discussions related to rainfall observation. This work is supported by the NASA Headquarters Physical Climate Program, the NASA Tropical Rainfall Measuring Mission (TRMM), and the Interdisciplinary Investigation of the Earth Observing System (EOS). These authors are grateful to Dr. R. Kakar for his support of this research. Acknowledgment is also made to the NASA Goddard Space Flight Center for computer time used in the research.
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Scatterplot of domain-averaged mass-weighted temperature vs water vapor after 25 days of integration from GCE model (runs 1 to 4 and runs 1W to 4W) and UCLA–CSU CEM simulations (using the same data from the Marshall Islands). 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. Observations from Tropical Ocean Global Atmosphere Coupled Ocean–Atmosphere Response Experiment (TC) and Marshall Islands (MI) regions are shown. Simulations cM, cW, and vW are from Xu and Randall (1999). Runs 1W to 4W are the runs that produced warm–humid SE states similar to Grabowski et al. (1996) (grouped with G in the same box). Runs 1 and 2 are centered at 259 K and 57 mm and are grouped with cM in the same box. Runs 3 and 4 are the runs that produced very cold and dry SE states.
Citation: Journal of the Atmospheric Sciences 58, 10; 10.1175/1520-0469(2001)058<1328:COASSO>2.0.CO;2
(a) Scatter diagram of surface relative humidity and the lower-tropospheric lapse rate after 25 days of the GCE model simulations. (b) is the same as (a) except with equivalent potential lapse rate temperature (S) (an indicator of stability).
Citation: Journal of the Atmospheric Sciences 58, 10; 10.1175/1520-0469(2001)058<1328:COASSO>2.0.CO;2
The precipitable water and the difference between surface evaporation and precipitation (LυE − LυP) for SE states simulated in Xu and Randall (1999), Sui et al. (1994) (S94), and Grabowski et al. (1996) (G96). Units are Watts per meter squared for LυE − LυP.
Individual terms of the column moisture budget for SE states simulated in Xu and Randall (1999) and Tao et al. (1999). Note that the LυP is the net condensation (sum of condensation, deposition, evaporation, and sublimation of cloud). The Lυ 〈
There are many differences in terms of dynamics, microphysics, surface flux calculations, and cloud–radiation interactive processes between the models used in Sui et al. (1994) and Grabowski et al. (1996). It is, perhaps, necessary to use just one CEM to understand/quantify the physical processes that determine the causes for warm–humid and cold–dry states.
Q1 and Q2 are, respectively, the apparent heat source and apparent moisture sink budget defined in Yanai et al. (1973).
Soong and Tao (1980), Tao and Soong (1986), Krueger (1988), Grabowski et al. (1996), Wu et al. (1998), Li et al. (1999), and many others have shown that many CRMs with reasonable physics can produce results in good agreement with observations if “observed” large-scale forcing is superimposed within the CRM as a main forcing. We do believe that no CRM is perfect yet.
The net condensation, 〈Lυ
Yanai et al. (1973, 1976) used the five soundings (formed a pentagon) that were located where the large-scale forcing as well as the observed precipitation and aerodynamically calculated latent heat fluxes were computed. The observed large-scale forcing (including large-scale vertical velocity) based on the careful budget analyses (both Q1 and Q2 budgets were balanced) done by Dr. Yanai was used by Sui et al. (1994), Grabowski et al. (1996), Tao et al. (1999), and Xu and Randall (1999). There was only one ship outside the pentagon, and it gave higher aerodynamically calculated latent heat fluxes. Perhaps, these higher latent heat fluxes outside the sounding network made Yanai suspect that latent heat fluxes were underestimated using the five stations located in the pentagon.
