Testing the Fixed Anvil Temperature Hypothesis in a Cloud-Resolving Model

Jun 08, 04:29 AM

Current Headlines: By Kuang, Zhiming Hartmann, Dennis L

ABSTRACT Using cloud-resolving simulations of tropical radiative- convective equilibrium, it is shown that the anvil temperature changes by less than 0.5 K with a 2-K change in SST, lending support to the fixed anvil temperature (FAT) hypothesis. The results suggest that for plausible ozone profiles, a decrease in the air's emission capability instead of ozone heating shall remain the control on the detrainment level, and the FAT hypothesis should hold. The anvil temperature also remains unchanged with other changes in the system such as the doubled CO2 mixing ratio, doubled stratospheric water vapor concentration, and dynamical cooling due to the Brewer-Dobson circulations. The results are robust when a different microphysics scheme is used.

(ProQuest-CSA LLC: ... denotes formulae omitted.)

1. Introduction

Tropical anvil clouds are observed to exert large cloud radiative forcing that is of the opposite sign in the longwave (LW) and shortwave (SW) (Hartmann et al. 1992). In the current climate, the LW and SW effects largely cancel at the top of the atmosphere (TOA: Ramanalhan el al. 1989). From the TOA energy budget point of view, it is important to understand whether or not this cancellation will hold under future climatic conditions (Kichl 1994; Hartmann et al. 200Ia). The radiative importance of these anvil clouds also extends beyond their TOA effects because they tend to cool the surface and heat the atmosphere. Such a differential healing enhances the atmospheric static stability.

Until recently, there have been few theories that predict how the anvils would respond and feed hack to climate change. In a recent paper. Hartmann and Larson (2002, hereafter HL02) argued that the temperature at which tropical convective anvils detrain should he insensitive to climate change. This will he referred to as the fixed anvil temperature (FAT) hypothesis.

Since the updrafts of deep convection are concentrated in small areas and eonvective heating of the atmosphere is mostly realized through adiahatic heating by compensating subsidence, there exists a dominant balance between clear-sky radiative cooling Qdr (negative lor cooling) and subsidence heating in the Tropics; that is, we have the diagnostic equation

... (1)

where theta is potential temperature, p is pressure, omega is the pressure velocity, and T is temperature. We shall define Gamma = dtheta/dp as a measure of the stratification. The anvil itself induces differential radiative heating (positive at the hase and negative at the top), which can he significant when the anvil fraction is large. However, this differential radiative heating mostly drives turbulence within the anvil cloud, instead of being compensated hy large-scale subsidence, and is therefore neglected in Eq. (1). The divergence field implied by the subsidence rates is

... (2)

and is expected to largely control the detraimncnt level of tropical anvils.

The deep Tropics are different from the exlratropics in that the radiative relaxation rate declines significantly before the tropical tropopause is reached because the very cold air in the upper tropical troposphere contains little water vapor (Hartmann et al. 2001h). HL02 argued that it is the rapid decrease in clear-sky radiative cooling rates with height/pressure that is important in Eq. (2). They then argued that the radiative emission capability of a noncloudy uppertropospheric air parcel is most strongly related to its temperature. This is because of the strong temperature dependence of the saturation water vapor pressure in the Clausius- Clapeyron relation and the fact that water vapor is the main emitter in the upper troposphere. Because of these, they reasoned, the temperature at the level where clear-sky radiative cooling rates rapidly decrease with height, and hence that of the anvils, should remain approximately the same as the surface temperature changes. As the FAT hypothesis attempts to relate the emission temperature of tropical anvils to fundamental constraints such as the Clausius- Clapeyron relation and the longwave emission lines of water vapor, it can potentially lend significant predictive power to studies of cloud-climate feedbacks.

Complementary tu an effort to test this hypothesis observationally (Xu el al. 2007). we will in this study focus on a numerical modeling approach. In 111.02. the FAT hypothesis was tested using mcsoscale models where convection is parameteri/ed. Il is desirable to test the hypothesis in a cloud-resolving model (CRM). A CRM has its own uncertainties, particularly with respect to the microphysics. which has to be parameterized. By explicitly including cumulus-scale motion, however, a CRM appears to better incorporate most of the relevant physical processes in the present problem. We shall use an atmosphere in radiative-convective equilibrium (RCE) as a first approximation to the tropical atmosphere.

Three-dimensional CRM studies on the sensitivity of tropical convection in RCE to SST variations have been conducted (Tompkins and Craig 1999). While their main interest was not on the anvil temperature, based on their results, these authors suggested an increase in the anvil temperature with an increase in SST. However, the resolution in the upper troposphere is quite coarse (~1 km) in that study. This limits their ability to accurately quantify the anvil temperature changes, as recognized by Tompkins and Craig (1999). To adequately test the FAT hypothesis, finer vertical resolution in the upper troposphere is needed.

2. Model and experimental setup

We use the System for Atmospheric Modeling (SAM) version 6.3, which is a new version of the Colorado State University Large Eddy Simulation/Cloud Resolving Model (Khairoutdinov and Randall 2003). The model uses lhe anclaslie equations of inolion with hulk microphysics. The prognostic iherniodynamic variables are the liquid water statie energy, total nonprecipitating water, and total precipitating water. The radiation schemes are those of the National Center for Atmospheric Research (NCAR) Community Climate Model version 3 (CCM3: Kichl et al. I1WS). Readers are referred to Khairoutdinov and Randall (2003) for details about the model. For this study, we use a simple Smagorinsky-type scheme for the effect of subgridscale turbulence. We have removed the diurnal cycle by fixing the solar /enith angle at 50.5' and adjusting the solar constant to yield a constant solar input of 414 W m ". The surface fluxes are computed using the MoninObukhov similarity theory.

For the experiments to he presented, we use a doubly periodic domain of 64 km X 64 km with the model top placed near 40 km. The hori/ontal grid si/e is uniformly I km. A total of % vertical layers are used. The vertical grid si/e increases gradually from 75 m near the surface to 300 m at ~5 km. It is then uniformly 300 m up to 20 km. where it gradually increases to 1 km. A waveahsorhing layer was placed in the upper third of the domain. As discussed in Kuang and Bretherton (2004), gravity waves excited in the upper troposphere become increasingly compressed in the vertical as they propagate upward into the lower stratosphere because of the increasing stratification. A much liner vertical grid is needed in the lower stratosphere to avoid the numerical dissipation of gravity waves, which was found to be important for the heal budget near the cold point tropopause. For the present problem, however, its effect is small so a uniform grid in this region is used to reduce the computational costs. We use a fixed ozone profile taken from the Tropical Ocean Global Atmosphere Coupled Ocean-Atmosphere Response Experiment (TOGA COARE: Webster and l.ukas 1992). All experiments are run for 75 days. It takes about 35 days for the model to reach radiativc-convcclivc equilibrium, so results averaged for the last 40 days are presented. All variables are sampled every 10 min.

3. Results

In Fig. 1. we show the domain-averaged temperature and cloud Tract ion as functions of height for a set of RCE experiments with SSTs of 32.5[degrees], 30.5[degrees], 28.5[degrees]. and 26.51C. A grid point is identified as cloudy when its cloud condensale specific humidity is greater than 10^sup -5^ kg kg^sup -1^. The relative error of the 40-day mean cloud fraction due to fluctuations of the cloud field is less than 5% for the anvil region. In Fig. 2. normali/ed cloud fraction and divergence (diagnosed from Eq. (2)| are shown as functions of temperature.

The results on anvil temperature strongly support the FAT hypothesis. The anvil temperature changes by less than 0.5 K (compared to ~6-K increases in upper-tropospheric temperature) for a 2-K. increase in the SST. The divergence diagnosed from Eq. (2) also appears to he a good predictor for the anvil detraimnent level.

While Eq. (1) is a very useful diagnostic relation, it is also instructive to have a prognostic view on how the balance is established. More specifically, as individual convective parcels shall detrain near their levels of neutral buoyancy (LNB), how are they connected to an increase in the radiative relaxation time scale, the key component that is linked to water vapor and hence temperature in the FAT hypothesis? To see this, let us consider a thought experiment where we have a mass flux distr^sub e^) for the ensemble of parcels arriving at the bottom of the cletrainment region (say T = 240 K). We shall consider M(theta^sub e^) as controlled by processes in the boundary layer and the bulk troposphere and treat it as external to our discussion. We further simplify the radiative processes in the detrainmenl region as relaxation processes toward a radiative equilibrium temperature profile with a relaxation time-scale profile, both treated as given. (In reality, radiative transfer is a global problem and the relaxation cannot be treated as local, and the boundary laver is not independent of conveelive processes in the free troposphere. This does not affect the current argument, however.) With these specifications, the problem is closed. We can assume that these parcels adapt to their LNB, a simplistic but reasonable view of the detrainment process (Folkins 2002). This will adjust the mass between constant U surfaces [i.e., theta(p) profile until Eq. (1) is satisfied). The final solution depends on the prescribed profiles of radiative equilibrium temperature and relaxation time scale. In a region of rapid increase in the radiative relaxation time scale, it (as opposed to the radiative equilibrium profile) will have the dominant effect on the final equilibrium temperature, lapse rate, and radiative cooling profiles, and hence the detrainment level. It is also possible to be in a regime where a rapid increase in the radiative equilibrium profile controls the detrainment so that the argument of HL02 no longer applies. For illustrative purposes, we have conducted a set of hypothetical experiments using the fixed ozone profile from the control run. except shifted downward/ upward by 4, 8, and 12 km, similar to that of Thuburn and Craig (2002). Each ozone profile is scaled by a constant to yield the same column ozone amount. The results (shown in Fig. 3) indicate that with an ozone profile shifted upward so that there is a smaller influence by ozone heating, the anvil temperature remains unchanged. However, when the ozone profile is shifted downward by 4 km to 12 km, the detrainment temperature increases as ozone heating starts to exert greater influence on the detrainment level. Such significantly downward-shifted o/one profiles, however, are unlikely in the real atmosphere, especially as tropical deep convection tends to reduce upper-troposphere ozone through the detrainmenl of ozone-poor boundary layer air. Therefore, for plausible ozone profiles, the decrease in the emission capability of air shall remain the control on the detrainmenl level, and the FAT hypothesis should hold.

We have also conducted experiments with a doubled CO2 mixing ratio, doubled stratospheric water vapor concentration, and dynamical cooling due to the Brewer-Dobson circulation, respectively. For the doubled CO2 run, an SST of 32.5[degrees]C was used, and for the other two runs, the SST was 30.5[degrees]C. Following previous studies (Thuburn and Craig 2002: Kuang and Bretherton 2004), the upwclling due to the BrewerDobson circulation is represented by a dynamical cooling term in the thermodynamic equation. The imposed large-scale vertical velocity is 0.3 mm s^sup - 1^ in the stratosphere and gradually goes to 0 from 100 to 250 hPa, the same as that in Kuang and Bretherlon (2004). In all three experiments, the anvil temperature remains approximately unchanged (Fig. 4). The largest change in anvil temperature is seen in the case with dynamical cooling in the stratosphere (~1 K), which is also captured in the divergence field derived from Eq. (2) (Fig. 5b). With the dynamical cooling term, the lower stratosphere is about 8 K cooler compared to the control case (Fig. 5a). The cooler lower stratosphere allows lor a greater radiative cooling in the upper troposphere (Fig. 5d). The case with dynamical cooling also has a weaker stratification above about 220 K (Fig. 5c). These two effects cause the 1-K shift in the anvil delruinment level.

We have tested the robustness of our results with respect to the microphysics treatment by repeating the experiments presented in Figs. 1, 2 using a different microphysics scheme (Krueger et al. 1995), which is a modified version of the Lin hulk microphysics scheme (Lin et al. 1983). This scheme was implemented in SAM hy P. N. Blossey (Blossey et al. 2007). The results are shown in Fig. 6. With this scheme, the clouds exhibit a clear trimodul distribution with a pronounced peak associated with the melting level, a feature observed in nature (Johnson et al. 1999). This peak is not as pronounced in simulations with the default SAM microphysics. The cloud covers are also different from the results in Fig. 1. The anvil temperature, however, slays the same with SST changes, indicating that our conclusion on FAT is robust with respect to microphysics schemes used in the model.

4. Conclusions

The fixed anvil temperature (FAT) hypothesis (Hartmann and Larson 2002) was tested using 3D CRM simulations of tropical radiative- convective equilibrium. While an earlier 3D CRM study suggested an increase in the anvil temperature with an increase in SST (Tompkins and Craig 1999). their resolution in the upper troposphere is too coarse (~1 km) lor the purpose of testing the FAT hypothesis. Our study uses liner resolution (300 m) in the upper troposphere and a longer integration time to allow sufficient signal-to-noise ratio. Our results strongly support the FAT hypothesis: the anvil temperature changes by less than 0.5 K with a 2-K change in SST. Further experiments suggest that for plausible ozone profiles, a decrease in the air's emission capability instead of ozone heating controls the detrainment level, and the FAT hypothesis should hold. The anvil temperature also remains approximately unchanged with other changes in the system such as doubled CO, mixing ratio, doubled stratospheric water vapor concentration, and dynamical cooling due to the Brewer-Dobson circulations. While the cloud distribution itself is sensitive to the microphysics scheme, the conclusion that the anvil temperature remains approximately unchanged with SST changes is robust when a different microphysics scheme is used. These results therefore support the basic idea behind the FAT hypothesis in the simple setting of RCE over a relatively small domain. How mesoscale and largescale dynamics would a fleet the FAT hypothesis is an interesting question that warrants further studies.

Acknowledgment. We acknowledge support from a NOAA Climate and Global Change postdoctoral fellowship while Z. Kuang was at University of Washington, a Harvard University start-up grant (Z. Kuang). and NASA Grant NNG05GA19G (D. L. Hartmann). We thank Marat Khairoutdinov for making the SAM model available. Peter Blossey for implementing the Krueger microphysics scheme in SAM. and Chris Walker for helping with the figures.

REFERENCES

Blossey, P. N., C. Bretherton, J. Cetrone, and M. Khairoutdinov, 2007: Cloud-resolving model simulations of KWAJEX: Model sensitivities and eomparisons with satellite and radar observations. J. Atmos. Sci., 64, 1488-1508.

Folkins, I., 2002: Origin of lapse rate changes in the upper tropical troposphere. J. Atmos. Sci., 59, 992-1005.

Hartmann, D. L., and K. Larson, 2002: An important constraint on tropical cloud-climate feedback. Geophys. Res. Lett., 29, 1951. doi:10.1029/2002GL015835.

_____, M. E. Ockert-Bell, and M. L. Michelsen, 1992: The effect of cloud type on Earth's energy balance: Global analysis. J. Climate, 5, 1281-1304.

_____, L. A. Moy, and Q. Fu, 2001a: Tropical convection and the energy balance at the top of the atmosphere. J. Climate, 14, 4495- 4511.

_____. J. R. Holton, and O. Fu, 2001b: The heal balance of the tropical tropopause, cirrus, and stratospheric dehydration. Geophys. Res. Lett., 28, 1969-1972.

Johnson. R. H., T. M. Rickenbach, S. A. Rutledge, P. E. Ciesielski, and W. H. Schubert, 1999: Trimodal characteristics of tropical convection. J. Climate, 12, 2347-2418.

Khairoutdinov, M. F., and D. A. Randall, 2003: Cloud resolving modeling of the ARM summer 1997 IOP: Model formulation, results, uncertainties, and sensitivities. J. Atmos. Sci., 60, 607-625.

Kiehl, J. T., 1994: On the observed near cancellation between longwave and shortwave cloud forcing in tropieal regions. J. Climate, 7, 559-565.

_____, J. J. Hack, G. B. Bonnn, B. A. Boville, D. L. Williamson, and P. J. Rasch, 1998: The National Center for Atmospheric Research Community Climate Model: CCM3. J. Climate, 11, 1131-1149.

Krueger, S. K., Q. A. Fu, K. N. Liou, and H. N. S. Chin, 1995: Improvements of an ice-phase microphysics parameterization for use in numerical simulations of tropical convection. J. Appl. Meteor., 34, 281-287.

Killing, Z. M., and C. S. Bretherton, 2004: Convective influence on the heat balance of the tropical tropopause layer: A cloud- resolving model study. J. Atmos. Sci., 61, 2919-2927.

Lin, Y. L., R. D. Parley, and H. D. Orville, 1983: Bulk parameterization of the snow field in a cloud model. J. Climate Appl. Meteor., 22, 1065-1092.

Ramanathan, V., R. D. Cess, E. F. Harrison, P. Minnis, B. R. Barkstrom, E. Ahmad, and D. Hartmann, 1989: Cloud-radiative forcing and climate: Results from the Earth Radiation Budget Experiment. Science, 243, 57-63.

Thuburn, J. and G. C. Craig, 2002: On the temperature structure of the tropical substratosphere. J. Geophys. Res., 107, 4017, doi:10.1029/2001JD000448.

Tompkins, A.M., and G. C. Craig, 1999: Sensitivity of tropical convection to sea surface temperature in the absence of large-scale flow. J. Climate, 12, 462-476.

Webster, P. J., and R. Lukas, 1442: TOGA COARE: The Coupled Ocean- Atmosphere Response Experiment. Bull. Amer. Meteor. Soc., 73, 1377- 1416.

Xu, K. M., T. Wong, B. A. Wielicki, L. Parker, Z. A. Eitzen, and M. Branson, 2007: Statistical analyses of satellite cloud object data from CERES. Part II: Tropical convective cloud objects during 1998 El Nino and evidence for s Fixed Anvil Temperature Hypothesis. J. Climate, 20, 819-842. ZHIMING KUANG

Department of Earth and Planetary Sciences, ami Division of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts

DENNIS L. HARTMANN

Department of Atmospheric Sciences, University of Washington, Seattle, Washington

(Manuscript received 22 December 2005, in final form 25 September 2006)

Corresponding author address: Zhiming Kuang, 20 Oxford St., Cambridge, MA 02138.

E-mail: kuang@fas.harvard.edu

Copyright American Meteorological Society May 15, 2007

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