ABSTRACT. A mesoscale model in a doubly periodic domain with specified sea surface ... of the evaporation and precipitation that occur in the climate system.
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Convective Organization, Tropical Cyclones and Climate Sensitivity Estimates. By Dennis L. Hartmann and Philip Regulski Department of Atmospheric Sciences University of Washington Seattle, Washington 98195
Submitted to Journal of Climate May 2005
Corresponding author address: Dennis L. Hartmann, Department of Atmospheric Sciences, University of Washington, Box 35640, Seattle, WA 98195.
2 ABSTRACT A mesoscale model in a doubly periodic domain with specified sea surface temperature (SST) is used to study tropical radiative-convective equilibrium states. It is shown that tropical mean relative humidity, cloud properties and implied climate sensitivity depend strongly on planetary rotation and the development of tropical cyclones in the model domain. Rotation leads to increased surface wind speeds, which speed up the hydrologic cycle and lead to an increase of atmospheric temperature. Tropical cyclones develop when uniform rotation is set to that of the Earth at 10˚N, if the model resolution is sufficient and the ambient vertical wind shear is not too great. The development of a tropical cyclone in the domain causes the precipitation and clouds to be organized by the synoptic and mesoscale flow. Precipitation intensity is increased, convective cloud area is decreased and average relative humidity in the free troposphere is decreased. Tropical cyclone development causes stronger sensitivity of the outgoing longwave radiation to surface temperature. The model results suggest that cloud and water vapor feedback processes in the tropics may be strongly sensitive to changes in the synoptic and mesoscale organization of the flow.
3 1. Introduction The role of clouds in climate sensitivity is believed to be one of the major uncertainties in projections of future climate in a CO2-warmed world (Cess et al., 1989; Cess et al., 1996; Houghton, 2001). Clouds and convection are important in climate sensitivity, both through their direct radiative effects and through their role in controlling the relative humidity in the troposphere, especially above the boundary layer. Approaches to the cloud feedback problem include estimation from observations, computation with numerical models, and validation of climate model behavior with observations. Estimation of the role of clouds in climate sensitivity using observations is difficult, since an analogy for climate change must be used, such as the annual cycle (Tsushima and Manabe, 2001), or El Niño cycles (Hartmann and Michelsen, 1993). Model estimates are dependent on approximations made in the models, and data comparisons have not yet been successful in reducing uncertainty in modeled climate sensitivity to the extent necessary (NRC, 2003). The tropics account for about half of the surface area of Earth and more than half of the evaporation and precipitation that occur in the climate system. The effects of clouds on absorbed solar radiation (SWI) and outgoing longwave radiation (OLR) are large in the tropics (Hartmann et al., 1992), and water vapor feedback is strongest there (Hallberg and Inamdar, 1993; Inamdar and Ramanathan, 1994). The water vapor greenhouse effect is so strong in the moist regions of the tropics that the removal of thermal energy to space by emission becomes inefficient, and over the warm oceans where convection moistens the upper troposphere the atmosphere seems to approach a condition of runaway greenhouse effect. Pierrehumbert(1995) has emphasized the
4 importance of dry, subsiding regions in the tropics for allowing energy to escape to space and preventing a runaway greenhouse effect. Ramanathan and Collins (1991) proposed that the sensitivity of convective cloud albedo to SST could control temperatures in the tropics, but this effect is only local and the net energetic effect of tropical convective clouds on the column energy balance is nearly neutral (Fu et al., 1992; Hartmann and Michelsen, 1993; Larson et al., 1999; Wallace, 1992). The radiative effect of clouds in the current climate seems to suppress local SST maxima, but not have a large effect the tropical mean energy balance (Hartmann et al., 2001). If marine boundary layer stratocumulus clouds are assumed to obey the empirically derived relationship between static stability and cloud fraction observed by Klein and Hartmann (1993), then a strong negative feedback can be produced in the tropics by marine boundary layer clouds (Larson et al., 1999; Miller, 1997). Larson and Hartmann (1999) found that even if tropical convective clouds are radiatively neutral, the fractional area occupied by convection can still be a strong control on tropical climate sensitivity because convection moistens the atmosphere. If the area of convection increases (decreases) with SST, then it would imply a water vapor feedback that is stronger (weaker) than implied by an assumption of fixed relative humidity. Lindzen et al. (2001) have presented an observational analysis suggesting that tropical convective anvils shrink in area as SST increases, and developed a simple model that produces very strong negative feedbacks and a stable climate. The observational inference of decreasing anvil cloud with SST has been questioned (Chambers et al., 2002a; Chambers et al., 2002b; Chou et al., 2002b; Hartmann and Michelsen, 2002a;
5 2002b; Lin et al., 2002; Lindzen et al., 2002), and the model parameters have been shown to be inconsistent with observations (Chou et al., 2002a; Fu et al., 2002). One can try to study the dependence of convective cloud area on SST by using models. To do this one needs an accurate model of cloud dynamics and thermodynamics and their interaction with the large-scale environment. A starting point is a radiativeconvective equilibrium calculation in which the interaction of convection with the largescale environment is explicitly calculated. Cloud-resolving models (CRM) can make important contributions to understanding the role of clouds in climate. Using a three dimensional CRM, Tompkins and Craig (1999a) found that convection is relatively insensitive to SST, in agreement with the two dimensional CRM studies of and Lau et al. (1994; 1993). Tompkins and Craig (1999b) also found that the microphysical processes are not sensitive to surface temperature – critical temperatures are merely shifted higher into the atmosphere in a warmer environment. As a result, cloud properties are insensitive to SST in their simulations. More recently Grabowski and collaborators (2000; 2002; 2003b; 2003a; Grabowski and Moncrieff, 2001) have used 2-D CRM domains that couple large-scale dynamics with small-scale convection to further investigate cloud microphysics impacts on tropical convection and its organization. Although still sensitive to microphysical and turbulent parameterizations, CRMs are appealing because of their ability to better resolve the spectrum of vertical motion and even simulate independent convective clouds. CRMs have clear advantages, but because of the cost of the computations, few threedimensional simulations have been conducted in domains large enough to capture the interactions between large-scale motions, mesoscale circulations and cloud-scale
6 convection that determine the equilibrium state of the tropical atmosphere. For instance, Grabowski et al. (2000a) ran a 2-month long simulation using a 2-D CRM with a horizontal domain of 4000 km which took over 15 days on a 64 processor Cray T3D computer. Larson and Hartmann (2003a; 2003b) (LHa,b) studied interactions among large and smaller scale dynamics, convection, radiation, and cloud microphysics by using a doubly periodic mesoscale model with parameterized convection. Though convection is parameterized, the model produces relationships between tropical radiation budget quantities and SST changes that are similar to those observed during El Niño events, and the simulations agree on many key points with the CRM studies of Tompkins and Craig (1999b) and Grabowski et al. (2000b). A key goal of LH was to investigate the sensitivity of cloud area to SST. They found that the high cloud fraction in the domain increased with SST, along with the average upper tropospheric humidity, which produced a strong positive water vapor feedback. LHb include sinusoidal varying SST gradients in the domain to simulate the Walker Circulation. LHb find a double-celled circulation that becomes more pronounced with greater SST ranges, a result matching the CRM used in Grabowski (2000a). They find that the energy budget of the model is more sensitive to the SST gradient than to the mean SST. Stronger SST gradients produced an increase in circulation, which increased the albedo of both the convective clouds and the boundary layer clouds in regions of subsidence. Increasing the average SST while keeping the SST gradient fixed produced a positive feedback, because the circulation slows down in a warmer climate through static stability increases (Knutson and Manabe, 1995). The present study increases the horizontal spatial resolutions used by LHa and
7 extends the work to cases in which rotation is added and tropical cyclones form. By varying SST and rotation, the effect of rotation on the tropical sensitivity implied by the model can be studied. Although modeling studies focusing on the tropics are accumulating rapidly, most do not include effects of rotation. Rotation induces organized circulation that may take the form of tropical cyclones. In the context of this study, tropical cyclones are defined as a low pressure weather system with a warm central core having an organized cyclonic circulation. It will be shown that this organization changes the distribution of temperature, cloud and water vapor in the model and gives a different relationship between SST and energy fluxes at the top of the atmosphere (TOA). Uncertainties in the convective microphysical parameterizations and other idealizations make the estimates of climate sensitivity derived from this model not directly applicability to the real world, but the sensitivity of these estimates to rotation and cyclone formation points out the potential importance of mesoscale and synoptic organization for climate sensitivity in the real world. The model is described in Section 2. Section 3 describes how the circulation in the model responds to SST, rotation and resolution. Section 4 describes how the hydrologic cycle in the model is affected by rotation and the presence of tropical cyclones. The response of cloud fraction and cloud temperature to SST and rotation are discussed in sections 5 and 6. The effects of rotation and associated circulation changes on implied climate sensitivity are discussed in Section 7.
8 2. Model and Experimental Design The Pennsylvania State University/National Center for Atmospheric Research Mesoscale Model (MM5) Version 2 is used for all the experiments. The MM5 is a nonhydrostatic, sigma-coordinate mesoscale model. A detailed description of this numerical model is found in Grell (1993). The MM5 is configured for non-hydrostatic simulation with 24 levels in the vertical, having finer level spacing in the boundary layer. The model includes the upper radiative boundary condition described in Klemp and Durran (1983) to avoid reflection of wave energy at the model top. The model physics include the boundary layer scheme described in Grenier and Bretherton (2001) and modified in McCaa (2001). The shallow convection scheme is described in Bretherton et al. (2004) and McCaa and Bretherton (2004). The Kain and Fritsch (1990) convective parameterization is used along with the cloud physics parameterization described in Reisner et al. (1998). The trigger function was changed in accordance with Su et al. (1999) to more realistically represent tropical convection. The model explicitly treats cloud water, cloud ice, rainwater, and snow. The radiation scheme is the Community Climate Model version 3 (CCM3) (Kiehl et al., 1996). The diurnal cycle in solar radiation is included, but the SST is fixed. A more complete description of the modeling procedure and the changes implemented to the original MM5 Version 2 can be found in LHa and Regulski (2004). Previous studies using the MM5 to simulate the tropics have shown that it can produce a reasonably realistic tropical weather and climate. Su et al. (1999) investigated the organization of tropical convection in the model. LHa showed that the cloud and
9 water vapor feedbacks in low-resolution, non-rotating simulations are in reasonable accord with estimates from observations. The experiments here use a model domain that is doubly periodic in the horizontal dimensions with uniform fixed sea surface temperature (SST). The model is run to radiative-convective equilibrium. The response of the equilibrium air temperature, humidity, clouds and radiation fluxes to changed SST is used to imply their possible role in climate sensitivity. The model includes a domain size of approximately 2000 km by 2000 km. A domain at least this large is required to represent evolving cloud clusters and their interaction with larger regions where convective heating can be balanced by clear-sky cooling. Model integrations are done with different horizontal spatial resolutions of 120km, 60km, 30km and 15km to test the sensitivity of the model results to resolution. Only a few integrations were done at 15km resolution, due to computer processing limitations. Pairs of integrations are performed with one having no rotation and the other a uniform rotation (f-plane) corresponding to 10˚N. Different combinations of resolution and rotation are run with different SSTs (297, 299, 301, 303, 305, 307ºK) and initial winds. Uniform initial winds of 0, 5, and 10ms-1 are applied to test the robustness of the results to initial conditions. It can take 30 days or more for the model to reach quasi-equilibrium. To ensure that averages representative of equilibrium are obtained, each of our simulations is run out to 180 days and only the last 120 days are used for analysis. Data are recorded every
10 6 hours. Radiation fields are taken every 30 minutes and averaged over 6-hour blocks.
3. Resolution, Rotation and Cloud Structure The natures of the cloud structures produced in the model under different conditions of model resolution, SST and rotation are discussed in this section. Without rotation, convection self-aggregates into separate regions of convection and subsidence within the domain for all simulated resolutions. Figure 1 shows an instantaneous map of OLR to illustrate the typical structure of a large-scale convective region with smallerscale convective elements embedded in it. As in Tompkins (2001), large-scale convective regions move both westward and eastward, and embedded within those regions are oppositely propagating convective elements. The small-scale organization of precipitation within the convective region becomes smaller in scale as the model resolution is increased. These results appear to support the hypothesis that convection is favored in regions that have been previously moistened because of convection-water vapor-radiation feedbacks (Bretherton and Blossey, 2004; Held et al., 1993; Tompkins, 2001). When rotation is included in the experiments, the structure of the convective organization depends on whether tropical cyclones form or not, which in turn depends on a combination of resolution, SST, and initial wind profiles. As spatial resolution is increased, tropical cyclones are more likely to form and their intensity increases. Tropical cyclones have a dramatic effect on the type of convective organization and the mean thermodynamic properties in the domain. The areas of convection are much more concentrated when a tropical cyclone is present and precipitation is more intense and
11 localized. Figs. 1 and 2 show typical maps of the structure of OLR and precipitation for non-rotating and rotating simulations, and illustrate the change in structure that occurs when cyclones form. Table 1 shows the average maximum wind speed and minimum sea level pressure in the domain for the last 120 days of the simulations where convection organized into a tropical cyclone. No tropical cyclone formation occurred for 120-km resolution. Increasing the grid resolution to 60 km allows for cyclone formation, although they are weak and can only be classified as “tropical storms.” At a resolution of 30-km, tropical cyclones reach higher intensities and can be considered Category-1 hurricanes on the Saffir-Simpson Scale. As resolution is increased to 15-km, the model results revealed a continued systematic increase in tropical cyclone intensity. Development of these storms takes place after 10-20 simulation days and storm strength oscillates with time over the course of the integration (not shown). Contrary to recent studies (Knutson and Tuleya, 1999; 2004), the model does not show increased intensity of tropical cyclones as SST is increased. Both the 15- and 30km resolutions show no trend in tropical cyclone intensity with increases in SST. In fact, the 60-km resolution simulations cease to form tropical cyclones when the SST is greater than 303 ºK. Emanuel (1988) has suggested on the basis of theoretical arguments that cyclone intensity should increase with SST. If we assume a fixed outflow temperature (Hartmann and Larson, 2002), then Emanuel’s (1988) model predicts a decrease in minimum sustainable central pressure from 900 to 850 hPa for an SST increase from 303 to 307K. In our 30 km integrations no significant change in average minimum pressure results
12 when this change is SST is made. Prediction of the intensity of tropical storms from first principles is complex and also involves the large-scale wind structure within which the storm is embedded (Emanuel et al., 2004; Holland, 1997). Pauluis and Held (2002a; 2002b) have investigated the entropy budget of convective systems and pointed out the importance of irreversible processes involving water in determining the maximum amount of work that can be produced by convection. Phase changes, diffusion of water vapor and dissipation of energy in falling raindrops are all important. The intensity of tropical storms and their dependence on SST is likely then to be sensitive to the details of how moist processes are treated in the model. The primary emphasis here is the potential implication of convective organization for climate sensitivity, and we will show that the development of tropical cyclones can have a strong impact on Earth’s exchange of energy with space. Whether tropical storm frequency or intensity will actually change significantly with climate will not be addressed here. Nonetheless, a brief consideration of simple formulas presented in Pauluis and Held (2002a) may suggest why tropical cyclone intensity is not sensitive to SST in these experiments. In a closed system in equilibrium, assuming all work is dissipated by friction, Pauluis and Held (2002a) derive the following equation for the work (W) generated by convection, as a function of the radiative cooling rate QR, and the temperatures at which the dissipation, Td, radiative cooling TR and surface heating Ts, occur.
T TR
Snf W = Td QR s Ts TR
(1)
13 The maximum work is extracted when the entropy production by non-frictional irreversible processes, Snf , is zero. In the tropics where the atmosphere contains large amounts of water vapor, most of the emission of thermal radiation to space originates in the atmosphere. If we assume that most of the emission comes from water vapor and the relative humidity distribution is fixed, then the radiative cooling of the atmosphere becomes almost independent of surface temperature. As Hartmann and Larson (2002) have suggested, as the atmosphere warms, the cloud and water vapor emitters move upward in the atmosphere and the emission temperature changes little. In this case the QR term in (1) becomes independent of temperature and so the maximum work that can be produced is only weakly dependent on surface temperature. Since the radiative cooling is not sensitive to surface temperature, we should expect that the precipitation and evaporation rates are not sensitive to SST. In the next section it will be shown that the precipitation rate becomes very insensitive to SST above about 300K, despite the fact that the surface saturation humidity increases about 7% for each degree of SST increase. The contribution of the temperature factor in (1) is a few percent per degree, if the radiative and dissipative temperatures are assumed constant. So to first order one can argue that the insensitivity of the cyclone intensity to SST is a consequence of the closed system and the inability of the model tropical atmosphere to export additional heat to space as the surface warms. The real Tropics are not a closed system and energy can be exported from the tropical atmosphere by transport to midlatitudes. Indeed, when we apply an artificial cooling to the atmosphere in the model, cyclone intensity is increased above the mean values listed in Table 1 (not shown).
14 Knutson and Tuleya (2004) summarize a large number of state-of-the-art numerical simulations and theoretical estimates that suggest tropical storm intensity will increase in a CO2-warmed world. Their consensus estimate is an 18% increase in precipitation rate near the storm center, a 14% increase in the central pressure depression and a 6% increase in the maximum surface wind speed before the end of the current century. The results presented herein suggest that an increase in tropical cyclone intensity or frequency could produce a negative climate feedback that is not currently incorporated into global climate models. 4.0 Rotation and the Hydrological Cycle A comparison of equivalent SSTs shows that air temperature profiles are warmer when rotation is included than when rotation is neglected (Figs. 3 and 4). Rotation warms the atmosphere for every resolution, whether a tropical cyclone is present or not. A possible explanation for the warming lies in the increasing intensity of the hydrological cycle. When rotation is added, the model boundary layer wind speed more than doubles and the evaporation increases by about 40%, irrespective of model resolution (Table 2). This suggests that the higher wind speeds cause increased evaporation that, in turn, leads to increased precipitation. The role of mesoscale systems in enhancing evaporation has been discussed by Esbensen and McPhaden (1996). Since releasing latent heat at a faster rate through increased precipitation must be balanced by increased atmospheric radiative cooling in order to achieve an energy balance, the atmosphere warms up when rotation is included. Between 297 and 303 K evaporation and precipitation increase with SST at the rate of 2.3% K-1 for the non-rotating case and 4.3% K-1 for the rotating cases, where a
15 difference of the 303K and 297K cases was used to compute these rates from the data in Table 3. Both are much less than the adiabatic rate computed from the ClausiusClapeyron relationship of 7% K-1 (Hartmann, 1994). Evaporation and precipitation can increase only at the rate at which radiative cooling of the atmosphere can remove the latent heating provided by precipitation. In the rotating case, the emission efficiency of the atmosphere is increased and precipitation can increase more rapidly with surface temperature. Both the mean precipitation rate and the sensitivity of precipitation rate to surface temperature are increased by more than 40% by the addition of rotation to the model (Table 3). It is interesting, however, that the rate of increase in the strength of the model hydrological cycle seems to slow down at the highest temperatures. This is likely because the increased water vapor in the atmosphere at higher temperatures makes the radiative cooling of the atmosphere less sensitive to SST. One can use a simplified aerodynamic drag law to show that the increased evaporation with rotation is associated with an increase in surface wind speed. Evaporative capacity of air is linearly dependent on wind speed U, the saturation specific humidity of air at anemometer level qa, and the relative humidity RH: Eair = * CDE * U * qa * (1-RH)
(2)
where is the density of air, and CDE the aerodynamic transfer coefficient for vapor (Hartmann, 1994). Table 4 shows the percentage change in each of these variables due to the addition of rotation for different SST values at 30-km resolution. Evaporation increases about 50% with the addition of rotation, while wind speed, relative humidity and saturation specific humidity in the air increase about 150%, 0%, and 8% respectively. Wind speed is the primary explanation for the increased evaporation. Because the
16 boundary layer scheme in the model uses a convective velocity in addition to the actual wind speed, the model evaporation is less sensitive to wind speed than (2) would suggest (Fairall et al., 1996).
5. Cloud Percentages, Liquid/Ice Amounts and Optical Depths Previous studies have shown that changes in the size of the convective area can alter the mean humidity and the radiation balance, even if convective clouds have little direct effect on the TOA radiation budget (Larson and Hartmann, 2003a; Larson et al., 1999). Thus, understanding how tropical cloud amounts will change with SST is critical in order to understand climate sensitivity. Cyclone formation in this model greatly changes the dependence of high cloud amount and average free-atmosphere relative humidity on SST. Rotation reduces the amount of high cloud and the rate at which it increases with SST, and it increases the amount of low cloud. Clouds are divided into three categories based on the International Satellite Cloud Climate Project (ISCCP) cloud categorization. ISCCP defines high clouds as existing above a pressure level of 440 hPa, medium clouds between the pressures 440 and 680 hPa, and low clouds at or below 680 hPa. In the model analysis, grid squares are considered cloud covered if the visible optical depth of the grid box exceeds 0.1. The optical depth is measured from the top of the model downward. Once the 0.1 optical depth threshold is reached, the cloud type is defined for that grid box. For this reason, low clouds may be obscured by high level clouds as in ISCCP. To remove some ambiguity, we also calculate low cloud percentages in regions free of high clouds. The average area of convection within the domain (defined by the cloud ice
17 threshold) increases with SST. Cloud coverage increases with SST are approximately 1.6, 1.6, and 2.1 % K-1 for the model resolutions of 120, 60, and 30-km, in close agreement with LHa. For the 30-km case without rotation, as the SST is increased from 297 ºK to 303 ºK high cloud amounts increase by 13% or about 2% K-1 (Table 5). The dependence of cloud area on SST in the non-rotating case is not sensitive to model resolution in the range from 30 to 120 km. Tropical cyclone formation has a significant effect on high cloud amounts. When resolution is increased and the model forms tropical cyclones, high cloud amounts are reduced and are much less sensitive to SST (Table 5). At 120-km resolution, cyclones do not form and the cloud fractions are similar to those shown in Table 5 for the non-rotating case at 30-km resolution. Cyclones dominate the area of deepest convection, and their structure does not vary much with SST, so that cloud properties are not sensitive to SST when cyclones form in the model. A significant increase in high cloud amount does occur when SST is raised to 305K and 307K. Fig. 4 shows the temperature increases from a base of 297 K. For the 307K case the warming extends across the tropical tropopause, and is associated with a large change in model behavior. While this case is interesting and may be important for understanding very warm climates, it is a subject of further study and we will not discuss it here. The resolution near the tropopause is probably not sufficient for this case. Tropical cyclones also play a major role in redistributing cloud liquid water content higher into the atmosphere (Fig. 5). When a cyclone is present cloud liquid water amounts are much higher from the top of the boundary layer to the freezing level.
18 Although high cloud area is reduced, average cloud ice amounts are not much changed by the cyclone. Low clouds play an important role in altering shortwave radiation budgets. Low cloud percentages are larger when convection organizes into a tropical cyclone (Table 5). In the non-rotating case the low cloud fraction increases with SST, but in the rotating case this does not occur. Because the boundary layer winds are stronger in the rotating case and the mechanical generation of turbulence is stronger, the boundary layer clouds are less constrained by the thermodynamic controls discussed in Larson et al. (1999).
6. Cloud Top Pressures and Temperatures Cloud top pressures and temperatures for low and high clouds at various SST values are shown in Table 6. Low clouds move downward to higher pressures and become much warmer as SST is increased as previously described in LHa. The thinning of the boundary layer and increasing low cloud top pressure is less pronounced for the rotating case. Hartmann and Larson (2002) proposed that the cloud top temperature of convective anvil clouds in the tropics should remain approximately constant as the surface temperature is increased. In this “Fixed Anvil Temperature Hypothesis” (FAT), it is asserted that the anvil clouds form where the temperature is such that clear sky cooling rate decreases precipitously with height and that this occurs at a fixed temperature because of the dependence of saturation vapor pressure on temperature. This hypothesis was tested by Hartmann and Larson (2002) using the non-rotating 120-km resolution version of this model. In the present work, we find that FAT holds for other resolutions
19 with or without rotation (Table 6). The cloud top pressure decreases with increasing SST, but the cloud top temperature remains about the same. Hartmann and Larson (2002) argue that the fixed convective cloud top temperature is dictated by the saturation vapor pressure dependence of the clear sky cooling rate. The high cloud temperature is constant within a few degrees, except for the rotating case at 307K, which is very different from the other cases in many respects, as previously mentioned.
7. Circulation, Relative Humidity, Radiation Budgets, and Climate Sensitivity The presence of a tropical cyclone shifts the model solution into a different convective regime with significantly different properties. High cloud amounts are reduced to about 20% when a cyclone is present, a reduction of 10-20%, with the larger reductions for higher SST (Table 5). Although the area of convection is decreased, the intensity of the updrafts within the cyclone increases the precipitation rate. The more rapid upward motion causes the saturation criterion to be reached more frequently when cyclones are present. The distribution of free-atmosphere relative humidity is affected by these changes. Fig. 6 shows the histogram of 500 hPa relative humidity with and without rotation at 30-km resolution for SST of 301K. For the non-rotating case the model produces a bimodal distribution with peaks around 20% and 75% relative humidity. This bimodal humidity distribution is similar to that often observed in the tropics (Brown and Zhang, 1997; Zhang et al., 2003). When a tropical cyclone develops in the model, the PDF of relative humidity becomes unimodal, with a large peak near 15-20% and with an attendant increase the occurrence of 100% relative humidity, indicating that the convection scheme has given way to grid cell saturation associated with strong vertical
20 velocity. The average relative humidity in the entire domain is reduced by the presence of the cyclone. The large-scale connection between convective regions where the atmosphere is heated and non-convective regions where it is cooled is important in determining the mean climate and its sensitivity to change. A fundamental question is whether the relative fraction of the tropics that is convective is sensitive to mean SST, and how this relates to large-scale, cloud-scale and microphysical processes. One way to explore the role of large-scale circulation is by examining the vertical motions. Using the cloud-ice threshold, we define grid-points as either convective or non-convective. Fig. 7 shows the vertical wind speed profiles for the 30-km resolution simulations with and without rotation for SSTs of 297 and 303K. As expected, regions defined by high clouds are regions where the average air motion is upward. As SST is increased, the vertical wind speed profiles of the regions with high clouds decrease in magnitude in the non-rotating case, a result that is independent of resolution. The mean vertical wind speeds of each region can be related by the equation: wmean = wcon · Acon + wnc · (1 – Acon)
(3)
where wcon and wnc are the average vertical velocities in regions with high clouds and without, and Acon is the area of the high cloud region. It is important to note that the vertical wind profiles in the mid-troposphere in the regions of downward motion are constrained by clear sky cooling rates and are not sensitive to SST or resolution. Applying conservation of mass (assuming density is constant at each pressure level) requires the mean vertical velocity over the domain to be zero. wcon · Acon + wnc · (1 – Acon) = 0
(4)
21 Since the vertical wind speed profiles remain equal in the regions free of high clouds while the vertical velocity in the regions with high clouds decreases as mean SST is increased, (4) implies that as wcon decreases, the area of convection increases. Without rotation, as SST increases, the magnitude of the upward vertical velocity profiles decrease, implying that the area of convection has increased, which results in increased mean upper tropospheric RH. Therefore RH in the upper troposphere is sensitive to SST when rotation is neglected (Table 7). The impact of tropical cyclones on the domain is to create upward vertical wind speeds that are stronger, reduce the fractional area occupied by convective clouds and to reduce the relative humidity above the boundary layer. Fig. 8 shows that relative humidity in the free troposphere increases with SST in the non-rotating case, and that the presence of tropical cyclones both reduces the relative humidity in the free troposphere and its sensitivity to SST (see also Table 7). The sensitivity of the climate can be inferred indirectly by studying the sensitivity of OLR, net absorbed shortwave radiation, and net radiation to changes to SST. The sensitivity of OLR to surface temperature (dOLR/dTs) changes sign when a tropical cyclone is present (Table 8). Without rotation, values are -0.6 and -1.1 W m-2 K-1 (60and 30-km resolutions, respectively), compared to +1.6, +2.1 and +1.3 W m-2 K-1 (60-, 30- and 15-km resolutions) with cyclone formation. The positive values of dOLR/dTs and dOLRCS/dTs associated with tropical cyclone development imply more longwave radiation is escaping to space due to the drier upper atmosphere. The sensitivity of the total greenhouse effect to SST is reduced by approximately half by the addition of
22 rotation, from 7.2 to 4.0 W m-2 K-1 for the 30-km resolution simulations, implying a more stable climate system. The sensitivity of longwave cloud forcing to SST (dC(LW)/dTs) is reduced by the presence of a tropical cyclone from 1.7 W/m2 K-1 to 0.7 W/m2 K-1 for the 30-km resolution case, primarily because of the large reduction in high cloud area and its reduced sensitivity to temperature when cyclones are present (Table 8). The sensitivity of absorbed shortwave radiation (SWI) to surface temperature (dSWI/dTs) also changes sign from negative to positive when a tropical cyclone is present (Table 9). This is a result of two competing effects. First, reduced high cloud amounts (10-20%) allow more SW radiation into the system, even though these high clouds are much more reflective. Average high cloud albedos increase from about 25% to 37% as a result of cyclone development (not shown), while fractional areas are reduced from about 35% to 20% (Table 5) . Second, the low cloud percentage in regions free of high cloud increases with a tropical cyclone. This reflects more SW radiation back to space but it is secondary to the high cloud effect. The changes in SW and LW cloud feedback induced by cyclone formation offset each other. The overall effect of tropical cyclones on implied climate sensitivity in these experiments is a very small reduction in sensitivity (Table 10). A large negative clearsky feedback is nearly offset by a large positive cloud feedback. Most of the positive cloud feedback comes from the reduced solar reflection resulting from reduced high cloud area.
23
8. Summary and Conclusion We have used radiative-convective equilibrium calculations with a doubly periodic regional climate model to investigate the response of air temperature, cloud and water vapor to the inclusion of rotation and the development of organized circulations in the model. By varying SST, rotation, and resolution, we investigated how the formation of tropical cyclones affects the climate sensitivity implied by the model. Simulations with fixed SST predict that the inclusion of rotation causes an increase in the intensity of the hydrological cycle that results in an increase in air temperature. The heating stems from an increase in precipitation and evaporation rates that is associated with increased surface wind speeds. The model results show that without rotation high cloud amount increases with SST. The inclusion of rotation, which allows for tropical cyclone formation at the higher resolutions (60-, 30- and 15-km) reduces high cloud amounts and makes them less sensitive to changes in SST. Including rotation alters the convective organization within the model. As predicted by Hartmann and Larson (2002), high cloud top temperature is not sensitive to rotation, mean SST, or the horizontal resolution of the model. Greater vertical resolution near the model’s upper boundary is necessary to test what happens when the convective layer reaches the tropopause, which may occur when the SST is very high. Both high and low cloud coverage is less sensitive to SST when rotation is included. Other properties such as humidity, cloud water, cloud ice, cloud heights and temperatures are also affected by rotation. While this is a simple experiment, it suggests
24 that mean air temperature and humidity can be affected by a reorganization of circulation, particularly if it changes the mean wind speed near the surface. If cyclone frequency or intensity increase in a warmed climate, the present results suggest that a negative climate feedback will also accompany the increased tropical storm activity. Due to smaller areas of convection, the upper troposphere RH is drier when a tropical cyclone is present. Tropical cyclones stabilize the model climate by creating a more efficient loss of OLR and reducing the greenhouse effect, although this effect is moderated by a positive shortwave feedback. These results suggest that to get climate sensitivity correct one must have a good simulation of the organization of convection on synoptic and meso scales, including the sensitivity of tropical cyclone development to changing climate. Although our simulations using the MM5 depend on the Kain-Fritsch cumulus parameterization scheme, we believe they provide a useful indication of the role rotation and synoptic organization can play in climate sensitivity. Realistic interactions among dynamics, convection, radiation, and cloud microphysics are included and many basic model behaviors agree well with observational studies and cloud-resolving models. Although our results point to the importance of convective organization for sensitivity, we note these simulations were done for a closed domain with constant SST and using a Coriolis parameter held constant throughout the domain. Future studies where these constraints are relaxed are needed.
Acknowledgments. We thank Kristin Larson and Marc Michelsen for assistance and advice. This work was supported by the Climate Dynamics Program, Atmospheric
25 Sciences Division, National Science Foundation under Grants ATM-9873691 and ATM0409075.
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34 Table 1. Average maximum wind speed (m s-1) and average minimum pressure (hPa) for simulations with rotation and with different model resolutions, SSTs and initial wind speeds. An entry that is marked with a NO means that tropical cyclone formation did not occur.
120-km Resolution 5 m/s
297 NO/996
299 NO/996
301 NO
303 NO/997
307
297
299
301
307
24.3/987
22.2/988
18.4/988
303 NO/998 NO/997 20.3/992 21.1/989
60-km Resolution 10 m/s 5 m/s 0 m/s -5 m/s
30-km Resolution 297 10 m/s 5 m/s 31.8/982
299
301
33.8/981
31.3/981
303 31.7/981 33.4/980
NO/997
305
307
30.1/982
32.8/981
15-km Resolution 297 5 m/s
299 41.0/971
301
303 40.3/975
307
35 Table 2. Hydrological cycle variables for the model simulations with mean SST of 297 ºK (initial wind speed profiles are 5 m/s for all runs). Boundary layer wind speed is averaged over the lowest three sigma levels. Evaporation and precipitation values are taken at the sea surface.
SST 297 ºK Rotation OFF
Resolution (km)
Rotation ON
120 60 30 Resolution (km) 120 60 30
Boundary Layer Wind Speed (m/s) 1.3 1.6 1.8 Boundary Layer Wind Speed (m/s) 4.0 4.9 4.5
Evaporation (mm/day)
Precipitation (mm/day)
2.5 2.5 2.6 Evaporation (mm/day)
2.5 2.7 2.9 Precipitation (mm/day)
3.3 3.7 3.6
3.3 3.9 3.8
36 Table 3. Hydrological cycle variables for the 30-km resolution model simulations (initial wind speed profiles are 5 m/s for all runs). Boundary layer wind speed is averaged over the lowest three sigma levels. Evaporation and precipitation values are taken at the sea surface.
Rotation OFF
SST (ºK)
Rotation ON
297 299 301 303 305 307 SST (ºK) 297 299 301 303 305 307
Boundary Layer Wind Speed (m/s) 1.8 1.8 1.8 1.6 1.8 1.5 Boundary Layer Wind Speed (m/s) 4.5 4.6 4.6 4.7 4.6 4.6
Evaporation (mm/day)
Precipitation (mm/day)
2.6 2.7 3.0 3.1 3.4 3.5 Evaporation (mm/day)
2.9 2.9 3.1 3.2 3.5 3.5 Precipitation (mm/day)
3.6 4.0 4.3 4.7 5.0 4.6
3.8 3.9 4.5 4.9 5.0 4.6
37 Table 4. Percent change to evaporation (E), wind speed (u), sub-saturation (1-RH), and saturation specific humidity (qa) that result from the addition of rotation to the 30 km simulations. is calculated by subtracting the values of the non-rotating model from the values that include rotation, which is then divided by the non-rotating values to obtain percent changes. SST (K) 297 299 301 303 305 307
E E 38 48 43 52 47 31
u u 150 156 156 194 156 207
(1-RH) (1-RH) -1 0 0 2 2 5
qa* qa * 9 6 8 5 5 6
38 Table 5. Percentages of cloudy and clear sky regions for the 30-km resolution simulations with and without rotation. The SST values used for each run are listed to the left of the table. All initial wind profiles are 5 m/s. Values for low clouds have two values. The first value gives percent low cloud coverage. The second value, enclosed in parenthesis, is the percentage of low cloudiness in regions free of high clouds.
Rotation Off 297K 299K 301K 303K 305K 307K Rotation On 297K 299K 301K 303K 305K 307K
High cloud
Low cloud
Clear Sky
28 35 36 41 41 46
25 (35) 27 (42) 35 (54) 30 (51) 35 (60) 27 (50)
46 38 29 29 24 28
18 19 19 21 24 38
40 (49) 42 (52) 42 (52) 42 (53) 41 (54) 37 (60)
41 38 39 36 35 25
39 Table 6. Cloud top pressures and temperatures for the 30-km model simulations.
Rotation Off 297K 299K 301K 303K 305K 307K Rotation On 297K 299K 301K 303K 305K 307K
Low Cloud Pressure Temperature (mb) (K) 784 279 798 283 813 286 829 290 833 293 842 296 795 800 798 802 807 828
282 285 287 290 293 299
High Cloud Pressure Temperature (mb) (K) 168 199 157 195 139 198 131 200 115 200 102 203 161 145 128 107 92 95
201 203 203 201 205 214
40 Table 7. Relative humidity percentages above the inversion for all of the 30-km resolution simulations. Rotation OFF SST (K) RH above inversion 297 33.9 299 41.2 301 44.1 303 50.7 305 48.7 307 53.4 Rotation ON SST (K) RH above inversion 297 26.7 299 27.2 301 29.1 303 28.2 305 30.6 307 42.0
41 Table 8. The sensitivity of longwave radiative energy balance components to SST for model equilibrium states. The units on all the quantities are W m-2 K-1. Subscript CS indicates a clear-sky value. OLR = outgoing longwave radiation at the top of the atmosphere, G = total greenhouse effect of the atmosphere = Ts4 – OLR, Ga = clear atmosphere greenhouse effect = Ts4 – OLRCS, C(LW) = longwave forcing by clouds = OLRCS – OLR. Rotation OFF dOLR dTs dOLRcs dTs dG dTs dGa dTs dC(LW) dTs Rotation ON dOLR dTs dOLRcs dTs dG dTs dGa dTs dC(LW) dTs
60-km -0.6
30-km -1.1
0.5
0.7
6.7
7.2
5.6
5.5
1.1
1.7
60-km 1.6
30-km 2.1
15-km 1.3
2.3
2.8
1.8
3.0
4.0
4.9
2.5
3.3
4.4
0.5
0.7
0.5
42 Table 9. The sensitivity of shortwave radiative energy balance components to SST for model equilibria. The units on all the quantities are W m-2 K-1. Subscript CS indicates a clear-sky value. SWI = absorbed solar radiation, C(SW) = shortwave cloud forcing = SWIcs – SWI. Rotation OFF dSWI dTs dSWIcs dTs dC(SW) dTs Rotation ON dSWI dTs dSWIcs dTs dC(SW) dTs
60-km -0.8
30-km -1.1
0.0
0.0
-0.8
-1.1
60-km 0.3
30-km 1.7
15-km 1.1
0.0
0.0
0.0
0.3
1.7
1.1
43 Table 10. The sensitivity of net radiation energy balance components to SST for the model equilibria. The units on all the quantities are W m-2 K-1. Subscript cs indicates a clear-sky value. R = net radiation at the top of the atmosphere, SWI = absorbed solar radiation, C(LW) = longwave cloud forcing = OLRcs - OLR, C(SW) = shortwave cloud forcing = SWIcs - SWI. Rotation OFF dR dTs dRcs dTs dC(LW) + dC(SW) dTs dTs Rotation ON dR dTs dRcs dTs dC(LW) + dC(SW) dTs dTs
60-km -0.2
30-km 0.0
-0.5
-0.7
0.3
0.6
60-km -1.3
30-km -0.4
15-km -0.2
-2.3
-2.8
-1.8
0.8
2.4
1.6
44 Figure Captions: Fig. 1 Contour map of OLR for non-rotating (a) and rotating (b) cases with 30km resolution and SST of 297K at day 145. Contours go from 100 to 300 W m-2 with an interval of 20 W m-2. Fig. 2. Same as Fig. 1. except precipitation rate with a contour interval of 5 mm day-1. The maximum in a) is 47 and in b) is 71 mm day-1. Fig. 3. Troposphere temperature profiles for 30-km resolution simulations with SSTs of 297 and 303 ºK respectively. Circles indicate non-rotating and X’s represent rotating cases. Fig. 4. Atmospheric temperature change profiles resulting from increasing the SST from a base of 297 K for simulations with rotation, and for 60- and 30-km resolutions. Two profiles are plotted for the 60-km Res.- 303-297 K cases and 30-km Res. 303-297 K cases to account for two different initial wind profiles of 5 m/s and 10 m/s. (the 60-km Res. 297 K - 10 m/s initial wind case does not form a cyclone and the warming above the inversion is less than that of the case that does form a cyclone.). Figure 5. Vertical profiles of cloud water and cloud ice (g kg-1) for the non-rotating (left) and rotating (right), 30-km resolution simulations for SSTs of 297 (dashed line) and 303 K (solid line). Figure 6. Histograms of relative humidity at 500hPa for 30-km resolution at 301K for non-rotating case and rotating case, for which a cyclone formed. Figure 7. Vertical wind speed profiles for the 30-km model simulations. The profiles of the simulations that included a tropical cyclone are overlaid with squares, and
45 simulations without tropical cyclone development are overlaid with diamonds. Two SSTs are shown. SSTs of 297 ºK are denoted by solid lines and SSTs of 303 ºK are denoted by dashed lines. Fig. 8. Relative humidity profiles for the 30-km model simulations. The profiles of the simulations that included a tropical cyclone are overlaid with squares, and simulations without tropical cyclone development are overlaid with diamonds. Two SSTs are shown. SSTs of 297 ºK are denoted by solid lines and SSTs of 303 ºK are denoted by dashed lines.
46
a)
b)
Fig. 1 Contour map of OLR for non-rotating (a) and rotating (b) cases with 30km resolution and SST of 297K at day 145. Contours go from 100 to 300 W m-2 with an interval of 20 W m-2.
47
a)
b)
Fig. 2. Same as Fig. 1. except precipitation rate with a contour interval of 5 mm day-1. The maximum in a) is 47 and in b) is 71 mm day-1.
48
Fig. 3. Troposphere temperature profiles for 30-km resolution simulations with SSTs of 297 and 303 ºK respectively. Circles indicate non-rotating and X’s represent rotating cases.
49
Fig. 4. Atmospheric temperature change profiles resulting from increasing the SST from a base of 297 K for simulations with rotation, and for 60- and 30-km resolutions. Two profiles are plotted for the 60-km Res.- 303-297 K cases and 30-km Res. - 303-297 K cases to account for two different initial wind profiles of 5 m/s and 10 m/s. (the 60-km Res. 297 K - 10 m/s initial wind case does not form a cyclone and the warming above the inversion is less than that of the case that does form a cyclone.).
50
Figure 5. Vertical profiles of cloud water and cloud ice (g kg-1) for the non-rotating (left) and rotating (right), 30-km resolution simulations for SSTs of 297 (dashed line) and 303 K (solid line).
51
Figure 6. Histograms of relative humidity at 500hPa for 30-km resolution at 301K for non-rotating case and rotating case, for which a cyclone formed.
52
Figure 7. Vertical wind speed profiles for the 30-km model simulations. The profiles of the simulations that included a tropical cyclone are overlaid with squares, and simulations without tropical cyclone development are overlaid with diamonds. Two SSTs are shown. SSTs of 297 ºK are denoted by solid lines and SSTs of 303 ºK are denoted by dashed lines.
53
Fig. 8. Relative humidity profiles for the 30-km model simulations. The profiles of the simulations that included a tropical cyclone are overlaid with squares, and simulations without tropical cyclone development are overlaid with diamonds. Two SSTs are shown. SSTs of 297 ºK are denoted by solid lines and SSTs of 303 ºK are denoted by dashed lines.
