The effects of stratospheric cooling and sea surface warming on tropical cyclone (TC) potential intensity (PI) are explored using an axisymmetric cloud-resolving model run to radiative–convective equilibrium (RCE). Almost all observationally constrained datasets show that the tropical lower stratosphere has cooled over the past few decades. Such cooling may affect PI by modifying the storm's outflow temperature, which together with the sea surface temperature (SST) determines the thermal efficiency in PI theory. Results show that cooling near and above the model tropopause (∼90 hPa), with fixed SST, increases the PI at a rate of 1 m s−1 per degree of cooling. Most of this trend comes from a large increase in the thermal efficiency component of PI as the stratosphere cools. Sea surface warming (with fixed stratospheric temperature) increases the PI by roughly twice as much per degree, at a rate of about 2 m s−1 K−1. Under increasing SST, most of the PI trend comes from large changes in the air–sea thermodynamic disequilibrium. The predicted outflow temperature shows no trend in response to SST increase; however, the outflow height increases substantially. Under stratospheric cooling, the outflow temperature decreases and at the same rate as the imposed cooling. These results have considerable implications for global PI trends in response to climate change. Tropical oceans have warmed by about 0.15 K decade−1 since the 1970s, but the stratosphere has cooled anywhere from 0.3 to over 1 K decade−1, depending on the dataset. Therefore, global PI trends in recent decades appear to have been driven more by stratospheric cooling than by surface warming.
The globally averaged intensity of tropical cyclones (TCs) is projected to increase under anthropogenic climate change (Knutson et al. 2010), with a shift toward stronger storms. This is a robust result from global climate model simulations and theoretical studies. Historical TC intensity trends are more ambiguous due to various data inhomogeneities and relatively short observational records, though there is some evidence to suggest a positive trend may have already occurred in the intensities of the strongest TCs (Elsner et al. 2008).
TC potential intensity (PI; Emanuel 1986; Bister and Emanuel 1998) is the theoretical upper limit of the wind speed of a TC given sea surface temperature (SST) and profiles of atmospheric temperature and humidity. PI is expected to increase in a warmer climate (e.g., Emanuel 1987), with trends having significant spatial variability due to regional differences in SST trends (e.g., Vecchi and Soden 2007). While PI has been challenged on theoretical grounds (e.g., Smith et al. 2008; Montgomery et al. 2009), to date very few alternative theories have been put forward that depend solely on properties of the local thermodynamic environment [Holland (1997) is one exception]. PI has been shown to provide a reasonable estimate of steady-state TC intensity in axisymmetric models (e.g., Hakim 2011), and it has also passed some observational tests (e.g., Wing et al. 2007). PI continues to provide a useful quantitative metric in assessing climate change impacts on TCs (e.g., Vecchi and Soden 2007; Ramsay and Sobel 2011; Emanuel et al. 2013; Vecchi et al. 2013).
Previous studies have focused mostly on the role of SST in driving observed and simulated TC intensity metrics. However, according to extant theory (Emanuel 1986; Bister and Emanuel 1998), SST is only one of several parameters that determine PI, the others being the so-called outflow temperature, which is the entropy-weighted mean temperature of the TC outflow as it extends to large radii, and the enthalpy difference between the sea surface and the air directly above it. While the temperature of the ambient tropopause is often used as a proxy for outflow temperature, recent work suggests it should be seen more as a lower limit because a significant portion of the outflow occurs below the tropopause (e.g., Emanuel and Rotunno 2011).
The cooling of the atmosphere near and above the tropopause should result in a decrease in outflow temperature and consequently an increase in PI (all other PI-relevant parameters being equal). Emanuel (2010a) suggested that such cooling has played an important role in driving the strong upward trends in PI for the tropical North Atlantic basin since about 1980. The cooling of the tropical tropopause over the North Atlantic has been more pronounced than in many other parts of the world, according to some reanalyses and satellite data, resulting in an amplified PI trend there (Emanuel et al. 2013). Vecchi et al. (2013) showed that stratospheric temperature trends at 70 hPa and above had a negligible effect on tropical-mean PI, while trends between 300 and 100 hPa had a much larger effect. Both Emanuel et al. (2013) and Vecchi et al. (2013) agree that the excessive cooling trends in the National Centers for Environmental Prediction (NCEP) reanalysis between about 300 and 100 hPa over the past few decades are likely to be spurious, and so PI trends derived from NCEP should be treated with caution.
Almost all observational and reanalyses data indicate that the tropical stratosphere has cooled over the past few decades (e.g., Lanzante et al. 2003; Thompson and Solomon 2005; Cordero and Forster 2006; Sherwood et al. 2008; Randel et al. 2009; Solomon et al. 2012; Emanuel et al. 2013; Vecchi et al. 2013). While this cooling trend appears to be a robust feature, including in global climate model projections (e.g., Cordero and Forster 2006), the exact mechanisms behind such cooling are uncertain. The wide spread in stratospheric cooling trends, including the apparently spurious trend in NCEP, has led to large uncertainties in past PI trends. There is also reduced confidence in trends derived from GCMs due to their inadequate representation of stratospheric processes (e.g., Emanuel et al. 2013; Vecchi et al. 2013).
In the current study, the impact of tropical stratospheric cooling on TC intensity is quantified using an axisymmetric cloud model (CM1; Bryan and Fritsch 2002; Bryan and Rotunno 2009) run with idealized external forcings to a state of radiative–convective equilibrium (RCE), as described in the next section. The broad approach here is similar to Nolan et al. (2007), but their focus was on TC genesis and its sensitivity to various external forcings in RCE, and they used a three-dimensional model.
This study adds to a growing body of recent research on the behavior of TCs in statistical equilibrium (e.g., Hakim 2011, 2013; Brown and Hakim 2013; Chavas and Emanuel 2012) and allows for a relatively direct measure of PI change under stratospheric cooling: bridging the gap between estimates of PI derived from observations and GCM data, on the one hand, and more qualitative theoretically based arguments on the other.
All simulations are carried out on the nonhydrostatic cloud model of Bryan and Fritsch (2002; CM1 v15). The axisymmetric mode of the model, used here, is configured following Rotunno and Emanuel (1987), although with several notable improvements including better conservation of mass and energy in reversible saturated conditions. The model has been used to study various properties of axisymmetric TCs (e.g., Hakim 2011; Bryan 2012; Rotunno and Bryan 2012; Persing et al. 2013) and is described in detail in Bryan and Rotunno (2009).
Sensible and latent heat fluxes are computed here using standard bulk aerodynamic formulae, with constant values of surface exchange coefficients for enthalpy Ck (set to 1.2 × 10−3) and momentum Cd (set to 2.4 × 10−3). Turbulent motions are parameterized using a Smagorinsky-type scheme, in which the horizontal and vertical eddy viscosities depend on prescribed horizontal and vertical length scales. For the present study, the horizontal length scale lh is set to 1000 m and the vertical length scale lυ is set to 100 m. These values have been shown to produce a reasonable agreement with observations of intense tropical cyclones (Bryan 2012).
The model domain is 25 km deep and extends radially out to 1500 km. The horizontal grid spacing is 2 km, and the vertical grid is stretched with the lowest model level at 30 m, increasing gradually to a constant grid spacing of 500 m above 6.5 km. A Rayleigh damping zone is introduced above 20 km. Precipitation and moist processes are parameterized by the National Aeronautics and Space Administration (NASA)–Goddard version of the LFO scheme. The Coriolis parameter is set to 5 × 10−5 s−1. Dissipative heating, which results in more intense TCs (and which also is an important term for energy conservation), is included using assumptions similar to those in Bister and Emanuel (1998). The initial temperature and moisture profiles are characteristic of the July–October hurricane season over the tropical North Atlantic (Dunion and Marron 2008). The model is initialized with a broad weak vortex, following Rotunno and Emanuel (1987). The sea surface temperature is fixed at 29°C, except for sensitivity tests.
A very simple radiation scheme is implemented in which the tropospheric cooling rate is fixed, while the stratospheric temperature is relaxed back to a specified value such that the profile is constrained to be close to isothermal. This approach is based on the three-dimensional RCE simulations reported in Pauluis and Garner (2006). Specifically, the cooling rate is given by
where Tstrat is the specified stratospheric (isothermal) temperature, which varies from 200 to 192 K. While this approach is admittedly crude, Hakim (2011) showed that for axisymmetric TCs in RCE, a fixed radiative cooling profile is a good approximation to solutions with fully interactive radiation.
PI is computed following Bister and Emanuel (1998, 2002), with dissipative heating switched on. (The FORTRAN code can be obtained here ftp://texmex.mit.edu/pub/emanuel/TCMAX.) The environmental temperature and moisture profiles used to calculate the PI are taken from the simulations, being spatially averaged between 500 and 1000 km and temporally averaged between days 40 and 120. Parcels are assumed to rise pseudoadiabatically. The ratio of surface exchange coefficients (Ck/Cd) is set to 0.6. Using a value of 0.5, as in the axisymmetric simulations, resulted in a somewhat lower PI (∼10%), though the sensitivities of PI to changes in SST and stratospheric temperature were about the same.
a. The steady-state tropical cyclone
After an initial spinup period of about a day, the vortex in the control simulation (SST = 29°C; Tstrat = 196 K) rapidly intensifies to 107 m s−1 by day 3. Simulations starting from a state of rest yielded similar results (not shown); however, the spinup period was longer, as demonstrated by Hakim (2011). The radial inflow, which is zero to begin with, increases quickly starting at about day 2 and acts to import large values of angular momentum radially inward. The maximum intensity reaches a pseudosteady state during days 4–10; however, during this time, the radius of maximum wind (RMW) continues to expand out to 50 km.
A state of RCE is attained after about 40 days, which is the time scale for most variables to reach a statistically steady state in the far field of the domain. Unless stated otherwise, all quantities in the results that follow should be taken to represent the RCE state (i.e., time averages between days 40 and 120).
For the control simulation the steady-state maximum intensity is 96.7 m s−1; however, the instantaneous maximum wind, output by the model every 6 h, is highly variable with a standard deviation of 12.4 m s−1 (Fig. 1). The steady-state maximum intensity is the same as the mean maximum intensity of the transient storm (i.e., from days 4 to 10). In contrast, Hakim (2011) found a considerably weaker steady-state vortex—by a factor of about ½—compared to his “superintense” storm reported at day 12. The largely different set of model parameters used in the current study, including different mixing lengths for turbulence, a much higher SST (29°C here vs 26.3°C), and a different radiation scheme, make such one-to-one comparisons with Hakim (2011) difficult.
b. RCE environments
Figure 2 shows equilibrium temperature profiles for the stratospheric cooling simulations (Fig. 2a) and sea surface warming simulations (Fig. 2b). The large-scale environment, taken to be the radial average between 500 and 1000 km, is characterized by mean subsidence on the order of a fraction of a centimeter per second and episodic bursts of congestus-type convection reaching up to 6 km. Compared to the transient phase environment during days 4–10, in which the storm reached a pseudosteady state in intensity, the RCE environment is more stable in the mid-to-upper troposphere (not shown). This is consistent with the lack of convection above 6 km in the far field of the domain after about 40 days.
While choosing an appropriate spatial scale to define the “environment” is admittedly subjective, the RCE temperature profile from the control run is in good agreement with an observed tropical-mean profile derived from the Southern Hemisphere Additional Ozonesonde (SHADOZ) data archive (Thompson et al. 2003) for the years 1998–2006 (Fig. 2), indicating that the RCE state is not too far from the time-mean tropical atmosphere. The mean environmental wind at 10 m is 5 m s−1, which is also a reasonable value for the tropics.
One important caveat is that the low-level wind field at large radii tends to increase with the decreasing radius, despite the environmental domain being well removed from the inner-core peak winds. This behavior is perhaps not surprising given the axisymmetric geometry of the model. Recent work by Chavas and Emanuel (2012) suggests that the size of the domain may act to artificially constrain the size of the steady-state vortex. Hakim (2011) also found that the equilibrium storm was significantly larger for a large domain size of 8000 km, though the steady-state intensity was similar to that obtained using a 1500-km domain. To test how serious this issue may be, a limited set of simulations was conducted in which the size of the domain was doubled (i.e., the outer wall was placed at 3000 km). The main differences observed in these simulations were that the storms took longer to reach statistical equilibrium (∼60 days instead of ∼40 days), particularly their size variables—and their steady-state maximum intensities were on average 5% higher. However, the sensitivity of steady-state maximum intensity to the imposed temperature of the stratosphere remained roughly the same.
The cold-point tropopause in the control run (SST = 29°C; Tstrat = 196 K) is at 17.25 km, which is roughly the same height as the observed cold-point tropopause from the SHADOZ data (Fig. 2). The tropopause height in the stratospheric cooling simulations shows some sensitivity to the imposed temperature, ranging from 16.75 (Tstrat = 200 K) to 17.75 km (Tstrat = 192 K), though this range is somewhat constrained by the 500-m vertical grid spacing near the tropopause.
The sea surface warming simulations indicate that the tropopause height is much more sensitive to changes in SST and corresponding tropospheric lapse rates, ranging from 16.25 (SST = 27°C) to 18.75 km (SST = 31°C). The mean rate of change is about 600 m °C−1. The predicted cold-point temperature is roughly 193 K for all SSTs: about 3 K lower than the imposed temperature of 196 K. The relatively stable tropopause temperature should not be surprising given that the stratospheric temperature is relaxed back to the same value.
Temperature changes in the mid-to-upper troposphere show an amplified response compared with the surface warming (Fig. 2a), in agreement with observations of the tropical-mean temperature variability and GCM output (e.g., Santer et al. 1996; Hurrell and Trenberth 1998; Fu et al. 2004; Santer et al. 2005; Fu et al. 2011). The moist adiabatic warming of the free troposphere in response to SST changes acts to reduce the potential intensity trend compared to, say, a change in relative SST—where the free tropospheric temperature remains relatively fixed despite a change in SST over a limited domain (e.g., Vecchi and Soden 2007; Ramsay and Sobel 2011).
c. Changes in potential intensity: sea surface warming versus stratospheric cooling
The sensitivities of the mean maximum wind speed of the vortex (at the level of maximum wind) to changes in SST and Tstrat are shown in Fig. 3. As the SST is increased, the maximum wind speed responds at a rate of 2.5 m s−1 °C−1. This sensitivity is larger than some of the previous SST–PI relationships obtained using single-column models [e.g., 2 m s−1 °C−1 in Emanuel (2010b); 1.4 m s−1 °C−1 in Ramsay and Sobel (2011)], as well as from GCM output comparing tropical-mean PI change to tropical-mean SST change (Vecchi and Soden 2007).
The effect of stratospheric cooling on the steady-state intensity is less than half the impact of surface warming (per degree), with a slope of −1 m s−1 K−1. This trend is almost entirely due to temperature changes occurring at and above the ambient tropopause (∼90 hPa; Fig. 2a) because the tropospheric temperature profiles remain more or less fixed up to the tropopause. Recent work by Vecchi et al. (2013) suggests that PI is mostly sensitive to temperature changes between 300 and 100 hPa, with temperatures at and above 70 hPa having a negligible effect, while results here suggest a sensitivity of PI to temperature changes above ∼90 hPa.
For comparison with the maximum winds explicitly computed by the model, the actual PI for each simulation was also computed (Fig. 4). The temperature profiles used to calculate the PI are the same as in Fig. 2, along with their corresponding mixing ratio profiles. Compared to the axisymmetric model, the PI shows a somewhat lower sensitivity to changes in SST, with a slope of 1.8 m s−1 °C−1. The sensitivity of PI to Tstrat matches the model, with a slope of −1 m s−1 K−1. Both the modeled maximum wind speeds and the PI calculations indicate that a 1° increase in SST has about the same effect as a 2° decrease at altitudes near and above the ambient tropopause (here ∼90 hPa).
Given that PI is determined by two thermodynamic parameters, one being the thermal efficiency of the tropical cyclone and the other being the difference between the saturation enthalpy of the sea surface and the enthalpy of the air in the boundary layer (the air–sea thermodynamic disequilibrium), it is useful to understand how these parameters respond to changes in SST and Tstrat. The relevant equation for the PI is
where is the ratio of surface exchange coefficients of enthalpy and momentum, is the thermal efficiency, and is the thermodynamic disequilibrium.
Figure 5 shows that for an increase in SST (with fixed Tstrat), PI change is driven mainly by a large increase in the thermodynamic disequilibrium, with only a small contribution from the thermal efficiency term. At first glance one might reasonably surmise that there is a strong dependence between SST and (k* − k), however, in RCE the thermodynamic disequilibrium must be balanced by the column-integrated radiative cooling (e.g., Emanuel 2010b; Chavas and Emanuel 2012), which increases here as the tropopause altitude increases. Therefore, the increase in PI with surface warming in RCE should not be viewed as a unique function of SST.
On the other hand, stratospheric cooling increases the PI primarily through the thermal efficiency (Fig. 5b). Taking the squared dependency of wind speed in (3) into account, the thermal efficiency (thermodynamic disequilibrium) contributes 82% (18%) to the total PI change under stratospheric cooling and 28% (72%) under sea surface warming.
d. Outflow temperature
The outflow temperature is an important, though often understated, metric in PI. All else being equal, a colder outflow will increase the thermal efficiency and hence the PI, as can be seen in (3). Figure 6 shows trends in two sets of outflow temperatures: one derived from the PI code (using characteristic environmental profiles described in section 3b) and the other determined explicitly from the simulated TCs. The PI–outflow temperature is estimated by taking the average temperature of two parcels lifted pseudoadiabatically from the RMW until their density temperatures match their respective environmental density temperatures.1 The first parcel is assumed to start out saturated at the SST, while the second has its origins in the boundary layer. The modeled outflow temperature, determined from the simulated TCs, is defined as the temperature at the point where an angular momentum surface, having passed through the RMW, intersects the line of zero azimuthal wind (e.g., Hakim 2011; Emanuel and Rotunno 2011).
The PI–outflow temperature shows no trend with increasing SST, remaining steady at about 196 K (∼2–3 K warmer than the ambient tropopause). The height of the corresponding outflow layer increases substantially, from ∼15.25 to ∼17.25 km, in sync with the lifting of the cold-point tropopause shown in Fig. 2. The stratospheric cooling simulations produce a significant decline in PI–outflow temperature with a slope that matches the imposed values of Tstrat (i.e., a 1-K decrease in Tstrat produces a 1-K decrease in To).
The modeled outflow temperature shows similar sensitivities to changes in SST and Tstrat compared with the To from PI but is 4–5 K warmer, and the simulated outflow layer is about 1000 m lower. Finally, most of the outflow in the model occurs well below the ambient tropopause. Inspection of the equilibrated radial mass flux averaged over 50–500-km radii in the control simulation reveals a peak at an altitude of 14.75 km, which is 2.5 km lower than the cold-point tropopause. Further, roughly 60% of the outflow occurs in the layer between 13 and 15 km. These findings are in agreement with the axisymmetric simulations reported in Emanuel and Rotunno (2011).
To the extent that stratospheric temperature trends can be separated from the warming trend of the global oceans over the past few decades, results here suggest that stratospheric cooling has played a large part in driving past PI trends, even when compared to the observed surface warming. The global tropical oceans have warmed by about 0.15°C decade−1 since the 1970s (Solomon et al. 2007), which would result in an increase in the tropical-mean PI by ∼1.25 m s−1 according to the idealized model used here. The extent of observed lower-stratospheric temperature changes in the tropics is more uncertain (e.g., Solomon et al. 2012), with cooling trends ranging from 0.3 to over 1 K decade−1, depending on the dataset. However, even a conservative estimate of 0.4 K decade−1 equates to a 1.2 m s−1 increase in the PI based on the current idealized model, which is comparable to the response to surface warming. Clearly, the higher end of possible past stratospheric cooling trends [e.g., Sherwood et al. (2008) and the Binary Database of Profiles (BDBP) analyzed in Solomon et al. (2012)] would imply an even greater PI trend.
While the surface warming and stratospheric cooling forcings are deliberately decoupled here, in the real world of course these processes occur simultaneously. It is therefore reasonable to expect that regions where both of these have been relatively large should have correspondingly large PI trends. This has been argued for the North Atlantic region, where lower-stratospheric cooling has probably played a large part in driving the observed PI trends—at least according to some datasets (e.g., Emanuel 2010a; Emanuel et al. 2013).
Results here also have important implications for interpreting TC intensity trends from global climate models. In particular, if CGMs fail to reproduce the cooling trend in the lower stratosphere—caused by, for example, a loss of ozone—then they will also likely underestimate PI trends. Vecchi et al. (2013) found a large discrepancy between tropical-mean PI trends derived from NCEP reanalysis and PI trends computed from the Geophysical Fluid Dynamics Laboratory (GFDL)'s High-Resolution Atmospheric Model (HiRAM). The large positive trend in NCEP was found to exceed all other estimates (including from other global reanalyses) and was attributed to excessive cooling in the layer between 300 and 100 hPa. On the other hand, temperature trends at 70 hPa and above were found to have a negligible effect. The current results show that temperature trends at levels above 100 hPa can have a considerable influence on PI, even when the upper-tropospheric temperature remains approximately fixed (Fig. 2a).
To what extent do the results herein apply to the real world? After all, the tropical atmosphere at any given time is not in RCE and tropical cyclones rarely achieve their PI. Even so, the RCE temperature profiles (Fig. 2) are close to the observed tropical-mean tropical profiles, and the moist adiabatic warming in response to SST change resembles that of the tropical-mean moist adiabatic warming exhibited by GCMs. The idealized model here could therefore be seen as representing the sensitivity of tropical-mean PI to changes in the tropical-mean atmosphere, while much larger fluctuations in PI are likely to occur on individual basin scales due to changes in relative SST (e.g., Vecchi and Soden 2007; Ramsay and Sobel 2011; Camargo et al. 2013).
Moreover, the theory of PI pertains to a “steady-state” maximum intensity, which for cloud-resolving simulations means that the storm must be in a state of (statistical) equilibrium with its environment (Hakim 2011). As discussed in Hakim (2011), most previous studies on axisymmetric TCs use typically a radiation scheme in which the temperature is relaxed back to a prescribed profile over a specified time scale (e.g., Rotunno and Emanuel 1987; Persing and Montgomery 2003). This places a strong constraint on the maximum intensity of the storm because the initial temperature profile acts to prevent the storm from reaching an equilibrated state with its environment. On the other hand, such a constraint allows one to test sensitivity to some important aspects of the upper troposphere, such as the shape of the tropopause (e.g., Rotunno and Emanuel 1987), which is more difficult to do here.
5. Summary and conclusions
The effects of stratospheric cooling and sea surface warming on the maximum intensity of tropical cyclones have been explored here using a nonhydrostatic cloud-resolving model (CM1; Bryan and Fritsch 2002) run to the idealized state of radiative–convective equilibrium (e.g., Hakim 2011). While many studies agree that mean PI will increase in response to increasing SST, much less work has been done on the influence of stratospheric temperature changes on PI (Emanuel 2010a,b; Emanuel et al. 2013; Vecchi et al. 2013). The temperature of the stratosphere is thought to affect the PI by altering the storm's outflow temperature, which together with the SST determines the thermal efficiency of the TC. Most observationally constrained datasets show a cooling trend near the tropopause transition layer over the past few decades; however, the large variability in these trends has led to uncertainty in PI trends (e.g., Vecchi et al. 2013).
The sensitivity of PI to stratospheric cooling has been quantified by assessing the statistically steady states of numerically simulated TCs, which respond to the imposed temperature of the stratosphere (while the SST is held fixed at 29°C). The cooling of the stratosphere results in an increase in both the steady-state maximum intensity and the PI at a rate of 1 m s−1 per degree of cooling, with almost all of the relevant temperature changes occurring at and above ∼90 hPa. Most of the PI trend (82%) is due to a reduction in outflow temperature and therefore a large increase in thermal efficiency. Sea surface warming (with a fixed stratospheric temperature) results in a PI trend about twice as large as the stratospheric cooling simulations, while the outflow temperature remains fixed. The steady-state maximum intensity increases at a rate of 2.5 m s−1 °C−1—slightly more than the corresponding PI change of 1.8 m s−1 °C−1. Most of the PI response to surface warming comes from an increase in the air–sea disequilibrium (72%); although this quantity is driven also by the column-integrated radiative cooling, which increases with increasing tropospheric depth (e.g., Chavas and Emanuel 2012).
Finally, the outflow temperature, as calculated by the model and estimated by the PI, shows almost no trend with increasing SST. However, the level at which the outflow occurs increases substantially in sync with a lifting of the cold-point tropopause. The stratospheric cooling simulations, on the other hand, show a substantial decline in outflow temperature that scales with the imposed cooling trend.
Further research is needed to understand the physical mechanisms that determine how tropical cyclones “feel” stratospheric temperature changes and at what levels such changes matter most (e.g., Vecchi et al. 2013). This is particularly crucial in the context of interpreting PI trends derived from GCMs.
This work has benefited from stimulating discussions with Kerry Emanuel, Steve Sherwood, Dan Chavas, and Bill Boos. Early discussions with Adam Sobel and Shuguang Wang helped formulate the general modelling approach. HAR thanks Gareth Berry and Kerry Emanuel for their valuable comments on an earlier version of the manuscript and three anonymous reviewers for their thoughtful and constructive reviews. HAR acknowledges funding from the ARC Centre of Excellence for Climate System Science and computing support from the Monash e-Research Centre—in partnership with the National Computing Infrastructure.
Density temperature is defined by Betts and Bartlo (1991) as “the temperature of an exactly saturated parcel that has the same density and virtual temperature at the same pressure level p as an unsaturated air parcel with temperature T, dewpoint TD, and corresponding mixing ratio, q.”