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David M. Romps

Abstract

Many analytic, but approximate, expressions have been proposed for the height of the lifting condensation level (LCL), including the popular expressions by Espy, Bolton, and Lawrence. Here, the exact, explicit, analytic expression is derived for an air parcel’s LCL as a function of its temperature and relative humidity. Unlike previous analytic expressions, some of which can have errors as high as hundreds or thousands of meters, this exact expression is accurate to within the uncertainty of empirical vapor pressure measurements: this translates into an uncertainty of around 5 m for all temperatures and relative humidities. An exact, explicit, analytic expression for the lifting deposition level (LDL) is also derived, and its behavior is compared to the LCL. At sufficiently cold temperatures, aerosols freeze homogeneously below the LCL; an approximate, implicit, analytic expression is given for this lifting freezing level (LFL). By comparing the LCL, LDL, and LFL, it is found that a well-mixed boundary layer can have an ice-supersaturated layer that is no thicker than 400 m.

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David M. Romps

Abstract

Using high-resolution cloud-resolving simulations with different CO2 concentrations, local precipitation fluxes are found to obey Clausius–Clapeyron (CC) scaling. Previous studies of the effect of CO2 concentration on precipitation extremes have used general circulation models, which are poor platforms for studying tropical convection because convection is parameterized. In idealized cloud-resolving simulations, it is possible to identify not only the changes in local precipitation fluxes, but also the factors responsible for those changes.

There are many properties of convection that can change as the atmosphere warms, each of which could produce deviations from CC scaling. These properties include the effective water-vapor gradient, cloud pressure depth, and cloud velocity. A simple theory is developed that predicts the changes in these properties consistent with CC scaling. Convection in the cloud-resolving simulations is found to change as predicted by this theory, leading to an ∼20% increase in local precipitation fluxes when the CO2 concentration is doubled. Overall, an increase in CO2 leads to more vigorous convection, composed of clouds that are wider, taller, and faster.

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David M. Romps

Abstract

Cloud-resolving simulations of convection over a surface temperature hot spot are used to evaluate the weak pressure gradient (WPG) and weak temperature gradient (WTG) approximations. The premise of the relaxed form of WTG—that vertical velocity is equal to buoyancy times a positive time scale—is found to be violated by thick layers of negative buoyancy in steady-state ascent. The premise of WPG—that horizontal divergence and pressure anomalies are collocated—is validated by these simulations. When implemented in a cloud-resolving model, WPG replicates buoyancy transients exceptionally well, including the adiabatic lifting of air below buoyancy anomalies. WTG captures neither this effect nor the associated triggering of moist convection. For steady states, WTG produces vertical velocity profiles that are too top heavy. On the other hand, WPG generates velocity profiles that closely match fully resolved hot-spot simulations. Taken together, the evidence suggests that WPG is a relatively accurate method for parameterizing supradomain-scale (SDS) dynamics.

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David M. Romps

Abstract

Analytic solutions are derived for a convecting atmosphere with mean ascent using a zero-buoyancy bulk-plume approximation for moist convection. It has been suggested that such solutions should serve as a model for the relationship between humidity, instability, and precipitation in the tropics, but it is shown here that this interpretation is incompatible with the observed weak temperature gradient (WTG). Instead, the solutions can be used to understand the atmospheric state averaged over all tropical convecting regions. Using the analytic solutions in this way, they predict the changes in humidity, instability, and precipitation as a function of the size of the moist patch in a convectively aggregated state.

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David M. Romps

Abstract

For an adiabatic parcel convecting up or down through the atmosphere, it is often assumed that its moist static energy (MSE) is conserved. Here, it is shown that the true conserved variable for this process is MSE minus convective available potential energy (CAPE) calculated as the integral of buoyancy from the parcel’s height to its level of neutral buoyancy and that this variable is conserved even when accounting for full moist thermodynamics and nonhydrostatic pressure forces. In the calculation of a dry convecting parcel, conservation of MSE minus CAPE gives the same answer as conservation of entropy and potential temperature, while the use of MSE alone can generate large errors. For a moist parcel, entropy and equivalent potential temperature give the same answer as MSE minus CAPE only if the parcel ascends in thermodynamic equilibrium. If the parcel ascends with a nonisothermal mixed-phase stage, these methods can give significantly different answers for the parcel buoyancy because MSE minus CAPE is conserved, while entropy and equivalent potential temperature are not.

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David M. Romps

Abstract

Analytic solutions are derived for a convecting atmosphere with mean ascent using a zero-buoyancy bulk-plume approximation for moist convection. It has been suggested that such solutions should serve as a model for the relationship between humidity, instability, and precipitation in the tropics, but it is shown here that this interpretation is incompatible with the observed weak temperature gradient (WTG). Instead, the solutions can be used to understand the atmospheric state averaged over all tropical convecting regions. Using the analytic solutions in this way, they predict the changes in humidity, instability, and precipitation as a function of the size of the moist patch in a convectively aggregated state.

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David M. Romps

Abstract

The Gregory–Kershaw–Inness (GKI) parameterization of convective momentum transport, which has a tunable parameter C, is shown to be identical to a parameterization with no pressure gradient force and a mass flux smaller by a factor of 1 − C. Using cloud-resolving simulations, the transilient matrix for momentum is diagnosed for deep convection in radiative–convective equilibrium. Using this transilient matrix, it is shown that the GKI scheme underestimates the compensating subsidence of momentum by a factor of 1 − C, as predicted. This result is confirmed using a large-eddy simulation.

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David M. Romps

Abstract

A method is introduced for directly measuring convective entrainment and detrainment in a cloud-resolving simulation. This technique is used to quantify the errors in the entrainment and detrainment estimates obtained using the standard bulk-plume method. The bulk-plume method diagnoses these rates from the convective flux of some conserved tracer, such as total water in nonprecipitating convection. By not accounting for the variability of this tracer in clouds and in the environment, it is argued that the bulk-plume equations systematically underestimate entrainment. Using tracers with different vertical profiles, it is also shown that the bulk-plume estimates are tracer dependent and, in some cases, unphysical. The new direct-measurement technique diagnoses entrainment and detrainment at the gridcell level without any recourse to conserved tracers. Using this method in large-eddy simulations of shallow and deep convection, it is found that the bulk-plume method underestimates entrainment by roughly a factor of 2. The directly measured entrainment rates are then compared to cloud height and cloud buoyancy. Contrary to existing theories, fractional entrainment is not found to scale like the inverse of height, the cloud buoyancy, or the gradient of cloud buoyancy. On the other hand, fractional detrainment is found to scale linearly with cloud buoyancy. Finally, direct measurement is used to diagnose the spatial distribution of entrainment and detrainment during the evolution of an individual deep cumulonimbus.

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David M. Romps

Abstract

An analytical model is derived for tropical relative humidity using only the Clausius–Clapeyron relation, hydrostatic balance, and a bulk-plume water budget. This theory is constructed for radiative–convective equilibrium and compared against a cloud-resolving model. With some reinterpretation of variables, it can be applied more generally to the entire tropics.

Given four variables—pressure, temperature, and the fractional entrainment and detrainment rates—the equations predict the relative humidity (RH) and the temperature lapse rate analytically. The RH is a simple ratio involving the fractional detrainment rate and the water-vapor lapse rate. When integrated upward in height, the equations give profiles of RH and temperature for a convecting atmosphere.

The theory explains the magnitude of RH and the “C” shape of the tropospheric RH profile. It also predicts that RH is an invariant function of temperature as the atmosphere warms, and this behavior matches what has been seen in global climate models and what is demonstrated here with cloud-resolving simulations. Extending the theory to include the evaporation of hydrometeors, a lower bound is derived for the precipitation efficiency (PE) at each height: PE > 1 − RH. In a cloud-resolving simulation, this constraint is obeyed with the PE profile taking the shape of an inverted C shape.

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David M. Romps

Abstract

Even in a small domain, it can be prohibitively expensive to run cloud-resolving greenhouse gas warming experiments due to the long equilibration time. Here, a technique is introduced that reduces the computational cost of these experiments by an order of magnitude: instead of fixing the carbon dioxide concentration and equilibrating the sea surface temperature (SST), this technique fixes the SST and equilibrates the carbon dioxide concentration. Using this approach in a cloud-resolving model of radiative–convective equilibrium (RCE), the equilibrated SST is obtained as a continuous function of carbon dioxide concentrations spanning 1 ppmv to nearly 10 000 ppmv, revealing a dramatic increase in equilibrium climate sensitivity (ECS) at higher temperatures. This increase in ECS is due to both an increase in forcing and a decrease in the feedback parameter. In addition, the technique is used to obtain the direct effects of carbon dioxide (i.e., the rapid adjustments) over a wide range of SSTs. Overall, the direct effect of carbon dioxide offsets a quarter of the increase in precipitation from warming, reduces the shallow cloud fraction by a small amount, and has no impact on convective available potential energy (CAPE).

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