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- Author or Editor: Raphaël Rousseau-Rizzi x

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## Abstract

We concur with Makarieva et al. that in our earlier work on the hurricane differential Carnot cycle, we neglected the work done in lifting water and the dissipation of kinetic energy in the outflow (we explicitly acknowledged neglecting these terms). Here, we relax those assumptions, affirm the conclusion of Makarieva et al. that the water lifting term is small, and show that the effect of outflow dissipation is negligible. We remind readers that the differential Carnot theory is not a closed theory for potential intensity as it does not specify the outflow temperature or the boundary layer moist enthalpy at the radius of maximum winds. The addition of enthalpy to the inflow can raise the boundary layer enthalpy, reducing subsequent surface fluxes, regardless of whether that addition comes from surface fluxes themselves or from dissipative heating. We show that while this may indeed reduce the effect of dissipative heating, it does not eliminate it. We disagree with Makarieva et al.’s assertions that dissipative heating does not increase potential intensity and that only latent heat fluxes can drive tropical cyclones when dissipative heating is included.

## Abstract

We concur with Makarieva et al. that in our earlier work on the hurricane differential Carnot cycle, we neglected the work done in lifting water and the dissipation of kinetic energy in the outflow (we explicitly acknowledged neglecting these terms). Here, we relax those assumptions, affirm the conclusion of Makarieva et al. that the water lifting term is small, and show that the effect of outflow dissipation is negligible. We remind readers that the differential Carnot theory is not a closed theory for potential intensity as it does not specify the outflow temperature or the boundary layer moist enthalpy at the radius of maximum winds. The addition of enthalpy to the inflow can raise the boundary layer enthalpy, reducing subsequent surface fluxes, regardless of whether that addition comes from surface fluxes themselves or from dissipative heating. We show that while this may indeed reduce the effect of dissipative heating, it does not eliminate it. We disagree with Makarieva et al.’s assertions that dissipative heating does not increase potential intensity and that only latent heat fluxes can drive tropical cyclones when dissipative heating is included.

## Abstract

Potential intensity (PI) is an analytical bound on steady, inviscid, axisymmetric hurricane wind speed. Studies have shown that simulated hurricane azimuthal wind speed can greatly exceed a PI bound on the maximum gradient wind. This disparity is called superintensity (SI) and has been attributed to the contribution of the unbalanced flow to the azimuthal wind. The goals of this study are 1) to introduce a new surface wind PI (PI_{s}), based on a differential Carnot cycle and bounding the magnitude of the surface winds; 2) to evaluate SI in numerical simulations with respect to diagnostic PI bounds on gradient wind (PI_{g}), azimuthal wind (PI_{a}), and surface wind (PI_{s}); and 3) to evaluate the validity of each PI bound based on the SI computations. Here, we define superintensity as the normalized amount by which each version of PI is exceeded by the quantity it bounds. Axisymmetric tropical cyclone simulations are performed while varying the parameterized turbulent mixing as a way of estimating SI in the inviscid limit. As the mixing length decreases, all three bounded wind speeds increase similarly from a sub-PI state to a marginally superintense state. This shows that all three forms of PI evaluated here are good approximations to their respective metrics in numerical simulations.

## Abstract

Potential intensity (PI) is an analytical bound on steady, inviscid, axisymmetric hurricane wind speed. Studies have shown that simulated hurricane azimuthal wind speed can greatly exceed a PI bound on the maximum gradient wind. This disparity is called superintensity (SI) and has been attributed to the contribution of the unbalanced flow to the azimuthal wind. The goals of this study are 1) to introduce a new surface wind PI (PI_{s}), based on a differential Carnot cycle and bounding the magnitude of the surface winds; 2) to evaluate SI in numerical simulations with respect to diagnostic PI bounds on gradient wind (PI_{g}), azimuthal wind (PI_{a}), and surface wind (PI_{s}); and 3) to evaluate the validity of each PI bound based on the SI computations. Here, we define superintensity as the normalized amount by which each version of PI is exceeded by the quantity it bounds. Axisymmetric tropical cyclone simulations are performed while varying the parameterized turbulent mixing as a way of estimating SI in the inviscid limit. As the mixing length decreases, all three bounded wind speeds increase similarly from a sub-PI state to a marginally superintense state. This shows that all three forms of PI evaluated here are good approximations to their respective metrics in numerical simulations.

## Abstract

Potential intensity (PI) has been shown to have a linear sensitivity to sea surface temperature (SST) of about 8 m s^{−1} K^{−1}, which is close to the sensitivity of PI in simulations subject to a weak temperature gradient (WTG) approximation. This suggests that most of the PI variance is associated with local rather than global SST variations. We verify that PI perturbations are approximately linear in SST, with slopes of 1.8 ± 0.2 m s^{−1} K^{−1} in radiative–convective equilibrium (RCE) and 9.1 ± 0.9 m s^{−1} K^{−1} in WTG. To do so, we simulate the sensitivity of both RCE and WTG states in a single-column model (SCM) perturbed by changing in turn CO_{2} concentration, aerosol concentrations, prescribed SST, and surface winds speeds. While PI is much more sensitive to SST in WTG than in RCE simulations, the SST itself is much less sensitive to radiative forcing in WTG than in RCE because of the absence of strong atmospheric response. Using these results, we develop a linear model, based on SST and midlevel saturation MSE perturbations, to partition SST and PI perturbations between local components occurring under a WTG constraint and global components that are representative of an RCE state. This model explains up to 95% of the variability of PI in reanalysis. The SCM-derived linear model coefficients are statistically indistinguishable from coefficients from a linear fit of reanalysis PI to SST and midlevel saturation MSE in most ocean basins. Our model shows that North Atlantic PI variations are explained almost entirely by local forcings in recent decades.

## Abstract

Potential intensity (PI) has been shown to have a linear sensitivity to sea surface temperature (SST) of about 8 m s^{−1} K^{−1}, which is close to the sensitivity of PI in simulations subject to a weak temperature gradient (WTG) approximation. This suggests that most of the PI variance is associated with local rather than global SST variations. We verify that PI perturbations are approximately linear in SST, with slopes of 1.8 ± 0.2 m s^{−1} K^{−1} in radiative–convective equilibrium (RCE) and 9.1 ± 0.9 m s^{−1} K^{−1} in WTG. To do so, we simulate the sensitivity of both RCE and WTG states in a single-column model (SCM) perturbed by changing in turn CO_{2} concentration, aerosol concentrations, prescribed SST, and surface winds speeds. While PI is much more sensitive to SST in WTG than in RCE simulations, the SST itself is much less sensitive to radiative forcing in WTG than in RCE because of the absence of strong atmospheric response. Using these results, we develop a linear model, based on SST and midlevel saturation MSE perturbations, to partition SST and PI perturbations between local components occurring under a WTG constraint and global components that are representative of an RCE state. This model explains up to 95% of the variability of PI in reanalysis. The SCM-derived linear model coefficients are statistically indistinguishable from coefficients from a linear fit of reanalysis PI to SST and midlevel saturation MSE in most ocean basins. Our model shows that North Atlantic PI variations are explained almost entirely by local forcings in recent decades.

## Abstract

Theories for the maximum intensity of tropical cyclones (TCs) assume steady state. However, many TCs in simulations that run for tens of days tend to decay considerably from an early steady state in the core (CS), before stabilizing at a final equilibrium steady state (ES). This decay raises the question of whether CS or ES should be used as a comparison to the maximum intensity theories. To understand the differences between CS and ES, we investigate why TCs decay and attempt to simulate a TC with steady intensity over a 100-day period. Using the axisymmetric Cloud Model 1, we find that the CS TC decay is due to a large-scale drying of the subsidence region. Such a drying is very pronounced in axisymmetric models because shallow-to-midlevel convection is not represented accurately enough to moisten air in the subsidence region. Simulations with an added moisture relaxation term in the subsidence region and dry cyclones without any moisture both remain in a steady state for over 100 days, without decaying appreciably after the spinup period. These simulations indicate that the decay in TC simulations is due to the irreversible removal of precipitation combined with the lack of a moistening mechanism in the subsidence region. Once either of these conditions is removed, the decay disappears and the CS and ES intensities become essentially equivalent.

## Abstract

Theories for the maximum intensity of tropical cyclones (TCs) assume steady state. However, many TCs in simulations that run for tens of days tend to decay considerably from an early steady state in the core (CS), before stabilizing at a final equilibrium steady state (ES). This decay raises the question of whether CS or ES should be used as a comparison to the maximum intensity theories. To understand the differences between CS and ES, we investigate why TCs decay and attempt to simulate a TC with steady intensity over a 100-day period. Using the axisymmetric Cloud Model 1, we find that the CS TC decay is due to a large-scale drying of the subsidence region. Such a drying is very pronounced in axisymmetric models because shallow-to-midlevel convection is not represented accurately enough to moisten air in the subsidence region. Simulations with an added moisture relaxation term in the subsidence region and dry cyclones without any moisture both remain in a steady state for over 100 days, without decaying appreciably after the spinup period. These simulations indicate that the decay in TC simulations is due to the irreversible removal of precipitation combined with the lack of a moistening mechanism in the subsidence region. Once either of these conditions is removed, the decay disappears and the CS and ES intensities become essentially equivalent.

## Abstract

Tropical cyclone (TC) potential intensity (PI) theory has a well-known form, consistent with a Carnot cycle interpretation of TC energetics, which relates PI to mean environmental conditions: the difference between surface and TC outflow temperatures and the air–sea enthalpy disequilibrium. PI has also been defined as a difference in convective available potential energy (CAPE) between two parcels, and quantitative assessments of future changes make use of a numerical algorithm based on this definition. Here, an analysis shows the conditions under which these Carnot and CAPE-based PI definitions are equivalent. There are multiple conditions, not previously enumerated, which in particular reveal a role for irreversible entropy production from surface evaporation. This mathematical analysis is verified by numerical calculations of PI’s sensitivity to large changes in surface-air relative humidity. To gain physical insight into the connection between the CAPE and Carnot formulations of PI, we use a recently developed analytic theory for CAPE to derive, starting from the CAPE-based definition, a new approximate formula for PI that nearly recovers the previous Carnot PI formula. The derivation shows that the difference in undilute buoyancies of saturated and environmental parcels that determines CAPE PI can in fact be expressed as a difference in the parcels’ surface moist static energy, providing a physical link between the Carnot and CAPE formulations of PI. This combination of analysis and physical interpretation builds confidence in previous numerical CAPE-based PI calculations that use climate model projections of the future tropical environment.

## Abstract

Tropical cyclone (TC) potential intensity (PI) theory has a well-known form, consistent with a Carnot cycle interpretation of TC energetics, which relates PI to mean environmental conditions: the difference between surface and TC outflow temperatures and the air–sea enthalpy disequilibrium. PI has also been defined as a difference in convective available potential energy (CAPE) between two parcels, and quantitative assessments of future changes make use of a numerical algorithm based on this definition. Here, an analysis shows the conditions under which these Carnot and CAPE-based PI definitions are equivalent. There are multiple conditions, not previously enumerated, which in particular reveal a role for irreversible entropy production from surface evaporation. This mathematical analysis is verified by numerical calculations of PI’s sensitivity to large changes in surface-air relative humidity. To gain physical insight into the connection between the CAPE and Carnot formulations of PI, we use a recently developed analytic theory for CAPE to derive, starting from the CAPE-based definition, a new approximate formula for PI that nearly recovers the previous Carnot PI formula. The derivation shows that the difference in undilute buoyancies of saturated and environmental parcels that determines CAPE PI can in fact be expressed as a difference in the parcels’ surface moist static energy, providing a physical link between the Carnot and CAPE formulations of PI. This combination of analysis and physical interpretation builds confidence in previous numerical CAPE-based PI calculations that use climate model projections of the future tropical environment.

## Abstract

This study performs cloud-resolving simulations of cumulus convection over an idealized surface-based convergence zone to investigate the mechanisms and sensitivities of deep convection initiation forced by mesoscale ascent. The surface convergence forms in response to a localized diurnal heating anomaly over an otherwise homogeneous and unheated surface, producing a strong boundary layer updraft over the center of the heat source. This updraft gives rise to a line of cumuli that gradually deepen and, in some cases, transition into deep convection. To statistically investigate the factors controlling this transition, a new thermal-tracking algorithm is developed to follow incipient cumulus cores as they ascend through the troposphere. This tool is used to isolate the impacts of key environmental parameters (cloud-layer lapse rate, midlevel humidity, etc.) and initial core parameters near cloud base (horizontal area, vertical velocity, etc.) on the ultimate cloud-top height. In general, the initial core size determines which thermals in a given cloud field will undergo the deepest ascent, and the sensitivity of cloud depth to initial core parameters increases in environments that are more hostile to deep convection. Diurnal midlevel moistening from detraining cumuli above the convergence line produces a small but robust enhancement in cloud-top height, particularly for smaller cores.

## Abstract

This study performs cloud-resolving simulations of cumulus convection over an idealized surface-based convergence zone to investigate the mechanisms and sensitivities of deep convection initiation forced by mesoscale ascent. The surface convergence forms in response to a localized diurnal heating anomaly over an otherwise homogeneous and unheated surface, producing a strong boundary layer updraft over the center of the heat source. This updraft gives rise to a line of cumuli that gradually deepen and, in some cases, transition into deep convection. To statistically investigate the factors controlling this transition, a new thermal-tracking algorithm is developed to follow incipient cumulus cores as they ascend through the troposphere. This tool is used to isolate the impacts of key environmental parameters (cloud-layer lapse rate, midlevel humidity, etc.) and initial core parameters near cloud base (horizontal area, vertical velocity, etc.) on the ultimate cloud-top height. In general, the initial core size determines which thermals in a given cloud field will undergo the deepest ascent, and the sensitivity of cloud depth to initial core parameters increases in environments that are more hostile to deep convection. Diurnal midlevel moistening from detraining cumuli above the convergence line produces a small but robust enhancement in cloud-top height, particularly for smaller cores.