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- Author or Editor: Nadir Jeevanjee x
- Journal of Climate x
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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
Clear-sky CO2 forcing is known to vary significantly over the globe, but the state dependence that controls this is not well understood. Here we extend the formalism of Wilson and Gea-Banacloche to obtain a quantitatively accurate analytical model for spatially varying instantaneous CO2 forcing, which depends only on surface temperature T s , stratospheric temperature, and column relative humidity (RH). This model shows that CO2 forcing can be considered a swap of surface emission for stratospheric emission, and thus depends primarily on surface–stratosphere temperature contrast. The strong meridional gradient in CO2 forcing is thus largely due to the strong meridional gradient in T s . In the tropics and midlatitudes, however, the presence of H2O modulates the forcing by replacing surface emission with RH-dependent atmospheric emission. This substantially reduces the forcing in the tropics, introduces forcing variations due to spatially varying RH, and sets an upper limit (with respect to T s variations) on CO2 forcing that is reached in the present-day tropics. In addition, we extend our analytical model to the instantaneous tropopause forcing, and find that this forcing depends on T s only, with no dependence on stratospheric temperature. We also analyze the τ = 1 approximation for the emission level and derive an exact formula for the emission level, which yields values closer to τ = 1/2 than to τ = 1.
Abstract
Clear-sky CO2 forcing is known to vary significantly over the globe, but the state dependence that controls this is not well understood. Here we extend the formalism of Wilson and Gea-Banacloche to obtain a quantitatively accurate analytical model for spatially varying instantaneous CO2 forcing, which depends only on surface temperature T s , stratospheric temperature, and column relative humidity (RH). This model shows that CO2 forcing can be considered a swap of surface emission for stratospheric emission, and thus depends primarily on surface–stratosphere temperature contrast. The strong meridional gradient in CO2 forcing is thus largely due to the strong meridional gradient in T s . In the tropics and midlatitudes, however, the presence of H2O modulates the forcing by replacing surface emission with RH-dependent atmospheric emission. This substantially reduces the forcing in the tropics, introduces forcing variations due to spatially varying RH, and sets an upper limit (with respect to T s variations) on CO2 forcing that is reached in the present-day tropics. In addition, we extend our analytical model to the instantaneous tropopause forcing, and find that this forcing depends on T s only, with no dependence on stratospheric temperature. We also analyze the τ = 1 approximation for the emission level and derive an exact formula for the emission level, which yields values closer to τ = 1/2 than to τ = 1.
