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Peter H. Stone

Abstract

Bergeron first suggested that atmospheric frontogenesis is caused by horizontal wind deformation fields acting on pre-existing horizontal temperature gradients. A three-dimensional time-dependent mathematical model of the atmosphere which incorporates this process through the initial conditions and boundary conditions is formulated. Dissipative processes are neglected and the equations are approximated by assuming that the Richardson number is initially large. The resulting equations are then solved analytically. The solution shows, under certain conditions, fronts developing with properties similar to many atmospheric fronts, thereby giving support to Bergeron's hypothesis.

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Peter H. Stone

Abstract

Eady's (1949) model is used to study the non-geostorphic baroclinic stability problem. Growth rates for various types of perturbations are found as a function of the Richardson number, Ri The results indicate that the conventional baroclinic instabilities dominate if Ri > 0.95; symmetric instabilities dominate if 1/4 Ri > 0.95; and symmetric instabilities dominate if Ri < 1/4. It is suggested that symmetric instabilities may play an important role in the dynamics of the atmospheres of the major planets of the solar system.

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Peter H. Stone

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Peter H. Stone

Abstract

A simple model for the structure of a non-rotating Hadley regime in an atmosphere with large thermal inertia is developed. The radiative fluxes are estimated by using a linearization about the radiative equilibrium state and the dynamical fluxes are estimated by using scaling analysis. The requirement that differential heating by these fluxes be in balance in both the meridional and vertical directions leads to two equations for the mean static stability and meridional temperature contrast. The solution depends on two parameters: the strength of the radiative heating, as measured by the static stability Ae of the radiative equilibrium state; and the ratio of the time it takes an external gravity wave to traverse the atmosphere to the time it would take the atmosphere to cool off radiatively, denoted by ε.

In the deep Venus atmosphere ε ≈ 10−5; the equations are therefore analyzed in the limit ε → 0. The large-scale dynamics has virtually the same effect on the lapse rate as small-scale convection: if Ae > 0 the radiative lapse rate is unchanged, while if Ae < 0 the lapse rate becomes subadiabatic, but only by an amount of order ε. Therefore, one need not invoke convection to explain the approximate adiabatic lapse rate in the Venus atmosphere, but a greenhouse effect is necessary to explain the high surface temperatures. The other properties of the solutions when Ae < 0 are consistent with observational evidence for the deep atmosphere: the horizontal velocities are typically ∼2 m sec−1, the vertical velocities ∼½ cm sec−1, and the meridional temperature contrast is unlikely to exceed 0.1K.

The same approach is used to study the time-dependent problem and determine how long it would take for a perturbed atmosphere to reach equilibrium. If Ae > 0 the adjustment is primarily governed by the radiative time scale, which is about 100 earth years for the deep Venus atmosphere. If Ae < 0 the adjustment is governed by an advective time scale which may be as short as 20 earth days. Published numerical studies of the deep circulation have only treated the first case, but their integrations were not carried beyond about 200 earth days and therefore do not describe true equilibrium states. Only the second case, Ae < 0, is consistent with the observations and it would be relatively easy to study numerically.

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Peter H. Stone

Abstract

The solutions of Eady's 1949 model of baroclinic stability are extended numerically to include the non-geostrophic perturbations which wore not covered by the analysis in Part I. It is found that the largest growth rates are never associated with these new perturbations, so the tentative conclusions of Part I are verified. The more exact numerical solutions lead only to slight quantitative modifications of the results of Part I. If we let Ri be the Richardson number, then the largest growth rates are associated with “geostrophic” baroclinic instability if Ri>0.950; with symmetric instability if ¼<Ri<0.950; and with Kelvin-Helmholtz instability if 0<Ri<¼. Geostrophic baroclinic instability and symmetric instability can exist simultaneously if 0.84<Ri<1, and symmetric instability and Kelvin-Helmholtz instability can exist simultaneously if 0<Ri<¼

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Jochem Marotzke and Peter H. Stone

Abstract

A theoretical analysis of the interactions between atmospheric meridional transports and the thermohaline circulation is presented, using a four-box ocean-atmosphere model in one hemisphere. The model is a simplified version of that developed by Nakamura Stone, and Marotzke and is amenable to analytical solutions. The ocean model is Stommel's; the atmospheric model gives the surface heat and freshwater fluxes as residuals of the atmospheric energy and moisture budgets, assumed in balance. Radiation at the top of the atmosphere depends linearly on surface temperature; atmospheric meridional heat and moisture transports are proportional to the meridional temperature gradient.

A Newtonian cooling law is derived for differential surface heat flux. The restoring coefficient is proportional to the efficiency of atmospheric transports and inversely proportional to the relative ocean area compared to total surface area. Surface freshwater flux increases with increasing temperature gradient and is inversely proportional to the ratio of ocean area to catchment area. The range of stable solutions with high-latitude sinking is smaller than in related, uncoupled box models due to the dependence of freshwater flux on the temperature gradient, which leads to a positive feedback with the thermohaline circulation. A strong control of the temperature gradient by atmospheric transports enhances the positive feedback between the salinity gradient and thermohaline Circulation simultaneously, it weakens the positive feedback between atmospheric moisture transport and the thermohaline circulation.

Overestimating the atmospheric moisture transport and underestimating oceanic mass transport both artificially destabilize the high-latitude sinking state. Overestimating the atmospheric heat transport and hence the Newtonian restoring coefficient can be artificially stabilizing or destabilizing. These erroneous sensitivities ate not alleviated if flux adjustments are added to obtain the correct mean climate, and then held fixed in climate change experiments. We derive alternate flux adjustment schemes, which do preserve the model's stability properties for particular sources of error.

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Giovanna Salustri and Peter H. Stone

Abstract

A diagnostic study of the forcing of the Ferret cell by eddy fluxes in the Northern Hemisphere is carried out. The quasi-geostrophic omega equation, and Oort and Rasmusson's data set are used. The effects of condensation associated with the large-scale motions are introduced to the omega equation by using the quasi-geostrophic moisture conservation equation. Thus the dry static stability is replaced by a moist static stability, and the forcing of the Ferret cell by eddy latent heat fluxes as well as sensible heat and momentum fluxes is included, Both effects tend to enhance the forcing of the Ferret cell. The numerical analysis indicates that the effects are small in January, but in July the maximum vertical velocities are enhanced by ∼30%.

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Peter H. Stone and Boaz Nemet

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Isentropic slopes calculated from Northern Hemisphere analyses of the zonal mean state of the atmosphere are compared with isentropic slopes calculated from baroclinic adjustment theory. In midlatitudes, the isentropic slopes are relatively close to the adjusted values in the layer from 2 to 7 km (800 to 400 mb). They also have very little variation in latitude and season, which implies that baroclinic eddy fluxes supply a strong negative feedback to changes in isentropic slopes. The vertical structure of the temperature field in the “adjusted” layers and the location of the layers suggest that vertical eddy heat fluxes play a significant role in this feedback process.

Isentropic slopes are also calculated from simulations of the current climate by the GISS Model II GCM and the NCAR CCM2. Both models have regions of apparent baroclinic adjustment similar to that in the Northern Hemisphere atmosphere. However, compared to the observations, the agreement of the simulations with baroclinic adjustment theory is not as good, and the isentropic slopes show stronger latitudinal and seasonal variations. The discrepancies are associated primarily with errors in the models’ meridional temperature gradients in the lower troposphere in midlatitudes. The seasonal changes in these gradients are much larger than in the observations, particularly in the CCM2, even though the model simulations were constrained by climatological sea surface temperatures.

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Peter H. Stone and Giovanna Salustri

Abstract

The Eulerian form of the Eliassen-Palm flux for quasi-geostrophic motion is generalized to include large-scale eddy forcing of condensation heating. Only the vertical component of the flux has to be modified; it is increased. The Eliassen-Palm theorem still holds, but instead of assuming that the diabatic heating is zero, one assumes that the diabatic heating excluding condensation associated with the large-scale motions is zero. The non-acceleration theorem also still holds, provided one adds the assumption that the Eulerian zonal mean moisture field is stationary. The generalization preserves the relationship between stationary wave energy flux and the Eliassen-Palm flux, but now wave condensation effects are automatically included. In addition, the generalization leads to a function describing the total eddy forcing of the moisture field.

The divergence of the generalized Eliassen-Palm flux is calculated from atmospheric observations and compared with the divergence of the standard flux. The eddy forcing of the zonal mean zonal wind and temperature fields is much stronger when condensation effects are included—for example, in the annual mean it is about two and one half times as strong. The eddy forcing of the moisture field is also calculated. It shows the expected tendency to dry out the subtropics and moisturize middle and high latitudes, but the effect of the meridional eddy flux of moisture is greatly enhanced by the effect of the Ferrel cell induced by the eddy heat fluxes.

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Amy Solomon and Peter H. Stone

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The sensitivity of the equilibrated state of a dry high-resolution quasigeostrophic β-plane channel model, coupled to both a simplified model of the atmospheric boundary layer and an interactive static stability, to changes in forcings is investigated. An earlier study with the same model found that with standard parameter values, the potential vorticity in the center of the channel just above the atmospheric boundary layer was homogenized. The new experiments show that this result is robust does not vary strongly with variations in forcing over a wide range of forcing parameters. This is so even though the meridional temperature gradients and static stability are generally sensitive to the forcing; that is, the changes in these cooperate to keep the meridional potential vorticity gradient zero. The potential vorticity gradients at higher levels are also robust although nonzero. The homogenization in the lower troposphere does disappear if the differential diabatic heating is decreased sufficiently or if the tropopause level is lowered sufficiently.

The model results are also used to assess proposed parameterizations of eddy effects. Stone's parameterization of the meridional eddy heat flux is most successful at reproducing the model's results for most of the experiments. However, no parameterizations of the eddy heat flux captured the results of the experiments in which the diabatic heating timescale was varied. In these experiments, changes in the eddy heat fluxes kept the tropospheric temperature structure essentially unchanged even though the timescale changed from 5 to 80 days.

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