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Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,#,Outline,Review,Using a simple dry AGCM to study,The tropospheric general circulation.,The distribution of relative humidity in the troposphere.,The connections between the stratosphere and the troposphere.,Strengths and weaknesses of simple models,OutlineReview,1,Terms and Concepts,Quasigeostrophic Scaling:,Potential vorticity definition:,Terms and ConceptsQuasigeostro,2,An Adjustment Problem:Homework!(Sort of),air,water,This example illustrates the impact of rotation(and some subtleties).,The diagram below represents the cross section of a channel going into the screen.,Initially,the fluid is sloped(gently)and is at rest.(Imagine holding it in place with a sheet of plexiglass.),1.Non-rotating case(,f=,0):estimate the cross channel transport of mass and cross-channel speed you would obtain afterwards,in terms of the slope,of,g,and of the mean layer depth.,An Adjustment Problem:Homewor,3,An Adjustment Problem:Homework!(Sort of),air,water,2.Rotating case(,f,0).On the,f,plane,you could imagine removing the plexiglass and setting up a geostrophically balanced flow into the screen with this original slope.In this case,there would be,no,cross-channel mass flux.This cant happen:why?(There are a couple of reasons.),3.For the ambitious:solve for the equilibrium height and estimate the cross-channel mass flux.Make as many simplifying assumptions as necessary.,An Adjustment Problem:Homewor,4,Review-1,Top-of-Atmosphere Radiation,Hartmann 1994,Transport is needed to explain the observed distribution of TOA radiation and the temperature distribution of the atmosphere.,Rotation supresses zonally symmetric circulations,so,Baroclinic waves(transient and stationary)must do the transport.,Review-1Top-of-Atmosphere R,5,Review 2,Meridional Velocity Correlations,Chang and Yu 1999,Chang 1993,Transient baroclinic waves transport much of the energy in the extratropics.,They travel in packets and have characteristic phase tilts that correspond to systematic effects on the mean flow.,A set of models of increasing complexity accounts for these structures.,Review 2Meridional Velocity,6,Review 3,Phillips(Holton),We described a sequence of linear models of baroclinic waves.,Eady(Gill),Charney(Gill),Simmons and Hoskins,Review 3Phillips(Holton)We,7,Review 4,Nonlinear Baroclinic Lifecycles,Nonlinear primitive equations models showed how baroclinic eddies can be set up,grow,and saturate.,But there needs to be a way of restoring the baroclinicity for them to be sustained.,Review 4Nonlinear Baroclinic,8,Transient Eddies in Climate Models,We have seen that we need(at least)a three-dimensional primitive equations model to properly capture baroclinic eddy structure.,We began talking about a,dry,nonlinear primitive equations model with the following forcing and dissipation:,Transient Eddies in Climate Mo,9,Baroclinic Turbulence Models:T.Schneider,Schneider 2004,Lets first look at a dry GCM developed by Tapio Schneider.,In his model,the tropospheric equilibrium temperature profile is convectively unstable.,The deep tropics are constrained to be close to an“effective”moist adiabat with strong thermal damping.In midlatitudes,the damping is weaker.,Notice that the end climate is stably stratified.The dark line in the upper third of the figure is the tropopause(defined in a special way).,Equilibrium Potential Temperature(input),Time Mean Potential Temperature(output),Baroclinic Turbulence Models:,10,Baroclinic Turbulence Models:T.Schneider,Schneider 2004,Whats interesting here is that there is no dry convective adjustment in the model:the,baroclinic eddies set the stratification of the extratropics.,In the same paper,Schneider argues that the same dynamics establishes the gross features of the tropopause.,Equilibrium Potential Temperature,Time Mean Potential Temperature,Baroclinic Turbulence Models:,11,Baroclinic Turbulence Models:T.Schneider,Schneider 2004,His definition of the tropopause is based on the flux of mass between isentropic surfaces,represented at right in a potential-temperature/latitude plot of mass streamfunction(bottom).This is the Brewer-Dobson circulation of the troposphere,with a strong midlatitude eddy driven component.,The dotted lines mark typical surface potential temperature values.Most of the return flow occurs at temperatures below the average surface temperature,in“cold air outbreaks.“,Time Mean Potential Temperature,Mass Streamfunction,Baroclinic Turbulence Models:,12,Baroclinic Turbulence Models:T.Schneider,Schneider 2004,Based on the idea that baroclinic eddies diffuse PV in the interior and potential temperature at the surface,Schneider derives the following scaling relationship:,This implies that the lowermost isentrope that reaches the tropopause should originate in the tropics.,The plot at left represents the LHS and RHS of this estimate for a very wide range of simulations.The estimate is very robust.
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