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Thoughts on Climate Theory Based on collaborations with Wenyu Zhou, Dargan Frierson, Sarah Kang, Erica Staehling, Gang Chen, Steve Garner, Ming Zhao Isaac Held, Reading, 2013

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1.Dependence of climate on convection schemes 2.Non-rotating radiative-convective equilibrium 3.Rotating radiative-convective equilibrium 4.Hypohydorstatic rescaling 5.Relative importance of upper and lower level baroclinicity in 3-layer QG model Complex number analogy: Examples of moving off the real axis

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Idealized moist atmospheric model Zonally symmetric climate, No seasons, no diurnal cycle, no clouds 3 different idealized convection schemes Dargan Frierson

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Rather than (or in addition to) trying to find the best convection parameterization, define interesting classes of schemes and try to map out how climate statistics vary across this space of models

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Non-rotating radiative convective equilibrium Hard to use as benchmark because of aggregation Larger domain Muller, Zhao

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Z Q(Z) Remove cloud-radiative interactions and wind speed dependence in surface flux, and keep domain small, to minimize worry about aggregation Compare response of radiative-convective equiliibrium to upper tropospheric heating in cloud-resolving and hydrostatic models with convective parameterization(in progress, Muller and Zhou). Initial result is that the two models behave very differently Is this a useful test?

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Wenyou Zhou – 25km hydro 307K295K f=20 (near surface winds) Rotating radiative-convective equilibrium

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8 Aqua – slab ocean (Tim Merlis. Andrew Ballinger) Comprehensive model

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5N20N SST = 301K

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1,000 km => 10,000 km

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Radius of Maximum winds Although resolution is marginal, model does produce systematic changes as parameters are varied As f increases, external scale of storm decreases but RMW decreases As SST increases, external scale increases but RMW decreases

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Study climate as a function of g – work in progress

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El Nino trend Poleward shift unlikely to be primarily forced by tropical warming Model generated zonal wind responses We have no quantitiatve theory for eddy momentum fluxes

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3 layer QG 3 winds, two interfaces (temperatures) Simplest system allowing one to talk about upper vs lower level temperature gradients (ongoing work with Erica Staehling)

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Statistically steady 3 layer QG, forced by thermal relaxation to produce a localized baroclinically unstable jet; Linear friction in lower layer only Parameters in analogous two-layer model: supercriticality radiative relaxation surface damping width of radiative equilibrium jet relative mass of two layers

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Can configure to try to make top layer look like stratosphere, but we focus here on very symmetric configuration: equal depth layers, identical density jumps, uniform radiative damping, identical strength and width of baroclinic zones in rad. eq.

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Modest displacement => jet and eddy energies shift latitude but remain vertically aligned Larger displacement => eventually splits into two jets, both winds and eddy energies vertically aligned

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Vertically averaged APE (upper layer radiative equilibrium jet ) Upper level radiative eq. shear

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Upper level baroclinicity appears to exert surprisingly strong control on latitude of stormtrack/surface westerlies in this model Developing a closure theory for this system challenging because of non-local character of eddy momentum fluxes Developing a perturbation theory (as in fluctuation-dissipation theory) for the response to a small change in upper level baroclinicity, given the statistics of a control simulation, might be easier.

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