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

1. Dependence of climate on convection schemes2. Non-rotating radiative-convective equilibrium3. Rotating radiative-convective equilibrium4. Hypohydorstatic rescaling5. Relative importance of upper and lower level baroclinicity in 3-layer QG model

Complex number analogy:Examples of moving off the real axis

Idealized moist atmospheric modelZonally symmetric climate,

No seasons, no diurnal cycle, no clouds3 different idealized convection

schemes

Dargan Frierson

Rather than (or in addition to) trying to find the bestconvection parameterization, define interesting classes

of schemes and try to map out how climate statistics varyacross this space of models

Non-rotating radiative convective equilibriumHard to use as benchmark because of “aggregation”

Larger domain

Muller, Zhao

Z

Q(Z)

Remove cloud-radiative interactions and wind speed dependence in surfaceflux, and keep domain small, to minimize worry about aggregation

Compare response ofradiative-convective equiliibriumto upper tropospheric heatingin cloud-resolving and hydrostaticmodels with convective parameterization(in progress,Muller and Zhou). Initial result isthat the two models behave very differently

Is this a useful test?

Wenyou Zhou – 25km hydro

307K295K

f=20 (near surface winds)

Rotating radiative-convective equilibrium

8

Aqua – slab ocean(Tim Merlis.Andrew Ballinger)

Comprehensive model

5N 20N

SST = 301K

1,000 km => 10,000 km

Radius ofMaximum winds

Although resolution ismarginal, model doesproduce systematic changesas parameters are varied

As f increases, externalscale of storm decreasesbut RMW decreases

As SST increases, externalscale increases but RMWdecreases

Study climate as a function of g – work in progress

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

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)

Statistically steady 3 layer QG, forced by thermal relaxationto 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

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.

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

Vertically averaged APE(upper layer

radiative equilibrium jet)

Upper level radiative eq. shear

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 challengingbecause 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.