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
Complex number analogy:
Examples of moving off the real axis
1.
2.
3.
4.
5.
Dependence of climate on convection schemes
Non-rotating radiative-convective equilibrium
Rotating radiative-convective equilibrium
Hypohydorstatic rescaling
Relative importance of upper and lower level
baroclinicity in 3-layer QG model
Idealized moist atmospheric model
Zonally symmetric climate,
No seasons, no diurnal cycle, no clouds
3 different idealized convection schemes
Dargan Frierson
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
Non-rotating radiative convective equilibrium
Hard to use as benchmark because of “aggregation”
Larger domain
Muller, Zhao
Remove cloud-radiative interactions
and wind speed dependence in surface
flux, and keep domain small, to
minimize worry about aggregation
Q(Z)
Z
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?
Rotating radiative-convective equilibrium
Wenyou Zhou – 25km hydro
f=20 (near surface winds)
295K
307K
Comprehensive model
Aqua – slab ocean
(Tim Merlis.
8
Andrew Ballinger)
SST = 301K
5N
20N
1,000 km => 10,000 km
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
Can we decrease separation between balanced and convective dynamics?
small earth : a ® a a
W ® a -1W
other time scales must be reduced
but g is not parameter in hydrostatic core
deep earth : g ® a -1g
hypohydrostatic :
Dw
Dw
®a2
Dt
Dt
Study climate as a function of g – work in progress
Model generated
zonal wind responses
El Nino
 Poleward shift unlikely to be
primarily forced by tropical
warming
trend
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 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
Additional parameters in three-layer model:
• relative mass of 3rd layer
• relative density jumps across the two interfaces
• relative radiative relaxation times
• relative width/strength of upper and lower
radiative equilibrium baroclinic zones
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
Upper level
radiative eq. shear
Vertically averaged APE
(upper layer
radiative equilibrium jet)
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.