Atmospheric general circulation in an idealized dry GCM without eddy-eddy interactions

Aspen Center for Physics
Workshop on Climate Modeling and Stochastic Flows

Atmospheric general circulation in an idealized dry GCM
without eddy-eddy interactions

Farid Ait-Chaalal and Tapio Schneider

California Institute of Technology
farid.ait-chaalal@gps.caltech.edu

June 26, 2012

Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 1 / 19

Motivation

No evidence for any inverse energy cascade to scales larger than the
Rossby deformation radius in the atmosphere.


Motivation

Previous work suggests that this is due to the eﬀect of baroclinic
eddies on the thermal stratiﬁcation that inhibits strong eddy-eddy
interactions (Schneider and Walker, 2006 ).


Motivation

How important are nonlinear eddy-eddy interactions for the zonally
averaged meridional circulation, the scale of the energy containing
eddies and the stratiﬁcation?


Motivation

First step: look at the climatology of an idealized dry GCM in
which the eddy-eddy interactions are removed.


Motivation

First step: look at the climatology of an idealized dry GCM in
which the eddy-eddy interactions are removed.
Long-term objective: build higher-order closures for the hierarchy of
moments to solve for the ﬂow statistics (work in progress with Brad
Marston, Brown University).


An idealized dry GCM

Based on the GFDL pseudospectral dynamical core (Schneider and Walker,
2006 ). Uniform surface, no seasonal cycle.



Radiative parametrization: Newtonian relaxation toward a
radiative-equilibrium proﬁle with pole-to-equator surface temperature
contrast ∆h (∆h =90K for an Earth-like climate).



Radiative parametrization: Newtonian relaxation toward a
radiative-equilibrium proﬁle with pole-to-equator surface temperature
contrast ∆h (∆h =90K for an Earth-like climate).
The model is dry but mimics some aspects of moist convection in a
convection scheme that relaxes temperature toward a prescribed
lapse rate (γ× dry adiabatic lapse rate, γ = 0.7 for an Earth-like
climate).


Dry GCM without eddy-eddy interactions

Removal of the eddy-eddy interactions (O’Gorman and Schneider,
2007 ).



2007 ).
Advection of a quantity a = a + a by the meridional ﬂow v = v + v
(zonal mean/eddy decomposition):

∂a ∂a ∂a ∂a ∂a ∂a
= −v = −v −v −v −v
∂t ∂y ∂y ∂y ∂y ∂y



2007 ).

∂a ∂a ∂a ∂a ∂a ∂a
= −v = −v −v −v −v
∂t ∂y ∂y ∂y ∂y ∂y
transformed into
∂a ∂a ∂a ∂a ∂a
= −v −v −v −v
∂t ∂y ∂y ∂y ∂y



2007 ).

∂a ∂a ∂a ∂a ∂a ∂a
= −v = −v −v −v −v
∂t ∂y ∂y ∂y ∂y ∂y
transformed into
∂a ∂a ∂a ∂a ∂a
= −v −v −v −v
∂t ∂y ∂y ∂y ∂y

Statistics of such a model are equivalent to a second order cumulant
expansion (third order cumulants set to 0 in the second order
equations).

Experiments

We compare the output of the full model with that of the model
without eddy-eddy interactions for 0.6 ≤ γ ≤ 1.0, for 0 ≤ ∆h ≤ 180K
and for three planetary rotation rates (ΩEarth ,2ΩEarth and 4ΩEarth )


Experiments

Simulations are run at T85 (128 latitude bands) with 30 σ-levels.
The climatology is obtained through an average over 400 days, after a
spin-up of 1600 days.


Experiments

Simulations are run at T85 (128 latitude bands) with 30 σ-levels.
The climatology is obtained through an average over 400 days, after a
spin-up of 1600 days.
We focus on the meridional zonally averaged circulation, and more
speciﬁcally on mid-latitudes.


Instantaneous vorticity ﬁelds

Full model No eddy-eddy

Typical instantaneous vorticity ﬁelds in the mid-troposphere (σ = 0.5)
O’Gorman and Schneider, 2007


Zonal flow


γ = 0.7
∆h = 90K
Earth’s
rotation

Contours: zonal flow in m.s−1
Colors: horizontal eddy momentum flux convergence
1 ∂ 2 2 −1
a cos φ ∂φ (u v cos φ) in m .s


Zonal ﬂow with varying ∆h


γ = 0.7
∆h = 30K
Earth’s rotation

γ = 0.7
∆h = 150K
Earth’s rotation


Zonal ﬂow with varying rotation rate


γ = 0.7
∆h = 90K
Earth’s rotation

γ = 0.7
∆h = 90K
4×Earth’s
rotation


Zonal ﬂow with varying the convective lapse rate γ


γ = 0.6
∆h = 90K
Earth’s rotation

γ = 0.9
∆h = 90K
Earth’s rotation


Zonal ﬂow in the no eddy-eddy model:
Summary

For large rotation rates, small ∆h , or, to a lesser extent small γ, the
model without eddy-eddy interactions forms realistic (magnitude and
location) subtropical and eddy-driven jets.


Zonal ﬂow in the no eddy-eddy model:
Summary

For large rotation rates, small ∆h , or, to a lesser extent small γ, the
model without eddy-eddy interactions forms realistic (magnitude and
location) subtropical and eddy-driven jets.
For moderate rotation rates, large ∆h or γ, the circulation is
compressed in the meridional direction, with the appearance of
secondary eddy-driven jets. This might be related to less isotropic
eddies. The subtropical jet is over-estimated and the vertical
structure of momentum ﬂux is not captured.


Potential vorticity eddy ﬂuxes

Parameters: γ = 0.7, ∆h = 150K and Earth’s rotation

Potential vorticity eddy ﬂuxes (colors), or equivalently the divergence of
the Eliassen-Palm vector F (red arrows)
−u v
F = a cos φ ∂θ
f v θ / ∂p

Potential vorticity eddy ﬂuxes

Parameters: γ = 0.7, ∆h = 90K and 4× Earth’s rotation

Potential vorticity eddy ﬂuxes (colors), or equivalently the divergence of
the Eliassen-Palm vector F (red arrows)
−u v
F = a cos φ ∂θ
f v θ / ∂p

Supercriticality Sc

A non-dimensional measure of near-surface isentropes slopes. Estimate the
mean level (pressure pe ) up to which baroclinic activity redistributes
entropy received at the surface (Schneider and Walker, 2006 ).

−f /β∂y θsurf (p surf − p e )
Sc = surf
∼
−2∂p θ (p surf − p trop ) (p surf − p trop )


Supercriticality Sc

For each γ, the collection of points is obtained by varying ∆h (smaller ∆h
corresponds to larger symbols).
2
10

Earth’s rotation 0
10
γ=0.6
γ=0.7
γ=0.8
γ=0.9
γ=1.0
Bulk stability (K)

Rescaled surface
pot. temp. gradient
−f /β∂y θs
Bulk stability
s
2
2∂p θ (p s − p t )
10
2× Earth’s
rotation
0
10

0 2 0 2
10 10 10 10
Rescaled surface potential temperature gradient (K)


Eddy energy

Scaling of the eddy available potential energy (EAPE) with the baroclinic
eddy kinetic energy (EKE), averaged over the baroclinic zone.
8
10
y=2.25x y=1.5x
γ=0.6
6
10 γ=0.7

10
γ=0.8
γ=0.9
Eddy APE (J m−2)

2
10

8
10
y=2.25x y=2.25x

6
10

2× Earth’s 4
10

rotation 2
10

2 3 4 5 6 2 3 4 5 6
10 10 10 10 10 10 10 10 10 10

Baroclinic EKE (J m−2)


Rossby and Rhines wavenumbers

Rossby wavenumber Rhines wavenumber
2 2
10 γ=0.6 10
γ=0.7
γ=0.8
γ=0.9

1
γ=1.0
1
10

0 0
10 0 1 2
10 0 1 2
10 10 10 10 10 10
Full model

2 2
10 10

2× Earth’s 10
1 1
10

rotation 0 0
10 0 1 2
10 0 1 2
10 10 10 10 10 10
No eddy−eddy model


Conclusions

The no eddy-eddy model performs better when the baroclinic activity
is weak (small γ, small ∆h and fast rotation in our experiments).
Realistic subtropical jet, eddy-driven jets (without any inverse
cascade) and stratiﬁcation.


Conclusions

The zonal eddy length scale are close to be reproduced, with a linear
scaling of EAPE with eddy EKE over a wide range of parameters.
However, the no edd-eddy model does not achieve a realistic
horizontal isotropisation of the baroclinic eddies.


Conclusions

When the baroclinic activity is strong, it is too shallow in the no
eddy-eddy model.


Conclusions

When the baroclinic activity is strong, it is too shallow in the no
eddy-eddy model. What is the rˆle of the eddy-eddy interactions
o
in determining the vertical structure of the mid-latitudes
troposphere?


Work in progress

A lot of data to analyze from the no eddy-eddy model...
Development of a stochastic forcing to mimic the behavior of the
eddy-eddy interactions for a wide range of atmospheric circulations.


Work in progress

A lot of data to analyze from the no eddy-eddy model...
Development of a stochastic forcing to mimic the behavior of the
eddy-eddy interactions for a wide range of atmospheric circulations.

Thank you


Atmospheric general circulation in an idealized dry GCM without eddy-eddy interactions

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