Atmospheric general circulation in an idealized dry GCM without eddy-eddy interactions
1. 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
2. Motivation
No evidence for any inverse energy cascade to scales larger than the
Rossby deformation radius in the atmosphere.
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 2 / 19
3. Motivation
No evidence for any inverse energy cascade to scales larger than the
Rossby deformation radius in the atmosphere.
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 ).
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 2 / 19
4. Motivation
No evidence for any inverse energy cascade to scales larger than the
Rossby deformation radius in the atmosphere.
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 ).
How important are nonlinear eddy-eddy interactions for the zonally
averaged meridional circulation, the scale of the energy containing
eddies and the stratification?
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 2 / 19
5. Motivation
No evidence for any inverse energy cascade to scales larger than the
Rossby deformation radius in the atmosphere.
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 ).
How important are nonlinear eddy-eddy interactions for the zonally
averaged meridional circulation, the scale of the energy containing
eddies and the stratification?
First step: look at the climatology of an idealized dry GCM in
which the eddy-eddy interactions are removed.
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 2 / 19
6. Motivation
No evidence for any inverse energy cascade to scales larger than the
Rossby deformation radius in the atmosphere.
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 ).
How important are nonlinear eddy-eddy interactions for the zonally
averaged meridional circulation, the scale of the energy containing
eddies and the stratification?
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).
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 2 / 19
7. An idealized dry GCM
Based on the GFDL pseudospectral dynamical core (Schneider and Walker,
2006 ). Uniform surface, no seasonal cycle.
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 3 / 19
8. 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).
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 3 / 19
9. 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).
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).
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 3 / 19
10. Dry GCM without eddy-eddy interactions
Removal of the eddy-eddy interactions (O’Gorman and Schneider,
2007 ).
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 4 / 19
11. Dry GCM without eddy-eddy interactions
Removal of the eddy-eddy interactions (O’Gorman and Schneider,
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
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 4 / 19
12. Dry GCM without eddy-eddy interactions
Removal of the eddy-eddy interactions (O’Gorman and Schneider,
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
transformed into
∂a ∂a ∂a ∂a ∂a
= −v −v −v −v
∂t ∂y ∂y ∂y ∂y
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 4 / 19
13. Dry GCM without eddy-eddy interactions
Removal of the eddy-eddy interactions (O’Gorman and Schneider,
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
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).
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 4 / 19
14. 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 )
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 5 / 19
15. 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 )
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.
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 5 / 19
16. 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 )
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.
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 5 / 19
17. Instantaneous vorticity fields
Full model No eddy-eddy
Typical instantaneous vorticity fields in the mid-troposphere (σ = 0.5)
O’Gorman and Schneider, 2007
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 6 / 19
18. Zonal flow
Full model No eddy-eddy
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
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 7 / 19
19. Zonal flow with varying ∆h
Full model No eddy-eddy
γ = 0.7
∆h = 30K
Earth’s rotation
γ = 0.7
∆h = 150K
Earth’s rotation
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 8 / 19
20. Zonal flow with varying rotation rate
Full model No eddy-eddy
γ = 0.7
∆h = 90K
Earth’s rotation
γ = 0.7
∆h = 90K
4×Earth’s
rotation
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 9 / 19
21. Zonal flow with varying the convective lapse rate γ
Full model No eddy-eddy
γ = 0.6
∆h = 90K
Earth’s rotation
γ = 0.9
∆h = 90K
Earth’s rotation
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 10 / 19
22. 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.
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 11 / 19
23. 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.
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 11 / 19
24. Potential vorticity eddy fluxes
Parameters: γ = 0.7, ∆h = 150K and Earth’s rotation
Full model No eddy-eddy
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
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 12 / 19
25. Potential vorticity eddy fluxes
Parameters: γ = 0.7, ∆h = 90K and 4× Earth’s rotation
Full model No eddy-eddy
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
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 13 / 19
26. 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 )
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 14 / 19
27. Supercriticality Sc
For each γ, the collection of points is obtained by varying ∆h (smaller ∆h
corresponds to larger symbols).
Full model No eddy-eddy
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)
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 15 / 19
28. Eddy energy
Scaling of the eddy available potential energy (EAPE) with the baroclinic
eddy kinetic energy (EKE), averaged over the baroclinic zone.
Full model No eddy-eddy
8
10
y=2.25x y=1.5x
γ=0.6
6
10 γ=0.7
Earth’s rotation 4
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)
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 16 / 19
30. 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.
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 18 / 19
31. 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.
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.
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 18 / 19
32. 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.
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.
When the baroclinic activity is strong, it is too shallow in the no
eddy-eddy model.
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 18 / 19
33. 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.
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.
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?
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 18 / 19
34. 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.
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 19 / 19
35. 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
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 19 / 19