atmospheric general circulation in an idealized dry gcm without eddy-eddy interactions
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Aspen Center for PhysicsWorkshop on Climate Modeling and Stochastic Flows
Atmospheric general circulation in an idealized dry GCMwithout 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 theRossby deformation radius in the atmosphere.
Previous work suggests that this is due to the effect of barocliniceddies on the thermal stratification that inhibits strong eddy-eddyinteractions (Schneider and Walker, 2006).
How important are nonlinear eddy-eddy interactions for the zonallyaveraged meridional circulation, the scale of the energy containingeddies and the stratification?
First step: look at the climatology of an idealized dry GCM inwhich the eddy-eddy interactions are removed.
Long-term objective: build higher-order closures for the hierarchy ofmoments to solve for the flow statistics (work in progress with BradMarston, Brown University).
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 2 / 19
Motivation
No evidence for any inverse energy cascade to scales larger than theRossby deformation radius in the atmosphere.
Previous work suggests that this is due to the effect of barocliniceddies on the thermal stratification that inhibits strong eddy-eddyinteractions (Schneider and Walker, 2006).
How important are nonlinear eddy-eddy interactions for the zonallyaveraged meridional circulation, the scale of the energy containingeddies and the stratification?
First step: look at the climatology of an idealized dry GCM inwhich the eddy-eddy interactions are removed.
Long-term objective: build higher-order closures for the hierarchy ofmoments to solve for the flow statistics (work in progress with BradMarston, Brown University).
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 2 / 19
Motivation
No evidence for any inverse energy cascade to scales larger than theRossby deformation radius in the atmosphere.
Previous work suggests that this is due to the effect of barocliniceddies on the thermal stratification that inhibits strong eddy-eddyinteractions (Schneider and Walker, 2006).
How important are nonlinear eddy-eddy interactions for the zonallyaveraged meridional circulation, the scale of the energy containingeddies and the stratification?
First step: look at the climatology of an idealized dry GCM inwhich the eddy-eddy interactions are removed.
Long-term objective: build higher-order closures for the hierarchy ofmoments to solve for the flow statistics (work in progress with BradMarston, Brown University).
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 2 / 19
Motivation
No evidence for any inverse energy cascade to scales larger than theRossby deformation radius in the atmosphere.
Previous work suggests that this is due to the effect of barocliniceddies on the thermal stratification that inhibits strong eddy-eddyinteractions (Schneider and Walker, 2006).
How important are nonlinear eddy-eddy interactions for the zonallyaveraged meridional circulation, the scale of the energy containingeddies and the stratification?
First step: look at the climatology of an idealized dry GCM inwhich the eddy-eddy interactions are removed.
Long-term objective: build higher-order closures for the hierarchy ofmoments to solve for the flow statistics (work in progress with BradMarston, Brown University).
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 2 / 19
Motivation
No evidence for any inverse energy cascade to scales larger than theRossby deformation radius in the atmosphere.
Previous work suggests that this is due to the effect of barocliniceddies on the thermal stratification that inhibits strong eddy-eddyinteractions (Schneider and Walker, 2006).
How important are nonlinear eddy-eddy interactions for the zonallyaveraged meridional circulation, the scale of the energy containingeddies and the stratification?
First step: look at the climatology of an idealized dry GCM inwhich the eddy-eddy interactions are removed.
Long-term objective: build higher-order closures for the hierarchy ofmoments to solve for the flow statistics (work in progress with BradMarston, Brown University).
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 2 / 19
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 aradiative-equilibrium profile with pole-to-equator surface temperaturecontrast ∆h (∆h=90K for an Earth-like climate).
The model is dry but mimics some aspects of moist convection in aconvection scheme that relaxes temperature toward a prescribedlapse rate (γ× dry adiabatic lapse rate, γ = 0.7 for an Earth-likeclimate).
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 3 / 19
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 aradiative-equilibrium profile with pole-to-equator surface temperaturecontrast ∆h (∆h=90K for an Earth-like climate).
The model is dry but mimics some aspects of moist convection in aconvection scheme that relaxes temperature toward a prescribedlapse rate (γ× dry adiabatic lapse rate, γ = 0.7 for an Earth-likeclimate).
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 3 / 19
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 aradiative-equilibrium profile with pole-to-equator surface temperaturecontrast ∆h (∆h=90K for an Earth-like climate).
The model is dry but mimics some aspects of moist convection in aconvection scheme that relaxes temperature toward a prescribedlapse rate (γ× dry adiabatic lapse rate, γ = 0.7 for an Earth-likeclimate).
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 3 / 19
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
∂t= −v
∂a
∂y= −v
∂a
∂y− v
∂a′
∂y− v ′
∂a
∂y− v ′
∂a′
∂y
transformed into
∂a
∂t= −v
∂a
∂y− v
∂a′
∂y− v ′
∂a
∂y− v′
∂a′
∂y
Statistics of such a model are equivalent to a second order cumulantexpansion (third order cumulants set to 0 in the second orderequations).
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 4 / 19
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
∂t= −v
∂a
∂y= −v
∂a
∂y− v
∂a′
∂y− v ′
∂a
∂y− v ′
∂a′
∂y
transformed into
∂a
∂t= −v
∂a
∂y− v
∂a′
∂y− v ′
∂a
∂y− v′
∂a′
∂y
Statistics of such a model are equivalent to a second order cumulantexpansion (third order cumulants set to 0 in the second orderequations).
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 4 / 19
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
∂t= −v
∂a
∂y= −v
∂a
∂y− v
∂a′
∂y− v ′
∂a
∂y− v ′
∂a′
∂y
transformed into
∂a
∂t= −v
∂a
∂y− v
∂a′
∂y− v ′
∂a
∂y− v′
∂a′
∂y
Statistics of such a model are equivalent to a second order cumulantexpansion (third order cumulants set to 0 in the second orderequations).
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 4 / 19
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
∂t= −v
∂a
∂y= −v
∂a
∂y− v
∂a′
∂y− v ′
∂a
∂y− v ′
∂a′
∂y
transformed into
∂a
∂t= −v
∂a
∂y− v
∂a′
∂y− v ′
∂a
∂y− v′
∂a′
∂y
Statistics of such a model are equivalent to a second order cumulantexpansion (third order cumulants set to 0 in the second orderequations).
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 4 / 19
Experiments
We compare the output of the full model with that of the modelwithout eddy-eddy interactions for 0.6 ≤ γ ≤ 1.0, for 0 ≤ ∆h ≤ 180Kand 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 aspin-up of 1600 days.
We focus on the meridional zonally averaged circulation, and morespecifically on mid-latitudes.
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 5 / 19
Experiments
We compare the output of the full model with that of the modelwithout eddy-eddy interactions for 0.6 ≤ γ ≤ 1.0, for 0 ≤ ∆h ≤ 180Kand 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 aspin-up of 1600 days.
We focus on the meridional zonally averaged circulation, and morespecifically on mid-latitudes.
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 5 / 19
Experiments
We compare the output of the full model with that of the modelwithout eddy-eddy interactions for 0.6 ≤ γ ≤ 1.0, for 0 ≤ ∆h ≤ 180Kand 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 aspin-up of 1600 days.
We focus on the meridional zonally averaged circulation, and morespecifically on mid-latitudes.
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 5 / 19
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
Zonal flow
γ = 0.7
∆h = 90K
Earth’srotation
Full model No eddy-eddy
Contours: zonal flow in m.s−1
Colors: horizontal eddy momentum flux convergence1
a cosφ∂∂φ(u′v ′ cos2 φ) in m2.s−1
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 7 / 19
Zonal flow with varying ∆h
γ = 0.7
∆h = 30K
Earth’s rotation
γ = 0.7
∆h = 150K
Earth’s rotation
Full model No eddy-eddy
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 8 / 19
Zonal flow with varying rotation rate
γ = 0.7
∆h = 90K
Earth’s rotation
γ = 0.7
∆h = 90K
4×Earth’srotation
Full model No eddy-eddy
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 9 / 19
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
Full model No eddy-eddy
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 10 / 19
Zonal flow in the no eddy-eddy model:Summary
For large rotation rates, small ∆h, or, to a lesser extent small γ, themodel without eddy-eddy interactions forms realistic (magnitude andlocation) subtropical and eddy-driven jets.
For moderate rotation rates, large ∆h or γ, the circulation iscompressed in the meridional direction, with the appearance ofsecondary eddy-driven jets. This might be related to less isotropiceddies. The subtropical jet is over-estimated and the verticalstructure of momentum flux is not captured.
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 11 / 19
Zonal flow in the no eddy-eddy model:Summary
For large rotation rates, small ∆h, or, to a lesser extent small γ, themodel without eddy-eddy interactions forms realistic (magnitude andlocation) subtropical and eddy-driven jets.
For moderate rotation rates, large ∆h or γ, the circulation iscompressed in the meridional direction, with the appearance ofsecondary eddy-driven jets. This might be related to less isotropiceddies. The subtropical jet is over-estimated and the verticalstructure of momentum flux is not captured.
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 11 / 19
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 ofthe Eliassen-Palm vector F (red arrows)
F = a cosφ
−u′v ′
f v ′θ′/ ∂θ∂pFarid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 12 / 19
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 ofthe Eliassen-Palm vector F (red arrows)
F = a cosφ
−u′v ′
f v ′θ′/ ∂θ∂pFarid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 13 / 19
Supercriticality Sc
A non-dimensional measure of near-surface isentropes slopes. Estimate themean level (pressure pe) up to which baroclinic activity redistributesentropy received at the surface (Schneider and Walker, 2006).
Sc =−f /β∂yθsurf
−2∂pθsurf
(psurf − ptrop)∼ (psurf − pe)
(psurf − ptrop)
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 14 / 19
Supercriticality Sc
For each γ, the collection of points is obtained by varying ∆h (smaller ∆h
corresponds to larger symbols).
Earth’s rotation
2× Earth’srotation
Full model No eddy-eddy
100
102
γ=0.6γ=0.7γ=0.8γ=0.9γ=1.0
100
102
100
102
100
102
Rescaled surface potential temperature gradient (K)
Bul
k st
abili
ty (
K)
Rescaled surfacepot. temp. gradient−f /β∂yθs
Bulk stability2∂pθ
s(ps − pt )
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 15 / 19
Eddy energy
Scaling of the eddy available potential energy (EAPE) with the barocliniceddy kinetic energy (EKE), averaged over the baroclinic zone.
Earth’s rotation
2× Earth’srotation
Full model No eddy-eddy
102
104
106
108
y=2.25xγ=0.6γ=0.7γ=0.8γ=0.9
102
103
104
105
106
102
104
106
108
y=2.25x
y=1.5x
102
103
104
105
106
y=2.25x
Baroclinic EKE (J m−2)
Edd
y A
PE
(J
m−
2 )
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 16 / 19
Rossby and Rhines wavenumbers
Earth’s rotation
2× Earth’srotation
Rossby wavenumber Rhines wavenumber
100
101
102
100
101
102
γ=0.6γ=0.7γ=0.8γ=0.9γ=1.0
100
101
102
100
101
102
100
101
102
100
101
102
100
101
102
100
101
102
No eddy−eddy model
Ful
l mod
el
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 17 / 19
Conclusions
The no eddy-eddy model performs better when the baroclinic activityis weak (small γ, small ∆h and fast rotation in our experiments).Realistic subtropical jet, eddy-driven jets (without any inversecascade) and stratification.
The zonal eddy length scale are close to be reproduced, with a linearscaling of EAPE with eddy EKE over a wide range of parameters.However, the no edd-eddy model does not achieve a realistichorizontal isotropisation of the baroclinic eddies.
When the baroclinic activity is strong, it is too shallow in the noeddy-eddy model. What is the role of the eddy-eddy interactionsin determining the vertical structure of the mid-latitudestroposphere?
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 18 / 19
Conclusions
The no eddy-eddy model performs better when the baroclinic activityis weak (small γ, small ∆h and fast rotation in our experiments).Realistic subtropical jet, eddy-driven jets (without any inversecascade) and stratification.
The zonal eddy length scale are close to be reproduced, with a linearscaling of EAPE with eddy EKE over a wide range of parameters.However, the no edd-eddy model does not achieve a realistichorizontal isotropisation of the baroclinic eddies.
When the baroclinic activity is strong, it is too shallow in the noeddy-eddy model. What is the role of the eddy-eddy interactionsin determining the vertical structure of the mid-latitudestroposphere?
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 18 / 19
Conclusions
The no eddy-eddy model performs better when the baroclinic activityis weak (small γ, small ∆h and fast rotation in our experiments).Realistic subtropical jet, eddy-driven jets (without any inversecascade) and stratification.
The zonal eddy length scale are close to be reproduced, with a linearscaling of EAPE with eddy EKE over a wide range of parameters.However, the no edd-eddy model does not achieve a realistichorizontal isotropisation of the baroclinic eddies.
When the baroclinic activity is strong, it is too shallow in the noeddy-eddy model.
What is the role of the eddy-eddy interactionsin determining the vertical structure of the mid-latitudestroposphere?
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 18 / 19
Conclusions
The no eddy-eddy model performs better when the baroclinic activityis weak (small γ, small ∆h and fast rotation in our experiments).Realistic subtropical jet, eddy-driven jets (without any inversecascade) and stratification.
The zonal eddy length scale are close to be reproduced, with a linearscaling of EAPE with eddy EKE over a wide range of parameters.However, the no edd-eddy model does not achieve a realistichorizontal isotropisation of the baroclinic eddies.
When the baroclinic activity is strong, it is too shallow in the noeddy-eddy model. What is the role of the eddy-eddy interactionsin determining the vertical structure of the mid-latitudestroposphere?
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 18 / 19
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 theeddy-eddy interactions for a wide range of atmospheric circulations.
Thank you
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 19 / 19
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 theeddy-eddy interactions for a wide range of atmospheric circulations.
Thank you
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 19 / 19
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