atmospheric general circulation in an idealized dry gcm without eddy-eddy interactions

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

[email protected]

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).

Motivation

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).

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):

∂t= −v

∂y= −v

∂y− v

∂a′

∂y− v ′

∂a′

transformed into

∂t= −v

∂y− v

∂a′

∂y− v ′

∂y− v′

∂a′

Statistics of such a model are equivalent to a second order cumulantexpansion (third order cumulants set to 0 in the second orderequations).

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 ′

∂t= −v

∂y= −v

∂y− v

∂a′

∂y− v ′

∂a′

transformed into

∂t= −v

∂y− v

∂a′

∂y− v ′

∂y− v′

∂a′

∂t= −v

∂y= −v

∂y− v

∂a′

∂y− v ′

∂a′

transformed into

∂t= −v

∂y− v

∂a′

∂y− v ′

∂y− v′

∂a′

∂t= −v

∂y= −v

∂y− v

∂a′

∂y− v ′

∂a′

transformed into

∂t= −v

∂y− v

∂a′

∂y− v ′

∂y− v′

∂a′

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.

Experiments

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’srotation

Contours: zonal flow in m.s−1

Colors: horizontal eddy momentum flux convergence1

a cosφ∂∂φ(u′v ′ cos2 φ) in m2.s−1

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’srotation

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, 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.

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.

Potential vorticity eddy fluxes

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

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

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)

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

γ=0.6γ=0.7γ=0.8γ=0.9γ=1.0

Rescaled surface potential temperature gradient (K)

Rescaled surfacepot. temp. gradient−f /β∂yθs

Bulk stability2∂pθ

s(ps − pt )

Eddy energy

Scaling of the eddy available potential energy (EAPE) with the barocliniceddy kinetic energy (EKE), averaged over the baroclinic zone.

Earth’s rotation

y=2.25xγ=0.6γ=0.7γ=0.8γ=0.9

y=2.25x

y=1.5x

y=2.25x

Baroclinic EKE (J m−2)

Rossby and Rhines wavenumbers

Earth’s rotation

Rossby wavenumber Rhines wavenumber

γ=0.6γ=0.7γ=0.8γ=0.9γ=1.0

No eddy−eddy model

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?

Conclusions

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?

Conclusions

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

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

atmospheric general circulation in an idealized dry gcm without eddy-eddy interactions

Technology

eddyeddy interactions

eddyeddy interactions

idealized dry gcmbased

inverse energy cascade

thermal stratication

baroclinic eddies

rossby deformation radius

higherorder closures