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

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Presentation given at the Aspen Center for Physics (http://www.aspenphys.org/). Workshop on
climate modeling and stochastic flows.

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

  1. 1. Aspen Center for PhysicsWorkshop on Climate Modeling and Stochastic FlowsAtmospheric 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. 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. 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. 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. 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. 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. 7. An idealized dry GCMBased 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. 8. An idealized dry GCMBased 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. 9. An idealized dry GCMBased 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. 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. 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. 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. 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. 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. 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. 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. 17. Instantaneous vorticity fields Full model No eddy-eddyTypical 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. 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. 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. 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. 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. 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. 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. 24. Potential vorticity eddy fluxesParameters: γ = 0.7, ∆h = 150K and Earth’s rotation Full model No eddy-eddyPotential vorticity eddy fluxes (colors), or equivalently the divergence ofthe 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. 25. Potential vorticity eddy fluxesParameters: γ = 0.7, ∆h = 90K and 4× Earth’s rotation Full model No eddy-eddyPotential vorticity eddy fluxes (colors), or equivalently the divergence ofthe 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. 26. Supercriticality ScA 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 ). −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. 27. Supercriticality ScFor each γ, the collection of points is obtained by varying ∆h (smaller ∆hcorresponds 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. 28. Eddy energyScaling of the eddy available potential energy (EAPE) with the barocliniceddy 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
  29. 29. Rossby and Rhines wavenumbers Rossby wavenumber Rhines wavenumber 2 2 10 γ=0.6 10 γ=0.7 γ=0.8 γ=0.9 Earth’s rotation 10 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 Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 17 / 19
  30. 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. 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. 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. 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. 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. 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

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