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- Author or Editor: Ulrike Burkhardt x
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Abstract
The mixing-length-based parameterization of horizontal diffusion, which was originally proposed by Smagorinsky, is revisited. The complete tendencies of horizontal momentum diffusion, the associated frictional heating, and horizontal diffusion of sensible heat in spherical geometry are derived. The formulations are modified for the terrain-following vertical-hybrid-coordinate system in a way that ensures energy and angular momentum conservation at each layer. Test simulations with a simple general circulation model, run at T42 horizontal resolution and for permanent January conditions, confirm the conservation properties and highlight the enhancement of nonlinear horizontal diffusion in areas of high baroclinic activity. The simulated internal variability is dependent on the nature of the horizontal diffusion, with high-frequency variability being enhanced over the northern continents and low-frequency variability being increased (decreased) over the Pacific (Atlantic) Ocean when using nonlinear rather than linear diffusion. Locally reduced horizontal dissipation over Europe is compensated by increased dissipation owing to vertical diffusion, indicating the potential importance of nonlinear horizontal diffusion for gravity wave–resolving simulations. Inspection of the spectral energy reveals that the scheme needs to be modified in order to damp unbalanced ageostrophic motions at the smallest resolved scales more efficiently. A corresponding empirical modification is proposed and proves to work properly.
Abstract
The mixing-length-based parameterization of horizontal diffusion, which was originally proposed by Smagorinsky, is revisited. The complete tendencies of horizontal momentum diffusion, the associated frictional heating, and horizontal diffusion of sensible heat in spherical geometry are derived. The formulations are modified for the terrain-following vertical-hybrid-coordinate system in a way that ensures energy and angular momentum conservation at each layer. Test simulations with a simple general circulation model, run at T42 horizontal resolution and for permanent January conditions, confirm the conservation properties and highlight the enhancement of nonlinear horizontal diffusion in areas of high baroclinic activity. The simulated internal variability is dependent on the nature of the horizontal diffusion, with high-frequency variability being enhanced over the northern continents and low-frequency variability being increased (decreased) over the Pacific (Atlantic) Ocean when using nonlinear rather than linear diffusion. Locally reduced horizontal dissipation over Europe is compensated by increased dissipation owing to vertical diffusion, indicating the potential importance of nonlinear horizontal diffusion for gravity wave–resolving simulations. Inspection of the spectral energy reveals that the scheme needs to be modified in order to damp unbalanced ageostrophic motions at the smallest resolved scales more efficiently. A corresponding empirical modification is proposed and proves to work properly.
Abstract
The diffusion–dissipation parameterizations usually adopted in GCMs are not physically consistent. Horizontal momentum diffusion, applied in the form of a hyperdiffusion, does not conserve angular momentum and the associated dissipative heating is commonly ignored. Dissipative heating associated with vertical momentum diffusion is often included, but in a way that is inconsistent with the second law of thermodynamics.
New, physically consistent, dissipative heating schemes due to horizontal diffusion (Becker) and vertical diffusion (Becker, and Boville and Bretherton) have been developed and tested. These schemes have now been implemented in 19- and 39-level versions of the ECHAM4 climate model. The new horizontal scheme requires the replacement of the hyperdiffusion with a ∇2 scheme.
Dissipation due to horizontal momentum diffusion is found to have maximum values in the upper troposphere/lower stratosphere in midlatitudes and in the winter hemispheric sponge layer, resulting in a warming of the area around the tropopause and of the polar vortex in Northern Hemispheric winter. Dissipation associated with vertical momentum diffusion is largest in the boundary layer. The change in parameterization acts to strengthen the vertical diffusion and therefore the associated dissipative heating. Dissipation due to vertical momentum diffusion has an indirect effect on the upper-tropospheric/stratospheric temperature field in northern winter, which is to cool and strengthen the northern polar vortex. The warming in the area of the tropopause resulting from the change in both dissipation parameterizations is quite similar in both model versions, whereas the response in the temperature of the northern polar vortex depends on the model version.
Abstract
The diffusion–dissipation parameterizations usually adopted in GCMs are not physically consistent. Horizontal momentum diffusion, applied in the form of a hyperdiffusion, does not conserve angular momentum and the associated dissipative heating is commonly ignored. Dissipative heating associated with vertical momentum diffusion is often included, but in a way that is inconsistent with the second law of thermodynamics.
New, physically consistent, dissipative heating schemes due to horizontal diffusion (Becker) and vertical diffusion (Becker, and Boville and Bretherton) have been developed and tested. These schemes have now been implemented in 19- and 39-level versions of the ECHAM4 climate model. The new horizontal scheme requires the replacement of the hyperdiffusion with a ∇2 scheme.
Dissipation due to horizontal momentum diffusion is found to have maximum values in the upper troposphere/lower stratosphere in midlatitudes and in the winter hemispheric sponge layer, resulting in a warming of the area around the tropopause and of the polar vortex in Northern Hemispheric winter. Dissipation associated with vertical momentum diffusion is largest in the boundary layer. The change in parameterization acts to strengthen the vertical diffusion and therefore the associated dissipative heating. Dissipation due to vertical momentum diffusion has an indirect effect on the upper-tropospheric/stratospheric temperature field in northern winter, which is to cool and strengthen the northern polar vortex. The warming in the area of the tropopause resulting from the change in both dissipation parameterizations is quite similar in both model versions, whereas the response in the temperature of the northern polar vortex depends on the model version.
