The Vertical Structure of the Eddy Diffusivity and the Equilibration of the Extratropical Atmosphere
Observations suggest that the time- and zonal-mean state of the extratropical atmosphere adjusts itself such that the so-called “criticality parameter” (which relates the vertical stratification to the horizontal temperature gradient) is close to one. T. Schneider has argued that the criticality par...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
American Meteorological Society
2013
|
| Online Access: | http://hdl.handle.net/1721.1/82888 https://orcid.org/0000-0002-3736-1956 |
| _version_ | 1826209602948038656 |
|---|---|
| author | Jansen, Malte Friedrich Ferrari, Raffaele |
| author2 | Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences |
| author_facet | Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences Jansen, Malte Friedrich Ferrari, Raffaele |
| author_sort | Jansen, Malte Friedrich |
| collection | MIT |
| description | Observations suggest that the time- and zonal-mean state of the extratropical atmosphere adjusts itself such that the so-called “criticality parameter” (which relates the vertical stratification to the horizontal temperature gradient) is close to one. T. Schneider has argued that the criticality parameter is kept near one by a constraint on the zonal momentum budget in primitive equations. The constraint relies on a diffusive closure for the eddy flux of potential vorticity (PV) with an eddy diffusivity that is approximately constant in the vertical.
The diffusive closure for the eddy PV flux, however, depends crucially on the definition of averages along isentropes that intersect the surface. It is argued that the definition favored by Schneider results in eddy PV fluxes whose physical interpretation is unclear and that do not satisfy the proposed closure in numerical simulations. An alternative definition, first proposed by T.-Y. Koh and R. A. Plumb, is preferred. A diffusive closure for the eddy PV flux under this definition is supported by analysis of the PV variance budget and can be used to close the near-surface zonal momentum budget in idealized numerical simulations. Following this approach, it is shown that O(1) criticalities are obtained if the eddy diffusivity decays from its surface value to about zero over the depth of the troposphere, which is likely to be the case in Earth’s atmosphere. Large criticality parameters, however, are possible if the eddy diffusivity decays only weakly in the vertical, consistent with results from quasigeostrophic models. This provides theoretical support for recent numerical studies that have found supercritical mean states in primitive equation models. |
| first_indexed | 2024-09-23T14:25:05Z |
| format | Article |
| id | mit-1721.1/82888 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T14:25:05Z |
| publishDate | 2013 |
| publisher | American Meteorological Society |
| record_format | dspace |
| spelling | mit-1721.1/828882022-09-29T09:21:23Z The Vertical Structure of the Eddy Diffusivity and the Equilibration of the Extratropical Atmosphere Jansen, Malte Friedrich Ferrari, Raffaele Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences Jansen, Malte Friedrich Ferrari, Raffaele Observations suggest that the time- and zonal-mean state of the extratropical atmosphere adjusts itself such that the so-called “criticality parameter” (which relates the vertical stratification to the horizontal temperature gradient) is close to one. T. Schneider has argued that the criticality parameter is kept near one by a constraint on the zonal momentum budget in primitive equations. The constraint relies on a diffusive closure for the eddy flux of potential vorticity (PV) with an eddy diffusivity that is approximately constant in the vertical. The diffusive closure for the eddy PV flux, however, depends crucially on the definition of averages along isentropes that intersect the surface. It is argued that the definition favored by Schneider results in eddy PV fluxes whose physical interpretation is unclear and that do not satisfy the proposed closure in numerical simulations. An alternative definition, first proposed by T.-Y. Koh and R. A. Plumb, is preferred. A diffusive closure for the eddy PV flux under this definition is supported by analysis of the PV variance budget and can be used to close the near-surface zonal momentum budget in idealized numerical simulations. Following this approach, it is shown that O(1) criticalities are obtained if the eddy diffusivity decays from its surface value to about zero over the depth of the troposphere, which is likely to be the case in Earth’s atmosphere. Large criticality parameters, however, are possible if the eddy diffusivity decays only weakly in the vertical, consistent with results from quasigeostrophic models. This provides theoretical support for recent numerical studies that have found supercritical mean states in primitive equation models. National Science Foundation (U.S.) (Award OCE-0849233) 2013-12-09T17:24:58Z 2013-12-09T17:24:58Z 2013-05 2012-11 Article http://purl.org/eprint/type/JournalArticle 0022-4928 1520-0469 http://hdl.handle.net/1721.1/82888 Jansen, Malte, and Raffaele Ferrari. “The Vertical Structure of the Eddy Diffusivity and the Equilibration of the Extratropical Atmosphere.” Journal of the Atmospheric Sciences 70, no. 5 (May 2013): 1456-1469. © 2013 American Meteorological Society https://orcid.org/0000-0002-3736-1956 en_US http://dx.doi.org/10.1175/JAS-D-12-086.1 Journal of the Atmospheric Sciences Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Meteorological Society American Meteorological Society |
| spellingShingle | Jansen, Malte Friedrich Ferrari, Raffaele The Vertical Structure of the Eddy Diffusivity and the Equilibration of the Extratropical Atmosphere |
| title | The Vertical Structure of the Eddy Diffusivity and the Equilibration of the Extratropical Atmosphere |
| title_full | The Vertical Structure of the Eddy Diffusivity and the Equilibration of the Extratropical Atmosphere |
| title_fullStr | The Vertical Structure of the Eddy Diffusivity and the Equilibration of the Extratropical Atmosphere |
| title_full_unstemmed | The Vertical Structure of the Eddy Diffusivity and the Equilibration of the Extratropical Atmosphere |
| title_short | The Vertical Structure of the Eddy Diffusivity and the Equilibration of the Extratropical Atmosphere |
| title_sort | vertical structure of the eddy diffusivity and the equilibration of the extratropical atmosphere |
| url | http://hdl.handle.net/1721.1/82888 https://orcid.org/0000-0002-3736-1956 |
| work_keys_str_mv | AT jansenmaltefriedrich theverticalstructureoftheeddydiffusivityandtheequilibrationoftheextratropicalatmosphere AT ferrariraffaele theverticalstructureoftheeddydiffusivityandtheequilibrationoftheextratropicalatmosphere AT jansenmaltefriedrich verticalstructureoftheeddydiffusivityandtheequilibrationoftheextratropicalatmosphere AT ferrariraffaele verticalstructureoftheeddydiffusivityandtheequilibrationoftheextratropicalatmosphere |