(c) 2013-2020 Lesley De Cruz and Jonathan Demaeyer
See LICENSE.txt for license information.
This software is provided as supplementary material with:
- De Cruz, L., Demaeyer, J. and Vannitsem, S.: The Modular Arbitrary-Order Ocean-Atmosphere Model: MAOOAM v1.0, Geosci. Model Dev., 9, 2793-2808, doi:10.5194/gmd-9-2793-2016, 2016.
Please cite this article if you use (a part of) this software for a publication.
The authors would appreciate it if you could also send a reprint of your paper to lesley.decruz@meteo.be, jonathan.demaeyer@meteo.be and svn@meteo.be.
Consult the MAOOAM code repository for updates, and our website for additional resources.
The atmospheric component of the model is based on the papers of Charney and Straus (1980), Reinhold and Pierrehumbert (1982) and Cehelsky and Tung (1987), all published in the Journal of Atmospheric Sciences. The ocean component is based on the papers of Pierini (2012), Barsugli and Battisti (1998). The coupling between the two components includes wind forcings, radiative and heat exchanges.
As the system of differential equations is at most bilinear in y[j] (j=1..n), y being the array of variables, it can be expressed as a tensor contraction (written using Einstein convention, i.e. indices that occur twice on one side of an equation are summed over):
dy / dt = T y y (y == 1)
i i,j,k j k 0
The tensor T that encodes the differential equations is composed so that:
- T[i][j][k] contains the contribution of dy[i]/dt proportional to y[j]*y[k].
- Furthermore, y[0] is always equal to 1, so that T[i][0][0] is the constant contribution to var dy[i]/dt.
- T[i][j][0] + T[i][0][j] is the contribution to dy[i]/dt which is linear in y[j].
Ideally, the tensor is composed as an upper triangular matrix (in the last two coordinates).
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Charney, J. G. and Straus, D. M.: Form-drag instability, multiple equilibria and propagating planetary waves in baroclinic, orographically forced, planetary wave systems, J. Atmos. Sci., 37, 1157-1176, 1980.
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Reinhold, B. B. and Pierrehumbert, R. T.: Dynamics of weather regimes: quasi-stationary waves and blocking, Mon. Weather Rev., 110, 1105-1145, 1982.
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Reinhold, B. B. and Pierrehumbert, R. T.: Corrections to "Dynamics of weather regimes: quasi-stationary waves and blocking", Mon. Weather Rev., 113, 2055-2056, 1985.
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Barsugli, J. J. and Battisti, D. S.: The basic effects of atmosphere–ocean thermal coupling on midlatitude variability, J. Atmos. Sci., 55, 477-493, 1998.
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Pierini, S.: Low-frequency variability, coherence resonance, and phase selection in a low-order model of the wind-driven ocean circulation, J. Phys. Oceanogr., 41, 1585-1604, 2011.
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Cehelsky, P. and Tung, K. K.: Theories of multiple equilibria and weather regimes - A critical reexamination. Part II: Baroclinic two-layer models, Journal of the atmospheric sciences, 44, 3282-3303, 1987.
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Vannitsem, S. and De Cruz, L.: A 24-variable low-order coupled ocean-atmosphere model: OA-QG-WS v2, Geoscientific Model Development, 7, 649-662, 2014.
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Vannitsem, S., Demaeyer, J., De Cruz, L., and Ghil, M.: Low-frequency variability and heat transport in a loworder nonlinear coupled ocean-atmosphere model, Physica D: Nonlinear Phenomena, 309, 71-85, 2015.
Please see the main article for the full list of references.
- DAPPER - Data Assimilation Package in Python for Experimental Research. The MAOOAM python implementation is available within the package.