Coupled ocean-atmosphere model OA-QG-WS v2
About
(c) 2013 Lesley De Cruz
See LICENSE.txt for license information.
This software is provided as supplementary material with:
- Vannitsem, S. and De Cruz, L.: A 24-variable low-order coupled ocean-atmosphere model: OA-QG-WS v2, Geosci. Model Dev. Discuss., 6, 6569-6604, doi:10.5194/gmdd-6-6569-2013, 2013.
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 svn@meteo.be and lesley.decruz@meteo.be.
Consult our website for any (future) additional resources.
Usage
Model and integration parameters can be specified in params.lua. Heating-dependent initial conditions for each of the 24 variables are defined in IC.lua.
To run a simulation, just run:
luajit aomodel.lua
In Windows:
luajit.exe aomodel.lua
This computes the mean and variance of each variable.
The LuaJIT source code can be obtained here.
Implementation notes
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).
The tensor for this model is composed in aotensor.lua and uses the inner products defined in inprod.lua.
References
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.
Reinhold, B. B. and Pierrehumbert, R. T.: Dynamics of weather regimes: quasi-stationary waves and blocking, Mon. Weather Rev., 110, 1105-1145, 1982.
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.
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.
Vannitsem, S.: Dynamics and predictability of a low-order wind-driven ocean-atmosphere coupled model, Clim. Dynam., doi:10.1007/s00382-013-1815-8, 2013.
Please see the article for the full list of references.