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The numerical stability of a parametrization of convective momentum transport
Author(s) -
Kershaw R.,
Grant A. L. M.,
Derbyshire S. H.,
Cusack S.
Publication year - 2000
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.49712656918
Subject(s) - parametrization (atmospheric modeling) , instability , momentum (technical analysis) , convection , limiting , numerical stability , stability (learning theory) , momentum diffusion , convective instability , mechanics , mathematics , physics , classical mechanics , numerical analysis , mathematical analysis , computer science , engineering , turbulence , mechanical engineering , finance , quantum mechanics , machine learning , economics , radiative transfer
The Gregory el at. parametrization of momentum transport by convection is shown to be more prone to numerical instability than other parts of the convection scheme, because of an additional element of numerical diffusion. The limiting Courant number for linear stability is (I + c ) −1 , where c is the parameter which controls the dependence of the pressure gradient on environment shear. Some revised numerical treatments cure the instability problem but reduce forecast skill, apparently because the diffusive element of the original formulation is beneficial, even though it is artificial. A possible solution to the problem is to use an implicit treatment of the original formulation which is absolutely stable.