Using the conservation of Rossby-Ertel
potential vorticity (q) in a barotropic atmosphere, a generalized
model can be constructed that applies at a single atmospheric level:¶
q/¶ t + J(y
,q), q = Ly , where y
is the streamfunction, J is the Jacobian operator, and L
is a linear spectral operator. For the standard barotropic model: L
= Ñ 2y
. To estimate the spectral relationship between potential vorticity
and streamfunction, reanalysis data may be used. An effective squared wavenumber
can be calculated by performing linear regression of each spherical harmonic
component of the potential vorticity against the same component of streamfunction: ,
where the primes indicate deviations from the time mean, the summations
are over the days of the employed time period, and the leading factor on
the right-hand-side uses time averaged static stability (indicated by brackets)
to normalize K2n,m
to values that can be compared directly with the appropriate squared wavenumber
for the sphere, n(n + 1).
Spectral relationships will be presented, in the form of effective wavenumber, for particular isentropic levels and time periods. Assessments of the goodness of fit of the linear regression to the data will be also shown. The total flow and deviations from the mean will be examined separately. Comparisons between the modified and standard barotropic models will be performed for some simple cases, for example the linear response to localized forcing on the sphere.
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12th Conference on Atmospheric and Oceanic Fluid Dynamics