A study is undertaken of a particular method of updating numerical prediction models. the method constrains the time development of a subset of the model fields toward a prescribed space-time estimate of those fields, while the other model variables are allowed to evolve in an explicitly unconstrained fashion. It represents an attempt to update the model by a form of dynamical relaxation.
An analysis of the method is carried out in the context of the primitive equations linearized about an isothermal basic state of no motion. It is shown that, for a particular form of the scheme and the availability of the time history of the mass field (or the wind field) on an f-plane, all the time- and space-scale error fields in the initial specification suffer an amplitude reduction of at least the order e−1 on the timescale of one day. On an equatorial β-plane it is shown that the same rate of amplitude reduction can be achieved if an accurate time history is known for both the mass field and the zonal-wind field. Numerical experiments performed with the nonlinear shallow-water equations for a mid-latitude β-plane geometry support these results and demonstrate that the technique compares favourably with the conventional direct insertion update method. Consideration is also given to the possible effects of errors in the prescribed fields and it is shown that the relaxation scheme can to some extent be tuned to offset the effect of this particular source of error.
This study of the relaxation update scheme, although not comprehensive, is nevertheless sufficient to indicate its potential. However, it is stressed that a trenchant assessment of the scheme's usefulness should be based at least in part upon its performance under more testing and realistic conditions.
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