The Dolph–Chebyshev Window: A Simple Optimal Filter

Analyzed data for numerical prediction can be effectively initialized by means of a digital filter. Computation time is reduced by using an optimal filter. The construction of optimal filters involves the solution of a nonlinear minimization problem using an iterative procedure. In this paper a simple filter based on the Dolph–Chebyshev window, which has properties similar to those of an optimal filter, is described. It is shown to be optimal for an appropriate choice of parameters. It has an explicit analytical expression and is easily implemented. Its effectiveness is demonstrated by application to Richardson’s forecast: the initial pressure tendency is reduced from 145 hPa per 6 h to 20.9 hPa per 6 h. Use of the filter is not restricted to initialization; it may also be applied as a weak constraint in four-dimensional data assimilation.