Use of randomization to diagnose the impact of observations on analyses and forecasts

A method is proposed to diagnose the impact of a complete set, or subsets, of observations on the reduction of error variance in an analysis and in the subsequent forecasts run from this analysis. A practical method to estimate the error reduction, based on a randomization procedure, is also introduced and investigated in a simple framework given by the analysis and forecast of wind on a circular domain using the nonlinear Burger's equation. The randomization procedure is also applied and tested in the French ARPEGE 4D‐Var assimilation. The first results in a real‐size data assimilation system are realistic and provide useful information on the use of observations in an operational analysis. Copyright © 2005 Royal Meteorological Society