ESTIMATION OF KEY ANALYSIS ERRORS USING THE ADJOINT TECHNIQUE

An iteration procedure minimizing the short-range forecast error leads , after some iterations, to so-called key analysis errors. These are e stimates of the part of analysis errors that is largely responsible fo r the short-range forecast errors. The first step of the minimization procedure provides a scaled gradient of the two-day forecast errors fo r which the 'energy' inner-product provides an efficient way of identi fying the analysis errors at scales that are relevant for forecast err or growth. By using an 'enstrophy' Like inner-product as an alternativ e to 'energy' the sensitivity gradient obtains an unrealistically larg e scale. Performing a few more steps in the minimization provides bett er estimates of the analysis error in the directions spanned by the le ading singular vectors of the tangent-linear model. On a case study it is shown that three steps provide key analysis increments which, when added to the analysis, both significantly improve the fit to the avai lable data and substantially improve the subsequent model integration. It does not appear to be beneficial to do more steps of the minimizat ion because of the uncertainty in the definition of the short-range fo recast error, and of approximations in the tangent-linear model. Key a nalysis errors represent an improved estimate of analysis errors compa red to the scaled gradient of day-2 forecast errors. In particular the geographical distribution shows the stability dependence of the scale d gradient. The projection of the gradient on the fastest growing erro rs limits maximum sensitivity to the major baroclinic zones. The close correspondence of evolved key analysis errors and forecast errors sho ws that key analysis errors are more realistically projecting on to fu ll analysis errors. The close link between the stability of the flow a nd the gradient of the forecast errors implies an unreasonably strong seasonal variation of analysis errors estimates. In contrast, key anal ysis errors are nearly seasonally independent, which means that their detrimental effect on forecast errors in absolute terms in summer and winter is comparable.