SENSITIVITY OF FORECAST ERRORS TO INITIAL CONDITIONS

The adjoint method has been used to calculate the sensitivity of short -range forecast errors to the initial conditions. The gradient of the energy of the day 2 forecast error with respect to the initial conditi ons can be interpreted as a sum of rapidly growing components of the a nalysis error. An analysis modified by subtracting an appropriately sc aled vector, proportional to the gradient, provides initial conditions for a 'sensitivity integration' that can be used to diagnose the effe ct of initial-data errors on forecast errors. Statistics of sensitivit y calculations for the month of April 1994 characterize the sensitivit y patterns as small-scale, middle or lower tropospheric structures whi ch are tilted in the vertical. The general pattern of these structures is known to be associated with the fastest possible growth of forecas t error When used as initial perturbations, they evolve rapidly into s ynoptic-scale structures, propagating both downstream and to higher at mospheric levels. On average, the sensitivity integration corrects for about a tenth of the day 2 forecast error, which indicates that indee d not all of the error is in the fastest-amplifying modes. But the fra ction of the error corrected at day 2 is important for an improvement in the medium-range, as this fraction continues to grow substantially in the non-linear regime. These results have proved that there is stil l scope for great improvement in the medium-range forecast, particular ly over Europe, by a better description of the initial conditions. The sensitivity experimentation suggests that many cases of major forecas t-errors may be explained by defects in the analysis. A small but well -chosen change in the analysis can frequently improve the forecast qua lity.