• Adjoint method;
  • Analysis error;
  • Forecast error;
  • Sensitivity studies


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 conditions can be interpreted as a sum of rapidly growing components of the analysis error. An analysis modified by subtracting an appropriately scaled vector, proportional to the gradient, provides initial conditions for a ‘sensitivity integration’ that can be used to diagnose the effect of initial-data errors on forecast errors.

Statistics of sensitivity calculations for the month of April 1994 characterize the sensitivity patterns as small-scale, middle or lower tropospheric structures which are tilted in the vertical. The general pattern of these structures is known to be associated with the fastest possible growth of forecast error. When used as initial perturbations, they evolve rapidly into synoptic-scale structures, propagating both downstream and to higher atmospheric levels.

On average, the sensitivity integration corrects for about a tenth of the day 2 forecast error, which indicates that indeed not all of the error is in the fastest-amplifying modes. But the fraction 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 still scope for great improvement in the medium-range forecast, particularly over Europe, by a better description of the initial conditions. The sensitivity experimentation suggests that many cases of major forecast-errors may be explained by defects in the analysis. A small but well-chosen change in the analysis can frequently improve the forecast quality.