FIGURE CAPTIONS

A cost function J = å_1,2 |Y(t_i) – X(t_i)|² was defined to measure the deviation between the model output X and the observations Y available at the time t₁ = 18:00 UTC and t₂ = 21:00 UTC on April 11, 1979. The MM5 adjoint model was used to efficiently compute the gradient of J with respect to the model initial conditions X(t₁). This gradient indicates how the model is sensitive to a small perturbation of initial fields. A small initial error in areas of strong gradient will have a comparatively bigger impact on forecast. Top panel shows the gradient of the cost function J with respect to the initial temperature field and reveals that the ulterior forecast over the Middle-West states will be very sensitive to the current conditions over New Mexico. The information provided by the gradient can also be exploited in a descent-like minimization procedure to reduce the cost function by optimization of the initial conditions. The optimized set of initial conditions can then be used for subsequent model integrations and extended forecasts. Bottom panel shows the 6^th forecast error valid at 00:00 UTC from non-optimized (left) and optimized (right) initial conditions. Only five descent steps were needed to decrease the cost function from two orders of magnitude. Such a convergence is only achieved for twin experiments, i.e., when observations are not real but created by the forecast model in separate runs. More than 30 iterations are usually needed for real observations. Plots are at level s = 0.85, contour level is 0.2K.

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