A valuable diagnostic for analyzing forecast error is the sensitivity of a forecast response function (such as the total rainfall over some area) to initial model fields. An integration of the adjoint of a forecast model can provide such sensitivity fields. However, adjoints makes linearization assumptions and can be very difficult to implement. The linearization assumptions are more problematic for mesoscale than for synoptic applications due to the greater importance of nonlinear physical processes including microphysics, which are difficult, if not impossible, to linearize.

This paper describes an alternate method of calculating sensitivity fields and presents results obtained thereby. The method takes advantage of powerful parallel computer systems by making a very large ensemble of mesoscale model forecasts to determine the sensitivity fields. This is in a sense the "brute-force" method of addressing the problem, which is only possible if such powerful computers are available. For example, we run an ensemble of over 2000 members in which the initial field of boundary-layer moisture is varied systematically throughout the geographic domain. Each ensemble member has a perturbation in water vapor placed at a different location, and the ensemble then has a complete set of perturbations. The effect of each of these perturbations on the forecast of any response function (such as rainfall over some region) is then calculated, in terms of the derivatives of the response function with respect to the perturbations. The complete sensitivity field is thus assembled from all of the ensemble members. This method makes no linearization assumptions, and should, thus, be more accurate than an adjoint-based approach. We will show results from several cases and compare our results with those from an adjoint model.