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For a forecast system that realistically reflects atmospheric synoptic-dynamic activity A_f =A_a.  If A_f < A_a the forecasting system underestimates atmospheric variability, which will contribute to a decrease in the RMSE.  Jumpiness is ““bad”” if we are dealing with a NWP model but ““good””, if we are dealing with post-processed deterministic forecasts to end-users.  On the other hand, if A_f > A_a the model overestimates synoptic-dynamic activity, which will contribute to increasing the RMSE.  This is normally ““bad”” for all applications.

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On average, dampening the variability (or jumpiness) of the forecasts reduces forecast error.   It can be shown, (see Fig12.A.13), that optimal damping is achieved when the variability is reduced by a proportion that is equal to cosine (β) or the ACC.

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Fig12.A.14: A 3-dimensional vector figure to clarify the relation between forecast jumpiness and error.  Two forecasts, f and g, are shown at a range when there is no correlation between the forecast and observed anomalies (f - c), (g - c) and (a - c). The angles between the three vectors are 90°. The angles in the triangle a-f-g measure up to 60° which means that there is a 50% correlation between the ““jumpiness”” (g - f) and the errors (f - a) and (g - a). The same is true for the correlation between (f - a) and (g - a).

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