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We have recently developed a hierarchical K-Means clustering method for weather images. Using this technique, it is possible to identify storms at different scales. In this paper, we will describe an error-minimization technique to identify movement between successive frames of a sequence and show that we can use the K-Means clusters as the minimization kernel. Using this technique in combination with the K-Means clusters, we can identify storm motion at different scales and choose different scales to forecast based on the time scale of interest.We will show examples of this storm identification and forecast in action on weather radar images.

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We determine all signals giving equality for the discrete Hirschman uncertainty principle. We single out the case where the entropies of the time signal and its Fourier transform are equal. These signals (up to scalar multiples) form an orthonormal basis giving an orthogonal transform that optimally packs a finite-duration discrete-time signal. The transform may be computed via a fast algorithm due to its relationship to the discrete Fourier transform.

One important criterion for a model's utility is its scope, the ability to predict a wide range of results. Scope is often difficult to ascertain without extensive data fitting. For example, J. E. Cutting, N. Bruno, N. P. Brady, and C. Moore (1992) compared 2 models of perceived visual depth by fitting many data sets that were arbitrarily generated from underlying functions. They then defined scope as the number of functions a model could account for. We present an alternative technique for scope evaluation that is based on analysis of the behavior of a model's parameters and does not require extensive data fitting. The technique examines the ratio between the overall interdependence among model parameters and their sensitivity, which we show to be inversely related to a model's scope.

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