A Markov Chain Model of Tornadic Activity

Mathias Drton Department of Statistics, University of Washington, Seattle, Washington

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Caren Marzban Department of Statistics, University of Washington, Seattle, Washington, and Center for Analysis and Prediction of Storms, University of Oklahoma, Norman, Oklahoma

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Peter Guttorp Department of Statistics, University of Washington, Seattle, Washington

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Joseph T. Schaefer Storm Prediction Center, Norman, Oklahoma

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Abstract

Tornadic activity in four U.S. regions is stochastically modeled based on data on tornado counts over the years 1953–98. It is shown that tornadic activity on a given day is mostly affected by the activity on the previous day. Hence, the process can be modeled as a Markov chain. A parametric nonhomogenous Markov chain model is developed based on the well-known increase of tornadic activity in the spring and summer months. This model, with only eight parameters, describes tornadic activity quite well. The interpretability of the estimated parameters allows a diagnosis of the regional differences in tornadic activity. For instance, a comparison of the values of the parameters for the four regions suggests that in the South tornado persistence is specific mostly to the early part of the year. Finally, within the framework of probabilistic forecast verification, it is shown that the Markov chain model outperforms the climatological model, even though the former is far simpler in terms of the number of parameters (8 and 366, respectively). The superior performance of the model is confirmed in terms of several measures of performance in all four regions. The exception is the southern Tornado Alley, where the reliability of the model forecasts is nonsignificantly inferior to that of the climatological ones.

Corresponding author address: Dr. Caren Marzban, 2819 W. Blaine Street, Seattle, WA 98199. Email: marzban@stat.washington.edu

Abstract

Tornadic activity in four U.S. regions is stochastically modeled based on data on tornado counts over the years 1953–98. It is shown that tornadic activity on a given day is mostly affected by the activity on the previous day. Hence, the process can be modeled as a Markov chain. A parametric nonhomogenous Markov chain model is developed based on the well-known increase of tornadic activity in the spring and summer months. This model, with only eight parameters, describes tornadic activity quite well. The interpretability of the estimated parameters allows a diagnosis of the regional differences in tornadic activity. For instance, a comparison of the values of the parameters for the four regions suggests that in the South tornado persistence is specific mostly to the early part of the year. Finally, within the framework of probabilistic forecast verification, it is shown that the Markov chain model outperforms the climatological model, even though the former is far simpler in terms of the number of parameters (8 and 366, respectively). The superior performance of the model is confirmed in terms of several measures of performance in all four regions. The exception is the southern Tornado Alley, where the reliability of the model forecasts is nonsignificantly inferior to that of the climatological ones.

Corresponding author address: Dr. Caren Marzban, 2819 W. Blaine Street, Seattle, WA 98199. Email: marzban@stat.washington.edu

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