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A Simplified Dynamical System for Tropical Cyclone Intensity Prediction

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Abstract

A simplified dynamical system for tropical cyclone intensity prediction based on a logistic growth equation (LGE) is developed. The time tendency of the maximum sustained surface winds is proportional to the sum of two terms: a growth term and a term that limits the maximum wind to an upper bound. The maximum wind evolution over land is determined by an empirical inland wind decay formula. The LGE contains four free parameters, which are the time-dependent growth rate and maximum potential intensity (MPI), and two constants that determine how quickly the intensity relaxes toward the MPI. The MPI is estimated from an empirical formula as a function of sea surface temperature and storm translational speed. The adjoint of the LGE provides a method for finding the other three free parameters to make the predictions as close as possible to the National Hurricane Center best-track intensities. The growth rate is assumed to be a linear function of the vertical shear (S), a convective instability parameter (C) determined from an entraining plume, and their product, where both S and C use global model fields as input. This assumption reduces the parameter estimation problem to the selection of six constants. Results show that the LGE optimized for the full life cycle of individual storms can very accurately simulate the intensity variations out to as long as 15 days. For intensity prediction, single values of the six constants are found by fitting the model to more than 2400 Atlantic forecasts from 2001 to 2006. Results show that the observed intensity variations can be fit more accurately with the LGE than with the linear Statistical Hurricane Intensity Prediction Scheme (SHIPS) formulation, and with a much smaller number of constants. Results also show that LGE model solution (and some properties of real storms) can be explained by the evolution in the two-dimensional S–C phase space. Forecast and other applications of the LGE model are discussed.

Corresponding author address: Mark DeMaria, NOAA/NESDIS/StAR, 1375 Campus Delivery, CIRA/CSU, Fort Collins, CO 80523. Email: Mark.DeMaria@noaa.gov

Abstract

A simplified dynamical system for tropical cyclone intensity prediction based on a logistic growth equation (LGE) is developed. The time tendency of the maximum sustained surface winds is proportional to the sum of two terms: a growth term and a term that limits the maximum wind to an upper bound. The maximum wind evolution over land is determined by an empirical inland wind decay formula. The LGE contains four free parameters, which are the time-dependent growth rate and maximum potential intensity (MPI), and two constants that determine how quickly the intensity relaxes toward the MPI. The MPI is estimated from an empirical formula as a function of sea surface temperature and storm translational speed. The adjoint of the LGE provides a method for finding the other three free parameters to make the predictions as close as possible to the National Hurricane Center best-track intensities. The growth rate is assumed to be a linear function of the vertical shear (S), a convective instability parameter (C) determined from an entraining plume, and their product, where both S and C use global model fields as input. This assumption reduces the parameter estimation problem to the selection of six constants. Results show that the LGE optimized for the full life cycle of individual storms can very accurately simulate the intensity variations out to as long as 15 days. For intensity prediction, single values of the six constants are found by fitting the model to more than 2400 Atlantic forecasts from 2001 to 2006. Results show that the observed intensity variations can be fit more accurately with the LGE than with the linear Statistical Hurricane Intensity Prediction Scheme (SHIPS) formulation, and with a much smaller number of constants. Results also show that LGE model solution (and some properties of real storms) can be explained by the evolution in the two-dimensional S–C phase space. Forecast and other applications of the LGE model are discussed.

Corresponding author address: Mark DeMaria, NOAA/NESDIS/StAR, 1375 Campus Delivery, CIRA/CSU, Fort Collins, CO 80523. Email: Mark.DeMaria@noaa.gov

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