Hurricane track forecast cones from fluctuations

Hurricane track forecast cones from fluctuations SUBJECT AREAS: ATMOSPHERIC SCIENCE STATISTICAL PHYSICS, THERMODYNAMICS AND NONLINEAR DYNAMICS GEOPHYSICS T. Meuel1, G. Prado1, F. Seychelles2, M. Bessafi3 & H. Kellay1 1 Université Bordeaux 1, Laboratoire Ondes et Matière d’aquitaine (UMR 5798 CNRS), 351 cours de la Libération 33405 Talence, France, 2Laboratoire de Physique ENS de Lyon (UMR CNRS 5672) 46, allée d’Italie F69007 Lyon, France, 3Université de la Réunion, Laboratoire de Génie Industriel, 15 Avenue René Cassin, 97751 Saint Denis de la Réunion, France. EARTH SCIENCES Received 13 February 2012 Accepted 22 May 2012 Published 14 June 2012 Correspondence and requests for materials should be addressed to H.K. () Trajectories of tropical cyclones may show large deviations from predicted tracks leading to uncertainty as to their landfall location for example. Prediction schemes usually render this uncertainty by showing track forecast cones representing the most probable region for the location of a cyclone during a period of time. By using the statistical properties of these deviations, we propose a simple method to predict possible corridors for the future trajectory of a cyclone. Examples of this scheme are implemented for hurricane Ike and hurricane Jimena. The corridors include the future trajectory up to at least 50 h before landfall. The cones proposed here shed new light on known track forecast cones as they link them directly to the statistics of these deviations. T ropical Cyclones (TCs), otherwise known as hurricanes or typhoons, are extreme atmospheric events which can be devastating upon landfall in populated areas. Several schemes are used to predict their trajectories1,2. Some predictions are based on the knowledge of previous hurricane tracks in the geographical area of interest and others use full scale numerical simulations1. Different statistical analyses are also carried out on the nature of the trajectory (i.e. linear versus recurved) for different basins, on the mean velocity and the deviations from predicted tracks, and on the landfall probability for different regions3–8. Since trajectories of TCs show large deviations from a generally predictable mean trajectory (which could be linear or recurved), prediction schemes can be imprecise, giving the statistical approaches a legitimate place. These deviations are difficult to predict as they are due to different factors such as the proximity of land and its topography, variations in the surrounding large scale flow, or modifications of the vortex structure itself1. In fact, track predictions usually include an estimate of the deviation of the trajectory from the predicted track in the form of so called track forecast cones which are based on error statistics from previous hurricane tracks as compared to predictions. Here we show that the statistical properties of these deviations, from say a predictable simple linear track, can be used to determine possible corridors or track forecast cones for TCs. This is based on recent observations suggesting that the deviations of the trajectory of generic vortices or TCs from a mean trajectory can be modeled with a universal law9 for their so called mean square displacement. This law appears for the random movement of generic vortices in two dimensions as has been shown in experiments and numerical simulations9–11. In particular we suggest that track forecast cones available today can be linked directly to this measure of the trajectory deviations around a mean and that unless these deviations can be understood, and the factors giving rise to them are fully taken into account in models and simulations, reducing such uncertainty will be a difficult task. The mean square displacement (MSD), a notion borrowed from statistical physics and the study of Brownian motion, is a measure of the deviation from a mean trajectory. A classical example where this notion has gained all its importance is that of a colloidal particle in a simple fluid. In the absence of flow, the particle, subject to thermal agitation of the surrounding fluid, will have a position which fluctuates in time. If this position is denoted X, the MSD is defined as follows: , (X(t 1 t9) 2 X(t9))2 . (the brackets denote an average over time t’) where X(t) is the instantaneous position of the particle at time t. As this position varies erratically in time, the particle will explore a certain area which is given by the MSD. According to statistical mechanics , (X(t 1 t9) 2 X(t9))2 .5 Dt where D is the so called diffusion coefficient which depends on the temperature, the radius of the particle and the viscosity of the fluid. This is known as normal Brownian diffusion. If a mean flow of constant velocity VX steers the particle in a particular direction, the position of the particle will have a fluctuating component dX(t) and a deterministic part given by the mean flow: X(t) 5 VXt 1 dX(t). In this case, the fluctuating part will have a MSD given by the previous expression while the mean position increases as VXt. While normal diffusion describes a large set of random movements, anomalous diffusion may occur under certain conditions. Perhaps the most famous example is random movement in the presence of so called Levy flights12,13 where the particle exhibits large jumps SCIENTIFIC REPORTS | 2 : 446 | DOI: 10.1038/srep00446 1 www.nature.com/scientificreports from time to time in its trajectory. A general form of the MSD is suggested by the expression , (X(t 1 t9) 2 X(t9))2 ., t a where the exponent a may take values smaller (subdiffusion) or larger (superdiffusion) than 1. Several examples of super diffusion have been observed experimentally such as the case of an object in a turbulent flow for example. Super diffusive behavior can be related to the interaction between the object and the medium12,13. Examples of entities that interact with the medium itself have been illustrated in the case of passive beads in a bath of self propelling bacteria14, and the movement of passive beads in a laminar rotating flow15. The isolated vortices, discussed below to illustrate the role of fluctuations, are randomly kicked by the turbulent agitation of the flow. These vortices must have an important reaction on the medium itself. The movement of vortices is also sensitive to the sign of vorticity variations16 which in a turbulent medium may show a complicated spatial and temporal distribution giving rise to a non trivial interaction with the moving vortex. TCs are also entities that interact with the surrounding flow, the topography, and that may change structure in the course of their movement giving possible reasons for changing course and engendering deviations from a simple track. Results As a way to introduce the concept of mean square displacement and show how it can be implemented for TCs, we illustrate this behavior using experiments on soap bubbles first. Indeed when half a soap bubble, deposit (...truncated)