Development of a Baseline Tropical Cyclone Model Using the Alopex Algorithm Robert DeMaria

Forecast “Skill” Skill is measured by comparison to simple benchmark “no- skill” models Benchmark forecast based on basic storm information –Storm initial position and intensity, previous 12 hour change, and current date Track and intensity benchmarks developed in 1972 and 1988 NHC wind radii benchmark model developed at CSU in 2004, but used very simple minimization algorithm Can benchmark wind radii model be improved using ALOPEX algorithm for minimization?

Benchmark Model and Error Function Benchmark model is a set of parametric equations with a total of 20 free parameters in matrix D Given azimuth, returns radius of maximum wind Error function created for optimization of D E =  [(R 34 -r 34 ) 2 +(R 50 -r 50 ) 2 +(R 64 -r 64 ) 2 ] + Penalty term –R 34,50,64 = observed radii –r 34,50, 64 = computed radii –Summation is over ~3000 data point from –Penalty term becomes large when values of D are non-physical

Previous Minimization Algorithm Very simple local search Guaranteed to get stuck in first minima found Starting point at best guess

Alopex Algorithm Designed for minimizing error in problems with large number of variables Does not get stuck in local minima Very general

Alopex Fundamentals Iterative Variables incremented in biased random directions –Correlation computed every iteration for every member of D –correlation i = ΔD i * ΔE –If error after previous iteration reduced, probability of incrementing in same direction is high –If error of previous iteration increased, probability of incrementing in same direction is low Temperature used to prevent getting stuck in local minima –After N iterations, T set to average correlation of all variables over N iterations

My Implementation Written in Fortran Values for N, initial D vals, increment, and penalty term found empirically Prevents increments that will produce non- physical results

Results Run for 5 million iterations Iteration # found smallest error of ~ 45 nmi Original algorithm found very similar D matrix with error of ~38 nmi

Future Work Remove purely physical increment limitation Run with more iterations Run with different starting location Fine tune using result as starting location smaller increment