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 = [(R34-r34)2+(R50-r50)2+(R64-r64)2] + Penalty term

– R34,50,64 = observed radii– r34,50, 64 = computed radii– Summation is over ~3000 data point from 1988-2004– 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– correlationi = ΔDi * 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 # 329068 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