SS: Metocean: A Statistical Hindcast and Forecast Model for the Loop Current
Authors: Forristall George Z. , Leben Robert R. , Hall Cody A. 
Published: July 2010

Abstract
Gulf of Mexico metocean engineering designs rely on hindcasts from the Gulf Eddy Model (GEM) for the location of the Loop Current and Loop Current Eddies (LCEs). The GEM database is limited to the years from 1985 to 2006. A longer LCE record is needed to calculate long return period currents and as a bottom boundary condition for a synthetic hurricane model. We simulate the Loop Current using a Markov chain transition matrix based on altimeter measurements. When an eddy separates from the Loop Current, it is simulated based on the statistics of historical eddy movements and shapes. The probability distribution of simulated times between eddy separations agrees very well with the separations observed in the altimetric record. The simulated Loop Current coverage agrees very well with the altimeter-derived coverage. The mean and standard deviation of eddy tracks also agrees very well with observed tracks. The model can be run either to hindcast hundreds of years of simulated Loop Current and LCE coverage or to produce ensemble forecasts from an observed starting position. The Loop Current and LCE time series can improve estimates of current speeds as well as provide the necessary information to calculate the interaction of the Loop Current and LCEs with hurricanes. The statistical forecasts of Loop Current and LCE positions exhibit better skill than most dynamical model forecasts.

Introduction
The Gulf Eddy Model (GEM) is the standard tool for hindcasting currents in the Loop Current and its eddies (LCEs). GEM is a simple kinematic model that represents eddies as ellipses. The GEM database is limited to the years from 1985 to 2006. Long time series of temperature fields in the Gulf are required for modeling a long time series of synthetic hurricanes. Having a long duration, more spatially complete synthetic Loop Current and LCE simulations provides more accurate estimates of extreme current speeds.
We first describe a Loop Current model based on a continuous daily time series of Loop Current maps produced from altimeter measurements at the Colorado Center for Astrodynamics Research (CCAR). The strategy for the synthetic model is to calculate the statistics of transitions between Loop Current positions. The model then proceeds as a Markov chain. Each time an eddy separates from the Loop Current, a statistical eddy model simulation is performed to model the free propagation of the eddy. This statistical eddy model is based on the GEM Path and Configuration (PnC) files that describe eddies as ellipses. We verified the accuracy of the eddy simulation model by comparing statistics of simulated and observed LCEs. The statistics include the probability distribution of total area occupied each day by the LCEs, the probability distribution of eddy translation speed, eddy tracks, the eddy separation rate, and the eddy center crossing frequency at 94° W.
The Loop Current and LCE models were first written to be used in a hindcast mode to produce hundreds of years of simulated LCEs as a bottom boundary condition for hurricane simulations. After it was developed, it became obvious that only slight modifications would be necessary to convert it to a forecast model. The forecast model is run many times from an observed initial condition to produce an ensemble forecast. The ensemble of statistically possible outcomes gives the probability of Loop Current or LCE water covering any site in the Gulf of Mexico. We verified the accuracy of the forecast model by initializing it with historical initial conditions and comparing the results to the subsequent observations.