### Background Information

In recognition of the increasing coastal population vulnerable to tropical cyclones and the inherent uncertainty of the National Hurricane Center (NHC) track forecasts, the National Weather Service (NWS) initiated a quantitative strike probability product beginning with the forecast of Hurricane Alicia in August of 1983. The strike probability product considered track error uncertainty, where bivariate normal distributions were fitted to the recent history of NHC track errors. A tropical cyclone “strike” was defined as when a storm moved 50 nmi to the right or 75 nmi to the left of a given location, and probabilities were provided at selected locations from 12 to 72 h. Except for periodic updating of the track error statistics, the operational probability product changed very little from 1983 through the 2005 hurricane season. Staring in 2006, NHC implemented an updated probability product that includes track, intensity and wind structure uncertainty information. The algorithm for the new product was developed by NESDIS/RAMMB and CIRA using a Monte Carlo Method under support from the Joint Hurricane Testbed.

### The Monte Carlo Probability Model

Monte Carlo(MC) methods are commonly used in problems where a direct simulation of the phenomena of interest is more straightforward than fitting specified probability distributions. The interaction of tropical cyclones with land makes the use of analytic formulas for tropical cyclone intensity error distributions difficult. For this reason an MC approach was used. A large number of plausible tracks (currently 1000) are determined by randomly sampling from the past 5 years of the NHC, Central Pacific Hurricane Center (CPHC) or Joint Typhoon Warning Center (JTWC) along and cross track error distributions and adding these to the official forecast track. Serial correlations of the errors are accounted for. A similar approach is used to determine the intensities of each of the realizations. Special procedures are employed for the case where the official forecast track is over water and the realization track is over land, and vice versa. Given the intensity and track of each realization, the radii of 34, 50 and 64 kt winds are estimated from a climatology and persistence radii model and its error distributions. The probability value at any given point is determined by counting the number of realizations where the storm comes within the radii of interest (34, 50 or 64 kt). Two types of probabilities are estimated, cumulative and incremental. The cumulative probabilities are those from 0 to 12, 0 to 24, … 0 to 120 hr. The incremental probabilities are those from 0 to 12, 12 to 24, …, 108 to 120 hr. A number of operational products are derived from the MC model, include text and graphical products. The probability products are generated for all storms in the Atlantic and eastern North Pacific that NHC is writing advisories for, all storms in the Central Pacific that CPHC is writing advisories for and all storms in the western North Pacific that JTWC is writing advisories for.

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### Product Improvements

Under continued funding from the JHT, an experimental version of the MC probability model is under development that includes variable track error distributions. The track error distributions are stratified into three groups depending on the value of the Goerss Predicted Consensus Error (GPCE). The GPCE values tend to be large when the spread of the dynamical track forecast models is large and vice versa. This version will confine or spread the probabilities, depending on the confidence in a particular track forecast. Figure 1 shows the NHC 72 h along track error distributions from 2002-2006 for the lower and upper terciles of the corresponding GPCE values. The distribution is much wider for the larger GPCE values.

*Figure 1. The 72 hr NHC along track error distributions from the 2002-2006 for the upper and lower terciles of the GPCE values.*

As a first test of the new product, Fig. 2 shows two versions of the 64 kt 0-120 hr cumulative probability product for a case from Hurricane Frances from 2004. The probabilities were generated using the NHC track error distributions corresponding to the lower and upper terciles of the GPCE values. Note the wider area of the probabilities for the higher GPCE values and the increased probabilities close to the forecasted track for the lower GPCE values.

*Figure 2. The 64 kt 0-120 hr cumulative probabilities for a case from Hurricane Frances starting at 0000 UTC on 01 September 2004. The probabilities using the NHC track error distributions corresponding to the lower (upper) and upper (lower) terciles of the GPCE values are shown.*

A parallel test of the GPCE-based MC probability model was performed for the cases from the 2008 Atlantic Hurricane Season. Click here for the 2008 GPCE test results.