PART II: PROBABILITY MODEL 



8. Unlike the physical model which simulates a physical process with 

 physical operations and the numerical models which simulate physical process- 

 es with mathematical operations, the probability model does not simulate a 

 physically realizable entity. The title 'model' is used for symmetry with the 

 other components of this project. The probability model is essentially an 

 assemblage with four specific tasks: select events for simulation by the 

 other three models, assign probabilities to these events, create stage- 

 frequency curves, and determine a measure of confidence in these curves. 



9. Ideally, there would be a long historical data record of the 

 desired quantity at the desired location (for example, 100 years of overtop- 

 ping data at Roughans Point). For this ideal case modeling would not be 

 necessary. An overtopping rate frequency curve could be created using well- 

 established statistical techniques which can be found in any hydrology text. 

 However, as is usually the case, sufficient data records for the quantities of 

 interest were not available. Therefore, three separate modeling efforts, a 

 physical overtopping model, a numerical storm surge model, and a numerical 

 wave model were implemented to overcome the lack of data. 



10. There are several possible approaches in establishing frequency 

 curves where the scarcity of data in the immediate study area requires a mod- 

 eling approach. The two most common are called the historical method and the 

 joint probability method (JPM). In the historical method, a series of histor- 

 ical events is recreated with the pertinent data being saved in the necessary 

 locations. In effect, it is like operating a time machine with the hindsight 

 to know what data to collect and where to collect it. Probability is assigned 

 to each event by a standard ranking method. For the JPM, the storm type is 

 parameterized. For example, hurricane wind fields can be defined by three 

 parameters, central pressure deficit, radius to maximum winds, and forward 

 speed. Then, an ensemble of synthetic events is simulated representing those 

 events which are possible in the study area. Probability is assigned to in- 

 dividual events by assigning probabilities to parameter values which determine 

 that event. If the parameters are independent, then the probability of the 

 event would be the product of the probabilities of the component parameters. 

 Several studies have been conducted using the above two methods, including 

 Meyers (1970) and Prater, Hardy, and Butler (in preparation). For the present 



11 



