Enhanced Wave Height Statistics

Figure 3 illustrates the parametric modelling applied to the joint frequency distributions of wave height and wind speed supplied from the Marine Databank as shown in Figure 2. It involves the use of two formulae each containing three modelling parameters as shown in Figure 3 , to be determined by best fitting of the data supplied. The first formula defines a curve to be fitted to the mean value Hr of the wave heights observed in each of the 13 classes of the Beaufort Scale used for the observations of wind speed. The second defines the scatter of the wave height observations about the mean curve, in terms of a formula for the standard deviation (sr) coupled with the use of a so-called Gamma distribution, to describe the shape P(Hs | Hr, sr) of the scatter.

 
Figure 2 - Sample of Data Array as Retrieved from the Marine Databank.
 
Figure 3 - Parametric Model of Joint Probability Distribution of Wave Height and Wind Speed.

To derive the required enhanced wave height distribution P(Hs), the relevant modelling parameters are first determined by best fitting of the array of '2-group' wave / wind data supplied. The formulae in the figure are then used (as explained in Appendix_A3) to compute P(Hs) from input of the separate distribution P(Wr) of 'normalized' All Wind frequencies also supplied, as shown in Figure 2.