The figure below shows the histograms of four sea condition variables (wave height, water level, wave steepness, and wave period) which are important for assessing the level of protection provided by a coastal flood defence system. The data are measured at high tide and there are about 235 days of data. These empirical marginal distributions do not look like any of the distributions we have previously identified.
Coastal engineers are interested not simply in the big values of water level or of wave heights, but their combined effect. For example the worst flooding will occur when the water level is large, the waves are high and have long periods. Knowing simply the separate distributions of the variables (i.e. what we have studied to date) will not tell us whether large values of the variables can occur together or occur separately. Thus it is the joint characteristics of these variables that we must study.
Unnumbered Figure: Link
Figure 5.1 (Link) shows the joint scatter plots for all the possible pairs of sea condition variables. Note that the sub-plots below the diagonal are a reflection of the sub-plots above the diagonal. We see a strong relationship between wave height and wave period, and evidence that there is some association between the values taken by the other variables.
Questions we might be interested in are:
How do we measure the association between the waves’ heights and the water level?
If the steepness is what values of wave height should we expect?
Are water level and steepness related?
What is the probability of obtaining an event with the water level plus the wave height exceeding 10m?
These type of questions can be addressed using methods based on the probability concepts introduced in this chapter.