Extreme Value Analysis

There are a number of aspects to determining design conditions where the long experience of our staff ensures reliable results. These include:

Experience of combining the use of models with extreme value analysis to get good results (e.g. using non-stationary wave modelling up to intermediate depth followed by EVA followed by stationary wave modelling over a limited shallow area including the design water levels);

Identifying the processes that will be determining for the design conditions and making sure that mixed populations are properly accounted for (e.g. cyclone climates and monsoon climates);
The availability of streamlined tools for carrying out extreme value analysis using the Peak over Threshold (POT) method or the Cumulative frequency distribution (CFD) method. These allow us to test the sensitivity of the results to data threshold and elimination of outliers.

Data extrapolation

Example of POT Weibull fit to data with Y = Hm0 (m) (left) and sensitivity of parameters of Weibull distribution to wave height data threshold (m) (right).

Pnorm [%], b, scaling parameter (m); c shape parameter and Hm0 (m) with 100-year return period.

Aktis has software with several distributions including the 3-parameter Weibull distribution, which we consider to be the most appropriate for most metocean phenomena. Our preference for the Weibull distribution is based on discussion in the Ph.D. thesis by C.F. de Valk[1] in which he argues that the tails of distributions we encounter in meteorology and oceanography frequently reduces to the Weibull shape. We are also developing the application of the Log-GW distribution which de Valk recommends as the most generally applicable distribution for Metocean data.

[1] C.F. de Valk. “A large deviations approach to the statistics of extreme events”. Ph.D. Thesis, 2016

Environmental Contour Plots

Our software to compute the wind speed, wave period or water level associated with an extreme wave height is well streamlined. However, for situations where the joint probability of extremes is critical, we are able to produce environmental contour plots. These plots visualise the extreme joint probability of occurrence of two parameters to enable easy choice of critical combinations.

Example environmental contour plots of Hm0 / U10 for a situation where wave height and wind speeds are well correlated.

The software used by Aktis to produce environmental contour plots uses an IFORM method (inverse first order reliability method). The interpretation of these plots is that combinations of conditions can be expected to occur outside of the contour about once in the relevant return period.

The particular version of IFORM (“Inverse First Order Reliability Method”) applied to derive environmental contours is based on not yet published research carried out by C.F. de Valk while working at UC Louvain in 2017. Please contact us for more details on how the method works and how the plots should be interpreted.