KDE Method for environmental contours

[d-andrievskaia]

My question is regarding methodology used for the environmental contours’ calculation, particularly with KDE method. So the concern is that, when plotting contours for different return periods (1, 5, 10, 100 - years), these contours are getting closer and closer to each other with an increase in return period, so for the small bandwidths the difference between contours becomes almost indistinguishable (I attach a couple of pics for an illustration). For other methods this tendency is also present, yet the contours are not that ‘tightly’ placed. Can such behaviour be considered as ‘normal’/expected?

[ssolson]

Hello @d-andrievskaia and thanks for your interest in MHKiT. I cannot provide detailed insight into this specific question but as @ryancoe mentioned by email I believe he has some articles he can share with you.

[ryancoe]

There's a good description of the KDE contours provided in the following papers:

• A. Eckert-Gallup and N. Martin, "Kernel density estimation (KDE) with adaptive bandwidth selection for environmental contours of extreme sea states," OCEANS 2016 MTS/IEEE Monterey, 2016, pp. 1-5, doi: 10.1109/OCEANS.2016.7761150.
• A. Eckert, N. Martin, R. G. Coe, B. Seng, Z. Stuart, and Z. Morrell, “Development of a Comparison Framework for Evaluating Environmental Contours of Extreme Sea States,” Journal of Marine Science and Engineering, vol. 9, no. 1, p. 16, Dec. 2020, doi: 10.3390/jmse9010016.
• Haselsteiner, A.; Ohlendorf, J.H.; Thoben, K.D. Environmental contours based on kernel density estimation. In Proceedings of the 13th German Wind Energy Conference DEWEK 2017, Bremen, Germany, 17–18 October 2017; UL DEWI: Bremen, Germany, 2017.

As you point out, this behavior of contours for increasing return periods being more tightly spaced is generally apparent in most (all?) contours, so yes, I would say this behavior is expected. The fact that the KDE distributions have relatively shorter tails when compared with other methods (and, by extension, the contours for increasing periods of return are more closely spaced) is just the nature of the contour, but not a bug. I believe you will find that if you increase the bandwidth you will get a larger spacing between the contours for different return periods (see the OCEANS paper above for some discussion on this). Note that the OCEANS paper focuses partially on adaptive bandwidth KDEs, but we subsequently put the adaptive bandwidth approach aside in favor of a fixed bandwidth (see pg. 8 of JMSE paper).

https://github.com/MHKiT-Software/MHKiT-Python/blob/21ff3a24c37c528b3e2b087a486fc1b80a932a16/mhkit/wave/contours.py#L50-L52

Hope this helps! If @aubreyeckert is able to add/correct anything I've said, that would be most welcome ;)

[d-andrievskaia]

Hello @ryancoe, thank you for your response and for the papers! I indeed noticed that with an increase in bandwidth we get a larger spacing between the contours for different return periods. Just had doubts about the nature of this tendency.

Thank you again!