17 Jan 2022
17 Jan 2022
Status: a revised version of this preprint is currently under review for the journal NHESS.

Bayesian hierarchical modeling of sea level extremes in the Finnish coastal region

Olle Räty, Marko Laine, Ulpu Leijala, Jani Särkkä, and Milla M. Johansson Olle Räty et al.
  • Finnish Meteorological Institute, P.O. BOX 503 FI-00101 Helsinki, Finland

Abstract. Occurrence probabilities of extreme sea levels required in coastal planning, e.g. for calculating design floods, have been traditionally estimated individually at each tide gauge location. However, these estimates include uncertainties, as sea level observations typically have only a small number of extreme cases such as annual maxima. Moreover, exact information on sea level extremes between the tide gauge locations and incorporation of dependencies between the adjacent stations is often lacking in the analysis.

In this study, we use Bayesian hierarchical modeling to estimate return levels of annual maxima of short-term sea level variations related to storm surges in the Finnish coastal region. We use the generalized extreme value (GEV) distribution as the basis and compare three hierarchical model structures of different complexity against tide gauge specific fits. The hierarchical model structures allow to share information on annual maximum sea levels between the neighboring stations and also provide a natural way to estimate uncertainties in the theoretical estimates.

The results show that, compared to the tide gauge specific fits, the hierarchical models, which pool information across the stations, provide narrower uncertainty ranges both for the posterior parameter estimates and for the corresponding return levels on most of the tide gauges. The estimated shape parameter of the GEV model is systematically negative for the hierarchical models, which indicates a Weibull-type of behavior for the extremes along the Finnish coast. This also suggests that the hierarchical models can be used to estimate theoretical upper limits of the extremes of short-term sea level variations along the Finnish coast. Depending on the tide gauge and hierarchical model considered, the median value of the theoretical upper limit was 47–73 cm higher than the highest observed sea level.

Olle Räty et al.

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on nhess-2021-410', Anonymous Referee #1, 27 Feb 2022
    • AC1: 'Reply on RC1', Olle Räty, 04 Jun 2022
  • RC2: 'Comment on nhess-2021-410', Anonymous Referee #2, 01 Mar 2022
    • AC2: 'Reply on RC2', Olle Räty, 04 Jun 2022

Olle Räty et al.

Data sets

Data files for the article "Bayesian hierarchical modeling of sea level extremes in the Finnish coastal region" Olle Räty and Milla M. Johansson

Model code and software

Supplementary Stan codes and R scripts Olle Räty and Marko Laine

Olle Räty et al.


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Short summary
We studied annual maximum sea levels in the Finnish coastal region. Our aim was to better quantify uncertainty in them compared to previous studies. Using four statistical models, we found out that those models, which shared information on sea level extremes across Finnish tide gauges, had smaller uncertainty in their results in comparison to tide gauge specific fits. These models also suggested that the shape of the distribution for extreme sea levels is similar on the Finnish coast.