Bayesian hierarchical modeling of sea level extremes in the Finnish coastal region
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)
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 files for the article "Bayesian hierarchical modeling of sea level extremes in the Finnish coastal region" https://doi.org/10.5281/zenodo.5807461
Model code and software
Supplementary Stan codes and R scripts https://doi.org/10.5281/zenodo.5805120
Olle Räty et al.
Viewed (geographical distribution)
This paper presents a spatial Bayesian hierarchical model of sea-level extremes and uses it to analyse tide gauge observations along the Finish coastline. Estimates of extreme sea-level event probabilities, which typically are expressed in terms of return levels, are crucial to flood risk quantification. However, such estimates are often subject to large uncertainty owing to issues related to the small sample sizes and large data dispersion typical of tide gauge observations. Furthermore, when using traditional single-site approaches, estimates of event probabilities are only possible at gauged locations. These issues can be partly overcome by exploiting spatial dependencies in extreme sea levels, or simply by pooling information across data sites, which leads to estimates of return levels with reduced uncertainty and allows for estimation at unobserved locations. Despite the advantages of spatial modelling, most studies of sea-level extremes to date have analyses extremes on a site-by-site basis. In this regard, this paper represents a valuable contribution to the literature on sea-level extremes. The paper shows that pooling information across space leads to more robust estimates of event probabilities, though in this study all tide gauge records are relatively long and as a result the single-site model (‘Separate’) is still able to estimate the GEV parameters with high confidence. The benefits of spatial modelling are much larger in regions with short tide gauge records, and this should be more strongly emphasized in the paper. The paper is well written, the methods are valid, and overall the results are interesting. I do not have any major objections to the paper, but I do have some comments and suggestions, as outlined below, that would like to see addressed before the paper is published in NHESS.
Extraction of annual maxima. Was the tidal component removed prior to extracting the annual maxima from the tide gauge records?
Equation 7. The Greek letters used to denote the GP standard deviation and length scale are different between the article and the Supplementary Information.
It is unclear to me what the authors mean by ‘empirical estimates’. The estimates from the Bayesian hierarchical models are conditional on the observations, so they are ‘empirical’ too, aren’t they?
Please add either posterior SDs or credible intervals to Table 2.
Discussion: Line ~335. While I agree that it should be emphasized that to quantify flood risk one should include mean sea level changes, I do not think that excluding mean sea level influences is a limitation of your study, rather it is a choice to focus on the storm surge component of sea level. The actual limitation is to assume stationarity, but this is discussed in the next paragraph.
Discussion. Another limitation that is not mentioned is that the Bayesian hierarchical models used in this study assume conditional independence in the likelihood. In other words, they assume that, after accounting for dependence in the marginal GEV parameter, the annual maxima are independent across stations. However, this assumption is unlikely to hold because the stations are geographically close and thus they are going to be affected by the same extreme events, which means that the time series of annual maxima are going to be correlated between stations (what is called ‘residual dependence’). Ignoring residual dependence means that your uncertainty estimates are narrower than they should be (probably only slightly), but other than that it should not significantly affect the estimates presented in the paper. This limitation should be discussed. Calafat and Marcos (2020) provide a way for addressing residual dependence, but I recognize that this is beyond the scope of this paper.