Comparison of tail models and data for extreme value analysis of high tide water levels along the Dutch coast

To assess the reliability of flood protection in the Netherlands, return values of wind speed and coastal water level for return periods up to several million years are needed. This is a major challenge, given that records of reliable wind measurements do not go back further than about 70 years, and water level measurements do not go back further than 70-140 years. 
Several ideas are currently explored to tackle this problem. One idea is to increase data volume by utilizing large datasets of simulations by numerical weather prediction models and hydraulic models forced by these simulations; see van den Brink (2018, 2020); de Valk and van den Brink (2020a). This approach relies heavily on the quality of these models. Furthermore, even large datasets such as the archived ECMWF seasonal ensemble forecasts leave a considerable gap in return period to be overcome. Therefore, a parallel effort is made to improve the extrapolation of the tails of distribution functions over a wide range of return periods: the Generalized Weibull (GW) tail, the log-Generalized Weibull (log-GW) tail, or the 1-parameter Weibull tail.
For these models and for two classical tail models, the Generalized Pareto (GP) tail and the exponential tail, we compare estimates of the tails of the distributions of high-tide water level and skew surge at 21 tide gauge stations derived from simulations by the WAQUA DCSM-5 shallow-water flow model driven by wind stress and surface pressure from the ECMWF SEAS5 seasonal ensemble forecast archive. For each tide gauge station, approximately 5800 years of data is used. 
Two methods are used to assess the estimates: the method from van den Brink and Können (2008), and Monte-Carlo simulation of the estimation of return values for very high return periods based on plausible models of the tails, derived from the SEAS5/DCSM-5 data. The latter method improves the method used in de Valk and van den Brink (2020a), but the results of both methods are not very different. 
For water level and surge, both the GW tail and the GP tail give accurate estimates if their shape parameters are estimated accurately from the complete set of SEAS5/DCSM-5 data. Overall, the GW tails performs best, in particular if all parameters (including the shape parameter) are estimated from a small 78-year subset. Earlier, this type of tail was found to be the most suitable one for wind and for pseudo-wind derived from stress (de Valk and van den Brink, 2020a). An additional advantage of using the GW tail both for (pseudo)wind speed and for surge/water level is that a power law for the wind-surge relation (a reasonable simplification) is preserved. 
In addition, tail estimates for water level and surge from SEAS5/DCSM-5 model simulations are compared to estimates from measurements at 6 tide gauge stations. The comparison is focused on the shape parameter (as errors in shape estimates are the main source of error in estimates of return values), regarded as a function of water level or surge. 
The results indicate that the estimates of the shape parameter of the GW tail from the model simulations are somewhat lower than the estimates from measurement data for relatively low water levels or surges (exceeded in more than 1 in 100 high tides). 
Only for low water levels and surge at Delfzijl, the shape is clearly underestimated by the simulated data. However, in the higher range of water levels or surges, the shape estimates from the. SEAS5/DCSM-5 simulaties for Delfzijl look more realistic than the estimates from the measurements. 
To understand these deviations at Delfzijl better, we need the results of the ongoing analysis of the effects of model resolution and other aspects of the atmospheric en hydraulic models on the simulated water levels and surges. 
This study was carried out within Maatwerk I&W under supervision by Marcel Bottema and Robert Slomp (WVL). Prof. dr. Pieter van Gelder carried out a review of this report, which was used in the final version and in the work that followed.