Volume 122, Issue 4 p. 2742-2759
Research Article
Free Access

Sea-level rise impacts on the temporal and spatial variability of extreme water levels: A case study for St. Peter-Ording, Germany

S. Santamaria-Aguilar

Corresponding Author

S. Santamaria-Aguilar

Institute of Geography, University of Kiel, Kiel, Germany

Correspondence to: S. Santamaria-Aguilar, [email protected]Search for more papers by this author
A. Arns

A. Arns

Research Institute for Water and Environment, University of Siegen, Siegen, Germany

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A. T. Vafeidis

A. T. Vafeidis

Institute of Geography, University of Kiel, Kiel, Germany

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First published: 11 March 2017
Citations: 11

Abstract

Both the temporal and spatial variability of storm surge water level (WL) curves are usually not taken into account in flood risk assessments as observational data are often scarce. In addition, sea-level rise (SLR) can further affect the variability of WLs. We analyze the temporal and spatial variability of the WL curve of 75 historical storm surge events that have been numerically simulated for St. Peter-Ording at the German North Sea coast, considering the effects induced by three SLR scenarios (RCP 4.5, RCP 8.5, and a RCP 8.5 high end scenario). We assess potential impacts of these scenarios on two parameters related to flooding: overflow volumes and fullness. Our results indicate that due to both the temporal and spatial variability of those events the resulting overflow volume can be two or even three times greater. We observe a steepening of the WL curve with an increase of the tidal range under the three SLR scenarios, although SLR induced effects are relatively higher for the RCP 4.5. The steepening of the WL curve with SLR produces a reduction of the fullness, but the changes in overflow volumes also depend on the magnitude of the storm surge event.

Key Points

  • Sea-level rise (SLR) results in a steeper storm water level curve that is proportionally greater for a moderate SLR scenario
  • When accounting for temporal variability of the water level curve estimated overflow volume can be up to three times higher
  • Overflow volume differences due to spatial variability can be similar to the difference between the T = 200 and T = 10,000 year event in one site

1 Introduction

Coastal flooding from extreme water levels (WL) is considered a major risk for coastal low-lying areas worldwide [Wong et al., 2014]. These regions are densely populated and often exhibit higher rates of growth and urbanization than the hinterland, which further exacerbates their exposure to flood hazard [e.g., Neumann et al., 2015; Hinkel et al., 2014]. In addition, the likelihood and intensity of current extreme WLs is expected to increase as a consequence of sea-level rise (SLR) [e.g., Church et al., 2013; Seneviratne et al., 2012]. For the development of effective coastal management strategies, it is therefore essential that flood risk assessments account for these factors.

For coastal management and protection, flood risk assessments at high temporal and spatial resolution are needed in order to account for local effects. At such resolutions, hydrodynamic models are able to simulate physical processes (i.e., atmospheric-ocean-land interactions) accounting for local geometries such as bathymetries and dike heights. However, these models are computationally expensive, which constrains their application to regional-to-local scales at high spatial resolution and limits the potential number of hazard scenarios that can be simulated [Ramirez et al., 2016].

Nevertheless, flood risk assessments need to cover a wide range of hazard scenarios, from high-probability of occurrence and low-consequences to low-probability and high-consequences, in order to account for uncertainties and sensitivity within the assessment [Hinkel et al., 2015; Nicholls et al., 2014]. The definition of low-probability hazard scenarios is complex because extreme WLs can arise from several combinations of mean sea level, tide, and surge conditions due to their different origin and high level of natural variability [e.g., Dangendorf et al., 2013, 2014]. In addition, most observed WL series are limited to 100 years or less, making it likely that observational records do not contain the worst physically possible conditions [e.g., Dangendorf et al., 2016].

Therefore, low-probability WLs are often estimated using extreme value statistics that are used to extrapolate beyond the range of observations. Although significant efforts have been directed toward reducing the uncertainties in extreme WLs [see, e.g., Haigh et al., 2010; Arns et al., 2013; Batstone et al., 2013], classical assessments usually only focus on peak WLs and thus do not include information about their duration and temporal evolution [Quinn et al., 2014], whereas reliable flood risk assessments require the entire WL curve to describe the temporal development of inundation. To overcome the lack of information related to the WL curve, simplified hazard scenarios are defined selecting the peak WL at certain return period (e.g., the 100 year return WL) and a WL curve is approximated using so-called “design curves.” The “design curves” are normally defined based on time series of historical events (e.g., the one at the highest ever recorded peak WL) [e.g., Dawson et al., 2005] or by superimposing the time series around the highest levels of each component (e.g., spring tide levels and the time series of the highest observed surge peak) and scaling to the return WL under investigation [e.g., Wadey et al., 2015; Gönnert and Gerkensmeier, 2015; Bruss et al., 2010]. Due to the scarcity of observed data (especially at extremes events), such synthetic extreme WL curves are often calculated at a single tide-gauge location and assumed representative for an entire area [e.g., McMillan et al., 2011]. As a result, uncertainties regarding both the temporal and spatial behavior extreme WLs are introduced.

An alternative method to produce extreme WL curves is shown in Wahl et al. [2011], who introduced an approach to stochastically simulate a large number of physically possible extreme WL curves using observational data as input. They parameterized WL curves of observed storm surge events and fitted distribution functions to the parameters. The distributions were then used to produce 10 million values of each of the WL parameters by a Monte Carlo simulation; these values were then interpolated to reconstruct WL curves. In a companion paper Wahl et al. [2012] present a bivariate statistical approach to estimate joint probabilities of storm-peak heights and their “intensity” (also termed “fullness,” which is defined as the area between the WL and the reference datum). A feature of this approach is that an event of equal joint probability can be generated by several different combinations (i.e., storm-peak heights and intensities), which results in different flooding extents and depths [e.g., Prime et al., 2016]. Although the WL curve of an extreme event which has not been observed but is physically plausible can be approximated using the above-mentioned methods of Wahl et al. [2011, 2012], the range of potential extreme WL curves is still too wide to be simulated using dynamic models. An assessment of potential implications of the variability of extreme WL curves on coastal flooding can be found in Quinn et al. [2014]. They analyzed the variability of WLs within the 6 h anterior and posterior to the storm peak of observed extreme WLs at several tide-gauged sites along UK. They showed that even if the variability of the WLs at times close to storm peak is low, they can have large effects upon overflow volumes. In addition, significant differences in WL variability between tide-gauged locations were found, showing the spatial variability of storm surge WL curves.

However, in some regions such as the German North Sea coast extreme WLs often last for more than 12 h, consisting of several high tides connected by very high low tides [Wahl et al., 2011]. This may increase the uncertainties related to the effects of the WL curve variability upon flooding because flooding is more likely at the times of the high tide. In addition, the German North Sea region is strongly affected by nonlinear shallow water effects, producing significant differences between WLs at neighboring tide-gauged locations [see, e.g., Arns et al., 2015b].

The above factors refer to the historical variability of extreme WLs. However, in order to assess future risk of flooding it is essential to also account for SLR and its impact on extreme WLs [see, e.g., Arns et al., 2015a]. To date, the most commonly used approach to include SLR effects in flood risk assessments is by linearly adjusting current extreme WL estimates upward by an amount equivalent to the projected SLR [see, e.g., Wadey et al., 2015]. Although this approach is justified in several regions of the world where changes in extreme WLs are driven by SLR alone [see, e.g., Menéndez and Woodworth, 2010], in the German North Sea a significant higher trend in extreme WLs has been reported [Mudersbach et al., 2013]. Furthermore, the study of Arns et al. [2015a] showed that a moderate SLR scenario can also produce nonlinear increases in extreme WL peaks in this region. These changes differ spatially along the coastline and are mainly due to variations in the tidal component. Therefore, it is possible that not only the extreme WL peaks are affected by SLR but also the entire WL curve, altering the storm surge intensity and inundation areas.

In this study, we explore the consequences of the temporal and spatial variability of extreme WLs time series on flood hazard assessments compared to assuming a temporally and spatially constant “design WL curve.” For this purpose, we analyze both factors along 13 locations of the German North Sea coastline. In addition, we evaluate potential changes in the WL curve of storm surge WLs and their variability predicted for three SLR scenarios: RCP 4.5, RCP 8.5, and RCP 8.5 HE (see Grinsted et al. [2015] and Slangen et al. [2014] for a detailed description). Furthermore, we quantify the effects of SLR induced changes on two parameters directly related to flooding: overflow discharge rates and fullness; in order to assess the potential consequences of the changes in the WL curve caused by SLR in flooding.

The paper is organized as follows: we first describe the characteristics of the study area as well as the WL data sets used (section 2). In section 3, we detail the methods used to correct the simulated WLs (section 3.1); to assess the impact of SLR on the WL curve of storm surge events and their temporal and spatial variability (section 3.2), and to analyze the effects of these factors on overflow rates and fullness (section 3.3). We present and discuss the results of the SLR induced changes on the WL curve variability and their consequences on overflow and fullness in section 4. Finally, we summarize the most important findings in section 5.

2 Study Area and Data

2.1 Study Area

The German North Sea coastline is a low-lying region, with some parts even below sea level, frequently threatened by extreme WLs. One of its largest communities directly bordering the North Sea is St. Peter-Ording, which is located on the west coast of the Eiderstedt peninsula (Figure 1). St. Peter-Ording is not surrounded by the barrier islands of the Wadden Sea (Figure 1) and is therefore highly exposed to extreme WLs. In the last century, the highest WLs have reached nearly 5 m above mean sea level [Kaiser and Kortenhaus, 2008].

Details are in the caption following the image

Location of the study area (upper left map) in the North Sea; bathymetry of the study area showing tide-gauge stations (as orange dots) and St. Peter-Ording locations (as pink dots) are shown in the upper right map. Sections of the dike-ring of St. Peter-Ording (modified from www.FLOODsite.net) and locations of numerically simulated WLs (lower map).

St. Peter-Ording has a population of 6300 permanent inhabitants and is the largest seaside resort in the state of Schleswig-Holstein with around 100,000 guests each year. A great part of the tourism sector is related to natural health treatments due to its sulfur spring and therefore, several hospitals, elderly and children's homes are located in this community. Part of the municipality also belongs to the Schleswig-Holstein Wadden Sea National Park, which has been part of the UNESCO World Heritage Site since 2009. The entire Eiderstedt peninsula is considered flood-prone as its elevation does not exceed 5 m NHN (local datum). Hence, if flooding occurs in St. Peter-Ording, the water can potentially spread far into the hinterland causing damages to assets of the Eiderstedt peninsula, as well as to agricultural fields, pastures, and flora of the park area due to salt water intrusion [Kaiser and Kortenhaus, 2008].

St. Peter-Ording is protected by a defense structure covering ∼15 km of coastline. This defense mainly consists of a dike ring with a length of more than 12 km, comprising several dike sections of different heights and lengths being covered by grass and asphalt, a natural dune belt and an overtopping dike with a retention reservoir behind the dike [Kortenhaus and Lambrecht, 2006]. The location of the different dike sections is shown in the lower map of Figure 1 and their characteristics in Table 1.

Table 1. Characteristics of the Different Sections of the Dike-Ring Protecting St. Peter-Ording and Design WLs for 2020a
Dike Sections Defence Type Year of Construction Height (m) Width (m) Inner Slope Outer Slope Length (m) Reference WL200 2020 (NHN + m)
1 Dike with grass cover 1996 8.28 1 3 6 670 5.3
2 Dike with grass cover 1996 8.35 1.5 3 6.4 996 5.3
3 Dike with grass cover 1996 8.19 1.5 3 6.5 1123 5.3
4 Dike with asphalt cover 1964 8.43 0.9 2.8 4.5 187 5.2
5 Dike with asphalt cover 1964 8.30 0 3.2 4.3 286 5.2
6 Dike with asphalt cover 1964 7 1.5 3 4.1 1381 5.2
7 Dunes 15 2.2 4 10 1010
8 Overtopping asphalt dike 6.22 1.7 4 3 1655 5.05
9 Dike with asphalt cover 1965 5.99 2.0 8 10 199 5.2
10 Dike with asphalt cover 1965 7.18 2.2 4.5 5.5 2986 5.2
11 Dike with grass cover 1965 6.98 3.5 4.8 8 1295 5.2
12 Dike with grass cover 1965 7.05 1.8 4.5 7 452 5.2
13 Dike with grass cover 1965 8 1 2.9 5.2 1042 5.2
  • a Modified from Kortenhaus and Lambrecht [2006] and MELUR [2012].

2.2 Data

For this study, there are no observational WL records available in the direct surroundings of St. Peter-Ording and the nearest available stations are located in enclosed areas at both sides of the Eiderstedt peninsula, in Büsum and Hüsum. WL records at those stations have been used in previous flood hazards assessments for St. Peter-Ording [Kaiser and Kortenhaus, 2008; Kortenhaus and Lambrecht, 2006]. However, analyses of observational records over the last decades indicate strong tidal dynamics in that region [see, e.g., Mudersbach et al., 2013; Arns et al., 2015a] and this is why WLs even at neighboring stations can differ significantly. We therefore use numerically simulated storm WLs (hereafter simulated WLs) presented in Arns et al. [2015a, 2015b] for 13 locations along the St. Peter-Ording coastline (equidistant spacing of ∼1 km, Figure 1) at a temporal resolution of 10 min. The WLs were simulated with a two-dimensional, depth-averaged barotropic tide-surge model of the entire North Sea using the MIKE21 FM (flexible mesh) modelling suite of the Danish Hydraulic Institute (DHI). The coastline resolution was resampled from 30 km along the open boundaries to 1 km at the German Bight coastline and a high resolution bathymetry (∼15 m) of the Wadden Sea areas was interpolated onto the flexible mesh. Hindcast WLs from 1970 to 2009 were simulated forcing model's open boundaries with astronomical tidal levels from the MIKE21 internal global tide model. Over the entire model domain, mean sea level pressure fields and 10 m wind fields from the CIRES 20th century reanalysis project [Compo et al., 2011] were used as atmospheric forcing. The same model was used to simulate WL changes under three different SLR scenarios, but keeping the atmospheric forcing identical to the hindcast run. In order to account for uncertainties related to future SLR projections, the scenarios considered are based on the RCP 4.5 (0.54 m), RCP 8.5 (0.71 m), and the RCP 8.5 high end (hereafter HE, of 1.74 m) scenarios. In each hindcast and scenario run, a total number of 75 storm surge events were simulated. Further details of model configuration can be found in Arns et al. [2015a, 2017].

Additionally, we use observed WLs from three gauged locations, provided by the Schleswig-Holstein Agency for Coastal Protection, National Parks and Ocean Protection (LKN-SH), in order to validate and correct the simulated WLs at St. Peter-Ording (for more information see section 3.1). The locations of the three stations (Büsum, Pellwormhaven, and Wittdün) are shown in Figure 1. The observed WLs are composed of hourly values covering the periods from 1997 to 2007 in Büsum, from 1995 to 2007 in Pellwormhaven, and from 1999 to 2009 in Wittdün. However, only the simultaneous data of the three tide-gauges (i.e., 1999–2007) are used for correction purposes.

3 Methods

3.1 Correction of Numerically Simulated WLs

Comparing observed and simulated WLs at the gauged sites shows good agreement, with a coefficient of determination of at least r2 = 0.8[–] at all three locations (Büsum, Pellwormhaven, and Wittdün). However, in order to further reduce systematic inaccuracies, a parametric bias correction is applied to the numerical-model outputs of both the hindcast and the three SLR scenarios. Arns et al. [2015a, 2015b] performed a nonparametric bias correction aiming at a correction of hindcast WLs that have also been recorded at some locations, adjusting each individual simulated and discrete WL value to the simultaneously observed WLs. However, this methodology is limited to the observational period and cannot be applied to scenario runs. For this reason, we focus on a parametric bias correction, which provides a transfer function that can be applied beyond the range of observations. The method essentially consists of fitting a parametric regression to the observed and simulated WLs of the hindcast and the three SLR scenarios [see, e.g., Ulm et al., 2016].

As there are no observed WLs available at the study area to validate and correct the simulated WLs, we use a multiple-linear regression model to transfer the observed data from the gauged stations to each ungauged St. Peter-Ording location. The model is constructed using the simulated WLs at the gauged sites as predictor variables and the simulated WLs of each St. Peter-Ording location as response variable. Assuming that the intramodel correlation is accurate, consistent, and constant, we can transfer the observed WLs from the gauged stations to each of the 13 ungauged Sankt Peter-Ording locations using the regression model and consider the transferred WLs as being representative. As mentioned in the previous section, WLs can significantly differ between tide-gauged sites and study locations due to local effects. However, Arns et al. [2015b] showed that there is a systematic bias between observed and simulated WLs, i.e., the model tends to overestimate low WLs and underestimate high WLs at all tide-gauged sites despite local effects, probably due to a coarse atmospheric forcing (spatial resolution of 2° and temporal resolution of 3 h). Therefore, the systematic bias can be reduced at the study sites using the transferred WLs, despite differences between the dynamics of the tide-gauged sites and the study locations.

Although there is high multicollinearity between the predictor variables, the predictions made with the multiple regression model are not affected as the predictor variables maintain the same multicollinearity pattern along the observed period of data [Studenmund, 1997]. On average, predictor correlation coefficients vary by approximately 0.02 between the observed and hindcast data set, indicating a constant pattern. Figure 2 shows a conceptual diagram of the transfer and correction approach.

Details are in the caption following the image

Conceptual diagram of WLs transfer and correction methodology: (a) Fitting the transfer models (multiple-linear regression) using the simulated WLs of the three gauged sites to each of the 13 St. Peter-Ording locations. (b) Transferring the observed WLs from the gauged sites to each of the 13 St. Peter-Ording locations using the transfer models. (c) Correction of the simulated WLs of each St. Peter-Ording location: the linear regression fitted to simulated (y axis) and transferred (x axis) WLs of one location is shown in the left graph; scatter of uncorrected simulated WLs versus transferred WLs (blue) and corrected simulated WLs versus transferred WLs (red) are shown in the right plot.

In order to transfer the WLs, we test the sensitivity of the multiple-linear regression model to different data sampling methods using the simulated and observed WLs of the tide-gauged sites (further details can be found in supporting information). The multiple-linear regression model constructed with the quantiles equally spaced in double logarithmic scale is chosen as transfer model due to its better performance. Therefore, multiple-linear regression models are fitted for each St. Peter-Ording location (equation 1) and are used to transfer the observed WLs to ungauged locations
urn:x-wiley:21699275:media:jgrc22206:jgrc22206-math-0001(1)
where SPO1 denotes the WLs of one St. Peter-Ording location, a1, b1, and c1 are the regression coefficients and B, P, and W denoting the WLs of the gauged locations Büsum, Pellwormhaven, and Wittdün.

On average, the constructed multiple-linear regression models have a coefficient of determination of r2 ∼ 1 [–]. Based on this value and on the low variation of predictor correlation coefficients, we can assume that the transferred WLs are representative as observed WLs at the study area. Once the observed WLs are transferred to each location, we perform the parametric bias correction by fitting linear regressions to the WLs in double logarithmic scale (Figure 3c). Although only systematic inaccuracies can be corrected by this procedure (see right graph of Figure 3c), the coefficient of determination increases from r2 = 0.87[–] to r2 = 0.98 [–] on average.

Details are in the caption following the image

Normalized set of hindcast events (light blue lines) and SLR scenarios (pink lines): (a) RCP 4.5 scenario, (b) RCP 8.5 scenario, and (c) RCP 8.5 HE scenario; and upper, mean, and lower envelopes (dark blue lines for the Hindcast scenario and red lines for the SLR scenarios) at location 6.

3.2 Analysis of Temporal and Spatial Variability of Storm WLs

We implement a modified version of the approach presented in Quinn et al. [2014] to assess the temporal variability of all storm surge events at each of the 13 locations of the study area, as well as for the hindcast and SLR scenarios. This approach is adopted because the WLs temporal variability is quantified relative to the storm peak, which is the parameter commonly used and recommended to perform extreme value analysis in this area, and consequently for flooding assessments [Kaiser and Kortenhaus, 2008; Wahl et al., 2011; Arns et al., 2013]. However, we modify the normalization approach in order not to alter the shape of the WL curves of the different scenarios, hence allowing comparisons between the individual scenarios. In addition, we modify the time window length and threshold level aiming to equalize these parameters to the ones used in the analysis of extreme events in our study area.

In a first step, we identify the storm water peaks at each location along the St. Peter-Ording coastline. Following the recommendations of Arns et al. [2013] on creating samples for extreme value analyses along the German North Sea coast, we select the storm peaks exceeding the 99.7th percentile at each location and scenario. According to the study of Wahl et al. [2011], the majority of storm surge event in the German North Sea region do not last longer than three tidal cycles. Therefore, in a second step we select the WLs within the 18 h before and after the storm peak (tidal high water), thus comprising three high tides.

In order to remove negative values prior to normalization, we refer all WLs to the lowest WL of the entire set of events (i.e., we add an offset of 180 cm to all WLs and scenarios). In addition, the SLR of all scenarios is removed before the events selection and normalization in order to analyze nonlinear changes in the WL curve driven by the SLR.

Next, we normalize the WL curves of the hindcast scenario relative to each of the three SLR scenarios, producing one normalized hindcast set of events per SLR scenario (Figure 3). The normalization of the WL curves is carried out by dividing each value (i.e., every 10 min) of every WL curve by the maximum storm peak of the corresponding SLR scenario.

Finally, we calculate the mean, standard deviation, 95th and 5th percentiles at each time step (i.e., each time point of the WL curve relative to the peak time) of the set of normalized events. The process is repeated for each scenario and location of the study area. The variability of the WLs at each time step is measured as the standard deviation obtained at this time step, and the 95th and 5th percentiles are the upper and lower envelope of the set of storm surge events.

3.3 Accounting for Effects of Storm WL Variability

Both the temporal and spatial WL variability can affect different processes contributing to inundations, such as overtopping and overflow discharge as well as erosion and breaching of defense structures. Therefore, we assess (1) the effects of storm WLs variability and (2) changes in the WL curve due to SLR, on two parameters related to the above-mentioned processes, namely overflow discharge rates and fullness. The first parameter is directly related to the volume of water flowing inland in a flooding event, while the fullness (parameter also named “intensity”) is a parameter used as a proxy of the energy input into defense structures during a storm event [Wahl et al., 2011, 2012; Salecker et al., 2011].

To analyze the effects of the WL curve variability, we produce three WL curves for each scenario with the same storm-peak value but different temporal behavior. For this purpose, we adjust the mean, 5th and 95th percentiles normalized WL curves to four storm-peak values corresponding to the T= {200, 500, 1000, 10,000} year events. The latter have been calculated following the recommendations of Arns et al. [2013] to perform extreme value analysis in the study area. In Figure 5, we show the Generalized Pareto Distributions (GPD) of the storm-peak values for all locations and scenarios, and the crest level of the lowest dike section (620 cm) of the study area (see section 2 for the characteristics of the dike ring). As shown in Figure 4, the only case in which a section of the dike can be exceeded is in the RCP 8.5 HE scenario. Therefore, we select the T = {200, 500, 1000, and 10,000} year storm-peak heights of the RCP 8.5 HE scenario (Figure 5).

Details are in the caption following the image

GPDs fitted for the different locations and scenarios: (a) hindcast, (b) RCP 4.5, (c) RCP 8.5, and (d) RCP 8.5 HE.

Details are in the caption following the image

Return WLs of the four events: (a) T = 200 year, (b) T = 500 year, (c) T = 1000 year, and (d) T = 10,000 year, at each St. Peter-Ording location.

In order to analyze the effects of the changes in the WL curve caused by SLR on overflow and fullness, we also estimate the WL curve for those storm-peak heights using the normalized WL curves of the hindcast, RCP 4.5 and RCP 8.5 scenarios. We must note that these are theoretical WL curves as the dike height cannot be exceeded in these scenarios.

To generate the WL curve for those storm-peak heights, we first rescale the WL curves of each scenario in order to set the normalized storm-peak height to 1. We then interpolate the WL curve from a temporal resolution of 10 to 1 min to improve the precision in the overflow rates and fullness estimations. For this purpose, we use the piecewise cubic hermite interpolation method based on the results of Wahl et al. [2011], who performed a sensitivity analysis of interpolation methods applied to the WL curve, finding the lowest errors for this method. We remove the offset of 180 cm added within the normalization stage, and thus the absolute values are referred to the NHN (i.e., the German ordnance datum).

We calculate theoretical overflow discharge rates using the general formula for a broad-crested weir [Kay 2008]:
urn:x-wiley:21699275:media:jgrc22206:jgrc22206-math-0002(2)
where urn:x-wiley:21699275:media:jgrc22206:jgrc22206-math-0003 is the overflow discharge rate (m3/s·m), H is the head of water over the crest (m), L is the crest width (m), and C is the weir coefficient (which in the case of broad-crested weirs takes the value of 1.6). The crest width of the dike section that can be exceeded by those events is 1.7 m.
The second parameter assessed is the fullness, which is defined as the area between the storm WL and the ordnance datum NHN:
urn:x-wiley:21699275:media:jgrc22206:jgrc22206-math-0004(3)
where the unit of fullness is cm2 and WL(t) is the WL curve over the entire duration of the event (36 h). We calculate the fullness of the events estimated by the T = {200, 500, 1000, 10,000} year WLs of the RCP 8.5 HE scenario and the WL curves of all scenarios.

4 Results and Discussion

4.1 Temporal and Spatial Variability of Extreme WLs

Figures 6, 7 and 8 present the spatial WL changes at each time step of the lower (5%), mean (50%), and upper envelopes (95%) between the hindcast and the three SLR scenarios. In these graphs, it can be observed that SLR caused WL changes at all three envelopes and in most of the time steps, with a magnitude ranging between ±15% (see, e.g., time steps −14 to −4 of Figure 6c). In the three scenarios, the lower envelope shows the highest WL changes (Figure 6), while the WL changes of the mean and upper envelope are of comparable magnitude (Figures 7 and 8).

Details are in the caption following the image

Spatial-temporal differences of the 5th percentile envelope (relative WLs in %) between (a) the RCP 4.5 scenario and the hindcast, (b) the RCP 8.5 scenario and the hindcast, and (c) the RCP 8.5 HE scenario and the hindcast. Positive values (red) represent an increase of the relative WL in the SLR scenarios (blue a decrease).

Details are in the caption following the image

Spatial-temporal differences of the mean envelope (relative WLs in %) between (a) the RCP 4.5 scenario and the hindcast, (b) the RCP 8.5 scenario and the hindcast, and (c) the RCP 8.5 HE scenario and the hindcast. Positive values (red) represent an increase of the relative WL in the SLR scenarios (blue a decrease).

Details are in the caption following the image

Spatial-temporal differences of the 95th percentile envelope (relative WLs in %) between (a) the RCP 4.5 scenario and the hindcast, (b) the RCP 8.5 scenario and the hindcast, and (c) the RCP 8.5 HE scenario and the hindcast. Positive values (red) represent an increase of the relative WL in the SLR scenarios (blue a decrease).

Although the WL changes of the three envelopes are not uniform, we observe a general pattern consisting of SLR induced increases of high-water peaks (hereinafter HWP) and decreases of low-water peaks (hereinafter LWP). This is consistent with the findings of Arns et al. [2015a], who reported an increase of HWP under the RCP 4.5 scenario produced by nonlinear changes in the tidal component. Their analysis pointed to an increase in the amplitude of the M2 tidal constituent and a decrease of the nonlinear constituents, resulting in an increase of the tidal range. However, in the RCP 4.5 scenario (Figures 6a, 7a, and 8a) we find that the increase of the HWP is spatially not uniform in magnitude and a decrease of the lower envelope HWP can also be observed in some locations (Figure 6a). The latter is true for the anterior HWP at locations 3 and 4, for the main storm peak of location 1, and for the posterior HWP at locations 6 and 7. We find that these spatial differences remain in the RCP 8.5 scenario (Figure 6b), while in the RCP 8.5 HE scenario, we observe a more regular pattern in the three envelopes (Figures 6c, 7c, and 8c). These spatially nonuniform WL changes with SLR show that the changes in the tidal component are highly influenced by local effects. This highlights the uncertainties which are introduced when using WLs from too distant locations as input for flood risk assessments.

Nevertheless, the WL changes caused by SLR are not only limited to the times of the HWP and LWP as we can observe WL changes at most of the time steps. In the three envelopes of all SLR scenarios, we observe that WL increases are mostly constrained to the time of the HWP (time steps −12, 0, and +12) plus 1 or 2 h. However, the decrease surrounding the LWP (time steps −6 and +6) generally comprises more time steps. Thus, the extreme WL curve becomes steeper with SLR, regardless of uncertainties related to future SLR projections.

Moreover, in several locations, we find nonlinear WL changes with SLR. In some cases, we observe higher WL changes for the RCP 4.5 scenario than for the RCP 8.5 (e.g., storm peak of the lower envelope at the southern locations, Figures 6a and 6b), or a different pattern between these two scenarios and the RCP 8.5 HE scenario. For example, in the flow phase (between time step +6 and +12) in the posterior HWP of the upper envelope (Figure 8), a moderate increase is found in the RCP 4.5 and RCP 8.5 scenarios and a decrease in the RCP 8.5 HE scenario. The different pattern of the WL changes in the RCP 8.5 HE scenario compared to the RCP 4.5 and RCP 8.5 is probably caused by the stronger reduction of shallow water effects related to the larger water depth of that scenario. Due to the shallowness of this area, a moderate rise of sea level may cause higher WL changes than an HE scenario.

We observe that the maximum variability values (between 10% and 12%) in the hindcast scenario (Figure 9) are reached at the flow phase of the posterior HWP (time steps from 6 to 12) and the ebb-phase of the anterior HWP (time steps from −12 to −6), whereas the lowest variability is obtained at the times of the main storm peak. We also find a high variability at the HWP times, which is higher for the anterior and posterior HWP (8–9%) than for the main storm peak (6–7%). One factor that may cause this high variability, besides the intensity of the different events, is the different duration of the storm events included in the analysis. As a consequence of the approach we use for selecting events, we also include storm events (i.e., the 99.7th percentile threshold exceedances) that last for less than 36 h, thus potentially resulting in a higher variability of WLs for the time further away from the storm-peak time. Due to the fact that flooding (overflow/overtopping) occurrence is more probable at the HWP times, the high values of variability obtained at these time steps highlight the uncertainties related to the use of a single WL curve (“design WL curve”) in flooding assessments.

Details are in the caption following the image

Spatial and temporal variability (standard deviation) of the normalized set of events from the hindcast scenario.

Regarding the spatial distribution of the WL variability, we find a generally higher variability at each time step for the southern locations than for the northern ones. As shown by Arns et al. [2015a, 2015b], small local changes in water depth can produce differences in frictional and shallow water effects due to the shallowness of the German North Sea coast and the strong tidal dynamics of this region. Therefore, differences in WL variability between northern (from 1 to 7) and southern locations may be due to differences in the bathymetric features between the northern and southern locations. Specifically, as the southern locations are situated closer to a tidal channel than the northern locations, WLs can be stronger affected by tidal currents, thus leading to increased WL variability. However, we cannot confirm these hypothesis based on the analysis performed and further research is needed in order to better describe the hydrodynamics of this area.

The WL changes caused by SLR have their subsequent impact on the variability. We can observe that the changes in the variability are of similar magnitude for the three SLR scenarios, with values ranging between ±6% (Figure 10). We do again find that the changes in the variability are spatially not homogeneous, as for some time steps we find an increase of the variability at some locations and a decrease at others. Nevertheless, we observe an increase of the LWP variability at most locations of the three SLR scenarios, excluding the second LWP of the RCP 8.5 HE scenario (Figure 10c). However, there is no clear pattern of the changes in the variability of the HWP as we find an increase in some cases and a decrease in others. For example, we observe an increase of the anterior HWP variability in the RCP 4.5 and RCP 8.5 scenarios (Figures 10a and 10b), whereas a decrease is found at this time step in the RCP 8.5 HE (Figure 10c). These nonuniform changes in the variability are in line with the observed WL changes due to SLR, and highlight the importance of accounting for local dynamics in this region.

Details are in the caption following the image

Differences of variability between (a) the RCP 4.5 scenarios and the hindcast, (b) the RCP 8.5 scenario and the hindcast, and (c) the RCP 8.5 HE scenario and the hindcast. Positive values (red) represent an increase of the variability in the SLR scenarios (blue a decrease).

4.2 Implications of Storm WL Variability on Overflow Rates and Fullness

Figure 12 shows the overtopping rates obtained for the events estimated by the T = {200, 500, 1000, 10,000} year WLs of the RCP 8.5 HE scenario and the WL curves of all scenarios. At each location, we show the overflow rates corresponding to one return WL of the RCP 8.5 HE scenario and each WL curve (lower, mean, and upper envelope) of the four scenarios (hindcast, RCP 4.5, RCP 8.5, and RCP 8.5 HE).

We observe higher overflow rates at the southern locations (from 7 to 13) compared to the northern ones (Figure 11). These spatial differences are mainly due to the storm-peak heights obtained for each location (Figure 5) because we have calculated overflow assuming an equal crest height at all locations. Although the dike-ring of St. Peter-Ording comprises dike sections of different heights, the estimated design WLs of the T = 200 year by 2020 (Table 1) are nearly identical for all dike sections, with the northern sections having the highest values [MELUR, 2012]. Importantly, we obtain a different pattern of the T = 200 year WLs for the RCP 8.5 HE scenario, namely: a greater spatial variability and higher values at the southern locations than at the northern locations (absolute values cannot be compared as they correspond to different scenarios). The discrepancies between the design values and the patterns that we obtained are probably due to the different approaches used to derive the return WLs at ungauged sites and the SLR induced changes. The local authority responsible for coastal protection in the study area uses an approach based on the Regional Frequency Analysis, which does not account for local hydrodynamics [Arns et al., 2015b].

Details are in the caption following the image

Overflow rates obtained for the (a) T = 200 year, (b) T = 500 year, (c) T = 1000 year, and (d) T = 10,000 year storm-peak heights of the RCP 8.5 HE scenario and the normalized WL curves of all scenarios.

The T = 200 year storm-peak heights differs between the northern and southern locations by approximately 30 cm, resulting in differences of overflow rates of around 1 × 107 and 1.5 × 107 cm3 · s−1 · m−1. These differences between locations are of similar magnitude to the difference between the overflow rates obtained from the T = 200 year (Figure 11a) and T = 10,000 year event (Figure 11d) at the same location. This high difference of overflow rates between locations for the same event highlights the importance of accounting for the spatial variability of extreme WLs. For example, if we assess flooding of the T = 200 year event only using information of extreme WLs of location 5, we are underestimating by 50% the overtopping rate at location 13, which corresponds to the overtopping resulting in location 5 for the T = 10,000 year event.

We also find differences in the overflow rates resulting from the upper, mean, and lower envelopes of all scenarios. Although the differences between the overflow rates of the lower and mean envelope are almost negligible at most of the locations, the overflow rates resulting from the upper envelope of all the events are up to three times higher. This confirms that the use of a single “design WL curve” is subject to high uncertainties when assessing flood risk in this region.

To evaluate the effects of WL changes due to SLR on overflow rates, we compare the hypothetical overflow rates obtained for the T = {200, 500, 1000, 10,000} storm-peak heights of the RCP 8.5 HE scenario and the WL curves of all scenarios at each location. The differences between the overflow rates resulting from the lower and mean envelope are almost negligible, although we can observe higher overflow rates for the WL curves of the hindcast scenario (blue bars) than for the SLR scenarios at some locations (see, e.g., locations 1–6). However, the differences of the overflow rates belonging to the upper WL curve (darker shades) of the different scenarios are higher, reaching up to 5 × 106 cm3·m−1·m−1. For this WL curve, there is no clear spatial pattern for the different scenarios. From locations 5 to 13, we find the highest overflow rates in all events for the WL curve of the RCP 4.5 scenario (red bars), whereas it corresponds to the WL curve of the RCP 8.5 at location 4 (green bars) and the hindcast scenario at location 1 (blue bars). In addition, we observe the relevance of the WL changes for the time steps beyond the storm peak comparing the overflow resulting for the different events at the same location. For example, we find a significant higher overflow for the T = 200 year event for the upper WL curve of the RCP 8.5 scenario compared to the hindcast scenario at location 3 (Figure 11a). However, the difference between the overflow of the T = 10,000 year event for these two scenarios is almost negligible (Figure 11b).

By contrast, we obtain the highest fullness values for the WL curves of the hindcast scenario at all locations and events. We must emphasize that the storm peak values of all events correspond to the RCP 8.5 HE scenario, and the WL curves have been constructed using the normalized WL curves (mean, 5th and 95th percentiles curves) of all scenarios (hindcast and SLR scenarios) in order to assess potential consequences of not accounting for changes in the WL curve. Therefore, the differences of fullness between the SLR scenarios and the hindcast scenario shown in Figure 12 are not absolute as the absolute values of the SLR scenarios would always be larger than the hindcast. In most cases, we observe that the differences from all WL curves of the RCP 8.5 HE scenario (green bars) are approximately two times higher than the ones of the other two scenarios (blue and red bars). However, comparing the values obtained for the other two scenarios we find different patterns depending on the event and location, with higher differences in some cases obtained for the RCP 4.5. For example, for the T = 200 year event we obtain higher fullness differences for the WL curve of the RCP 4.5 (Figure 12a, blue bars) than for the WL curve of the RCP 8.5 (red bars), whereas for the other three events we obtain higher differences for the WL curve of the RCP 8.5 in more than half of the locations (see, e.g., locations 10–13). Regarding the differences obtained for each WL curve (i.e., mean, 5th and 95th percentiles WL curves), we observe in general lower differences for the upper WL curve of all scenarios (lighter shades), which are nearly negligible at some locations for the RCP 4.5 and RCP 8.5 scenarios.

Details are in the caption following the image

Differences in fullness obtained between the WL curves of the hindcast and the three SLR scenarios of the (a) T = 200 year, (b) 500 year, (c) T = 1000 year, and (d) T = 10,000 year events of the RCP 8.5 HE scenario.

These results are in line with the WL changes discussed in the previous section and specifically with the increase of the tidal range with SLR that results in a steeper WL curve. The reduction of the fullness related to the WL curves of the SLR scenarios is due to the fact that the WL increase close to the HWPs (i.e., around the 2 h before and after the HWP) is relatively lower than the decrease of the WLs at the remaining time steps of the WL curve. This is more noticeable for the lower and mean WL curves, where we obtain greater decreases of the fullness. In addition, we find a greater reduction in fullness at those locations where we obtained a lower relative increase of the HWP (e.g., locations 2 and 3). This suggests that if SLR induced changes in the WL curve are not accounted for when estimating fullness, this parameter will be overestimated and so will the energy input upon the defense structures.

5 Conclusions

In this study, we have assessed the temporal and spatial variability of historic extreme WLs at St. Peter-Ording in the German Bight, and potential changes in the WL variability as consequence from SLR. In addition, we have quantified the effects of WL variability on overflow volumes and fullness in order to assess potential consequences on flooding.

We found a high degree of WL variability highlighting the uncertainties related to the assumption of defining a “design” WL curve as representative for a region in flooding assessments. The high WL variability obtained at the times around the anterior and posterior HWPs is of particular importance as the WL height of those peaks is usually excluded in extreme value analysis, where only the storm-peak height is commonly analyzed, and the overflow/overtopping occurrence is more probable at those time steps. This study shows that the anterior and/or posterior HWP height of some historical events nearly reached the level of the storm-peak height, showing that is possible that an extreme event of two or even three HWPs in a row of similar height can occurs in the future. The temporal variability of the WL curve produces high differences in overflow volumes, with the upper WL curve resulting in rates that are double or even triple than those computed with the lower WL curve.

In general, SLR produces an increase of the WLs around the times of the HWPs and a decrease of the WLs around the times of the LWPs. This generally results in higher overflow volumes for the WL curves of SLR scenarios compared with the hindcast WL curves. However, this general pattern is not linear with SLR, resulting in a higher increase in the overflow volume for the WL curves of the RCP 4.5 and RCP 8.5 scenarios compared to the WL curve of the RCP 8.5 HE scenario. Therefore, a low to moderate SLR may have greater relative effects over the WL curve than an HE scenario in the study area. In addition, we found both spatial WL variability and WL changes caused by SLR along the study area, which highlights the role of the local (∼1 km) shallow water processes on WLs. These spatial variations also have significant impacts on overflow volumes and return WLs, which can be of the same order as the different overflow volume obtained for the T = 200 year and T = 10,000 year events at the same location. Therefore, the assumption of a constant WL curve along a flooding model domain in this spatial scale at the study area may entail high uncertainties with respect to overflow volumes.

The changes caused by SLR over the WL curve of the analyzed storm surge events from the RCP 8.5 HE scenario produce a decrease in fullness compared to the values estimated for the hindcast WL curves. Therefore, if SLR induced changes in the WL curve are not taken into account (i.e., if only the changes induced by SLR in the storm peak values are considered), fullness will be overestimated.

This study has focused on a small region of the German North Sea coast where SLR is predicted to induce high impacts on the WL curve of storm surge events. The results of this study cannot be directly extrapolated to other areas of the world because SLR induced effects are highly spatially variable and strongly depend on local features (i.e., bathymetry, coastal morphology, etc.). However, the methodology presented here can be used to locally assess SLR impacts on the WL curve of storm surge events in those regions where SLR induced changes in the tidal levels have also been reported and predicted [see, e.g., Idier et al., 2017; Mawdsley et al., 2015].

Further research should include potential changes on the bathymetry induced by SLR such as changes in tidal channels and sand bar locations, which may affect the hydrodynamics of the region by altering propagation processes (e.g., dissipation by bottom friction) [e.g., Bilskie et al., 2016] and thus affecting the variability of extreme WLs.

Acknowledgments

S. Santamaria-Aguilar and A.T. Vafeidis were supported by the EU FP7 project RISES-AM (grant agreement 603396). A. Arns was funded by the University of Siegen. All data used in this paper is properly cited and referred to in the reference list. We acknowledge the support of the Agency for Coastal Protection, National Parks and Ocean Protection of Schleswig-Holstein for providing the tide-gauge series, which are available for scientific purposes under request (http://www.schleswig-holstein.de/DE/Landesregierung/LKN/lkn_node.html). We would also like to acknowledge the two anonymous reviewers for providing constructive and valuable comments that helped improving the paper.