Very severe storm tides in the German Bight (North Sea) and their potential for enhancement

Storm tides are an essential hazard for the German North Sea coasts. For coastal protection and economic activities, planning information on probability and magnitude of extreme storm tides and their possible future changes is important. This study focuses on the most extreme events and examines whether they could have become more severe under slightly different conditions still remaining within the physical plausibility. In the face of limited amount of observational data on very severe events, an extensive set of model data is used to extract 5 most extreme storm tide events for locations in the German Bight, in particular Borkum and the Ems estuary. The data set includes water levels and respective atmospheric conditions from a hindcast and future climate realizations without sea level rise describing today’s and possible future conditions. A number of very severe events with water levels exceeding those measured near Borkum since 1906 has been identified in the data set. A possible further amplification of the highest events is investigated by simulating these events for the North Sea 10 with different phase lags between the astronomical tide given at the open model boundaries and the wind forcing. It was found that superposition of spring tide conditions, different timing of the astronomical high water and atmospheric conditions during the highest storm event would cause an enhancement of the highest water level up to about 50 cm. The amplified water levels of the two highest events from the data set are used to analyse the effects in the Ems estuary using a high-resolution model of the German Bight. Additionally, the influence of an extreme river runoff and of sea level 15 rise is studied. The extreme river runoff of 1200 m3s−1 increases the highest water levels by several decimeters in the narrow upstream part of the Ems estuary. This effect diminishes downstream. The sea level rise increases the water level in the downstream part of the Ems estuary by the amount applied at the model boundary to the North Sea. In the upstream part, its influence on the water level decreases. This study may serve as a first step towards an impact assessment for severe storm tides and their implications for coastal 20 areas and activities. 1 https://doi.org/10.5194/nhess-2019-351 Preprint. Discussion started: 29 November 2019 c © Author(s) 2019. CC BY 4.0 License.

held within the project XtremRisK (Gönnert et al. (2013), Oumeraci et al. (2015)) developed a more combinatorial approach merging estimates of various storm tide components such as surge, external surge, tides and their non-linear interactions derived from observation. Both studies were mainly focused on the Elbe estuary and resulted in constructing and investigating events exceeding the observed ones. 60 Without changing the atmospheric forcing possible amplification can occur due to different configurations of existing atmospheric situations and astronomical tide. In particular, altered timing of atmospheric storm relative to the tidal phase may lead to variations in maximum water level. In addition to semidiurnal tidal variations the longer fluctuations of the tidal components can be considered reflecting the situation where particular atmospheric storm may coincide with spring tide instead of neap tide. In the present study we pursue this strategy to investigate the potential for very severe storm tides to be enhanced.
Whereas Jensen et al. (2006) looked at particular observed storms and the amplification of their peak water levels, the current study deals with a large set of met-ocean hindcast and climate realizations to detect extraordinary storm events, focusing on both storm tide height and duration. The used climate realizations incorporating CMIP3 and CMIP5 scenarios reflect only the changes in the atmospheric conditions and do not include mean sea level rise and local bathymetry changes. A variety of future climate realizations underlines large uncertainties regarding possible future changes in storm climate for the region of interest 70 (e.g. Feser et al. (2015), Ganske et al. (2016)). Hereafter we assume that extremes from the used simulations represent also plausible events for the present climate conditions as storm statistics in these simulations show no or minor significant changes towards 2100 in combination with very strong inter-decadal variability for wind speed and surge levels (e.g. Gaslikova et al. (2013)).
From this data set the most extreme storm tide events were selected for three distinct parts of the German Bight -East 75 Frisian and North Frisian coasts and Elbe mouth (Figure 1). A set of dynamical large-scale simulations was produced to examine whether the identified storm tides could have become more extreme under different constellations of peak winds and tides. Hereby, a regional hydrodynamic model, which covers the North Sea and parts of the North East Atlantic to ensure the incorporation of external surges was used.
To investigate local effects of such extremely severe events near the coast and specifically in the estuaries, the Ems estuary 80 was chosen for further experiments and analyses. The estuary represent one of the main German estuaries. In addition to dykes along the North Sea coast and the whole estuary the upper Ems estuary is protected by a storm surge barrier. Operating the barrier influences the water levels both upstream and downstream of the barrier (Rego et al. (2011), BAW (2007). Such effects under extreme storm tide contidions are of additional interest. Moreover, the town Emden as an example for a typical harbor town with importance for marine trade, was chosen as a focus point within the estuary. To adequately transfer the acquired 85 extreme storm tides to the coasts and assess their impact within an estuary, a more detailed hydrodynamic model for the German Bight including the German estuaries has been used ( Figure 1). Additional factors, which may lead to the amplification of water levels at the coast and which are more relevant at local scales and shallow water (effects of varying river discharge and possible future sea level rise) were considered and incorporated in the sensitivity study here.  (2014)). In outer parts of the estuaries of Ems, Weser and Elbe the mean tidal range can exceed 3 m (e.g. Niemeyer and Kaiser (1999)). Thus, a specific storm in the southern North Sea has different influences on the water levels at the different coastal strips and in the estuaries.
The Ems estuary is situated in the German Bight in the southern North Sea at the border between the Netherlands and Germany ( Figure 1). Coming from the wide mouth of the estuary near the island of Borkum it is narrowing towards Knock, 100 but again widening into the Dollart bay south of Emden. Upstream of the Dollart the narrow and shallower part of the Ems estuary begins. The influence of the tide can be observed until Herbrum. At the mouth of the Ems near Borkum the tide is characterised by mean tidal high water MHW NHN + 1,15 m and mean tidal low water MLW NHN -1,31 m (DGJa (2014), NHN (Normalhöhennull) presents the German standard elevation zero.) In the center of the estuary at Emden the mean tidal range increases to 3,28 m with mean tidal high water MHW = NHN + 1,48 m and mean tidal low water MLW = NHN -1,80 m 105 (DGJb (2018)). The mean freshwater discharge into the Ems estuary is 80 m 3 s −1 , the highest discharge observed is 1200 m 3 s −1 (February 1946) (DGJb (2018)). Large freshwater discharges occur frequently in the months from January to April (Krebs and Weilbeer (2008)).

Data set
For the detection and ranking of extreme storm tides, a set of numerical simulations has been used for which atmospheric as 110 well as marine data exist and for which the water levels were simulated with the same hydrodynamic model. This set includes a multi-decadal hindcast (Weisse et al. (2014), Weisse et al. (2015)) based on downscaled NCEP-NCAR global reanalyses (Kalnay et al. (1996)) and six multi-decadal climate change realizations up to 2100 with respective control simulations. The atmospheric simulations include four realizations of the CMIP3 emission scenarios A1B and B1 and two realizations of the CMIP5 emission scenario RCP8.5 (for emission scenarios see e.g. Nakicenovic and Swart (2000), Houghton et al. (2001) 115 and Stocker et al. (2013), for CMIP5 simulations see e.g. Taylor et al. (2010)). They were simulated with different global models (ECHAM5-MPIOM (e.g. Röckner et al. (2003), Marsland et al. (2003)), EC-EARTH (e.g. Hazeleger and Coauthors (2010)), CMCC (Scoccimarro et al. (2011))) starting at different initial conditions. The global atmospheric simulations were downscaled with different regional circulation models (different versions of CCLM (e.g. Rockel et al. (2008), Hollweg et al. (2008)), RCA4 (e.g. Samuelsson et al. (2011))) before they were used to force the hydrodynamic model TRIM-NP (Kapitza 120 and Eppel (2000), Pätsch et al. (2017)) to calculate water levels in the North Sea and Northeast Atlantic (e.g. Gaslikova et al. (2013), see also Figure 2). The climate realizations do not include any rise in mean sea level. Water level changes are due to changes in the atmospheric forcing only. Furthermore, possible changes in bathymetry within the course of the time are neglected in the hindcast as well as in the climate realizations.

Selection of events and enhancement experiments
The analysis of extreme storm tides is mainly focused on the East-Frisian coast in particular on Borkum and the Ems estuary.
However, the impact of storms in the North Sea varies along the coasts depending on the wind direction and the resulting wind set up. Therefore, from the data set, time series of hourly water levels were extracted for a location seaward of the island of Borkum (in the following mentioned as "Borkum") and two other locations in the German Bight ( Figure 1): one location in the 130 outer Elbe estuary (mentioned as "Elbe Mouth") and one location seaward of the North-Frisian island of Amrum (mentioned as "Amrum").
Figure 2 describes the workflow for the simulation of the original water levels included in the data set and for the construction of the amplified water levels. A potential amplification due to tidal variations is tested for selected events at Borkum, whereas Elbe Mouth and Amrum are used to compare the effects at Borkum with those at other coasts of the German Bight. A potential 135 amplification of the selected events in the North Sea as well as nearer to the coast in the German Bight and the Ems estuary is investigated in the following by four steps.
In step 1, extreme storm events are selected from the corresponding time series using three criteria: -height of water levels, -duration of water levels countinuously exceeding 1.15 m (MHW at Borkum, DGJa (2014)) and 140 -chain of events within one week.
Water levels are considered with respect to NHN. The selected events for Borkum are ranked with respect to their water levels and their durations. For the further analysis of a possible amplification, the highest event, the longest event and the strongest event chain from the selected events were chosen. In the following these events are mentioned as "EH", 'EL" and "EC", respectively.

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In step 2, possible amplification of the selected extreme events due to different combinations between wind field and astronomical tide was tested. Maximum water levels may be increased by variations of relative propagation and arrival time of tidal high water and atmospheric storm. They may also become higher if the specific storm occurs around spring tides rather than around neap tides.
Thus, ensembles of large-scale North Sea water level simulations for each selected event were generated. For ensemble one, 150 the astronomical tide given at the open model boundaries was shifted hourly within +/-6 h around the wind speed maximum.
For ensemble two, the highest spring tide found in the respective climate realization was used instead of the original tide and the astronomical tides were shifted again hourly. For each member of ensemble one and two water level time series were extracted for the three locations, in these cases with a time resolution of 20 minutes. The time series for Borkum were analysed with respect to the strongest amplification. Furthermore, the effects of the amplification procedures for Borkum were compared to the corresponding effects at Elbe Mouth and Amrum.
Respective data from the ensemble members with the highest amplified water levels near Borkum (in the following identified by "_a") for each event were used for further fine-grid simulations of the German Bight and the Ems estuary in steps 3 and 4.
In step 3, high resolution water level simulations for the German Bight and the attached estuaries for the ensemble member with the highest amplified water levels near Borkum for the selected events derived from step 2 were performed.

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In step 4, the events from step 3 were further amplified by applying an increased river runoff to examine the impact of runoff variations and a sea level rise to place the results in the context of future climate change. For these amplification simulations the highest observed river runoff for the Ems of 1200 m 3 s −1 (1946( , DGJb (2018) was assumed. This extreme river runoff was  For consistency reasons, the simulations in steps 2 were performed with the same hydrodynamic model TRIM-NP which was used previously for the considered data set of hindcast and climate realizations. The model TRIM-NP (Nested and Parallized, Kapitza and Eppel (2000), Pätsch et al. (2017)) is based on the model TRIM (Tidal Residual Intertidal Mudflat) developed by Casulli and Cattani (1994)) and was used in 2D mode. The model domain covers the North Sea and adjacent parts of the 175 Northeast Atlantic (Figure 1) to allow the generation of realistic external surges. The model solves the Reynolds-averaged Navier Stokes equations on a regular Arakawa-C grid with Cartesian coordinates and is used in the present study with a resolution of 12.8 km x 12.8 km without further nesting. The model time step was 4 minutes and the output was stored every 20 minutes. Drying and wetting of near-shore points is enabled. The water level simulations were driven by the 10 m height wind and mean sea level pressure (SLP) fields from the atmospheric data mentioned above and by astronomical tides from 180 the FES atlas (Lyard et al. (2006)) at the lateral open boundaries. The wind influence is parameterized using an approach from Smith and Banke (Smith and Banke (1975)). While this approach is based on wind speed measurements between 3 and 21 ms −1 which are exceeded during storm surges, previous studies have shown that this approach is suitable for the North Sea and applicable for storm surges (Jensen et al. (2006)). For a detailed description of the original water level simulations and model performance see Gaslikova et al. (2013) and Weisse et al. (2014).

"German Bight" model for the fine-grid simulations
For the high-resolution modelling of the German Bight and the attached estuaries of the rivers Ems, Weser and Elbe (Figure 1) for the selected events in steps 3 and 4, the hydrodynamic numerical model UnTRIM 2 (Casulli (2008)) is used.
UnTRIM 2 is a 3D finite difference / finite volume numerical model. It solves the shallow water equations and the transport equation of salt on an unstructured orthogonal grid (Casulli and Walters (2000)). The use of the subgrid technology described 190 by Casulli (2008) allows discretizing the model bathymetry with a much finer resolution than the computational grid. In areas like the German Wadden Sea with its large tidal flats, this allows describing dry and wet areas in greater detail as well as better representation of the water volume. Thus, the bathymetry can be captured in detail while the computations can still be performed on a relatively coarse grid. As a result, large time steps can be used and the computational costs are kept low.
The algorithm also guarantees conservation of mass and water depths greater than zero regardless of time step size and is 195 unconditionally stable. The German Bight model is forced by wind, river runoff, salinity and water level. For these simulations, the same wind fields which were used in step 2 for the North Sea simulations were used. In UnTRIM 2 , the wind parameterization is similar to that in TRIM-NP. River runoff is applied at the upstream end of the estuaries. Based on the balance between coastal protection and nature conservation the barrier should protect the estuary against storm tides higher than NHN + 3.70 m. The barrier is closed when water levels at the barrier are exceeding NHN + 3.50 m and it is 205 reopened when water levels upstream and downstream of the barrier are equal. In order to ensure the protective function of the storm surge barrier in case of a sea level rise of 100 cm, the height of the gates were increased from its original 7 m to 8 m in nature to 9 m in the model. Different classifications of storm tides exist using e.g. water levels above a reference height or the probability of water levels.

Extreme storm tides at the coasts of the German Bight
Here, the classification of the Bundesamt für Seeschifffahrt und Hydrographie (Federal Maritime and Hydrographic Agency, see Müller-Navarra et al. (2003)) is used: A storm tide is an event with water levels exceeding mean tidal high water (MHW) at least by 1.5 m, a severe and a very severe storm tide denote events exceeding MHW by 2.5 m and 3.5 m, respectively.
Following the procedure described in the previous chapter, events were selected for Borkum and ranked with respect to their water levels and their durations. In Figure 3 time series for the five highest storm tides extracted from the data set are compared with the highest observed storm tides for Borkum showing that the data set includes storm tides higher than observed during the past 110 years. The events observed in 2006 and 2013 denote the second and third highest storm tides (DGJa (2014) 2013)). This event has also a comparably long lasting time period with water levels higher than the long-term MHW of 1.15 m (DGJa (2014)).

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The chosen chain of storm tides (EC, Figure 4 bottom) was found in one of the A1B realizations (November 2030). The longest event (EL) with water levels exceeding MHW for 45 h is included as first event in the chain of storms. Furthermore, the highest high water of 4.66 m in EL just reaches the water level for a very severe storm tide and presents the second highest event extracted from the data set (orange curve in Figure 3). EL/EC includes in total seven storm high waters within less than eight days.

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The effective wind is used here as a relevant representative of the local wind activity. It is the projection of the horizontal wind vector on that direction which is most effective in producing surges at the coast (see e.g. Ganske et al. (2018)). During EH and EL/EC the single events follow the effective wind variations shown exemplarily for Borkum (dashed black curves in Figure 4). According to the classification of general weather situations causing severe storm surges along the German coasts (e.g. Kruhl (1978)) the storm tracks causing events EH and EL (not shown here) belong to the "North-West Type" (for areas of 235 tracks of the different categories see Figure 3 in Gerber et al. (2016)) .

Amplification analysis for selected extreme storm tides for Borkum
In the original event EH the maximum high water coincides with the maximum of the effective wind and the maximum surge occurs about four hours before the astronomical high water. Figure 5 displays the original event EH and the ensemble member with the highest high water obtained from the experiments with shifting wind and astronomical tide hourly against each other.

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In this case, a 5 h shifting leads to the highest water levels. The event EH consists of two high waters (peak 1 and peak 2) classified as at least severe storm tides. After the amplification the highest peak 2 becomes smaller whereas the lower peak 1 originally reaching 3.93 m now comes up to 4.88 m. Due to the diurnal inequality the astronomical tide underlying peak 1 is about 20 cm higher than that underlying peak 2 and due to the 5 h shifting it coincides with stronger wind velocities, whereas the astronomical tide of peak 2 coincides with weaker wind velocites. Thus, by only shifting the astronomical tide against the 245 wind field, an amplification of the highest high water in the event EH of 15 cm is obtained. Figure 6 shows the ensemble member with the highest high water from the simulation experiments with replacement of the original astronomical tide by the largest spring tide together with hourly shifting between astronomical tide and wind field. The high water of the replaced astronomical spring tide is about 40 cm higher than the astronomical high water of peak 2 in event EH. This amplification procedure results in a high water of 5.23 m presenting an amplification of 50 cm.

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For the original event EH the time period with water levels greater than MHW is about 33 h corresponding to approximately three tidal cycles. Due to the amplification procedures this time period varies up to +/-1 h except two ensemble members for which it is prolonged up to about four tidal cycles. For these two members which show no amplification concerning the highest high water the low water before peak 1 and the low water after peak 2 do not fall below MHW. For all other members either the low water before peak 1 or the low water after peak 2 falls below MHW.

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In case of the event chain (EC) including the longest event (EL, Figure 4), both amplification procedures -shifting of the astronomical tide against the wind and replacement of the original astronomical tide with the highest spring tide together with shifting -results in an increase of the highest high water by only few centimeters. In the original event EL the highest high water already coincides with an astronomical spring tide only few centimeters lower than the highest one. Thus, both applied procedures lead to relative changes of the three highest water level peaks, however not to a substantial absolute increase of the 260 highest water level during EL. Furthermore, the length of EL shows nearly no changes. Possible amplification was tested for EL; for the two following smaller events in EC there are ensemble members showing an increase of single high waters up to 20 to 30 cm.
For further analysis of effects in the Ems estuary, the original EL/EC water levels are used whereas for event EH the amplified water levels due to the spring tide replacement together with tide shifting are used, in the following mentioned as EH_a ( Figure   265 6, red curve).

Comparison of amplified extreme storm tides at different coastal strips
EH and EL/EC (Figure 4) are analyzed for Borkum for possible amplification. Although these highest events are selected and ranked for Borkum, they cause severe storms at the other coasts of the German Bight represented here by Elbe Mouth and Amrum. In particular, EH and EL/EC give the second and third highest events at Elbe Mouth and the third and fourth highest 270 events at Amrum in the data set. From Figure 4 it can be seen that the specific ranking of the single high waters during each event differs between the locations, but the duration of the events is comparable. The high water occurs about 1.3 h and 2 h later at Elbe Mouth and Amrum, respectively, compared to Borkum.
The effects of the amplification procedures adjusted for Borkum are exemplarily compared to those at Elbe Mouth and Amrum for event EH (Figure 6). In general, the water level changes caused by the amplification procedures for Borkum are 275 similar at the other two locations. In case of the 5 h shift of the astronomical tide, peak 1 increases for Elbe Mouth and Amrum as well. In case of the replacement of the original astronomical tide with the spring tide and hourly shifting, peak 1 shows no or only small changes whereas peak 2 increases. Nevertheless, for location Elbe Mouth in the outer Elbe estuary and for Amrum at the North-Frisian coast the relative impact of the two procedures differs from that for Borkum. At Elbe Mouth both procedures cause similar maximum high waters of 5.35 m (+ 49 cm) and 5.23 m (+ 37 cm), respectively, during the event, 280 whereas at Amrum the 5 h shifting results in the highest high water of 5.25 m (+ 56 cm) as there the original peak 1 is higher than peak 2.
The particular amplification mechanisms were adjusted to maximize water levels at Borkum. Thus, other time lags might lead to higher water levels at Elbe Mouth and Amrum. This is demonstrated by the olive curves in Figure 6 which show the highest amplified water levels for these two locations for differing ensemble members. For Amrum the blue and olive curves 285 reach the same highest high waters, but for the olive curve the amplification is based on peak 2. For Elbe Mouth the olive curve provides an amplification of 72 cm. The olive curves both for Elbe Mouth and Amrum originate for the same ensemble member which incorporates replacement by the spring tide together with tide shifting.
As for Borkum also Elbe Mouth and Amrum show some changes in the time period with water levels exceeding MHW.
For Elbe Mouth, this time period is reduced by about one tidal cycle for few members mainly with replaced spring tide. For 290 Amrum, this time period is prolonged up to about one tidal cycle for few ensemble members.

Impact of Q and SLR on water levels at Emden
Based on the fine-grid simulations of the German Bight, the impact of additional amplifications on the selected extreme events EH_a and EL/LC is investigated for the Ems estuary. Here, additional amplification refers to a sea level rise (SLR) and to an 295 increase in river runoff (Q) of the Ems.
Time series of the water levels at Emden in the Ems estuary are shown in Figure 7 for event EH_a and in Figure 8 for event EL/EC with operated storm surge barrier for a simulation without amplification and for simulations with increased Q and applied SLR. EH_a reaches peak water levels of 6.61 m at Emden without additional amplification which is 5.13 m higher than the long-term mean tidal high water level MHW of 1.48 m (DGJb (2018)) and leads to the classification of EH as a very severe 300 storm surge which is in agreement with its classification at Borkum. EL/EC reaches peak water levels of 5.96 m at Emden which also classifies the event as a very severe storm surge. Both events reach water levels that exceed the highest observed water level of 5.17 m at Emden (1906( , DGJb (2018).
Changing the river runoff from 80 m 3 s −1 to 1200 m 3 s −1 increases the tidal high and low waters at Emden only by a few centimeters (see Figures 7 and 8, red and dashed grey lines). This effect is even weaker for the storm tides (see events with 305 open storm surge barrier in Table 1). In the wide and deep estuarine part near Emden the tidal volume strongly exceeds the river runoff so that the impact of river runoff on water levels is small. As the tidal volume is increased during the storm surge, the impact of river runoff is even smaller during this period.
At Emden, applying a SLR to the events leads to an increase in tidal high water, tidal low water and the highest water level during storm tide in the range of the applied SLR (Figures 7 and 8 and Table 1). This behaviour can be seen in both EH_a and 310 EL/EC. The observed influence of river runoff and sea level rise agrees with the behaviour analyzed in a sensitivity study by Rudolph (2014).
Increasing the river runoff results at Emden in nearly no change in the occurence time of the highest water during storm surge (see events with open storm surge barrier in Table 1). The increased water depth caused by a sea level rise increases the propagation velocity of the tidal wave entering the Ems estuary which causes the tidal high water to occur earlier by 10 to 20 minutes at Emden (Table 1) for the events investigated.
For the event EH_a the time period with water levels greater than MHW is about 33 h similar to the time period at Borkum.
Due to an increase in runoff to 1200 m 3 s −1 or to a sea level rise of 0.5 m this time period shows only small changes less than an hour. But for a sea level rise of 1 m this time period is prolonged by one tidal cycle up to about 45 h (Figure 7). For event EL the time period with water levels continuously greater than MHW is about 2 tidal cycles. This differs from the conditions at 320 Borkum where four consecutive tidal cycles are continously above MHW. In the Ems estuary the tidal range is greater than at Borkum with lower low waters and higher high waters. Thus, the time periods around the two low waters following the highest high water are below MHW for about 2 to 3 hours. In case of a sea level rise of 1 m the event EL is prolonged by two tidal cycles as the mentioned two low waters become higher than MHW (Figure 8).

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To investigate the influence of Q and SLR along the Ems estuary, the highest water levels HW during EH_a and EL at each location along the longitudinal profile are analyzed for simulations with an open storm surge barrier. Closing the barrier separates the estuary into two parts and alters the effects of Q and SLR. Figure 9 shows the impact of an increase of Q from 80 m 3 s −1 to 1200 m 3 s −1 on HW for both EH_a (black lines) and EL/EC (red lines). For both events, the increased river runoff rises the highest water levels by several decimeters in the narrow 330 and shallow upper part of the Ems estuary upstream of the Dollart (bight in the Ems estuary south of Emden, Figure 1). The influence of Q on the highest water levels decreases towards Dukegat where the Ems becomes deeper and wider and disappears towards the mouth of the estuary. As mentioned before, Emden is located in an area of the Ems estuary where the influence of the river runoff on the highest water levels is in the range of some centimeters (see also Figures 7 and 8 and Table 1).
Upstream of Papenburg the influence of the bathymetry on the highest water levels during storm surge can be observed 335 clearly marked by a sudden decrease in HW in case of low discharge. In the area of Papenburg the estuary is very narrow, the dike line is close to the estuary, whereas the upper part of the estuary is characterized by wide foreshore areas that are flooded only during events of high discharge or storm surges. In addition the depth of the estuary is decreasing significantly upstream of Papenburg, as seagoing ships are not using this part of the Ems estuary.
The described bottleneck close to Papenburg prevents the water during storm surge to enter the upstream area undisturbed, 340 which results in lower water levels in this area. For events with high river runoff the wide foreshore areas upstream of Papenburg are already flooded before the storm surge depending on the amount runoff and the height of the tide before the storm tide.
Increasing the SLR from 0 to 1 m while the river runoff remains unchanged at 80 m 3 s −1 leads to a longitudinally varying increase of the highest water levels along the whole estuary for both EH_a and EL/EC (Figure 10  In the lowlands close to the mouth of the Ems draining of urban (e.g. Emden) and agricultural areas (e.g. Knock) is of major 350 interest. The aim of the sewer at Knock is to drain the low lying hinterland (with a ground level of about NHN + 0 m) and keep the inland water level at Knock lower than NHN -1.40 m (KLEVER (2018)). At Knock the mean low water MLW is NHN -1.58 m so that draining without pumping is only possible for a short time even during mean tides. Caused by long lasting high water levels during storm tides only restricted draining is possible.
For the chain of storm tides EC (see Figure 8) even without amplification pumping is needed nearly during the whole period 355 of 176 hours (see Table 2). The water must be pumped against a water level in the Ems higher than MHW for about 90 hours. This period will increase by about 40 hours in case of a sea level rise of 100 cm.

Influence of the storm surge barrier in the Ems estuary
For the investigation of the impact of SLR and runoff along the Ems estuary as shown above, the storm surge barrier in the Ems is considered to be open. When operated, the storm surge barrier in the Ems has a significant influence on highest water 360 levels both upstream and downstream ( Figure 11). The barrier is closed at a defined water level of NHN + 3,50 m and reopened when the water levels on both sides of the barrier are equal.
In the protected area upstream of the barrier the water levels are no longer influenced by the storm surge coming from the North Sea. Only the amount of river runoff that flows into the protected area in the period the barrier is closed contributes to the highest water level. The second process increasing the highest water levels is the shortening of the estuary that takes place when the barrier is closed. This reduces the stretch where dissipation of the tidal wave can occur and leads to the reflection of a more energetic wave and thus increase the highest water levels. This behaviour has been investigated in other studies and is also described in 380 Summarizing, a closed storm surge barrier will always lead to increased highest water levels downstream of the barrier but the magnitude of the increase depends on the current velocity conditions present at closure. In case of the analysed events, at Emden this increase ranges between 19 and 25 cm (Table 1). In general, the highest water levels are reached close to the storm surge barrier, they decrease towards the river mouth. Closing the barrier keeps the storm tide out of the area upstream. Only 385 the river runoff fills the protected area during the period when the barrier is closed. Consequently, closing the barrier during a storm tide leads to significantly lower highest water levels upstream of the barrier (Figure 11).
Applying a SLR and an increased Q to events with operated storm surge barrier leads to increased highest water levels downstream of the barrier due to the SLR and increased highest water levels upstream of the barrier due to the runoff coming from upstream (see Figure 11). This holds true for all events and respective simulations. Figure 11 demonstrates how the water 390 level upstream depends on the length of period with closed barrier. For a SLR of 1 m and a runoff of 1200 m 3 s −1 , the water levels during event EH_a are considerably higher than those for event EL although for the reference cases (no SLR, mean runoff) the water levels are similar. For event EH_a the barrier has to be closed for the first storm tide (see Figure 7) and could only be reopened after the second storm tide due to the considerably elevated water levels around low tide. This leads to a continuous closure period of 17 h. For event EL the water levels allow to close and open the barrier for each storm tide 395 separately (see Figure 8) leading to a closure period of 7 h 5 min. Combining these different closure periods with the extreme runoff results in lower water levels for EL than for EH_a upstream of the barrier. In case of mean runoff and no sea level rise the length of the closure period is not influencing the highest water level during the storm tide upstream of the barrier. It shows that the protected area upstream of the barrier is big enough to store even the extreme discharge of 1200 m 3 s −1 for all closure periods investigated. For all events and amplifications the highest water levels upstream of the operated barrier remain lower 400 than those reached in case of the open barrier (see Figure 10 and Figure 11).
The highest water levels at Emden for the simulations without further amplification and an operated storm surge barrier are 6.61 m for EH_a and 5.96 m for EL/EC (Table 1). Applying amplified conditions (Q=1200 m 3 s −1 and SLR=1 m) leads to an increase of highest water levels to 7.65 m for EH_a and 7.01 m for EL/EC (Figures 7 and 8). The highest measured water level at Emden is 5.17 m (DGJb (2018)). Thus, the extreme events EH_a and EL/EC identified and elaborated in this study exceed 405 this water level even without the application of further amplification through river runoff and sea level rise.

Summary and discussion
This study aims to find extreme storm tides in the North Sea and Ems estuary that are physically possible but have not been observed yet. Numerical simulation data from both hindcast and climate realizations have been searched to detect extreme storm tides, i.e. storms causing either very high water levels (event EH) or water levels exceeding mean tidal high water for 410 a longer time (event EL) or where multiple storm tides occur within one week (event EC). Both extreme events (EC contains EL) selected according to these criteria originate from the climate realizations and there from the first half of the emission scenario period, although from two different realizations. This underlines the strong inter-decadal variability and the absence of a considerable increase of extreme storm tides towards 2100. Thus, the found highest water levels exceeding the water levels measured since the beginning of the 20th century at Borkum (Figure 3) could be possible under present-day conditions.
Using numerical simulations for the North Sea, the selected events were amplified by shifting the astronomical tide against the wind field for optimization of their interaction and by inserting the highest spring tide from the data set. By these amplification procedures based only on the co-timing of the atmospheric storm and the tidal phase, the water level at Borkum is increased by about 50 cm and a maximum water level of 5.23 m is reached for the event EH_a, thus, exceeding the highest measured event in 1906 by more than 1 m (see dashed red line in Figure 3). Moreover, the enhancement mechanisms proposed  (Table 1).
Against the background of climate change, coastal protection strategies and usage of the hinterlands it is not only important to know the possible height of an extreme event but also its duration. Moreover, the event EC shows that several high storm tides within a week could be possible. The low-lying land protected by dykes in this area is drained both using the gradient 435 in the water level towards the Ems and with pumps. A prolongation of the duration of higher water levels in the Ems will hinder the natural drainage. The infrastructure in terms of more powerful pumps must be improved because the water has to be pumped for a longer period against higher water levels in the Ems estuary.
In the Ems estuary at Emden, the highest water level for the event EH_a is 6.61 m with operated storm surge barrier and without further enhancement. In case of a runoff of 1200 m 3 s −1 and a sea level rise of 1 m it reaches 7.65 m. These water 440 levels exceed the highest water level observed in the event in 1906 by about 1.4 m and 2.4 m, respectively. Nevertheless, the simulated highest water levels as listed in Table 1 do not reach today's dyke height at Emden of NHN + 7,60 m except for two cases which include a future sea level rise of 1 m. The upper part of the Ems estuary is protected by the storm surge barrier even against extreme events with amplified discharge or sea level rise.
The obtained amplified water levels for event EH_a of 5.23 m at Borkum and of 6.61 m at Emden are in a similar order 445 of magnitude as the maximum water levels of 4.99 m and 6.09 m, respectively, reported by Jensen et al. (2006) (see there   Table 10 for an ensemble member of 1976) as an estimate of extreme event with low probability of occurrence. There, the investigation was focused on the Elbe estuary. Possibly, other ensemble members than reported might result in higher water levels for Borkum and Emden. Still the comparability of extreme water levels estimated by different procedures and based on different original data sets supports the plausibility of the results. Moreover, there is a potential for further enhanced realistic 450 storm tide events to emerge when both methods, namely varations in atmospheric conditions as done by Jensen et al. (2006) and interplay with different tidal phases as done in the present study, are combined.
Depending on track, intensity and velocity, each storm affects the German coastal stripes differently. For the East-Frisian coast storm winds from northern directions lead to higher storm tides whereas for the North-Frisian coast storm winds from western directions have more impact. Thus, the ranking of extreme storm tide events elaborated in this study differs in detail 455 for the different coastal stripes of the German Bight. As this work focuses on the East-Frisian coast with the Ems estuary, the amplification procedures were adjusted specifically for Borkum. However, the methods for the identification and amplification of storm tides used here could be transferred to other coasts and estuaries.
So far, a fixed bathymetry was assumed for all simulations. However, the heterogeneous bathymetry of the German Bight, in particar the Wadden Sea and the estuaries, has been subject to changes due to natural processes and anthropogenic influences 460 which will proceed in the future. Consideration of changing bathymetry would give an insight on the effect of morphodynamic states on extreme storm tides.
In the present study the effects of a coincidence of a severe storm tide and extreme runoff were assessed to give an upper limit of water levels. So far, an independent probability of occurrence of extremes was assumed. Consideration of joint probabilities or consideration of them as a compound event might narrow down the range of possible water level extremes.

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Events like event EC with a series of storm tides within a week might require special arrangementss for the management of the impact of the storm tide. Not only the drainage of the hinterland must be sufficient, but also manpower to watch and operate coastal protection measures must be avaiable in adequate numbers. The drainage situation may become worse in case of the coincidence of a storm event with heavy rain. The results of this study may contribute to the development of a flexible adaptation route to the impacts of climate change in coastal areas considering the interests of coastal protection, draining of 470 the hinterland and navigation in the waterway Ems.
Author contributions. The simulations for the North Sea (1) and the Ems estuary (2) have been performed and analysed by IG and LG (1) and TB and ER (2), respectively. All authors contributed to the preparation of the manuscript.
Competing interests. The authors declare that they have no conflict of interest.
Acknowledgements. The observational data for Borkum were kindly provied by the German Federal Maritime and Hydrographic Agency            (2019)