External surges in the North Sea were first discovered by Corkan (1948) and in the following years also confirmed by other studies in the same area (e.g. Corkan, 1950; Darbyshire and Darbyshire, 1956; Rossiter, 1958) to be progressive anomalies in tide gauge data along the British coast. Tomczak (1958) investigated a progressive wave at the Dutch and German North Sea coast, which was not recorded at British tide gauges but also coincided with a low-pressure cell travelling eastwards over the North Sea. During his analysis of residuals (after considering astronomical tides, local wind and air pressure effects), Koopmann (1962) also analysed the propagation of external surges, entering from the northern boundary of the North Sea along the British Isles and the Belgian and Dutch coasts to the German coast, and described a contribution to the high water levels of the devastating flood on 16 and 17 February 1962. This event was also examined by Bork and Müller-Navarra (2005), who isolated the external surge using a numerical model. The work of Schmitz et al. (1988), using a numerical model to cover the entire North Sea basin, was able to verify the assumptions about the generation of external surges in the northeast Atlantic and their path of propagation into the North Sea. Still, besides the work of Gönnert (2003), who manually investigated external surges in the North Sea occurring between 1971 and 1995, no comprehensive datasets of external surges, identifying their occurrence within observational records, are known to the authors.

Similar phenomena to the external surges in the North Sea are known in other shelf seas like the Irish Sea (Brown and Wolf, 2009), the Moreton Bay on the Australian coast (Treloar et al., 2010) and the Leizhou Bay, which borders the South China Sea (Liu et al., 2018). As of now, besides the surges in the North Sea, they have only been identified for singular events and have not been statistically assessed over long periods of time. Aside from the lack of analysis stretching over longer periods of time, no comparative study between different sea basins has been conducted so far.

In more recent studies, external surges are often considered in the analysis of storm surge events using numerical models. While Prandle (1975) used tide gauge measurements of external surges to define boundary conditions for a model of the Thames Estuary, recent models use nested grids to incorporate external surges among other water-level oscillations over time and space for varying weather conditions (e.g. Brown and Wolf, 2009; Comer et al., 2017; Ganske et al., 2018). Large-scale models of the surrounding oceans are used to produce water levels from wind and air pressure data as boundary conditions for the smaller, more refined models of the actual study area. Ganske et al. (2018) mention external surges as a potential reason for differences in predicted and modelled storm surge heights at the German coast. Many of the high storm surge water levels that occurred during moderate wind speeds coincided with raised water levels at the northern entrance of the North Sea, showing that water-level elevations originating from the northeast Atlantic are an important factor in the prediction of storm surge heights.

External surges exhibit certain similarities to meteotsunamis, as both are long waves that are generated by air pressure cells and propagate in shallow water conditions. Both are strongly dependent on Proudman resonance (Proudman, 1929) to amplify the water-level displacement that is expected by estimations like the inverted barometer law (IBL). The generation of meteotsunamis has been studied numerous times in numerical models (Vilibić, 2008; Vennell, 2007, 2010). They are further amplified by slopes in the ocean bed, especially the continental shelf (Dogan et al., 2021). Meteotsunamis have been identified around the world, for example in the Adriatic Sea (Vilibiæ, 2008), the Japanese coast (Kubota et al., 2021), the Yellow Sea (Kim et al., 2016., 2021) and the Gulf of Mexico (Olabarrieta et al., 2017). They have also occurred in the North Sea (de Jong, 2004; Sibley et al., 2016) but can be differentiated by their characteristics like period, amplitude and their effect on water levels. For example, the recorded meteotsunamis in the North Sea have periods of the order of 1 h and can also travel northwards, while external surges have longer periods of 8 h to several days and travel anticlockwise (Gönnert, 2003). So far, no comprehensive body of literature on similarities or differences between external surges and meteotsunamis has been identified.

After careful consideration of existing research on external surges, it can be concluded that external surges can significantly raise water levels along the North Sea coast. However, available knowledge of external surges is small, and translation of knowledge and impacts resulting from external surges into practical approaches, e.g. in terms of concepts for design level for coastal protection facilities, is still rare. An exception to the missing translation of this knowledge into practice is given by the multi-method approach to calculate design water level of the Free and Hanseatic City of Hamburg that involves detailed analysis of the individual storm surge components tide, external surges, wind surge and their non-linear interactions (Gönnert and Gerkensmeier, 2015; LSBG, Agency for Roads, Bridges and Waters Hamburg, 2012).

In this context, the present work aims to provide a methodology for further external surge research and a comprehensive dataset for the North Sea and to collect existing knowledge about external surges. The methodology can be used not only to include additional locations in the detection of external surges, but also to support local authorities in considering external surges for the protection of their communities. The research conducted in this study consists of the following specific objectives:

to improve and automate an existing method of detection of external surges in the North Sea;

The study focuses on the North Sea basin, complementing earlier studies about external surges in this area. The North Sea is a shelf sea connected to the northeast Atlantic through a 400 km wide opening to the Norwegian Sea and the narrower English Channel, which is 34 km wide at its narrowest point. The depth of the North Sea is on average 95 m but varies between less than 20 m at the Dogger Bank and 700 m in the Norwegian Trench. Also, the coastal morphology in this focus area is very diverse: fjords at the Scottish and Norwegian coasts, cliffs on the west coasts, and marshlands at the southern and southeastern coasts, which border the Netherlands, Germany and Denmark (OSPAR Commission, 2000). These marsh coasts also include the unique biotope of the Wadden Sea (Lotze et al., 2005; Reise et al., 2010). In order to capture the dynamics of external surge propagation when entering the North Sea basin, four tide gauges, as shown in Fig. 1, were selected for the analysis of non-tidal residuals that are distributed over the west coast of Great Britain, the Netherlands and Germany.

The British tide gauges in Aberdeen and Immingham have already been used in several previous studies (Gönnert, 2003), sometimes alongside additional tide gauges on the British coast (Koopmann, 1962). The height of the external surge at the Aberdeen tide gauge was used as a proxy for the height during its entrance into the North Sea (Bruss et al., 2011; Ganske et al., 2018), while Immingham is close to the location where most external surges reach their maximum height. The model of Bork and Müller-Navarra (2005) determines the maximum height to occur at the estuary The Wash, about 55 km south of the Humber Estuary, which coincides with the location of the maximum tidal range on the eastern British coast (ABPmer, 2008). However, the Immingham tide gauge provides more comprehensive data and shows only a small difference to tidal ranges in The Wash. Hence, these first two tide gauges can be assumed to be representative of important characteristics of external surges. The tide gauge in Cuxhaven has been regularly used as reference tide gauge in German coastal protection considerations, as it provides a continuous data series (a continuous record has been available since 1918 and tidal high and low waters since 1843) and is influenced neither by barriers like the East Frisian Islands nor by the Elbe Estuary fluxes. These three tide gauges have also been used in the study by Gönnert (2003), which serves as a benchmark for the present study. Additionally, the present study uses the tide gauge Texel Noordzee (hereafter called Texel) because it is located at an almost even distance to Immingham and Cuxhaven and can thus supplement information about the propagation of external surges after they reached their maximum height near Immingham. Water levels at these tide gauges are influenced by the local bathymetry, such as their position in an estuary or harbour basins, or man-made structures like breakwaters (Spencer et al., 2015; Serafin et al., 2019). Still, these tide gauges are used in the herein conducted study, as they cover the desired timespan, maintain comparability and quantify the effects of external surges on coastal areas, which is the main focus of this study. Inaccuracies in the height of the external surge due to variations of density (Mehra et al., 2009) and runoff in the estuary (Müller-Navarra and Bork, 2011) fall within the general uncertainties of the study, e.g. due to the calculation of astronomical tides.

All data used in this study were provided by local authorities, mostly through open-access data portals. To receive uniform input data, all data were filtered to contain only hourly measurements, and tide gauge data as well as astronomical tides were transformed to be in reference to the Amsterdam Ordnance Datum (NAP). Missing or unlikely data like wind speed above 35 m s-1 and air pressure above 1050 hPa or below 950 hPa were flagged and combined with the flags from the quality checks of the data providers. In the data of the tide gauge in Texel, two gaps, spanning more than a week, exist between 11 January and 22 November 2002 and 16 June and 2 July 2020. Flagged values are still used in the calculation of residuals, as the flags can also indicate successfully verified data. Overall, of the 227 928 data points per location, the fractions flagged as missing or unreasonable are given in Table 1.

The weather data used to hindcast wind setup at the tide gauges in Texel and Cuxhaven are provided by the meteorological institutions as the following products:

mean wind direction (average of the last 10 min before the full hour),

To isolate external surges from hydrographic records, all other major components have to be eliminated. The methodology was developed by Gönnert (2003) but was adapted for this study to make the time steps independent from tidal cycles and therefore enable a more refined analysis. While Gönnert (2003) used the average residual between high and low water, resulting in time steps of 6.25 h, here the time steps are shortened to 1 h, allowing more precise assertions of the duration, height and timing of the events. Figure 2 gives an overview of the general steps in this process, consisting of three automated steps, each eliminating one contributor to water levels, and the consecutive manual quality check. Each step is explained in further detail in the following three subsections.

Criteria for external surges are assessed by varying the minimum height in Aberdeen and the maximum offset between Aberdeen an Immingham. The minimum height in Aberdeen is found to be suitable for the uncertainties of the hindcast of tides and wind setup. If the minimum height is reduced by 10 cm, more than 50 % of the additionally detected surges cannot clearly be differentiated from fluctuations in residuals due to wind setup and other factors. For an increase of the temporal offset from 5 to 7 h, the error rate is only 24 %, meaning that 76 % of the additionally detected surges match external surges in their general behaviour like heights at the four tide gauges and periods. However, to maintain comparability between this study and the study conducted by Gönnert (2003), these surges are not included in the dataset. Moreover, external surges have to be studied further to discern whether an offset of 7 h between Aberdeen and Immingham is physically possible. This would require extensive research about the propagation of external surges, which is beyond the scope of this paper. Using the dataset with a longer allowed offset between Aberdeen and Immingham would, however, invalidate the comparison of data collected by Gönnert (2003) and this study.

External surges found in this study are mainly compared to the dataset of Gönnert (2003), which spans the years 1971 to 1995. To distinguish between the datasets, the dataset of Gönnert is hereafter called DataSet1, and the dataset derived from the automated approach is called DataSet2.

The occurrence of external surges in the North Sea basin is strongly coupled to storm systems in the North Atlantic. Although the process of the physical meteo-oceanic coupling is not within the scope of this work, it will be important to correlate the observations from the tide gauge data to general weather patterns. To briefly repeat meteorological conditions in a context of surge generation, the European weather situations during the beginning of the observed external surges are assembled first. The European weather situations were originally defined by Hess and Brezowski (1977) and determined by Werner and Gerstengarbe (2010) for the duration from 1881 to 2009. From 2010 onwards, the records from the German Meteorological Service (2021) are used. The Agency for Roads, Bridges and Waters Hamburg (2012) found 61 of the 73 external surges of DataSet1 to occur during four weather situations (western situation cyclonic: WZ, western situation anticyclonic: WA, southwestern situation anticyclonic: SWA, high-pressure bridge central Europe: BM).

The characterization of external surges with respect to low-pressure cells can be summarized from Werner and Gerstengarbe (2010) as follows:

WZ. Single disturbances with high-pressure cells in between travel from Ireland over the British Isles and North and Baltic Sea towards eastern Europe. The driving low-pressure cells are located north of 60∘ N.

Overall, 65 external surge events were identified between 1995 and 2020 (labelled DataSet2); the statistical base parameters of this new dataset are listed in Table 5.

Several of those events consist of more than a single external surge and are identified as a sequence or series of external waves in the residual water-level oscillations. Figure 5 gives examples of both a single external surge (Fig. 5a) and an event consisting of three external surges (Fig. 5b), arriving with gaps of 22 h between the first and second surge and 43 h between the second and third surge. For those events, it is possible that they depend on the same meteorological origin caused by storm systems in the northeast Atlantic. Moreover, they can interact with each other in the North Sea, as they can remain there for more than 48 h depending on their celerity and wavelength. This can also be seen in Fig. 5b: during the arrival of the second external surge in Aberdeen, the residual at the Cuxhaven tide gauge is still at around 30 cm caused by the first external surge. It also shows possible effects of the interaction of the first two surges: while the two external surges are mostly uniform and of similar height in Aberdeen and Immingham (the peak height varies by around 15 cm), the second external surge is 30 cm higher in Texel and 50 cm higher in Cuxhaven. To verify whether this behaviour is caused by interactions of the two external surges or other influences, more detailed studies should be conducted using numerical models or residuals at other tide gauges. In this study, the term “serial external surges” is used for series of identified external surges in close succession. In total, 101 external surges were found in 65 external surge events. Some of those external surges were also detected by the automated detection but grouped with other external surges; others do not match the required height or offset between Aberdeen and Immingham but were identified during the manual review of the external surges. Since they occurred shortly before or after a detected external surge, and preceding external surges may alter the height and timing of the external surge, they are also included in the dataset. The grouping into external surge events has therefore been conducted manually.

Figure 6 shows the heights of each external surge and the time since the previous external surge (note the logarithmic scale). Additionally, the sum line of events depending on their time since the previous surge is also shown.

A closer inspection of the sum line reveals two frequency peaks: one peak exists for external surges occurring less than 100 h after the last surge, and the second peak is for a timespan between 230 and 375 d (5500 and 9000 h). The second peak originates from the very rare occurrence of external surges during spring and summer months, resulting in similar timespans between the last surge in winter and the first surge in the following autumn. The first peak however indicates that the frequency of serial external surges is way higher than would be expected by the random close occurrence of two independent external surges. A threshold duration of 72 h is chosen, as the definition of serial external surges should not only include their increased occurrence, but also their origin (the same or closely succeeding low-pressure cells) and their possible impact (interaction with each other and modulation of storm surges). The occurrence of serial external surges has not been addressed in the recent literature so far.

In DataSet2, a third of the external surge events consisted of more than one surge. Of those, 11 events contain two surges, and the other 10 contain three or more surges. One special event can be found in February 1997: from 18 February onwards, six consecutive external surges were detected, all within 72 h of each other. The calculated residuals for this event are plotted in Fig. 7.

This series of surges lasted until 27 February. From 28 February to 3 March two additional surges can be seen in the residuals that loosely resemble external surges but do not match the criteria defined previously. The weather conditions in northwestern Europe were consistent during the period with westerly winds and low-pressure cells over the Atlantic, which match the conditions that Gönnert (2003) found to be the most prominent during the detection of external surges.

The dataset from Gönnert (2003) (labelled DataSet1) was not previously analysed with regards to serial external surges. This study hence uses that dataset with a focus on detecting additional serial surge events, appending them to those found in the 1995 to 2020 dataset. In total 73 external surges can be grouped into 63 events. In eight cases or 12.7 % of the external surge events, two external surges were detected less than 3 d apart, which is slightly less than in DataSet2. By contrast, only one event containing three surges is found so that the overall percentage of serial external surges is lower in this dataset. This aberration might be due to the different time steps of the analysis and cannot be interpreted as a significant trend. All in all, 30 serial surge events are identified; of those, 19 consist of two surges and 3 of four or more (see Table 5).

Figure 8 shows the number of external surges per year for both datasets and their moving 5-year average.

In comparison to the external surges found by Gönnert (2003), the total number of external surges increases, while the number of external surge events decreases slightly. The increased number of external surges can mainly be explained by the higher temporal resolution that enables a clearer distinction between single external surges and the focus on serial external surges. On the other hand, the decrease in the number of external surge events is rather small and can mainly be attributed to the period from 2001 to 2006, when only six events were detected. Due to this variability in their occurrence, no significant trend can be determined, as linear, polynomial or logarithmic trend lines predict an increasing, constant or falling number of external surges respectively.

The distribution of external surges over the year (see Fig. 9) – an important distribution with respect to its co-influence with wind surge effects in coastal waters – is not equal but shows a strongly increased occurrence during autumn and winter months with January having the highest number of external surges.

Only eight of the 172 external surges from DataSet1 and DataSet2 occurred during the spring and summer months from April to August. The comparison of distributions between the two datasets shows a 10-fold increase in external surges in September and a decrease of 65 % in March. This may hint towards a shift of the main external surge season to start earlier in the year but also end earlier. As of now, the datasets do not span a sufficient timeframe to verify this assumption. A one-tailed t test (using the day of arrival after 1 July) found earlier arrival by 6 d between DataSet1 (M=183.0, SD = 50.5) and DataSet2 (M=177.1, SD = 63.3). However this difference was not found to be significant (t(170)=0.681, p=0.248>0.05).

The height of the external surges matches previous studies and simulations (Schmitz et al., 1988; Gönnert, 2003; Bork and Müller-Navarra, 2005). Figure 10 shows boxplots of the heights of the recorded external surges.

Beginning with an average height of 56 cm in Aberdeen, the external surge height increases along the British coast and reaches 83 cm in Immingham. During their propagation along the southern and southeastern coast of the North Sea, their averaged height decreases to 57 and 60 cm at the Texel and Cuxhaven gauges respectively. Nonetheless, the maximum height of the external surges can reach 100 cm in Aberdeen with a single even higher event with 118 cm. The highest overall surge height was recorded in Immingham with 192 cm. In Texel and Cuxhaven, the highest events are also more than double the average height with 164 and 148 cm respectively. The most extreme event in Texel should be further assessed, as it is almost 60 cm higher than the second highest. This exceptionally high external surge was recorded on 5 December 2013 as the storm Xaver also crossed the North Sea. The predictability of heights based on the British tide gauges is higher in Texel than in Cuxhaven. For both locations, the height is more closely related to the height in Immingham than in Aberdeen. The ratios of heights hTexhImm and hCuxhImm show 3 times the variance in Cuxhaven compared to Texel. In Texel, only seven of the 101 external surges are recorded higher than in Immingham with a maximum increase of 17 cm. These growing surges reach heights between 58 and 103 cm in Texel. An increase in heights between Immingham and Cuxhaven is also rare but more prevalent with 20 % of the events showing a height increase. Among those are two of the highest recorded surges, reaching 148 and 121 cm. The closer correlation between Immingham and Texel can be explained by the shorter distance and minimizing potential for currents or local weather to influence the surge height.

Figure 11 correlates the weather situations as per Hess and Brezowski's (1977) definition (see Sect. 2.5 for the description of the weather patterns) with the number of external surges that was detected at the time of the weather situation.

The Agency for Roads, Bridges and Waters Hamburg (2012) already collected the weather situations during the years 1971 to 1995 and found that the weather situation WZ produces by far the most external surges with about half of the external surges being recorded during this weather situation. The three other main weather situations that were found during external surges are WA, SWA and BM. These weather situations show the characteristics that were previously associated with external surges in the North Sea with low-pressure cells over the North Atlantic and disturbances travelling eastwards and account for more than 80 % of the detected external surges. Including DataSet2, an additional main weather situation prone to generating external surges (NWZ) is however identified. From only three external surges in the older dataset, the number of external surges during this weather situation more than doubles. Two other weather situations also show an increase in relevance: BM and SWA. Meanwhile, the share of external surges caused during the weather situations WZ and WA slightly lost relevance. Still, these variations lie within the natural variability of the occurrence of external surges.

Serial external surges seem to be more prevalent during certain weather conditions, namely WZ and SWA situations, which show the highest ratios of external surges to the number of external surge events. They also seem to be supported by long-lasting weather situations. Table 6 shows that 20 of the 30 serial events did not happen during changing weather situations, including the series of six external surges, and only one event (consisting of four external surges) was driven by three different weather situations.

These observations are based on a rather small sample size, so they should be assessed by further, more detailed studies of the weather conditions that cause external surges, for example, the analysis of travel paths of the low-pressure cells. The weather situation also influences the average height of the external surges with the highest occurring during WZ and BM conditions with 57 cm in Aberdeen and the lowest during the SWA situation only reaching 51 cm.

Increased water levels caused by external surges along the North Sea coast are of particular interest when it comes to co-occurrence with storm surge events. Storm surge events, in most cases, are composed of tide and wind surge. Combined events of tide, wind surge and external surges have the potential to cause extreme water levels along the North Sea coast, challenging current and future coastal protection strategies and actions. Therefore, analysing combined events of external and storm surges is an essential step. Combined events of external surge and storm surge events can be generated by two different meteorological situations: on the one hand, both phenomena are initiated by two different extra-tropical cyclones in close succession. Due to different propagation velocities both phenomena arrive at a tide gauge at the same time. On the other hand, both phenomena are initiated by the same extra-tropical cyclone (Gönnert and Gerkensmeier, 2015). Whether the wind setup is defined as a storm surge or not depends on the chosen definition of these events. For this analysis, storm surges are defined as events reaching peaks of at least +1.5 m above mean high water (moving average of the previous 5 years) in Cuxhaven, or a wind setup of at least 2 m is reached independently of the tidal phase (definition follows the determination of the Agency for Roads, Bridges and Waters Hamburg (2012), who is responsible for assessing the design water level for public coastal protection facilities of the Free and Hanseatic City of Hamburg). Following this definition, 21 % or 16.7 % out of 126 external surge events recorded between 1971 and 2020 occurred during or close to a storm surge event in the German Bight. Moreover, serial external surge events, a phenomenon that was analysed in this study for the first time, can be observed more frequently during combined events. Particularly the number of external surges in the series increases during combined events, compared to observed single events (see Table 7). As stated before, the statistical correlations have to be verified by further research about the interactions between external and storm surges.

With regard to a more detailed analysis of the average height of the external surges during storm surge events, DataSet2 shows an increase to an average of 64 cm in Aberdeen and 70 cm in Cuxhaven (compared to average heights without storm surges of 56 cm in Aberdeen and 60 cm in Cuxhaven as described in Sect. 3.1). It confirms former findings for average heights of external surges during storm surge events compiled for DataSet1 (1971–1995) (Agency for Roads, Bridges and Waters Hamburg, 2012). Local effects of the extra-tropical cyclones involved during the development of these combined events might play a role in this development. One special example of an external surge occurring during a storm surge is the external surge during the storm Xaver on 5 and 6 December 2013. The external surge, which was earlier detected by Fenoglio-Marc et al. (2015) using satellite altimetry, contributed to record water levels at some parts of the German coast (Dangendorf et al., 2016) and, in the present study, reached a calculated height of 146 cm at the Cuxhaven tide gauge. Upon closer inspection, this calculation was most likely influenced by missing wind records at some German weather stations, bringing the maximum height to 95 cm. Still, extraordinary heights were calculated in Immingham and Texel (Spencer et al., 2015; Kettle, 2020), highlighting the need for further, detailed analysis of single external events using multiple approaches to assess the occurrence and impact of the highest external surges.