1 Introduction

Storm surges are a tsunami-like sea level perturbation due to extreme low- or high-pressure weather systems, causing an enhancement or a decrease in the sea level at the coastline compared to the usual astronomical tides. When this change is positive, surges threaten coastal communities, causing floods and damage to coastal infrastructures, and occasionally claiming the lives of people. The most dangerous situation is when a surge wave coincides with a spring tide high water event.

Surges are a threat to coastal communities in Scotland (Werritty et al. 2007). In particular, this study is focused on the surges affecting some areas of the Clyde Sea, in the south-west of Scotland. This area has been struck by several floods due to storm surges, since the well-documented massive surge of 1953 (Hickey 2001), such as the 5th January 1991 event that caused extensive flooding and damage estimated as £7 M (Kaya et al. 2005). In the aftermath, a pilot study was appointed to estimate the economic damage due to storm surge (Townson and Collar 1993). Subsequently, the Scottish Environmental Protection Agency (SEPA) commissioned an Early Warning system for flooding events, including the development of a hydrodynamic model (Kaya et al. 2005) for forecasting dangerous surge events, which are estimated to cause £0.45 M per year damage.

In contrast to south-west Scotland, coastal communities in Northern Ireland separated from Scotland by the North Channel are less exposed to flooding risk caused by storm surge events (Hankin et al. 2008). A statistical study (Orford and Murdy 2015) highlighted that the majority of the large surges that have been recorded in Belfast Lough were caused by westerly winds, associated with the positive North Atlantic Oscillation (NAO) phase, while only 20 % of the largest surge were caused during the negative NAO phase.

Fig. 1
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Position of the Clyde Sea and the North Channel in the Great Britain Islands. Main places cited in the paper are shown

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The Clyde Sea is a semienclosed fjordic basin and is connected to the North Atlantic Ocean and to the Irish Sea through the North Channel (Fig. 1). Matthews et al. (1999) divided the Clyde Sea in two main regions: the inner Clyde, which comprises the various sealochs and the Clyde Estuary, which are most influenced by the freshwater input and contain deep areas, and secondly, the outer Firth that is the wide and shallow sea area that communicates with the North Channel and is more influenced by the ocean climate. The tidal motion of the region is mainly driven by the \(M_2\) amphidrome, situated north of the Clyde Sea, near the Isle of Mull (Pingree and Griffiths 1979). Due to the amphidrome, the bathymetry and the coastline, maximum tidal currents in the Inner Clyde Sea are less than 0.4 m/s, while those in the North Channel exceed 1.4 m/s (Dietrich 1950). The main consequence is that the Clyde Sea shows a strong stratification (Pingree et al. 1978), while the North Channel is well mixed since the bottom layer occupies all of the water column (Davies et al. 2004).

Although the Clyde Sea and the North Channel have been well studied with respect to tidal-driven (Davies and Hall 1998), wind-driven (Davies and Hall 2000; Davies et al. 2001) and stratification-driven (Simpson and Rippeth 1993; Rippeth and Simpson 1996) circulation, surge propagation and internal generation of surge waves in the Clyde Sea are not well studied. These two features are the focus of this paper, together with the climatology of the storm surges.

Fig. 2
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Images from the 28 December 2011 storm in Helensburgh (Photos Joanna Heath)

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Here, we explore three storm surges in December 2011 (8–9, 13 and 28 December 2011). December 2011 was one of the stormiest months on record for Scotland. The storm surge on the 8–9 December 2011 (Storm Friedhelm, nicknamed by the british press as Hurricane Bawbag) caused severe flooding on all the west coast of the UK, from Cumbria to the Orkneys island, causing an estimated £100 M of damages in Scotland alone. In Ayr, the maximum recorded wind gust during the storm exceeded 36 m/s. The 13 December and the 28 December surges flooded part of the town of Helensburgh, situated between Gare Loch and the Clyde Estuary. Helensburgh (about 15,000 inhabitants) is often flooded in severe surge conditions or when mild or strong surges are coupled with spring tide conditions. Figure 2 shows some pictures taken on the 28 December 2011 in Helensburgh: coastal defences were overwhelmed, and the marina, the pier, and the streets near the coastline were flooded.

2 Methods

2.1 The hydrodynamic model

The water circulation of the Clyde Sea and the North Channel was simulated using Finite-Volume Community Ocean Model (FVCOM), which was developed by Chen et al. (2003) mainly for simulating the flow of complex shelf and estuarine areas. FVCOM was later updated by a joint team from Woods Hole and the University of Massachussets (Chen et al. 2006). FVCOM has been applied successfully for surge forecast and hindcast purposes. In particular, it was modified for the hindcast of hurricane-generated storm surges (Rego and Li 2009b): Rego and Li (2009a) modelled the effect of hurricanes-induced storm surge on the low-lying coastline of Louisiana, while Weisberg and Zheng (2008) used an FVCOM model for studying the effect of an Ivan-like hurricane on Florida coastline. The effects on the coastline of Texas of the storm surge wave induced by Hurricanes Rita and Ike were studied by Rego and Li (2010a, b). The FVCOM model is based on the numerical solution of primitive equations in 3-D. The model equations in Cartesian, sigma-layers coordinates are reported in Chen et al. (2003). The model solves the equations on an unstructured grid using a finite-volume approach (Versteeg and Malalasekera 2007), optimized for parallelization on a MPI cluster (Cowles 2008). Horizontal and vertical closure of the governing equation was made with a default setup of the \(k-\epsilon\) model and Smagorinsky turbulent closure schemes for vertical and horizontal mixing, respectively (Rodi 1993; Smagorinsky 1963).

2.2 Model forcings

Various datasets were used to force the model. Tidal boundary conditions were extracted from the European Shelf OTPS local solution (Egbert et al. 2010), an open-source software for tidal predictions based on the TOPEX/Poseidon satellite data observations and on tidal harmonic components from the major ports. To account for storm surges generated outside the model domain, residuals were extracted from the tide gauges closest to the model boundary and added to the tidal elevations (Table 1). Tide gauge data were from the UK tide gauge network and were provided by the British Oceanographic Data Centre (BODC) and by the Scottish Environmental Protection Agency (SEPA). For simulating surges generated internally in the model domain, wind and pressure fields were provided to the hydrodynamical model from the ERA-Interim dataset (Dee et al. 2011) at a time resolution of 3 h and a spatial resolution of 0.125\(^{\circ }\) × 0.125\(^{\circ }\). The ERA-Interim data were covering the 2002–2011 period, in which the simulations were carried out. To evaluate river contribution to surge events in the Clyde Sea, eight rivers were included in the model. River discharge informations for the period 2005–2011 were provided by SEPA with a 15-min resolution. The locations and main features of those rivers are reported in Table 2.

Table 1 List of tide gauges used for the estimation of the residuals
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Table 2 Location and properties of the river data provided by Scottish Environmental Protection Agency (SEPA)
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The implementation of the model forcings was made using MATLAB, modifying the FVCOM MATLAB toolbox developed by Geoffrey Cowles and Pierre Cazenave. The results were plotted using MATLAB \(m\_map\) toolbox (Pawlowicz 2000). Although the model can run in baroclinic, the outputs showed in this paper are all from barotropic run.

2.3 Calibration and validation procedure

The model was calibrated using the water elevation recorded by the tide gauge data from Millport in 2007 for 11 months (the first month was considered spin-up time). After the calibration, the model was run for the whole of the year 2003 and then validated (first month, December 2002: spin-up time) by two different methods.

Firstly, the model was validated by extracting the water level harmonic components (Codiga 2011) and comparing these with the recorded tide gauge. The performance of the model was assessed by calculating the root-mean-square error based on the harmonic components extracted from all the tide gauges reported in Table 3. This first method was carried out to assure that the model reproduced the tidal wave propagation in the Clyde Sea.

Table 3 Position of the tide gauges used for the validation of the model
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Secondly, the model was validated for the total water level, in order to evaluate the agreement between the recorded and the hindcast water level due to surge and tides. In this case, this validation was based on the reproduction of residual elevations at the boundaries. We used five different tide gauges at various locations in the domain. Four different statistical indices were used for the validation:

$$\begin{aligned} \hbox {Bias}= & {} \frac{1}{N} \sum \limits _{i=1}^N \left( x_{o_{i}}-x_{m_{i}} \right) \end{aligned}$$
(1)
$$\begin{aligned} \hbox {RMSE}= & {} \sqrt{\frac{1}{N} \sum \limits _{i=1}^N \left( x_{o_{i}}-x_{m_{i}} \right) ^2} \end{aligned}$$
(2)
$$\begin{aligned} \hbox {NRMSE}= & {} \frac{\hbox {RMSE}}{\hbox {max}(x)-\hbox {min}(x)} \end{aligned}$$
(3)
$$\begin{aligned} R^2= & {} \left( \frac{\sum \nolimits _{i=1}^N \left( x_{o_{i}}-\overline{x}_{o} \right) \left( x_{m_{i}}-\overline{x}_{m} \right) }{\sqrt{\sum \nolimits _{i=1}^N \left( x_{o_{i}}-\overline{x}_{o} \right) ^2 \left( x_{m_{i}}-\overline{x}_{m} \right) ^2}} \right) ^2 \end{aligned}$$
(4)

The bias is used to assess if there are some significant, the root-mean-square error (RMSE) represent the sample standard deviation between observed and modelled values, the normalized root-mean-square error (NMRSE) is used to understand the percentage significance of the RMSE on the total water level, while the \(R^2\) is the Pearson correlation coefficient that measures the linear correlation between the modelled and the observed values. For the analysis of the surge residuals, also the standard deviation \(\sigma\) of the total water level has been used. The expression of \(\sigma\) is the same as the root-mean-square (RMSE).

Water levels at tide gauges were provided by the British Oceanographic Data Center (BODC) and by the Scottish Environmental Protection Agency (SEPA).

2.4 Surge historical analysis

For the surge historical analysis of the Clyde Sea, the tide gauge data from Millport was available for a 30-year period (1985–2014), from British Oceanographic Data Center (BODC), including both total water level and residuals. Storms that generated the surge wave were tracked using wind (m/s) and pressure (Pa) data from ECMWF ERA-Interim reanalysis (Dee et al. 2011), at a time resolution of 3 hours and a spatial resolution of 0.125\(^{\circ }\) × 0.125\(^{\circ }\) from 1985 to 2014.

Using the Millport tide gauge, we identified the largest surges based on the residuals. Storms with residuals exceeding 1 m were considered. Storms were classified into five different categories, depending on the path and the evolution of the storm from ERA-Interim data.

Since residuals are often not associated with spring high water events, at Millport, the standard deviation of the total water level was estimated and the events exceeding 2\(\sigma\) and 3\(\sigma\) were identified as potentially damaging surge events, and the distribution of the residuals with the astronomical tidal elevation was studied.

2.5 Grid generation

Generation of the computational grid for the Clyde Sea and for the North Channel followed the guidelines reported in the FVCOM User manual (Chen et al. 2006). Since no grid generator was included in the code, the SMS grid generator was used (Aquaveo 2007; Banks et al. 2014) to create the computational mesh. FVCOM adopts an unstructured grid approach, with triangular elements (Ferziger and Perić 2002). Unstructured grids can represent complex coastlines better than rectangular grids and potentially provide more realistic flows, enabling the geography of the coastline to affect the propagation of tidal and surface waves in a realistic manner. FVCOM has some quality requirements for the computational mesh. In particular, it should meet these requirements:

  • Minimum interior angle of each element: \(30^{\circ }\)

  • Maximum interior angle of each element: \(120^{\circ }\)

  • Maximum slope: 0.1

  • Element area change: 0.5

  • Connecting elements: should be less than 8 for each node

The grid was generated using the Global Self-consistent, Hierarchical, High-resolution Geography Database (GSHHG) coastline from NOAA (Wessel and Smith 1996), joint with the SeaZone high-resolution coastline for the internal areas of the Clyde Sea. Bathymetric information was, then, interpolated on the grid using SMS. The bathymetry used was the GEBCO (Fisher et al. 1982) with a spatial resolution of 30 arc second, interpolated with the high-resolution bathymetry from SeaZone. Figure 3 shows the computational grid used for this study. The grid was generated with the boundaries far away from the area of study. This avoids boundary noise influencing the circulation in the study area and reduces the issue of unphysical speeds or water elevations within the Clyde Sea domain. The resolution varies between 5 km at the open ocean boundaries to <100 m in lochs, such as Loch Fyne and the area of the Clyde Estuary.

Fig. 3
figure 3

Computational grid generated with SMS used for the FVCOM Clyde Sea model

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2.6 December 2011 storms

ERA-Interim datasets were used to hindcast pressure conditions during the three storms that occurred in December 2011. Between 8 and 9 December 2011 Britain experienced an extremely intense extratropical cyclone, with hurricane-force winds hitting Scotland and Northern England. Wind gusts exceeding 42 m/s were reported, causing widespread damage. The extratropical cyclone was nicknamed by the British press Hurricane Bawbag. Figure 4 shows the evolution of the storm between 8 and 9 December 2011 over Great Britain. The storm was formed in the North Atlantic Ocean and moved quickly to Scotland. On the 8 December at 12:00 UTC, the pressure minimum was 957 hPa, with maximum sustained wind gusts at surface exceeding 47 m/s. At the 9 December at 00:00 UTC, the minimum was over the North Sea, passing through Orkney-Fair Isle channel.

Fig. 4
figure 4

Evolution of the mean sea level pressure (hPa) during Hurricane Bawbag from 8 December 2011 00:00 UTC. The pressure field is plotted every 6 h: a 08/12/2010 00:00 UTC, b 08/12/2010 06:00 UTC, c 08/12/2010 12:00 UTC, d 08/12/2010 18:00 UTC, e 09/12/2010 00:00 UTC and f 09/12/2010 06:00 UTC

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Fig. 5
figure 5

Evolution of the mean sea level pressure (hPa) during the Cyclone Hergen from 13 December 2011 00:00 UTC. The pressure field is plotted every 6 h: a 13/12/2010 00:00 UTC, b 13/12/2010 06:00 UTC, c 13/12/2010 12:00 UTC, d 13/12/2010 18:00 UTC, e 14/12/2010 00:00 UTC and f 14/12/2010 06:00 UTC

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Fig. 6
figure 6

Evolution of the mean sea level pressure (hPa) during the 28 December storm from 00:00 UTC. The pressure field is plotted every 6 h: a 28/12/2010 00:00 UTC, b 28/12/2010 06:00 UTC, c 28/12/2010 12:00 UTC, d 28/12/2010 18:00 UTC, e 29/12/2010 00:00 UTC and f 29/12/2010 06:00 UTC

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A few days later, a strong depression formed over the North Atlantic Ocean, with a pressure minimum less than 945 hPa, that was the lowest recorded pressure in UK since 2000. Figure 5 shows the evolution of Cyclone Hergen. The path and the evolution of this cyclone was very similar to the Hurricane Bawbag, generating a very large storm surge where the residuals exceeded 1 m in Millport, flooding Helensburgh and other towns in the Clyde Sea. The M4 weather buoy of the Marine Ireland, off the Donegal coast recorded a surface wave with a height of 20.4 m.

The last storm considered in this study occurred on the 28 December 2011 and generated a surge wave that in Millport exceeded 0.7 m. The storm followed the same path of the other two previous storms, with the low pressure in the North Atlantic Ocean moving to Orkneys-Fair Isle channel. In this storm, however, the pressure minimum was less intense, and the damages were less than the other two (Fig. 6).

3 Results

3.1 Surge climatology of the Clyde Sea

Between 1985 and 2014, the Millport tide gauge recorded 92 surge events that exceeded 1 m. Sources of storm were classified into five main categories (Table 4), depending on the position of the low pressure minimum that caused the storm surge (Table S1 of the supporting material provides more details of the 90 storms considered). Percentages were evaluated from the Table S1 based on the frequency of occurrence of those events in the 30 years of records in Millport. The most common pattern for a weather system causing a large surge event in the Clyde is a low-pressure system moving from the North Atlantic Ocean to, generally, the Fair Isle Channel (Table 4). In this case, the storm surge could be generated either in the open North Atlantic itself (case 1) or close to the western coastline of Scotland (case 2), depending on where the storm reaches its maximum. It is also possible for a pressure minimum from the North Atlantic Ocean to move over the Scottish mainland (north of the Clyde Sea, between 56 and 60 N) and generate a storm surge near the Clyde Sea (case 3). Severe storm surges are rarely internally generated in the Clyde: This is the case of a low-pressure system moving from the North Atlantic Ocean to Ireland and to Clyde Sea itself (case 4). In this case, the storm surge is caused in response to the local field of wind and pressure. An extremely rare case is when the wind circulation around a low-pressure system over the North Sea causes a storm surge in the Irish Sea and the Clyde Sea (case 5). Case 5 has only once been recorded, on the 31 December 2006.

Table 4 Classification of depression that caused large storms in the Clyde Sea, compared with Table 1 in Olbert and Hartnett (2010)
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Comparing results in Table 4 with the results in Table 1 of Olbert and Hartnett (2010), it is possible to see that for both for Irish water and for the Clyde Sea, the largest part of storms come from SW and pass to the north of the Clyde: The same storm events that can cause damages on Irish coastal cities can cause floodings in the Clyde Sea. However, the frequency of storms generated when the minimum is south of 55 N is very low in the Clyde Sea (about 9 % of the severe storms), but is about 29 % for the more southerly Irish coastline.

Fig. 7
figure 7

Monthly frequency of the surges in Millport exceeding 1 m in the period 1985–2014. The frequency is calculated as the number of storms occurring in the month divided by the total number of storms in the record

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Figure 7 shows the climate statistics for the occurrence of storms based on the month of occurrence. As expected, the autumn–winter period (from November to February) is the stormiest period for the Clyde Sea, in which the majority of the large storm surges are recorded. However some surges exceeding 1 m in Millport are recorded also in spring and in summer months.

3.2 Extreme water level climatology of the Clyde Sea

Flooding events in the Clyde are not only connected to the extremes of surge residuals, but to the coincidence of high residuals and spring tide. The standard deviation of the total water level at Millport was evaluated, over the period 1985–2014. All the recorded elevations exceeding 2\(\sigma\) and 3\(\sigma\) were then extracted (Fig. 8). The most frequent situation for water level exceeding 2\(\sigma\) was when moderate surge residuals (between 0.5 and 0.8 m) occured at the same time as spring high tide events (with water level exceeding 1.2 m, tidal range exceeding 2.2–2.4 m). Conversely, extreme events (water level > 3\(\sigma\)) were recorded when the residual was less than 0.5 m. Events with sea level exceeding 3\(\sigma\) occurred only in 7 years over the 30 analysed (about 23.3 %). As expected, there is no relation between the occurrence of severe surge and astronomical spring high tides.

Fig. 8
figure 8

Surge residuals (calculated as total water level minus the astronomical tidal contribution) versus astronomical tidal elevations for large water level events in Millport, blue points are recorded water level exceeding 2\(\sigma\) (1.75 m) in Millport, while red crosses are recorded water level exceeding 3\(\sigma\) (2.63 m). \(\sigma\) is the standard deviation of the water level (0.89 m). The black and the green line represent the 2\(\sigma\) and the 3\(\sigma\) respectively

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3.3 Model calibration and validation

The final parameter settings of the hydrodynamic model after the calibration procedure are shown in Table 5. The results of the sea level validation are reported in Tables 6 and 7 for semidiurnal and diurnal components, respectively. The results show that the model performed well against tidal harmonic component (both semidiurnal and diurnal, Tables 6, 7, respectively). In particular, the main component in the Clyde Sea and in the North Channel is the \(M_2\) component. Considering the results from all ten tide gauges, the Root-Mean-Square Error for the \(M_2\) harmonic component was 1.19 cm and 7.06\(^{\circ }\) for the amplitude and the phase, respectively.

Table 5 Model parameters after the calibration
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Table 6 Comparison of the observed and modelled amplitude and phase for dominant semidiurnal tidal components for the year 2003 \(h_0\) and \(g_0\) are the observed amplitude in cm and the phase degrees respectively and \(h_m\) and \(g_m\) are the modelled amplitude in cm and the phase degrees
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Since our focus is on surge events, it is important to understand how the model agrees with the observation for total water level. In Table 8, we report the statistical comparison between observed and modelled water level in different areas of the domain. The RMSE for the total water does not exceed 20 cm and 5 % of the total water level. Analysing the residuals between modelled and recorded water level, we conclude that the model underestimates the total water level (<1 cm for all the tide gauges considered).

Table 7 Comparison of the observed and modelled amplitude and phase for dominant diurnal tidal components for the year 2003 \(h_0\) and \(g_0\) are the observed amplitude in cm and the phase degrees respectively and \(h_m\) and \(g_m\) are the modelled amplitude in cm and the phase degrees
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Table 8 Statistical analysis of the surge model performance for the year 2003
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Table 9 Statistical analysis of the surge model performance during November–December 2011. In Port Ellen tide gauge, there were no valid data for the comparison
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3.4 Surge spatial statistics

Results reported here are based on the 2003 that was a relatively calm year for storm surge events (Table S1). For years like 2011, in which several surge exceeding 1 m were recorded in Millport, the results for the maximum and the average effect of the surge are larger (Figs. 9b, 10b).

Fig. 9
figure 9

Root-mean-square effect of different forcings on total water level (m): a Atlantic surges, b local wind and pressure, c combined effect. The RMSE was evaluated for the first figure as the difference of the simulation with surge boundaries and no local wind compared to a simulation with only tides, in the second case, the difference was between the wind and pressure only compared to the tidal simulation, while in the last case, we compared the total surge simulation with the tidal simulation. The RMSE was evaluated for the year 2003 (1 month spin-up in December 2002)

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Fig. 10
figure 10

Maximum modelled effect for different forcings on total water level (m): a Atlantic surges, b local wind and pressure, c combined effect. The maximum was evaluated for the first figure as the difference of the simulation with surge boundaries and no local wind compared to a simulation with only tides, in the second case, the difference was between the wind and pressure only compared to the tidal simulation, while in the last case, we compared the total surge simulation with the tidal simulation. The maximum difference was evaluated for the year 2003 (1 month spin-up in December 2002)

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Models were run with different surge forcing, in addition to tidal forcing, and each one was compared with a model run with only tidal forcing. Figure 9 shows the root-mean-square deviations (calculated as the RMSE) between each model run and the tide only simulating, with Fig. 9a showing the effect of the external surge, Fig. 9b showing the effect of the local wind and pressure fields, and Fig. 9c showing the combined external surge and local wind and pressure. Figure 10 shows the maximum effect of (a) the external surge forcing, (b) the local wind and pressure fields, and (c) the combined external and local surge. Both figures show that the amplitude of the surge wave increased towards the fjordic areas of the Clyde Sea, located to the north of the estuary. In particular, the strongest effect in the Clyde Sea is recorded in the estuary and in Loch Fyne, with a maximum combined effect of Atlantic surge and local surge of 1.2 m. In the estuary, in particular, the surge wave can be up to 1.5 m (Fig. 10c) without considering the effect of the Clyde river discharge.

The effect of the Atlantic storms is stronger than the effect of the local wind on the surge. From the previous analysis of historical records, only 9 % of the recorded surge events at Millport exceeding 1 m were generated internally. However, in combination with the storms from outside, local conditions can significantly enhance the water level and contribute to severe surges.

Collectively these findings, based on a 1-year run in both summer and winter conditions, indicate that the Clyde Sea areas most exposed to severe surges are the estuarine areas and the fjordic areas, in which the largest deviation from the astronomical tidal elevation are recorded. This suggests that the funnelling effects due to the complex coastline of the Clyde Sea are extremely important for the enhancement of the water level.

Our results also indicate that the North Channel is not as exposed as the Clyde Sea to severe surges, due to the deeper bathymetry: The increase in the surge wave is, in fact, recorded in the shallow water area between the Clyde Sea and the North Channel. However, Figs. 9b and 10b show that in Belfast Lough, the local wind and pressure field can cause an enhancement greater than the surrounding North Channel (an average of 0.04 m, max effect of 0.25 m compared to the North Channel, that is an enhancement that can be compared to the Clyde Sea) due to the funnelling effect of the Belfast Lough on the surge wave. However, due to the location of the Belfast Lough, the Atlantic surge wave is not significantly amplified by the bathymetry or the coastline to be dangerous to the city of Belfast. In addition to this, the effect of the River Lagan is not considered in this study.

3.5 River contribution

To assess the contribution to sea level from river inflow, the model was run for the period in which the river inflow provided by SEPA was available (2005–2013). In particular, for this analysis, the year 2005 was considered. The results that we obtained from the simulation indicate that the water level enhancement due to the interaction between river, surge and tides was only significant in the inner part of the Clyde Estuary and did not have any far-field effect. No significant effects were found for the other rivers included in the simulation.

3.6 December 2011 storm surges

Three storms in December 2011 were hindcast to study the interaction between the surge wave and the tidal wave. The performance of the model was evaluated during December 2011 (Fig. 11; Table 9), and the model accurately predicted the total water level during this stormy period. Figures 12, 13 and 14 show the results of the model for the Clyde Sea at high water in Millport for each storm. For the first storm, the peak of the surge wave arrived after the maximum astronomical tide. In fact, the model hindcast shows a very strong enhancement of the water level in coincidence with the subsequent low astronomical tide (Fig. 12). Due to this lag between the peak storm wave and the high tide, as well as the coincidence with a neap tide period, the maximum total modelled water level did not exceed 2–2.5 m during the storm, despite a 1–1.5 m surge wave (Fig. 12b). The surge wave was effectively enhanced by the shallow bathymetry and the coastline of the sea lochs during this surge. The difference in height of the surge wave between the central part of the Clyde and the sealochs was 0.2–0.4 m. Nevertheless, in the northern sea lochs (Loch Fyne and the estuary of the Clyde in particular) and on the coastline near Ayr, some limited flooding events were reported. Unfortunately, the Millport tide gauge malfunctioned and did not record the peak period of the storm. The hydrodynamic model, in this case, was able to reconstruct the coupling between the surge wave tidal wave, predicting a surge wave exceeding 1 m in the Millport area. Conversely, in the North Channel, the surge never exceeded 1 m (Fig. 12b), and the maximum water level elevation was never >2 m (Fig. 12a).

Fig. 11
figure 11

Comparison between modelled and recorded water level and astronomical tide in Millport tide gauge for the month of December 2011; red is the modelled water level and blue is the observed water level

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Fig. 12
figure 12

Water level in the Clyde Sea at high water during Hurricane Bawbag: a total water level, b surge contribution

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Fig. 13
figure 13

Water level in the Clyde Sea at high water during Cyclone Hergen: a total water level, b surge contribution

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Fig. 14
figure 14

Water level in the Clyde Sea at high water during the 28 December storm: a total water level, b surge contribution

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The surge caused by Cyclone Hergen (Fig. 13) occurred at the same time as a spring tide period, so even though the surge wave was less intense than the one caused by Hurricane Bawbag, the total water level was higher, exceeding 2.5 m in the Clyde Sea and more than 3 m southward in the northern Irish Sea (Fig. 13a). This coupling between strong surge and spring tides caused the flooding in many costal communities in the Clyde Sea, in particular in Helensburgh.

The last storm (Fig. 2 for the photos of that day, Fig. 14 for the model results) was less intense than the other two storms analysed. Nevertheless, many coastal communities were still flooded, and much damage was recorded. The storm surge in the Clyde Sea never exceeded 1 m (Fig. 14b), but the spring tide conditions caused an high sea level in the sea lochs, in particular in the Clyde Estuary similar to the storm caused by the Hergen cyclone. This coupling caused another flood in streets near to the seafront in Helensburgh (Fig. 2).

3.7 River contribution during storm surges

The model was run in 2011 with and without river inflow and the output were compared in order to study the river effect on the total water level. For the first storm, the contribution of the rivers was very small: The Clyde river contributed up to 0.02 m in the estuary and in neighbouring areas, while no substantial contribution was coming from the other rivers. Also for the second storm, the maximum river contribution to storm surge was <0.01 m, while for the third storm was <0.02 m. In both cases, this contribution was from the Clyde river.

4 Conclusions

Our analysis of the historical tide gauge data showed that the highest water elevations in the Clyde Sea are recorded when spring high tides coincide with moderate to severe surge conditions, that from the statistical analysis in Fig. 7 usually occur during late autumn–winter. Approximately 90 % of storm surges with residuals >1 m were generated outside the Clyde Sea. The storms generating those events usually follow a particular pattern, with the low pressure from the Atlantic moving to the north of mainland Scotland or further north, over the Orkneys or the Fair Isle Channel. Only 8.9 % of storm surges exceeding 1 m can be explained by a low pressure over the Clyde or the North Channel.

The surge generation processes in the Clyde Sea contrast with mechanisms in other semienclosed basins around the world. In the Adriatic Sea, for example, large surges (such as acqua alta events in Venice) are internally generated by Bora or Scirocco winds (Orlić et al. 1994; Wakelin and Proctor 2002). Similarly, the majority of surges are internally generated in the Baltic Sea (Suursaar and Sooäär 2007), and in the Mediterranean Sea itself (Ullmann and Moron 2008). Other semienclosed basins, in fact, such as the bays in the west coast of the USA,are usually protected from surges from outside due to their complex coastline and bathymetry, such as Chesapeake Bay, and only very strong local winds can cause floods and large surges (Li et al. 2006). However, in all of these cases, the extent of the basin is larger than that in the Clyde, and/or the open ocean connecting channel is narrower and/or is oriented in the opposite direction to the climatological wind. The Clyde Sea is also a very particular semienclosed basin, if compared to the classification made by Pickard and Emery (Pickard and Emery 1990; Cessi et al. 2014), since it shows some features of the first case (single strait, exchange flow is separated vertically), and some of the second case (multiple straits, substantial net flow into/out of each strait). The Clyde Sea (joint with the North Channel) could be considered a semienclosed basin of the case B in the Pickard and Emery classification, since two entrances are present, but the Clyde Sea is separated from the North Channel due to an abrupt change in the bathymetry. All of these factors contribute to the peculiar surge climate of the Clyde Sea.

Our high-resolution model of the sea level dynamics in the Clyde Sea shows that the surge wave from the open boundaries is enhanced by the funnelling effect of the sealochs and estuary in the northern Clyde Sea and by the steep bathymetry at the entrance of the semienclosed basin. In addition, the external surge is often exacerbated by the local field of wind and pressure.

Our results illustrate these phenomena in greater detail than has been possible with previous surge models of the region (Townson and Donald 1985; Townson and Collar 1986; Kaya et al. 2005). The hindcasting of the three storms in the Clyde Sea during December 2011 corroborates the experience of coastal flooding patterns. In particular, the 28 December flooding event in the Inner Clyde was due to only a moderate surge wave, with residuals in Millport <0.6 m (Fig. 14), but this coincided with a spring high tide leading to an extreme total sealevel elevation.

The future development of this high-resolution model will be the operational stage, in which this model will be used for flood forecasting purposes, given the satisfactory results when used for surge hindcasting. This will be achieved through the nesting the model with a large-scale model and forecasted wind and pressure from an atmospheric model instead of the climatological wind.