Using 18th century storm-surge data from the Dutch Coast to improve the con•dence in •ood-risk estimates

For the design of cost-effective coastal defence a precise estimate is needed of the 1/10 000 per year storm surge. A more precise estimate requires more observations. Therefore, the three greatest storm surges that hit the northern part of the Holland Coast in the 18th century are reconstructed. The reconstructions are based on paintings, drawings, written records and shell deposits that have recently appeared. The storm-surge levels of these storms have been estimated using numerical modelling of the coastal processes. Here we show how these reconstructions can be used in combination with extreme value statistics to give a more con•dent estimate of low probability events.

of the maximum extreme event used to de•ne the crest level and width of dunes and dykes. In 2009 the law was amended so that each dyke ring had an exceedance probability for the whole dyke rather than per section.
The extreme safety standards re•ect the vulnerability of the economically most valuable part of the Netherlands, which is mostly below sea level ( van Dantzig, 1956;Deltacommissie, 1960). Wo rking with such extremely low exceedence probabilities presents anumber of statistical challenges, as tide-gauge records are at most three centuries long. The most extreme storm-surge events are likely not represented in these records. To quantify such extreme storm surges, the distribution of observed surges as distilled from tide-gauge records is extrapolated by applying extreme value statistics (de Haan, 1990;Coles, 2001). Using this technique, an estimate can be given of various properties of the 1 /10 000 per year storm. The surge is the most important of these properties when assessing the safety afforded to the Dutch lowlands by the fronting coastal dunes ( van de Graaff, 1986).
The effective design of the coastal defence depends on how high a 1 /10 000 per year storm surge will be, but this is not precisely known. Using extreme value statistics, vanden Brink et al. (2004) showed that the con•dence interval of the 1 /10 000 per year surge is between 2.9 and 6.5 mf or the Hoek van Holland station (Fig. 1). Using the upper limit of this rather large con•dence interval (3.6 m) would likely lead to an unnecessarily expensive design of the coastal defence system. One could neglect the large con•dence interval and just use the most likely estimate but it is undesirable to hide the uncertainty from the view of probabilistic engineers. A better alternative would be to reduce the size of the con•dence interval. This can be done by increasing the number of observations (the size of the con•dence interval depends on 1 2 ,where is the number of observations)or by introducing other variables that reduce the error in the surge estimates. In this study,wefocus on increasing the number of observations by adding data from discrete events described and analysed in historical records.
Previous studies on creating am ore reliable estimate of the 1 /10 000 per year storm surges have combined data from various sources. Storm surges for which data are available can be subdivided into four groups, on the bases of surge data availability.
Pre-historic. No measurements or written records are available. The effects of individual storms are traced back using geological records. Sedimentological analyses provide estimates of surge or run-up, but commonly the date of the storm cannot be constrained well. An example of ageological study on surge heights was published by Jelgersma et al. (1995), who concluded that storm surges of up to 5moccurred in the past.
Historical storms. Written records and artworks are available and can be used to trace back the magnitude and impact of astorm. The date of the storm is usually known and the associated magnitude can be constrained from descriptions or from incidental measurements. No monitoring series of regular consistent measurements are available. Although the earliest records date from 838 AD (Buisman and Engelen, 1995), they become increasingly abundant (with multiple accounts for single events) from the 16th century onwards (Buisman and Engelen, 1996;Gottschalk, 1971). One disadvantage of using these older records is that the exact time of the peak water level is commonly missing. Therefore, the difference between the peak water level and the astronomical tide can not always be determined accurately. Peak water level, relative to mean sea level, is also a useful parameter, but introduces uncertainty when used in the prediction of exceedence levels. An example of late historical records are ship logs, used for example by Wheeler et al. (2010).
Measured storms. Series of measurements are available, collected by automated monitoring systems or by dedicated and trained of•cials. For the Dutch coast, the earliest tidal station in Amsterdam was installed in 1700. Most of the main stations along the North Sea coast that are still in use were installed during the late 19th century.
Modelled storms. Based on variable input data, series of models are run to create aw ide variety of possible storms and associated surges. Van den Brink et al. (2004) used adataset of seasonal forecast ensemble runs that were used as samples in an extreme value analysis. Because the con•dence interval is dependent on sample size, they were able to reduce the interval from 3.6 mto 0.9 m.
In this paper we focus on historical storms, more specifically the greatest storm surges along the Northern Holland coast of the 18th century.W ec ombine the results with an analysis of measured data from the 20th century.P ooling historical records with measurement series has proved useful for estimating •ood frequencies for return periods 100 yr in •uvial research (Macdonald et al., 2006). We do not include the 19th century because including this period requires ad ifferent approach. The romanticism movement and later the impressionism movement didn't result in paintings that are very useful for coastal reconstructions. Measurements from the 19th century are more prevalent but these need to be checked with special attention to possible errors and changes in vertical reference levels, for example. This extra effort makes the 19th century records an interesting topic for future research.
From as tatistical view, combining information on storm surges from the 18th and 20th centuries implies that the storms from the 18th century are from the same "population" as the storms from the 20th century.T he trend in storminess is sensitive to the area and period. For example, De Kraker (2005) found that there was no signi•cant change in storm climate over the period 1400-1625 for Southern Holland. Others (Smits et al., 2005;Va utard et al., 2010) found that if there had been achange in storminess it would have been more likely adecrease than an increase, based on the periods 1962-2002 and 1979-2008. The decrease can be partly attributed to increased surface roughness (for example due to urbanisation, growth of forests). Another important aspect is the relative sea-level rise. The sea-level rise along the Dutch coast has been constant since at least 1890  and possibly longer (Jevrejeva et al., 2008). For this study, we assume ac onstant storminess and constant relative sealevel rise over the last century.
Several inventories of 18th century extreme events provide ag ood collection of information. Extreme water levels and related •ood marks (stones with inscriptions) were listed and discussed by Van Malde (2003) and numerous written records were assembled by Buisman and Engelen (2006). These inventories can be supplemented by information from historical paintings. An example of such an approach is given by Camuffo (2010), who used paintings of Ve nice (Italy) to determine ac onstant sea-level rise between 1700 and 2000. McInnes (2008) uses art to show coastal changes along the coast of the Isle of Wight (United Kingdom).
In this study we analyse historical paintings and drawings. In addition, we combine the analytical results with information obtained from geological records, •eld measurements and numerical models, to constrain the estimate of the 1 /10 000 water level and the associated morphological effect. Because several different-sized inches were used in the 18th century (varying in length between 0.024and 0.027 m), it is not always clear what the exact metric translation is. Hence some of the notes below are given in inches. These values are only used to determine the ranking in the order column. a Based on van Gelder (2000) A: very severe •oods; B:heavy •oods; C:less heavy •oods; D: small •oods. b For the North Holland coast c In Amsterdam "0.31 mlower than 1717"; in Harlingen "9inches lower than 1717". d In Amsterdam and Rheede the water level "has not been so high since 1717"; in Amsterdam"7inches lower than 1717"; "3inches less than 1717" (van Malde, 2003), no comparison with 1715 was found. e In Amsterdam "as high as in 1717"; in Elburg "this •ood is far higher than that of 1717"; in Delfshaven: •ood stone: NAP +2.675 m( van Malde, 2003). f Some reports indicate that this storm resulted in ah igher surge than 1775, for example in Beulake (village drowned in 1776), "1 feet higher than 1775", Delfshaven "higher than in 1775", •ood stone: NAP +2.704 m( van Malde, 2003). On average for the northern Holland coast records, this storm was 0.2 mlower.

2T he storm surges of the 18th century
To be able to reduce the large con•dence interval of the predicted 1 /10 000 per year storm surge, it is insuf•cient to have observations or estimates of high surges, as it is unknown for which period and ordinal an individual surge is ar epresentative value. Is it the biggest surge in ac entury or is it the second biggest surge in adecade? A•xed time window and an ordering of the storms are required to improve the estimate of the 1 /10 000 per year water level.
To determine which storm surges are the three biggest, the ordering has to be found. Several studies of historical •oods (Buisman and Engelen, 2006; van Gelder, 1996;van Malde, 2003) were used to determine the order of the storm surges. The time window used in this study is the 18th century and we try to estimate the three highest storm surges along the northern part of the Holland Coast. The two most severe storm events occurred in 1775 and 1776. The storm surge of 1715 is also designated as amoderately severe storm (van Gelder, 1996), but for the northern part of the Netherlands it was not so severe. For the study area the 1717 storm is ranked the third biggest of the 18th century as shown in Table 1.
For the three biggest storm surges (1717, 1775, 1776) we reconstruct the peak water level. For the 1717 storm we use paintings as our main source. For the 1775 storm we use geological records. The 1776 storm surge is estimated on the basis of the average difference of reported water level from the 1775 and 1776 storms.  Lang and Homann (1963) recounted the conditions during the storm of 1717. An extract:

Christmas •ood 1717
On the 25 of December, around 1am, the NW storm increased rapidly and abruptly in strength until it formed ah urricane of such proportions that it seemed as if the earth was shaking. The sea was whipped to such an extent that several skippers reported that it was no longer possible to distinguish air and water.T he hurricane lasted all night and did not lose much of its strength during Christmas Day.T he evening was marked by severe thunder-, rain-and hailstorms. The storm kept blowing from the NW direction [. ..] until the 26 of December. In the morning of Boxing Day the storm lost some of its strength, but around 3pm the storm regained some of its strength and brought adownburst with rain and hail. It was not until the 27 that the weather cleared and the sun reappeared.
The storm caused major •oods in the northern Dutch provinces Friesland and Groningen, in northern Germany and in Denmark. Extensive damage reports were made after the storm (Extract van, 1717b). The number of victims exceeded 10 000.

Available data 1717 storm
Because the damage and number of casualties were so great, the 1717 storm is well documented. Information about the characteristics of the storm and its effect can be found in incidental measurements, maps, one •ood mark and historical records such as letters and poems. Ab rief overview of the historical records of the 1717 storm was given by Lang and Homann (1963). Av ery detailed analysis of the storm and the effects in Germany can be found in Jakubowski-Tiessen (1992). Associated surge levels are included in an inventory of storm surges made by Van Malde (2003). Temperature records are available through the Royal Netherlands Meteorological Institute (cf. Buisman and Engelen, 1995). Several documents provide narrative overviews and damage reports, including Nette aantekeningen (1717a); Extract van (1717b); Cramer von Baumgarten (1817); Bógaert (1719); Specht (1740); Schenk (1740); van Brussel (1776).
Focussing on our area of interest, the Northern Holland coast, and in particular on Egmond aan Zee (Fig. 1), paintings and drawings of Egmond beach, before and after the storm, were analysed to reconstruct the coast.

Reconstruction 1717 storm surge
Because there is such alarge collection of paintings available for the 1717 storm, we were able to reconstruct pre-and poststorm pro•les of Egmond beach.
The post-storm pro•le was measured on the 8ofFebruary 1718, just over am onth after the storm. The measurement recorded the angles and elevations of the beach and the adjacent dune relative to mean high water.
Reconstructing the pre-storm pro•le required acombination of different data resources. Starting point was the analysis of ac ollection of paintings and drawings available of the Egmond aan Zee area between 1600 and 1700. Am ap of 1686 was used to determine the position of the church, the most prominent structure of the town, located near the beach. Most of the painters chose aview where at least the church tower was visible without obstructions. The church was positioned in athree-dimensional model of the coastal town. The paintings were aligned using the church as areference point (Fig. 2). Structural coastal erosion can be seen in the fact that the paintings from the earlier part of the 17th century were painted from avantage point farther from the coast than that of those from later times. The positioning of aseries of pictures from 1620 in the 3-D model gives an estimate of the contemporary coastline. From comparing the 1686 map with reconstructions based on the older paintings, we estimate that the structural retreat of the coast was about 66 mi nt he period 1620-1686, i.e. 1m per year. This rate corresponds to the rate reported by de Ruig (1998). When using this rate to extrapolate the map of 1686 to 1717, we obtain an estimate of the width of the dune top that would have been approximately 17 m(48 min1686 minus 31 1myr 1 ,see Fig.2).
The beach width is assumed to be the same as that of the post-storm pro•le and the angles of the beach and dune are assumed to have been similar to the slopes from the average of that same area between 1963-1973 de Graaf et al., 2003, pro•le 7-3800 from the JARKUS dataset).
As no paleobathymetry information is available, both the pre-and post-storm pro•le up to mean high water are based on the bathymetry from the 1963 pro•le of the JARKUS dataset.
To get arough estimate of the precision of the paintings, we analysed the intra-and inter-painter variance. As reference points we use the upper two parts of the Egmond aan Zee church tower. This steeple is present in 80 of the 96 paintings and drawings. The ratio between the height of the upper and second highest part of the steeple are determined for each image. The average ratio was 0.95, with astandard deviation overall of 0.22 (Fig. 2). Images with ratios below 0.7 and above 1.2 were not included in the •nal analysis.

Probabilistic modelling 1717 storm surge
The pre-storm pro•le was used to set up an XBeach model (cf. Roelvink et al., 2009). XBeach is am orphodynamic model capable of capturing the physical processes in the nearshore that cause most of the coastline change during storm surges. The XBeach model uses the following parameters as input: water level, signi•cant wave height, peak wave period, grain diameter and bathymetry/topography.T he result of interest here is an estimate of the post-storm pro•le. Starting with the pre-storm pro•le, the XBeach model was run using different storm-surge levels. The surge levels, wave height and peak periods were drawn from the same distribution that is used for the safety-assessment method (WL Delft Hydraulics, 2007). The storm-surge level with the erosion closest to the "observed"erosion was selected, as judged from the erosion volume.
This gave an estimated magnitude of 5 /100 per year (Fig. 3), which corresponds to awater level of 3.1 mtogether with a signi•cant wave height of 6.8 mand apeak period of 10.4 s.

The storm surge of 15 November 1775
The largest storm surge of the 18th century was caused by the November 1775 storm. Buisman (1984) and Buisman and Engelen (2012)    North Sea. "Along the entire beach one saw nothing but ship wrecks, rigging, cargo and bodies being washed to the shore. "2 00 Ships were lost!

Available data 1775 storm
More records exist for the 1775 storm than for the data for the 1717 storm. Unfortunately,t he church at Egmond aan Zee was no longer available as ar eference point for a3 -D reconstruction because the steeple fell into the sea during the storm surge of 1741. In 1746 an ew church was built at the landward end of the village. Most of the relevant records for the 1775 event were gathered by interestedindividuals who made meteorological and hydrodynamic measurements. Historical records about morphology,such as the post-storm pro•le for 1717, are not known for this storm.
New useful evidence about the 1775 storm became available recently.A fter as torm surge hit the Dutch coast on 9November 2007, old storm-surge deposits were discovered in the eroded dunes near Heemskerk (Fig. 1). These deposits were recognized as the remnants of one or two historical storm surges. The layers consisted of sand, shells and bricks. Details of the layers and the associated reconstruction were provided by Cunningham et al. (2011). Luminescence dating placed the storm-surge layers at the end of the 18th century (Cunningham et al., 2009). Major storm surges occurred in 1775 and 1776. The maximum observed water level in Petten (the location closest to Heemskerkwith observations)was the same. Hence, no clear distinction was possible between the two storm surges. In the modelling used to reconstruct the storm, it was assumed that the deposits were from the 1775 storm surge (Pool, 2009 Other useful information used in to reconstruct the 1775 storm damage to the coast are the wind-force observations from 20 km south of Heemskerk(KNMI, 2011, maximum wind force 14 "noppen", 17.2-20.7 ms 1 ), the maximum storm surge related water level recorded at Petten (25 km north of Heemskerk, 2.8 ma bove the 1775 m.s.l.) (van Malde, 2003) and the median grain diameter, as derived from asieve analysis of sand in the deposits. The water-level observation comes from a1793 report on the sea-defence system at Petten and is not accurate (Conrad, 1864). Conrad emphasized that the reference level used was about 1m too high, requiring an upward correction of the surge level, and that open coast storm-surge measurements made before the 19th century are commonly inaccurate.

Reconstruction 1775 storm surge
As for the 1717 storm, we needed to constrain the values of the relevant parameters to be used as input for the XBeach model. The 1775 event has rather detailed information available on the driving conditions (wind force) but little on the post-storm pro•le. The approach to •ll in the missing gaps therefore differs from the approach used for the 1717 storm. Forward modelling starting from the wind force was used instead of inverse modelling.
The water levels, signi•cant wave height and peak period all depend on the magnitude of the storm. The wind speeds that were measured in Zwanenburg, aland-based station south of Egmond, were used as stochastic variable. They were translatedto North Sea wind speeds using the open water transformation (van Ledden et al., 2005) based on the Charnock'sr elation (Charnock, 1955), an empirical expression for aerodynamic roughness. These offshore wind speeds were used to estimate the wind-induced surge using the Weenink method (Weenink, 1958). The tide was estimated on the basis of water-level observations made at Katwijk during the period 1737-1739. The wave characteristics were estimated using the Sverdrup-Munk-Brettschneider growth curves (Holthuijsen, 2007). The median grain diameter was derived from the grain-size distribution of the storm-surge deposits (Cunningham et al., 2009). The palaeobathymetry was based on ac ombination of JARKUS data and sounding data (de Graaf et al., 2003), as for the 1717 scenario, assuming that the bathymetry did not change much over the period 1775-2011. The validity of this assumption is likely,inthe light of acomparison of the recent bathymetry with areconstruction of historical contour lines by Haartsen et al. (1997). For the construction of the palaeotopography, the 2007 data were used from the "Actueel Hoogtebestand Nederland" (AHN -Actual Elevation Database). The beach and the strong anthropogenic frontal dune were removed, assuming that the topography behind the dune resembles the topography in 1775 (before frontal dunes were under heavy anthropogenic in•uence). From this reconstructed bathymetry and topography,acharacteristic transect was selected for further analysis.

Probabilistic modelling 1775 storm surge
The same XBeach model was used as for the 1717 storm, but with different boundary conditions and paramater settings. Unlike for 1717, the goal was not inverse modelling the erosion pro•le but assessing what type of storm could have resulted in asurge and run up capable of depositing the shell beds that were exposed in the dune scarp following the 2007 storm surge. The 2% exceedance level of the run-up is assumed to be the level where the shell would have been deposited.
We •nd that the storm pro•le of the con•dence interval of the run-up level includes the height of the storm-surge layer at 6.5m (Fig. 4). Therefore, we assume that the shell deposits found can indeed be from the 1775 storm. Using the exceedance lines for run-up levels as calculated by Philippart et al. (1995), the associated storm surge has a 3 /10 000 per year exceedance probability.

The storm surge of 21 November 1776
This storm surge occurred only one year after the major storm surge of 1775. This storm surge is measured on several locations along the Dutch coast. We estimate that the storm of 1776 resulted in astorm surge approximately 0.2 mlower than the 1775 storm surge. This difference is based on the average of the differences of locations where both the 1775 and 1776 stations were recorded (van Malde, 2003).
The corresponding exceedance probability would be 8 /10 000 per year, based on the probability distributions estimated by Philippart et al. (1995).

3A nupdated con•dence interval for the 1 /10 000 per year storm surge
To improve the con•dence interval associated with the extrapolation of the monitoring series of water levels that started in the late 19th century,w eu sed am ethod comparable to the one developed by Van Gelder (1996). From the three new data points (water levels for 1717, 1775, 1776), the aposteriori distribution for the 1 /10 000 yr storm surge can be created. The availability of estimates of the three highest annual water-level maxima of the 18th century implies that The reconstruction in this study has resulted in new estimates for the magnitude of the three biggest storm surges in the 18th century.T he characteristics of the storms are shown in Table 3. Using this information, we were able to constrain the con•dence interval for the 1 /10 000 storm surge. Using the Gumbel method, the con•dence interval decreased by 30 %b ecause the number of observations increased almost twofold.
For the generalised extreme value approach, with af ree shape parameter,the con•dence interval is much larger.T he large con•dence interval here is caused by the large standard error of the shape parameter. This can be seen in Fig. 6, which shows the records for Egmond, based on ac ombination of an inverse-squared-distance weight of the records from the IJmuiden station Noordersluis ( 1981), IJmuiden Buitenhaven ( 1981 and Den Helder. Because two of the three storms from the 18th century have alower observed return period than their estimated return period, the GEV •t results in apositive shape parameter. This positive shape also results in ah igher estimate of the 1 /10 000 per year water level (6 mcombined versus 4.6 m for the 20th century). Computations were done using the R software (R Development Core Team, 2009) with the ismev (Coles and Stephenson, 2010) package and am odi•ed version (custom log-likelehood method for con•dence bounds) of the fExtreme (Wuertz ,2009) package. Fig. 6. Return level plot for the location Egmond for the period 1932-2010, 1700-1800 and the combined •t. The upperrowrepresents a •t using the Gumbel distribution (Generalised Extreme Value distribution with 0). The lowerrowrepresents a•tusing the Generalised Extreme Va lue distribution using afree parameter. The circles represent observed  and estimated (1700-1800) water levels plotted against the observed return period. The black solid line represents the •tted return water level as afunction of the return period. The outer blue lines follow the lower and upperbound of the 95 %con•dence interval. The vertical dashed line marks the con•dence interval for the 1/10 000 per year water level.
Ta ble 3. Estimated magnitude of the three largest storm surges of the 18th century at the northernHolland coast.

Discussion
The reconstructed water levels from the three storms are very high. They correspond to return periods of 20 yr, 3300 yr and 1300 yr as derived from extrapolation of the monitoring records. Clearly,c aution is required when combining these water-level return periods with the water levels measured by tide gauges. An umber of possible causes of the apparent mismatch are inaccurate reconstruction and parametrisation, coincidence or change in storm climate.
It is dif•cult to give as olid estimate of the precision of these numbers, but based on the painter reliability and on the skill of the XBeach model (used with al ot of uncertain inputs), the standard error of the high-water estimates could be around 25 %or1m. So it could well be that the storms were in fact smaller than estimated here. Lower peak levels would of course result in al ower and narrower con•dence region. It is dif•cult to give aproper estimate of the probability that three such large storms occurred in the 18th century,s ince such an assessment cannot be made solely on the basis of the 20th century monitoring series. It would be more informative to present uncertainties around the peak levels of individual storm surges, so that the return periods could also be presented with uncertainty intervals.
Research into changes in storminess over the periods of decades have not shown any clear indications that the coastal storminess has changed. Research into changes over the period of three centuries shows adecrease in storminess. This can be seen in relation to the stormy end of the Little Ice Age (e.g. Hass, 1996). Although higher storms were found in an earlier century than the last one, this research should not be used to conclude that the coastal storminess has decreased.
The best approach to analyse changes in storminess over a multi-century timescale would be to construct am eta analysis using different types of records over awider area combined.

5C onclusions and recommendations
In this study we use historical record, a3 -D reconstruction of Egmond aan Zee and storm-surge layers in the dunes to reduce the size of the con•dence interval associated with the 1 /10 000 per year storm surge as determined by extrapolation of tide gauge monitoring series. This approach was successful in the procedure where the con•dence interval was based on aGumbel distribution, but not in the generalised extreme value approach, the estimate of the 1 /10 000 per year water level is much higher and the con•dence interval is slightly larger if the historical reconstructions are included with the generalised extreme value approach.
Al ogical step for further research would be to include storms from the other centuries where historical records are available. Also, the statistical method of including historical observations can still be improved, perhaps by applying aB ayesian approach to the combination of measurements, historical records and model simulations.
Although partially successful, our approach is less effective in increasing the con•dence than the method used by Van den Brink et al. (2004) as the con•dence interval depends on the number of (real and modelled) observations or datapoints. The maximum number of observations that can be extracted from history is limited by the length of history itself, which is much shorter than the return period of the design storm used in safety assessments of the Dutch coast.
Because the use of simulations is limited by physical knowledge and by assumptions that are put into the simulation model, other methods should also be examined. As discussed before, geological records can provide additional insight into storm surges that have left geological signatures, but from astatistical point of view these are hard to incorporate as the representative period is unknown. Alast approach would be to look at other coasts and combine the distributions of multiple coasts into an estimate of the surge distribution.
Paintings and other images are av aluable data source in determining coastal change and, indirectly,storm-surge magnitude. Although the paintings are not always reliable, series of images covering extensive time periods provide as olid basis for reconstructing structural erosion. When combined with data from monitoring and measurement surveys, they may be very useful in many coastal areas in the developed world.