The North Sea Storm Surge Atlas

Performance assessment and uncertainty analysis

Jurgen Klein

February 2015

The North Sea Storm Surge Atlas

Performance assessment and uncertainty analysis

Master thesis Civil Engineering and Management Faculty of Engineering Technology University of Twente

Author: Jurgen Klein Location and date: Amersfoort, February 26, 2015

Exam committee: Graduation supervisor Prof. dr. S.J.M.H. Hulscher University of Twente Daily supervisor Dr. ir. P.C. Roos University of Twente External supervisors Dr. ir. M. Van Ledden Royal HaskoningDHV Ir. N.J.F. Van den Berg Royal HaskoningDHV Dr. ir. H.W. Van den Brink Royal Dutch Meteorological Institute

Abstract

Current storm surge forecasting is often carried out by detailed real-time computer modeling. These models are accurate, but also have long calculation times. Also, the forecast horizon is short and the possibilities for scenario assessment are limited. For safety issues, such as the operation of storm surge barriers, as well as for shipping, forecasting on the mid-term (4-10 days ahead) is important. In 2014, a North Sea Storm Surge Atlas was developed by Royal HaskoningDHV, KNMI and Deltares, which uses a new and innovative method to predict storm surges in the North Sea area. As such, it provides quick insight of storm surges for five to ten days ahead, based on a large offline database of predefined and pre-calculated storms, rather than performing all calculations real-time. Currently, a pilot version of the North Sea Storm Surge Atlas is operational. Parallel to the operational method of the Storm Surge Atlas, another method to use the database for storm surge forecasting is developed. This research focuses on the validation and uncertainty identification of two possible methods for the North Sea Storm Surge Atlas. This is done by hindcasting 33 historical storms and comparing these simulations to observed water levels. The Storm Surge Atlas uses an EOF analysis to decompose pressure fields in to time coefficients (principal components) of derived spatial patterns (EOFs). With this method, a pressure field can be described by 50 principal components, rather than over 2000 grid points. The first method (A - resampling) is based on comparing the principal components of pressure fields of a weather forecast to those of the pressure fields in the database. When the best matching pressure is found, the corresponding pre-calculated storm surge is retrieved and used as a forecast of the storm surge. The matched storm surges for every pressure field in the weather forecast are concatenated to make a storm surge forecast for several days. The second method (B - regression) uses a multiple linear regression model. The direct correlation between the principal components of the pressure fields in the database and the pre- calculated surges is used for the regression. To forecast the storm surge from a forecasted pressure field, the regression coefficients are multiplied with the principal components of the forecasted pressure field. To assess the performance of both Storm Surge Atlas methods A and B, 33 historical storms have been selected and hindcasted and compared to observed water levels. The performance assessment is done for 11 locations, of which 6 are located at the North Sea coast of the United Kingdom and 5 at the Dutch coast. A comparison between method A and B is then made for the performance on peak water level, duration of the storm water level and timing of the peak. In general, the results show that method A performs slightly better than method B. When looking more in-depth to the results of peak water levels, we see that method A has a more structural underestimation with less variability, whereas method B has a larger variability in

i under- and overestimation. At Hoek van Holland the Storm Surge Atlas performs rather well. Heavy storms as in De- cember 1999 and December 2013 are underestimated by method A, whereas method B is better able to predict the storm surge. However, in other situations method B has much larger deviations. At this location also simulated water levels made by the state-of-the-art numerical model WAQUA are available (using the same input data). This model is also used to build the database of pre-calculated storm surges. Method A performs better at Hoek van Holland compared to the WAQUA simulations, although a systematic underestimation (bias) of 12 centimeters is found. The next step in this research is the identification and classification of different sources of uncertainty in methods A and B in the Storm Surge Atlas. A list of uncertainties is made and several of these sources are assessed for their sensitivity regarding the performance of the Storm Surge Atlas. From this analysis, it is found that method A can be improved by including the barometric average of the pressure field in finding the best match. Also, improvements are found when the database is enlarged. Last, improvement is found when no smoothening function is used. This smoothening function corrects for any discontinuities in the concatenated storm surge. This indicates that the peak storm surge is quite influenced by any bad matches prior to the peak water level. It can be concluded that the North Sea Storm Surge Atlas is able to hindcast historical storm surges quite well, with large time savings compared to real-time modeling. The North Sea Storm Surge Atlas can be a valuable addition in the field of storm surge forecasting, e.g. for scenario analysis, quick assessments of possible developments of a storm. It is recommended to use Storm Surge Atlas method A (resampling) as basis for further development. Further improvement of the Storm Surge Atlas may be found by including the pressure gradients or wind fields in the matching with the database. Furthermore, a coupling of a parameterization of extra-tropical storms and the Storm Surge Atlas may provide additional information in finding a matching storm in the database.

ii Preface

This thesis is the final part of my master Civil Engineering and Management at the University of Twente. The thesis focuses on a performance assessment and uncertainty analysis of the North Sea Storm Surge Atlas. The North Sea Storm Surge Atlas is a new and innovative way of storm surge forecasting, developed by Royal HaskoningDHV, in collaboration with KNMI and Deltares. Writing this preface marks the end of a great and very interesting period. I worked with great pleasure on the subject and learned a lot about meteorology in combination with hydrodynamics. In the beginning I had to put a lot of effort in learning Python, Fortran, LATEX and of course refreshing MATLAB, but in the end it paid off and I really enjoyed it. First, I would like to thank all my supervisors. To start with Mathijs for his enthusiasm and interesting ideas and discussions during my graduation project. Thank you Niels, for all your help on daily basis and your hands-on tips and tricks. Henk, thank you for all your feedback and good ideas, I really enjoyed our meetings at KNMI. Pieter, you were the one who tipped me about this topic and this graduation project. Thank you for this and all your feedback and motivation in past months. Suzanne, thank you for your critical view and questions during our meetings. I am very grateful to have worked at Royal HaskoningDHV during this graduation project. It was great to work with so many interesting and smart people around me and I want to thank all my colleagues in who helped me and gave me a great time. The winners certificate of ‘Wie is de Mol’ in Utrecht still hangs proudly on the wall! Special thanks to Erwin, who helped me during the difficult start of the project to get the Storm Atlas working. Last, but not least, I would like to thank all my family, friends and fellow master students for their support and the great time during my years at the university!

Jurgen Klein Amersfoort, February 26, 2015

iii iv Contents

Abstract i

Preface iii

1 Introduction 1 1.1 Storms surge forecasting ...... 1 1.2 North Sea Storm Surge Atlas ...... 2 1.3 Research objective and research questions ...... 2 1.4 Research methodology ...... 3 1.5 Report outline ...... 4

2 Storms, storm surges and storm surge forecasting 5 2.1 Introduction ...... 5 2.2 The development of a storm ...... 5 2.3 The development of a storm surge ...... 7 2.4 Current storm surge forecasting ...... 9

3 The North Sea Storm Surge Atlas 13 3.1 Introduction ...... 13 3.2 Building the database of pre-calculated storm surges ...... 14 3.3 Description of pressure ﬁelds by EOF analysis ...... 16 3.4 Method A - resampling from database ...... 18 3.5 Method B - multiple linear regression ...... 23

4 Storm Atlas performance 29 4.1 Introduction ...... 29 4.2 Performance indicators ...... 29 4.3 Selection of locations ...... 32 4.4 Selection of historical storms ...... 34 4.5 Data selection ...... 34 4.6 Validation ...... 36

v 4.7 Comparison of methods A and B ...... 47

5 Uncertainty analysis 49 5.1 Introduction ...... 49 5.2 Identification and classification of sources of uncertainty ...... 49 5.3 Overview of classification of uncertainties ...... 55 5.4 Prioritization of sources of uncertainty ...... 57

6 Discussion 59 6.1 Performance assessment methodology ...... 59 6.2 Performance of the Storm Atlas compared to real-time models ...... 62 6.3 Method A - resampling ...... 62 6.4 Method B - regression ...... 62

7 Conclusions and recommendations 63 7.1 Conclusions ...... 63 7.2 Recommendations ...... 65

Bibliography 67

Appendices 71

A EOF analysis 71 A.1 Introduction ...... 71 A.2 Preprocessing ...... 72 A.3 Finding the Empirical Orthogonal Functions (EOFs) ...... 73 A.4 Singular Value Decomposition ...... 74

B Comparison tidal data 77

C Improvements of the operational Storm Atlas 79 C.1 Introduction ...... 79 C.2 Improvements in operational version (resampling) ...... 79 C.3 Improvement in method B (regression) ...... 80

D Graphs of hindcasted storms in Hoek van Holland 81

E Matched pressure ﬁelds 115

F Sensitivity analysis method A - resampling 127

vi Chapter 1

Introduction

1.1 Storms surge forecasting

Every year several storms occur in the North Sea area. Well-known is the North Sea storm of 1953, which led to the largest natural disaster in The Netherlands in the 20th century. More recently, the storms of November 2006, November 2007 and December 2013 caused extreme water levels at the coasts of the United Kingdom, Belgium and The Netherlands. In 1999 a storm caused by extra-tropical cyclone Anatol was responsible for one of the highest measured water levels along the Danish coast, causing dike breaches, killing twenty people and causing billions of euros in economic damages (Tatge, 2009). Strong winds blowing over the water, in combination with a low pressure ﬁeld, result in a rise of water level of the sea, also known as a storm surge (Pugh, 1987). Low-lying deltas such as in The Netherlands and other coastal areas are prone to ﬂooding, which can cause large economic damages and risks the lives of thousands of people. Storm surge forecasting is important for safety, for example for timely and adequate operation of storm surge barriers and information for shipping. Preparation for an extreme storm surge needs to be started days before the event takes place. Nowadays, forecasting of storm surges is done by using computer simulations of combined hydrodynamic and meteorological models. In current practice, storm surge modeling is done by detailed numerical hydrodynamic models. These models use the input of weather forecasts and make real-time calculations to forecast the storm surge. State-of-the-art models are able to forecast the water levels accurately. In particular on the short term (2-3 days ahead) the performance of these models is good. On the mid-term (4-10 days ahead), the uncertainty in the weather forecast increases, and with that also the uncertainty in storm surge forecast. Another drawback of these real-time models is posed by the high computational times, which can take up to hours. Within this timespan, a weather forecast may be outdated, because of new developments in e.g. storm track or storm intensity. Therefore, a very quick way of storm surge forecasting can have added value.

1 2 CHAPTER 1. INTRODUCTION

Figure 1.1: Closure of the Maeslantkering at Hoek van Holland during a heavy storm in November 2007 ( c Royal HaskoningDHV)

1.2 North Sea Storm Surge Atlas

Recently, Royal HaskoningDHV developed a North Sea Storm Surge Atlas, in collaboration with the Royal Dutch Meteorological Institute (KNMI) and Deltares (Caires et al., 2014). Using a large offline database with pre-calculated and pre-defined storms, this model forecasts the storm surge using a quick algorithm for a comparison of the weather forecast and the storms in the database. The basic idea behind the North Sea Storm Surge Atlas is to omit time consuming hydrodynamic calculations by making these calculations upfront and store them in a database. When this database consists of enough possible weather scenarios, a storm surge forecast from the database can be used, instead of a real-time calculation. At this moment there is a first operational version of the Storm Surge Atlas, making storm surge forecasts for an ensemble of weather forecasts. This way, a bandwidth of the storm surge forecast is retrieved, which gives insight in the uncertainties of a storm surge forecast.

1.3 Research objective and research questions

At this moment, there are two diﬀerent methods which can be used for the prediction of surge levels. The ﬁrst is based on resampling (method A) and the second on a multiple linear regression (method B). In the overall process of the development of the Storm Atlas for the North Sea, the next step to be taken is a performance assessment of these two methods and an uncertainty analysis of the current model. With this performance assessment and uncertainty analysis, we aim 1.4. Research methodology 3 to get more insight in the current performance, which will help us to increase the performance by reducing the uncertainties.

The research objective of this graduation project therefore is:

“To gain more insight in the uncertainties of the Storm Atlas and to explore possibilities for improvement, by assessing the performance with a validation of the Storm Atlas and by an uncertainty analysis.”

The following research questions have to be answered to achieve the research objective. As the research objective is composed of several elements, we formulate four main research questions, with several sub-questions:

1. What is the Storm Surge Atlas and how do both possible methods A and B work? 2. How accurate does the Storm Surge Atlas predict storm surges at the North Sea? (a) What are suitable performance indicators for the Storm Surge Atlas? (b) How accurate are the forecasts made by the Storm Atlas, using the different methods A and B, compared to observed water levels? (c) What are the differences in performance of the different methods A and B of the Storm Surge Atlas? 3. What are the uncertainties in the Storm Surge Atlas?

(a) What are the sources of uncertainty in the Storm Surge Atlas? (b) What is the classiﬁcation of the identiﬁed uncertainties in the Storm Surge Atlas? 4. How can the Storm Surge Atlas be improved, in order to get a better performance?

1.4 Research methodology

To achieve the research objective and to answer the research questions, the following research methodology is used:

First, a background of storms, storm surges and storm surge forecasting is given. This part • is based on literature study. As this research focuses on the North Sea area, the focus is on extra-tropical storms. Next, a detailed analysis of both methods is done, by in-depth analysis of the model code. • Furthermore, theoretical background on EOF analysis is found in literature. From the analysis of the model code, improvements for the operational Storm Atlas are made.

For the performance assessment of both Storm Atlas methods, ﬁrst performance indicators • are obtained from previous research done by Van den Berg (2013). Also, the scope of this research is further reﬁned by making a selection of the locations around the North Sea coast and selecting historical storm for hindcasting. 4 CHAPTER 1. INTRODUCTION

The performance assessment is done by using both methods of the Storm Atlas to hindcast • the selection of historical storms. The results of this hindcast are compared to observed data. First data of observed water levels is collected. Also data for the tidal signals are collected, using Delft Dashboard (Deltares, 2008). Next, pressure ﬁeld data from the re-analysis model ERA-interim is used to simulated water levels.

For the analysis of the hindcasted water levels, the performance regarding the defined • performance indicators for the different stations and storms is researched. For this analysis MATLAB is used. These results are used for a comparison of both Storm Atlas methods. For further analysis of the performance of methods A and B, more focus is put on the • performance at Hoek van Holland. The simulated water levels are compared observed water levels, but also compared to a simulation by WAQUA, using the same input data as the Storm Surge Atlas. During the research, uncertainties are identified. The identified uncertainties are qualita- • tively described and classified according to the classification of Walker et al. (2003).

A sensitivity analysis is carried out for several sources of uncertainty. This analysis is used • to ﬁnd out which sources of uncertainty are of importance for the performance of the Storm Surge Atlas.

1.5 Report outline

In this thesis the following structure is used:

Chapter 2: Storms, storm surges and storm surge forecasting This chapter gives background on the formation of (extra-tropical) storms and how these storms inﬂuence the water level and generate storm surges. Furthermore current operational storm surge forecasting modeling is presented.

Chapter 3: Concept of the North Sea Storm Surge Atlas In chapter 3 the North Sea Storm Surge Atlas is presented. This is an alternative way of storm surge forecasting. In the Storm Atlas concept two possible methods can be used, which will be presented in this chapter. Research question 1 will be answered in this chapter. Chapter 4: Storm Atlas performance Next, the performance of both methods of the Storm Atlas is assessed. Results from the hindcasting of historical storms are presented. Research question 2 is addressed in this chapter. Chapter 5: Uncertainty analysis Chapter 5 presents the uncertainties identiﬁed during the research. The presented uncertainties are also classiﬁed in this chapter. Research questions 3 and 4 is answered in this chapter.

Chapter 6: Discussion Chapter 6 discusses the limitations of the Storm Atlas and limitations of this research. Chapter 7: Conclusions and recommendations In this ﬁnal chapter, the main conclusions and answers to the research questions are formulated. Also some recommendations following from the research are given. Chapter 2

Storms, storm surges and storm surge forecasting

2.1 Introduction

Storms over the North Sea may cause high water levels, particularly at coastal boundaries, which are known as storm surges. Pugh (1987) defines the surge height as the non-tidal component of the deviation of the water level from mean sea level. This definition is complicated by the possible non-linear interactions between tides and surges. This makes it complex to distinguish a tidal and non-tidal component. Also terms as non-tidal residual, meteorological residual and set-up are used to refer to surge. In this thesis, the terms storm surge and set-up will be used. Sometimes terms like storm tide or tidal wave are used for surges, but this is not correct, as tides are driven by astronomical forcing. To understand the development of a storm surge, first the meteorological processes of the development of a storm are studied in section 2.1. Next, the effects of the storms on the hydrodynamic system are presented in section 2.2. The information presented in this chapter serves as background information for the following chapters which will discuss the North Sea Storm Surge Atlas.

2.2 The development of a storm

Storms in the North Sea region are formed at the Atlantic Ocean as a result of the collision of air masses at the polar front. The polar front separates the polar and tropical air masses. These air masses differ in temperature, density and moisture. At the polar front, small disturbances may give incipient waves in the front, which cause warm and cold fronts to develop (see figure 2.1). The cold front moves southward and the warm front goes northward. The cold air is heavier than the warm air, which causes the warm air to move up vertically. Here, the air cools down and condensation of air moist leads to precipitation. This precipitation intensifies the rising of warm air and a low pressure area develops at the surface, known as a depression (see figure 2.2). The cold front moves faster than the warm front, and moves towards the warm front. Near the depression, the front collides and a so-called occlusion front is formed (see figure 2.3). At

5 6 CHAPTER 2. STORMS, STORM SURGES AND STORM SURGE FORECASTING

(a) (b)

Figure 2.1: Stationary polar front (2.1a). Incipient wave develops from small disturbance (2.1b) (Michaelsen, 2008)

(a) (b)

Figure 2.2: Warm and cold front are developed (2.2a), depression develops. Warm air moves upward, resulting in precipitation (2.2b) (Michaelsen, 2008) 2.3. The development of a storm surge 7

(a) (b)

Figure 2.3: Cold front moves towards warm front, and near the depression an occluded front develops (2.3a). At the point where warm and cold front meet, warm air is moved upward (2.3b) (Michaelsen, 2008) this point the warm air between the two fronts will be moved upward and a fully occluded front is developed (see figure 2.4). Because the warm air moves upward, the supply of warm air to the depression is cut off and the depression will dissipate (Ackerman and Knox, 2012). The storms described here are classified as extratropical storms, meaning that they generally occur outside the tropical areas around the middle latitudes of Earth. Compared to tropical storms, the extra-tropical storms are less intense, but they spread over a larger area. Also, the changes in an extratropical storm are slower than in a tropical storm (Weather Underground, 2014). The storms are moved easterly by the (polar) jet streams. Jet streams are narrow, fast flowing air currents high in the atmosphere, which are found near the places where two air masses meet. Typically two jet streams are found in each Hemisphere, i.e. the polar jet (near the polar front) and the sub-tropical jet (see figure 2.5). The jet streams are caused by a combination of the earth’s rotation and atmospheric heating by solar radiation. The Coriolis effect makes the jet streams move easterly. Atmospheric pressure gradients cause the air to start moving. In a frictionless situation, the forces due to pressure gradients are balanced by the Coriolis force. Because of this balance, winds will be generated along the isobars in counter-clockwise direction (in the Northern Hemisphere). Due to friction, the winds will deflect slightly towards the center of the depression (Proudman, 1953). These winds are called gradient winds. Figure 2.6 shows an example of a pressure field over the North Sea. The shown pressure field belongs to the storm of 1953. In this situation, because of the high pressure gradient at the western side of the depression, strong winds towards The Netherlands were generated, resulting in a high storm surge at the Dutch coast.

2.3 The development of a storm surge

Storms over the North Sea have eﬀects on the water levels and cause storm surges. According to Pugh (1987), the main drivers of a storm surge are the wind and air pressure. The combination of these drivers determines the set-up along the coast. 8 CHAPTER 2. STORMS, STORM SURGES AND STORM SURGE FORECASTING

(a) (b)

Figure 2.4: Occluded front is fully developed (2.4a). Warm air is moved upward and the supply of warm air to the depression is cut oﬀ (2.4b) (Michaelsen, 2008)

Figure 2.5: Schematization of jet streams (Wikipedia, 2008) 2.4. Current storm surge forecasting 9

Figure 2.6: Pressure ﬁeld of 1 February 1953 over the North Sea. The dotted line shows the track of the depression (Pugh, 1987)

The gradient winds, as describes in section 2.2, blow over the water surface and set the water into motion. In shallower regions, the water piles up, resulting in a high setup at the closed boundaries of the system (the coast) (National Weather Service, 2008). Gradient winds are parallel to the isobars of the pressure field. When the path of a storm is directed more to the south, the winds have more dominant north-south component at the North Sea, resulting in a high storm surge in the southern part of the North Sea, see figure 2.6. Figure 2.7 shows the pressure field of a storm in 1981, resulting in an extreme water level in Esbjerg, Denmark. Because of the more northern path of the storm, the gradient winds are more westerly, giving high surges at the eastern part of the North Sea basin. Another characteristic of a storm is low air pressure, which causes the water level to rise. This is the so-called inverted barometer effect (Proudman, 1953). For every mbar the air pressure lowers, the water will rise 1 cm. The North Sea storm of 1953 had a pressure center of 964 mbar MetOffice (2014). Compared to atmospheric pressure, this gives an inverted barometer effect of up to 0.5 meter. Note that the locations of the set-up due to winds and set-up due to the inverted barometer effect are not the same. The highest set-up due to the inverted barometer effect will occur at the pressure center, whereas the strongest winds occur at the largest pressure gradients. In figure 2.6 the set-up due to the barometric effect occurs near Denmark, whereas the highest set-up due to wind occurs in the southern part of the Netherlands.

2.4 Current storm surge forecasting

In the current situation, real-time modeling is used for the forecasting of storm surges at the North Sea coast. In the Netherlands WAQUA-in-Simona/DCSM98 is used for these calculations. Other countries use diﬀerent models, e.g. POLCOMS in the United Kingdom and OPTOS in Belgium. These numerical hydrodynamic models use a weather forecast as input and solve the 10 CHAPTER 2. STORMS, STORM SURGES AND STORM SURGE FORECASTING

Figure 2.7: Pressure ﬁeld of 24 November 1981 over the North Sea, resulting in an extreme water level in Esbjerg, Denmark. The dotted line shows the track of the depression (Lamb, 1991).

Navier-Stokes equations in order to forecast the eﬀect on the water levels. Detailed numerical modeling is computationally intensive and therefore computation times can be high, in the order of hours. In The Netherlands, a distinction is made between short-range (48 hours ahead) and medium- range forecasts (48 - 240 hours ahead) (De Vries, 2011). For the short-range, a deterministic approach is used for forecasting the water levels at a high resolution. To increase the performance, a Kalman-ﬁlter is used for real-time data assimilation of sea level observations. For the medium-range, a probabilistic approach is used. An ensemble of weather forecasts of the ECMWF Ensemble Prediction System is used as input for WAQUA. The outcomes are transformed into water level probabilities as a function of location and time. Figure 2.8 shows an example of such an ensemble forecast and corresponding probabilities at the high and low tidal peaks. It is clearly seen that further in the future, the uncertainty grows and the water level probabilities are more spread. 2.4. Current storm surge forecasting 11

Figure 2.8: Ensemble forecast for Hoek van Holland made by KNMI for June 2009. For the low and high waters, probability distributions are shown. 12 CHAPTER 2. STORMS, STORM SURGES AND STORM SURGE FORECASTING Chapter 3

The North Sea Storm Surge Atlas

3.1 Introduction

The idea of developing a Storm Atlas for the North Sea followed from the work of Royal Haskon- ingDHV in New Orleans after hurricane Katrina. As a part of this work, a Hurricane Surge Atlas was developed. The Hurricane Surge Atlas consists of over 300 hypothetical hurricanes. The hydrodynamic effects of these hurricanes were pre-calculated with a numerical hydro-dynamical model (ADCIRC SL15). Because of their relatively clear meteorological structure (compared to extratropical storms), these storms can be parameterized relatively easily by location of landfall, center air pressure, size (diameter) and wind speeds. Based on this parameterization, a forecasted storm can be compared to the storms in the database and the best look-a-like is selected (Kluskens and Van Ledden, 2009). In the North Sea area, we cope with extra-tropical storms, which are more complex. The main assumption in the North Sea Storm Surge Atlas is that the pressure fields in a weather forecast are a good predictor of the storm surge. The winds are directly caused by air pressure gradients and winds and (low) air pressure are the main drivers of a storm surge. Because of this assumption, the Storm Atlas is based on a large offline library of predefined and pre-calculated storms. Using smart algorithms to link the current weather forecast to the pre-calculated weather in the database makes the time consuming real-time numerical calculations obsolete. This way we can reduce the calculation times drastically. This chapter describes the concept of the North Sea Storm Surge Atlas, which consists of two major parts: First there is the offline part of building the library. Section 3.2 explains the calculations of the storm surge and section 3.3 explains a smart and efficient way of describing the pressure fields, which is used for easy calculation. Next, two possible methods are presented to make a storm surge forecast. The first method focuses on finding the best match between the pressure fields in the weather forecast and the pressure fields in database (section 3.4). When the best match is found, it is assumed that the pre-calculated storm surge can be used as a forecast of the storm surge corresponding to the weather forecast. This method is referred to as the resampling method, or method A. The second method is based on a linear regression (section 3.5). This method assumes a direct relation between the spatial structures in the pressure fields and the occurring storm surge. For this relation, regression coefficients are extracted from the database and used to forecast a storm surge for the current weather forecast. This method is referred to as the regression method, or method B.

13 14 CHAPTER 3. THE NORTH SEA STORM SURGE ATLAS

3.2 Building the database of pre-calculated storm surges

For the Storm Atlas, it is important to build a database which is large enough, especially with regard to the number of extreme events (storms). If only the available historic measurements would be used, the number of events available will be limited. Therefore, to build a large database, the Storm Atlas uses weather scenarios. The long-term weather scenarios are retrieved from the European Centre for Medium-Range Weather Forecasts (ECMWF). The ECMWF is an independent intergovernmental organization, which provides (amongst others) weather forecasts for the medium range (10 days) and for the long-term (7 months) (ECMWF, 2014). ERA-interim is a global climate reanalysis from ECMWF. The dataset is based on a 2006 version of the IFS model, consisting of seasonal weather forecasts for 7 months ahead. Based on hindcasting, the dataset is available from 1979 onwards, and is continuously extended. At the beginning of every month an ensemble of long term forecasts is available (Dee et al., 2011). These data consist of pressure fields and wind fields with 6-hourly resolution, which can be used, for example, to forecast an El Niñoin tropical areas. However, in a climate as around the North Sea, hardly any skill can be detected in the ensemble of forecasts. Initial conditions may give a skill in the first forecasted month, but after that these long-term forecasts cannot be interpreted as reliable forecasts of the upcoming weather. However, they can still be interpreted as weather scenarios (a possible future), which we will use as realistic weather scenarios in the Storm Atlas. The current operational Storm Atlas uses about 1200 scenarios, each with a length of 7 months, adding up to 700 years of weather scenario. At this moment, not the entire ERA- interim database is used, in order to limit computation times in the building of the database. The database can be extended to 4000 years of weather scenarios1. It is assumed that the selected weather scenarios contain enough events. Figure 3.1 presents the number available events at Hoek van Holland. It shows that there are not a lot of extreme events available, but for less extreme events, there are numerous events available. For example, the storm in November 2006 had a maximum storm surge of about 1.5 meter, for which about 500 events are available in the database. The wind and pressure fields of the weather scenarios are used to forecast the storm surge. For this calculation WAQUA-in-Simona/DCSM98 (Dutch Continental Shelf Model) is used. This is a state-of-the-art model from Rijkswaterstaat. This model is also used by KNMI for day-to-day forecasts of the water levels along the Dutch coast (Grinten et al., 2012). These calculations are made without the tidal signal. This means that tide-surge interactions are not taken into account. The calculated storm surges for 37 coastal locations around the North Sea are archived in the database. The storm surge predictions have an hourly resolution. The result is a database with 700 years of pressure fields coupled to WAQUA surge calculations for 37 coastal stations. For an efficient description of the pressure fields, an EOF analysis is used (section 3.3).

1The data from January 1981 till August 2012 is available. In this period, every month an ensemble of 15 forecasts with a length of 7 months is made. In the period May 2011 till April 2012, an ensemble of 51 predictions is available. This amounts to about 7000 available weather scenarios with each a length of 7 months. The scenarios have a 6-hourly resolution. Assuming that these scenarios are independent, the total time period of the dataset is about 4000 years. The assumption that the scenarios are independent and thus represent a long period, implies that the models used for forecasting these scenarios are able to reproduce the current climate variability, that the current climate is stationary, and that the physical relations implemented in the models are valid in extreme situations (Caires et al., 2014). 3.2. Building the database of pre-calculated storm surges 15

103

102

101 Number of available surges

100 3.0 > 1.4 - 1.6 1.8 - 2.0 2.0 - 2.2 2.2 - 2.4 2.4 - 2.6 2.6 - 2.8 2.8 - 3.0 1.6 - 1.8

Height of surge peak [m]

Figure 3.1: Number of available surges in database at Hoek van Holland with a peak height. The storm surges will give extreme water levels in combination with the tidal signal. The height of the water level depends on the coincidence of the surge and tide. Therefore no exceedance frequencies of the storm surges can be given. In 1953 the storm surge was approximately 3 meters at Hoek van Holland. 16 CHAPTER 3. THE NORTH SEA STORM SURGE ATLAS

3.3 Description of pressure ﬁelds by EOF analysis

As described in chapter 2, we are especially interested in the air pressure and pressure gradients. The gradients in the air pressure cause winds, which are (combined with the air pressure itself) the main driver of storm surges. In the database of the Storm Atlas, pressure fields are used. The pressure gradients are indirectly taken into account by the spatial pressure differences. With the chosen area boundaries, every pressure field is described with over 2000 grid points. For computational reasons, we use a smart and efficient algorithm to describe the pressure fields. In the Storm Atlas, an empirical orthogonal function analysis (EOF analysis) is used to describe the pressure fields. An EOF analysis seeks structures that explain the maximum amount of variance in a dataset, consisting of a time series of gridded data at P points and N timesteps (Lorenz, 1956). The EOF analysis decomposes a dataset X(t, s), where X is a matrix consisting of air pressure anomalies and t and s give the time and spatial position as:

M X X(t, s) = ck(t)uk(s) (3.1) k=1 where M is the number of modes in the field, using a set of spatial functions (spatial patterns) uk(s) and time coefficients ck(t). Often a limited number of modes can be used to describe almost all variance in the dataset. Following Hannachi et al. (2007), we will use the term ‘EOFs’ or ‘eigenvectors’ for the spatial patterns and the term ‘principal components’ (or short PCs) for the time coefficients in this thesis2. Note that the EOF analysis only decomposes the data, so it is basically a different way of presenting the same data. In practice, an EOF analysis is used to find a limited number of spatial patterns and time series that capture most of the variance in dataset, in order to reduce the number of variables. In the Storm Atlas, the EOFs have been derived from a subset of the ECMWF dataset. These EOFs describe patterns of variability with respect to the climatology in the dataset. The EOFs are ranked such that the first EOF explains most of the variance, followed by the second and so on. Figure 3.2 shows the first four EOFs. Each of these EOFs has an eigenvalue, which is a measure for the explained variance in the data by this EOF. The EOFs are ranked in order of decreasing eigenvalues, which means that the first EOFs explain most of the variance. Figure 3.3 shows the eigenvalues of the first 50 eigenvalues. Because many of the EOFs have only very low eigenvalues, we only have to use a limited number of EOFs to explain most of the variance. Using 50 EOFs, we can explain over 99.9 % of all variance in the dataset where the EOFs are extracted from. Any pressure field can now be projected onto the EOFs. These are the principal components of the pressure field. Thus, if there are K EOFs defined, there are also K principal components per pressure field. Also, if there is a time series of n pressure fields, every EOF has a time series of principal components with n elements. The k’th PC, corresponding to the k’th EOF at time

2The terminology in EOF analysis differs quite a lot (Björnssonand Venegas, 1997). In geophysics, the method is better known as a geographically weighed principal component analysis (PCA) and because of the link with PCA sometimes terms are mixed up, while meaning the same thing. Thus, it is important to make clear which terminology will be used in this thesis. The spatial patterns (uk(s)) are sometimes called the ‘EOFs’, ‘eigenvectors’, ‘principal component loadings’, or just ‘principal components (PCs)’. The time series (ck(t)) are called ‘EOF time series’, ‘EOF weightings’, ‘expansion coefficients’, ‘principal component time series’, ‘principal component scores’, or just ‘principal components (PCs)’. 3.3. Description of pressure fields by EOF analysis 17

Figure 3.2: The derived ﬁrst four EOF eigenvectors. The eigenvectors are derived from a subset of the ERA-interim dataset. In this subset, the ﬁrst EOF explains approximately 60% of all variance, the second EOF accounts for 30%, the third 6% and the fourth EOF explains approximately 2%. 18 CHAPTER 3. THE NORTH SEA STORM SURGE ATLAS

20 Explained variance (%)

0 0 5 10 15 20 25 30 35 40 45 50 EOF eigenvector

Figure 3.3: Eigenvalues of the first 50 eigenvectors (in order of decreasing eigenvalues) t is given by: P X ctk = xtjukj (3.2) j=1 where ctk is the principal component of k’th EOF ukj and xtj is the anomaly of the air pressure at time t and grid point j. All pressure fields which are used to build the database (section 3.2) are decomposed using the derived EOFs. The resulting principal components are also stored in the database, linked to the surge calculations. In the current operational version of the North Sea Storm Surge Atlas, 50 EOFs are used to describe the pressure fields. Using the EOF analysis, we are able to reduce the pressure fields data from values at over 2000 grid points to only 50 principal components. Because all pressure fields are projected on the same EOFs, the values of principal components can be compared. A more detailed description of the EOF analysis is given in Appendix A.

3.4 Method A - resampling from database

The first method is based on resampling a surge forecast from the database, by finding the best matching pressure field. This method can be seen as a sort of look-up table. The operational version of the Storm Atlas is based on this method. Figure 3.4 shows a schematic overview of method A - resampling.

3.4.1 Input data

In the operational Storm Atlas, NOAA weather forecasts are used as input data. These weather forecasts consist of an ensemble of 20 possible weather conditions, which are calculated on a 1 degree grid. Also, there is a more accurate weather forecast available at a grid resolution of 0.5 3.4. Method A - resampling from database 19

Figure 3.4: Flow diagram of Storm Atlas method A - resampling 20 CHAPTER 3. THE NORTH SEA STORM SURGE ATLAS degrees. The 6-hourly pressure fields from these weather forecasts are preprocessed and projected on the EOF eigenvectors (as in section 3.3), to find the principal components. These principal components are used for the comparison of the forecasted pressure fields and the pressure fields in the database.

3.4.2 Matching

In Storm Atlas method A, it is assumed that if a pressure field of the weather forecast resem- bles a pressure field in the database, the storm surge corresponding to weather forecast can be approximated by the pre-calculated storm surge from the database. Therefore we want to look into the database for the best match between the pressure fields from the weather forecast and the pressure fields from the weather scenarios. However, one can imagine that the development of the storm in time is also important for the development of the storm surge, rather than just one forecasted pressure field at a certain moment in time. For this reason, also some history of the storm is taken into account, by matching not just one pressure field, but three consecutive forecasted pressure fields, with three consecutive pressure fields in the database. The differences between the values of the principal components of the first 50 EOFs of three forecasted pressure fields and the principal components of any three consecutive pressure fields in the database are squared and summed. Thus, the distance D between a forecasted pressure field at time t and a pressure field at time T in the database is calculated as:

2 50 2 X X h database forecast i D(t, T ) = Wd PC (T d∆t) PC (t d∆t) (3.3) k − − k − d=0 k=1 in which PC is the principal component of the k-th EOF. We sum over 50 EOFs and over 3 timesteps: t = 0, t = 6 and t = 12 hours (∆t = 6hours and d = 0, 1, 2 respectively). Wd − − − is the weight of each timestep. The weights are set as W0 = W1 = 1 and W2 = 0.5. Next, the best match is defined as the pressure field with the principal components PCdatabase for which D is minimum. Note that one match is made for the entire North Sea. The location of interest (e.g. Hoek van Holland or Aberdeen) does not influence the matching procedure. The surges for the different locations are read from the matched timestep in the database.

3.4.3 Surge forecasting

When the best match between the forecasted pressure fields and the pressure fields in the database is found, the pre-calculated surges are used as pre-diction for the surge level for the next 6 hours. The surge predictions for all pressure fields in the 10-day weather forecast are concatenated to one surge prediction for the next 10 days, with hourly resolution. It should be noted that the surge predictions may have discontinuities, caused by the matching principle. The resampled storm surge basically consists of consecutive 6-hourly pieces of surge. When 2 sequential pressure fields in the weather forecast do not match to 2 sequential pressure fields in the database, the surge predictions may not be continuous. Of course, physi- cally it is not possible for a storm surge to have a sudden jump is surge level and thus the surge prediction should have no discontinuities. To tackle this problem a smoothening technique is applied based on an exponential function. With this function, the first 5 hours of storm surge of 3.4. Method A - resampling from database 21 each resampled pressure field are corrected, such that the discontinuities are reduced and a more smooth development of the storm surge arises. Figure 3.5 shows an example of the smoothening function. 22 CHAPTER 3. THE NORTH SEA STORM SURGE ATLAS

1.2 Resampled storm surge 1 Smoothened storm surge

0.8

0.6 Jump 0.4 Surge [m]

0.2

0.2 − 6 4 2 0 2 4 6 8 10 − − − time [hours]

Figure 3.5: Schematic representation of the eﬀect of the smoothening function. The hours 0,..., 5 are corrected, such that the jump between 0 and 1 hour is reduced. − 3.5. Method B - multiple linear regression 23

3 Simulated water level Simulated storm surge 2 Tide

0 Water level [m + MSL]

1 −12/20 12/20 12/21 12/21 12/22 12/22 12/23 12/23 Date in 2003 (month/day)

Figure 3.6: Simulated storm surge at Hoek van Holland in December 2003 by Storm Atlas method A - resampling

3.4.4 Example

Figure 3.6 shows an example of a simulated storm. In this ﬁgure, the storm of December 2003 is shown for location Hoek van Holland. The simulated storm surge is added to the astronomical tidal signal, resulting in a simulated water level. At some points a sudden change in the slope (the development) of the storm surge. This indicates that the resampled storm surge originates from a diﬀerent location in the database and a discontinuity occurred (as described in section 3.4.3). The jump in this discontinuity was corrected, but results in a sudden change of slope.

3.5 Method B - multiple linear regression

Method B uses a multiple linear regression to forecast the water levels at the coastal stations. At a predefined location of interest (e.g. Hoek van Holland or Aberdeen) the relative contribution of each EOF eigenvector to the storm surge (modeled by WAQUA) is examined. The relative contributions of the eigenvectors are expressed in regression coefficients, which are based on the correlation of surge levels and EOF eigenvalues. As in method A, the Storm Atlas uses an offline and a real-time part. In the offline part, the EOF eigenvectors, eigenvalues and regression coefficients are determined (section 3.5.1), which are used in the real-time part to forecast the storm surge (section 3.5.2). Figure 3.7 shows a schematic overview of method B - regression. 24 CHAPTER 3. THE NORTH SEA STORM SURGE ATLAS

Figure 3.7: Flow diagram of Storm Atlas method B - regression 3.5. Method B - multiple linear regression 25

3.5.1 Regression coeﬃcients

The regression coefficients represent the contribution of the eigenvalue of each EOF-eigenvector to the storm surge at the predefined location. The regression coefficients are derived from the database with pre-calculated storms. For this calculation, also the two previous timesteps (t = 6 hours and t = 12 hours) are taken into account. The number of EOF eigenvectors that are− taken into account− is set to 50. Equation 3.4 gives the regression model used for this analysis:

2 X h i ζ(t) = β (d)PC (t d∆t) + β (d)PC (t d∆t) + + β (d)PC (t d∆t) + (3.4) 1 1 − 2 2 − ··· 50 50 − d=0 which states that the surge ζ is a function of the regression coeﬃcients β and principal components PC, with a error term .

3.5.2 Surge forecasting

When the regression coefficients of the locations of interest are known, the storm surge forecast can be made using pressure fields from the weather forecast. As in method A, the weather forecast from NOAA or the weather forecast from ECMWF can be used. These pressure fields are decomposed into EOF eigenvalues using the EOF eigenvectors as obtained in section 3.3. By multiplying the regression coefficients with the EOF eigenvalues of the forecasts, we find the surge prediction corresponding to the forecasted pressure field. This multiplication is done for every pressure field of the 10-day forecast, resulting in a 10-day surge level prediction. The storm surge is thus calculated as:

2 50 X X h i ζi(t) = βi,k(∆)PCk(t ∆) (3.5) − ∆=0 k=1 where ζ is the surge level at station i along the North Sea coast, PC is the principal component of the kth EOF eigenvector at timestep t ∆ and β is the regression coeﬃcient of the surge at location i for the kth eigenvector and ∆th−timestep in respect to t. Because the pressure ﬁelds have a six hour resolution, the surge also has a six hour resolution. A cubic spline is used to interpolate the values onto a time grid with a one hour resolution.

3.5.3 Example

Figure 3.8 shows the simulated water level, consisting of a simulated storm surge and a tidal signal. We see initially a negative surge, resulting in a small set-down, but after that a high surge builds up, coinciding with high tide, resulting in a simulated water level of almost 3 meters above mean sea level. Because of the use of the cubic spline, we see a more smoothly development of the storm surge compared to figure 3.6. Finally, figure 3.9 shows the relative contribution of the different EOFs to the peak storm surge of 2003 at Hoek van Holland. These are the regression coefficients multiplied with the principal component of the 50 EOFs in the three timesteps (t = 0, t = 6 hours and t = 12 hours). When we look at the influence of e.g. the third EOF at Hoek van− Holland (figure 3.9),− we can see that the storm surge is quite strongly influenced by both t = 0 and t = 6 hours. In − 26 CHAPTER 3. THE NORTH SEA STORM SURGE ATLAS

3 Simulated water level Simulated storm surge 2 Tide

0 Water level [m + MSL]

1 −12/20 12/20 12/21 12/21 12/22 12/22 12/23 12/23 Date in 2003 (month/day)

Figure 3.8: Simulated storm surge at Hoek van Holland in December 2003 by Storm Atlas method B - regression the case of the second EOF, the influence of six hours before is even stronger than the influence at that time. This can be explained by the response time of the North Sea basin. It takes time for a surge to build up and travel towards the coast (Hoek van Holland in this case). We can also see that the influence of the timestep t = 12 hours is relatively small for most EOFs, except for the second EOF. − 3.5. Method B - multiple linear regression 27

t = 0 t = -6 hours 40 t = -12 hours

0 Relative contribution to surge [%]

0 5 10 15 20 25 30 35 40 45 50 EOF

Figure 3.9: Relative contribution of the EOFs to the peak storm surge of the 2003 storm at Hoek van Holland. Equation 3.5 shows that the storm surge is a summation of the contributions of 50 EOFs over 3 timesteps. Negative values indicate a counter eﬀect on the storm surge, resulting a lowering of the surge level. 28 CHAPTER 3. THE NORTH SEA STORM SURGE ATLAS Chapter 4

Storm Atlas performance

4.1 Introduction

In this chapter the performance of the North Sea Storm Surge Atlas is examined. This performance is measured by hindcasting historical storm events and comparing the modeled water levels with observed water levels. The first step is to define specific performance indicators (section 4.2). Next, historical storms are selected and a selection of the output locations is made (sections 4.3 and 4.4). For the hindcasting of the storms, input data for the Storm Atlas is needed, which consist of pressure fields over the North Sea and a tidal signal. Also data from observed water levels are retrieved (section 4.5). Both methods described in chapter 3, are validated in section 4.6.

4.2 Performance indicators

To measure the performance of the Storm Atlas for the North Sea, indicators are needed to express the performance in quantitative way. These indicators have to represent the goal of the Storm Atlas. It is envisioned that the Storm Atlas is applied in decision-making during storm events. In these events, critical aspects of the storm are the peak water levels which are an indication of the severity of the loading for the ﬂood defense system. Also, the timing and duration of the loading are important aspects. Hence, the following parameters have been selected as performance indicators:

Peak water level The comparison between the predicted peak water level and the observed peak water level gives information on the accuracy of the Storm Atlas to predict maximum water level. Every storm has a different peak water level for a certain location and also every location has a different peak water level for a certain storm. To make a comparison the peak water level difference is calculated as the simulated peak water level minus the observed peak water level. Positive values mean that the simulated water levels are higher than observed, negative values are an underprediction of the peaks. Duration The duration of the surge is also important as an indicator for the duration of e.g. the loads

29 30 CHAPTER 4. STORM ATLAS PERFORMANCE

on hydraulic structures. In this research, the duration of the storm surge is expressed as the time that the water level is above a certain threshold. Following Van den Berg (2013), this threshold is set at 75% of the maximum observed water level. As for the peak water level, to make a comparison between the different locations and storms, the difference in duration between simulated duration and observed duration are calculated. Timing of the peak water level The timing of the peak water level is defined as the moment in time when the peak water level occurs. The timing of the peak water level is an indicator of the timing of the storm surge. The timing of the storm surge is important for the coincidence with the tidal signal. If the timing of the peak surge differs e.g. three hours, it may result in a higher or lower water level. The peak surge level does not have to be equal to the peak water level. Due to the tidal signal, it is possible for the timing of the peak water level to ‘jump’ to another tidal peak, when observed and simulated peak water level are not found in the tidal peak. To make a comparison between the different locations and storms, the difference in duration between simulated duration and observed duration are calculated. Computation time Besides the aspect of the storm surges, also other aspects are important. One of the purposes of the Storm Atlas is to make quick assessments of storm surge predictions. The extent to which a model is quick can be defined as the needed computational times. Thus, we have added computation time as an additional performance indicator. As this will be influenced by the computational power of the computer used to make the calculations, the calculation time is given qualitatively.

Figure 4.1 shows a representation of the peak water level diﬀerence and diﬀerence in timing of the peak water level. The duration is not shown. The performance indicators will be expressed as the root mean squared error (RMSE), bias and standard deviation. The RMSE is a measure of the total error. The RMSE can be decomposed into a bias and a standard deviation. The bias is a measure for the systematic error. The standard deviation indicates the random error. The ISO standard 5725 characterizes the performance in terms of accuracy, trueness and precision for respectively the total error, systematic error and random error. Figure 4.2 gives a overview of these relations, according to Menditto et al. (2007). 4.2. Performance indicators 31

3 Obs. peak water level Peak water level diﬀerence

2 Sim. peak water level

Water level (m) 0 Timing diﬀerence

1 − Observed water level Simulated water level

11/08 11/08 11/09 11/09 11/10 11/10 11/11 11/11 Date in 2007 (month/day) (a) Peak water level and timing of peak water level

Obs. peak water level 2 Storm duration 75 percent of obs. peak water level

Water level (m) 0

1 − Observed water level Simulated water level

02/29 02/29 03/01 03/01 03/02 03/02 03/03 03/03 Date in 2008 (month/day) (b) Storm duration

Figure 4.1: Schematic overview of performance indicators in water levels during a storm in November 2006 32 CHAPTER 4. STORM ATLAS PERFORMANCE

Figure 4.2: Overview of total error, systematic error and random error (Menditto et al., 2007)

4.3 Selection of locations

The Storm Atlas aims to predict storm surges at different locations in the North Sea area. Therefore the performance of the Storm Atlas has to be assessed at different locations along the North Sea coast. In this study different locations along the North Sea coast will be taken into account. The Norwegian North Sea coast is excluded, as the Storm Atlas does not generate output here. The following 11 stations have been selected for the performance assessment:

1. Aberdeen 2. North Shields 3. Immingham 4. Lowestoft 5. Southend on Sea / Sheerness 6. Dover 7. Vlissingen 8. Hoek van Holland 9. IJmuiden 10. Den Helder 11. Delfzijl

The selected locations are shown in Figure 4.3. It shows the distribution of the locations along the North Sea coast. The stations are chosen such that there is a quite an equal distribution along the North Sea coast. From historical perspective it is known that the prediction of storm surges in the southern part of the North Sea is more diﬃcult. Therefore, in this part more stations are taken into account. Unfortunately, no time-series of observed water levels are available for the Belgian, German and Danish coastal stations for which the Storm Atlas also generates output. 4.3. Selection of locations 33

Figure 4.3: Overview of selected locations for performance assessment 34 CHAPTER 4. STORM ATLAS PERFORMANCE

4.4 Selection of historical storms

For the validation of the two methods of the North Sea Storm Surge Atlas, a list of historical storms has been reviewed. The initial selection of storms is based on the storms used in the research of De Jong (2012) and Van den Berg (2013). However, for this research, the selection of storms is further bounded by the availability of pressure fields as input data. The input data is only available from 1979 till now. The famous storm from 1953 is therefore not taken into account. The selection of storms is extended using the storm catalog from the KNMI Hydra Project (KNMI, 2013). Furthermore, the storms for which Rijkswaterstaat has made storm surge reports are added Rijkswaterstaat (2014). After every storm, the event is classified by Rijkswaterstaat, based the observed water levels and their exceedance probabilities. For this research the storms with classification ‘intermediate storm surge’, which is used for the heaviest storms in our storm selection. For the Dutch stations, these storms caused water levels with an exceedance frequency of 10−1–10−2 year−1. The selected storms are shown in table 4.1.

4.5 Data selection

4.5.1 Pressure ﬁelds

In this research, we want to validate the methodology of the Storm Atlas. Ideally, the hindcasting of observed weather would generate a storm surge forecast equal to the observed storm surge. The deviations due to uncertainty in the weather forecasts is outside the scope of this research. For the hindcasting of the historic storms, pressure ﬁelds of the ERA-interim database of the European Center for Medium-Range Weather Forecasts (ECMWF) are used. ERA-interim is a project for global climate re-analysis. The values of the ERA-interim dataset are assumed to be the observed pressure ﬁelds. The ERA-interim data covers the period from 1979 till now and have a 6-hourly resolution (Dee et al., 2011).

4.5.2 Historical water levels

For the historical water levels along the Dutch coast, the database of Rijkswaterstaat is used. For the selected storms a period of 8 days around the storm is selected. This data has its reference level at NAP, the Dutch ordnance datum. The output of the Storm Atlas gives water levels with mean sea level as reference level. Kwanten (2006) provides the diﬀerences between these reference levels. The data for the stations along the coast of the United Kindom is provided by the British Oceanographic Data Centre (BODC). This data uses UK Admiralty Chart Datum as reference levels, which is roughly equal to the lowest astronomical tide (LAT), rather than mean sea level, which is used as a reference level in the Storm Atlas. For the conversion from Admiralty Chart Datum to ordnance datum (O.D. Newlyn) are given by the National Tidal and Sea Level Facility of the National Oceanographic Centre (National Oceanographic Centre, 2014). The Permanent Service for Mean Sea Level (PSMSL) gives information on the conversion of O.D. Newlyn to Revised Reference Level (RLR) and from there to mean sea level (PSMSL, 2014). For Hoek van Holland, also a simulation from WAQUA is available. For this simulation, the input data comes from the same dataset as the pressure ﬁelds used in this study. This makes is possible to make a comparison in model context for Hoek van Holland. 4.5. Data selection 35

Table 4.1: Overview of selected storms for validation

Classiﬁcation Number Date Notes by Rijkswaterstaat No observed data for Aberdeen, 1 14-02-1979 IJmuiden and Southend on Sea 2 01-02-1983 3 27-11-1983 No observed data for North Shields 4 14-02-1989 low storm surge No observed data for Dover 5 26-01-1990 intermediate storm surge 6 28-02-1990 low storm surge 7 12-12-1990 low storm surge 8 20-12-1991 low storm surge 9 11-11-1992 low storm surge 10 23-01-1993 low storm surge 11 21-02-1993 low storm surge 12 14-11-1993 intermediate storm surge No observed data for Aberdeen 13 19-12-1993 low storm surge 14 28-01-1994 intermediate storm surge No observed data for Aberdeen 15 13-03-1994 low storm surge 16 01-01-1995 low storm surge 17 10-01-1995 low storm surge 18 29-08-1996 low storm surge 19 29-10-1996 low storm surge 20 05-08-1999 low storm surge 21 06-11-1999 low storm surge 22 03-12-1999 low storm surge No observed data for Aberdeen 23 29-01-2000 low storm surge 24 27-10-2002 low storm surge 25 21-12-2003 low storm surge 26 31-10-2006 intermediate storm surge 27 11-01-2007 low storm surge 28 18-01-2007 low storm surge No observed data for Dover 29 18-03-2007 low storm surge 30 09-11-2007 intermediate storm surge 31 01-03-2008 low storm surge 32 21-03-2008 low storm surge 33 06-12-2013 intermediate storm surge No observed data for Southend on Sea 36 CHAPTER 4. STORM ATLAS PERFORMANCE

4.5.3 Tidal data

To compare the predicted storm surge by the Storm Atlas and the occurred storm surge from the historical data, we need to subtract the tidal signal from the historical data. To this end, the datasets in DelftDashboard, part of OpenEarthTools, are used (Deltares, 2008). In DelftDash- board there are two databases available, the tidal stations by the International Hydrographic Organization and the tidal stations of XTide. For the stations along the Dutch coast, also tidal predictions by Rijkswaterstaat are available, but this database is only available for 2013 and 2014 (Rijkswaterstaat). A comparison between the data from IHO and XTide is made in Appendix B. We choose to use the IHO database, because of the availability and the use of this database in the current operation version of the Storm Atlas.

4.6 Validation

The selected storms are hindcasted using both Storm Atlas methods. For the resampling method, an improved version of the Storm Atlas is used, as described in appendix C. Figure 4.4 gives two examples of resampled storms. In this figure, the simulated water level (consisting of the simulated storm surge and the tidal signal) is shown, together with the observed water level. These figures can be made for all storms at all locations, for both methods. From figure 4.4, we can already see that some storms are resampled fairly well and some storms are not. In appendix D graphs for all storms at Hoek van Holland can be found, for both methods. In this section, first method A (resampling) will be validated, using the defined indicators. Next, the regression method will be validated. We choose to use boxplots to show the results of the validation, because it also gives a representation of the variability in the results. For all three performance indicators, the boxplots are made. These boxplots show results of all storms per location and for all locations per storm. The box shows the 25-th and 75-th percentile, with the red line showing the 50-th percentile (the median). The whiskers show the outer values within 1.5 IQR (interquartile range, which is the distance between the 25-th and 75-th quartile). Outliers× are defined as values outside 1.5 IQR and shown by the red plus signs. This is schematized in figure 4.5. ×

4.6.1 Method A - resampling

First the resampling method is validated, which is based on finding a resembling storm in the database. Figures 4.8 and 4.9 show the results of this validation as boxplots for respectively the performance per location and per storm. Appendix D shows graphs of all resampled storms at Hoek van Holland, with the observed water levels. Also, WAQUA is used to make a storm surge prediction for all storms. The ERA-interim pressure fields which are used as input for the Storm Atlas, are also used as input for these calculations. For these calculations only results at Hoek van Holland are available. The results from the WAQUA calculations are also shown in the graphs of appendix D. The first performance indicator is the peak water level. Figure 4.8a shows the performance at the different locations along the North Sea coast. We see that on average, the simulated peak water levels are too low. Notable is that the performance in the southern part of the North Sea (i.e. stations Dover, Vlissingen, Hoek van Holland) perform slightly better than the other locations, whereas from historical perspective the southern North Sea is more difficult to model. We also see a clear outlier at Delfzijl, which is the storm in 2006, which is underestimated by 4.6. Validation 37

Observed water level 2 Simulated water level Simulated storm surge Tide

Water level (m) 0

1 −10/29 10/30 10/30 10/31 10/31 11/01 11/01 11/02 11/02 Date in 2006 (month/day) 105 · (a)

Observed water level 2 Simulated water level Simulated storm surge Tide

Water level (m) 0

1 −02/28 02/29 02/29 03/01 03/01 03/02 03/02 03/03 03/03 Date in 2008 (month/day) 105 · (b)

Figure 4.4: Hindcasted storms of 2006 and 2008, using the resampling method of the Storm Atlas 38 CHAPTER 4. STORM ATLAS PERFORMANCE

Figure 4.5: Overview of selected locations for performance assessment far. Figure 4.9a shows the performance of each storm. The figure shows that most storms are underestimated, which was already known from the validation per station. A few storms are remarkable. Storms 14 (in January 1994) gives on average an overestimation of the storm surge. The water level of storm 15 (March 1994) is slightly underestimated by most storms, but there are also quite some locations with a large overestimation. Storms 22 (in 2006) and 26 (in November 2007) both show a remarkably large underestimation for all stations along the North Sea coast. All three storms are classified as intermediate storm surges, which may suggest that the Storm Atlas is having difficulties in simulating stronger storms. The next performance indicator is the duration. For this indicator, we look at the time that the water level is above 75% of the peak water level. Figures 4.8b and 4.9b show boxplots of the duration per station and per storm. We see that the duration of the simulated storm water level is quite similar to the observed duration, although there also quite some simulations where the simulated duration is less than observed. It has to be noted that the duration of the high water levels is also greatly influenced by the tidal signal. Especially at locations with a high tidal range, the tidal signal will cause the water level to drop below the 75% threshold, with the result that the duration of the storm water level will not exceed the tidal cycle. Also, due to the hourly resolution of the data, the exceedance of the 75% is quite coarse. When we compare the performance on peak water level and storm duration, we see that both the peak water level and the duration are underestimated. For storm 8 we see that both are overestimated. This indicated that the Storm Atlas not only the peak is flattened, but the entire course of the storm surge is underestimated. Next, we look at the timing of the peak water level. For this analysis the moment of simulated peak water level is compared to the observed peak water level. Because water levels are used for this is analysis instead of surge levels, also the tidal signal influences the result. The boxplots show the results of this analysis. We see that there are quite some outliers in timing of the peak at around 12 hours (or a multiple of 12) before or after the observed peak. This indicates that the simulated peak water level occurs at another tidal peak. In appendix D bar graphs are shown of the distance as calculated by equation 3.3. Figure 4.6. Validation 39

0 Simulated surge [m]

1 − 0 100 200 300 400 Distance [-]

Figure 4.6: Distance (as calculated with equation 3.3) versus the observed storm surge at Hoek van Holland. A clear trend can be found that for higher storm surge, higher distances occur.

4.6 shows the relation between the distance and the simulated storm surge. It is found that for a larger simulated surge, the distance also increases. When the distance of a timestep is compared to the error between the simulated water level and observed water level, no clear relationship occurs, as shown in ﬁgure 4.7a. Thus a larger distance does not mean that the error is larger. Some matches with high distances have almost no error. The same can be concluded if error between the simulated storm surge and WAQUA storm surge is compared to the distance.

4.6.2 Method B - regression

Method B of the Storm Atlas, which is based on a multiple linear regression model is also validated. This is done in the same way as method A. First, we look at a comparison of the simulated and observed the peak water level. Figures 4.10a and 4.11a show the differences between the simulated and observed peak water level per station and per storm. We see that at the in the southern part of the North Sea, the water levels are on average overestimated, where at the other locations the water levels are underestimated. When we look at the peak water levels per storm, we cannot find a clear pattern. We see under- and overestimations of the peak water levels. Next, we look at the duration of the storm surge, shown in figures 4.10b and 4.11b. Like with method A, we see that the duration is overestimated for the storms which peak levels are also overestimated. Looking at the different locations, we see that, although the peak levels are slightly underestimated for Den Helder and Delfzijl, the duration is slightly overestimated. Finally we examine the timing of the peak water level. Figures 4.10c and 4.11c show the results of this indicator. Looking at the locations along the North Sea coast, we see that almost all locations have storms if which peak is given in a later tidal peak. Aberdeen, North Shields and Immingham have simulated peak water levels found 24 hours later than observed. Looking at the different storms, again we see that storm 1 is not represented well by the 40 CHAPTER 4. STORM ATLAS PERFORMANCE

1 −

0 100 200 300 400

Sim. water level minus obs. water level [m] Distance [-] (a) Distance versus error between simulated and observed water level at Hoek van Holland

0.5

0.5 −

1 − 0 100 200 300 400

Sim. storm surge minus WAQUA surge [m] Distance [-] (b) Distance versus error between simulated storm surge and WAQUA storm surge at Hoek van Holland

Figure 4.7: Distance (as calculated with equation 3.3) versus error 4.6. Validation 41

Storm Atlas. This is due to low water levels, which give easier a peak water level at another tidal peak. Storm 13 is remarkable because almost all storms give a peak water level much later than the observed peak.

4.6.3 Analysis of remarkable storms for Hoek van Holland

In this section, we take a more detailed look at the performance of the Storm Atlas at Hoek van Holland (particularly method A) and we try to ﬁnd explanations for the possible diﬀerences between the observed and simulated water levels.

Storm 1 - Februay 1979 This storm was retrieved from the KNMI HYDRA-project. Apparently, strong winds over land occurred during this storm, but on sea no extreme weather conditions occurred. Because of this, almost no surge appeared. On the other hand gives this ‘storm’ an idea of the performance of the Storm Atlas in easy weather Storm 5 - January 1990 This depression crossed England over land, where the center pressure lowered drastically. When it came over the North Sea, the depression was developed to a heavy storm and moved towards Denmark and Norway. This path is remarkable, because most storms come from direction of Iceland, northern over Scotland and bend southward towards the North Sea. Looking at the distance between the forecasted pressure field and the best matching pressure field in the database, we see an extreme high value. This indicates that the Storm Atlas was not able to find a good matching storm. It is probably due to the path of the storm that the Storm Atlas could not find a good matching storm in the database. Storm 6 - February 1990 Looking at storm 6, we see that the Storm Atlas has difficulties finding a good match at two moments during this storm. This storm actually consisted of a combination of multiple depressions and storms. The Storm Atlas may find difficulties finding a good match because of the quick follow-up of the depressions. Storm 13 - December 1993 At this storm, we see that the Storm Atlas follows the WAQUA surge calculations rather good. Both the Storm Atlas and the WAQUA surge calculation have an overestimation of the storm surge. Storm 18 - August 1998 This storm is remarkable for the time of the year it occurred. In Hoek van Holland, the resulting water levels were not extreme compared to storm in the winter period. However, water levels as they occurred, appear in the period of May till August only once in 400 year. A depression originated above south Germany and moved north west towards Amsterdam. From there it moves further north towards Denmark and fills up again. Because of a high pressure field above England, the pressure gradients are high and winds become strong above the southern part of the North Sea. Because the depression came from the south, winds did not fetch the North Sea for a long period and the build up of a storm surge was not very high. 42 CHAPTER 4. STORM ATLAS PERFORMANCE

2 Overprediction - too high

1 − Water level diﬀerence [m]

2 Underprediction - too low − (a) Peak water level

Overprediction - too long 4

2 −

4 Storm duration diﬀerence [hours] − Underprediction - too short (b) Storm duration

Overprediction - too late

10 − Time diﬀerence peak [hours] Underprediction - too early Dover Delfzijl IJmuiden Aberdeen Lowestoft Vlissingen Den Helder Immingham North Shields Southend on Sea Hoek van Holland (c) Timing of the peak water level

Figure 4.8: Storm Atlas method A (resampling): Results of the performance per station on the 3 performance indicators 4.6. Validation 43

2 Overprediction - too high

1 − Water level diﬀerence [m]

2 Underprediction - too low − (a) Peak water level

Overprediction - too long 4

2 −

4 Storm duration diﬀerence [hours] − Underprediction - too short (b) Storm duration

Overprediction - too late

10 − Time diﬀerence peak [hours] Underprediction - too early Storm 1 Storm 2 Storm 3 Storm 4 Storm 5 Storm 6 Storm 7 Storm 8 Storm 9 Storm 10 Storm 11 Storm 12 Storm 13 Storm 14 Storm 15 Storm 16 Storm 17 Storm 18 Storm 19 Storm 20 Storm 21 Storm 22 Storm 23 Storm 24 Storm 25 Storm 26 Storm 27 Storm 28 Storm 29 Storm 30 Storm 31 Storm 32 Storm 33 (c) Timing of the peak water level

Figure 4.9: Storm Atlas method A (resampling): Results of the performance per storm on the 3 performance indicators 44 CHAPTER 4. STORM ATLAS PERFORMANCE

2 Overprediction - too high

1 − Water level diﬀerence [m]

2 Underprediction - too low − (a) Peak water level

Overprediction - too long

10 −

Storm duration diﬀerence [hours] Underprediction - too short

(b) Storm duration

20 Overprediction - too late

10 − Time diﬀerence peak [hours] Underprediction - too early 20 − Dover Delfzijl IJmuiden Aberdeen Lowestoft Vlissingen Den Helder Immingham North Shields Southend on Sea Hoek van Holland (c) Timing of the peak water level

Figure 4.10: Storm Atlas method B (regression): Results of the performance of per station on the 3 performance indicators 4.6. Validation 45

2 Overprediction - too high

1 − Water level diﬀerence [m]

2 Underprediction - too low − (a) Peak water level

Overprediction - too long

10 −

Storm duration diﬀerence [hours] Underprediction - too short

(b) Storm duration

20 Overprediction - too late

10 − Time diﬀerence peak [hours] Underprediction - too early 20 − Storm 1 Storm 2 Storm 3 Storm 4 Storm 5 Storm 6 Storm 7 Storm 8 Storm 9 Storm 10 Storm 11 Storm 12 Storm 13 Storm 14 Storm 15 Storm 16 Storm 17 Storm 18 Storm 19 Storm 20 Storm 21 Storm 22 Storm 23 Storm 24 Storm 25 Storm 26 Storm 27 Storm 28 Storm 29 Storm 30 Storm 31 Storm 32 Storm 33 (c) Timing of the peak water level

Figure 4.11: Storm Atlas method B (regression): Results of the performance per storm on the 3 performance indicators 46 CHAPTER 4. STORM ATLAS PERFORMANCE

It is notable that the resampling method predicts this storm surge rather good, whereas method B overestimated the surge level by 1.5 meters. Storm 22 - December 1999 This is a famous storm in Denmark, the so-called ‘December-Orkanen’. This depression developed west of Ireland and looking at the path, it crossed England, where the center pressure lowered drastically. When it came over the North Sea, the depression was developed to a very heavy storm and moved towards Denmark. This path is rather remarkable. Most storm come from direction of Iceland, northern over Scotland and bend southward towards the North Sea. When we look at the distance between the forecasted pressure field and the best matching pressure field in the database, we see an extreme high value. This indicates that the Storm Atlas was not able to find a good matching storm. It is probably due to the path of the storm that the Storm Atlas could not find a good matching storm in the database. Storm 26 - October 2006 In November 2006, a heavy storm crossed the North Sea. In the Netherlands, this storm got the name ‘Allerheiligenvloed’. Especially in the Northern part of the Netherlands, very high storm surges occurred. In Delfzijl, it was even the highest water level ever recorded. This storm had quite complex pressure fields, which changed and deepened rather quickly above the North Sea. Looking at the simulated water levels, we see a large underestimation of the peak water levels of almost 1 meter. However, when these pressure fields are used in WAQUA, also a large underestimation occurs and the Storm Atlas prediction follows the WAQUA- calculation rather good. It looks like the input data was not able to resemble this storm well. Storm 30 - November 2007 November 2007, a depression came north from Scotland and moved toward and over south Norway, resulting in high wind speeds stretching over the North Sea from north to south. Because the center of the depression moved slowly, a large surge built up and moved south. In the Netherlands, for the first time, the Maeslantkering was closed during storm conditions. Because of the closure of the Maeslantkering, the set-up at the seaside was some decimeters higher. This may be an explanation for the underestimation of the Storm Atlas and WAQUA. Storm 32 - March 2008 During the storm in March 2008, no extreme high waters occurred. However, a so-called ‘polar low’ developed at the Doggersbank area. This local phenomenon caused locally for extreme winds and extra set-up. This polar low was not captured by the weather models and also cannot be identified in the ERA-interim data. Storm 33 - December 2013 In December 2013, a very heavy storm crossed the North Sea. This storm resulted at most coastal location for the highest water levels since the 1953 disaster. At Hoek van Holland, locally very heavy precipitation occurred. This resulted in a local extra set-up of several decimeters. However, this set-up occurred not during the peak of the surge. The effect from the precipitation was present anymore at time of the peak surge. 4.7. Comparison of methods A and B 47

4.7 Comparison of methods A and B

As described in section 4.2, the results of the performance assessment can be given in terms of total error (RMSE), systematic error (bias) and random error (standard deviation). For a comparison of the performance of both methods, the results of the hindcasted storms are aggregated. Table 4.2 shows the aggregated results of all hindcasted storms for all locations. The peak water levels have a comparable RMSE, but the random error of method A is smaller than method B. This makes method A more precise. On the other hand is the trueness of method B better. Looking at the duration of the storm water level, we see that method A performs slightly better than method B. As discussed in section 4.6, it is likely that the underestimation of the duration is linked to the underestimation of the peak water level. When the entire surge is underestimated, also the duration will be underestimated. Next, we look at the timing of the peak water level. Method A performs better on this indicator. The RMSE is fairly large for both methods. This is due to the large deviations as an effect of the tidal signal. Because of the tidal signal, the peak water level can be found at another tidal peak. We see for method B a larger bias and large standard deviation. Therefore the performance of method A is better. When we look at the computation times of the both methods, we see that the regression method is much faster than the resampling method. The resampling method needs to compare the forecasted pressure fields with all pressure fields in the dataset, which is more time consuming than the simple multiplications which are done in the regression method. Although the regression method is faster, the resampling method cannot be classified as slow. Compared to current operational models, both methods are much faster. In table 4.3 a comparison is made for the performance of both methods at Hoek van Holland. Besides a comparison of the observed and simulated water levels, also a comparison of the water level calculated by WAQUA with the simulated water level is made. This comparison shows that method A performs better for the peak water level. Compared to WAQUA the RMSE of the peak water level is a lot smaller than for method B, which is due to the lower standard deviation of method A. 48 CHAPTER 4. STORM ATLAS PERFORMANCE

Table 4.2: Comparison of the performance of both Storm Atlas methods A and B. The aggregated results of all storms at all locations are shown.

Performance Method A Method B indicator Resampling Regression Peak water level RMSE (m) 0.47 0.51 Bias (m) -0.31 -0.09 Standard deviation (m) 0.36 0.51 Duration RMSE (hours) 1.20 1.73 Bias (hours) -0.62 0.06 Standard deviation (hours) 1.03 1.73 Timing of peak RMSE (hours) 7.03 7.43 Bias (hours) -0.13 1.43 Standard deviation (hours) 7.03 7.28 Computation time Order of minutes Order of seconds

Table 4.3: Comparison of the performance of both Storm Atlas methods A and B at Hoek van Holland

Performance Method A Method B indicator Resampling Regression Peak water level RMSE (m) 0.39 0.46 Bias (m) -0.11 0.19 Standard deviation (m) 0.37 0.41 Duration RMSE (hours) 0.85 1.96 Bias (hours) -0.16 0.66 Standard deviation (hours) 0.83 1.85 Timing of peak RMSE (hours) 6.05 7.39 Bias (hours) -0.94 2.21 Standard deviation (hours) 5.98 7.05 Peak water level compared to WAQUA RMSE (m) 0.33 0.52 Bias (m) -0.12 0.18 Standard deviation (m) 0.31 0.48 Chapter 5

Uncertainty analysis

5.1 Introduction

To improve the North Sea Storm Surge Atlas, a first step is to identify the sources of uncertainty. When the uncertainties are identified, we use a classification scheme to classify the sources of uncertainty. From this classification we can learn more about the uncertainties and possible ways of reducing the specific uncertainty. For the classification of the uncertainties, we use the typology of Walker et al. (2003). This typology classifies each source of uncertainty in three dimensions:

i The location of uncertainty – where the uncertainty manifests itself within the model complex; ii The level of uncertainty – where the uncertainty manifests itself along the spectrum between deterministic knowledge and total ignorance;

iii The nature of uncertainty – whether the uncertainty is due to the imperfection of our knowledge or is due to the inherent variability of the phenomena being described.

The identified uncertainties are classified according to this typology. Following Brugnach et al. (2008) and Warmink (2011), the third dimension is extended with third nature of uncertainties, being ambiguity. When the uncertainties are classified, we can make a prioritization to give a direction to which uncertainties should be addressed first, in order to improve the performance. This prioritization can be based on a combination of the uncertainty of the source and the sensitivity of the outcome to this source. Also, the classification is taken into account.

5.2 Identiﬁcation and classiﬁcation of sources of uncertainty

In this section, the identiﬁed sources of uncertainties are listed. First, in subsection 5.2.1, sources of uncertainty are listed which are present in both method A and method B of the Storm Atlas. In subsection 5.2.2 the sources of uncertainty which are speciﬁcally found in method A (resampling) are listed. Finally, in subsection 5.2.3 the uncertainties for method B (regression) are given.

49 50 CHAPTER 5. UNCERTAINTY ANALYSIS

For the classification of the sources of uncertainty, the decision trees of Warmink (2011) are used. For each of the dimensions of uncertainty according to Walker et al. (2003), a decision tree is available to find the correct classification. The classification is made by the author of this thesis.

5.2.1 Uncertainties in both methods and B of the Storm Atlas

Weather forecasts The operational version of the Storm Atlas uses the weather forecast from the National Oceanic and Atmospheric Administration (NOAA) as input. At NOAA the so-called GFS- model is used to make these forecasts. The operational storm surge forecasting models in the Netherlands at KNMI use the ensemble of forecasts from ECMWF as input. The quality of the weather forecasting models differs, and therefore influences the quality of the storm surge forecast. According to Persad (2014), both models have their own strengths and weaknesses. The quality of the ECMWF weather forecast is significantly better on mid-term (more than four days ahead), especially in winter periods. In the validation of the Storm Atlas, this source of uncertainty was excluded, by using the ‘observed’ pressure fields from the ERA-interim database. This way, the validation of the model was focused on the forecasting of the storm surge, rather than the validation of the weather forecasting models. However, the operational Storm Atlas is influenced by the uncertainty in the weather forecast. The quality of the pressure fields used as input data in this study does however influence the performance of the Storm Atlas. In chapter 4, it is shown that the input data used in this study also generates deviations from the observed values when the input data is used for WAQUA-in-Simona/DCSM98. This may indicate that the pressure fields e.g do not include small scale phenomena as in March 2008. Tidal data In the North Sea Storm Surge Atlas, forecasts of the storm surge are made. To get the forecast of the water levels, the tidal signal is added to the forecasted surge. There is an uncertainty in the tidal signal. At this moment the tidal signal which is used in the operational Storm Atlas is retrieved from two sources. The first source is the tidal prediction of Rijkswaterstaat, which provides the tidal prediction of the station along the Dutch coast and at the offshore stations in Dutch zone of the North Sea (see figure 5.1). The second source is the tidal database from the International Hydrographic Organization. This database is used for all station, where Rijkswaterstaat does not provide tidal data. Another possible tidal database is XTide (Flater, 1998). This database is, like the IHO database, accessible through Delft Dashboard, part of Open Earth Tools from Deltares (Deltares, 2008). Also, it is possible to use a long time series of observed water levels at each ouput location of the Storm Atlas, and do a Fast Fourier Transformation to find the tidal constituents in the time series. Appendix B gives a comparison of the different databases. For the validation of the base- line model (chapter 4), the IHO-database is used for all stations, because of the limited availability of the Rijkswaterstaat database for historic storms. Uncertainty in surge calculation The database is built up from pre-calculated storm surges. These surge are calculated with WAQUA-in-Simona/DCSM98. This model is also a schematization of reality, which means that there also will be an uncertainty in the outcome of these pre-calculated surges. 5.2. Identification and classification of sources of uncertainty 51

Figure 5.1: Economic zonation of the North Sea, according to De Hauwere (2012) 52 CHAPTER 5. UNCERTAINTY ANALYSIS

Climatology As described in A, the climatology is subtracted from the pressure fields. The climatology is defined as the time-averaged atmospheric pressure at every grid point. This climatology is calculated from a subset of the database. The choice of the subset of the database may influence the time average. The climatology used for the derivation of the principal components of the pressure fields in the database is the same as used to find the principal components in the weather forecast. The sensitivity in the climatology is assumed to be low. Number of EOFs used to describe the pressure fields In section 3.3, the EOF analysis is described as a method of describing the pressure fields. Using the EOF analysis, the data from the pressure fields at over 2000 grid points can be described with just 50 principal components. With this data reduction however, also some information will be lost. We use a limited number of EOFs to describe the EOFs and this influences the quality of the description of the pressure field. Figure 3.3 shows that almost all variance is explained using 50 EOFs. We see that a lot of EOFs almost have no influence on the explained variance. However, when all explained variance is summed, the result is not 100%, so not all variance in the (original) dataset is explained. Number of consequential timesteps used As described in chapter 3, several consequential timesteps are used in the Storm Atlas. This is done to take into account the meteorological development of a storm. In the current operational version, three timesteps are used (being t = 0, t = 6 and t = 12 hours). It is possible to reduce or extend the number of timesteps. − − Tide surge interaction As stated in the description of the Storm Atlas, in the resampling method, no tide surge interactions are taken into account. It is assumed that the tidal signal does not interact with the storm surge and therefore that these can be added, after the surge is forecasted. Also, it is assumed that the calculation of the storm surges in the database by WAQUA are not affected by the tidal signal. Also in the regression method, the tide surge interaction is not taken into account. It is assumed that the calculation of the regression coefficients is not influenced by the tidal signal. In reality however, interaction occurs between the storm surge and tidal signal. For example, the speed of a storm surge traveling towards the coast is influenced by the water depth (and thus by the tidal signal). It is because of this principle that in idealized schematized situations, the storm surge is skewed and the peak water level occurs before the peak of the tidal signal occurs. Land sea mask As described in the methodology of the Storm Atlas, the pressure fields, which are used as input, are multiplied with a land-sea-mask, in order to retrieve the pressure fields over water. Errors in this land-sea-mask influence the fields which will be matched, and therefore can influence the storm surge forecast. Also, due to the resolution of the land-sea-mask and the input data, small local geometries are not taken into account. The land sea mask used to build the database is equal to the land sea mask used for preprocessing the pressure of the weather forecast. The sensitivity of the land sea mask is assumed to be low. Area boundaries of matched pressure fields The area of the pressure fields is bounded. When the boundaries are chosen too large, 5.2. Identification and classification of sources of uncertainty 53

weather patterns are matched which ar not relevant for the storm surge at the North Sea. On the other hand, when the boundaries are chosen to narrow, not all effects which influence the surge are taken into account. The chosen boundaries are arbitrary. Some expert are convinced that in numerical modeling a large area, extending to e.g. Iceland, needs to be used to include also long period signals. This might also be the case for the Storm Atlas. However, other experts say a smaller area may help to focus the matching on the area which influences the storm surge most, or help to find clear relations between the EOFs and the storm surge. Software problems Software errors in the programs which are used in the Storm Atlas can also influence the storm surge forecasts. Minor errors in the model code (e.g. the timing of the surge in appendix C), but also larger bugs can occur. During the research a bug fix was done in the sub-program CDO (Climate Data Operators from the Max-Planck-Institut fürMete- orologie). This program is used for the EOF-analysis. The database was built with the version without bugfix and the historical storms were resampled using the fixed version of CDO. Because of the bugfix the principal components of the EOFs were not comparable anymore.

5.2.2 Uncertainties in method A - resampling

Size of the database In section 3.2 the ERA-interim dataset is described. As stated, in the operational version only a part of the dataset is used. At this moment approximately 500 years of weather scenarios is used, which can be extended to about 4000 years. The resampling method is influenced by the size of the database. When the database is larger, the probability of finding three similar sequential pressure fields in the database is larger. Especially in the case of more extreme events, the freedom of choice for a best match is limited by the size of the database. Exclusion of spatial barometric average As described in appendix A, the spatial average of every pressure field is removed, before looking for the best match in the database. The idea behind this, is to look for the pressure field with matching relative pressure differences, rather than absolute matching pressure. Weights of the timesteps The resampling method of the Storm Atlas matches three sequential pressure fields of the weather forecast with three sequential pressure fields in the database. This is done, in order to find a match which has also a development of the storm that looks alike. The timesteps t = 0, t = 6 hours and t = 12 hours can be given different weights. In the operational version the− timet = 12 hours− has a weighting factor of 0.5, which means that differences between the field of− twelve hours before has less influence in the determining the ‘best match’. Weights of the different EOFs In the development of the operational version of the Storm Atlas, the emphasize was put on Hoek van Holland and the other parts of the Dutch coast. It was found that the EOF with the north-south component (the third EOF in the operational version, comparable with the second EOF of figure 3.2) had a strong correlation with the skewed surge at Hoek van Holland (Caires et al., 2014). Therefore an additional weighting of this EOF was implemented. 54 CHAPTER 5. UNCERTAINTY ANALYSIS

Figure 5.2: Schematic representation to select the best surge analogue, based on its match with the previous surge (Caires et al., 2014)

For the validation of the Storm Atlas, this weighting was removed, because this was found to arbitrary and in order to make the model more broadly applicable. For example, for the British coast, the EOF with the east-west component will have a strong correlation. Number of best analogues In the operational version of the Storm Atlas, the first five best matches were selected. From these five best matching pressure fields, the storm surges are selected and compared to the storm surge forecast of the previous timestep. The choice of the best match was than based on a minimal difference between the slopes and jumps of the surges. Figure 5.2 shows a schematic representation of this principle. For the validation of the resampling method of the Storm Atlas, the multiple analogues were not taken into account and only the best matching pressure field was used as a forecast of the storm surge. Smoothening function in resampling method The matched surges of the resampling method consist of part of six hours. A lot of these six-hourly surges will not be continuous. To smoothen the matched surges, a smoothening function is applied. In the operational version, an exponential function is used to correct the jumps. In this function it is assumed that the sixth hour of each forecasted timestep is correct and the five preceding hours are corrected.

5.2.3 Uncertainties in method B - regression

In the regression method, the regression coeﬃcients are calculated from the database. When more storms are incorporated in this calculation, the general relation between the storm surge and the principal components of the EOFs becomes more clear. Spline in regression method The regression method of the Storm Atlas uses a spline function to interpolate the six hourly surges to one hourly surges. Diﬀerent splines are applied, like a linear, quadratic or cubic spline. In the model used for validation, a cubic spline is used.

5.3 Overview of classiﬁcation of uncertainties

The identified uncertainties are classified according to this typology. Following Brugnach et al. (2008) and Warmink (2011), the third dimension is extended with third nature of uncertainties, being ambiguity. Table 5.1 gives an overview of the classification of the identified uncertainties. The classification is made by the author. Table 5.1: Classification of the sources of uncertainty, according to the typology of Walker et al. (2003)

Location Level Nature Context Input Model Model Parameter Statistical Scenario Qualitative Recognized Natural Epistemic Ambiguity structure technical ignorance variability Sources of uncertainty for both methods A and B Weather forecast . x . . . . x . . x . . Tidal data . x . . . . x . . . x . Pre-calculated surge . x . . . x . . . . x . Climatology . x . . . . x . . x x . Number of EOFs . . x . . . x . . . x . Number of timesteps . . x . . . x . . . x . Tide-surge interaction . . x . . . . x . . x . Land-sea-mask x . . . . . x . . . x . Area boundaries x . . . . . x . . . . x Software problems . . . x . . . . x . x . Sources of uncertainty for method A Size of database . . x . . . x . . . x . Barometric eﬀects . . x . . . x . . . x . Weights of timesteps . . . . x . . x . . x . Weights of EOFs . . . . x . . x . . x . Number of analogues . . x . . . . x . . x . Smoothening . . x . . . x . . . x . Sources of uncertainty for method B Size of database . . x . . . x . . . x . Spline . . x . . . x . . . x . 5.4. Prioritization of sources of uncertainty 57

5.4 Prioritization of sources of uncertainty

In appendix F a sensitivity analysis of several sources of uncertainty of method A is carried out. The sensitivity analysis shows the sensitivity of the outcomes of the validation to the source of uncertainty. The following sources of uncertainty are examined:

Number of EOFs • Number of timesteps • Weights of different timesteps • Multiple analogues • Smoothening function • Size of the database • Barometric effect • In appendix F the detailed results of the sensitivity analysis are shown. As in chapter 4, the results are shown in boxplots and aggregated results are given (for all station in table 4.2 and for Hoek van Holland in table 4.3). From this analysis, it is found that the sensitivity of the Storm Atlas for most of the examined sources of uncertainty is low. Appendix F shows the influence of the number of timesteps for method A (resampling). The validation of method A is done, using only 1 timestep (t = 0), using 2 timesteps (timestep t = 12 hours is excluded and when timestep t = 0 is excluded) and using 4 timesteps (when timestep− t = 18 hours added and when timestep t = +6 hours is added). The results on the performance indicators− of the Storm Atlas do not change much for most cases. We find a decrease in performance when timestep t = 0 is excluded. It seems important to have a matching pressure field at t = 0 to forecast is storm surge for the next 6 hours. A remarkable improvement is found when no smoothening function is used. The systematic error of the peak water level decreases by 5 cm at Hoek van Holland, compared to the observed water levels as well as compared to WAQUA. The smoothening function corrects the simulated storm surge for discontinuities caused by the concatenation of the 6 hour surges. The surge is smoothened towards the previous matched timestep. This can be caused by a poorly matched storm surge prior to the peak water level. The storm surge during the peak water level will than be corrected, while the matched storm surge was actually good. Also, case where the smoothening function is inversed is studied. In this case, the smoothening function corrects the storm surge towards the following matched timestep, rather than towards the previous timestep. Figure F.1 shows the differences between the smoothening functions. In this case, an improvement is found in the total error, although the systematic error is improved less than in case of no smoothening function. This indicates that the storm surge during the timestep after the peak water level is sometimes poorly simulated. In appendix F, case 15 shows the influence of the enlarged database. The database was extended to approximately 4000 years. It is found that the values of the performance indicators are not influenced much by the extension. However, when we look more in detail at the distance (equation 3.3, for the base case shown in appendix D), we see that this value lowers, especially for the higher values, which shows that the matched pressure fields are more alike. Looking at 58 CHAPTER 5. UNCERTAINTY ANALYSIS the water levels, we see that certain storms improve, but other storms deteriorate. No clear explanation can be found for this. Improvement of the performance of the Storm Atlas is also found in the case of the extended database and the inclusion of the barometric average. Examining the different storms more in detail, it is found that for some storms the performance increases, whereas others deteriorate. Although the systematic error increases a little, the total error decreases. Chapter 6

Discussion

In this research, the North Sea Storm Surge Atlas is presented as a new way of storm surge forecasting. By using a large offline library of predefined and pre-calculated storms, the Storm Atlas is able to forecast storm surges using a smart and quick algorithm. There are two possible methods for this algorithm: resampling (method A) and regression (method B). Both methods are assessed on their performance and sources of uncertainty are identified. In this chapter both methods are discussed and future steps are recommended. Also assumptions made in this research are discussed.

6.1 Performance assessment methodology

In this research a performance assessment is carried out for two possible methods of the Storm Atlas. This performance assessment has limitation. First there is the limitation of the number of stations which is validated with the historical storms. During this research, some assumptions have been made and limitations occurred.

6.1.1 Performance indicators

The performance assessment in this study is done for the water levels, rather than surge levels. In the end, the water level is the variable which is of interest. However, the tidal signal influences the limits the duration quite a lot, since the peak water level often coincides with a high tide. The drop in tide, will cause the water level also to drop below the threshold. This can be seen in figure 4.1. Also, in case of the timing of the peak water level, the tidal may cause the timing of the peak to ‘jump’ to the next high tide. The interpretation of this performance indicator is therefore more difficult. High values can be seen as outliers, where a different peak water level is found, not corresponding to the observed storm. We have seen that the duration of the waterlevel, as defined in this study, is not good performance indicator for the duration of the simulated of storm surges. The temporal resolution of the data is another issue. Because of the hourly resolution of the output data of the Storm Atlas, the performance assessment is also done with data with hourly resolution. This results especially in the duration of the storm water level in coarse results. Nevertheless, these outcomes can help in the interpretation of the development of the entire storm surge.

59 60 CHAPTER 6. DISCUSSION

6.1.2 Selection of locations and storms

The selection of the locations influences the quality of the performance assessment. The southern part of the North Sea is emphasized, by taken a higher density of locations. Also the density along the Dutch coast is higher than along the British coast. Furthermore, no locations at the German and Danish coast are taken into account. Because of this, no conclusions can be made of the performance in this part of the North Sea. In this part of the North Sea, other physical processes may be important, compared to the British and Dutch coas. Storms move easterly and often have landfall at Denmark of Germany. For example the storm in December 1999 was one of the strongest storms at Esbjerg (Denmark), resulting in one of the highest storm surges ever recorded. At Hoek van Holland however, the storm surge was not extreme. The low center pressure of the storm passed right over Denmark, which indicates that the inverted barometer effect contributed quite a lot. It has to be noted that Delfzijl is known to be a difficult station for the prediction of high water levels. Also the current operational high resolution numerical hydro-dynamic models have difficulties in predicting the storm surge at Delfzijl. Since the surges in the Storm Atlas are based on WAQUA calculations, the reliability of the storm surge forecast at this station can be questioned. The selection of storms has been focused on the Dutch coast. The selection has been made mainly on the storm surge reports from Rijkswaterstaat, resulting in storms which are significant for the Dutch coast. Storms which give high water levels at the Dutch coast do not always also result in high water levels at the British coast. Figure 6.2 shows the skewed surges of all storms at the different locations along the North Sea. The skew surge is difference between the peak water level and the peak of the tidal signal, as schematized in figure 6.1. The skew surge is generally lower than the straight set-up at the maximum water level, because of the time difference between the peak water level and tidal peak. We see that the selection of storms gives significant storm surge for all selected locations. However, we see that along the British coast not all storms result in high surges, whereas the same storms do give high surges at the Dutch coast. It is also notable that at Delfzijl, the range of skewed surges is very high and skewed surges appear to be more extreme than at the other locations.

6.1.3 Input data - pressure ﬁelds

In the performance assessment of the Storm Atlas, pressure fields from the ERA-interim dataset are used as input for the Storm Atlas. It is assumed that these pressure fields resemble the actually occurred pressure fields. However, when we use these pressure fields as input for WAQUA- in-Simona/DCSM98, we also find deviations between the WAQUA calculations and the observations. For certain storms, the forecast by the Storm Atlas and the forecast by WAQUA are almost the same, but deviate from the observed levels. Assuming that WAQUA is well able to predict storm surges at Hoek van Holland, this may indicate that the quality of the input data is less than assumed. 6.1. Performance assessment methodology 61

Figure 6.1: Schematization of skew surge (Van den Brink, 2005)

1 Observed skew surge [m] 0

1 − Dover Delfzijl IJmuiden Aberdeen Lowestoft Vlissingen Den Helder Immingham North Shields Southend on Sea Hoek van Holland

Figure 6.2: Observed skew surges of all 33 storms at the different coastal stations. Each line represents 1 specific storm. Where the lines are discontinuous, no data is available for the specific storm at the that location. 62 CHAPTER 6. DISCUSSION

6.2 Performance of the Storm Atlas compared to real-time models

In this study, we have looked at the performance of the newly developed North Sea Storm Surge Atlas. Also, another method based on multiple linear regression is evaluated. A performance assessment has been carried out for the current versions and a ﬁrst sensitivity analysis is done. Goal of the Storm Atlas is not to replace the current real-time models, but to have an added value on their predictions. The low computation times are a big advantage compared to real-time models, and despite the fact that computers improve and computation times are still reducing, both methods of the Storm Atlas will be signiﬁcantly faster. Therefore, for further development of the Storm Atlas, the focus should be put on applications where the low computation times are important, e.g. scenario analysis. When we compare the results of the hindcasting of historical storms to the current real- time models, we see that uncertainties in the outcomes are higher than for the current real-time models, which are known for their small uncertainties. However, the Storm Atlas is able to give a reasonable indication of the storm surge forecast.

6.3 Method A - resampling

The first method uses an EOF analysis to compare the forecasted pressure fields with the pressure fields in the database. This EOF analysis focuses especially on the gradients in the pressure fields, rather than the absolute values, which is done by describing the variability in air pressure from the mean of each field. It is assumed that the gradient winds are dominant in the development of storm surges. Because of this assumption, the inverted barometer effect is less taken into account. Further research may focus on the question whether this influences the performance of the storm surge prediction. In the performance assessment we have seen that method performs less for heavier storms. The performance of this method is especially influenced by the quality and the size of the database. Especially for more extreme storms, the freedom of choice is limited and because of that the performance may decrease. The distance between the forecasted pressure field and the best matching pressure field in the database is in some cases very high compared to other matches. This indicates that the size of the database is too limited to make a good storm surge forecast. There seems to be a correlation between the distance between the pressure fields and the quality of the surge forecast.

6.4 Method B - regression

In method B, an important limitation is the interpretation of the EOFs and their physical interpretation. The linear regression model implicitly assumes a causal relationship between the EOFs and the storm surge at a certain location. EOFs however, are empirical pattern determined from the dataset. This does not mean that EOFs have a physical explanation. Assuming a physical relationship between the EOFs and the storm surge may therefore not be correct. Also, linearity of the relationship can be questioned. Chapter 7

Conclusions and recommendations

This research focuses on the North Sea Storm Surge Atlas. The objective of the research was “To gain more insight in the uncertainties of the Storm Atlas and to explore possibilities for improvement, by assessing the performance with a validation of the Storm Atlas and by an uncertainty analysis”. In this ﬁnal chapter, answers to the research questions as stated in chapter 1 are formulated. Furthermore, section 7.2 gives recommendations for further research.

7.1 Conclusions

1. What is the Storm Surge Atlas and how do both possible methods A and B work?

This question has been answered in chapter 3. The Storm Atlas is a new concept for storm surge forecasting. Contrary to current real-time storm surge forecasting, which is done by detailed numerical modeling, the Storm Atlas uses a large offline database with predefined and pre- calculated storms. Using this database, the Storm Atlas is able to forecast storm surges omitting the time consuming numerical calculations. Two possible methods may be applied to forecast the storm surge with the Storm Surge Atlas. The first method (method A - resampling) compares a sequence of three pressure fields in a weather forecast to any three sequential pressure fields in the database. The comparison is based on an EOF analysis of the pressure fields, which enables the pressure fields to be described by expansion functions (principal components) of 50 predefined spatial structures (EOFs). The best match between the forecasted pressure fields and the pressure fields in the database is selected and the pre-calculated storm surge corresponding to the matched pressure field in the database is directly used as storm surge forecast. The second method (method B - regression) uses a multiple linear regression model to forecast the storm surge. A direct relation between the expansion functions (principal components) of the spatial patterns (EOFs) in the pressure field and the storm surge at a location of interest is assumed. The parameters of the regression are derived from the pre-calculated database. The forecasted storm surges are than calculated by analyzing forecasted pressure fields for spatial structures and applying the regression model.

63 64 CHAPTER 7. CONCLUSIONS AND RECOMMENDATIONS

Currently, a pilot version of the North Sea Storm Surge Atlas is operational, based on method A (resampling). The forecasted storm surges are added to the tidal signal and the forecasted water levels are represented in a web-based interface. With the operational version, also visual- ization in a Flood Early Warning System (FEWS) is possible.

2. How accurate does the Storm Surge Atlas predict storm surges at the North Sea?

In chapter 4 the performance of the two methods for quick determination of storm surge has been assessed. As a first step, performance indicators are defined in terms of peak water level, duration of the storm water level, and timing of the peak water level. Furthermore, computation time is taken into account for making a comparison between methods A and B. Next locations along the North Sea coast and historical storms are chosen. 11 stations along the Dutch and British coast have been selected. Unfortunately no data was available for stations at the Danish and German coast. A set of 16 historical storms in the period from 1979 till now are selected. For the input data of the Storm Atlas, pressure fields from the ERA-interim dataset are used. The performance assessment shows that on average the Storm Atlas underestimates the historical storms. Both methods have approximately the same root mean squared error, however the method based on resampling has a larger bias and smaller variance in outcomes than the regression method. This means that the accuracy of the resampling method is less, but the precision of the outcomes is higher. Looking at the duration of the storm water level, we see that the resampling method performs better, but also here the bias is slightly larger than for the regression method. This bias is linked to the bias in peak water level, because the duration is compared to the observed peak water level. A bias in peak water level, in combination with a bias in duration indicates that the entire development of the storm surge is underestimated, rather than just a flattening of the peak level. In the timing of the peak water level, it is found that the resampling method performs better. Both methods find some of the highest peak water levels at a different tidal cycle than observed. The regression method however has more of these outliers.

3. What are the uncertainties in the Storm Surge Atlas?

In chapter 5, the identified uncertainties have been listed. The uncertainties are classified according the model of Walker et al. (2003), giving a classification for location, level and nature of the different sources of uncertainty.

4. How can the Storm Surge Atlas be improved, in order to get a better performance?

In chapter 5 an sensitivity analysis for several identified sources of uncertainty is carried out. From this sensitivity analysis, it is found that most of the examined sources of uncertainty do not give a structural improvement of the performance. To improve the Storm Surge Atlas, the database should be extended. It has to be noted that the extension of the database has a negative effect on the calculation times. It is therefore recommended to extend the database selectively, 7.2. Recommendations 65 adding only the storm events and no calm weather. Also, including the spatial average of the pressure field in the matching improves the Storm Surge Atlas. Last, the smoothening function should be adjusted, such that the correction is done forward in time. Also, we have seen that there is uncertainty in the tidal signal. A comparison of three different sources for the tidal signal is made in this study. Further research may conclude which source is most reliable.

7.2 Recommendations

Based on this research, the first recommendation is to use method A (resampling) as a basis for further development of the North Sea Storm Surge Atlas. It is shown that the performance of both methods A and B compared to observations are alike for the aggregated results. However, looking more in detail to Hoek van Holland, the performance of method A is better, especially in model context (compared to WAQUA water level forecasts). Also, the identified uncertainties give a first direction to a more detailed and quantitative uncertainty assessment and improvement of the Storm Atlas. Quantification of uncertainties in the Storm Atlas could be a next step. The second recommendation based on this research is to extend the performance assessment in model context. In this research has shown that the performance at Hoek van Holland compared to observation differs from the comparison to WAQUA simulations. An advantage of a comparison in model context is that uncertainties in pre-calculated surges can be excluded. An- other advantage is that in an performance assessment in model context can be done for surges rather than water levels, thus uncertainty and influence of the tidal signal is excluded. Also, the performance assessment of the storm surge simulation can be specified to different locations. Next, the Storm Atlas can be based on pressure gradients or wind fields, rather than pressure differences. The EOF analysis decomposes the (anomaly) pressure field such that as much variance as possible is included in few EOFs. Most variance is found in the locations with largest anomalies, which may not be the area with strongest winds. Since wind is the main driver of a storm surge, the area of interest in the pressure field is the area with the largest pressure gradients. By including the pressure gradient or wind field, the main driver of storm surges is included directly, rather than indirectly by relative pressure differences. To use pressure gradients or wind fields in an EOF analysis, it is a possibility to extend the EOF analysis to a Complex EOF (CEOF) analysis, such that the EOF analysis can be performed on vector field rather than a scalar field. The fourth recommendation is for further research is to investigate to what extent the surges corresponding to the matching pressure fields differ. Especially when the database is extended, most pressure fields will find several look-a-likes in the database. If the corresponding storm surges differ too much, it may indicate matching solely based on pressure fields may not be enough and that there is a need for a more unique characterization of the storm. A parameterization of extra-tropical storms can be helpful for such a characterization. If the Storm Atlas can be coupled to a parameterization, it may help to characterize a storm more uniquely and to find a good match in the database. Furthermore, a parameterization can provide a basis to extend the Storm Atlas towards a tool for scenario analysis. The research of De Jong (2012) and Van den Berg (2013) can be used as starting point. Fifth, it is recommended to find alternative locations where an extra-tropical Storm Atlas could be applied. This can help in the further marketing of the Storm Atlas as a product. For application in the North Sea area, the added value of a Storm Atlas needs to be clarified. Compared to current storm surge forecasting, the Storm Atlas could have its added value in 66 CHAPTER 7. CONCLUSIONS AND RECOMMENDATIONS scenario analysis. Finally, it is recommended to start with an update of the operational version of the North Sea Storm Surge Atlas. Some mistakes and flaws in the current operational version are found, as well as new updates in the used software. Based on this research, a first improvement of the operation version can be made. Bibliography

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EOF analysis

A.1 Introduction

The Storm Atlas uses an EOF analysis to describe the pressure fields. Hannachi (2004) gives an overview of the development and methods for EOF analysis. Also possible extensions are described. The original purpose of EOF analyses was to reduce the large number of variables of the original data, without removing much of the explained variance. Lately, EOF analysis is used to find individual modes of variability. In most cases in literature, temporal variability in a dataset is tried to explain by the temporal modes. For example, finding seasonal patterns or yearly patterns in a database of near-shore sandbars, as in Aubrey (1979). EOF analyses are based on a principal component analysis, which was introduced by Pearson (1901). Lorenz (1956) introduced the EOF analysis to the field of meteorology and is the basis of this method. Preisendorfer (1988) is one of the standard works for an extensive background on EOF analysis. As stated in chapter 3, the concept of the North Sea Storm Surge Atlas assumes that storm surges can be predicted solely on the pressure fields at mean sea level. Therefore, we try to describe the pressure fields in a smart and less data intensive way by an EOF analysis. Contrary to most research, for the Storm Atlas we are interested in an accurate description of the spatial variability, rather than the temporal variability. In the Storm Atlas, the temporal variability will be taken into account by match several sequential pressure fields or forecasting the surge based in regression of several timesteps. An EOF-analysis basically results in three variables. First there are the eigenvectors. These are spatial patterns which explain the variance in space. They can be represented in maps. Next, there are the eigenvalues. Every eigenvector has an eigenvalue, which gives the percentage of the explained variance in the dataset by that eigenvector. The eigenvalues are typically represented by a spectrum. In general, when ordered in from high to low, this spectrum shows an exponential decreasing curve, which indicates that most of the variance can be explained by a limited number of eigenvectors. Finally, there are the Principal Components. These explain the variance in time, corresponding to each eigenvector. The Principal Components can be represented as a timeseries for every eigenvector. The lengths of these timeseries are equal to the number of pressure fields (or timesteps). The principal component is a projection of every timestep on the corresponding EOF. Thus, with the EOF analysis we try to find structures (or patterns) in the variance in a dataset. We do this by finding the eigenvectors of a covariance matrix of the gridpoints. An

71 72 APPENDIX A. EOF ANALYSIS

EOF analysis decomposes a continuous space-time ﬁeld X(t, s), where t represents time and u(s) represents the spatial location, as:

M X X(t, s) = ck(t)uk(s) (A.1) k=1 where M is the number of modes contained in the field, using an optimal set of basis functions of space uk(s) and expansion functions of time ck(t). It can be helpful to think of the rows of Z as points in a p-dimensional euclidean space Ep. Every measurement from t = 1 . . . n is then a point in Ep, and all points together form a swarm. For example, a situation with three (grid-)points, p = 3, n points form a swarm in a three-dimensional space. In this situation we can find three orthogonal vectors, which can (in combination) explain the variance of the every point in the dataset. These vectors are chosen, such that the first vector maximizes the explained variance, the second vector maximizes the remaining explained variance, and so on. These vectors are the EOFs of the dataset. The projections of each point on the different vectors are the principal components of that point. It has to be noted that an EOF analysis finds modes of variability. These modes are driven by the dataset, and may not necessarily be explained as physical modes. The interpretation of the modes into physical processes will be a subjective interpretation (Björnssonand Venegas, 1997). There are several sources, which give a good description and mathematical background on performing EOF analyses. There are many extensions of EOF analyses, like rotated EOFs, extended EOF analysis, canonical correlation analysis, complex (or Hilbert) EOFs, and many others (Hannachi et al., 2007; Hartmann, 2014). In this research, we only use an EOF-analysis in its regular form. Hannachi et al. (2007) gives a clear explanation of the two most used methods to calculate the EOFs. The first method which is used is based on the eigenvalue problem of a covariance matrix of the different grid points . The second method is based on a Singular Value Decomposition (SVD) of the data matrix. This is a powerful tool from linear algebra. Compared to the first method, the SVD-method is more abstract and less easy to understand, therefore both methods will be explained (sections A.3 and A.4). Before these methods can be used, we have to do some preprocessing of our data (section A.2).

A.2 Preprocessing

As a ﬁrst step, we need to do some preprocessing of the sea level pressure data, to make the data ready for an EOF analysis. As input for the EOF analysis we use a matrix A with P grid points and N timesteps.

  a a a P 11 12 ··· 1  a21 a22 a2P  A = (a , a ,..., a )T =  ···  (A.2) 1 2 N  . . .. .   . . . .  aN aN aNP 1 2 ··· First we subtract the climatology of each ﬁeld. The climatology is deﬁned as the time-averaged pressure of each grid point. For computational reasons, we only use a subset of N timesteps in A.3. Finding the Empirical Orthogonal Functions (EOFs) 73 the entire dataset to calculate the climatology, where N is assumed to be representative for the entire dataset.

N 1 X a¯p = anp (A.3) N n=1 The climatology is now calculated for each grid point. For every timestep, we now subtract the climatology for the corresponding grid point. Resulting in data matrix X0, with:

0 a = anp a¯p (A.4) np − Contrary to ordinary EOF-analysis, we are especially interested in the gradients of the variability, rather than the absolute values. This is because the wind (the main driver of a storm surge) is related to the pressure gradient. Thus, a strong pressure gradient with an overall high air pressure will give the same wind as with an overall low pressure. Therefore we remove the spatial average of the ﬁeld at every i th timestep:

P 0 1 X 0 a¯ n = a (A.5) P np p=1 The anomaly ﬁeld A for our EOF-analysis then becomes:

0 0 xnp = a a¯ n (A.6) np −

  x x x P 11 12 ··· 1  x21 x22 x2P  X =  ···  (A.7)  . . .. .   . . . .  xN xN xNP 1 2 ··· A.3 Finding the Empirical Orthogonal Functions (EOFs)

The first step to find the eigenvectors is to calculate the covariance matrix of the matrix of anomalies: 1 S = XT X (A.8) N which contains covariances sij (with i, j = 1, . . . p) between the time series of the field at any two grid points (si, sj). So: N 1 X sij = xtixtj (A.9) N t=1 The aim of the EOF analysis is to find a linear combination of all variables, in this case grid points, that explains the maximum variance, that is to find a unit-length direction u = T (u1, . . . , up) such that Xu has maximum variability. This readily yields as:

max(uT Su), s.t. uT u = 1 (A.10)

The solution to equation A.10, is a simple eigenvalue problem: 74 APPENDIX A. EOF ANALYSIS

Su = uλ (A.11) where S is the covariance matrix, u is an eigenvector and λ the corresponding eigenvalue. Or in matrix notation: SU = UΛ (A.12) where the columns of U contain the eigenvectors and Λ is a diagonal matrix containing the eigenvalues λ. Because of the symmetry of S, this relation can also be written as:

S = UΛUT (A.13)

By deﬁnition the covariance matrix S is symmetrical and therefore diagonalisable. The k’th EOF is therefore the k’th eigenvector uk of S. The corresponding eigenvalue λk is then:

T 1 2 λk = u Suk = Xuk (A.14) k N k k

and thus gives a measure of the variance of the data accounted for in direction uk. The eigenvectors are usually sorted in decreasing order of their corresponding eigenvalues as λ 1 ≥ λ λP . 2 · · · ≥ To get the principal components, we make a projection of the anomaly ﬁeld on onto the k’th T EOF uk = (uk1, uk2, . . . , ukP ) . Thus the k’th principal component ck = Xuk has elements ctk, t = 1,...N, which are given by:

P X ctk = xtpukp (A.15) p=1

A.4 Singular Value Decomposition

For easy calculation we do not have to solve the eigenvalue problem, but we can use a singular value decomposition. This section shows the link between singular value decomposition and the method based on covariances. Singular Value Decomposition is a powerful tool from linear algebra, which is based on the Eckart-Young theorem (Davis, 2002). This theorem states that for any real matrix X, two orthogonal matrices V and U can be found, for which the product is a real diagonal matrix with no negative elements. Rearranging the matrices in the statement of the Eckart-Young theorem shows that any real matrix can be written as the product of three other matrices:

X = VΛUT (A.16)

where X is an m n real matrix, V is an m m orthogonal matrix, Λ is an m n rectangular diagonal matrix with× non-negative real numbers,× and U is an n n orthogonal matrix.× × The matrix Λ is diagonal (Λ = Diag(λ1, λ2, . . . , λr), where r = min(n, p)), which contains the singular values. The columns of V and U contain respectively the so-called left and right singular vectors. A.4. Singular Value Decomposition 75

1 To show the link with the covariance method, we need a matrix Y = X. Because of this √N 1 scaling with factor , matrices V and U will not be aﬀected, but the singular values (Λ) will √N be multiplied with the scaling factor:

VY = VX U = U Y X (A.17) 1 ΛY = ΛX √N

From A.8 it follows that the covariance matrix of X is calculated as:

1 T SX = X X N 1 = (√NYT )(√NY) (A.18) N = YT Y

If we perform a singular value decomposition on S, we get:

T SX = Y Y T T T = (VY ΛY UY ) (VY ΛY UY ) T T T = UY ΛY VY VY ΛY UY (A.19) T T = UY ΛY ΛY UY 2 T = UY ΛY UY

We now see the similarity of equations A.13 and A.19 and we see that UY contains the 2 eigenvectors of the covariance matrix. The corresponding eigenvalues are found as ΛY . From equations A.16 and A.17 we ﬁnd that the right singular vectors of X (the columns of U) are equal to the eigenvectors of the covariance matrix. The eigenvalues of the covariance 2 matrix (ΛY) are related to the singular values in matrix X as:

2 1 2 1 2 ΛY = ( ΛX ) = ΛX (A.20) √N N where I is the identity matrix. The principal components PC can be calculated by the projection of X on the eigenvectors U, or by multiplication of the left singular vectors and the singular values:

PC = XU = VΛUT U (A.21) = VΛ

This shows that the EOF eigenvectors and the principal components can be found by using an singular value decomposition on the anomaly matrix X. 76 APPENDIX A. EOF ANALYSIS Appendix B

Comparison tidal data

For the performance assessment of the Storm Atlas for the North Sea, the storm surges as predicted by the Storm Atlas and the observed storm surges are compared. To determine the observed storm surges, the observed water levels have to be divided in the tidal signal and the storm surge. To determine the tidal signal, the databases in DelftDashboard are used. Within DelftDashboard there are two databases of tidal stations available. The ﬁrst database is retrieved from the International Hydrographic Organization (IHO), the second database is generated by the XTide model (Flater, 1998) The IHO and XTide datasets of DelftDashboard are compared to the tidal predictions of Rijkswaterstaat for an arbitrary month. This is done at two diﬀerent locations: Hoek van Holland and Delfzijl. We adjust the XTide tidal predictions by 2 hours.

77 78 APPENDIX B. COMPARISON TIDAL DATA Appendix C

Improvements of the operational Storm Atlas

C.1 Introduction

In this study, two methods (A and B) of the Storm Atlas are used. Method A (resampling) is based on the current operational version, method B (regression) is newly developed. At the start of this research some errors have been removed and improvements have been made in both methods. These improvements are described in this appendix. The improved versions of both methods have been used for the validation.

C.2 Improvements in operational version (resampling)

In the operational version of the Storm Atlas, some minor mistakes are made in the pre-processing of the pressure field data. As a first step of this research, the pre-processing of the pressure field data is improved. In the operational version of the Storm Atlas, first the climatology is subtracted from the pressure fields. Next, the resulting fields of anomalies are multiplied by a land-sea-mask, which basically sets all pressure values over land to zero. As described in appendix A, also the spatial averages are subtracted, because we are interested in the gradients of these anomalies, rather than the absolute values. However, in the operational version of the Storm Atlas, as a side effect of subtracting the spatial average, also the values over land change to nonzero values. When these fields are used to derive the EOFs, also variance over land has to be explained, which will influence our EOFs. Because the spatial average will be different for each field, the values over land are also different for each field and with that also the variance which has to be explained by the EOFs. After this was corrected, by setting the land parts to zero after subtracting the spatial average, the EOFs were derived again. As a result of the corrections, the former first EOF (as found in Caires et al. (2014)) was not present anymore. Because the first EOF explain much of variance, this also influenced the resampling and regression. Furthermore, a correction was done in the timing of the storm surge. After the best match was found, the storm surge is read from the database, but in the model script, the surge of six

79 80 APPENDIX C. IMPROVEMENTS OF THE OPERATIONAL STORM ATLAS hours later was read. This also was corrected for.

C.3 Improvement in method B (regression)

In the regression method, a spline is used to interpolate between the 6-hourly calculated storm surge. This spline function, however, is written in Fortran-90/95, where the regression method is written in Fortran-77. Both functions did not compile well together. In this study, a cubic spline function is used in the post-processing of the data. Appendix D

Graphs of hindcasted storms in Hoek van Holland

In this appendix figures are given of the hindcasted storms in Hoek van Holland. For every storm, as listed in table 4.1, (a) shows the results of the simulations with Storm Atlas method A (resampling). The observed water levels, simulated storm surge, simulated water levels, the tidal signal from the IHO database and the water levels as forecasted by WAQUA are shown. In the top figure, the distance, calculated according equation 3.3, is shown for the resampled pressure field. The x-axis is the same as in the figure below. Since the matched pressure fields have a 6-hourly resolution, the bars also have a 6-hour interval. The values of the distance are a measure of the well the best matched pressure field matches to pressure field used as input. Since the values of the principal components are very large, also the absolute values of the distances are very large. The values itself have no physical meaning. Therefore, the distance is normalized such that the smallest distance of all resampled pressure fields (of all 33 storms) is 1. This way, the values of the distance give an indication of the distance compared to each other. Figures (b) shows the results of the simulations with Storm Atlas method B (regression). In this figure, also the observed water levels, simulated storm surge, simulated water levels, the tidal signal from the IHO database and the water levels as forecasted by WAQUA are shown. Obviously, the observed water levels, tidal signal and simulated water levels by WAQUA are the same for figures (a) and (b).

81 82 APPENDIX D. GRAPHS OF HINDCASTED STORMS IN HOEK VAN HOLLAND

400

300

200

Distance [-] 100

0 Water level [m + MSL] 1 −

02/13 02/13 02/14 02/14 02/15 02/15 02/16 02/16 Date in 1979 (month/day) (a) Resampling method

0 Water level [m + MSL] 1 −

02/13 02/13 02/14 02/14 02/15 02/15 02/16 02/16 Date in 1979 (month/day) (b) Regression method

Figure D.1: Storm 1 83

400

300

200

Distance [-] 100

0 Water level [m + MSL] 1 −

01/31 01/31 02/01 02/01 02/02 02/02 02/03 02/03 Date in 1983 (month/day) (a) Resampling method

0 Water level [m + MSL] 1 −

01/31 01/31 02/01 02/01 02/02 02/02 02/03 02/03 Date in 1983 (month/day) (b) Regression method

Figure D.2: Storm 2 84 APPENDIX D. GRAPHS OF HINDCASTED STORMS IN HOEK VAN HOLLAND

400

300

200

Distance [-] 100

0 Water level [m + MSL] 1 −

11/26 11/26 11/27 11/27 11/28 11/28 11/29 11/29 Date in 1983 (month/day) (a) Resampling method

0 Water level [m + MSL] 1 −

11/26 11/26 11/27 11/27 11/28 11/28 11/29 11/29 Date in 1983 (month/day) (b) Regression method

Figure D.3: Storm 3 85

400

300

200

Distance [-] 100

0 Water level [m + MSL] 1 −

02/13 02/13 02/14 02/14 02/15 02/15 02/16 02/16 Date in 1989 (month/day) (a) Resampling method

0 Water level [m + MSL] 1 −

02/13 02/13 02/14 02/14 02/15 02/15 02/16 02/16 Date in 1989 (month/day) (b) Regression method

Figure D.4: Storm 4 86 APPENDIX D. GRAPHS OF HINDCASTED STORMS IN HOEK VAN HOLLAND

400

300

200

Distance [-] 100

0 Water level [m + MSL] 1 −

01/25 01/25 01/26 01/26 01/27 01/27 01/28 01/28 Date in 1990 (month/day) (a) Resampling method

0 Water level [m + MSL] 1 −

01/25 01/25 01/26 01/26 01/27 01/27 01/28 01/28 Date in 1990 (month/day) (b) Regression method

Figure D.5: Storm 5 87

400

300

200

Distance [-] 100

0 Water level [m + MSL] 1 −

02/27 02/27 02/28 02/28 03/01 03/01 03/02 03/02 Date in 1990 (month/day) (a) Resampling method

0 Water level [m + MSL] 1 −

02/27 02/27 02/28 02/28 03/01 03/01 03/02 03/02 Date in 1990 (month/day) (b) Regression method

Figure D.6: Storm 6 88 APPENDIX D. GRAPHS OF HINDCASTED STORMS IN HOEK VAN HOLLAND

400

300

200

Distance [-] 100

0 Water level [m + MSL] 1 −

12/11 12/11 12/12 12/12 12/13 12/13 12/14 12/14 Date in 1990 (month/day) (a) Resampling method

0 Water level [m + MSL] 1 −

12/11 12/11 12/12 12/12 12/13 12/13 12/14 12/14 Date in 1990 (month/day) (b) Regression method

Figure D.7: Storm 7 89

400

300

200

Distance [-] 100

0 Water level [m + MSL] 1 −

12/19 12/19 12/20 12/20 12/21 12/21 12/22 12/22 Date in 1991 (month/day) (a) Resampling method

0 Water level [m + MSL] 1 −

12/19 12/19 12/20 12/20 12/21 12/21 12/22 12/22 Date in 1991 (month/day) (b) Regression method

Figure D.8: Storm 8 90 APPENDIX D. GRAPHS OF HINDCASTED STORMS IN HOEK VAN HOLLAND

400

300

200

Distance [-] 100

0 Water level [m + MSL] 1 −

11/10 11/10 11/11 11/11 11/12 11/12 11/13 11/13 Date in 1992 (month/day) (a) Resampling method

0 Water level [m + MSL] 1 −

11/10 11/10 11/11 11/11 11/12 11/12 11/13 11/13 Date in 1992 (month/day) (b) Regression method

Figure D.9: Storm 9 91

400

300

200

Distance [-] 100

0 Water level [m + MSL] 1 −

01/22 01/22 01/23 01/23 01/24 01/24 01/25 01/25 Date in 1993 (month/day) (a) Resampling method

0 Water level [m + MSL] 1 −

01/22 01/22 01/23 01/23 01/24 01/24 01/25 01/25 Date in 1993 (month/day) (b) Regression method

Figure D.10: Storm 10 92 APPENDIX D. GRAPHS OF HINDCASTED STORMS IN HOEK VAN HOLLAND

400

300

200

Distance [-] 100

0 Water level [m + MSL] 1 −

02/20 02/20 02/21 02/21 02/22 02/22 02/23 02/23 Date in 1993 (month/day) (a) Resampling method

0 Water level [m + MSL] 1 −

02/20 02/20 02/21 02/21 02/22 02/22 02/23 02/23 Date in 1993 (month/day) (b) Regression method

Figure D.11: Storm 11 93

400

300

200

Distance [-] 100

0 Water level [m + MSL] 1 −

11/13 11/13 11/14 11/14 11/15 11/15 11/16 11/16 Date in 1993 (month/day) (a) Resampling method

0 Water level [m + MSL] 1 −

11/13 11/13 11/14 11/14 11/15 11/15 11/16 11/16 Date in 1993 (month/day) (b) Regression method

Figure D.12: Storm 12 94 APPENDIX D. GRAPHS OF HINDCASTED STORMS IN HOEK VAN HOLLAND

400

300

200

Distance [-] 100

0 Water level [m + MSL] 1 −

12/18 12/18 12/19 12/19 12/20 12/20 12/21 12/21 Date in 1993 (month/day) (a) Resampling method

0 Water level [m + MSL] 1 −

12/18 12/18 12/19 12/19 12/20 12/20 12/21 12/21 Date in 1993 (month/day) (b) Regression method

Figure D.13: Storm 13 95

400

300

200

Distance [-] 100

0 Water level [m + MSL] 1 −

01/27 01/27 01/28 01/28 01/29 01/29 01/30 01/30 Date in 1994 (month/day) (a) Resampling method

0 Water level [m + MSL] 1 −

01/27 01/27 01/28 01/28 01/29 01/29 01/30 01/30 Date in 1994 (month/day) (b) Regression method

Figure D.14: Storm 14 96 APPENDIX D. GRAPHS OF HINDCASTED STORMS IN HOEK VAN HOLLAND

400

300

200

Distance [-] 100

0 Water level [m + MSL] 1 −

03/12 03/12 03/13 03/13 03/14 03/14 03/15 03/15 Date in 1994 (month/day) (a) Resampling method

0 Water level [m + MSL] 1 −

03/12 03/12 03/13 03/13 03/14 03/14 03/15 03/15 Date in 1994 (month/day) (b) Regression method

Figure D.15: Storm 15 97

400

300

200

Distance [-] 100

0 Water level [m + MSL] 1 −

12/31 12/31 01/01 01/01 01/02 01/02 01/03 01/03 Date in 1994/1995 (month/day) (a) Resampling method

0 Water level [m + MSL] 1 −

12/31 12/31 01/01 01/01 01/02 01/02 01/03 01/03 Date in 1994/1995 (month/day) (b) Regression method

Figure D.16: Storm 16 98 APPENDIX D. GRAPHS OF HINDCASTED STORMS IN HOEK VAN HOLLAND

400

300

200

Distance [-] 100

0 Water level [m + MSL] 1 −

01/09 01/09 01/10 01/10 01/11 01/11 01/12 01/12 Date in 1995 (month/day) (a) Resampling method

0 Water level [m + MSL] 1 −

01/09 01/09 01/10 01/10 01/11 01/11 01/12 01/12 Date in 1995 (month/day) (b) Regression method

Figure D.17: Storm 17 99

400

300

200

Distance [-] 100

0 Water level [m + MSL] 1 −

08/28 08/28 08/29 08/29 08/30 08/30 08/31 08/31 Date in 1996 (month/day) (a) Resampling method

0 Water level [m + MSL] 1 −

08/28 08/28 08/29 08/29 08/30 08/30 08/31 08/31 Date in 1996 (month/day) (b) Regression method

Figure D.18: Storm 18 100 APPENDIX D. GRAPHS OF HINDCASTED STORMS IN HOEK VAN HOLLAND

400

300

200

Distance [-] 100

0 Water level [m + MSL] 1 −

10/28 10/28 10/29 10/29 10/30 10/30 10/31 10/31 Date in 1996 (month/day) (a) Resampling method

0 Water level [m + MSL] 1 −

10/28 10/28 10/29 10/29 10/30 10/30 10/31 10/31 Date in 1996 (month/day) (b) Regression method

Figure D.19: Storm 19 101

400

300

200

Distance [-] 100

0 Water level [m + MSL] 1 −

02/04 02/04 02/05 02/05 02/06 02/06 02/07 02/07 Date in 1999 (month/day) (a) Resampling method

0 Water level [m + MSL] 1 −

02/04 02/04 02/05 02/05 02/06 02/06 02/07 02/07 Date in 1999 (month/day) (b) Regression method

Figure D.20: Storm 20 102 APPENDIX D. GRAPHS OF HINDCASTED STORMS IN HOEK VAN HOLLAND

400

300

200

Distance [-] 100

0 Water level [m + MSL] 1 −

11/05 11/05 11/06 11/06 11/07 11/07 11/08 11/08 Date in 1999 (month/day) (a) Resampling method

0 Water level [m + MSL] 1 −

11/05 11/05 11/06 11/06 11/07 11/07 11/08 11/08 Date in 1999 (month/day) (b) Regression method

Figure D.21: Storm 21 103

400

300

200

Distance [-] 100

0 Water level [m + MSL] 1 −

12/02 12/02 12/03 12/03 12/04 12/04 12/05 12/05 Date in 1999 (month/day) (a) Resampling method

0 Water level [m + MSL] 1 −

12/02 12/02 12/03 12/03 12/04 12/04 12/05 12/05 Date in 1999 (month/day) (b) Regression method

Figure D.22: Storm 22 104 APPENDIX D. GRAPHS OF HINDCASTED STORMS IN HOEK VAN HOLLAND

400

300

200

Distance [-] 100

0 Water level [m + MSL] 1 −

01/28 01/28 01/29 01/29 01/30 01/30 01/31 01/31 Date in 2000 (month/day) (a) Resampling method

0 Water level [m + MSL] 1 −

01/28 01/28 01/29 01/29 01/30 01/30 01/31 01/31 Date in 2000 (month/day) (b) Regression method

Figure D.23: Storm 23 105

400

300

200

Distance [-] 100

0 Water level [m + MSL] 1 −

10/26 10/26 10/27 10/27 10/28 10/28 10/29 10/29 Date in 2002 (month/day) (a) Resampling method

0 Water level [m + MSL] 1 −

10/26 10/26 10/27 10/27 10/28 10/28 10/29 10/29 Date in 2002 (month/day) (b) Regression method

Figure D.24: Storm 24 106 APPENDIX D. GRAPHS OF HINDCASTED STORMS IN HOEK VAN HOLLAND

400

300

200

Distance [-] 100

0 Water level [m + MSL] 1 −

12/20 12/20 12/21 12/21 12/22 12/22 12/23 12/23 Date in 2003 (month/day) (a) Resampling method

0 Water level [m + MSL] 1 −

12/20 12/20 12/21 12/21 12/22 12/22 12/23 12/23 Date in 2003 (month/day) (b) Regression method

Figure D.25: Storm 25 107

400

300

200

Distance [-] 100

0 Water level [m + MSL] 1 −

10/30 10/30 10/31 10/31 11/01 11/01 11/02 11/02 Date in 2006 (month/day) (a) Resampling method

0 Water level [m + MSL] 1 −

10/30 10/30 10/31 10/31 11/01 11/01 11/02 11/02 Date in 2006 (month/day) (b) Regression method

Figure D.26: Storm 26 108 APPENDIX D. GRAPHS OF HINDCASTED STORMS IN HOEK VAN HOLLAND

400

300

200

Distance [-] 100

0 Water level [m + MSL] 1 −

01/10 01/10 01/11 01/11 01/12 01/12 01/13 01/13 Date in 2007 (month/day) (a) Resampling method

0 Water level [m + MSL] 1 −

01/10 01/10 01/11 01/11 01/12 01/12 01/13 01/13 Date in 2007 (month/day) (b) Regression method

Figure D.27: Storm 27 109

400

300

200

Distance [-] 100

0 Water level [m + MSL] 1 −

01/17 01/17 01/18 01/18 01/19 01/19 01/20 01/20 Date in 2007 (month/day) (a) Resampling method

0 Water level [m + MSL] 1 −

01/17 01/17 01/18 01/18 01/19 01/19 01/20 01/20 Date in 2007 (month/day) (b) Regression method

Figure D.28: Storm 28 110 APPENDIX D. GRAPHS OF HINDCASTED STORMS IN HOEK VAN HOLLAND

400

300

200

Distance [-] 100

0 Water level [m + MSL] 1 −

03/17 03/17 03/18 03/18 03/19 03/19 03/20 03/20 Date in 2007 (month/day) (a) Resampling method

0 Water level [m + MSL] 1 −

03/17 03/17 03/18 03/18 03/19 03/19 03/20 03/20 Date in 2007 (month/day) (b) Regression method

Figure D.29: Storm 29 111

400

300

200

Distance [-] 100

0 Water level [m + MSL] 1 −

11/08 11/08 11/09 11/09 11/10 11/10 11/11 11/11 Date in 2007 (month/day) (a) Resampling method

0 Water level [m + MSL] 1 −

11/08 11/08 11/09 11/09 11/10 11/10 11/11 11/11 Date in 2007 (month/day) (b) Regression method

Figure D.30: Storm 30 112 APPENDIX D. GRAPHS OF HINDCASTED STORMS IN HOEK VAN HOLLAND

400

300

200

Distance [-] 100

0 Water level [m + MSL] 1 −

02/29 02/29 03/01 03/01 03/02 03/02 03/03 03/03 Date in 2008 (month/day) (a) Resampling method

0 Water level [m + MSL] 1 −

02/29 02/29 03/01 03/01 03/02 03/02 03/03 03/03 Date in 2008 (month/day) (b) Regression method

Figure D.31: Storm 31 113

400

300

200

Distance [-] 100

0 Water level [m + MSL] 1 −

03/20 03/20 03/21 03/21 03/22 03/22 03/23 03/23 Date in 2008 (month/day) (a) Resampling method

0 Water level [m + MSL] 1 −

03/20 03/20 03/21 03/21 03/22 03/22 03/23 03/23 Date in 2008 (month/day) (b) Regression method

Figure D.32: Storm 32 114 APPENDIX D. GRAPHS OF HINDCASTED STORMS IN HOEK VAN HOLLAND

400

300

200

Distance [-] 100

0 Water level [m + MSL] 1 −

12/05 12/05 12/06 12/06 12/07 12/07 12/08 12/08 Date in 2013 (month/day) (a) Resampling method

0 Water level [m + MSL] 1 −

12/05 12/05 12/06 12/06 12/07 12/07 12/08 12/08 Date in 2013 (month/day) (b) Regression method

Figure D.33: Storm 33 Appendix E

Matched pressure ﬁelds

In this appendix, figures are shown of the found matches in the database. The figures consist of 6 subfigures and have the configuration as shown in figure E.1:

A In the shown figures, the top left subfigure shows the observed water level, simulated water level, simulated storm surge and WAQUA water level. Basically it is a zoom in from the figures in appendix D. The black line shows the moment where the pressure field is matched.

B Top middle is the pressure field, used as input for the Storm Atlas. The black rectangle shows the boundaries used in the Storm Atlas for matching the pressure field. Pressure out of the boundaries is not taken into account. C Top right is the pressure field, found by the Storm Atlas as ‘best match’. D Bottom left shows the distance, as shown in appendix D. The arrow shows timestep of the pressure fields on the right. In blue, the distance of the best match is shown. In yellow the distance of the second best match is shown, in red the distance of the third best match. By definition, the distance of the third best match is larger than the distance of the second best match is larger than the distance of the best match. Therefore, the distances are placed behind each other.

E Bottom middle is the pressure ﬁeld found as ‘second best match’. F Bottom right is the pressure ﬁeld found as ‘third best match’.

A B C

D E F

Figure E.1: Overview of graphs shown in this appendix

115 116 APPENDIX E. MATCHED PRESSURE FIELDS

5 1.04 x 10 10 10 5 5 1.02 0 0 1 Best match 3rd best match −5 −5 0.98 −10 −10

64 62 60 58 56 54 52 50 48 64 62 60 58 56 54 52 50 48

5 1.04 x 10 10 10 5 5 1.02 0 0 1 2nd best match −5 −5 Original field (input) 0.98 −10 −10

64 62 60 58 56 54 52 50 48 64 62 60 58 56 54 52 50 48 30 25 20 15 Water levels 10 Date in 1983 (month/day) 5 Distances of best three matches 3 2 1 0 0 50 −1

3.5 2.5 1.5 0.5

400 350 300 250 200 150 100 −0.5 −1.5 Water level (m) level Water

Figure E.2: Storm 3. This match clearly shows that the spatial averaged pressure is not taken into account in the process of finding a best match. The best matching pressure field has on average a higher pressure than the pressure field uses as input. The water level predicted by WAQUA is higher than predicted by the Storm Atlas. 117

5 1.04 x 10 10 10 5 5 1.02 0 0 1 Best match 3rd best match −5 −5 0.98 −10 −10

64 62 60 58 56 54 52 50 48 64 62 60 58 56 54 52 50 48

5 1.04 x 10 10 10 5 5 1.02 0 0 1 2nd best match −5 −5 Original field (input) 0.98 −10 −10

64 62 60 58 56 54 52 50 48 64 62 60 58 56 54 52 50 48 30 25 20 15 Water levels 10 Date in 1989 (month/day) 5 Distances of best three matches 3 2 1 0 0 50 −1

3.5 2.5 1.5 0.5

400 350 300 250 200 150 100 −0.5 −1.5 Water level (m) level Water

Figure E.3: Storm 4. In this storm, the isobars in best matching pressure ﬁeld are more horizontal compared to the original pressure ﬁeld, where the isobars are more in north-south direction, creating a bigger fetch for Hoek van Holland. The Storm Atlas underestimates this storm surge. 118 APPENDIX E. MATCHED PRESSURE FIELDS

5 1.04 x 10 10 10 5 5 1.02 0 0 1 Best match 3rd best match −5 −5 0.98 −10 −10

64 62 60 58 56 54 52 50 48 64 62 60 58 56 54 52 50 48

5 1.04 x 10 10 10 5 5 1.02 0 0 1 2nd best match −5 −5 Original field (input) 0.98 −10 −10

64 62 60 58 56 54 52 50 48 64 62 60 58 56 54 52 50 48 30 25 20 15 Water levels 10 Date in 1990 (month/day) 5 Distances of best three matches 3 2 1 0 0 50 −1

3.5 2.5 1.5 0.5

400 350 300 250 200 150 100 −0.5 −1.5 Water level (m) level Water

Figure E.4: Storm 4. The average spatial pressure in the matched ﬁeld is less than in the original ﬁeld. Nevertheless, the storm surge is predicted fairly well for the next 6 hours. 119

5 1.04 x 10 10 10 5 5 1.02 0 0 1 Best match 3rd best match −5 −5 0.98 −10 −10

64 62 60 58 56 54 52 50 48 64 62 60 58 56 54 52 50 48

5 1.04 x 10 10 10 5 5 1.02 0 0 1 2nd best match −5 −5 Original field (input) 0.98 −10 −10

64 62 60 58 56 54 52 50 48 64 62 60 58 56 54 52 50 48 30 25 20 01/27 15 Water levels 10 Date in 1990 (month/day) 5 Distances of best three matches 3 2 1 0 0 50 −1

3.5 2.5 1.5 0.5

400 350 300 250 200 150 100 −0.5 −1.5 Water level (m) level Water

Figure E.5: Storm 5. The storm surge is underpredicted by the Storm Atlas. However the isobars are quite the same in the best matching pressure ﬁeld as in the original ﬁeld, the spatial average in the best match is higher. It seems the storm from the database is less heavy than the forecasted storm 120 APPENDIX E. MATCHED PRESSURE FIELDS

5 1.04 x 10 10 10 5 5 1.02 0 0 1 Best match 3rd best match −5 −5 0.98 −10 −10

64 62 60 58 56 54 52 50 48 64 62 60 58 56 54 52 50 48

5 1.04 x 10 10 10 5 5 1.02 0 0 1 2nd best match −5 −5 Original field (input) 0.98 −10 −10

64 62 60 58 56 54 52 50 48 64 62 60 58 56 54 52 50 48 30 25 20 15 Water levels 10 Date in 1990 (month/day) 5 Distances of best three matches 3 2 1 0 0 50 −1

3.5 2.5 1.5 0.5

400 350 300 250 200 150 100 −0.5 −1.5 Water level (m) level Water

Figure E.6: Storm 6. According to the distance, the matched pressure ﬁeld matches very well with the forecasted pressure ﬁeld. However, the storm surge forecast is much too low. 121

5 1.04 x 10 10 10 5 5 1.02 0 0 1 Best match 3rd best match −5 −5 0.98 −10 −10

64 62 60 58 56 54 52 50 48 64 62 60 58 56 54 52 50 48

5 1.04 x 10 10 10 5 5 1.02 0 0 1 2nd best match −5 −5 Original field (input) 0.98 −10 −10

64 62 60 58 56 54 52 50 48 64 62 60 58 56 54 52 50 48 30 25 20 15 Water levels 10 Date in 1999 (month/day) 5 Distances of best three matches 3 2 1 0 0 50 −1

3.5 2.5 1.5 0.5

400 350 300 250 200 150 100 −0.5 −1.5 Water level (m) level Water

Figure E.7: Storm 22. This storm surge is underestimated by approximately 0.5 meter, also the distance is very high, indicating that the pressure fields do not match well. However, looking at the pressure field, the spatial structure looks a good look-a-like. The isobars are a little more toward a north-south direction in the input field. 122 APPENDIX E. MATCHED PRESSURE FIELDS

5 1.04 x 10 10 10 5 5 1.02 0 0 1 Best match 3rd best match −5 −5 0.98 −10 −10

64 62 60 58 56 54 52 50 48 64 62 60 58 56 54 52 50 48

5 1.04 x 10 10 10 5 5 1.02 0 0 1 2nd best match −5 −5 Original field (input) 0.98 −10 −10

64 62 60 58 56 54 52 50 48 64 62 60 58 56 54 52 50 48 30 25 20 15 Water levels 10 Date in 2002 (month/day) 10/26 5 Distances of best three matches 3 2 1 0 0 50 −1

3.5 2.5 1.5 0.5

400 350 300 250 200 150 100 −0.5 −1.5 Water level (m) level Water

Figure E.8: Storm 24. This storm is also underestimated. The matched pressure ﬁeld does not seem resemble a heavy storm as the input pressure ﬁeld indicates. 123

5 1.04 x 10 10 10 5 5 1.02 0 0 1 Best match 3rd best match −5 −5 0.98 −10 −10

64 62 60 58 56 54 52 50 48 64 62 60 58 56 54 52 50 48

5 1.04 x 10 10 10 5 5 1.02 0 0 1 2nd best match −5 −5 Original field (input) 0.98 −10 −10

64 62 60 58 56 54 52 50 48 64 62 60 58 56 54 52 50 48 30 25 20 15 Water levels 10 Date in 2002 (month/day) 5 Distances of best three matches 3 2 1 0 0 50 −1

3.5 2.5 1.5 0.5

400 350 300 250 200 150 100 −0.5 −1.5 Water level (m) level Water

Figure E.9: Storm 24. This storm is overestimated, as well as the average spatial pressure. 124 APPENDIX E. MATCHED PRESSURE FIELDS

5 1.04 x 10 10 10 5 5 1.02 0 0 1 Best match 3rd best match −5 −5 0.98 −10 −10

64 62 60 58 56 54 52 50 48 64 62 60 58 56 54 52 50 48

5 1.04 x 10 10 10 5 5 1.02 0 0 1 2nd best match −5 −5 Original field (input) 0.98 −10 −10

64 62 60 58 56 54 52 50 48 64 62 60 58 56 54 52 50 48 30 25 03/19 20 15 Water levels 10 Date in 2007 (month/day) 5 Distances of best three matches 3 2 1 0 0 50 −1

3.5 2.5 1.5 0.5

400 350 300 250 200 150 100 −0.5 −1.5 Water level (m) level Water

Figure E.10: Storm 29. The storm surge is underpredicted. The north-south component of the input pressure ﬁeld does not seem to be resembled by the best match very well. 125

5 1.04 x 10 10 10 5 5 1.02 0 0 1 Best match 3rd best match −5 −5 0.98 −10 −10

64 62 60 58 56 54 52 50 48 64 62 60 58 56 54 52 50 48

5 1.04 x 10 10 10 5 5 1.02 0 0 1 2nd best match −5 −5 Original field (input) 0.98 −10 −10

64 62 60 58 56 54 52 50 48 64 62 60 58 56 54 52 50 48 30 25 20 15 Water levels 10 Date in 2013 (month/day) 5 Distances of best three matches 3 2 1 0 0 50 −1

3.5 2.5 1.5 0.5

400 350 300 250 200 150 100 −0.5 −1.5 Water level (m) level Water

Figure E.11: Storm 33. This storm is underestimated by almost 1 meter. However, the matched pressure ﬁeld seems a good match. as well as the average spatial pressure. 126 APPENDIX E. MATCHED PRESSURE FIELDS Appendix F

Sensitivity analysis method A - resampling

In this appendix, graphs and aggregated results are shown for the sensitivity of several sources of uncertainty of the North Sea Storm Surge Atlas method A - resampling. The following cases have been examined:

1. New weights timesteps - all equal In the current operational version weight are applied for of the different timesteps (W∆ in equation 3.3). These are set to 1 for timesteps t = 0 and t = 6 hours and 0.5 for t = 12 hours. The influence of these weights is examined by changing− them all to 1. This− way also the influence of timestep t = 12 hours can be examined. − 2. New weights timesteps - t = 6 hours high weight As with the case described above,− the influence of the weights and the influence of timestep t = 6 hours is examined by giving this timestep a weight of 2. − 3. Only 10 EOFs The current operational Storm Atlas uses 50 EOFs to find a best matching pressure field. In this case, this number is reduced to 10 EOFs. 4. Only 5 EOFs The current operational Storm Atlas uses 50 EOFs to find a best matching pressure field. In this case, this number is reduced to 5 EOFs. 5. Only 3 EOFs The current operational Storm Atlas uses 3 EOFs to find a best matching pressure field. In this case, this number is reduced to 3 EOFs.

6. Matching with 1 timestep (t = 0) The number of timesteps which is used for finding a best matching storm in the database influences the matching with the database. In the current version of the Storm Atlas, three consequential pressure fields are matched to include the meteorological development of a storm. In this case, only one timestep is used, being t = 0. In this case, the input pressure field and the resampled pressure field can be easily compared, as this will be the best match of that single field, not influenced by other pressure fields.

127 128 APPENDIX F. SENSITIVITY ANALYSIS METHOD A - RESAMPLING

7. Matching with 2 timesteps (t = 0 and t = 6 hours) The number of timesteps which is used for finding− a best matching storm in the database influences the matching with the database. In the current version of the Storm Atlas, three consequential pressure fields are matched to include the meteorological development of a storm. In this case, only two timesteps are used, being t = 0 and t = 6 hours. − 8. Matching with 2 timestep (t = 6 and t = 12 hours) The number of timesteps which is− used for finding− a best matching storm in the database influences the matching with the database. In the current version of the Storm Atlas, three consequential pressure fields are matched to include the meteorological development of a storm. In this case, only two timesteps are used, being t = 6 and t = 12 hours. This implicitly assumes that the storm surge is not depending on− the current− pressure, but is entirely caused by the weather of 6 to 12 hours ago. 9. Matching with extra timestep t = 18 hours In this case the matching of the pressure− fields is based on 4 consequential timesteps, where t = 18 hours is added as an additional pressure field to match. − 10. Matching with extra timestep t = +6 hours In this case the matching of the pressure fields is based on 4 consequential timesteps, where t = +6 hours is added as an additional pressure field to match. 11. Using multiple analogues As described in section 5.2, the operational version uses an algorithm which searches for 5 best matching pressure fields and chooses the best match based on the extent to which the surge corresponding to the matched pressure field connects to the simulated surge in the previous timestep. For the validation of the Storm Atlas in chapter 4, this algorithm was removed. This case uses the algorithm to see the effects on the performance of the Storm Atlas. 12. No smoothening function As described in section 3.4.3, a smoothening function is applied to reduce the discontinuities in the simulated storm surge due to matches from different locations in the database. This smoothening function influences the shape of the matched storm surge and therefore can influence the performance. In this case, no smoothening function is applied. 13. Inversed smoothening function In this case the smoothening function is inversed. As described in section 3.4, a smoothening function is used to decrease the discontinuities. This smoothening function examines the ‘jump’ at t = 0 of the matched timestep. The selected surge is than corrected backwards, where t = 5 hours is assumed to be correct. The values of t = 0, 1,..., 4 are corrected to decrease the jump between t = 1 hour and t = 0. In this case the values of t = 1, 2,..., 5 are corrected to decrease the jump− between t = 5 hour and t = 6 hours (which is the first hour is the next matched timestep). Figure F.1 shows the difference between the original smoothening function and the inversed smoothening function. 14. New inversed smoothening function Rather than the exponential smoothening function as used in case 13, a quadratic function is used. The exponential function also corrected t = 0 slightly. This was corrected for by the quadratic function. The correction of the other timesteps also slightly changed. 129

1.2 Resampled storm surge 1 Smoothened storm surge

0.8

0.6 Jump 0.4 Surge [m]

0.2

0.2 − 6 4 2 0 2 4 6 8 10 − − − time [hours] (a) Original smoothening function

1.2 Resampled storm surge 1 Smoothened storm surge

0.8 Jump

0.6

0.4 Surge [m]

0.2

0.2 − 6 4 2 0 2 4 6 8 10 − − − time [hours] (b) Inversed smoothening function

Figure F.1: Schematic representation of the eﬀect of the smoothening function. The hours 0,..., 6 are corrected, such that the jump is reduced. The resampled storm surge is (a) and (b) are the same. 130 APPENDIX F. SENSITIVITY ANALYSIS METHOD A - RESAMPLING

15. Extended database In this case the database is extended to approximately 4000 years. This way the Storm Atlas has more possible weather scenarios to find a best match. 16. Extended database including barometric effect As described in appendix A, for the EOF analysis, besides the time average (climatology), also the spatial average of each field is removed to retrieve the anomalies. By removing the spatial average, the Storm Atlas focuses more on relative pressure differences. If a certain pressure gradient occurs at (average) high pressure or (average) low pressure, the generated winds should be the same. However, by removing the spatial average, the inverted barometer effect as described in chapter 2 is omitted. Also, the average spatial pressure can be seen as an indicator for the intensity of the storm. In this case the barometric effect is taken into account in the EOF analysis, by not removing the spatial average of each pressure field. New EOFs are derived and the database is projected on these new EOFs. In this case, the extended database from case 15 is used.

Table F.1 shows the results of the diﬀerent cases on the aggregated results. Table F.2 shows the values of the performance indicators at Hoek van Holland. Since at Hoek van Holland also a WAQUA calculation of the storm surge is available, the performance of the peak water level of the Storm Atlas compared to WAQUA is made. This comparison is made for the observed peak water level and the simulated peak water level within 8 hours range of the observed peak water level. This way, the water levels at the same tidal peak are compared. Next, per case, the boxplots as in chapter 4 are given. Table F.1: Comparison of the performance of the diﬀerent cases for Storm Atlas method A. The aggregated results for all stations are shown.

Performance indicator Base caseCase 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8 Case 9 Case 10 Case 11 Case 12 Case 13 Case 14 Case 15 Case 16 Peak water level RMSE (m) 0.47 0.49 0.50 0.48 0.46 0.48 0.48 0.48 0.54 0.51 0.51 0.50 0.46 0.47 0.47 0.49 0.47

131 Bias (m) -0.31 -0.32 -0.33 -0.31 -0.32 -0.29 -0.31 -0.34 -0.40 -0.34 -0.34 -0.36 -0.27 -0.3 -0.29 -0.31 -0.32 St dev. (m) 0.36 0.38 0.37 0.37 0.33 0.38 0.37 0.34 0.36 0.38 0.38 0.35 0.37 0.36 0.36 0.37 0.35 Duration RMSE (hours) 1.20 1.24 1.24 1.25 1.22 1.13 1.20 1.22 1.30 1.31 1.28 1.37 1.36 1.35 1.35 1.29 1.37 Bias (hours) -0.62 -0.63 -0.66 -0.63 -0.66 -0.54 -0.59 -0.71 -0.76 -0.73 -0.71 -0.78 -0.72 -0.75 -0.72 -0.70 -0.80 St dev. (hours) 1.03 1.07 1.05 1.08 1.02 0.99 1.04 1.00 1.06 1.09 1.07 1.12 1.16 1.13 1.14 1.08 1.11 Timing of peak RMSE (hours) 7.03 6.84 7.35 7.00 7.44 7.63 7.64 7.43 7.03 7.12 7.44 7.25 7.34 7.56 7.47 7.15 7.45 Bias (hours) -0.13 0.05 0.14 -0.42 -0.15 -0.92 -1.04 -0.53 -0.64 -0.37 -0.36 -0.32 -0.53 -0.97 -0.94 0.08 -1.26 St dev. (hours) 7.03 6.83 7.35 6.99 7.44 7.58 7.57 7.42 7.00 7.11 7.44 7.25 7.33 7.50 7.41 7.15 7.35 Table F.2: Comparison of the performance of Storm Atlas method A (resampling) at Hoek van Holland

Performance indicator Base caseCase 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8 Case 9 Case 10 Case 11 Case 12 Case 13 Case 14 Case 15 Case 16 Peak water level RMSE (m) 0.39 0.41 0.40 0.40 0.32 0.38 0.36 0.32 0.44 0.41 0.38 0.37 0.41 0.36 0.38 0.38 0.38 Bias (m) -0.11 -0.09 -0.13 -0.10 -0.11 -0.09 -0.14 -0.14 -0.23 -0.13 -0.11 -0.19 -0.06 -0.09 -0.08 -0.09 -0.17 St dev. (m) 0.37 0.40 0.38 0.39 0.30 0.37 0.34 0.28 0.38 0.38 0.36 0.32 0.41 0.35 0.37 0.37 0.33

132 Duration RMSE (hours) 0.85 0.90 0.75 0.94 0.88 0.79 1.12 0.95 0.95 1.30 0.94 0.95 1.02 0.97 0.94 1.02 0.95 Bias (hours) -0.16 -0.25 -0.19 -0.19 -0.28 -0.06 -0.38 -0.41 -0.34 -0.44 -0.25 -0.53 -0.16 -0.31 -0.19 -0.28 -0.41 St dev. (hours) 0.83 0.87 0.73 0.92 0.84 0.79 1.05 0.86 0.89 1.22 0.90 0.79 1.00 0.92 0.92 0.98 0.86 Timing of peak RMSE (hours) 6.05 6.29 6.36 6.35 7.44 6.69 7.33 6.81 6.64 6.28 6.53 7.13 6.06 6.81 6.81 7.42 6.70 Bias (hours) -0.94 -0.56 -0.50 -1.31 -0.94 -2.44 -0.81 -0.91 -1.59 -0.50 -0.50 -0.47 -0.94 -0.94 -1.64 0.69 -1.66 St dev. (hours) 5.98 6.27 6.34 6.22 7.38 6.23 7.29 6.75 6.44 6.26 6.51 7.11 5.99 6.75 6.60 7.39 6.49 Peak water level compared to WAQUA RMSE (m) 0.33 0.37 0.36 0.33 0.29 0.35 0.34 0.29 0.41 0.36 0.32 0.33 0.32 0.28 0.28 0.32 0.28 Bias (m) -0.12 -0.10 -0.14 -0.11 -0.12 -0.10 -0.15 -0.15 -0.24 -0.14 -0.12 -0.20 -0.07 -0.10 -0.09 -0.10 -0.18 St dev. (m) 0.31 0.36 0.33 0.31 0.26 0.34 0.30 0.24 0.33 0.33 0.29 0.26 0.32 0.26 0.27 0.31 0.21 133

2 Overprediction - too high

1 − Water level diﬀerence [m]

2 Underprediction - too low − (a) Peak water level

Overprediction - too long 4

2 −

4 Storm duration diﬀerence [hours] − Underprediction - too short (b) Storm duration

Overprediction - too late

Figure F.2: Storm Atlas method A (resampling): Results of case 1 on the performance per station on the 3 performance indicators 134 APPENDIX F. SENSITIVITY ANALYSIS METHOD A - RESAMPLING

2 Overprediction - too high

1 − Water level diﬀerence [m]

2 Underprediction - too low − (a) Peak water level

Overprediction - too long 4

2 −

4 Storm duration diﬀerence [hours] − Underprediction - too short (b) Storm duration

Overprediction - too late

Figure F.3: Storm Atlas method A (resampling): Results of case 1 on the performance per storm on the 3 performance indicators 135

2 Overprediction

1 − Water level diﬀerence [m]

2 Underprediction − (a) Peak water level

4 Overprediction

2 − Storm duration diﬀerence [hours] 4 Underprediction − (b) Storm duration

Overprediction

20 Time diﬀerence peak− [hours] Underprediction Dover Delfzijl IJmuiden Aberdeen Lowestoft Vlissingen Den Helder Immingham North Shields Southend on Sea Hoek van Holland (c) Timing of the peak water level

Figure F.4: Storm Atlas method A (resampling): Results of case 2 on the performance per station on the 3 performance indicators 136 APPENDIX F. SENSITIVITY ANALYSIS METHOD A - RESAMPLING

2 Overprediction

1 − Water level diﬀerence [m]

2 Underprediction − (a) Peak water level

4 Overprediction

2 − Storm duration diﬀerence [hours] 4 Underprediction − (b) Storm duration

Overprediction

20 Time diﬀerence peak− [hours] Underprediction Storm 1 Storm 2 Storm 3 Storm 4 Storm 5 Storm 6 Storm 7 Storm 8 Storm 9 Storm 10 Storm 11 Storm 12 Storm 13 Storm 14 Storm 15 Storm 16 Storm 17 Storm 18 Storm 19 Storm 20 Storm 21 Storm 22 Storm 23 Storm 24 Storm 25 Storm 26 Storm 27 Storm 28 Storm 29 Storm 30 Storm 31 Storm 32 Storm 33 (c) Timing of the peak water level

Figure F.5: Storm Atlas method A (resampling): Results of case 2 on the performance per storm on the 3 performance indicators 137

2 Overprediction

1 − Water level diﬀerence [m]

2 Underprediction − (a) Peak water level

4 Overprediction

2 − Storm duration diﬀerence [hours] 4 Underprediction − (b) Storm duration

Overprediction

Figure F.6: Storm Atlas method A (resampling): Results of case 3 on the performance per station on the 3 performance indicators 138 APPENDIX F. SENSITIVITY ANALYSIS METHOD A - RESAMPLING

2 Overprediction

1 − Water level diﬀerence [m]

2 Underprediction − (a) Peak water level

4 Overprediction

2 − Storm duration diﬀerence [hours] 4 Underprediction − (b) Storm duration

Overprediction

Figure F.7: Storm Atlas method A (resampling): Results of case 3 on the performance per storm on the 3 performance indicators 139

2 Overprediction

1 − Water level diﬀerence [m]

2 Underprediction − (a) Peak water level

4 Overprediction

2 − Storm duration diﬀerence [hours] 4 Underprediction − (b) Storm duration

Overprediction

Figure F.8: Storm Atlas method A (resampling): Results of case 4 on the performance per station on the 3 performance indicators 140 APPENDIX F. SENSITIVITY ANALYSIS METHOD A - RESAMPLING

2 Overprediction

1 − Water level diﬀerence [m]

2 Underprediction − (a) Peak water level

4 Overprediction

2 − Storm duration diﬀerence [hours] 4 Underprediction − (b) Storm duration

Overprediction

Figure F.9: Storm Atlas method A (resampling): Results of case 4 on the performance per storm on the 3 performance indicators 141

2 Overprediction

1 − Water level diﬀerence [m]

2 Underprediction − (a) Peak water level

4 Overprediction

2 − Storm duration diﬀerence [hours] 4 Underprediction − (b) Storm duration

Overprediction

Figure F.10: Storm Atlas method A (resampling): Results of case 5 on the performance per station on the 3 performance indicators 142 APPENDIX F. SENSITIVITY ANALYSIS METHOD A - RESAMPLING

2 Overprediction

1 − Water level diﬀerence [m]

2 Underprediction − (a) Peak water level

4 Overprediction

2 − Storm duration diﬀerence [hours] 4 Underprediction − (b) Storm duration

Overprediction

Figure F.11: Storm Atlas method A (resampling): Results of case 5 on the performance per storm on the 3 performance indicators 143

2 Overprediction - too high

1 − Water level diﬀerence [m]

2 Underprediction - too low − (a) Peak water level

Overprediction - too long 4

2 −

4 Storm duration diﬀerence [hours] − Underprediction - too short (b) Storm duration

Overprediction - too late

Figure F.12: Storm Atlas method A (resampling): Results of case 6 on the performance per station on the 3 performance indicators 144 APPENDIX F. SENSITIVITY ANALYSIS METHOD A - RESAMPLING

2 Overprediction - too high

1 − Water level diﬀerence [m]

2 Underprediction - too low − (a) Peak water level

Overprediction - too long 4

2 −

4 Storm duration diﬀerence [hours] − Underprediction - too short (b) Storm duration

Overprediction - too late

Figure F.13: Storm Atlas method A (resampling): Results of case 6 on the performance per storm on the 3 performance indicators 145

2 Overprediction - too high

1 − Water level diﬀerence [m]

2 Underprediction - too low − (a) Peak water level

Overprediction - too long 4

2 −

4 Storm duration diﬀerence [hours] − Underprediction - too short (b) Storm duration

Overprediction - too late

Figure F.14: Storm Atlas method A (resampling): Results of case 7 on the performance per station on the 3 performance indicators 146 APPENDIX F. SENSITIVITY ANALYSIS METHOD A - RESAMPLING

2 Overprediction - too high

1 − Water level diﬀerence [m]

2 Underprediction - too low − (a) Peak water level

Overprediction - too long 4

2 −

4 Storm duration diﬀerence [hours] − Underprediction - too short (b) Storm duration

Overprediction - too late

Figure F.15: Storm Atlas method A (resampling): Results of case 7 on the performance per storm on the 3 performance indicators 147

2 Overprediction - too high

1 − Water level diﬀerence [m]

2 Underprediction - too low − (a) Peak water level

Overprediction - too long 4

2 −

4 Storm duration diﬀerence [hours] − Underprediction - too short (b) Storm duration

Overprediction - too late

Figure F.16: Storm Atlas method A (resampling): Results of case 8 on the performance per station on the 3 performance indicators 148 APPENDIX F. SENSITIVITY ANALYSIS METHOD A - RESAMPLING

2 Overprediction - too high

1 − Water level diﬀerence [m]

2 Underprediction - too low − (a) Peak water level

Overprediction - too long 4

2 −

4 Storm duration diﬀerence [hours] − Underprediction - too short (b) Storm duration

Overprediction - too late

Figure F.17: Storm Atlas method A (resampling): Results of case 8 on the performance per storm on the 3 performance indicators 149

2 Overprediction - too high

1 − Water level diﬀerence [m]

2 Underprediction - too low − (a) Peak water level

Overprediction - too long 4

2 −

4 Storm duration diﬀerence [hours] − Underprediction - too short (b) Storm duration

Overprediction - too late

Figure F.18: Storm Atlas method A (resampling): Results of case 9 on the performance per station on the 3 performance indicators 150 APPENDIX F. SENSITIVITY ANALYSIS METHOD A - RESAMPLING

2 Overprediction - too high

1 − Water level diﬀerence [m]

2 Underprediction - too low − (a) Peak water level

Overprediction - too long 4

2 −

4 Storm duration diﬀerence [hours] − Underprediction - too short (b) Storm duration

Overprediction - too late

Figure F.19: Storm Atlas method A (resampling): Results of case 9 on the performance per storm on the 3 performance indicators 151

2 Overprediction - too high

1 − Water level diﬀerence [m]

2 Underprediction - too low − (a) Peak water level

Overprediction - too long 4

2 −

4 Storm duration diﬀerence [hours] − Underprediction - too short (b) Storm duration

Overprediction - too late

Figure F.20: Storm Atlas method A (resampling): Results of case 10 on the performance per station on the 3 performance indicators 152 APPENDIX F. SENSITIVITY ANALYSIS METHOD A - RESAMPLING

2 Overprediction - too high

1 − Water level diﬀerence [m]

2 Underprediction - too low − (a) Peak water level

Overprediction - too long 4

2 −

4 Storm duration diﬀerence [hours] − Underprediction - too short (b) Storm duration

Overprediction - too late

Figure F.21: Storm Atlas method A (resampling): Results of case 10 on the performance per storm on the 3 performance indicators 153

2 Overprediction

1 − Water level diﬀerence [m]

2 Underprediction − (a) Peak water level

4 Overprediction

2 − Storm duration diﬀerence [hours] 4 Underprediction − (b) Storm duration

Overprediction

Figure F.22: Storm Atlas method A (resampling): Results of case 11 on the performance per station on the 3 performance indicators 154 APPENDIX F. SENSITIVITY ANALYSIS METHOD A - RESAMPLING

2 Overprediction

1 − Water level diﬀerence [m]

2 Underprediction − (a) Peak water level

4 Overprediction

2 − Storm duration diﬀerence [hours] 4 Underprediction − (b) Storm duration

Overprediction

Figure F.23: Storm Atlas method A (resampling): Results of case 11 on the performance per storm on the 3 performance indicators 155

2 Overprediction - too high

1 − Water level diﬀerence [m]

2 Underprediction - too low − (a) Peak water level

Overprediction - too long 4

2 −

4 Storm duration diﬀerence [hours] − Underprediction - too short (b) Storm duration

Overprediction - too late

Figure F.24: Storm Atlas method A (resampling): Results of case 12 on the performance per station on the 3 performance indicators 156 APPENDIX F. SENSITIVITY ANALYSIS METHOD A - RESAMPLING

2 Overprediction - too high

1 − Water level diﬀerence [m]

2 Underprediction - too low − (a) Peak water level

Overprediction - too long 4

2 −

4 Storm duration diﬀerence [hours] − Underprediction - too short (b) Storm duration

Overprediction - too late

Figure F.25: Storm Atlas method A (resampling): Results of case 12 on the performance per storm on the 3 performance indicators 157

2 Overprediction - too high

1 − Water level diﬀerence [m]

2 Underprediction - too low − (a) Peak water level

Overprediction - too long 4

2 −

4 Storm duration diﬀerence [hours] − Underprediction - too short (b) Storm duration

Overprediction - too late

Figure F.26: Storm Atlas method A (resampling): Results of case 13 on the performance per station on the 3 performance indicators 158 APPENDIX F. SENSITIVITY ANALYSIS METHOD A - RESAMPLING

2 Overprediction - too high

1 − Water level diﬀerence [m]

2 Underprediction - too low − (a) Peak water level

Overprediction - too long 4

2 −

4 Storm duration diﬀerence [hours] − Underprediction - too short (b) Storm duration

Overprediction - too late

Figure F.27: Storm Atlas method A (resampling): Results of case 13 on the performance per storm on the 3 performance indicators 159

2 Overprediction - too high

1 − Water level diﬀerence [m]

2 Underprediction - too low − (a) Peak water level

Overprediction - too long 4

2 −

4 Storm duration diﬀerence [hours] − Underprediction - too short (b) Storm duration

Overprediction - too late

Figure F.28: Storm Atlas method A (resampling): Results of case 14 on the performance per station on the 3 performance indicators 160 APPENDIX F. SENSITIVITY ANALYSIS METHOD A - RESAMPLING

2 Overprediction - too high

1 − Water level diﬀerence [m]

2 Underprediction - too low − (a) Peak water level

Overprediction - too long 4

2 −

4 Storm duration diﬀerence [hours] − Underprediction - too short (b) Storm duration

Overprediction - too late

Figure F.29: Storm Atlas method A (resampling): Results of case 14 on the performance per storm on the 3 performance indicators 161

2 Overprediction - too high

1 − Water level diﬀerence [m]

2 Underprediction - too low − (a) Peak water level

Overprediction - too long 4

2 −

4 Storm duration diﬀerence [hours] − Underprediction - too short (b) Storm duration

Overprediction - too late

Figure F.30: Storm Atlas method A (resampling): Results of case 15 on the performance per station on the 3 performance indicators 162 APPENDIX F. SENSITIVITY ANALYSIS METHOD A - RESAMPLING

2 Overprediction - too high

1 − Water level diﬀerence [m]

2 Underprediction - too low − (a) Peak water level

Overprediction - too long 4

2 −

4 Storm duration diﬀerence [hours] − Underprediction - too short (b) Storm duration

Overprediction - too late

Figure F.31: Storm Atlas method A (resampling): Results of case 15 on the performance per storm on the 3 performance indicators 163

2 Overprediction - too high

1 − Water level diﬀerence [m]

2 Underprediction - too low − (a) Peak water level

Overprediction - too long 4

2 −

4 Storm duration diﬀerence [hours] − Underprediction - too short (b) Storm duration

Overprediction - too late

Figure F.32: Storm Atlas method A (resampling): Results of case 16 on the performance per station on the 3 performance indicators 164 APPENDIX F. SENSITIVITY ANALYSIS METHOD A - RESAMPLING

2 Overprediction - too high

1 − Water level diﬀerence [m]

2 Underprediction - too low − (a) Peak water level

Overprediction - too long 4

2 −

4 Storm duration diﬀerence [hours] − Underprediction - too short (b) Storm duration

Overprediction - too late

Figure F.33: Storm Atlas method A (resampling): Results of case 16 on the performance per storm on the 3 performance indicators