Developing a parametric model for storms
to determine the extreme surge level at the
Dutch coast
Equation Chapter 1 Section 1
Date
June 2012
Graduate
Matthijs S. de Jong
E-mail: [email protected]
Educational Institution
Delft University of Technology, Faculty of Civil Engineering & Geosciences,
Department of Hydraulic Engineering, Section of Coastal Engineering,
In collaboration with Royal Haskoning
Graduation committee:
Prof. Drs. Ir. J.K. Vrijling, Delft University of Technology
Dr. Ir. P.H.A.J.M. van Gelder, Delft University of Technology
Dr. Ir L.H. Holthuijsen, Delft University of Technology
Dr. Ir. M. van Ledden, Royal Haskoning
Ir. C. den Heijer, Delft University of Technology and Deltares
ABSTRACT
This research examines the feasibility of developing a joint probability method to determine the
extreme water level for the Dutch coast, resulting from the passage of (wind)storms over the North
Sea. This has been done by means of a parametric model, which determines the hydraulic boundary
conditions from a set of significant storm parameters.
To date no study has been done to analyse the water level for the Dutch coast based on the passage
of storms over the North Sea. The rationale for this research is to obtain physical knowledge in
predicting the water level for the Dutch coast. This provides a better understanding of the
contribution of storm characteristics to high water levels, and can therefore be very useful in the
forecasting of extreme surges from the passage of these storms.
The results from this study offer indeed further insight in the significant storm characteristics, which
cause high water levels. As with any model the results depend critically on the volume and the
quality of the available data. For this research the dataset is relatively small. A larger dataset will not
only offer more data, but also provide more understanding of the interdependence of storm
parameters, and hence a more reliable estimation of the extreme water level.
Additionally, this study offers a basis for expansion to obtain further understanding of the behaviour
of water in the North Sea basin. Particularly, the wind field analysis is not only applicable for the
water level estimation, but can also be used to for analysing waves. It can also be worthwhile to
investigate whether this method is also applicable for other regions and countries.
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PREFACE
This is the final report of the MSc Thesis ‘Developing a parametric model to determine the extreme
surge level at the Dutch coast’. The graduation work is for the Hydraulic Engineering specialization
‘Coastal Engineering’, and embodies the work done from the June 2011 until June 2012 for Royal
Haskoning.
From start to finish this study has been very challenging and very instructive. The subject of this
study, to determine the Hydraulic Boundary Conditions for the Dutch coast, is highly topical. Every
research leading to improvement of the defence of the Dutch coastline is of great value. I was very
happy to make a small contribution to this effort.
I would like to thank the members of the graduation committee for their supervision and support.
My thanks go to Prof. Drs. Ir. H. Vrijling, Dr. Ir. P.H.A.J.M. van Gelder, Dr. Ir. L.H. Holthuijsen,
Dr. Ir. M. van Ledden en Ir. C. den Heijer for the useful feedback and for reviewing my report. Special
thanks go to Mathijs van Ledden for acting as a sounding board, and offering me the graduate
internship at Royal Haskoning.
Furthermore, I would like to thank Kees den Heijer, Marco Westra and Eelco Bijl for helping me with
writing the simulation model in Matlab. I would also like to thank Koos Doekes (Helpdesk Water),
Geert Groen (K.N.M.I.), Henk van den Brink (Meteo Consult), Sofia Caires, Jacco Groeneweg en Frank
den Heijer (Deltares) for providing information and help on different issues. My thanks go to all my
direct colleagues and graduate interns at Royal Haskoning for their support and the pleasant working
environment.
Lastly, I would like to express my sincere gratitude towards my family and friends for always believing
in me, and giving everlasting support. Especially my parents and my brother Steven for listening to
my endless stories related to my Master thesis, without completely understanding the context of it
all. Thanks!
Matthijs de Jong
Rotterdam, June 2012
“After climbing a great hill one only finds that there are many more hills to climb”
Nelson Mandela
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CONTENTS
ABSTRACT ......................................................................................................................................................... I
PREFACE ........................................................................................................................................................... II
CONTENTS ....................................................................................................................................................... III
LIST OF SYMBOLS ............................................................................................................................................. V
ABBREVIATIONS AND DEFINITIONS ................................................................................................................ VII
LIST OF FIGURES ............................................................................................................................................ VIII
LIST OF TABLES ................................................................................................................................................ XI
1
INTRODUCTION........................................................................................................................................ 1
1.1
1.2
1.3
1.4
2
SCOPE OF THE RESEARCH .............................................................................................................................. 2
PROBLEM DEFINITION .................................................................................................................................. 3
THESIS OBJECTIVES ...................................................................................................................................... 6
STRUCTURE OF THE REPORT .......................................................................................................................... 7
A PARAMETRIC MODEL FOR SURGES FROM STORMS TRAVELLING OVER THE NORTH SEA ...................... 8
2.1
INTRODUCTION TO STUDY AREA ..................................................................................................................... 8
2.1.1 Introduction ....................................................................................................................................... 8
2.1.2 The passage of storms over the North Sea ........................................................................................ 9
2.1.3 Storm surges for the Dutch coast .................................................................................................... 10
2.2
STRUCTURE OF A PARAMETRIC MODEL .......................................................................................................... 13
2.3
MATHEMATICAL DESCRIPTION OF THE PRESSURE FIELD ..................................................................................... 14
2.3.1 Analysis of the pressure field ........................................................................................................... 15
2.3.2 Central pressure .............................................................................................................................. 16
2.3.3 Radius to maximum winds .............................................................................................................. 17
2.3.4 Holland B parameter ....................................................................................................................... 17
2.4
MATHEMATICAL DESCRIPTION OF THE WIND FIELD........................................................................................... 17
2.4.1 Storm track of the wind field ........................................................................................................... 17
2.4.2 Geostrophic wind............................................................................................................................. 18
2.4.3 Gradient wind .................................................................................................................................. 20
2.4.4 Surface wind .................................................................................................................................... 21
2.5
DEPENDENCIES BETWEEN THE STORM PARAMETERS ......................................................................................... 22
2.5.1 Dependency between Rmax and Holland B parameter ................................................................... 22
2.6
STORM SET-UP ASSOCIATED WITH THE PRESSURE- AND WIND FIELD .................................................................... 22
2.6.1 Wind set-up modelling .................................................................................................................... 23
2.7
DETERMINATION OF THE EXTREME STORM SURGE ........................................................................................... 27
3
ANALYSIS OF HISTORICAL STORMS ........................................................................................................ 29
3.1
STORM INVENTORY ................................................................................................................................... 29
3.1.1 Selection criteria .............................................................................................................................. 29
3.1.2 Availability of input and validation data ......................................................................................... 30
3.2
SELECTION OF STORM DATASET.................................................................................................................... 31
3.2.1 Analysis of the “skewed” set-up ...................................................................................................... 32
3.3
PRESSURE FIELD ANALYSIS........................................................................................................................... 32
3.3.1 Working assumptions for the pressure field .................................................................................... 33
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3.3.2 Central pressure .............................................................................................................................. 34
3.3.3 Radius to maximum winds .............................................................................................................. 35
3.3.4 Holland B parameter ....................................................................................................................... 38
3.4
MOVEMENT OF THE STORM DEPRESSION ....................................................................................................... 40
3.4.1 Working assumptions for analysing the storm track ...................................................................... 40
3.4.2 Location of the boundaries .............................................................................................................. 41
3.4.3 Forward movement of the storms ................................................................................................... 43
3.4.4 Angle of approach of the storms ..................................................................................................... 44
3.5
DATASET OF THE STORM PARAMETERS .......................................................................................................... 46
4
VALIDATION OF THE MODEL .................................................................................................................. 48
4.1
WIND FIELD MODEL VALIDATION.................................................................................................................. 48
4.1.1 Maximum wind speed ..................................................................................................................... 48
4.1.2 Wind field modelling ....................................................................................................................... 49
4.1.3 Wind speed model validation .......................................................................................................... 51
4.1.4 Wind direction validation ................................................................................................................ 53
4.1.5 Validated model .............................................................................................................................. 54
4.2
WIND SET-UP VALIDATION.......................................................................................................................... 54
4.2.1 Measured straight set-up for Hook of Holland ................................................................................ 54
4.2.2 Wind set-up validation .................................................................................................................... 56
4.3
CONCLUSIONS OF THE CALIBRATED MODEL..................................................................................................... 59
5
PROBABILISTIC ANALYSIS OF THE IMPACT OF EXTREME STORMS FOR THE DUTCH COAST .................... 61
5.1
MODEL DESCRIPTION OF THE DETERMINATION OF THE HBC .............................................................................. 61
5.2
PROBABILISTIC INPUT VARIABLES .................................................................................................................. 62
5.2.1 Input of the storm parameters ........................................................................................................ 62
5.2.2 Input of the tide level and the basin bathymetry/geometry ........................................................... 62
5.3
SIMULATION OF THE EXTREME WATER LEVEL FOR HOOK OF HOLLAND ................................................................. 63
5.3.1 Introduction ..................................................................................................................................... 63
5.3.2 Analysis of the extreme water levels ............................................................................................... 68
6
CONCLUSIONS AND RECOMMENDATIONS ............................................................................................. 71
6.1
6.2
CONCLUSIONS .......................................................................................................................................... 71
RECOMMENDATIONS................................................................................................................................. 74
7
BIBLIOGRAPHY ....................................................................................................................................... 76
8
APPENDIXES ........................................................................................................................................... 79
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LIST OF SYMBOLS
Variable
Unit
Description
Z
m
Water level
S
m
Wind set-up
H
m
Astronomical water level
G
m/s
W9
m/s
Wind speed during 9 hours of constant exceendance
α1
-
Empirical parameter
P
mbar
Air pressure
∆p
mbar
Pressure gradient
pc
mbar
Central pressure of a depression
pa
mbar
Ambient pressure
A
m
Radius to maximum winds in x-direction
B
m
Radius to maximum winds in y-direction
ra
m
Distance from storm centre in x-direction
rb
m
Distance from storm centre in y-direction
RMAX
m
Radius to maximum wind speed
B
-
Holland B parameter
Rd
J kg K
Gas constant of dry air
Ts
K
Sea surface Temperature
F
s
ρa
kg/m
Air density
ug
m/s
Geostrophic wind in x-direction
vg
m/s
Geostrophic wind in x-direction
Ω
rad/s
Angular speed of the earth (=7.29*10 )
Φ
°
Latitude coordinate
Λ
°
Longitude coordinate
C
m /2/s
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Acceleration of gravitiy
-1
-1
-1
Coriolis parameter
3
1
-5
Chézy bottom friction parameter
V
Delft University of Technology
Vgr
m/s
Geostrophic wind speed
R
m
Distance from the storm centre
Vg
m/s
Gradient wind speed
Cfm
m/s
Forward movement of storm depression
θl
°
Angle from the storm translation direction to the profile location
Cfm
m/s
Forward movement of storm depression
Β
°
Deflection of the surface wind direction from the isobar
R
m
Radius of the earth (6.373 x 10 )
D
m
Angular distance between two geostrophic coordinates
F
m
The fetch / basin length
D
m
The depth
C
-
Empirical coefficient in the formula by Voortman
Α
-
Factor to describe the basin shape
Χ
s /dm
Correction coefficient in the model by Van den Brink
Δ
°
Correction coefficient in the model by Van den Brink
Φ
°
Clockwise wind direction with respect to the North
Ε
-
Normal random variable
I
-
Position of data points in increasing order
N
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The number of data points
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ABBREVIATIONS AND DEFINITIONS
Abbreviation
Description
HBC
Hydraulic boundary conditions
JPM
Joint Probability Method
JPM-OS
Joint Probability Method – Optimal Sampling
MSL
Mean Sea Level
NAP
Amsterdam Ordnance Datum / Normaal Amsterdams Peil
POT
Peak over Threshold
A.M.
Annual Maximum
Bft
Beaufort, unit in which the wind is expressed
hPa
Hectopascal, unit in which the aire pressure is expressed
GMT
Greenwich Mean Time, astronomical time at the meridian of the 0°
longitude
UTC
Universal Time Coordinated, corresponds to the GMT
K.N.M.I.
Royal Netherlands Meteorological Institute
DCSM
Dutch Continental Shelf Model
HIRLAM
High Resolution Local Area Modelling for numerical weather prediction
ECMWF
European Centre for Medium-range Weather Forecasts
HIRLAM
High Resolution Local Area Modelling
WAQUA
Water movement and water quality simulation system, able to perform twodimensional computations.
Isobar
Line that connects points with the same pressure
Trough
A region of the atmosphere in which the pressure is low relative to the
surrounding regions at the same level
2
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LIST OF FIGURES
Figure 1: Actual level in the Netherlands (Waterland.net) ..................................................................... 2
Figure 2: Frequency analysis ‘avant-la-lettre’; 1920 – publication with number of storm surges above
water level at Hook of Holland (Vrijling and Gelder, 2005) .................................................................... 3
Figure 3: Gumbel plot for water levels at Hook of Holland. Black: 118 years of observations (18882005). Red: data from eight 108-years chunks of ESSENCE-WAQUA/DCSM98 and corresponding fits
for the present climate (1950-2000) Blue: All 867 years of data together. The bars at the right margin
indicate the 95% confidence intervals for the 10000 years return value. (source: Van den Brink,2005)
................................................................................................................................................................. 4
Figure 4: The new approach for determining the HBC by analysing storms ........................................... 5
Figure 5: Bathymetry chart of the North Sea with the location of Hook of Holland and Vlissingen ...... 9
Figure 6: Frontal wave depression and storm development ................................................................ 10
Figure 7: Resonance in water basin....................................................................................................... 12
Figure 8: Focus of research.................................................................................................................... 13
Figure 9: Conceptual model of the storm surge analysis ...................................................................... 14
Figure 10: Analysis of the pressure field in the conceptual model ....................................................... 15
Figure 11: Analysis of the wind field in the conceptual lmodel ............................................................ 17
Figure 12: Wind speeds associated with the pressure gradient (Floor, 2004)...................................... 19
Figure 13: The asymmetry in wind speeds due to the forward movement of the storm ..................... 20
Figure 14: The deflection angle of the surface wind relative to the geostrophic wind (Floor, 2004)... 21
Figure 15: Analysis of the storm set-up in the conceptual mode ......................................................... 23
Figure 16: Relation between the wind speed and the wind set-up ...................................................... 23
Figure 17: surge model including the pressure effect, and without the pressure effect (Brink, 2005) 25
Figure 18: Analysis of the extreme storm surge in the conceptual model ........................................... 27
Figure 19: Parametric model to determine the wind set-up for the Dutch coast ................................ 28
Figure 20:(a) Pressure gradient of a storm (Klaver, 2005); (b) Estimation of the central pressure for
weather charts ...................................................................................................................................... 34
Figure 21: Normal distribution of the central pressure of the 21 storms (975 mbar,15.05 mbar) ...... 35
Figure 22: (left) Different methods for the determination of the pressure field for the storm of 1953;
(right) Pressure difference between methods and the measured pressure ......................................... 36
Figure 23: Measured RMAX from weather charts compared with the RMAX from method 1 .................. 37
Figure 24: (left) Radius to maximum winds with Method 1 for the significant storms [km]; (right)
Ascending lognormal distribution with μ=552 km and σ=213 km, based on the significant storms .... 37
Figure 25: (left) Measured RMAX from weather charts compared with the RMAX from method 2; (right)
without the storm of 1928 R2=0.7356 ................................................................................................... 38
Figure 26: (left) Radius to maximum winds with Method 2 for the significant storms [km]; (right)
Ascending lognormal distribution with μ=688 km and σ=236 km, based on the significant storms .... 38
Figure 27: RMAX from method 1 compared to Holland B parameter ..................................................... 39
Figure 28: RMAX from method 2 compared with the Holland B parameter ........................................... 40
Figure 29: Significant storm depressions at Hook of Holland travelling over the North Sea ................ 41
Figure 30: Location of the storm depression at 5.5°E and 12.5°E longitude. The locations indicate
whether the storm has a North-Westerly or a South-Westerly direction. ........................................... 42
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Figure 31: (left) Latitudinal starting location of storms at 5.5°E longitude; (right) Ascending lognormal
distribution of the latitudinal coordinate at 5.5°E (58.61°, 2.60°) ........................................................ 43
Figure 32: (left) Averaged forward speed of the storms between 5.5°E and 12.5°E longitude; (right)
Ascending lognormal distribution of the forward speed of the storm (14.67 m/s, 5.24 m/s) ............. 44
Figure 33: (left) Averaged angle of approach of the storms between 5.5°E and 12.5°E longitude [°N];
(right) Figure 34: Cumulative distribution function of the angle of approach including three
distribution functions [°W]. ................................................................................................................... 44
Figure 35: Surface wind field [m/s] for the storm of 01-03-2008 before entering the North Sea if only
this single storm is taken into account. The axes are 1:50 [km] ........................................................... 51
Figure 36: Measured and calculated wind field of the storm of 01-03-2008 ....................................... 52
Figure 37: (left) Observed exceeded wind speed over 9 hours compared with the computed wind
speed; (right) Comparison without the storm of 17-02-1962 and 21-12-2003 .................................... 53
Figure 38:Calibrated wind speed for the storm of 01-03-2008............................................................. 54
Figure 39: Calibration of the tidal prediction by MIKE21 for the storm of 14-02-1989 ........................ 55
Figure 40: Comparison of the wind set-up by RWS and MIKE21 for Hook of Holland.......................... 56
Figure 41: (left) Comparison of the computed and observed wind set-up for Hook of Holland; (right)
Wind setup model by Voortman based on the exceeded wind speed over 9 hours ............................ 58
Figure 42: 95% confidence interval of the observed and computed wind set-up for Hook of Holland 59
Figure 43: (left) Simulated tidal water level with MIKE 21; (right) Weibull distribution of the estimated
high tidal water level for Hook of Holland with μ=1.163 [NAP + m] and σ=0.081 [NAP + m].............. 63
Figure 44: Time interval for determination of the 9 hourly wind speed and direction ........................ 64
Figure 45: Simulated high water level for the parametric storm model based on the fitted ambient
pressure and the wind set-up model by Voortman .............................................................................. 65
Figure 46: Straight set-up compared to the “skewed” set-up based on the storm analysis ................ 65
Figure 47: Simulated and measured high water level over time for the parametric storm model based
on the fitted ambient pressure and wind set-up model by Voortman. With on the right hand side the
95% confidence interval for both 10-4/year water level measurements. ............................................. 66
Figure 48: Storm parameters of the extreme surge levels compared to the parameters of the ......... 69
Figure 49: Sketch for an one-dimensional wind set-up model ............................................................. 79
Figure 50: Measured “skewed” set-up over time (Brink, 2005)............................................................ 82
Figure 51: Significant storm tracks for Hellevoetsluis in the period of 1898 until 1916 (source: Delta
Report 1961).......................................................................................................................................... 84
Figure 52: Significant storm tracks for Hellevoetsluis in the period of 1916 until 1939 (source: Delta
Report 1961).......................................................................................................................................... 84
Figure 53: Significant storm tracks for Hellevoetsluis in the period of 1939 until 1946 (source: Delta
Report 1961).......................................................................................................................................... 85
Figure 54: Significant storm tracks for Hellevoetsluis in the period of 1946 until 1956 (source: Delta
Report 1961).......................................................................................................................................... 85
Figure 55: HIRLAM weather chart (source: K.N.M.I.) ............................................................................ 88
Figure 56: Reanalysis of the weather chart (source: Wetterzentrale) .................................................. 88
figure 57: Exponential distribution through wind set-up dataset > 1.80 m .......................................... 90
Figure 58: Astronomical high tide for extreme storms for Hook of Holland based on the “skewed” setup (Source: Deltares) ............................................................................................................................. 91
Figure 59: Return period of the sea water level (NAP + cm) for Hook of Holland (Source: Deltares) . 92
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Figure 60: (left) Observed radius to maximum winds compared to the measured for Method 1; (right)
Observed radius to maximum winds compared to the measured for Method 2 ................................. 92
Figure 61:Correlation between the Holland B parameter and the RMAX for Method 1 for all storms;
Correlation between the Holland B parameter and the RMAX for Method 1 (1953-2008) .................... 92
Figure 62: Correlation between the Holland B parameter and the RMAX for Method 2 for all storms;
Correlation between the Holland B parameter and the RMAX for Method 2 (1953-2008) .................... 92
Figure 63: (left) Observed averaged wind speed compared with the computed wind speed; (right)
Comparison without the storm of 21-12-2003 ..................................................................................... 93
Figure 64: (left) Observed max. wind speed compared with the computed wind speed; (right)
Comparison without the storm of 21-12-2003 ..................................................................................... 93
Figure 65: (left) simulated and observed wind field for 01-02-1953; (right) ) simulated and observed
wind field for 12-02-1962 ...................................................................................................................... 94
Figure 66: (left) simulated and observed wind field for 17-02-1962; (right) The pressure gradient of
the storm of 17-02-1962 ....................................................................................................................... 94
Figure 67: (left) simulated and observed wind field for 03-01-1976 (25hrs); (right) wind field for 0301-1976 (40 hrs) .................................................................................................................................... 95
Figure 68: (left) simulated and observed wind field for 14-02-1989; (right) ) simulated and observed
wind field for 12-12-1990 ...................................................................................................................... 95
Figure 69: (left) simulated and observed wind field for 21-12-2003; (right) ) simulated and observed
wind field for 09-11-2007 ...................................................................................................................... 96
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LIST OF TABLES
Table 1: Properties for the North Sea (Voortman et al., 2002) ............................................................. 25
Table 2: Correction coefficients for the wind set-up model by van den Brink ..................................... 26
Table 3: Retrieving dataset of storm parameters ................................................................................. 30
Table 4: Available dataset for the wind field and water level ............................................................... 31
Table 5: Data selection of the significant storms at Hook of Holland ................................................... 32
Table 6: Storm parameters for dataset ................................................................................................. 46
Table 7: Distribution function for independent storm parameter ........................................................ 47
Table 8: Distribution function for dependency between Holland B and RMAX ...................................... 47
Table 9: Maximum wind speed of the storm using the storm parameters .......................................... 49
Table 10: Available wind data for several measurement stations ........................................................ 49
Table 11: Geostrophic coordinates of the measurement stations (N.L. = Northern Latitude, E.L. =
Eastern Longitude) ................................................................................................................................ 50
Table 12: Observed and computed wind speed [m/s] at Hook of Holland ........................................... 52
Table 13: Observed 9 hourly exceeded wind speed and direction compared with the calibrated 9
hourly exceeded wind speed and direction .......................................................................................... 53
Table 14: Straight set-up for the significant storms .............................................................................. 56
Table 15: Input parameters to determine the wind set-up .................................................................. 57
Table 16: Calibrated fetch and effective depth to determine the wind set-up .................................... 58
Table 17: Calibration coefficients used for the hydraulic variables ...................................................... 60
Table 18: Model description of the JPDF of the hydraulic conditions .................................................. 62
Table 19: Distribution function for independent storm parameter ...................................................... 62
Table 20: Simplifications in the model that result in possible inaccuraciesFout!
Bladwijzer
niet
gedefinieerd.
Table 21: Transformation of the water level for the relative sea level rise .......................................... 89
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1
Introduction
“The ocean rushes twice a day with huge waves across the country, so that one might
wonder whether in this eternal struggle of nature this piece of land belongs to the land or
to the sea. On the hills, or rather, with hands elevated residences (the mounds) lives an
unhappy folk. At high tide they are like sailors, at low tide rather castaways. And when
they are conquered by the Romans, they call it slavery!”
Gaius Plinius Secundus maoir
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1.1
Scope of the research
The protection of the land against the sea is an important issue for the Netherlands.
Already since the era of the Romans the Netherlands have been fighting against the sea,
as mentioned by the Roman Gaius
Plinius. This is mainly because the
Netherlands is a low lying-country
with approximately 40% of its land
below mean sea level (MSL), as is
represented by the blue area in Figure
1. In the 12th century farmers started
building dikes to protect their land. A
century later water boards, the oldest
democratic institutions in the
Netherlands (Ronde et al., 2003), got
the responsibility to maintain the dike
system and water levels. In 1798, the
institution
Rijkswaterstaat
was
founded to give a national guidance to Figure 1: Actual level in the Netherlands (Waterland.net)
the water management.
Especially storm surges are a major threat for the Dutch coastal areas. These surges occur
when severe storms travel over the North Sea. To defend the coastline against these
surges, safety standards are applied. The first known implementation of safety standards
for the Dutch dikes and flood defences, based on a storm surge analysis, dates to the
report of “Staatscommissie voor den Waterweg” in 1920, see Figure 4. It was however not
until the storm surge of 1953 that new measurements were analysed.
After this flood the Delta committee was formed that consisted of a group of experts, who
advised the Minister in taking measures to prevent a next flood disaster. One of the
recommendations was that the Netherlands should be protected to withstand a storm
surge with a probability of occurrence of 5*10-4 - 10-4/year (Maris et al., 1961a),
depending on the economic value of the hinterland. The argument for this was that the
dikes in the Netherlands should be safely protected for a period of 100 years. For the
coast of Holland the probability of occurrence was set to 1% per 100 years. This safety
standard is still applied today.
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Figure 2: Frequency analysis ‘avant-la-lettre’; 1920 – publication with number of storm surges above water
level at Hook of Holland (Vrijling and Gelder, 2005)
This thesis focusses on the determination of the extreme storm surge levels. The current
norm of the 10-4/year storm surge for the Dutch coast is determined with the use of
statistical extrapolation of the water level, based on a series of water level measurements
with a length of around 100 years (for the western Wadden Sea a length of 50 years due
to the construction of the Afsluitdijk). The extrapolation gives an estimation of the design
water level with a return period of 10000 years. As the statistical extrapolation to the
10-4/year storm surge reaches far beyond the duration length of the current
measurements, a relatively large 95% confidence interval arises of about 3.5m.
1.2
Problem definition
Several studies have been made to determine the 10-4/year surge level. This extreme
surge level is necessary to describe the Hydraulic Boundary Conditions (HBC) that
describes the safety standards of the Dutch coast. The first method to determine the 104
/year surge level for the Dutch coast was established by the Delta committee in 1960. An
analysis of consistency was used in extremely high water levels along the coast based on
observations, and physical and statistical extrapolation at Hook of Holland. With this
knowledge similar levels in the other stations could be determined. Based on the dataset
that was extracted, the design level at Hook of Holland determined by the Delta
Committee resulted in NAP + 5 m for a 10-4/year water level.
This method is still used today to determine the basic water levels for the Dutch coast
(V&W, 2007). This is complimented by a second method, which uses hydrodynamic
computer models based on manipulated data from a limited number of severe storms. At
Hook of Holland the resulting basic level still remains NAP + 5 m.
(Voortman, 2002) proposed an alternative method in which the hydraulic effects are
described as a function of the wind speed, astronomical tide and basin geometry. He
computed the exceedance probability of extreme water levels for various locations, and
came to the conclusion that for these locations the probability of exceedance of extreme
water levels is higher than currently estimated. For example, at Delfzijl the 10-4/year
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water level is at NAP + 6.15 m, for which Voortman estimated that this water level is
already reached at 4x10-3/year. It should be noted that the observed dataset shows a
considerable spread around the calibrated model by Voortman.
(Brink, 2005) used a climate model to determine the hydraulic boundary conditions for
the Dutch coast. Using data of the ECMWF seasonal prediction system, he calculated the
surge at high-tide for the coastal station Hook of Holland. Based on this research it was
found that The GEV location parameter u (representing the surge level with an
exceedance probability of once a year) estimated from the ECMWF dataset equals that of
the observational record within one cm. With the use of the dataset of Van den Brink the
10-4/year surge level was estimated at NAP + 3.96 m, which is almost equal to the surge
level of NAP 3.78 m based on observational records, see Figure 3. This surge level is based
on the “skewed” setup, for which the tidal water level should be included. It is however
interesting that the 95%-confidence interval of the 10-4/year surge level is reduced from
3.52m for the observational set to 0.84m for the ECMWF set (a factor four). It is unknown
whether uncertainties in the ECMWF model are also taken into account for the
determination of this extreme surge level.
Figure 3: Gumbel plot for water levels at Hook of Holland. Black: 118 years of observations (1888-2005).
Red: data from eight 108-years chunks of ESSENCE-WAQUA/DCSM98 and corresponding fits for the present
climate (1950-2000) Blue: All 867 years of data together. The bars at the right margin indicate the 95%
confidence intervals for the 10000 years return value. (source: Van den Brink,2005)
To reduce the uncertainty of 10-4/year surge level, (Baart et al., 2011) introduces a new
method to determine storm surges over a longer period of time. He reconstructed the
three greatest storm surges that hit the northern part of the Holland Coast in the 18th
century. This was done with the use of paintings, drawings, written records and shell
deposits. He concluded that this method narrowed the range of uncertainty when using
the Gumbel distribution, but results in a slightly wider uncertainty range from the GEV
approach. This approach is less effective in increasing the confidence than the method
used by Van den Brink. On the other hand this study shows that paintings and such are
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potential data sources in determining the coastal change and, indirectly, storm surge
magnitude, in the absence of accurate data.
As the water level information along the coast only exists over a period of approximately
the last 100 years, an extrapolation is needed of two orders of magnitude to determine
the HBC (Brink, 2005). This results in a large uncertainty, as can be seen in Figure 3. As
mentioned above, several studies have been made in estimating the surge level. These
studies are done to reduce the confidence interval, and/or to provide physical knowledge
in analysing the water level for the Dutch coast. A next step would be to further analyse
the physics behind the wind statistics. One method to achieve this goal is by coupling
storm parameters to the wind field causing the extreme storm surge levels, see Figure 4.
Voortman and Van den Brink already have done research in the determination of the
water level set-up with the use of wind statistics. To date no research has been done in
estimating the water level for the Dutch coast based on the passage of a storm over the
North Sea. The advantage of a parametric model that describes these depressions is that
it provides physical knowledge in the estimation of the water level. Furthermore, insight
in the storm characteristics that influence the water level set-up for the North Sea also
provides better basis for forecasting the effect of these storms. Another advantage is that
the simulated wind field based on storm parameters is not only applicable for estimating
the water level for the Dutch coast, but may also be a tool for simulating and
understanding the behaviour of waves for the North Sea and their joint probability.
Significant
storm
parameters
Bathymetry and
geometry of the
North Sea
Astronomical
tide
Pressure field for
the North Sea
Wind field for
the North Sea
External setup
Wind set-up
Wave set-up
Pressure setup
Total water
level increase
Hydraulic boundary conditions
Figure 4: The new approach for determining the HBC by analysing storms
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1.3
Thesis objectives
The goal of this study is to establish the relationship between the main characteristics of
North Sea storms and the resulting wind/pressure set-up, as shown in the green path in
Figure 4, in order to determine the Hydraulic Boundary Conditions for the Dutch coast.
Therefore, this study is to determine the 10-4/year water level for Hook of Holland, with
the use of a parametric model for storms passing the North Sea. In order to achieve this
goal, several key questions have to be answered:
What are the storm parameters that determine the associated pressure- and wind setup, in the event of the passage of a storm over the North Sea?
For the description of the parametric model it is necessary to identify the storm
parameters and their values that influence the pressure- and wind set-up at Hook of
Holland as a consequence of a storm passing the North Sea.
What are possible dependencies between these storm parameters?
It is essential in the realisation of a reliable model to ensure that it takes into account any
dependencies between the parameters used in this model. If possible dependencies are
not taken into account, combinations of parameter data will be used in the model that
would never happen in reality. Consequently, the model outcomes would be less reliable.
How accurate do the results of the model coincide with the observed values of specific
storms, and how do possible deviations contribute to the uncertainty of the model
outcomes?
With the parametric model a wind field can be simulated in space and time. When the
wind field is determined for a specific location of a measurement station, the outcomes
can be compared to the wind statistics. On the basis of this comparison, the parametric
model is calibrated and validated. Differences in the model outcomes have to be
addressed and clarified.
What is the 10-4/year water level for the Dutch coast based on the parametric model,
and how well does this compare with the current estimation method?
With the use of the calibrated parametric model the 10-4/year water level can be
estimated. Therefore use is made of the Monte Carlo approach1. The resulting extreme
water level is compared to the current estimation method. Based on the comparison of
these two approaches, conclusions and recommendations are drawn.
Which storm parameters are significant for generating extreme water levels?
The sensitivity of the results of the model to the various parameters will be investigated.
1
A class of computational algorithms that relies on repeated random sampling to compute the
results.
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1.4
Structure of the report
Chapter 2 contains a discussion of the aspects and behaviour of storm depressions in the
North Sea. It then sets out the focus and structure of the model that will be used to
determine the extreme surge level for the Dutch coast, and discusses the elements in this
model.
In chapter 3 the reference area is explained. The selection criteria, available resources and
retrieved dataset are determined for the historical storms over the North Sea. Based on
this dataset the significant storm parameters are analysed and their dependencies
evaluated. This data will be used as input for the parametric model.
Chapter 4 uses the dataset from the previous chapter to calibrate and validate the wind
field and set-up for the Dutch coast.
In chapter 5 the resulting calibrated model is used to estimate the water surge level at
Hook of Holland, with the use of a joint probability method. The result is compared to the
current determination of the HBC.
The last chapter contains conclusions and recommendations.
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2
A parametric model for
surges from storms travelling
over the North Sea
Equation Section (Next)
Chapter 2 consists of the theoretical knowledge available for analysing storm depressions
and the wind field and –set-up that are associated with this phenomenon. Furthermore,
this chapter provides an overview of the focus of this research. Paragraph 2.1 gives an
introduction of the parametric model. Therefore, the study area is introduced, the
description is given of a storm depression, and the focus of this research is explained. The
following paragraphs describe how the extreme surge level can be determined using the
knowledge available for storm depressions. In Paragraph 2.4 possible dependencies
between storm parameters are described. The next paragraph describes earlier studies
that have been done to determine the wind set-up based on the storm parameters. Lastly,
the method to describe the water level set-up is explained.
2.1
Introduction to study area
2.1.1 Introduction
For the analysis of how the pressure- and wind field interact with the North Sea and cause
a set-up for the Dutch coast, the location and bathymetry of the North Sea has to be
known. The North Sea is a marginal sea that is located between Great Britain, Scandinavia,
Belgium and the Netherlands, which can be seen in Figure 5. It is around 970 km long and
580 km wide and very shallow in the south, only 25 to 35 meters. For this reason shallow
water phenomena have a big influence on the water level and wave height for the Dutch
coast, located in the south. The sea is connected to the Atlantic Ocean that has a much
greater depth than the North Sea.
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Figure 5: Bathymetry chart of the North Sea with the location of Hook of Holland and Vlissingen
2.1.2 The passage of storms over the North Sea
For this study a storm is defined as a severe cyclonic windstorm that is associated with
areas of low atmospheric pressure. For the North Sea, these storms travel across the
North Atlantic towards Europe. This is because the storms travel with the jet stream,
which has a westerly direction for this region.
The European (wind)storms mostly occur during the winter periods. The reason is that
winds occur due to pressure differences between two locations. During the winter period,
higher pressure differences occur than during the summer, due to the higher differences
in temperature between the North Pole area and the tropics.
A storm is formed in a region with two different airs, see Figure 6. For the Netherlands the
depressions are caused because the atmospheric circulation of the cold air from the Pole
meets with the warm air from the Tropics. The polar front in the figure shows the
separation line. Because the cold front moves faster than the warm front, the isobars
change into waves and ridges. When the occlusion takes place, the storm depression will
become fully grown and a low pressure area is created.
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Figure 6: Frontal wave depression and storm development
When the storm travels over the Northern Hemisphere, the associated wind field has a
counterclockwise rotation due to the Coriolis force. As the earth rotates, the Coriolis force
drives the winds around the centre of the depression, spiral towards the centre, where
the air escapes vertically.
Most of the storms are already generated in the Atlantic Ocean. Based on earlier research
(Maris et al., 1961b), the starting point can differ greatly. It is however analysed that for
the significant storms for the Dutch coast most of the storms cross Denmark. This can be
clarified due to the counterclockwise rotation of the wind. The most unfavourable
situation will occur for the Dutch coast when the depression is at a location nearby
Denmark. For that situation the wind field pushes the water in the North Sea basin
towards the Dutch coast. This will result in a wind set-up, leading to a higher water level
for the coast, which is referred to as a storm surge.
2.1.3 Storm surges for the Dutch coast
A storm surge is an offshore rise of water that is associated with a low pressure weather
system, which is for this situation a storm travelling over the North Sea. This low pressure
system causes strong winds blowing over the ocean’s surface that pile up the water
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against the coast. The storm surge can be separated into several important processes that
result in this phenomenon. These processes and other important phenomena resulting in
the total water level are discussed below in more detail:
The wind set-up
For the Dutch coast, the main component of the total surge level is the wind set-up that is
caused by the wind field of a storm. The winds parallel to the coast transport water
toward the coast causing a rise in the sea level. This is explained by the Ekman transport
(Stewart, 2008). This term is given for the 90 degree net transport of the surface layer due
to the wind. The direction of the transport is dependent on the hemisphere. For the
Northern Hemisphere, this transport is 90 degree angle to the right of the direction of the
wind. Secondly, winds blowing toward the coast push water directly toward the coast.
This will also result in a wind set-up. For extreme storms surges for the Dutch coast this
wind set-up is mainly around 150-200 cm (for the storm of 1953 around 250-300 cm).
The pressure set-up
The pressure effect of a storm depression will cause the water level to rise in regions of
low atmospheric pressure and fall in regions of high atmospheric pressure. The low
pressure inside the storm raises the sea level by one centimetre for each millibar decrease
in pressure, which is often described as the inverted-barometer (IB) effect. This effect can
reach up to about 10-20 cm, depending on the pressure difference and the distance
between the storm centre and the point of measurement. Compared to the wind set-up,
the pressure set-up is relatively small for the Dutch coast. For most storms, the pressure
set-up is around 10 cm of the total storm surge (Brink, 2005).
The external set-up
The external surge can be defined as the water movements travelling from the deep
Atlantic Ocean into the North Sea. In an unfavourable situation the storm depression
travels over the North Atlantic Ocean, passing the Scottish coast. Water will be pushed
into the North Sea, causing an increase of the water volume in the North Sea. The
external surge travels counterclockwise over the North Sea and causes an increasing
water level for the Dutch coast (Pugh, 1996). The same as for the pressure set-up, the
external set-up does not contribute that much to the storm surge. The relationship
between the wind-, pressure- and external set-up is approximately 15:1:1 for high storms.
The wave set-up
This set-up is the change in the MSL due to the presence of waves. This set-up is primarily
present in and near the coastal surf zone, and is caused by wave run-up and other wave
interactions that transport water toward the coast. Furthermore, edge waves are
generated by the wind that travels along the coast. The wave set-up is significantly low, in
the order of a few centimetres.
Tidal water level
The tide is the slow rise and fall of the ocean waters in response to the gravitational pull
of the Moon and the Sun. The usual interval between successive high tides is 12.4 hours
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as the arrival of the crests of these waves represent high tide. The Moon exerts a greater
influence on the water on Earth than the Sun. The astronomical tide is well understood
and can be predicted for any time at many locations. For this research use is made of
MIKE 21 Modelling system that includes a program for tidal analysis and prediction
module.
In the method by Vrijling and Bruinsma it was assumed that the astronomical tide and the
wind set-up were independent of each other, so that the water level can be determined
more easily. This is because the astronomical tide is generated by celestial bodies and
set-up by wind fields. Therefore, both phenomena can be seen as independent variables,
which mean that the water level can be described as:
z(t )  s(t )  h(t )
z (t ) :
h(t ) :
(2.1)
Water level
Astronomical tide
The relative sea level rise
The level of the oceans of the world has been gradually increasing for thousands of years.
The relative sea level rise for the Netherlands does not only consider the worldwide sea
level rise due to melting of the North- and South Pole, but also the subsidence of the
landmass. Because this research is based on a long time period of measurements, it is
necessary to take into account the relative sea level rise over time.
Resonance in the North Sea basin
The North Sea can be seen as a rectangular basin. When the wind travels over this basin,
it pushes the water up against one side, in this case the Dutch coast. Due to the
bathymetry and geometry of the North Sea basin which leads to resonance, see Figure 22.
For one this phenomenon occurred for the storm surge of December 1954. During the
period of 21-24 of December two storm surges occurred for the Dutch coast. It is shown
that the period between the maxima of the two storms (about 36 hours) was such as to
cause almost complete resonance under the prevailing circumstances for the North Sea
(Weenink, 1956). E.g. after a set-up of about 1 m, the additional increase after one period
would be about 0.25 m.
Figure 7: Resonance in water basin
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Other meteorological effects
There are several meteorological effects that can also influence the total water level
increase, e.g. rain-oscillation and the polar low phenomenon. The latter is a small-scale,
short-lived atmospheric low pressure system that can in some situations result in a set-up
of around 50 cm. As these effects rarely have a big influence on the total water level
increase, they are not taken into account for this research.
2.2
Structure of a parametric model
The background of this research is very extensive. Based on the time and the focus of the
main objective, this thesis focusses only on the water level increase due to the effect of a
single storm over the North Sea. Figure 8 describes the phenomena that are analysed and
those that are left out in this research. Also the threat of river floods is left out.
Wind set-up
Storm surge
Pressure set-up
Water level
Astronomical tide
External set-up
Sea level rise
Hydraulic boundary
conditions
Other phenomena
Resonance
Meteorological
effects
Waves
Wave set-up
Figure 8: Focus of research
This research uses a parametric model to describe the surge level for the Dutch coast.
Therefore use is made of an analytical approach that determines the input storm
parameters based on weather charts. For a more complex method, the storm parameters
of depressions drawn in the weather charts should be computed with the use of
sophisticated computational models. This outcome can be placed in a computer model for
simulation of the direct wind-driven surge component [ADCIRC (Resio, 2007), DCSM (Bijl,
1997)].
There is a good database of weather charts of extreme storms that occurred over the
North Sea. As this is of interest for this research, it is possible to use these meteorological
weather charts to determine the storm parameters, instead of using a reanalysis dataset.
It is more labour-intensive, but provides a more reliable outcome of the storm depression
analysis.
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Combining earlier studies related to this research and the focus of this research, results in
the following conceptual model to determine the hydraulic boundary conditions, see
Figure 9.
Significant
Storm
parameters
Astronomical
tide
Bathymetry and
geometry of
the North Sea
Input:
Deterministic
/Probabilistic
Pressure field
Physical
modelling
Wind field
Pressure set-up
Wind set-up
Extreme
storm set-up
Output:
Deterministic
/Probabilistic
Hydraulic Boundary
Conditions
Figure 9: Conceptual model of the storm surge analysis
The first step in the determination of the hydraulic boundary conditions is to analyse the
occurring pressure- and wind field contributing to a storm. Therefore, physical knowledge
has to be retrieved in analysing storm depressions. Furthermore use is made of a study
done by (Resio, 2007), in which hurricanes for the coast of Louisiana are described using a
parametric storm model. For a first analysis of the wind, a stationary wind field is
assumed. The next step is to analyse how this wind field interacts with the North Sea
while moving in time and space. The storm parameters that determine the track and wind
field of the storm are extracted from the available weather charts. Secondly,
dependencies between these parameters are examined. A detailed description of this
step can be found in paragraph 2.3 and 2.4.
Next, it is analysed how the wind field of the simulated storm determines the occurring
wind set-up. For the wind set-up use is made of various methods in describing the set-up
with the use of the wind speed and wind direction. As the wind set-up depends on the
fetch and depth of the basin, the bathymetry and geometry of the North Sea has to be
taken into account. For this study Hook of Holland is the reference area for the
determination of the total set-up. Paragraph 2.5 describes the set-up.
Finally, it is explained how the HBC for Hook of Holland are determined using the tidal
amplitude and the total storm set-up. As the tidal amplitude is a well-known
phenomenon, it can be predicted with the use of a modelling system. For a more detailed
description, see paragraph 0
2.3
Mathematical description of the pressure field
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Figure 10: Analysis of the pressure field in the conceptual model
This paragraph describes physical knowledge in analysing the pressure field of a storm
depression. Furthermore, the storm parameters that contribute to the determination of
the pressure field are described in more detail.
2.3.1 Analysis of the pressure field
Based on the knowledge of a few principles of large-scale atmospheric motions a simple
approach can be followed to obtain ocean surface winds. The primary driving force for
atmospheric motions is the pressure gradient force. This force is produced by differences
in barometric pressure between two locations, and is responsible for the flow of air from
an area of high pressure to an area of low pressure.
Several studies have been done to describe the pressure gradient of a storm. Most of the
methods are used for hurricanes (Harper, 2002). There are also methods applicable for
storm depressions that occur in the North Sea (Bijl, 1997).
Bijl performed a study by using ‘parametric storms’ (Bijl, 1997), which considers the
parameters of a storm to be conditional upon a limited number of parameters. This study
continued with an earlier study done by Ferier (Ferier et al., 1993). To understand the
pressure field that occurs above the North Sea, Bijl uses the following methodology:
First, a definition was made of the computational grid in spherical coordinates (λ,ϕ). This
spherical grid is transformed into a planar grid (x,y). The reason for this is that the degree
of longitude changes while going in a north-south direction. Due to this it is very complex
to determine the pressure on a spherical grid. The next step is to calculate the pressure at
each point of the planar grid. Therefore, the pressure at a certain grid point (i,j) is
determined by:
p(i , j)  pa  p  e
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(
a2 b2

)
2 ra2 2 rb2
Delft University of Technology
(2.2)
Δp : Pressure gradient = pa -pc [mbar]
pa : Ambient pressure [mbar]
pc : Central pressure [mbar]
a : Radius to maximum winds in x-direction [m]
ra : distance from storm centre in x-direction [m]
b : Radius to maximum winds in y-direction[m]
rb : distance from storm centre in y-direction [m]
The pressure computed with this formula is the surface pressure at a distance r from the
storm centre. With the given pressure field, the data is transformed back to the original
spherical grid. Next, the corresponding geostrophic wind field can be calculated for the
artificial pressure field. The last step is to calculate the wind speed at sea level. Therefore,
Bijl used a reduction factor (65%) and a rotation (15⁰ counter clock-wise), based on the
study by Ferier.
For this research use is made of the formula that was used by (Holland, 1980) for
hurricanes, for which a circular pressure field is assumed:
p  pc  pe ( R max/ r )
B
(2.3)
R max : Radius to maximum winds [m]
B:
Holland B parameter [-]
The rationale for using this study is that less input parameters have to be taken into
account for the parametric model compared to Bijl’s method. Furthermore Holland
extended the original form by including a parameter B that enables variation in the
degree of pressure gradient near the maximum winds and thus captures the peakedness
in the related wind profile. This parameter is essential in describing the pressure field for
storm depressions for the North Sea. The study by Holland follows from a study by
(Schloemer, 1954), who considered a functional form of a number of pressure profiles.
As described in the paper of Harper, the Holland B parameter is widely accepted and used
in many related studies. For a better analysis of the pressure field this parameter has
been taken into account for this research.
2.3.2 Central pressure
An important parameter for the determination of the storm surge is the central pressure.
First of all, the central pressure is necessary to determine the pressure gradient, which
influences the wind fields that generate a wind set-up. Secondly, the central pressure is of
importance to determine the occurring pressure set-up. A lower central pressure will
mostly result in a higher pressure gradient, and therefore a higher pressure set-up. This
parameter can be retrieved from several resources. The minimum central pressure of a
storm is somewhere between 950 and 960 mbar, whereas the maximum central pressure
of a high-pressure area nearby this depression is around 1035-1040 mbar.
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2.3.3 Radius to maximum winds
The radius of maximum winds is the distance between the central low pressure point and
the location where the maximum wind speeds occur, so where the greatest pressure
gradient occurs. Storm depressions with a large radius mostly have high wind speeds at a
distance further from the centre of the storm than in case of a low radius.
For one the size of the storm depression influences the wind set-up for the Dutch coast.
As the tongue of cold air is sharper, the isobaric temperature gradients on both sides of
the tongue grow. In other words, there is a correlation between the activity of a
depression and the isobaric temperature differences in the undisturbed frontal zone at
the beginning (Maris et al., 1961b)
2.3.4 Holland B parameter
In order to define the shape of the profile of the pressure gradient, the Holland B
parameter is initiated. Following from the study by Holland, for the case of hurricanes this
parameter is in the range of 1.0 to 2.5. Equation (2.15) shows that the square root of this
parameter is proportional the maximum gradient wind speed.
This parameter plays an important role in estimation of the maximum wind speed in
analysing storm depressions.
2.4
Mathematical description of the wind field
Figure 11: Analysis of the wind field in the conceptual lmodel
2.4.1 Storm track of the wind field
For the analysis of the wind speed and direction at a measurement point for a given time
period, the forward movement of the storm and the angle between the centre of the
wind field (storm depression) and the measurement point have to be determined. The
forward speed of the storm is necessary for the determination of the duration of the
storm over the North Sea. Secondly, the forward movement contributes to the wind field
caused by the depression, which is explained later on in Figure 13.
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In order to determine the forward movement of the storm, it is necessary to analyse the
time intervals between the measurements and the distance that has been travelled
during the intervals. Therefore, the coordinates of the storm depression over time need
to be analysed given
x / t  C fm [m / s]
(2.4)
C fm : forward movement of the storm [m/s]
The spatial distance is the distance between two points that are given in longitudinal and
latitudinal coordinates. The following equation is used:
x 
 (cos  sin  )2  (cos  sin   sin  cos  cos  ) 2
1
2
1
2
1
2
arctan 

R
sin 1 sin 2  cos 1 cos 2 cos 

(2.5)




1 : Latitude coordinate point 1
2 : Latitude coordinate point 2
 : Longitude difference point 1 and 2
R : Radius of the earth (=6372.8 [km])
x: angular distance [km]
The same as for the forward movement, the angle of approach can be determined with
the use of equation(2.5). The angle of approach is the formulated as the angle between
the spatial distance horizontal and vertical, between the assumed boundary conditions.
For the vertical spatial distance 1° latitude is about 112 km. The angle of approach is of
importance for the determination of the distance between the storm centre and the point
of measurement per time step.
This angle of approach also influences the wind direction of the wind field over the time
period.
2.4.2 Geostrophic wind
The balance between the Coriolis force and the pressure gradient results in the motion
called the geostrophic wind. This balance is generally valid for large-scale flows; in free
atmosphere above the friction layer; under steady state conditions and with straight
isobars. For the geostrophic wind speed the following relationship is used:
(ug , vg ) 
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18
1   p  p
,


f a   y  x 
Delft University of Technology
(2.6)
p : atmospheric pressure [mbar]
f : Coriolis parameter [s 1 ]
 a : air density [kg/m3 ]
u g : geostrophic wind in the x (positive towards east) [m/s]
vg : geostrophic wind in the y (positive towards north) [m/s]
As can be seen in the formula, a higher pressure gradient leads to higher wind speeds,
which is more clearly shown in Figure 12.
Figure 12: Wind speeds associated with the pressure gradient (Floor, 2004)
Secondly, the Coriolis force determines the wind speeds that can occur. The size of the
force is enhanced with increases in latitude, as can be seen in the following formula:
f  2 sin 
(2.7)
 : angular speed of the Earth's rotation (7.29 105 [rad/s])
: latitude coordinate
Therefore, the geostrophic wind will increase with decreasing latitude.
For storm depressions with a circular pressure field, the formula for the geostrophic wind
speed can be simplified. Instead of determining two wind speeds in different directions,
the formula can be written as:
Vg 
1 p

f  a r
(2.8)
Vg : Geostrophic wind speed [m/s]
r : radius from centre of the storm [m]
For further analysis a geostrophic wind is assumed for a circular storm depression.
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2.4.3 Gradient wind
This geostrophic wind neglects frictional effects and is therefore a good approximation for
instantaneous flow in mid-latitude mid-troposphere. For the wind speed at sea surface
there is always friction from the ground. This results in the so called gradient wind.
In general, the atmospheric flow patterns are not straight, but move along curved
trajectories. This indicates an additional acceleration along the radius of curvature. This
balance motion is known as the gradient wind:
Vgr2
rt
 fVgr 
1 p

a r
(2.9)
Vgr : gradient wind speed [m/s]
rt : radius of curvature of the trajectory [m]
Around a low pressure centre, the Coriolis and centrifugal forces act together to balance
the pressure gradient force. For the geostrophic flow only the Coriolis force balances the
pressure gradient. Consequently, the speed of the gradient wind around a cyclone is less
than that of a geostrophic wind corresponding to the same pressure gradient.
Until now the storm is considered to be stationary. To account for the asymmetry in wind
speeds due to the storm forward movement, see Figure 13, Blaton’s adjustment for the
radius of curvature is used (Georgiou, 1985):
C
1 1
 (1  fm sin  )
rt r
Vgr
(2.10)
 : angle from the storm translation direction to the profile location [°]
Figure 13: The asymmetry in wind speeds due to the forward movement of the storm
The following relation is derived when substituting Blaton’s adjustment in the gradient
wind speed formula:
Matthijs de Jong
20
Delft University of Technology
1 
p 
Vgr  (C fm sin   rf )  (C fm sin   rf )2  r 
2 
r 
(2.11)
By substituting the formula for the pressure gradient (2.3) and the gradient wind
speed(2.11), the formula can be written as:
1
p  R max   ( R max/ r )B

2

e
(C fm sin   rf )  (C fm sin   rf ) 
2
a  r 

B
Vgr 





(2.12)
2.4.4 Surface wind
The surface wind speed is decelerated and deflected from the gradient wind speed, due
to surface friction. The delta committee used a reduction factor of ¾ (Schalkwijk, 1947) to
compute the surface wind. This reduction factor is strongly dependent on the difference
between the air and sea temperature. In (Ferier et al., 1993) a reduction factor of 65%
and a rotation of 15⁰ counter-clockwise of the geostrophic wind was used. The current
methodology for calculating the surface wind is:
Vs  Vgr (cos   sin  )
(2.13)
 : Deflection of the surface wind direction from the isobar [°]
In literature a ratio of 2/3 is often used, which results in a deflection angle of 17° (Klaver,
2005), see Figure 14. This ratio and related deflection angle are used in this study.
Figure 14: The deflection angle of the surface wind relative to the geostrophic wind (Floor, 2004)
There are many relationships proposed for relating the central pressure of a storm and
maximum winds for hurricanes. Almost all of these pressure-wind models are of the form:
Vg ;max  a  p x
(2.14)
Vg ;max : Maximum wind [m/s]
a, x : empirical constants
By assuming a constant air density at MSL, the maximum equivalent gradient wind speed
for the storm is at r= RMAX and can be shown as:
Matthijs de Jong
21
Delft University of Technology
0.5
Vg ;max
B  B
 ( pn  pc )
   ( pn  pc )0.5
e  e 
(2.15)
As can be seen, this formula is derived from (2.14).
2.5
Dependencies between the storm parameters
2.5.1 Dependency between Rmax and Holland B parameter
Based on earlier research (Harper and Holland, 1999) indicated that for the Australian
Cyclones, B is a linear function of central pressure, modelled as:
B  2.0  ( pc  900) /160
(2.16)
So that as the central pressure decreases, B increases. In later studies it was found that
there is a weak correlation between the RMAX and the Holland B parameter. (Vickery and
Wadhera, 2008) found that B could be modelled as a function of a non-dimensional
parameter, A:
A
R max f
(2.17)

p 
2 Rd Ts  ln 1 

pc  e 

Rd : Gas constant of dry air (287.04 J kg 1K 1 )
Ts : Sea surface temperature (5°C; 278.15 K)
This relationship between B and A is expressed as
B  1.732  2.237 A, r 2  0.336
A more recent study by (Xiao et al., 2009) showed that a normal distribution is used for
the B parameter with a mean value determined as a function of RMAX, in which ε is a
normal random variable:
B  d0  d1Rmax  
2.6
Storm set-up associated with the pressure- and wind field
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Delft University of Technology
(2.18)
Figure 15: Analysis of the storm set-up in the conceptual mode
2.6.1 Wind set-up modelling
One of the earliest studies in determining the wind set-up using the wind speed was done
by (Weenink, 1958). He came to the conclusion that the wind set-up can be determined
using a quadratic function of the wind speed as input parameter. Weenink studied the
wind set-up on the North Sea, and derived an analytical model which describes the wind
set-up by splitting up the North Sea in five sub-basins, all with their own contribution to
the total set-up. Based on his study the time interval between the maximum hourly
averaged wind speed and the maximum wind set-up is equal to 6 hours, see Figure 16.
Figure 16: Relation between the wind speed and the wind set-up
Vrijling and Bruinsma derived an equation for the determination of the wind set-up for
the 9-hourly wind speed:
s(W9 )  1
s:
Wind set-up [m]
W9 :
Exceeded wind speed over 9 hours [m/s]
1 :
Empirical parameter [-]
g:
Gravity acceleration [m/s2 ]
Matthijs de Jong
23
W92
g
(2.19)
Delft University of Technology
Use is made of the parameter W9 that is used in the wind set-up formulas by Weenink and
is often used as a characteristic value for the short-period wind speed in a wind field. The
method pointed out that during extreme HW-levels, the significant wind direction on the
Southern North Sea comes from a direction between 285° and 360°.
Storm surge model by Voortman
In 2002, Voortman continued with the study done by Vrijling and Bruinsma. In his study,
the wind speed was chosen as the input parameter. The reason for this choice is that the
water level is influenced by more than one process, namely the astronomical tide and the
wind field. Therefore, it is doubtful whether a pure stastical analysis is valid for this data.
The basis of this choice is available in the study of (Wieringa and Rijkoort, 1983)
The model is developed to write the JPDF of hydraulic conditions nearshore as a function
of the properties of the wind field; the geometry of the North Sea basin; the astronomical
tide and the bathymetry nearshore. Following Weenink, the function for the wind set-up
can be written as2:
s  d  d 2 
2cW92F
g
(2.20)
F : The fetch / basin length [m]
d : the depth [m]
c : the empirical coefficient
 : factor to describe the basin shape [-]
The function is only valid for a simplified one-dimensional situation. Therefore, the
parametric model is based on a several simplifying assumptions. First, a uniform wind
field is assumed, which means that the wind is constant in both time and space. The basin
geometry is simplified to a rectangular basin with a constant depth and a constant length.
Next to that the depth is assumed to be constant. For this situation it is assumed that the
dominant wind direction in a storm provides the direction in which to define the
schematisation for the North Sea basin.
An effective depth is defined as the depth for which the function leads to the same wind
set-up at the measuring location as the complete model. Voortman derived the bottom
profiles based on the North Sea map in 10° sectors from Schiermonnikoog Noord
(Publications, 1997). Table 1 shows the related fetch and effective depth wind set-up for
each sector.
2
Appendix A: A one-dimensional model for the water level increase due to a uniform wind field
Matthijs de Jong
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Delft University of Technology
Sector
(°N)
250
260
270
280
290
300
310
320
330
340
350
360
Fetch
(km)
260
295
270
370
460
570
580
675
675
675
675
470
Mean depth
(m)
20.5
23.0
26.4
32.7
41.0
41.2
50.1
67.5
65.1
66.8
120.0
75.9
Effective depth wind set-up
(m)
16.0
21.3
23.2
29.0
31.3
32.6
42.7
54.8
53.9
55.4
56.6
47.3
c (10-6)
2.05
2.5
2.23
2.49
2.13
2.17
2.24
2.26
2.33
1.76
1.76
1.51
Table 1: Properties for the North Sea (Voortman et al., 2002)
Because this method has been applied for Schiermonnikoog-Noord it is unknown what
the dependency is for this situation and the determination of the wind set-up at Hook of
Holland.
Storm surge model by Van den Brink
The thesis by (Brink, 2005) determined the water level at the Dutch coast during storm
surges for a simulated period of around 1600 years, by varying storm parameters of the
extreme events for the North Sea, see Figure 17. The data that was used for this method
was provided by ECMWF, the European Centre for Medium-Range Weather Forecasts.
Figure 17: surge model including the pressure effect, and without the pressure effect (Brink, 2005)
In order to calculate the surge at high tide at the coastal station Hook of Holland from the
meteorological, Van den Brink derived a formula, based on the simplifying the tables used
by (Timmerman, 1977). This resulted in the following equation:
Matthijs de Jong
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Delft University of Technology
2 (   )
 u 
 
)
  sin(
30.87 
360
setup  
[m]
10
2
W9 : wind speed [m/s]
 : clockwise wind direction with respect to the North [°]
 : correction coefficient [s 2 /dm]
 : correction coefficient [°]
Measurement station
Hoek van holland
Vlissingen
IJmuiden
Delfzijl
Den Helder
Harlingen
α [s2/dm]
-36.7676
-33.968
-36.3626
-52.7938
-35.5137
-42.3493
Β [°]
-47.4535
-46.5788
-47.1307
-50.9918
-48.0564
-37.031
Table 2: Correction coefficients for the wind set-up model by van den Brink
The correction coefficients, see Table 2, were used to fit the equation into time- and
space- averaged values based on the tables by Timmerman. The wind speed is divided by
30.87 (= 60 knots), because the sinusoidal function was fitted for the values used by
Timmerman for a wind speed of 60 knots. Furthermore, the function is divided by 10,
because the tables used are noted in decimetre. This surge equation was validated by
comparing the 1957 – 2002 observed annual extreme surges in Hook of Holland with the
annual extreme surges calculated from the equations above using the wind and pressure
of the ERA40-Reanalysis data. The results are shown in Figure 3.
Matthijs de Jong
26
Delft University of Technology
(2.21)
2.7
Determination of the extreme storm surge
Figure 18: Analysis of the extreme storm surge in the conceptual model
The determination of the HBC for this parametric storm model depends on the tidal water
level and the storm set-up that combines the pressure- and wind set-up. This study is
interested in the 10-4/years water level for Hook of Holland. Therefore use is made of the
Monte Carlo method. This method simulates the physical process as described in Figure
19, by using different starting conditions for the input parameters: Location of the starting
point; angle of approach; forward speed; central pressure; radius to maximum winds and
the Holland B parameter.
Therefore it is necessary to determine the probability distribution of the input parameters
and to analyse whether there are dependencies between these parameters, and take
them into account in the Monte Carlo method.
Matthijs de Jong
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Delft University of Technology
Figure 19: Parametric model to determine the wind set-up for the Dutch coast
For the tidal water level prediction use is made of MIKE21 (DHIgroup). With this program
the hourly tidal water level for Hook of Holland can be simulated from 1900 until present.
As the wind set-up had a duration that is much larger than the period of the astronomical
tide, it is assumed that the maximum storm surge level occurs at or very near
astronomical high water.
Matthijs de Jong
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Delft University of Technology
3
Analysis of historical storms
Equation Section (Next)
This chapter describes the method that has been used to collect the input storm
parameters. First of all the selection procedure and available resources for these
significant parameters are described. The next paragraphs contain information of
retrieving the dataset, and determine the probability distribution function per storm
characteristic. Possible dependencies between these storm parameters are discussed.
Lastly, the retrieved dataset has been summarized.
3.1
Storm inventory
In order to derive the extreme hydraulic loads for the Dutch coast, the input parameters
for the model have to be determined. For the analysis of these storm parameters it is
essential that the retrieved dataset is valid. Therefore the storms that are further
analysed are based on a selection procedure.
3.1.1 Selection criteria
For homogeneity and consistency reasoning use has been made of the selection
procedure by the Delta commission in 19603. The criteria for the storm selection
procedure are based on the following considerations:

The storms are relevant in terms of extreme hydraulic loads. The selected storms
are based on the P.O.T. method, as this research is interested in the extreme
conditions.

The storm depression selection is applied (Vrijling, 2002). This physical
consideration distinguishes the wind directions and course of the depression
which causes the storm. Determining the probability function of extremes
selected by this method, is only suitable for U.L.S. analysis.

The astronomical tide is stochastically independent of the wind set-up.

The storms are selected that result in the highest “skewed” set-up4, due to lack of
information about the straight set-up for the significant storms. It is assumed that
storms that cause the highest “skewed” set-up also result in a high straight setup.
3
4
Appendix B: Working method of the Delta committee
Appendix C: Difference between skew and straight set-up
Matthijs de Jong
29
Delft University of Technology

The measurements stations for the validation and calibration are based on the
wind and water level observation at Hook of Holland (HoH), due to availability of
studies related to HoH. The wind field observation for the storm of 1953 is based
on the measurement station at Vlissingen, as this is to only available material.

For the evaluation of the wind set-up model a sufficient number of storms is
needed. For a first analysis a threshold of hskewed ≥ 155 cm has been used. This
threshold gives 31 significant storm surges in the period of 1887 – 2008.
3.1.2 Availability of input and validation data
For the input dataset it is necessary to have an overview of the availability of the different
resources5. Furthermore, the dataset has to be consistent. For the consistency, the
analysis is purely focused on the real datasets measured over the available period of
observations. Secondly, homogeneity is essential for the validation of the dataset.
Because charts of different resources can diverge from one and each other, only weather
charts are used from the K.N.M.I..
Based on these criteria, the data has been extracted from the Delta report in 1960storm
surge reports and archive available at K.N.M.I., on internet (KNMI, 2003) and in the storm
catalogue (Groen and Caires, 2011), see Table 4.
Period
1898 –
1956
Time
Delta report
Storm track
Delta report
Pressure
Delta report
Radius
K.N.M.I.
archive
Angle
K.N.M.I.
archive
1956 –
1973
1973 –
1981
1981 –
2010
K.N.M.I.
archive
Storm surge
reports
Storm surge
reports
K.N.M.I.
archive
Storm surge
reports
Storm surge
reports
K.N.M.I.
archive
Storm surge
reports
Storm surge
reports
K.N.M.I.
archive
K.N.M.I.
archive
Storm surge
reports
K.N.M.I.
archive
K.N.M.I.
archive
Storm surge
reports
Table 3: Retrieving dataset of storm parameters
In the Delta report a study was done to analyse the storm tracks of the storm depression
for the period 1900 until 1956. The K.N.M.I. has an archive with available weather charts
between 1888 and 1988. Furthermore there are digitized reports between 2003 and
2011. Already since 1953 storm surge reports are available for storms over the North Sea.
Since 1973, however, the storm surge reports contain more relevant information for
analysing the storm parameters, e.g. the storm track with several characteristics at
different time intervals.
For the validation of the wind set-up model, the water level and wind field measurements
need to be collected. The water level measurements are based on the high water level
dataset from Deltares.
5
Appendix D: Resources for storm analysis
Matthijs de Jong
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Delft University of Technology
For the wind field several locations are used, based on the available observations (KNMI).
For the water level measurements Hook of Holland is chosen as reference area. RWS
provides the water level data between 1970 and 2008 (RWS). Furthermore there is also
data available for the storm of 1953 for Vlissingen.
Wind field
1962 – present
1953, 1957 – present
Hook of Holland
Vlissingen
Water level
1970-2008
Table 4: Available dataset for the wind field and water level
3.2
Selection of storm dataset
Based on the selection criteria the following dataset of storms is obtained, see Table 5.
The “skewed” set-up has been transformed to 2009, taking into account the relative sea
level rise6.
In total 31 storms are retrieved. However, for the storms until 1895 and during the 2nd
World War there are no weather charts available to determine the wind field around the
storm depression. Furthermore, only storms are analysed with a North-Westerly
direction, based on the storm depression selection. Therefore, the storms of 1906, 1921
and 1972, with a South-Westerly direction, are not used for this study.
As a result, 21 significant storms are relevant for further research.
Date of
storm surge
Storm
number
Waterlevel
skew
setup
Tidal
level
Available
resources
1889/02/09
1894/12/22
1895/01/23
1895/12/07
1
307
359
292
298
228
250
194
178
79
109
98
120
Wetterzentrale
Wetterzentrale
Wetterzentrale
K.N.M.I.


1897/11/29
2
295
178
117
K.N.M.I.


1898/02/03
3
258
181
77
K.N.M.I.


1904/12/30
4
325
206
119
K.N.M.I.


1905/01/07
5
279
159
120
K.N.M.I.


1906/03/12
1907/02/21
6
319
257
180
162
139
95
K.N.M.I.
K.N.M.I.
-

1908/11/23
7
295
166
129
K.N.M.I.


1916/01/13
8
328
220
108
K.N.M.I.


1919/12/19
9
267
157
110
K.N.M.I.


1921/11/06
-
290
174
116
K.N.M.I.
-
6
7
Step 1:
Storm track
analysis
Step 2:
7
Wind field
analysis
-
-
Appendix E: Dataset of the storms
For some storms weather charts are missing to determine several storm parameters
Matthijs de Jong
31
Delft University of Technology
1928/11/26
10
323
181
142
K.N.M.I.


1940/12/07
-
290
167
123
Delta report

-
1944/01/26
-
292
174
118
Delta report

-
1944/02/05
-
263
164
99
Delta report

-
1946/02/24
-
280
179
101
Delta report

-
1949/03/01
11
294
165
129
K.N.M.I.


1953/02/01
12
409
293
116
K.N.M.I.


1954/12/23
13
323
210
113
K.N.M.I.


1962/02/12
14
262
168
94
K.N.M.I.


1962/02/17
15
284
187
97
K.N.M.I.


1972/11/13
1976/01/03
16
250
309
157
168
93
141
K.N.M.I.
K.N.M.I.


1989/02/14
17
286
177
109
K.N.M.I.


1990/12/12
18
255
157
98
K.N.M.I.


2003/12/21
19
274
156
118
K.N.M.I.


2007/11/09
20
319
187
132
K.N.M.I.


2008/03/01
21
234
155
79
K.N.M.I.


Table 5: Data selection of the significant storms at Hook of Holland
3.2.1 Analysis of the “skewed” set-up
The dataset of highest set-up measurements at Hook of Holland are based on the
“skewed” surge. When extrapolating the record8, of the “skewed” set-up, the once in the
10.000 years “skewed” set-up is somewhere around NAP + 3.8 m with the use of the
Gumbel distribution. With a mean astronomical tide of around NAP + 1.2 m when using
the “skewed” set-up, the total water level will be around NAP + 5.0 m, which coincides
with the current hydraulic boundary condition for Hook of Holland.
3.3
Pressure field analysis
For a first analysis the pressure field of the storm is analysed, for which the following
parameters are of interest:
8

Central pressure [mbar]

Radius to maximum wind speed [km]

Holland B parameter [-]
Appendix F: Extrapolation of the skew setup dataset
Matthijs de Jong
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Delft University of Technology
3.3.1 Working assumptions for the pressure field
For a first analysis of the storm depression, several working assumptions have to be
made. These assumptions are done to provide a simpler approach of the determination of
the significant storm parameters, which need to be extracted from the dataset. As the aim
of this study is to realise a simplified model to determine the water set-up for Hook of
Holland, the following assumptions have been made:

For some weather charts the centre of the storm is not determined. For these
cases, use is made of available data in the Delta Report, or the central pressure is
estimated by assuming a constant line along the slope of the available pressure
gradient, see Figure 20.

For the determination of the pressure field of a storm depression, the weather
chart is used for which the pressure field has the most influence on the North Sea.
This is the case when the storm depression is located to the East of the North Sea,
between 10° and 15°E longitude.

For the ambient pressure two values are used, and therefore two methods for the
determination of the wind field. For the first value, the ambient pressure is
chosen as the difference between the lowest- and highest pressure area for a
storm depression. The second value is based on a fitted value of 1050 mbar. The
rationale is that this value results in a more accurate approximation of the total
pressure field, which is necessary to determine the wind field. A second
advantage is that only one input parameter in necessary. The ambient pressure at
sea level is left out, due to a high underestimation of the actual pressure/wind
field.

The isobars of a storm depression are rather complicated to model. Compared to
a typhoon or hurricane, the isobars of a storm depression are not necessarily
circular. As this model represents a simplified approach of the real storm
depression, the depression is assumed to be circular. This reduces the number of
input parameters.
Based on the weather chart, a simple analysis can be made of the geostrophic wind speed
around the storm centre. The weather charts that are used show a pressure field
travelling over the whole North Sea. Secondly, a line is plotted from the central pressure
of the storm perpendicular to the isobars around it. Given the longitude and latitude
Matthijs de Jong
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Delft University of Technology
coordinates of the intersection points, and the pressure gradient between two
consecutive isobars9, the geostrophic wind can be calculated.
3.3.2
Central pressure
For situations where the weather charts, the data from the Delta committee and the SSR’s
do not provide the exact central pressure, this value is estimated by assuming a constant
line along the slope of the pressure gradient, see Figure 20.
Figure 20:(a) Pressure gradient of a storm (Klaver, 2005); (b) Estimation of the central pressure for weather
charts
The central pressures for the significant storms vary between 950 and 990 mbar. The
depth of the central pressure alone does not determine the strength of the storm. This is
also stated in the report of the Delta committee and can be clarified by the pressure
gradient formula. The pressure gradient influences the wind field, which is determined by
not only the central pressure, but also the ambient pressure and radius to maximum
winds. Based on BestFit, the normal distribution shows the best resemblance with the
central pressure. Therefore, a mean central pressure is used of 975 mbar, with a standard
deviation of 15.05 mbar.
9
Before 1953 the weather charts were measured in mmHg (= mercury), with 760 mmHg is around
1013 mbar. For these charts the pressure gradient between two isobar lines is 6.67 mbar. After
1953 this pressure gradient is 5 mbar.
Matthijs de Jong
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Delft University of Technology
Figure 21: Normal distribution of the central pressure of the 21 storms (975 mbar,15.05 mbar)
3.3.3 Radius to maximum winds
The radius to maximum winds and the Holland B parameter are determined with the use
of two methods, based on the working assumption. For the first value, the ambient
pressure is chosen as the difference between the lowest- and highest pressure area for a
storm depression. The second value is based on a fitted value of 1050 mbar. The rationale
is that this value results in a more accurate approximation of the total pressure field,
which is necessary to determine the wind field. A second advantage is that only one input
parameter in necessary. The ambient pressure at sea level is left out, due to a high
underestimation of the actual pressure/wind field.
To estimate the parameters, use is made of the least square method, fitting the measured
pressure gradient and the pressure gradient based on the formula. With the central
pressure and the radius from the storm centre known, the only parameter that needs to
be determined is the ambient pressure.
Most models use the ambient pressure at sea level, which is about 1013 mbar. The
disadvantage of this ambient pressure is that the pressure field at further distance of the
storm centre is underestimated. This can be clarified with the formula(2.3), for which the
highest pressure that can be measured is the ambient pressure:
 p p
r 
c
 p  pc  ( pn  pc )  pn
For a better estimation of the total pressure field, it is therefore necessary to take into
account an ambient pressure that is high enough to determine the pressure field.
Therefore, use is made of two methods:

Method 1: pn  pcH [mbar]

Method 2: pn = 1050 [mbar] (arbitrary ambient pressure)
Matthijs de Jong
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Delft University of Technology
(3.1)
pcH : Central pressure of high pressure area [mbar]
Both methods have the advantage that the total pressure field can be determined more
accurate. The disadvantage is that for method 1 another parameter has to be determined,
namely the central pressure of the highest pressure area. And for method 2, the value of
1050 [mbar] is purely based on a fitted value. The high pressure fields for the storms in
this research are between 1020 and 1045[mbar]. The value of 1050 [mbar] is significantly
high to provide a good estimation of the total pressure field. Figure 22 shows the
measured pressure field and the determined pressure field with the use of the different
ambient pressures. The fitted ambient pressure provides the best estimate of the
measured pressure field.
Figure 22: (left) Different methods for the determination of the pressure field for the storm of 1953; (right)
Pressure difference between methods and the measured pressure
For a better observation the difference between the measured pressure from the storm
centre and the measured pressure using several methods is shown in Figure 22 (right).
The ambient pressure at sea level shows an extreme underestimation the pressure field
far away from the storm centre.
Method 1: Total pressure difference
For the determination of the RMAX and the Holland B parameter for method 1, it is
necessary to determine the central pressure at the high pressure area. Therefore, more
data is necessary to determine the pressure field. A second disadvantage is that a few old
weather charts do not show clearly the high pressure field.
Based on the available dataset of 21 storms, the radius to maximum winds from the
weather chart has been compared with the radius to maximum winds from method 1, see
Figure 23.
Matthijs de Jong
36
Delft University of Technology
Figure 23: Measured RMAX from weather charts compared with the RMAX from method 1
This method shows a good correlation between both measurements. BestFit shows that
the lognormal distribution has the best fit with the dataset, for which the mean is at 552
km, with a standard deviation of 213 km.
1200
Radius to maximum winds [km]
1100
1000
900
800
700
600
500
400
300
200
2
4
6
8
10
12
14
Storm number
16
18
20
Figure 24: (left) Radius to maximum winds with Method 1 for the significant storms [km]; (right) Ascending
lognormal distribution with μ=552 km and σ=213 km, based on the significant storms
Method 2: Fitted ambient pressure
This method has a higher deviation with the weather charts compared to the first
method; see Figure 25 (left). Furthermore it is noticeable that the storm of 1928 has a big
influence on the correlation. For this storm the computed radius to maximum wind is
significantly higher than the measured radius. The formula for analysing the pressure
gradient from the centre of the storm has a smooth curve, and does not take into account
deviations in the real pressure field. For the storm of 1928 a second peak of high wind
speeds occurs that fits the correlation with the measured radius. When this storm is not
taken into account the correlation is R2=0.7356.
Matthijs de Jong
37
Delft University of Technology
Figure 25: (left) Measured RMAX from weather charts compared with the RMAX from method 2; (right)
2
without the storm of 1928 R =0.7356
Figure 26 (left) shows that some of the latest storms have a low radius to maximum
winds. Secondly, the figure shows that this radius can vary significantly per storm, with
the lowest radius around 350 km and the highest around 1150 km. BestFit shows that the
lognormal distribution has the best fit with the dataset, for which the mean is 688 km
with a standard deviation of 236 km.
1300
Radius to maximum winds [km]
1200
1100
1000
900
800
700
600
500
400
300
2
4
6
8
10
12
14
Storm number
16
18
20
Figure 26: (left) Radius to maximum winds with Method 2 for the significant storms [km]; (right) Ascending
lognormal distribution with μ=688 km and σ=236 km, based on the significant storms
3.3.4 Holland B parameter
The Holland B parameter is compared to the RMAX of the different methods. Secondly, the
dependency of this parameter will be analysed based on the formulas in paragraph 2.3.4.
Method 1; total pressure difference
For a first analysis of the Holland B parameter is assumed to be an independent variable,
with a lognormal distribution with a mean of 1.75 and a standard deviation of 0.55.
In Figure 27 the dependency between the Holland B parameter and the radius to
maximum winds with method 1 is determined. The figure shows that for most storms the
Holland B parameter varies between 1 and 2 (18 from 21). Based on these figures, it is
shown that there is some correlation between B and the RMAX. The normal distribution of
the Holland B parameter has a mean of 1 and a standard deviation of 0.15.
M1
B  ( Rmax
 0.0021  0.61)  
Matthijs de Jong
38
Delft University of Technology
(3.2)
For which the 95% confidence interval depends on ε, the normal distribution of the
Holland B parameter, with μ=1 [-] and σ=0.15 [-].
Dependency between the Rmax and Holland B parameter (R 2=0.5054)
Dataset of storms
Dependency Rmax and Hb
95% confidence interval
3.5
Holland B parameter [-]
3
2.5
2
1.5
1
300
400
500
600
700
800
900
Radius to maximum winds with Method 2[km]
1000
Figure 27: RMAX from method 1 compared to Holland B parameter
Method 2: Fitted ambient pressure
For a first analysis of the Holland B parameter is assumed to be an independent variable,
with a lognormal distribution with a mean of 1.23 and a standard deviation of 0.4.
For method 2 the dependency between the Holland B parameter and the radius to
maximum winds based on Method 2 shows some deviation. Also for this situation the
storm of 1928 has been left out. A first analysis shows that 17 out of 20 storms have a
Holland B parameter between 0.6 and 1.4. The storms with a Holland B parameter mostly
indicate a higher radius to maximum winds. Figure 28 shows that there is a linear
correlation between these input parameters based on the following formula:
M2
B  ( Rmax
 0.0014  0.33)  
For which the 95% confidence interval depends on ε, the normal distribution of the
Holland B parameter, with μ=1 [-] and σ=0.175 [-].
Matthijs de Jong
39
Delft University of Technology
(3.3)
Dependency between the Rmax and Holland B parameter (R 2=0.5054)
2.2
Holland B parameter [-]
2
Dataset of storms
Dependency Rmax and Hb
95% confidence interval
1.8
1.6
1.4
1.2
1
0.8
400
500
600
700
800
900
1000
Radius to maximum winds with Method 2[km]
1100
Figure 28: RMAX from method 2 compared with the Holland B parameter
The analysis has also been done for the latest storms from 1953 until 2008. The weather
charts for these storms are more accurate, and therefore result in a better analysis of the
storm parameters retrieved from the charts. The results are shown in appendix H10.
3.4
Movement of the storm depression
Secondly, the trajectory that the low pressure area follows on the Earth’s surface is
analysed. Depending on the available data from the Delta report and the weather charts
from K.N.M.I., the location of the storm depression can be determined over time.
3.4.1 Working assumptions for analysing the storm track
The following working assumptions have been made with regard to analysing the track of
the storm depression in the weather chart:

The weather charts are analysed at MSL, as these pressure fields directly influence
the wind field for the North Sea. No analysis is done for the topography at 500
mbar.

The centre of the lowest pressure area is chosen as the location of the storm
depression.
10
Appendix G: Analysis of the radius to maximum winds and the Holland B
Matthijs de Jong
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Delft University of Technology

The track of the depression is determined by the circulation-pattern in the upper
atmosphere. One circulation-pattern can cause several storm depressions to
occur at the same time. As the parametric model focusses on one storm
depression, this research only takes into account the most significant storm
depression.

For simplicity the forward movement of the storm is averaged between the
boundary conditions.

For simplicity the angle of approach is averaged between the boundary
conditions.

For homogeneity in time the weather charts are based on the GMT (Greenwich
Mean Time).
3.4.2 Location of the boundaries
Given the time, coordinates and pressure fields of the significant storm depressions, the
storm track of the different storms can be analysed. These storm tracks are shown in
Figure 29, with the use of OpenEarth (Koningsveld et al., 2010)11.
Figure 29: Significant storm depressions at Hook of Holland travelling over the North Sea
Figure 29 shows that about 81% of the storms travel over the Atlantic Ocean, to the North
of the Scottish coast. 13% travels over Great Britain, whereas the storm of 2003 is
developed in the North Sea. The storms travelling over the Atlantic Ocean can result in an
11
OpenEarth is a free and open source that deals with data, models and tools in marine and coastal
engineering projects
Matthijs de Jong
41
Delft University of Technology
external surge that contributes to the wind set-up for the North Sea. Furthermore, the
storms are mostly located above Denmark. This is because storm depressions travelling
over the Northern Hemisphere cause a counter-clockwise wind. When the storm
depression is around Denmark this counter-clockwise wind field will have the most
negative effect on the North Sea.
For an analysis of the direction of the significant storms, the location of the storm is
determined for the boundaries at 5.5° and 12.5° longitude. These boundaries are chosen
as the storm depression has a high influence on the North Sea basin for these boundaries.
Furthermore, all storms can be taken into account (the storm of 2003 is originated in the
North Sea). Based on the significant storms and the available dataset, see Table 5, 25 of
the 28 storms can be analysed. It follows from Figure 30 that 89% of these storms have a
North-Westerly direction. As mentioned before the storms of 1906, 1921 and 1972 have a
SW/SWW direction for the given boundary conditions, given the three points that are
situated right of the line.
Figure 30: Location of the storm depression at 5.5°E and 12.5°E longitude. The locations indicate whether
the storm has a North-Westerly or a South-Westerly direction.
Most of the significant storms tend to travel between 55° and 58° Northern latitude when
crossing 5.5°E, and between 54° and 57° Northern latitude when crossing the 12.5°
Eastern longitude. This can also be seen in Figure 30. Due to several peaks, the averaged
latitude lies around 58.5°. As Figure 31 indicates, the extreme storms do not tend to show
a clear trend of shifting over the North Sea over time. The two peaks, storms 14 and 15,
are measured during the storm period of February 1962, which travelled at high Northern
latitude.
Further research of the storm parameters will only include the 21 significant storms that
have all the available material for analysing the pressure- and wind field for the North Sea.
Matthijs de Jong
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Delft University of Technology
Figure 31: (left) Latitudinal starting location of storms at 5.5°E longitude; (right) Ascending lognormal
distribution of the latitudinal coordinate at 5.5°E (58.61°, 2.60°)
Based on the computer program Bestfit (Palisade, 1994), the Lognormal distribution has
the best fit for the starting latitudinal position of the storm centre. To describe this
lognormal distribution in the Monte Carlo approach, μ is 58.61°N with a standard
deviation of 2.6°. Use is made of the KS-test12 that compares a sample, the starting
position, with a reference probability distribution. As Figure 31 indicates, the latitudinal
starting location of the storm lies between 50° and 70° Northern latitude, which are used
as the lower and upper boundary in this model. There is no theoretical knowledge for
using this probability distribution.
It is however known that storm depressions tend to travel the path with the least
resistence. As the geography of Norway is dominated by mountain ranges, it would be
likely that most storms travel around these mountainous areas. This indicates that the
storms mostly travel beneath Norway, over the North Sea. As this dataset only includes 21
storms, it is recommended to analyse the path of a larger dataset of storms and how they
are influenced by the high areas in Norway. For this analysis, the lognormal distribution is
used for the starting location using BestFit.
3.4.3 Forward movement of the storms
The forward movement of the storms is determined by analysing the distance and time
interval between the chosen boundaries. The accuracy of this distance depends on the
number of weather charts per day made by K.N.M.I.. As mentioned in Appendix E, this
number changes for different time periods and with that the accuracy of the storm track.
For this research the forward movement of the storm is assumed to be averaged between
the boundaries. This forward speed of the storm over the North Sea is shown in Figure 32.
The average speed is about 15 m/s. As the figure shows, a high “skewed” set-up can also
occur for storms that travel slowly over the North Sea, near 6 m/s, and storms that travel
fast, about 25 m/s. For these 21 significant storms there is however no clear dependency
between the forward movement of the storm and the latitudinal starting point.
12
KS-test: Kolmogorov-Smirnov goodness-of-fit test
Matthijs de Jong
43
Delft University of Technology
Figure 32: (left) Averaged forward speed of the storms between 5.5°E and 12.5°E longitude; (right)
Ascending lognormal distribution of the forward speed of the storm (14.67 m/s, 5.24 m/s)
For the forward movement of the significant storms the lognormal distribution shows the
best reference probability distribution, for which the mean latitude is 14.67 m/s and the
standard deviation 5.24 m/s. This is however purely based on the available dataset, as
there is no physical reason for applying this distribution. The same distribution has been
used for the forward movement of typhoons in Suo-Nada Bay, Japan (Klaver, 2005).
3.4.4 Angle of approach of the storms
The angle of approach is determined with the use of the spatial distance in horizontal and
vertical direction. The geographic coordinates of the storm are known for the given
boundaries. The distance between these coordinates can be converted from radians to
kilometres as measured along the mean radius of the Earth. The latitudinal distance of 1°
is about 111.2 km. With these distances known, the angle of approach can be computed,
which is shown in Figure 33.
Figure 33: (left) Averaged angle of approach of the storms between 5.5°E and 12.5°E longitude [°N]; (right)
Figure 34: Cumulative distribution function of the angle of approach including three distribution functions
[°W].
Depending on the storm depression selection, only storms with a North-westerly direction
are taken into account. Therefore the distribution that is used must lie between 270° and
Matthijs de Jong
44
Delft University of Technology
360°. Except for the Beta distribution, all other distributions in BestFit do not meet this
requirement. The Beta distribution however leaves out several scenarios that can also
occur. With the use of Matlab the best fit that also meets the requirement is the Rayleigh
distribution, with mu is 22.46 [°W] (KS-test: 0.153). The GEV distribution exceeds the left
boundary (270°), and the Weibull exceeds the right boundary (360°). This research use is
made of the Rayleigh distribution for the angle of approach.
Matthijs de Jong
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Delft University of Technology
3.5
Dataset of the storm parameters
The complete dataset of storm parameters that has been analysed for further research is
shown in Table 6. These outcomes and their distributions will be used for the parametric
model in Chapter 5, which eventually will be used to determine the water level for the
Dutch coast.
Date of
storm surge
[yy/mm/dd]
1895/12/07
1897/11/29
1898/02/03
1904/12/30
1905/01/07
1907/02/21
1908/11/23
1916/01/13
1919/12/19
1928/11/26
1949/03/01
1953/02/01
1954/12/23
1962/02/12
1962/02/17
1976/01/03
1989/02/14
1990/12/12
2003/12/21
2007/11/09
2008/03/01
Starting
point at
5.5°E
lon
[°N lat]
Forward
speed
Angle of
approach
Central
pressure
[m/s]
[°]
[mbar]
62.4
55.7
57.3
56.6
57.9
59.5
60.1
57.9
57.8
56.4
56.3
55.8
57.9
61.7
66.4
56.4
57.7
61.3
55.5
60.1
60.1
12.1
13.0
18.2
24.7
15.4
6.8
8.5
10.9
12.2
8.9
16.2
10.1
14.1
22.5
16.6
10.9
17.5
19.0
13.3
11.0
26.1
327.8
276.2
311.2
290.1
306.6
275.9
296.1
309.6
291.8
289.6
295.8
312.3
297.8
286.5
311.4
292.5
272.6
337.1
273.8
293.1
291.2
962.7
959
978
982.7
977
956
984.7
978
990
969.3
981.0
963
977.5
952.5
952.5
967.5
990
982
970
979
968
Radius to max
winds[km]
Method 1 Method
2
323
385
1045
535
545
761
611
407
508
582
486
620
390
1039
849
281
423
380
273
485
686
551
607
1158
669
578
954
883
577
664
1058
549
693
477
1055
861
341
463
523
363
569
854
Holland B
1
2
1.0
1.7
3.6
1.4
1.6
1.8
2.7
1.6
1.6
1.4
1.7
1.4
1.6
2.0
2.8
1.1
1.8
1.6
1.0
1.8
1.7
0.7
0.9
2.3
1.0
1.4
1.2
1.3
1.0
1.1
0.8
1.3
1.2
1.2
1.9
2.2
0.9
1.4
0.9
0.7
1.3
1.1
Table 6: Storm parameters for dataset
With the use of the KS-test and the Chi-square test the distribution for each storm
characteristic has been analysed. As there is too little known about these storm
parameters, the distribution functions are purely based on the measurements, without
including physical knowledge.
Storm parameters
Starting location
Forward movement
Angle of approach
Central pressure
Radius to maximum
Matthijs de Jong
Probability
Distribution
Lognormal
Lognormal
Rayleigh
Normal
wind Lognormal
46
Mean [μ]
58.61 [°]
14.67 [m/s]
22.46[°]
975 [mbar]
552 [km]
Standard deviation [σ]
2.6°
5.25 m/s
15.05 mbar
213 [km]
Delft University of Technology
speed method 1
Holland B parameter method 1 Lognormal
Radius to maximum wind Lognormal
speed method 2
Holland B parameter method 2 Lognormal
1.75 [-]
688 [km]
0.55 [-]
236 [km]
1.23 [-]
0.4 [-]
Table 7: Distribution function for independent storm parameter
For a second analysis the Holland B parameter is assumed to be dependent on the radius
to maximum winds.
Storm parameters
Distribution
function
Holland B parameter (Method Normal
1)
Holland B parameter (Method Normal
2)
Mean μ
Standard deviation σ
1 [-]
0.15 [-]
1 [-]
0.175 [-]
Table 8: Distribution function for dependency between Holland B and RMAX
Matthijs de Jong
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Delft University of Technology
4
Validation of the model
Equation Section (Next)
For the validation of the model use is made of the wind- and water statistics for Hook of
Holland and Vlissingen. First the wind field will be modelled with the use of the wind field
description in Chapter 2 and the input parameters described in Chapter 3. Both the wind
speed and the wind direction are validated and calibrated with respect to the available
observations. Next, the wind set-up is computed with the use of the calibrated wind field
model. The computed wind set-up is also validated and calibrated based on the available
observations for the North Sea.
4.1
Wind field model validation
4.1.1 Maximum wind speed
For a first analysis the maximum surface wind speed is computed based on equation
(2.15). This formula shows that the maximum wind speed can be determined with the use
of the Holland B parameter, the ambient pressure and the central pressure of the storm
depression. The results for both methods are shown in Table 9.
Storm
1895/12/07
1897/11/29
1898/02/03
1904/12/30
1905/01/07
1907/02/21
1908/11/23
1916/01/13
1919/12/19
1928/11/26
1949/01/03
1954/12/23
1953/02/01
1962/02/12
1962/02/17
1976/01/03
1989/02/14
Matthijs de Jong
Computed maximum winds [m/s]
Vgradient;
Vsurface;
Vgradient;
Method 1
Method 1
Method 2
42.3
28.2
41.1
52.4
34.9
49.9
75.5
50.4
70.0
45.5
30.3
45.5
56.9
37.9
55.3
60.8
40.5
57.8
52.7
35.1
50.4
47.9
31.9
46.7
45.5
30.4
44.5
46.1
30.7
43.5
53.7
35.8
51.5
56.5
37.7
54.5
51.7
34.5
49.9
75.0
50.0
74.3
86.7
57.8
79.6
47.4
31.6
46.4
53.0
35.4
50.5
48
Vsurface;
Method 2
27.4
33.3
46.7
30.3
36.9
38.6
33.6
31.1
29.7
29.0
34.3
36.3
33.2
49.5
53.1
30.9
33.7
Delft University of Technology
1990/12/12
2003/12/21
2007/11/09
2008/03/01
51.2
43.0
54.8
56.6
34.1
28.7
36.5
37.8
43.5
41.8
52.0
52.3
29.0
27.9
34.7
34.9
Table 9: Maximum wind speed of the storm using the storm parameters
For both methods the maximum surface wind speeds have a lognormal distribution, for
which the mean is 35-36 [m/s] with a standard variation of about 6 [m/s]. Due to the
storms of 1962, the extreme wind speeds based on the distribution is about 54 [m/s].
Based on an earlier research (Holthuijsen et al., 1995), the maximum wind speed for the
North Sea was suggested at 50 [m/s] by meteorologists.
The extreme winds that occur for the huge storm depressions in 1962 cause the
distribution to reach a wind speed up to 54 [m/s]. It should however be notified that
these storms are located at high Northern latitude and therefore are effected by the
mountainous areas of Norway. These areas influence the pressure/wind field, and thereby
the related maximum wind speed. As this research is based on a simplified approach, this
is not taken into account.
The extreme high winds of the storm of 1898 can be clarified due to 3 low-pressure
centres that are shown in the weather chart. These 3 centres influence the pressure
gradient, which makes it difficult to estimate the pressure gradient based on one
significant low pressure area (working assumption).
4.1.2 Wind field modelling
After analysing the wind speed and direction with the input parameters described in
Chapter 3, the outcomes will be verified with the storms for which wind data is available
(1953 and 1962-present), see Table 10.
Wind data
Measurement station
HoH
19530201
19620212
19620217
19760103
19890214
19901212
20031221
20071109
20080301
Vlissingen
x
x
x
x
x
x
x
x
x
Table 10: Available wind data for several measurement stations
Furthermore, the geostrophic coordinates are used to determine the distance between
the storm coordinates and the measurement location, see Table 10 and Table 11.
Matthijs de Jong
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Delft University of Technology
Measurement station
Hook of Holland
Vlissingen
Latitudinal coordinate
52° N.L.
51.2° N.L.
Longitudinal coordinate
4.1° E.L.
3.2° E.L.
Table 11: Geostrophic coordinates of the measurement stations (N.L. = Northern Latitude, E.L. = Eastern
Longitude)
The results are than calibrated, after which the uniform wind speed over a time period of
9 hours will be determined and used in the formula of Voortman.
For the determination of the 9 hourly wind fields, the hourly geographic coordinates of
the storm have to be analysed. Therefore, use is made of the starting point of the storm,
the angle of approach and the forward movement. With these coordinates, the wind field,
speed and direction, per hour can be simulated. Furthermore, the location of the
measurement station is known.
With the use of formula(2.12), the gradient wind speed has been determined. Use is made
of a Coriolis parameter of 1.15 104 rad/s, for a latitude location of 52° (location of Hook
of Holland). The air density above sea surface will only slowly vary for different
temperatures. For the North Sea the winter temperature is assumed to be 5-6⁰ C, which
results in an air density of 1.27 kg*m-3. As the storm parameters are known, it is necessary
to determine the radius from the centre of the storm to the point of measurement, and
the angle from the storm translation direction to the profile location. With the use of the
hourly storm coordinates, these input parameters can be calculated.
For an explanation of this research, the storm of 2008 is discussed in more detail. The
related research for the other storms can be found in the appendixes. For the storm of
2008 Figure 35 shows the simulated surface wind field just before entering the North Sea.
Due to the forward movement of the storm, a higher wind field occurs to the South of the
storm centre. When the storm travels over the North Sea this will lead to high winds,
around 20 m/s, in the Southern North Sea. As has been concluded from studies by
(Weenink, 1958) and (Timmerman, 1977), the total wind set-up at Hook of Holland is
mostly caused by the wind set-up that occurs in the Southern North Sea.
Matthijs de Jong
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Delft University of Technology
Figure 35: Surface wind field [m/s] for the storm of 01-03-2008 before entering the North Sea if only this
single storm is taken into account. The axes are 1:50 [km]
4.1.3 Wind speed model validation
With the hourly simulated wind field of the storm known, the surface wind field based on
the computed model is compared with the observed surface wind field, see Figure 36. The
figure shows that the wind direction based on a constant angle of approach of the storm
shows a good approximation for the real wind direction.
Comparing the wind speed shows that the computed wind speed gives an
underestimation of the real wind speed. This computed wind speed is based on Method 2
(fitted ambient pressure). When applying the wind speed estimated by Method 1, the
computed wind speed will become even lower. This can be clarified by the
underestimation of the pressure gradient in Figure 22.
The measurement of the wind field is based on a 25 hours wind field. For further research
the maximum wind speed, the averaged wind speed and the uniform wind speed over 9
hours will be computed and compared with the available observed wind dataset.
Matthijs de Jong
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Delft University of Technology
Figure 36: Measured and calculated wind field of the storm of 01-03-2008
For the storms that can be verified, see Table 10, the wind statistics are computed with
the use of the given storm parameters based on Method 2. These storms are compared
with the observed wind speeds, for which the results are shown in Table 12.
Observed wind speed [m/s]
Storm
1953020113
19620212
19620217
19760103
19890214
19901212
20031221
20071109
20080301
Max
25,7
19,5
16,0
23,0
16.3
19.0
19.1
17.9
17.8
Averaged
24,4
17,3
15,4
21,2
15.3
17.5
16.3
15.6
16.6
W9
22,6
14,8
14,5
18,9
14.0
15.8
14.1
12.2
15.0
Computed wind speed [m/s]
Max
19.0
15.4
8.5
20.2
14.0
18.8
23.2
11.3
16.0
Averaged
18.8
15.0
8.4
19.8
13.3
18.0
22.5
11.2
15.3
W9
18.4
14.4
8.1
19.2
12.4
16.8
21.3
10.9
14.2
Table 12: Observed and computed wind speed [m/s] at Hook of Holland
In Figure 37 the results for the observed and computed 9 hourly exceeded wind speeds
are compared with each other. Further analysis regarding the maximum- and averaged
winds is shown in Appendix I14. The figure shows that by leaving out the storms of 21-122003 and 17-02-1962, gives a good correlation (0.734) between the observed and
computed wind speed. The rationale to leave out the storm of 2003 is that this storm has
a relatively short duration, which is not taken into account in the model. Therefore, this
storm shows significantly higher wind speed then the actually observed wind speed.
Secondly, the storm of 17-02-1962 shows a large deviation with the actual wind field
(underestimation). This is due to a second peak in the pressure field that occurs in the
North Sea that is not taken into account when applying the current formula for analysing
this pressure field, see Appendix J.
13
The wind speed for the storm of 1953 is determined for measurement station Vlissingen, due to
lack of information
14
Appendix H: Comparison of the computed and observed winds
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Delft University of Technology
Figure 37: (left) Observed exceeded wind speed over 9 hours compared with the computed wind speed;
(right) Comparison without the storm of 17-02-1962 and 21-12-2003
Leaving out these two storms, results in a more accurate analysis of the determination of
the wind field. For the calibration factor the computed wind has to be multiplied by
1.0725, see Figure 37 (right), to determine the observed surface wind speed.
4.1.4 Wind direction validation
The dominant wind direction and the calibrated with speed are given in Table 13.
Storm
Observed W9
wind speed
[m/s]
1953/02/01
1962/02/12
1962/02/17
1976/01/03
1989/02/14
1990/12/12
2003/12/21
2007/11/09
2008/03/01
22.6
14.8
14.5
18.9
14.0
15.8
14.1
12.2
15.0
Computed W9
wind speed
after calibration
[m/s]
19.7
15.4
8.7
20.6
13.2
18.0
22.8
11.7
15.3
Observed W9
wind direction
[°]
Computed W9
wind direction
[°]
303
242
290
265
318
332
270
337
300
298
269
291
275
257
320
260
277
274
Table 13: Observed 9 hourly exceeded wind speed and direction compared with the calibrated 9 hourly
exceeded wind speed and direction
The results show that for some storm the computed wind direction differs greatly from
the observed wind direction. For one this is caused by the assumption that the storm is
circular and travels constantly in one direction. In reality the angle of approach and
forward movement of the storm can differ while travelling over the North Sea. Secondly,
the assumed circular pattern of the isobars can easily be affected by the shape of the
storm depression itself, the location of the occlusion front nearby the point of
measurement, and possible other storms. For example, the storm of 1989 is influenced by
two storms. As for this research the second storm depression is not taken into account,
the real wind field will differ from the computed wind field.
Matthijs de Jong
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Delft University of Technology
4.1.5 Validated model
The calibration factor included in computing the wind speed for the storm of 2008 results
in the following wind speed, see Figure 38. The figure shows that there is still some
variation, which can be a result of taking a constant parameter for the storm parameters.
Secondly, local winds can occur caused by continuous fluctuation in the pressure
gradients between the isobars over time. Another reason why the computed wind is not
equal to the observed is that this scenario only takes into account one storm depression,
whereas in reality multiple storms occur after each other. For a complete overview of all
the verified storms, see Appendix J15. The estimated 9 hourly exceeded wind speed for the
storms used for this validation are taken into account for further research.
Figure 38:Calibrated wind speed for the storm of 01-03-2008
4.2
Wind set-up validation
With the use of the calibrated wind field, the wind set-up can be computed. Therefore,
use is made of two methods. First, the wind set-up at Hook of Holland is based on the
formula of (Voortman et al., 2002), see equation (2.6). A second estimation for the wind
set-up, is based on the method of (Brink, 2005), see equation (2.16). This formula was
derived more recently with the use of an ensemble study of (Timmerman, 1977). Both
formulas are based on the study by (Weenink, 1958).
4.2.1 Measured straight set-up for Hook of Holland
For the method by Voortman use is made of the straight setup. In order to estimate this
setup, the astronomical tide is simulated for the storms used in this research. As the high
water level and time of occurrence are known, the related tidal level can be computed in
order to estimate the straight set-up, see Table 1416. The straight set-up can also be
retrieved from the measured dataset by Rijkswaterstaat (RWS). The disadvantage is that
this dataset only contains necessary information about the storms since 1962.
For homogeneity reasons the straight set-up used for this research is estimated by
predicting the astronomical tide using MIKE 21. As the time of occurrence of the high
water level is known, the astronomical tide for that time and location can be predicted.
15
16
Appendix I: Simulated wind fields compared to the real wind field
Not able to find the dataset for the storm of 12-02-1962
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Delft University of Technology
The straight set-up is the difference between the high water level and the astronomical
tide.
First, the tidal predictions of MIKE 21 were adjusted to the tidal measurements by RWS to
take into account the different reference level that is used by MIKE, see Figure 39. RWS
uses NAP as reference level, which is also used for this research. As most storms indicate,
the tidal level based on the dataset of RWS is about 22 cm higher than the computed tidal
level. Therefore, the tidal water level by MIKE is calibrated to the tidal level at NAP by
adding 22 cm to the data.
The advantage of this method is that instead of 8 storms, 18 storms can be used for
further research. As this program only operates after 1900, the tide for the storms before
1900 cannot be computed, and are therefore left out in this analysis.
Figure 39: Calibration of the tidal prediction by MIKE21 for the storm of 14-02-1989
As the high water level and the tidal level are known for all the significant storms, the
straight set-up can be computed. The results are shown in Table 14.
MIKE 21
Year
Time
[yy/mm/dd]
1895/12/07
1897/11/29
1898/02/03
1904/12/30
1905/01/07
1907/02/21
1908/11/23
1916/01/13
1919/12/19
1928/11/26
1949/01/03
[hh:mm]
18:55
18:15
9:55
21:30
4:55
8:40
14:45
22:25
14:15
1:40
16:20
Matthijs de Jong
High Water
[cm]
268
268
276
296
250
228
266
300
239
296
270
H.W.
Correction
[cm]
298
298
307
325
279
257
295
328
267
323
294
55
RWS
Tide
Ref. level
[cm]
117
81
82
94
79
52
124
97
Set-up
Ref. level
[cm]
208
198
175
201
249
215
199
197
Set-up
[cm]
-
Delft University of Technology
1953/02/01
1954/12/23
1962/02/12
1962/02/17
1976/01/03
1989/02/14
1990/12/12
2003/12/21
2007/11/09
2008/03/01
4:20
14:00
20:20
3:02
17:08
8:35
11:30
13:40
2:45
8:55
385
300
240
262
298
279
249
272
318
234
409
323
262
284
309
286
255
274
319
234
103
81
108
49
112
100
72
79
101
70
306
242
154
235
197
186
183
195
218
164
304
178
176
193
200
190
204
183
Table 14: Straight set-up for the significant storms
Figure 40 shows the comparison of the straight wind set-up measured by RWS and
estimated by MIKE21. Based on the number of storms there is a correlation between
these two different methods for analysing the wind set-up. Whereas the measured data
by RWS is more reliable, MIKE21 is used for further analysis as more storms can be taken
into account. Due to homogeneity only the estimated wind set-up by MIKE21 is used.
Figure 40: Comparison of the wind set-up by RWS and MIKE21 for Hook of Holland
4.2.2 Wind set-up validation
For the formula of the wind set-up by Voortman the main characteristics are the wind
speed and the wind direction that influences the fetch and the effective depth. In this
study Hook of Holland is chosen as study area and therefore the input variables for the
fetch and depth differ from the study by Voortman, who uses Schiermonnikoog-Noord as
reference area. Due to time and focus of this study, the input dataset for
Schiermonnikoog is used, for which the fetch and effective depth will be corrected to the
situation of Hook of Holland. For the fetch, the distance between Schiermonnikoog and
Hook of Holland will be added to the total fetch, which is approximately 200 km. The
effective depth is calibrated with the use of the Least Squared method. Furthermore, it is
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unknown whether this formula takes into account the pressure set-up that is
approximately 10 cm for Hook of Holland.
The input parameters for the method of Voortman that are based on the calibrated
exceeded wind speed over 9 hours and the mean wind direction, are shown in Table 13.
year
18951207
18971129
18980203
19041230
19050107
19070221
19081123
19160113
19191219
19281126
19490103
19530201
19541223
19620212
19620217
19760103
19890214
19901212
20031221
20071109
20080301
W9-cal
[m/s]
17.34
24.41
9.35
17.8
17.9
16.91
12.41
17.88
14.77
18.1
19.35
21.72
19.93
15.43
8.68
20.55
13.34
18.04
22.9
11.74
15.28
Wind_dir
[N°]
307.9
261.0
352.4
275.3
289.0
260.9
279.9
292.5
275.5
273.4
280.1
198.9
281.9
269.3
291.6
275.0
257.0
320.2
260.9
277.1
273.7
Fetch
[km]
577.9
292.5
626.5
322.8
451.4
292.7
368.8
487.2
324.8
303.5
370.8
557.7
386.8
271.8
477.2
320.4
284.5
675.0
292.7
341.0
307.2
Eff Depth
[m]
40.6
21.5
54.4
26.3
31.1
21.5
28.9
31.6
26.4
24.1
29
32.5
29.4
23.1
31.5
26.1
19.7
54.8
21.5
27.3
25.4
c
[10^-6]
2.2
2.5
1.7
2.4
2.2
2.5
2.5
2.1
2.4
2.3
2.5
2.2
2.4
2.3
2.1
2.4
2.4
2.3
2.5
2.4
2.3
Table 15: Input parameters to determine the wind set-up
With these given input parameters the wind set-up can be computed. Therefore, the
computed wind set-up has to be calibrated to the observed wind set-up by RWS and MIKE
21, based on the different reference area for Hook of Holland. Based on the added 200
km fetch, the effective depth per mean wind direction can be calibrated, using the Least
Squared Method. The results are shown in Table 16.
Year
Fetch
[km]
Eff. depth
[m]
c
[10^-6]
18951207
18971129
18980203
19041230
19050107
19070221
19081123
777.9
492.5
826.5
522.8
651.4
492.7
568.8
28.5
15.1
38.1
18.4
21.8
15.1
20.3
2.2
2.5
1.7
2.4
2.2
2.5
2.5
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57
Computed
Wind set-up
[cm]
205.5
201.4
220.2
106.9
Delft University of Technology
19160113
19191219
19281126
19490103
19530201
19541223
19620212
19620217
19760103
19890214
19901212
20031221
20071109
20080301
687.2
524.8
503.5
570.8
757.7
586.8
471.8
677.2
520.4
484.5
875.0
492.7
541.0
507.2
22.2
18.5
16.9
20.3
22.8
20.6
16.2
22.1
18.3
13.8
38.4
15.1
19.1
17.8
2.1
2.4
2.3
2.5
2.2
2.4
2.3
2.1
2.4
2.4
2.3
2.5
2.4
2.3
206.6
143.8
216.9
251.2
323.9
262.2
151.9
269.0
143.3
167.1
93.4
151.5
Table 16: Calibrated fetch and effective depth to determine the wind set-up
As stated in the previous chapter, the storms of 17-02-1962 and 21-12-2003 are not taken
into account, as the calibrated wind speed does not coincide well enough with the
observed wind speed, due to a wrong assumption of the wind field based on the
simplifications.
Figure 41: (left) Comparison of the computed and observed wind set-up for Hook of Holland; (right) Wind
setup model by Voortman based on the exceeded wind speed over 9 hours
Figure 41 shows that there is a lot of variation between the observed and computed wind
set-up based on the exceeded wind speed over 9 hours. This spreading is also visible in
the formula used by Voortman that shows a considerable spread of the dataset around
the calibrated model.
When comparing the computed wind set-up with the observed wind set-up, the observed
wind set-up is approximately 1.0613 times the computed wind set-up. Secondly, the 95%
confidence interval in Figure 42 shows that there is a rather high uncertainty in the
estimation of the wind set-up
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Delft University of Technology
350
Dataset
Dependency
95% confidence interval
computed wind set-up [cm NAP]
300
250
200
150
100
50
0
0
50
100
150
200
250
observed wind set-up [cm NAP]
300
350
Figure 42: 95% confidence interval of the observed and computed wind set-up for Hook of Holland
This high spreading can for one be clarified by the simplifications that were done in
estimating the wind field based on the storm track and form of the depression. Secondly,
more recent storms have to be used for further analysis, for which better data is available.
In that case the measured wind set-up for Hook of Holland can be used, instead of a using
an estimated wind set-up. Lastly, the formula used by Voortman to compute the wind setup based on the wind field contains a considerable spread. The rationale for this spread is
that the wind speed in the wind field over the North Sea is not equal to the observed wind
speed used at the measurement station Terschelling-West, used for this model.
4.3
Conclusions of the calibrated model
With the storm analysis in Chapter 3 and the available dataset of observations, several
input parameters have to be modified to provide more reliable outcomes. These are
stated in the following formula’s and Table 17:
Wind speed
W9obs  W9com  c1
(4.1)
Tidal level
haobs  hacom  c2
(4.2)
Fetch
F obs  F com  c3
(4.3)
Effective depth
d obs  d com  c4
(4.4)
Wind set-up
s obs  s com  c5
(4.5)
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Delft University of Technology
Hydraulic variable
Wind speed
Tidal level (NAP)
Fetch
Effective depth
Wind set-up
Calibration coefficient
C1
C2
C3
C4
C5
Calibration value
1.0725
22 [cm]
200 [km]
0.7
1.0613
Table 17: Calibration coefficients used for the hydraulic variables
The focus of this research is to analyse whether it is possible to simulate the tidal water
level for the Dutch coast based on a simplified approach. Therefore, use is made of the
calibrated model explained in this chapter. As there remain several shortcomings of this
approach the simulated high water level contains an uncertainty. Further research is
necessary to reduce this uncertainty.
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Delft University of Technology
5
Probabilistic analysis of the
impact of extreme storms for
the Dutch coast
Equation Section (Next)
This chapter analyses the simulated storms based on the Monte Carlo approach (Heijer,
2012). With the use of the parametric model and the input distribution of each
parameter, the extreme water level can be computed for the Dutch coast. The first
paragraph provides an introduction of the type of variables that are used in the
parametric model. The second paragraph contains a brief description of the input
variables in the model. Next, the water level is simulated based on both the independency
and assumed dependency between the storm parameters. The results are examined and
discussed more briefly.
5.1
Model description of the determination of the HBC
The model for the probabilistic analysis of the hydraulic boundary conditions for Hook of
Holland depends on different input variables. These input distributions are the storm
parameters, described in Chapter 3, the astronomical tide, and the basin geometry and
bathymetry. Based on these input variables, several intermediate processes are executed
in order to compute the total water level for Hook of Holland. The intermediate processes
are described in Figure 9 or in more detail in Figure 19. This research is only interested in
the total water level, and therefore the wave height and period are left out. The variables
and models that are necessary to describe the JPDF of the hydraulic boundary conditions
are stated in Table 18.
Variable
Storm parameters
Tide level
Basin geometry /
bathymetry
Type of variable
Input
Input
Input
Model describing variable
Probability model
Probability model
Probability model
(deterministic)
Pressure field
Pressure set-up
Wind field
Wind set-up
Water depth
Fetch
Intermediate
Intermediate
Intermediate
Intermediate
Intermediate
Intermediate
Dependence model
Dependence model
Dependence model
Dependence model
Dependence model
Dependence model
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Delft University of Technology
Total water level
Output
Dependence model
Table 18: Model description of the JPDF of the hydraulic conditions
5.2
Probabilistic input variables
To determine the hydraulic boundary conditions for Hook of Holland use is made of the
Monte Carlo approach. The input variables are based on the distribution functions that
offer the best fit with the available dataset.
5.2.1 Input of the storm parameters
There is little research done into the analysis of the values of storm parameters for storms
over the North Sea. The distribution functions used for each parameter have been based
on the dataset of historical storms used in this research. These are explained in more
detail in Chapter 3. Most variables appeared to fit best under a lognormal distribution.
For Monte Carlo the input parameters with a lognormal distribution have to be
transformed with the use of the Lognormal(2) distribution using BestFit. Thus the mean
and standard deviation of the lognormal distribution are respectively μ1=exp(μ+(σ2/2))
and σ1=√(exp(2 μ - σ2)[exp(σ2-1]. The resulting input parameters are shown in Table 19.
Storm parameters
Starting location
Forward
movement
Angle of approach
Central pressure
RMAX; method 1
B; method 1
RMAX; method 2
B; method 2
Probability
Distribution
Lognormal
Lognormal
Rayleigh
Normal
Lognormal
Lognormal
Lognormal
Lognormal
Mean
M.C.
[μ]
input
58.61 [°]
4.07
14.67 [m/s]
2.63
22.46[°]
975 [mbar]
552 [km]
1.75 [-]
688 [km]
1.23 [-]
6.24
0.51
6.48
0.15
Standard
deviation [σ]
2.6°
5.25 m/s
M.C. input
15.05 mbar
213 [km]
0.55 [-]
236 [km]
0.4 [-]
0.37
0.3
0.33
0.32
4.44e-2
0.35
Table 19: Distribution function for independent storm parameter
5.2.2 Input of the tide level and the basin bathymetry/geometry
As the wind set-up has a duration, which is much larger than the period of the
astronomical tide, it is assumed that the maximum storm surge level occurs at or very
near astronomical high water (Vrijling et al., 2006). MIKE 21 is used to predict and
generate the tidal water for every hour in the period from 1990-2009. The average time
between two high tides is 12 hours and 25 minutes. On this basis it is assumed that the
number of high tidal levels during this time period can be derived by extracting the
highest
1
high tides. Through this dataset a Weibull distribution is fitted with μ=1.163
12.4
[NAP + m] and σ=0.081 [NAP + m], see Figure 43.
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Delft University of Technology
Figure 43: (left) Simulated tidal water level with MIKE 21; (right) Weibull distribution of the estimated high
tidal water level for Hook of Holland with μ=1.163 [NAP + m] and σ=0.081 [NAP + m]
The fetch and effective depth determine the total wind setup that occurs for the Dutch
coast. These parameters are available in Table 1 (Voortman et al., 2001). In chapter 4 the
fetch and depth are calibrated for Hook of Holland.
5.3
Simulation of the extreme water level for Hook of Holland
5.3.1 Introduction
With the use of the Monte Carlo simulation the total water level can be simulated for
different storm scenarios. In order to determine the 10-4/years storm surge, a relative
large number of storms have been simulated to provide a reliable outcome. For this study
the extreme water level is based on 106 storm samples.
The storm samples have to be organised and transformed in order to determine the
extreme water level. This is done with the use of the Gumbel/Weibull method (Vrijling et
al., 2006), for which the approximation of the order of the plot position is:
i
N 1
(5.1)
i : Position of data point in increasing order [-]
N : The number of data points [-]
These results are based on the historical extreme storms that occurred. Since the
exceedance probability of hydraulic boundary conditions per year is of interest and not
per storm depression, the ratio between these two has to be taken into account. The
results are describes as an exceedance probability per year. As this dataset is based on 18
of the extreme storms in 108 years, the transformation is:
18
 0.167 [] . For this
108
transformation the storms before 1900 are left out, due to unavailable data of these
storms.
The observations have to be put in order of increasing magnitude, to determine the
parameters of the cumulative probability distribution. In order to extract the variables of
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Delft University of Technology
the intermediate process of the model, most importantly is to determine the 9 hourly
exceeded wind speed and mean wind direction over this interval. With the starting point
of the storm at 5.5° E.L., the storm is simulated for a time period of 35 hours, starting 10
hours before approaching the 5.5° E.L., see Figure 44.
Figure 44: Time interval for determination of the 9 hourly wind speed and direction
5.3.2 Extreme water level for independency between storm parameters
Based on the Gumbel/Weibull method for the plot position, and the necessary
transformation for this dataset, the extreme water level can be plotted against the
probability of occurrence. For this method use is made of the fitted ambient pressure to
describe the pressure field and the formula by Voortman to determine the wind set-up.
Figure 45 shows the observed water level17 and the simulated high water level,
respectively the green and the red line. It is assumed that all the storm parameters are
independent. The figure shows that the estimated 10-4/year water level based on the
parametric model for storms on the North Sea is approximately NAP + 5.45 m.
The current estimation method to determine the 10-4/year water level is based on an
extrapolation through the observed water level measurements. The Gumbel distribution
is used to determine this extreme water level for Hook of Holland, which results in a
water level of approximately NAP + 5.0 m. Using the extreme value statistics it is shown
that the confidence interval of the 10-4/year water level is between NAP + 2.9 and 6.5 m
for Hook of Holland, which implies a rather large confidence interval of 3.6 m.
As Figure 42 indicates, there is a rather high spread around the simulated wind set-up
based on the parametric model, and the observed wind set-up. When this spread is taken
into account in the model outcomes, it is shown that the spread around the 10-4/year
water level results in an even larger confidence interval of 4.4 m.
17
These water level measurements are based on storm surges with a skew set-up ≥ 30 cm.
Matthijs de Jong
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Delft University of Technology
Figure 45: Simulated high water level based on complete independency between the storm parameters
-4
with the 95% confidence interval for the 10 /year water level
The model however simulates that the high straight set-up interacts with the high tidal
level. In reality it is found that this situation almost never occurs. Therefore, current
methods describe the high water level using the high tidal level and the “skewed” set-up,
see Appendix C. This set-up takes into account possible dependencies between the high
straight set-up and the high tidal water level and thereby results in lower water level
estimation.
The storms used in this research show that the “skewed” set-up is about a factor 1.12
smaller than the straight set-up, see Figure 46. For a first approximation of computing the
high water level based on the “skewed” set-up, this factor is used to calibrate the
simulated straight set-up. With this approach the 10-4/year water level is approximately
NAP + 4.9 m.
Figure 46: Straight set-up compared to the “skewed” set-up based on the storm analysis
Matthijs de Jong
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Delft University of Technology
Figure 47: Simulated and measured high water level over time for the parametric storm model based on
the “skewed” set-up.
The resulting 10-4/year water level based on the “skewed” set-up and the high tidal level
compares with the current estimation method. It is recommended to do good research in
the application and the determination of the “skewed” set-up in these models.
5.3.3 Extreme water level for dependency between storm parameters
For a second analysis it is assumed that there is a dependency between the storm
parameters. Possible dependencies have been studied and discussed in Chapter 3. With
the use of the number of storms in this research a weak correlation has been found
between the radius to maximum winds and the Holland B parameter, which respectively
describes the distance from the storm centre to the location where maximum winds occur
and the parameter that describes the shape of the pressure field.
When applying this correlation in the model, the simulated the 10-4/year water level is
about NAP + 5.55 m. This implies that the total water level will slightly increase with the
assumption that there is a dependency between the Rmax and Holland B parameter.
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Figure 48: Simulated high water level with assumed dependency between the storm parameters
Figure 49 shows the simulated storm parameters for both independency and dependency
between the parameters. A highly notable difference is that the simulated storms based
on independent storm parameters show that barely storms occur with both a high radius
to maximum winds and a high Holland B parameter. However, when the assumed
dependency is taken into account, these storms do occur.
The distributions of the storm parameters for both methods show that the highest
number of storms occurs with a relatively low radius to maximum winds and Holland B
parameter.
Figure 49: (Left) Comparison of storm parameters based on independency between these parameters;
(right) Comparison of storm parameters based on dependency between these parameters;
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5.3.4 Analysis of the extreme water levels
With the use of the simulated storms by Monte Carlo, the storm parameters can be
analysed for which the extreme surge levels occur. For this analysis the storms are taken
into account with a water level above NAP + 5 m. By comparing the storm parameters of
the storms that result in an extreme surge levels with the complete set of storms, it is
shown which situations cause the highest surge levels for Hook of Holland.
Figure 50: (left) angle of approach for the total number of storms compared to the extreme storms; (right)
latitudinal starting point at 5.5° E.L. for the total number of storms compared to the extreme storms
As Figure 50 indicates the extreme storms do not show a shift in the angle of approach.
This model thereby implies that the angle of approach of storms passing the North Sea
does not influence the water level height for the Dutch coast. The right figure however
shows that extreme storms at 5.5° Eastern Longitude, about the same longitude as Hook
of Holland (4.1° E.L.), are mostly situated at 55°-56° Northern Latitude, crossing the North
Sea approximately through the middle. Compared to the total number of storms the
extreme storms show a strong preference, suggesting that the latitudinal location of the
storm, when it is at 5.5° E.L. is significant for the occurring water level.
Figure 51: (left) Forward movement for the total number of storms compared to the extreme storms;
(right) Central pressure for the total number of storms compared to the extreme storms
Both the forward movement and the central pressure of the storm have a high impact on
the occurrence of an extreme water level. For the forward movement of the storm a
relatively low speed causes the wind field to act longer on the North Sea basin, and
thereby results in a higher wind set-up. A lower central pressure of a storm mostly results
in a higher pressure difference. In an unfavourable situation, depending on the radius to
maximum winds and the Holland B parameter, the high pressure difference results in a
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high pressure gradient. This, in turn, influences the strength of the wind field of the storm,
and thereby results in a high wind set-up. In other words, it is more plausible for a storm
with a low central pressure to result high wind fields and consequently a high wind set-up.
Figure 52: (left) Radius to maximum winds for the total number of storms compared to the extreme
storms; (right) Holland B parameter for the total number of storms compared to the extreme storms
The extreme water levels mostly occur due to a very low radius to maximum winds and a
low Holland B parameter. This is however in combination with the central pressure and
the latitudinal point at which the storm crosses the North Sea at 5.5° E.L.. Figure 52
indicates that the storms have a maximum wind speed about 500 km outside the storm
centre.
Based on the model outcomes the only parameter that does not have that great impact
on the height of the water level for the North Sea is the angle of approach.
For a feasibility check of the possible occurrence of the storms, the parameters are
compared to current observations. Based on the storm analysis in Chapter 3, it is only
questionable whether a low depth of the central pressure of about 920 mbar can occur.
Observations over the past century show that the lowest pressure has been measured at
the British Islands, with a depth of 936 mbar (Wikipedia, 2012). As these observations are
based on the available data of about 100 years, it is certainly not excluded that an even
lower pressure field can travel above the North Sea in a period of 10000 years. Based on
the dataset of historical storms used in this model both the forward movement and the
latitudinal starting point of the storms can occur.
5.3.5 Conclusions based on the results
An important conclusion that can be drawn is that applying a parametric model based on
storms over the North Sea shows a good estimation of the extreme water level for the
Dutch coast.
Compared to the current situation in the determination of the HBC based on water level
observations this method does not offer better results. The same as for the current
method, this approach is only based on about 100 years of storm data. Secondly, there
are multiple simplifications made in the parametric model that result in a higher
uncertainty in the estimation of the extreme water level.
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The advantage however is that this method provides physical knowledge in the realisation
of the extreme water level for the Dutch coast. More insight is available in the significance
of each storm parameters contributing to this water level, which is valuable information in
the forecasting of the extreme storms over the North Sea. Furthermore, for a later stage
this insight can be useful to analyse whether certain trends occur for the storm
parameters that are taken into account.
Additionally, this study offers a basis for expansion to obtain further understanding of the
behaviour of water in the North Sea basin. Particularly, the wind field analysis is not only
applicable for the water level estimation, but can also be used for analysing waves and
the joint probability of waves and water levels.
As for the scope of this research it is also of interest whether this parametric model is
applicable for other regions and/or countries.
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6
Conclusions
recommendations
and
Equation Section (Next)
6.1
Conclusions
The developed parametric model for Hook of Holland compares with the current
estimation method for the determination of the extreme water level. As the data is
limited and several meteorological effects are difficult to take into account, the results are
subject to a considerable spread. Therefore, this approach is still less effective in
increasing the confidence than the current method. The advantage is that it allows
physical knowledge in the formation of the water level for Hook of Holland, as the
significant parameters contributing to a high water level can be subtracted. Furthermore,
changes in meteorological conditions over a longer period of time can be taken into
account in this model. In conclusion, this method provides valuable information that
contributes to the estimation of the water level for Hook of Holland.
With regard to the thesis objectives of this research, there are a number of conclusions
that can be drawn. These are discussed briefly for each objective.
What are the storm parameters that determine the associated pressure- and wind setup, in the event of the passage of a storm over the North Sea?
The analysis of the actual storm parameters shows that the values are often subject to
meteorological influences, which cannot be taken into account in this model. For example
the isobars that describe the pressure field can be affected by troughs and secondary
storm fields. In order to get a best approximation of the reality, assumptions have been
made, for which the input parameters and their patterns have been standardised. This
results in deviations between actual and simulated data, which contributes to the range
of uncertainty in the model. For some storms it was found that the characteristics were
such that they were not included in the samples against which the model was tested.
What are possible dependencies between the storm parameters?
Based on the storm analysis the resulting radius to maximum winds from out of the
centre of the storm and the Holland B parameter, which determines the shape of the
pressure field, show a weak linear dependency. As the number of storms is relatively
small it is uncertain whether this correlation needs to be taken into account. If this
dependency is taken into account in the model, the extreme water level decreases by
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some centimetres. Based on earlier research for hurricanes there was also a weak
correlation observed between these parameters. No other significant dependencies were
found, based on the analysis of sample of storms.
How accurate do the results of the model coincide with the observed values of specific
storms, and how do possible deviations contribute to the uncertainty of the model
outcomes?
This model shows that after calibration the simulated wind field coincides well with the
observed wind field for most cases. In reality there are however several phenomena that
influence this wind field, e.g. sudden changes in the storm track, secondary storm
depressions, troughs and the shape of the depression. As these phenomena are not
represented in this model, the approach does not hold for all storms.
With regard to the wind set-up, the observed set-up shows a considerable spread around
the result of calibrated model. This spread is partly based on the manner in which the
observed set-up is derived by subtracting the tidal prediction (MIKE 21) from the water
level statistics. The other cause of the spread is attributed to the noticeable deviation in
the formula by Voortman to compute the wind set-up with the use of the wind statistics.
It is remarkable that storms with a relatively low wind speed can still cause a significant
set-up for the Dutch coast.
What is the 10-4/year water level for Hook of Holland based on the parametric model,
and how well does this compare with the current estimation method?
Assuming complete independence between the storm parameters the results show a
10-4/year water level of approximately NAP + 5.45 m. If dependency between the Radius
to maximum winds and the Holland B parameter is assumed, the extreme water level at
10-4/year will increase by only 0.1 m. This compares with the NAP + 5m water level for
Hook of Holland, as derived under the current method.
The results of the model suggest that much higher water levels can occur, albeit with a
very low probability. It is however questionable whether the algorithm by Voortman also
applies for these extreme circumstances. In addition, the model has been calibrated in a
manner which shows the best fit with the observed water levels. Particularly, the
adjustment of the fetch and depth in as applied for Hook of Holland may contribute to the
very high water levels.
There is a considerable spread between the simulated water level and the observed
values. The model presupposes a quasi-stationary movement of the wind field, i.e. the
parameters are constant over time, and thereby it does not take into account the
dynamics of the built up of the actual wind field. The spread of the observed values
around the calibrated model is symmetrically distributed, suggesting that there is no bias
in the model.
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Compared to the current estimation method this method does not offer better results.
This method is also based on limited data. Moreover, the use of multiple variables in this
model creates a wider spread of uncertainty. However, the current method of
extrapolation presupposes unchanging meteorological conditions over time. The model
can project the consequence of changes of these conditions.
Which storm parameters are significant for generating extreme water levels?
Comparison of the parameters of those storms that result in an extreme surge levels with
the complete set of storms, shows that the parameters with the most significant impact
on the extreme water levels are: the central pressure, the latitudinal starting point, the
forward movement of the storm, the radius to maximum winds and the Holland B
parameter.
The probability distribution of the angle of approach is not different for extreme surge
levels compared to the complete set of storms.
The model results show that there are no considerable changes with respect to the storm
parameters contributing to the extreme water levels, when dependencies are assumed in
the model or not. This is explained by the fact that the assumed dependency between the
parameters mainly has effect on storms with a large radius to maximum winds, whereas
the extreme water levels occur due to storms with a small radius to maximum winds.
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6.2
Recommendations
As this model was deliberately developed in a simplified form, to test its usefulness, a
number of assumptions and simplifications have been made. It is recommended to
investigate whether the robustness and quality of this model can be improved
significantly, by addressing the following points. First the improvements of this method
with respect to the storm analysis are discussed. Secondly, more general
recommendations are stated for the application of this model.
Recommendations and observations of the storm analysis

The storm parameters used in this research are constant over time. In reality, the
storm parameters change while travelling over the North Sea. Possible trends and
patterns underlying these changes should be further analysed to determine
whether it would be possible to incorporate this in the model.

For the analysis of this model the storm is based on a singular pressure field. In
reality, multiple storm depressions can influence the pressure field, and thereby
the water level. Similarly, the model does not take into account of the
phenomenon of resonance, occurring in the event of the storms passing the
North Sea in a short time interval. Resonance can considerably increase the water
level. Adjusting the model to include these events would considerably enhance its
complexity.

This model describes the storm as a circular pressure field. In practice the
pressure fields are more elongated. The use of a pressure field as an ellipse would
offer a more accurate representation of the actual pressure field, although it
requires more input parameters.

For this research only extreme storms have been analysed. Analysis of a larger
amount of storms would offer more insight in the probability distributions and
dependencies between the storm parameters and thereby provides more
reliability. Furthermore, the usage of recent storms shows more accuracy.

In the absence of actual data for older storms, the ambient pressure applied in
this model is based on a fitted value of 1050 mbar, which results in a good
estimation of the actual pressure field. As more future data become available it
would be advisable to use actual ambient pressure based on the value of the
central pressure of the high pressure area.

The fetch and effective depth is calibrated and validated for Hook of Holland
based on the properties for the North Sea basin by Voortman for
Schiermonnikoog-Noord. A similar study should be done for Hook of Holland, to
obtain a more reliable dataset as input for this model.

The model does not use observed data for tidal water level and straight set-up, as
this data is only available for Hook of Holland for the last 40 years. Instead, the
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tidal water level and the straight set-up have been constructed with the use of the
MIKE 21 model that predicts the tide. For future applications of the model, the
observed dataset would obviously lead to more reliability results.

Current literature determines the observed high water levels with the use of the
high tidal level and a “skewed” set-up, which takes account of the fact that the
measured set-up does not occur at the same time as the observed high tide.
Based on the results of this model, the straight set-up is approximately a factor
1.12 higher than the skewed set-up. This leads to an overestimation of the water
level in the model. Further analysis is needed to adjust the model to reflect the
skewed set-up.

The pressure set-up has been included in the wind set-up, as this is considered
not to have a significant effect on the results of the model. For more accuracy the
pressure set-up should be determined and used separately in the model.

The effect of external set-up for the Dutch coast from storms travelling over
Atlantic Ocean into the North Sea has not been taken into account. This may be of
little impact but contributes to the quality of the model.

The wind field simulated by this model does not only affect the water level in the
North Sea basin, but also influences the presence and behaviour of waves. The full
impact of storm surges can only be assessed if the effect of waves is included.
Further research is needed that analyses the effect of the pressure/wind field on
both the water level and the waves, and their joint probability.

Applying the model for other locations along the Dutch coast would give more
insight in the applicability of the model. It deserves further investigation to
determine whether this model can be applied more universally.

For this research use has been made of weather charts by K.N.M.I. and the Delta
report. The handling and processing was largely done manually, and took
considerable time and effort. These charts can also be retrieved digitally from the
NCEP reanalysis. In an event of a more regular use of this model, it should be
considered to develop an algorithm for automatically extracting the storm
parameters used in this model. .
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7
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Equation Section (Next)
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8
Appendixes
Appendix A: A one-dimensional model for the water level increase due
to a uniform wind field
For describing the joint probability distribution, Voortman (Voortman et al., 2002) used the basic
hypothesis that the wind effects are independent of the astronomical tide. This assumption appears
to be reasonable for deep water conditions. Under this assumption, the water level can be obtained
by superposition of the astronomical tide and the wind set-up.If an infinitesimal water body is
considered, see Figure 53, than the force exerted on the water body by the wind field can be written
as:
Fu  cl l u 2 dx
(7.1)
l : density of air [kg/m3 ]
u:
wind speed [m/s]
cl :
empirical coefficient [-]
Figure 53: Sketch for an one-dimensional wind set-up model
The hydrostatic forces F1 and F2, see figure, are given by:
1
 w g (d1  h1 ) 2
2
1
F2   w g (d 2  h2 ) 2
2
F1 
(7.2)
w : density of water [kg/m3 ]
g:
accelaration of gravity [m/s2 ]
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Rearranging the momentum equation leads to the following differential equation for the wind setup:
cu92
dh

dx g (d ( x)  h( x))
(7.3)
In this formula c denotes the empirical coefficient combining the densities of water and air and the
empirical coefficient cl.
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Appendix B: Working method of the Delta committee
The meteorological and mathematical-statistical research for the determination of the basic levels
and high water exceedance lines is in principle based on the station of Hook of Holland. In order to
homogenise the selection of the available dataset is based on (Dantzig and Hemelrijk, 1960):
A. The cause of the dangerous high water during a storm is caused by the depression, of which
the core is travelling with its own unique storm track. The measurements are based for the
period 1898 until 1956 for Hellevoetsluis, for which the high- and low set-ups ≥ 160 cm. 49 of
the resulting 69 skewed set-ups were depression during the significant period November
until January. Based on the findings of the K.N.M.I. the storm tracks travel between:

At 10° Western Longitude (W.L.): Between 51° Northern Latitude (N.L.) and 67° N.L.;
all 41 depressions

At 10° W.L.: Between 51° N.L. and 67° N.L.; all 48 depressions

At 10° Eastern Longitude: Between 51° N.L. and 67° N.L.; all 46 depressions, except
for 1
B. De statistical series was assembled from the high water observations at Hook of Holland by
limiting the selection using the Van der Ham selection criteria:

The significant storm tracks for the Dutch coast were analysed. Findings of K.N.M.I. show
that the most dangerous depressions move eastwards over the North Sea.

The statistical data is based on the high-water observations at Hook of Holland, with the
focus only on the set-up conditions for the potential dangerous depressions.

Only one high-water level per depression was selected.

The high-water set-up must be larger than 50 cm.

Only storms were taken into account that occurred in the winter period (Nov-Jan). This is
to avoid inhomogeneity.

Some weather charts were missing due to World War II, which leaves out depressions
that occurred during the period of 1939 until 1945.

The K.N.M.I. implemented a threshold of NAP + 1.70 m.
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Appendix C: Difference between skewed and straight set-up
The wind field that pushes the water towards the Dutch coast results in a set-up above the
astronomical tide. For the characterisation of the storm surge at a station nowadays use is made of
the high water level, including this “skewed” setup. The term “skewed” set-up is introduced, which
means that the measured set-up does not occur at the same time as the observed high tide that
causes the high water level (Kok, 1988).
Figure 54: Measured “skewed” set-up over time (Brink, 2005)
In shallow waters, the wind set-up can be quite high and cause a significant increase of the
propagation velocity of the tidal wave. Accordingly, the instantaneous offset between the sea water
level and the tidal levels will include effects of the interaction between the tidal wave and the
atmospheric factors, and cannot always be considered independent from the tidal height. Therefore
(Dillingh et al., 1993) have decided to consider the “skewed” high water in their extreme value
analysis, instead of the straight set-up, the vertical offset, see Figure 54.
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Appendix D: Resources for storm analysis
For the Based on earlier studies, e.g. Delta committee 1960, there are several resources that obtain
the necessary dataset for this research, namely:

K.N.M.I.: Storm surge reports, weather charts, storm catalogue (Groen and Caires, 2011)

Delta report 1960: Deutsche Seewarte, Daily Weather Reports, Historical Weather Maps,
Wetteranalyse und Wetterprognose (Sherhag, 1949), K.N.M.I. weather charts

Wetterzentrale Deutschland (Wetterzentrale, 2011)

Atmospheric Sciences (Godfrey, 2010)

The ECMWF archive
The Delta committee investigated the tracks of depressions associated with storm surges and the
extreme possibilities of north-westerly gales. For the study 49 depressions were analysed with a sea
level rise greater than 160 cm at Hellevoetsluis during the period 1898 – 1956. The advantage is that
for most of these depressions the water set-up at Hook of Holland is more than 150 cm.
This appendix shows the storm depressions which are used for this research. Some interesting
conclusions that were done after the investigation:

87.5 % of the depressions with a set-up greater than 200 cm followed a track with a
southerly component

The majority of the storm surge depressions reached their maximum depth in the North Sea
area

The possibility of still greater pressure gradients should not be excluded

In the North Sea area winds of about 35 m/s are possible during at least one hour, but winds
of this velocity will not easily occur over the full width of the North Sea
Matthijs de Jong
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Delft University of Technology
Storm track analysis
Figure 55: Significant storm tracks for Hellevoetsluis in the period of 1898 until 1916 (source: Delta Report 1961)
Figure 56: Significant storm tracks for Hellevoetsluis in the period of 1916 until 1939 (source: Delta Report 1961)
Matthijs de Jong
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Delft University of Technology
Figure 57: Significant storm tracks for Hellevoetsluis in the period of 1939 until 1946 (source: Delta Report 1961)
Figure 58: Significant storm tracks for Hellevoetsluis in the period of 1946 until 1956 (source: Delta Report 1961)
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Delft University of Technology
Storm surge reports
In the past a lot of storm surges have threatened the Netherlands. The first documented dates from
838 (Buisman and Engelen, 1995). In 1883 the first storm surge report was presented, containing
information about the significant wind speed, the observed surge level and the damage that
occurred. Over time these reports became more useful, due to more and precise data about the
storm surge. A lot of information about the storm depression and the related storm surge can be
retrieved form this report. However, until the flood disaster in 1953 the reports failed to give
relevant information about the several storm parameters, e.g. the storm track. The available dataset
of storm surge reports (n.d. = no data available; the days calculated from 1900):
storm surge reports
water level
set-up
time
dag
maand
jaar
Cm
Cm
days
12
12
1883
n.d.
n.d.
-
9
2
1889
n.d.
228
-
22
12
1894
n.d.
250
-
13
1
1916
n.d.
220
5857
1
2
1953
n.d.
293
19391
16
2
1962
260
187
22693
13
2
1965
n.d.
130
23786
2
11
1965
n.d.
100
24048
30
11
1965
n.d.
135
24076
10
12
1965
259
146
24086
16
11
1966
275
140
24427
30
11
1966
215
98
24441
23
2
1967
205
109
24526
28
2
1967
236
114
24531
5
10
1967
203
90
24750
10
11
1969
216
91
25517
2
2
1969
230
150
25236
20
2
1970
158
82
25619
3
10
1970
212
102
25844
3
11
1970
172
55
25875
21
11
1971
235
118
26258
13
11
1972
218
157
26616
2
4
1973
224
128
26756
19
11
1973
234
129
26987
14
12
1973
274
146
27012
28
10
1974
210
108
27330
27
11
1974
234
126
27360
3
1
1976
294
168
27762
20
1
1976
243
142
27779
12
11
1977
265
137
28441
30
12
1977
232
116
28489
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Delft University of Technology
12
1
1978
199
62
28502
2
1
1979
160
25
28857
18
12
1979
231
114
29207
6
11
1979
210
86
29165
20
4
1980
236
128
29331
1
1
1981
204
124
29587
24
11
1981
237
134
29914
11
3
1982
213
99
30021
16
12
1982
222
101
30301
18
1
1983
239
113
30334
2
2
1983
262
153
30349
4
1
1984
236
117
30685
14
2
1989
279
177
32553
26
1
1990
190
75
32899
12
12
1990
251
157
33219
27
2
1990
284
137
32931
20
12
1991
225
107
33592
11
11
1992
227
89
33919
21
2
1993
255
146
34021
25
1
1993
235
133
33994
14
11
1993
265
121
34287
19
12
1993
187
66
34322
28
1
1994
270
145
34362
14
3
1994
192
70
34407
2
1
1995
261
135
34701
10
1
1995
239
150
34709
29
8
1996
184
67
35306
29
10
1996
171
109
35367
5
2
1999
238
126
36196
6
11
1999
242
126
36470
4
12
1999
242
125
36498
29
1
2000
205
115
36554
21
12
2003
272
156
37976
8
2
2004
252
130
38025
31
10
2006
247
139
39021
12
1
2007
180
90
39094
19
1
2007
185
61
39101
18
3
2007
240
104
39159
9
11
2007
316
187
39395
1
3
2008
234
155
39508
21
3
2008
275
149
39528
Table 4: Storm surge data at Hook of Holland
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Delft University of Technology
K.N.M.I. weather charts
The K.N.M.I. has a database that includes weather charts during 1881 – 1988. Around 1983 these
weather charts are drawn by a computer, and after 1988 they were digitized. These weather charts
are especially useful to determine the radius of the storm depression, where the available
information from storm surge reports and the Delta report fail to do so.
Interesting is to sea that over time several different weather charts were used to illustrate the storm
depression over the North Sea.
Time period
1883 – 1900
1900 – 1939
1939 – 1946
1946 – 1970
1970 – 1985
1983 – 2003
2003 – 2011 (KNMI, 2003)
Weather charts per day
1
3
0 (Second World War)
2
2
?
4 [digital]
Time of measurement
07:00/08:00
07:00/08:00; 14:00; 18:00/19:00
01:00; 13:00
12:00; 00:00
00:00; 06:00; 12:00; 18:00
Figure 59: HIRLAM weather chart (source: K.N.M.I.)
Figure 60: Reanalysis of the weather chart (source: Wetterzentrale)
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Delft University of Technology
Appendix E: Dataset of the storms
For the selection of the storms use has been made of the available dataset by Deltares. The dataset
contains the high-water measurements at Hook of Holland, during the storm period of 1 October
until 15 March. Data is available from 1887 until now. The record consists of the occurred high water
level in [NAP + m], the for 2009 transformed level in [NAP + m] and the high water set-up (“skewed”
set-up).The transformation to take into account the relative sea level rise is shown in Table 20.
Period [year]
Until 1964
1965
From 1966
Transformation of the relative sea level
0.12*(2009-year)+16.8
18
0.33*(2009-year)
Table 20: Transformation of the water level for the relative sea level rise
YY/MM/DD
UUMM
19530201
18941222
18890209
19160113
19541223
19041230
18950123
19620217
20071109
18980203
19281126
19060312
19460223
18971129
19890214
18951207
19211106
19440126
19620212
19760103
19401206
19081123
19490301
19440205
19070221
19050107
19191219
19721113
19901212
20031221
20080301
420
2340
955
2225
1400
2130
1610
302
245
120
140
1645
1855
1815
835
1855
1905
320
2020
1708
1925
1445
1620
0
840
455
1415
737
1130
1340
855
Matthijs de Jong
Waterlevel (NAP + cm) Reformed level
(NAP + cm)
385
409
328
359
276
307
300
328
300
323
296
325
262
292
262
284
318
319
228
258
296
323
290
319
256
280
268
298
279
286
268
298
263
290
267
292
240
262
298
309
265
290
266
295
270
294
238
263
228
257
250
279
239
267
238
250
249
255
272
274
234
234
89
High water set-up
(cm)
293
250
228
220
210
206
194
187
187
181
181
180
179
178
177
176
174
174
168
168
167
166
165
164
162
159
157
157
157
156
155
Delft University of Technology
Appendix F: Extrapolation of the “skewed” set-up dataset
The wind set-up for the Dutch coast has been analysed with different distributions. The exponential
and the Weibull distribution give the best fit with the dataset based on the KS-test. The figure below
shows the exponential distribution based on the extreme observations of the “skewed” set-up,
without the storm of 1953. The 10-4/year “skewed” set-up is around NAP + 3.8 m. When the storm of
1953 is taken into account, this extreme load will increase significantly to NAP + 4.7 m. For a first
analysis it can however be assumed that the storm of 1953 does not coincide with the line. The
Gumbel distribution that is currently used to determine the hydraulic boundary conditions for Hook
of Holland also shows a deviation of the storm of 1953 with the best fitted line through the total
dataset, see Figure 63.
figure 61: Exponential distribution through wind set-up dataset > 1.80 m
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Delft University of Technology
Figure 62: Astronomical high tide for extreme storms for Hook of Holland based on the “skewed” set-up (Source:
Deltares)
For the determination of the total water level, the astronomical high tide can be added to the
“skewed” set-up. This astronomical high tide, based on the dataset for the “skewed” set-up, has a
Weibull distribution as can be seen in Figure 62. Based on the “skewed” set-up and the distribution
of the astronomical tide, the resulting sea water level is shown in Figure 63.
Matthijs de Jong
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Delft University of Technology
Figure 63: Return period of the sea water level (NAP + cm) for Hook of Holland (Source: Deltares)
Appendix G: Analysis of the radius to maximum winds and Holland B
Both methods show a rather good correlation between the measured radius to maximum winds
based on the different methods and for the weather charts. . The figures beneath provide the
correlation between the estimated radius to maximum winds and the Holland B parameter based on
the two different ambient pressure assumptions. As the storms after 1953 provide more precise
weather charts it was assumed that there is a better correlation between the parameters. However,
as can be seen in the figures, the storms between 1953 and 2008 do not necessarily provide a better
correlation. For further analysis use is made of the complete dataset of 21 storms.
Figure 64: (left) Observed radius to maximum winds compared to the measured for Method 1; (right) Observed radius to
maximum winds compared to the measured for Method 2
Figure 65:Correlation between the Holland B parameter and the RMAX for Method 1 for all storms; Correlation between
the Holland B parameter and the RMAX for Method 1 (1953-2008)
Figure 66: Correlation between the Holland B parameter and the RMAX for Method 2 for all storms; Correlation between
the Holland B parameter and the RMAX for Method 2 (1953-2008)
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Delft University of Technology
Appendix H: Comparison of the computed and observed winds
For a further analysis of the computed winds, the averaged- and maximum computed wind fields are
compared with the observed winds for the significant storms.
Figure 67: (left) Observed averaged wind speed compared with the computed wind speed; (right) Comparison without
the storm of 21-12-2003
Figure 68: (left) Observed max. wind speed compared with the computed wind speed; (right) Comparison without the
storm of 21-12-2003
For both the averaged and the maximum winds there is a correlation when leaving out the storm of
2003. For both measurements, the computed wind is around 0.8 of the total wind.
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Delft University of Technology
Appendix I: Simulated wind fields compared to the real wind field
In this appendix the simulated wind fields for the storm verification analysis is compared with the
observed wind field. Therefore the computed wind field is determined by using Method 2 (fitted
ambient pressure). Furthermore, the calibration factor has been taken into account, see Chapter 4.2.
Figure 69: (left) simulated and observed wind field for 01-02-1953; (right) ) simulated and observed wind field for 12-021962
The simulated winds for 01-02-1953 and 12-02-1962 are slightly underestimated compared to the
observed winds. Addition of the calibration factor results in a better fit. The wind direction of the
storm of 1962 differs from the simulated wind direction. This is mainly because, for simplicity
reasons, the storm is simulated as a circular depression, which in reality is not the case. For the storm
of 1962, the isobars are influenced by the location of the trough and occlusion front. Therefore, the
wind direction at the measurement station (Hook of Holland) is not completely dependent on the
storm location over time.
Figure 70: (left) simulated and observed wind field for 17-02-1962; (right) The pressure gradient of the storm of 17-021962
The simulated storm of 17-02-1962 shows a clear underestimation of the real surface wind field. As
for the storm of the 12th of February, this storm has a very low central pressure (950 mbar), and
travels at high Northern latitude. In this case, the distance between the storm centre and the
measurement point (Hook of Holland) is about 1500 km. For this great distance, the assumed circular
storm depression can differ greatly, which is shown in Figure 70 (right).
Matthijs de Jong
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Delft University of Technology
Figure 71: (left) simulated and observed wind field for 03-01-1976 (25hrs); (right) wind field for 03-01-1976 (40 hrs)
Based on Figure 71 (left) the peak of the storm of 03-01-1976 seems to be wrongly interpreted based
on the observed wind field. However, when the time duration is stretched to 40 hours, it is shown
that the simulated winds match the observed winds very well. An important observation for this
storm is that a second less significant storm centre occurs near the centre used for this research
(working assumption: only the most significant storm centre is used). This influences the pressure
gradient, and therefore the wind field that occurs around the depression.
Figure 72: (left) simulated and observed wind field for 14-02-1989; (right) ) simulated and observed wind field for 12-121990
For the storm of 1989, a small peak occurs in the observations. Based on the dataset, the quality
code of this peak is supposed to be valid. However, around this peak there is several data missing.
Therefore, the reliability of this measurement is doubtful. For the determination of the maximum
observed wind speed based on the computed wind speed, this peak is left out. As the wind field is
influenced by two storms, the wind speed- and direction differ from one and each other. The
computed wind direction is only simulated based on a singular storm, whereas in this specific
situation there were two storms active on the North Sea.
The simulated storm of 1990 shows a good estimation for the observed wind. The wind direction
shows that the wind direction crosses the.360°N direction. Another notification is that the computed
wind direction for the first 10 hours is lower than the assumed wind direction. Also for this situation
Matthijs de Jong
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Delft University of Technology
the real wind direction is influenced by the location of the cold front and the occlusion front, which
modifies the circular storm depression assumed in this research.
Figure 73: (left) simulated and observed wind field for 21-12-2003; (right) ) simulated and observed wind field for 09-112007
Figure 73 shows that the wind speed of the storm of 2003 is overestimated. As the storm surge
reports mentions, this storm is quiet severe, but with a very short duration. The storm is generated in
the North Sea itself. This simulation model does not take into account the storm duration, and
therefore results in a much higher wind speed than actually occurring. Further research how to take
into account the storm duration is recommended.
The same as for the storm of 1976, there are multiple storm centres that influence the wind field for
the North Sea. Behind the significant storm centre, a new storm centre is generated that results in an
extra increase in wind speed after 15 hours, which is not taken into account.
Water Set-up Tidal Latitude Angle Forward
Central
Radius Holland B
level
level
movement
pressure
[m]
[m]
[m]
[° N]
[°N]
[m/s] [km/h] [mbar]
[km]
[-]
2,0
1,1
0,9
56,9
309 10,9
39
980
1.057
1,0
2,2
0,9
1,3
54,6
304 15,5
56
1.003
382
1,1
1,9
0,9
1,0
56,5
315 17,6
63
975
1.150
1,3
2,8
2,0
0,8
57,8
300 18,3
66
948
651
1,6
1,4
0,3
1,1
60,9
302 20,9
75
974
414
1,3
1,8
0,7
1,1
62,3
281 12,0
43
972
1.018
1,2
2,2
0,9
1,2
58,9
286
7,1
25
978
572
0,6
3,1
2,1
1,0
57,6
276
9,0
32
962
644
1,6
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