Water levels and their probability

A.2 Water levels and their probability

The design water level at Dordrecht is NAP +3.01 m. The probability of occurrence for this water level is 1:2000 year. The dikes around the island of Dordrecht are dimensioned to be able to avert floods up to this water level. For the development of a sound river side urban design it is necessary to know more about the range of expected water levels and corresponding probability of occurrences besides the design water level. Through statistical analysis, the range of water levels and probabilities have been calculated.

A.2.1 Assessment location

The water levels are calculated for a representative location in the river. This location is situated near the study area where the river Beneden Merwede bifurcates into the rivers Noord and Oude Maas. The exact location is RD (105832, 426058), river kilometre 976 (see Figure A.1).

Noord

Papendrecht, Dike ring16

Zwijndrcht, Dike ring 17

Beneden Merwede

Dordrecht,

Oude Maas

Dike ring 22

Figure A.1 Assessment location (arrow) and study area (box).

A.2.2 Frequency analysis and corresponding water levels

A high water level can be the result of one or several factors. For the UFM project the frequencies of exceedance for the water levels have been calculated using the Hydra-B computer program (Geerse, 2003). This program considers the following random variables which determine the water levels at Dordrecht:

- Rhine discharge (at Lobith) - Meuse (at Lith) - Sea water level (at the Maasmond) - Wind velocity (at Schiphol) - Wind direction (at Schiphol) - Operational situation of the Maeslant- and Hartel defences (open or shut) - The prediction of the sea water level at Hoek van Holland.

An extreme water level at Dordrecht can be caused by an extreme sea level or by an extreme river discharge. However, the probability of an extreme sea level (> NAP

+3.5m) and a simultaneous extreme river discharge (> 10,000 m 3 /s at Lobith) is negligible. The statistical analysis therefore only considers combinations of either an

extreme sea level and a moderately high river discharge, or an extreme river discharge in combination with a moderately high sea level. For the remaining random variables more or less normal values are considered. Two scenarios can therefore be distinguished:

• Sea levels are extremely high, river discharges are up to considerably high. •

River discharges are extremely high, sea levels are up to considerably high.

When the sea level at Rotterdam reaches NAP +3 m, the storm surge barriers are shut. It should be taken into consideration though that these defences can fail. For this study the probability of a failure is set to 1/1000 per closure although new insight shows that a probability of 1/100 is a more realistic measure (Deugd, 2006). The first scenario can therefore be divided into the following two sub scenario’s:

• The defences are shut due to high water levels at sea •

The defences are open due to failure of the defences while the sea levels are high.

This results in a total of three possible scenarios:

1 Flood defences are shut due to extreme sea levels (no failure). High water levels at Dordrecht are caused by extreme sea levels in combination with considerably high river discharges.

2 Flood defences are open. Sea levels are not extremely high. High water levels at Dordrecht are caused by extreme river discharges in combination with considerably high sea levels.

3 Flood defences are open, but should be shut (failure of defences). High water levels at Dordrecht are caused mainly by extreme high sea levels.

Within Hydra-B the random variables are varied over the range of possibilities for the above mentioned scenarios. Every combination of variables has a certain probability of occurring (frequency). Some of the variables are correlated which means that the frequency is not defined by the product of the individual frequencies. Every combination of variables leads to a certain water level at Dordrecht with a corresponding probability. All combinations which lead to the same water level define the limit state function Z (see Figure A.2). The frequency of exceedance is derived from the summation of all probabilities of the combinations which lead to a higher water level than Z.

Sum of all possibilities in this area, make up the frequency of exceedance for Z=3

Discharge Lobith

Z=3.00 Z=2.90

Design point for Z=3

Z=2.80

Water level Maasmond

Figure A.2 Example of limit state function

Some combinations have a negligible probability of occurrence, e.g. the combination of

a water level at the Maasmond of 6 m +NAP and an eastern wind. These combinations are not taken into account. Only the plausible combinations are considered. The combinations for Dordrecht are taken from the RAND2001 database: ‘Benedenrivieren Rijnd juli29u’.

The design point is that point of function Z, with the largest probability of occurrence. However, the probability of occurrence for the exact combination of variables at the design point is very smal. The design point is merely a representative for all points that make up for the function Z and thus for the corresponding water level. The design point can be considered as an example scenario for all possible combinations which result in the same water level.

Using Hydra-B the design points for several frequencies of exceedance were calculated. The variables of two design points were selected for the hydraulic calculations; scenarios A and B. Table A.1 gives an overview of the variable values for the two scenarios. For ccenario A, the Rhine and Meuse river discharges are the main cause for the extreme water level at Dordrecht. The sea water level is moderately high and the storm surge barrier is open. For scenario B, the sea water level of NAP + 4.71 m is extremely high. The storm surge barrier in the Nieuwe Waterweg is assumed to have failed and thus open. Due to a considerable discharge of the Rhine and Meuse rivers (though not as extreme as in scenario A) the water level at Dordrecht reaches NAP + 3.10 m. A third scenario, in which the storm surge barrier in the Nieuwe Waterweg fails, was found very improbable and was therefore not evaluated.

Table A.1

Variables for scenario A and B.

Scenario

Wind

u wind

Water levels Discharge Discharge Water level

direction

speed m/s

at the

Rhine

Meuse at

Maasmond

Stadswerven m+NAP

3.1 Discharge Rhine: discharge at Lobith

Discharge Meuse: discharge at Lith