Tools to Evaluate Flood Defense Policy, Which Model is Acceptable Nijmegen 2005 Robert Slomp

7/28/2019 Tools to Evaluate Flood Defense Policy, Which Model is Acceptable Nijmegen 2005 Robert Slomp

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Tools to evaluate flood defense policy, which model is acceptable?

Abstract (gewijzigd)

The level of flood protection along Dutch rivers has been significantly improved with

the Delta Plan Large Rivers (D.G.R. in Dutch). At the moment plans are being made foradditional safety in the project Room for Rivers. Policy has always been made on the

basis of minimum design water levels for rivers and estuaries. The use of design water

levels in policy is an acceptable simplification if dike design remains unchanged.

However this is not the case, since dikes are usually constructed for a design period of 50

years. Both design criteria and design water levels have significantly changed in the past

40 years. So many ongoing Dutch studies are flawed. The error margin (in decimeters or

in chance of failure) is the same order of magnitude as the effect of the proposed

measures. To solve this flaw the whole river and dike system has to be evaluated with

one consistent check using the same design criteria and correct data. For most policy

issues along the Rhine Branches and Meuse, it does not really matter which model

(probabilistic or deterministic) is used, the major threat being extreme discharges. Inthe deltas this is not the case, storm surges and wave action are as important as the

extreme discharges so probabilistic models have to be used in the consistent check. If all

flood defenses along rivers, lakes and deltas are to be considered together, the same

probabilistic model should be used, using realistic data. The Hydra-B/VIJ model makes

this possible.

R.M. Slomp, Msc. Rijkswaterstaat, RIZA, Ministry of Transport, Public Works and

Water Management, Lelystad, the Netherlands.

.

.

.

Since 1953 policy decisions in the Netherlands for flood defences have been based on

changes in design water levels and subsequently changes in their return periods. The use of

changes in design water levels in policy is an acceptable simplification if dike design remains

unchanged. However this is not the case, since dikes are usually constructed for a design

period of 50 years. Both design criteria and design water levels have significantly changed in

the past 40 years.

This paper will show that due to incorrect use of evaluation models and models for dike

design the Dutch dike system along the Rhine-braches and the Meuse will not be as safe asdecided by law. The dike reinforcement programme of 1996 to 2000, Delta Plan Large Rivers

(D.G.R. in Dutch) has left weak spots in the dike system. A number of the weak spots in dike

design and evaluation were known during the programme the actual minimum design

discharge was 1000 m3/s higher on the Rhine an 150 m3/s higher on the Meuse river, the

critical wave overtopping limit was raised during the project from 0,1 lit/s/m to 1 lit/s/m. The

minimum design discharge changed on account of the high discharges of 1993 and 1995. The

new design discharges however were only published in 2001 [DWW, 2001], after the

completion of the programme. Each of these two weak spots was a policy decision and has

an effect of about 20 tot 30 centimetres in dike height. The programme Room for Rivers has

to solve the first problem, higher minimum design water levels caused by the higher minimum

design discharges. Use of probabilistic models like Hydra-B [Slomp et al, 2001] or Pc-ring[Vrouwenvelder et al, 2002] is not necessary to show these weak spots. To demonstrate the


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effect of these weak spots in dike design a deterministic model can be used, Hydra-0 (zero)

[Steetzel, 2004]. Probabilistic models do however provide insight into the chances of a dike

failing on account of these weak spots. Probabilistic models also make the evaluation of

uncertainties concerning the minimum design conditions water levels and waves possible.

A special problem is the use of flood storage reservoirs and their effect on the chance of dike

failure. The most important flaw in policy studies along the Rhine Branches and Meuse willbe covered in this paper, the assumption dike design has not changed in the past 40 years.

First two models Hydra-B and Hydra-0 will be explained.

Hydra-B, a probabilistic tool to evaluate dike heights and reinforcement measures, is the

official tool (by law) to evaluate dike heights in the delta of the Rhine and Meuse. Hydra-B is

described in detail by its designer in [Geerse, 2003]. Along Dutch lakes and rivers the height

of flood defences is based on three major threats river discharges, storm surges and waves and

their combinations. On the major rivers Rhine and Meuse the river discharges are the

dominant threat (River area, R in the map below). Around the storm surge barrier in

Rotterdam the river discharge is insignificant (Sea area, S). On the lakes Haringvliet and

Hollandsch Diep and in the IJsseldelta all three threats are important (transitional area, T). Inthe IJssellake area storm surges and waves are the dominant threat (Lake area, L). In the

IJssellake area and IJsseldelta a modification of Hydra-B can be used, Hydra-VIJ. This model

will be officially introduced in 2006 along with the new minimum design water levels.

Figure 1, Boundaries between River, lake and the sea influence.

Hydra-B calculates:

- water levels per return period and specifically the minimum design water levels of

2001 for the Rhine and Meuse delta published in [DWW, 2001]

- the minimum necessary dike levels per return period (range 10 to 10 000 years)

- the chance of failure due to water levels per dike section and enclosed system of dikes

a ring of dikes and higher ground

- the chance of failure in height due to water levels and waves

- design conditions for the evaluation of the strength of outer layers of dikes.


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Hydra-B integrates previous models, can be used in the whole Rhine and Meuse delta and is

more precise. The probabilistic Hydra-B model is also valid outside of areas with storm

surges. Therefore the reach of the model was extended to Lobith and Borgharen, where the

Rhine and Meuse enter the Netherlands and to Zwolle along the IJssel. Since storm surges are

not important on the Rhine Branches and Meuse (an effect of 2 to maximum 5 centimetres in

the design water level) these could be discarded. This means that 9 flood waves can properlycharacterize each river, Rhine and Meuse. So in these river dominated areas WAQUA, a 2

dimensional hydrodynamic model, was used to calculate maximum water levels per flood

wave along the dikes and not only a the centre of the river [Havinga, 2005]. Hydra-B is

usually filled with water levels from SOBEK, a 1 dimensional hydrodynamic model, on

account of the large number of different water level calculations, 6768, in the Rhine and

Meuse delta. Water levels per flood wave were selected from the calculations for 6 000

locations at the base of the river dikes [van den Bosch, 2005], one every 100 meters, 25

meters from the outer crest. The WAQUA model was modified to accept the large number of

locations [Havinga, 2005]. Hydra-B was calibrated for these new river reaches by [Duits,

2005], calibration between Borgharen and Boxmeer is still underway. The research version of

Hydra-B was also improved to make the study of uncertainties concerning the minimumdesign conditions water levels and waves possible. Evaluating the use of flood storage areas

has been possible since 2001. This extended research version is called Hydra-BT [Duits,

2005] and was used in this study.

Hydra-B uses the Bretschneider formula to determine the waves [TAW, 1985]. For each of

the 6 000 locations for each wind direction the effective fetch and the mean bottom height

over the fetch length was determined using GIS. These data were stored in the databases

containing the water level information per location. Using the water level, the hydra-B model

determines the water depth and subsequently Hydra-B can calculate waves for 5 wind speeds

for each of the 16 wind directions. Reduction of wave growth by islands, high levees and

dense river forests has been neglected in the current calculations. These aspects are especially

important in the deltas, e.g. the nature reserve the Biesbosch. Using Hydra-B on 135 dike

cross sections, one every km, of dike ring 43, the Betuwe, a number of cross sections with

very low return periods for dike failure were found, between 100 to 500 years. The criterion

for failure is the exceedence of wave overtopping with more than 0,1 l/m per s. Such low

return periods are astonishing, therefore dike design and dike evaluation methods were

verified.

Design criteria are described in the Leidraad Bovenrivieren [TAW, 1985]. Dike evaluation

criteria are described in [TAW, 2002]. A new model Hydra-0 (zero), a deterministic model,makes it possible to evaluate the dike heights rapidly.


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This deterministic model is filled with the same type of data as Hydra-B but water levels are

only given for the design discharge of 2001, 16000 m3/s at Lobith for the Rhine and 3600

m3/s for the Meuse at Boxmeer. Waves are determined for only one design wind speed per

wind direction. Design wind speeds per wind direction are given in [TAW, 1985] and

presented in (figure 2). Hydra-0 uses the water levels, waves and dike cross sections to

calculate wave run up height in m + NAP. This wave run up height is a good approximationfor design heights of dikes. Soil settling and soil subsidence have to be added to obtain the

official design height. This was neglected is this study since these are relatively small in the

study area (R, see figure 1).

To properly fill the model with cross sections for the Rhine branches and Meuse some 6 000

cross sections, one for each location every 100 meters along the dike, have been made using

the profile generator [Santbergen, 2005]. This was done using the three most important dike

characteristics which influence wave run up on a dike [De Waal, 1999]:

Figure 2: Design wind speeds

Rhine Branches and Meuse

0

2

4

6

8

10

1214

-40 60 160 260 360

winddirection 360 degrees

designwindspeeds

(potentialwindl)

IJ ssel km 879-980,

Rhine km 858-867,Pannerdens kanaal km868-878 Waal 869-914Lek /NedR. km 880-929Meuse km 150- 200

Waal km 914-955 enLek km 929-943, Meusekm 200-235

- the slope of the last section of a dike, almost always 1 in 3,

- the dike height,

- the dike normal, perpendicular line,

A 1 in 3 external slope is a good estimation for river dikes on the Rhine Branches and Meuse.

When design discharges occur the rivers are full, water depths usually exceed 3 to 4 meters,

even on the fore shore. Wave reduction by dams, raised for shores, flood plains forests can

therefore considered minimal along the Rhine and Meuse. About 1 to 2 % of external slopes is

1 in 4 in places where wave action is large, the data has yet not been corrected for this

information. Along the sea and lake shores some dikes usually have a flat area shoulder in

the dike cross section to reduce wave action, this is not common on rivers.

Dike heights were received from the RWS-DWW, [DWW/AGI, 2004], some cuts in the

dike, for roads, still have to be removed from the data. This is less than 1% of the data. A

detailed verification of dike heights is still underway by Rijkswaterstaat DWW, some data on

recent dike reinforcements still has to be included. This is mostly in the transitional areas, the

deltas: Lek and Hollandsch Diep.


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The dike normal, perpendicular line, was determined through signal filtering [Van den

Bosch, 2005]. If the dike normal is chosen for a 50 or 100 meter stretch in stead of a 500 to

1000 meter stretch, the dike normal shows a significant difference of up to 50 (see figure 3).

In wide rivers, with a large wave action, an error of 5 in the dike normal results in a 0,07 m

error in dike height, an error of 30 results in a maximal error between 0,25 to 0,5 m [Lodder,

2003].

Figure 3: Choice of fil ter for determining the dike

normal,

perpindicular line, 0 is north,dike ring 16, Alblasserwaard

-100

-500

50

100

150

58000 58500 59000 59500 60000

location

dike

normal

dike normal every meter

normal filtered for (50m) stretches

normal fitered for (100m) stretches

normal filtered for (500m)stretches

normal filtered for (1000m)stretches

The water levels were determined at the base of the dike and not at the centre of the river,

local effects and centrifugal force cause differences up to a number of decimetres. In large

oxbows (3 to 4 km) along the river differences can be more than half a meter. In the table

below for a number of locations along dike ring 52, Oost Veluwe the difference in the water

level between the centre of the river and dike is illustrated.

Location

minimumdesigndischarge2001

difference betweencentre of the river anddike location for thedesign discharge

Dkr 52 IJ ssel km 924-925 Locatie 1_210458_458075 9,908 -0,01








Dkr 52 IJ ssel km 924-925 Locatie 9_209869_458612 9,908 -0,11Dkr 52 IJ ssel km 930-931 Locatie 9_209708_464579 8,662 -0,31


Table 1: Difference between water levels at the middle of the river and the dike

The use of omni directional wave action on the dike in stead of only perpendicular also has a

large effect on the dike height, e.g. up to 0,65m. This is shown at Andelst on the Waal (a wide

river) and Culemborg on the Lek (a narrow river).


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Location Rhine Branch dike ring

actual dikelevel (in m

+ NAP)

design waterlevel 1996 (in

m + NAP)

designheight1996, omnidirectionalwave action(in m +

NAP)

design height1996,perpendicularwave action

(in m +NAP)

differencein design

heightCulemborg Lek 43, Betuwe 8,28 6,99 7,88 7,68 -0,2

Andelst Waal 43, Betuwe 13,49 13,03 14,39 13,75 -0,64

Table 2: Difference in design height due to use of omni directional wave action

In addition to this, the repartition of water over the Rhine Branches at the time of a design

discharge is a matter of policy and not a hydraulic calculation. In reality more water (about

150 m3/s) flows to the north (the IJssel) and less to the west (the Waal). This means a rise in

design water levels of about 15 cm on the IJssel and a drop of 5 cm on the Waal.

Four graphs are shown for a dike ring along the IJssel, the Northern Rhine Branch, Dike ring

52, Eastern Veluwe The first graph, figure 4 concerns the check on the minimum freeboardof 50 cm, almost 40% of the dikes do not meet this criterion in 2001. The second graph, figure

6, shows the check on surplus dike height on account of wave action, only 12% of this dike

ring complies to the minimum design criteria in 2001. This is astonishing since most dikes

along the east shore of the IJssel, the northern Rhine Branch were built for a design discharge

of more than 16 000 m3/s, see figure 5.

Figure 4 the check on minimum freebo ard of 50 cm,

in m in 2001, dike ring 52, Oost Velu we

free distrubution at bifurcation points

0%1%4%

30%

32%

19%

8%

4%

1%

1%

-1.0


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Figure 6: The check on s urplus dike h eight in m in 2001, free

dist ribut ion at bifur cation points , dike r ing 52,

Oost Veluwe 64 km, 600 cross sections

critical overtopping rate 0,1 l/mper s, Hydra-0 (RWS)

1%

7%

25%

26%

28%

9%

3%

1%

0%

0%

-1.0


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Comparing figures 6 and 7 shows that the official HR2001 minimum design water levels give

a much too favourable view of surplus dike height. Almost 10% of the dikes are more than 70

cm too low in 2001 and 90% of dikes are too low in general (figure 6). If the design

discharges are lowered through the project Room for Rivers (RvdR), according to the

difference between official design water levels (HR2001 and HR 1996), 10% of dikes remain

too low (figure 8). Only if the project proposal (VKA, Voor Keurs Alternatief) is completely

carried out dike levels with be acceptable (see figure 9) for dike ring 52. The remaining 9%

insufficient dike height (less than 0,20 m) is only a problem for dikes with a very steep inner

slope e.g. 1 in 2. 0,20 m to 0,30 is also the difference between 0,1 and 1 l/m per s in criticalovertopping rate.

Figure 8: the check on surplus d ike heigh t in 2015, using

HR 1996, design water lev els at the b ase of the dike .

Dike ring 52, Oost Veluwe 64 km, 600 cross section, critical

overtopping rate 0,1 l/m per s, using Hydra-0 (RWS)

0%0%0%2%

13%

22%

32%

21%

8%

2%

-1.0


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For the dike ring 43, Betuwe, Tieler en Culemborger Waarden, 135 km of dikes, similar

graphs are shown. The situation with the free distribution at bifurcation points changes the

geographical position of dikes which are too low. The general problem does not alter. The

dike ring borders both river branches, so if less water goes to the Waal and more toPannerdens Kanaal/Nederrijn, or vice versa, it does not really change the scope for the dike

ring as a whole. In 2001 there is a minor problem for the minimum freeboard, but 20% of the

dikes have a real problem (>0,2 m deficiency in dike height) on account of wave overtopping.

This problem only diminishes slightly to 18% if RvdR is carried out according to its task, the

difference in design water levels of 2001 and 1996. But even after the current proposal (VKA)

has been carried out in 2015 14 % of the dikes remain too low.

Figure 10 the check on minimum freeboard of 50 cm, in m, in 2001,

dike ring 43, Betuwe, Tieler en Culemborger Waarden

.

0%0%0%0% 11%

17%

29%

26%

17%

-1.0 < -0,8

-0,8 < -0,6

-0,6 < -0,4

-0,4 < -0,2

-0,2 < 0.0

0.0 < 0,2

0,2 < 0,4

0,4 < 0,60,6 < 0,8

Figure 11: The check on surplus dike hei ght in m, i n 2001,

using official design w ater levels, dike ring 43

Betuwe, Tieler en Culemborger Waarden

135 km, critical overtopping rate 0,1 l/m per s using Hydra-0 (RWS)

0%2% 8%

14%

17%

17%

14%

16%

5%

7%-1.0 < -0,8

-0,8 < -0,6

-0,6 < -0,4

-0,4 < -0,2

-0,2 < 0.0

0.0 < 0,2

0,2 < 0,4

0,4 < 0,6

0,6 < 0,8

0,8 < 0.0


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Figur e 12: The che ck on sur plus dik e heig ht in m in 2015,

dike ring 43 (differen ce in d esign water levels 2001 - 1996 solve d),

critical over topping rate 0,1 l/m per s, using Hydra-0 (RWS)

0%3%7%

8%

12%

18%

14%

14%

15%

7%

2%-1.0 < -0,8

-0,8 < -0,6

-0,6 < -0,4

-0,4 < -0,2

-0,2 < 0.0

0.0 < 0,2

0,2 < 0,4

0,4 < 0,6

0,6 < 0,8

0,8 < 0.0

>1.0

Figure 13: The check on sur plus dike height in m in 2015,

RVDR project pr oposal VKA carr ied out,

free distr ibution at bifurcation points, dike ring 43,

critical over topping rate 0,1 l/m per s, using Hydra-0 (RWS)

0%0% 7%7%

14%

15%

18%

15%

11%

6%

7%

-1.0 < -0,8

-0,8 < -0,6

-0,6 < -0,4

-0,4 < -0,2

-0,2 < 0.0

0.0 < 0,2

0,2 < 0,4

0,4 < 0,6

0,6 < 0,8

0,8 < 0.0

>1.0

For 2001 the check on surplus dike height has been carried out for all dike rings in the Rhine

Branches (580 km) and Meuse (125 km), in total 705 km, excluding the deltas and special

structures 7 km. This is illustrated (in figures 14 and 15) for the dike rings with design waterlevels based on a 1250 year return period. Approximately the same results are obtained using

600 cross section data, chosen randomly every km, instead of the 6000, chosen randomly

every 100 meters, presented in the pie charts. Differences between categories of surplus dike

heights is less than 2%.

Along the Rhine Less than 50% of all dikes have sufficient height in 2001, 10% of dikes in

2015 , this is the dike category , with dike surplus heights of [-0,8 m


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The main reasons are:

- The design discharge will probably rise by 200 m3/s in 2006, on account of the

high discharges in 2003

- The flow wave characteristics will also change on account of the high discharges

in 2003 and the possible introduction of a new statistical method

- The freeboard of the new dikes 0,30 cm or 0,50 m along the Meuse(from Eijsdento Boxmeer, a stretch of 150 km) is still unknown, this is a policy decision.

- The effects of retention reservoirs on the Meuse

- The introduction of a new 2 dimentional WAQUA model for the Meuse. This new

model includes a larger portion of the valley of the Meuse. Simulation of extreme

discharges, above the design discharge of 3800 m3/s, will be more realistic.

Each of these items have been evaluated separately but not in conjunction.

Figure 14 Surplus dike heights in m in 2001 Meuse,

dijkrings 36, 36a, 37, 38, 39and 41,

approx. 125 km, cross sections every 100 meters,critical overtopping rate 0,1 l/m per s, calculated with Hydra-0 (RWS)

0%0%1% 8%

25%

25%

19%

9%

8%

5%

-1.0


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return period for water flowing over the dike in 2001, free distribution at bifurcation points, is

4500 years. The return period for wave overtopping, critical over topping rate 0,1 l/m per s is

. years. When one evaluates the dike ring with a probabilistic model (figure 16) the

situation looks more favorable than with a deterministic model (figure 11). This was to be

expected, since each situation is statistically weighed. If the deltas have to be compared

with the Rhine branches and Meuse use of the same model is therefore necessary.

Figure 16: The check on surplus dike height in m, in 2001,

dike r ing 43, Betuwe, Tieler en Culemborger Waarden

135 km, critical overtopping rate 0,1 l/m per s using Hydra-B0%0% 6%

6%

16%

12%

20%

14%

17%

9% -1.0 < -0,8

-0,8 < -0,6

-0,6 < -0,4

-0,4 < -0,2

-0,2 < 0.0

0.0 < 0,2

0,2 < 0,4

0,4 < 0,6

0,6 < 0,8

0,8 < 1.0

Conclusions:

Using the official design criteria from [TAW, 1985] the following conclusion is reached. 50%

of dikes Along the Rhine Branches and 65% of dikes along the Meuse are high enough in

2001. After implementation of Room for Rivers in 2015 at least 10% of dikes along the Rhine

Branches still have to be reinforced to accommodate wave action.

Large differences were found in surplus dike heights in relation to earlier studies due to four

causes:

- The fact that new cross sections to evaluate the dike were determined every 100

meters, instead of the usual larger dike stretches up to a number of kilometres.

- The dike normal (perpendicular line) was determined through signal filtering for

100 meter sections instead of averages for 500 to 1 km sections,

- The use of omni directional wave action instead of only wave action perpendicularto the dike.

- The use of water level data at the base of the dike and no longer at the centre of the

river. This is common practice in some areas along the Rhine during dike

construction, but not in policy studies.

So the reason for most projects concerning flood defence policy being flawed is the

assumption dike design is correct, without verifying this. Reasons are

- Design water levels and design criteria have changed over the last 40 years.

- Dike design depends on personal choices of the water board, the consultancies and

Rijkswaterstaat.

- The continued use of the same cross section data from dike design in dikeevaluation and policy studies


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To solve this flaw the whole river and dike system has to be evaluated with one consistent

check using the same criteria. For most policy issues along the Rhine Branches and Meuse, it

does not really matter which model is used, the major threat being extreme discharges in

combination with some wave action. Both probabilistic models like Hydra-B or PC-Ring or

deterministic models, like Hydra-0 can provide insight into the policy issues. However majorassumptions should be verified. Dike design has not been uniform in the last half century.

Data should be gathered from scratch if possible.

The use of 600 or 6000 cross sections, if both are chosen randomly, delivers approximately

the same result, differences between categories of surplus dike heights is less than 2%. This

margin of error is acceptable to determine flood defence policy.

Use of probabilistic models in stead of deterministic models delivers a more favourable

picture on surplus dike height. If all flood defences along rivers, lakes and deltas are to be

considered together, the same probabilistic model should be used, using realistic data. Since

the R.v.d.R. project covers both the deltas and the rivers a probabilistic model should be usedin the whole project area.

Recommendations:

The following information should be provided centrally using Hydro Dynamic and GIS

models.

- a random selection of a sufficient number of dike cross sections

- calculation of the dike normal for the cross sections filtered for 100 meter

stretches

- maximum water levels per flood wave for locations at the base of the dike for

these cross sections

- calculation of effective fetch for all wind directions for these locations

- bottom height per effective fetch per wind direction for these locations

The following information is still needed from water boards

- type of flood defence dike, wall, sheet piling, flood barrier or other structure

- cross section data (e.g. e.g. outer crest level, crest level, inner and outer slope,

shoulders, fore shores, dams and the types of dike revetment per slope).

- Information on soil settling and soil subsidence (very important in the deltas)

- Local information on the subsoil, very important for areas prone to piping, this

determines the necessary width for the dike (this problem is not covered in thispaper)


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References

[van den Bosch, 2005]

Aanpassing Profiel Generator, Hydra Tools, Verslag modelbouw, P. van den

Bosch, Alkyon Hydraulic Consultancy & Research, January 2005

[DWW, 2001]

Hydraulische Randvoorwaarden 2001 voor het toetsen van primaire waterkeringen, Ministerie

van Verkeer en Waterstaat, DWW, RIZA, RIKZ, 2001

[DWW/AGI, 2004]

Hoogte bestand, Rijkswaterstaat DWW/AGI, November 2004

[Geerse, 2003]

Probabilistisch model hydraulische randvoorwaarden benedenrivierengebied, C.P.M. Geerse,

RIZA - werkdocument 2003.128x. RIZA Lelystad, december 2003.

[Lodder, 2003]

Berekening implicaties van de invoering van Hydra-B Rapportage van implicatie

berekeningen ten behoeve van de introductie van Hydra-B voor actuele dijkprofielen in het

benedenrivierengebied, Q.Lodder, december 2003 werkdocument 2003.183x

[Rijkoort Wierenga, 1980]

Windklimaat van Nederland, KNMI, 1980

[Slomp et al, 2001]

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Onderbouwing, toelichting en analyse van verschillen ten op zichte van het verleden.

R.M. Slomp, C.P.M. Geerse, H. de Deugd RWS-RIZA-rapport 2001.017

[Steetzel, 2004]

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Alkyon Hydraulic Consultancy and Research, December 2004.

[TAW, 1985]

Leidraad voor het ontwerpen van rivierdijken. Deel 1 Bovenrivierengebied. Technische

Adviescommissie voor de Waterkeringen. Staatsuitgeverij s Gravenhage, september 1985

[TAW, 2002]

Voorschrift Toetsen op Veiligheid, Technische Adviescommissie voor de Waterkeringen.

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[De Waal, 1999]

Achtergronden Hydraulische Belastingen Dijken IJsselmeergebied. Deelrapport 9:

Modellering dammen, voorlanden en golfoploop. J.P. de Waal. RIZA rapport 99.046. RIZA

Lelystad, 25 maart 1999.


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[Santbergen, 2005]

Aanpassing Profiel Generator HYDRA Tools, Gebruikshandleiding. P. Santbergen, Alkyon

Hydraulic Consultancy & Research, January 2005

[Vrouwenvelder et al, 2002]

Belastingmodellen Benedenrivierengebied - fase 2/Concept met aanvullende berekeningen.A.C.W.M. Vrouwenvelder, H.M.G.M. Steenbergen, F.L.M. Diermanse. TNO-rapport 2001-

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Tools to Evaluate Flood Defense Policy, Which Model is Acceptable Nijmegen 2005 Robert Slomp

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