4.1 Water
balance.................................................................................................................. 2
4.1.1 Evaporation
and precipitation............................................................................................ 2
4.1.2 Runoff............................................................................................................................ 3
4.1.3 References
to Water balance........................................................................................... 4
4.2 River
drainage................................................................................................................... 6
4.2.1 River
morphology............................................................................................................. 6
4.2.2 Q by
measurement........................................................................................................ 11
4.2.3 Q on
different water heights in the same profile................................................................. 11
4.2.4 Calculating
Q with rounghness........................................................................................ 11
4.2.5 Using
drainage data....................................................................................................... 14
4.2.6 Probability
of extreme discharges................................................................................... 17
4.2.7 Level and
discharge regulators........................................................................................ 19
4.2.8 References
to river drainage............................................................................................ 20
4.3 Water
reservoirs.......................................................................................................... 22
4.3.1 Terminology.................................................................................................................. 22
4.3.2 Water
delivery............................................................................................................... 23
4.3.3 Capacity
calculation...................................................................................................... 23
4.3.4 Avoiding
floodings by reservoirs....................................................................................... 24
4.3.5 Water
management and hygiene..................................................................................... 25
4.3.6 Maps
concerning local water management....................................................................... 26
4.3.7 References
to Water reservoirs....................................................................................... 27
4.4 Polders............................................................................................................................. 28
4.4.1 Need of
drainage and flood control................................................................................... 28
4.4.2 Artificial
drainage........................................................................................................... 29
4.4.3 Polders......................................................................................................................... 31
4.4.4 Drainage
and use.......................................................................................................... 32
4.4.5 Weirs,
sluices and locks................................................................................................ 33
4.4.6 Coastal
protection......................................................................................................... 35
4.4.7 References
to Polders.................................................................................................... 36
4.5 Networks
and crossings.............................................................................................. 37
4.5.1 Networks...................................................................................................................... 37
4.5.2 Crossings..................................................................................................................... 38
4.5.3 Bridges......................................................................................................................... 40
4.5.4 Harbours
P.M................................................................................................................ 42
4.5.5 References
to Networks and crossings............................................................................ 42
The surface of the Earth is ample half a billion km^{2} and there is 1.39 billion km^{3}
water. So, if water was equally
dispersed the Earth would be fully covered by a 2.7km deep ocean (Fig. 1). The 48m upper layer would be ice. However, 29% is
land. It contains 3% of all existing water, but 2/3 is frozen.
If all ice would
melt by gobal warming sea level would raise 66m.
1000
km3 
salt 
fresh 
total 
m3/m2 
mm 
atmosphere 

12,9 
12,9 
0,025 
25 
sea 
1 338 000 

1 338 000 
2 624 
2 624 021 
land, from which 
12 957 
35 004 
47 960 
94 
94 057 
snow and ice 

24 364 
24 364 
48 
47 782 
subterranean 
12 870 
10 530 
23 400 
46 
45 891 
lakes 
85,4 
91 
176,4 
0,346 
346 
soil moisture 

16,5 
16,5 
0,032 
32 
swamps 

2,1 
2,1 
0,004 
4 
life 
1,1 

1,1 
0,002 
2 
total 
1 350 957 
35 004 
1 385 960 
2 718 
2 718 079 


Fig. 1
Total amount of water on Earth 


Fortunately the sun still adds snow to the poles.
You can evaporate 1m^{3} water by 2.26GJ,
2.26GWs, 630kWh or 72Wa (say 72 m^{3} natural gas). The Earth’s surface
receives 81 PW from sun. So the sun could evaporate 1.1 million km^{3}
per year.
Actually less then
half is evaporated in unsaturated air only (Fig. 2). It falls down discharging its solar heat in the same time as soon as the
air becomes saturated in cooler areas by condensation (precipitation). That is nearly 1m^{3}/m^{2}
or 1m and more precise 957mm (Fig. 2).

evaporation 
precipitation 
runoff 
evaporation 
precipitation 
runoff 

1000 km3/a 
mm/a 

sea 
419 
382 

1157 
1055 

land 
69 
106 
37 
467 
717 
250 
total 
488 
488 

957 
957 



Fig. 2
Yearly gobal evaporation, precipitation and runoff 


Areas like deserts receive less then 200mm, areas like tropical rain forests more then 2 000mm average per year (Fig. 3).
WoltersNoordhof (2001) page 181 
Fig. 3 Global distribution of precipitation 

Europe has the same extremes (Fig. 4).
WoltersNoordhof (2001) page 61 
Fig. 4 European distribution of precipitation 

The Netherlands receive from 700mm in East Brabant until 900mm in central Veluwe (Fig. 5), but there have been years of 400mm and 1200mm.
Huisman, Cramer et al. (1998) page 18 
WoltersNoordhof (2001) page 53 
Fig. 5 Distribution of precipitation in The Netherlands 
Fig. 6 Precipitation minus evaporation in The Netherlands 


When precipitation exceeds evaporation as soon as lakes and subterranean aquifers have
been filled up water runs off subterranean or along brooks and rivers (Fig. 8 and Fig. 9).
Harrison and Harrison (2001) 
Fig. 7 European river system 

The Netherlands receive runoff from catchment areas of rivers Rhine (entering The Netherlands in Lobith), Meuse and
Scheldt (Fig. 7).
Huisman, Cramer et al. (1998) page 21 
Huisman, Cramer et al. (1998) page 13 
Fig. 8 Major soil types and average annual runoff in The Netherlands 
Fig. 9 Received runoff in The Netherlands 


The river Rhine has a catchment area of 180 000km^{2} characterised by 1 775mm precipitation minus 1 392mm evaporation average per year in that area until Lobith. So, 383mm, 69km^{3}/year or at average 2000m^{3}/sec water runs off and comes in at Lobith. Snow and ice in mountains level out season fluctuations of rivers storing precitipation in winter, releasing it in summer. Nevertheless, in February at its normal annual maximum it is 8km^{3} or 3000m^{3}/sec causing water level 10m NAP at Lobith. But in 1995 17m NAP and 13 000m^{3}/sec is measured at Lobith.
Jong (1995) collected weeks of frontpage news about floodings retrievable in the Chair library. Evacuation of 50 000 inhabitants was ordered by Royal Commissioner of Gelderland Terlouw when floodings threatened Betuwe area behind Lobith in 1995. Afterwards, the threat of floodings caused plans to inundate polders preventively in case of emergency, but a polder of 1km^{2} x 1m = 1 000 000m^{3} would have stored water for 77 seconds only. So, retention in Rhine basin have to increase, bottoms deepened or dikes along rivers have to be heightened. But which height is enough?
Harrison, H.
M. and N. Harrison (2001) Schiereiland Europa. De hooggelegen
gebieden (Berlijn) Reschke & Steffens.
Huisman, P., W. Cramer, et al., Eds. (1998) Water in the Netherlands NHVspecial (Delft) NHV, Netherlands Hydrological Society NUGI 672 ISBN 9080356522 URL Euro 20.
Jong, T. M.
d. (1995) Krantenknipsels watersnoodramp 1995 (Rotterdam) NRC.
WoltersNoordhof,
Ed. (2001) De Grote Bosatlas 2002/2003 Tweeënvijfstigste editie + CDRom
(Groningen) WN Atlas Productions ISBN
9001121004.
The morphology of a river system and its discharge quantity Q depends on human impact, the proportion of subterranian and
surface runoff (Fig. 8), the character and load of transported eroded
material and the directions, velocities and quantities caused by slopes in the catchment
area.
Fig. 10 shows a landscape with 24 x 24 squares (sloped
mountain areas or polders) with 4 possible drainage directions, producing converging trucated
river systems. Computer programme Jong (2003) ‘river(drainage.exe)’ (see www.bk.tudelf.nl/urbanism/team
publications 2003), made from the ‘random walk’ example of Leopold and Wolman cited by Zonneveld (1981), arouses such
random landscapes producing river systems. The image is built up in columns
from upper left to down below. The programme prevents convergent arrows and
smallest circuits by changing lowest arrow 90^{o} into right or
downward if they occur. So, the runoff tends towards ‘South East’ as if the landscape has a main slope.
Watersheds become visible separating catchment areas. Why do they
concentrate into separate basins and converge into main streams? Draw them and
calculate the discharge Q for some outputs taking European precipitation and
evaporation values into account. Suppose surfaces and altitudes, draw the
altitude lines and estimate velocities.



Zonneveld (1981) 
Fig. 10
Directions of drainage in a landscape 
Fig. 11
Surface streams caused by Fig.
10 


You can divide a river system in different truncation orders from source to output. Fig. 12 shows four methods. Strahler (above right) concerns small source brooks without tributaries above as first order. Streams collecting water form first order are second order rivers and so on. Try to divide Fig. 11 in such orders[a].
_{} 

Zonneveld (1981) page 179 
After
Zonneveld (1981) page 183 
Fig. 12 Four methods to distinguish ‘orders’ 
Fig. 13 Average number and length of orders in ‘random walk rivers’ 


Leopold and Wolman calculated random walk rivers have 4.4 upstream branchings of lower Strahler order at average. In practice it varies between 2 and 5. This ‘bifurcation ratio’ plays a rôle in traffic as well, though street patterns and artificial drainage systems in flat lands are not like a tree but like a lattice (compare Alexander (1966))[1]. If there are 20km streets per km^{2}, you can best raise some 7km of them into the order of neighbourhood roads and transform 2km into district ways. So, the optimal proportion between the density of ways and sideways in a lattice seems to be approximately a factor three according to Nes and Zijpp (2000).
Suppose a metropolis of 30km radius has 60 x 60 = 3600km^{2} surface with
2km/km^{2} district ways processing 1000 motor vehicles per hour. There should be 7200km
district ways in a grid of average 1x1km. To calculate density from the grid
mesh bordered by 4km district roads, you have to count them half
because they serve adjacent meshes as well. Many of them would be overloaded by
through traffic when you would not raise 1/3 of them into city highways (2400km in a grid of 3x3km, 0.67km/km^{2}) with a capacity
of 3000 mv/h and less exits. However, on their turn they would be overloaded.
So, this argument produces a semi logaritmic range of orders (Fig. 14).

km nominal mesh 
km/metropolis 
km/km^{2} inclusive density 
exclusive 
mv/h 
district roads 
1 
72000 
2,00 
1,33 
1000 
city highways 
3 
24000 
0,67 
0,47 
3000 
local highways 
10 
7200 
0,20 
0,13 
10000 
regional highways 
30 
2400 
0,07 
0,05 
30000 
national highways 
100 
720 
0,02 
0,02 
100000 
and so on 


nearly 3.00 
2.00 
total 






Fig. 14
Theoretical orders of urban traffic infrastructure 







The total density of ways is 2km/km^{2}. One third of them we have transformed into highways of several orders. So, the density of ways includes the highways. Exclusing highways, there are 1.33km/km^{2} small district ways left. If we would like to reduce the amount of exits of local highways to save velocity, we have to disconnect district ways into dead ends. If we like to connect them mutually with extra parallel service roads along side the city highway we need the inclusive density at least.
If we try to draw a system of highways in a square of 60x60km (Fig. 15) we firstly draw a grid of 10x10km. There are 14 local highways of 60km, but 6 of them we transform into a higher order. So, their exclusive density is 8x60/3600=0.13 indeed (Fig. 14). However, we can not fill 10km space between local highways with 3.3 city highways. So we choose 3 highways lowering the inclusive density from 0.67 into 0.60km/km2. This causes a raise of exclusive district way density from 1.33 into 1.40, but on this scale we can not draw them anyhow.




Fig. 15 Orders of dry and wet connections in a lattice 


For wet connections the same applies when we call city highways races, local highways brooks and regional highways rivers. The bifurcation ratio of brooks before meeting a river within these regular latices seems to be 20 (Fig. 16 left). However, 4 boundary sections could be used as a mirror axis (dash dotted lines) subsequently counting half. The same density could be reached with a bifurcation ratio 2 and 5 orders (Fig. 16 right).

Feather like 
Tree like 
density 
29 sections 
29 sections 
bifurcation ratio 
18 
2 
number of ‘orders’ 
2 
5 



Fig. 16 Feather and tree like connection patterns 


In the squares of Fig.
15 tree
like connection patterns seem to require a little higher density and consequenly
higher costs when restricted to bifurcation ratio 2.[b]
If somebody can design a lower density within this boundary conditions I will
publish it next time. On the other hand, tree like opening up every point of
the area makes many variants and diversity of locations possible when you have more space to lay out (Fig. 17).

Feather like 
Tree like 
density 
96 sections 
98 sections 
bifurcation ratio 
18 
2 
number of ‘orders’ 
2 
6 or 9 



Fig. 17 Feather and tree like connection patterns opening up a square 


Perhaps opening up a 9 x 9 square in a treelike way with
bifurcation ratio 3 could reach the same or even lower densities and consequently
lower costs. Try it. Does it result in less nodes and
longer sections? The number and characteristics of nodes and the length of
sections are important for spatial quality. Which rôle does the length of
individual sections L play instead of total length per order in Fig. 13?
The average
length L of a random walk river section is related to its catchment area A by L(A)=A^{0.64}. If length L is given the inverse
produces the catchment area, A(L)=L^{1.563} (Fig. 18 and Fig. 19).
_{} 
_{} 


Fig. 18 Catchment area related to the length of a river section 
Fig. 19
Logaritmic representation of Fig.
18 


Check Fig. 11 by counting the corresponding squares
in Fig. 10 of a
specified order and its length. Compare your measurements with Fig. 19 and Fig. 13.
The sections of a river have different morphologies dependent
on the coarsegrainedness of transported material and the character of its
banks Fig. 20. Near
glaciers rough
material is laid down in talus. So the water takes diverse and changing
courses. Lower sections still bear rough material wearing out the outside parts
of a bend into meanders, because rough material laid
down there in the same time becomes a water barrier until heavy showers force a
break through Fig. 21 and Fig. 22.
From
Allan cited by Zonneveld (1981) page 148 
From Hoppe cited by Zonneveld (1981) page 149 
Fig. 20 Forms of deposit 
Fig. 21 Move of Rhine near Neuss from Roman times (a) via Middle Ages (b) until recently 


In low lands finer deposits raise the bed in calm periods forcing water to wear away easier courses producing a twining river landscape with temporary islands.


Zonneveld (1981) page 143 
Zonneveld (1981) page 144 
Fig. 22
Meandering river with historical deposits 
Fig. 23 Twining river 


The Rhine area behind Lobith is an example of both processes (Fig. 24).
From
Lobith Rhine distributes water via Waal, Lower Rhine and IJssel in historically changing proportions.

Huisman, Cramer et al. (1998) page 38 
Fig. 24 Historical distribution of Rhine
water from Lobith 



Escher 1948 cited by Zonneveld (1981) page 160 
Zonneveld (1981)page 161 
Fig. 25 Delta development with
river (R), topsets (d) and foresets (D) 
Fig. 26 Mississippi delta 


The velocity v of water can be measured on different vertical lines h with mutual distance b in a cross section of a river (Fig. 27). You can multiply v x b x h and summon the outcomes in cross section A to get Q = S(v*b*h).
Akker and Boomgaard (2001) 
Fig. 27 Profile of a river 

For example: asked the river
drainage Q (Fig. 29),
given h_{i}, b_{i} and v_{i} from profile subdivisions
(Fig. 28).
_{} 
_{} 
_{} _{} 
_{} 

height
h 
width
b coordinate
B 
velocity
v 



Fig. 28
Data from profile 






_{ } _{} _{} _{} _{} 
_{ } _{} _{} _{} 
_{} 
_{} 
_{} 
profile subdivisions 
drainage per subdivision 
velocity 
surface 
drainage 


Fig. 29
Drainage (profile subdivisions and velocities) 


H varies,
but you can measure it easily. Then you can calculate drainage Q(H) by a
formula characteristic for the profile concerned. However, periods of high
drainage Q or regular floodings in winter change profile and formula. Comparing
measurements like in paragraph 1.2.2 on different water heights you find a curve often
looking like a parabola, approached by Q = a*H^{b} or H=(Q/a)^{1/b}
(Fig. 30). Parameters ‘a’ and ‘b’
characterise the profile.
_{} 


Akker and Boomgaard (2001)}.}. 
Fig. 30 ‘Measurements’ M_{i} and Q(a,B,H)
= a*H^{B} or the inverse H(a,B,Q)= (Q/a)^{1/B} to get H on the yaxis 
Fig. 31
Change of boundary condition downstream; a ‘drowning’
waterfall 


Measurements deviate from the formula because velocity varies. When measuremens can not be simulated by a smooth curve, probably boundary conditions downstream change by high water levels. Then you have to make two graphs, one until the point of change, one for the higher values. When for example a waterfall downstream suddenly ‘drowns’ at increasing water levels (Fig. 31) the slope of the curve can change by sudden increase of velocity. When Q=0 at H_{0} ¹ 0, for instance when we want to express H_{0} related to a reverence surface like NAP, we need a correction like Q = a(HH_{0})^{b}.
You can find constants a and b by the least
squares method provided by Excel using graphs. Put measurements of height and
drainage calculated according to Fig.
30 in two columns. Make a point graph and select it.
Choose ‘add trend’ in ‘graph’ from the main Excel window above,
choose power, 
click both lowest, 
click axis, 
choose logarithmic, 
and you produce graphs like Fig. 32 and Fig. 33 with power regression line and formula.
With R^{2} near to 1 you have a reliable formula. In Fig. 32 we used ‘measurements’ of Fig. 30 putting the independently variable measurements on the xaxis this time to find a=0.0003 and b=8.7398.


Fig. 32 ‘Measurements’ M_{i} and Q(a,b,H) = a*H^{b} 
Fig. 33
Logarithmic representation of Fig. 32 


The
logarithmic representation log Q = log a + b log (HH_{0}) produces a
straight line easy to extrapolate to other heights and drainages. But be
careful, there could be jumps in velocity by downstream events. If you have
made graphs before and after the jump because measuremens could not be
simulated by a smooth curve, each interval in Fig.
33 has different slopes representing different
behaviour.
Just like
wind, water slows down by roughness of the bed. The cross length of roughness in a
wet profile P (Natte Omtrek) is calculated by summing
hypothenuses of triangles according to Pythagoras characterised by the square
root of (b_{i})^{2}+(h_{i}‑h_{i‑1})^{2}
(see Fig. 27 and Fig.
35).
Considering
the profile as a function H=f(x) we can read the waterlevel H from accompanying left border x_{1}=l and right border x_{2}=r
as values from f(x) (Fig. 34). The cross length of roughness P (Natte Omtrek) and
the surface of the wet cross section A are both calculated as a function of H (Fig. 35).
P H A 
Cross length by Pythagoras:_{} _{}_{
}Surface wet
cross section: _{}_{ }_{} 




Fig. 34
Profile as a function 
Fig. 35
Calculating wet cross section A and cross length of
roughness P (NatteOmtrek) 



When we
divide the surface of the wet cross section A of a stream by this cross length of roughness P we get a measure
indicating what part of the flowing water is hindered by roughness called
‘hydrolic radius’ R = A/P in metres.
Method
Chézy
The average
velocity of water v = Q/A in m/sec is dependent on this radius R, the roughness
C it meets, and the slope of the river as drop of waterline s, in short
v(C,R,s).
According
to Chézy v(C,R,s)=CÖRs m/sec, and Q = Av = ACÖRs m^{3}/sec. Calculating C
is the problem.
Method
StricklerManning
Instead of v=CÖRs, StricklerManning used _{ }with roughness n token from Fig. 36._{}
_{Characteristics of bottom and slopes} 
_{n} 

_{} 
_{from} 
_{until} 
_{Concrete} 
_{0.010} 
_{0.013} 
_{Gravel bed} 
_{0.020} 
_{0.030} 
_{Natural streams:} 
_{} 
_{} 
_{Well maintained, straight} 
_{0.025} 
_{0.030} 
_{Well maintained, winding} 
_{0.035} 
_{0.040} 
_{Winding with vegetation} 
_{0.040} 
_{0.050} 
_{Stones and vegetation} 
_{0.050} 
_{0.060} 
_{River forelands:} 
_{} 
_{} 
_{Meadow} 
_{0.035} 

_{Agriculture} 
_{0.040} 

_{Shrubs} 
_{0.050} 

_{Tight shrubs} 
_{0.070} 

_{Tight forest} 
_{0.100} 

Akker and Boomgaard (2001) 

Fig. 36 Indication of roughness values n according to StricklerManning_{} 


Method
Stevens
Instead of v=CÖRs Stevens used v=cÖR considering
Chézy’s CÖs as a constant c to be
calculated from local measurements. So, Q = Av = cAÖR m^{3}/sec and c is calcuated by c=(AÖR)/Q. When we measure H and Q several times (H_{1},
H_{2} …H_{k} and Q_{1}, Q_{2} … Q_{k}),
we can show different values of A(H)ÖR(H) resulting
from Fig.
35 as a straight line in a graph (Fig. 37). We can add the corresponding values of Q we found
earlier in the same graph reated to A(H)ÖR(H). When we read today on our inspection walk a new water
level H1 on the sounding rod of the profile concerned we can interpolate H1
between earlier measurements of H and read horizontally an estimated Q1 between
the earlier corresponding values of Q to read Q from graph.
_{} 

Fig. 37 Graph used according to Stevens with ‘measurements’ of Fig. 32 

However,
from these ‘measurements’ c appears to be not very constant, but the graph
remains a practical way to estimate Q from H.
Once you collected drainage data throughout a year you can put
them in a hydrograph (afvoerverlooplijn).



Akker and Boomgaard (2001)}.}. 
Akker and Boomgaard (2001)}.}. 

Fig. 38 River with continuous base
discharge 
Fig. 39 River with periodical base
discharge 



Fig. 38 shows peaks caused by periods of much precipitation and fast discharge. Fig. 39 shows the behaviour of a season bound river, periodically dry.
A duration line (Fig. 40) shows frequency of discharges arranged from minimum to maximum. The x‑axis shows how long river discharges are less then indicated on yaxis. The river characterised in Fig. 40 never falls dry: 0% of time it has less discharge then indicated on the yaxis left, but the maximum discharge is indicated right: the whole period concerned it was less then that.
A duration line is not a probability curve to estimate discharge on a
certain day. After all, river discharges on subsequent days are not
independent, but strongly related in periods like seasons. Cumulated periodes
of low discharge may indicate measures to prevent shortages in use of water.
Cumulated periods of highest (peak) discharges determine measures concerning
maintenance, prevention of risks and design. The longer the included time
series, the more useful they are. Often they are not long enough to determine a
design frequency considering the life span of civil works.


Akker and Boomgaard (2001) 
Akker and Boomgaard (2001) 
Fig. 40 Duration line 
Fig. 41 Dataset with peak discharges 


Drainage hydrology knows two data sets characterising peak discharges; annual maximum series indicating maxima only and partial duration series indicating peaks exceeding a reference level like the top of summer dikes. Fig. 41 shows an example of both. To make discharges statistically independent we use separate ‘river years’. P_{1}  P_{4} are an annual maximum series of 4 river years. To make a partial duration series we need P_{1}', P_{3}' and P_{4}' as well. The lower the reference level, the more peaks we take into consideration.
The peak discharge Q_{T} exceeded once in average T years (‘return period’) is called ‘Tyears discharge’. Even if Q exceeds Q_{T} once in average 10 years (T=10year) it can happen 2 years in succession. There are large fluctuations round the average. Extreme values vary more per year then per 10 year. For T>10 we can use extreme values of highest and lowest values known from the past. If there are no discharge data you can ask older people or read markings of historical high water level former inhabitants left behind. However they are not useful if river morphology (profile) and subsequently Q(H) has changed by nature, artificial normalisation or raising dikes.
The probability of extreme values is called ‘extreme value
distribution’. It is described in
different ways, for instance like Gumbel type I for maxima, Weibull type III for minima, LogGumbel, Pearson or LogPearson type III distribution.
In 1941
Gumbel described an extreme value distribution, successful in
hydrological applications since then. The Gumbel I distribution is often used
for maximum discharges. It
supposes independent observations of extreme values X_{1}, X_{2},
X_{3}...X_{n} (for example successive year maxima) to be
exponentially distributed. Then P’, the cumulative probability discharge will
be equal to or smaller then earlier observations learned (Q£X) is approximated by
P’ = exp(exp(y)) and the reverse y = ln(ln(P’)). The
complementary probability P = 1 ‑ P’ discharge Q
will exceed an observation (Q>X) is 1/T and the reverse
P’ = 1 – P = 1 – 1/T. So, the ‘reduced
variable’ y = ln(ln(1 – 1/T)).
When we
arrange the measurements from maximum m=1 until minimum m=N (the number of
years we were measuring), return period T = (N+1)/m (‘plotting
position’) and P = m/(N+1).
To resume: _{} , _{}. So, we can make a graph _{}_{ }expressing
P in y.
But we can also express T in y and
make a graph _{}_{ }(Fig. 42).
Fig. 42 shows return period once a year (T) has probability 1
(P), once in two years has probability 0.5 or 50%. Both are expressed in y. To
see once in 1000 years we should represent the vertical axis logaritmically (Fig. 43). The Gumbel I distribution becomes a straight line
when we stretch out T and P properly around their common value 1. Then T and P
look proportional to y. In that case we can put them on the horizontal axis
alongside y to get so called ‘Gumbel paper’ (Fig.
44). The vertical axis now is free to give water level H
a place. When we know how many times every observed water level occurred last
years, we can calculate the return time T, put the observation on Gumbel paper
and read immediately the probability P of that observation without calculating
reduced variate y. Many observations give a cloud of points. We can draw a
straight line though that cloud and estimate which water level could occur in
1000 years or the reverse formulate a risk and read the desired height of dikes!






Fig. 42 T(y) and P(y) 
Fig. 43
Fig. 42 Logaritmically 
Fig. 44 Gumbel I paper 



The
horizontal axis of Fig. 44 is ‘Gumbel distributed’. You can distribute the vertical
axis logarithmically if there is much sprawl in the cloud of observations. Some
observations could deviate too much to be reliable. They could be observed
wrongly, calculated, put on paper or even emerge by copying.

Akker
and Boomgaard (2001)}.}. 
Fig. 45
Estimating an extreme value graph missing data 

To analyse
extreme minimal discharges you can use ‘log – Gumbel III distribution’ with
plotting position T=(N+0.5)/(m0.25) so, P=(m0.25)/(N+0.5).
When you
have no properly measured discharge data one should rely on information about water levels in the past. For
one point in the graph you can assume ‘bank full level’ once in 1.5 year (Fig. 45). This corresponds to usual height of dikes or
raisings along the banks. A next point in the graph could be obtained from
markings by the inhabitants (for example the highest level in the past 20
years).

Ankum (2003) page 156 
Fig.
46 Level regulator with
level as target 


Ankum (2003) page 156 
Fig. 47 Discharge regulator with
discharge as target 

Ankum (2003) page 167 
Fig. 48 ‘Manners’ of regulation 

The fixed regulators are called weirs (stuwen), manual or automatic regulators are called gates (schuiven).
Akker, C. v. d. and M. E. Boomgaard (2001)
Hydrologie (Delft) DUT Faculteit Civiele Techniek en Geowetenschappen.
Alexander, C. (1966) A city is
not a tree (London) [s.n.].
Ankum, P. v. (2003) Polders en
Hoogwaterbeheer. Polders,
Drainage and Flood Control (Delft) Delft University of Technology, Fac. Civiele Techniek en Geowetenschappen,
Sectie Land en Waterbeheer: 310.
Huisman, P., W. Cramer, et al., Eds. (1998) Water in the Netherlands
NHVspecial (Delft) NHV, Netherlands Hydrological Society NUGI 672 ISBN 9080356522 URL Euro 20.
Jong, T. M. d. (2003) Riverdrainage.exe
(Zoetermeer) MESO.
Nes, R. v. and N. J. v. d. Zijpp
(2000) Scalefactor 3 for hierarchical road networks: a natural phenomenon?
(Delft) Trail Research School Delft University of Technology.
Zonneveld, J. I. S. (1981) Vormen in
het Landschap. Hoofdlijnen van de geomorfologie (Utrecht / Antwerpen)
Uitgeverij Het Spectrum ISBN
9027462097.
Snow and
ice in mountains are most important forms of water storage. They level out season fluctuations
of rivers like Rhine storing precitipation in winter, releasing it in summer
when we need it most. At lower scale water reservoirs buffer fluctuations in runoff for water supply in dry periods,
provide 23% of world electricity production and avoid downstream floodings (retention). Retention in Rhine Basin has great impact on runoff reaching Lobith (Fig. 49).

Huisman, Cramer et al. (1998) 
Fig. 49
Retention in Rhine basin 

Within the
Netherlands water is stored in shallow reservoirs. Afsluitdijk and Detawerken created large reservoirs for watermanagement in The Netherlands.
They are primarily meant for safety, but serve more purposes. For example, the
Northern Delta basin serves fresh water supply and stop the inward push of salt
water. Rhine water now can be used for water demand around IJsselmeer and makes river IJssel navigable. IJsselmeer stores remaider of precipitation in winter
to meet the demand of agriculture in summer. Summer and winter water level in
the IJsselmeer is regulated by weirs in Afsluitdijk. Outlet waterways around
polders (boezem) serve as reservoirs as well.
Polders themselves have regulated water levels (polderpeil) as negative reservoirs with inlets
and outlets on boezem waters.
A water
reservoir has ‘useful storage’ (nuttige berging) S and ‘dead storage’ (dode berging) below discharge opening (Fig. 50).
The height
and width of a possible emergency overflow determines maximum capacity. Surface
A is largest there, so the extra (effective) storage slowing down high upstream
discharge avoiding floodings downstream can be substantial, be it not useful
for other purposes (Fig. 50).
The storage
of original river bed (dotted line in Fig.
50) is hardly part of effective storage, but nearly
fully part of artificial useful storage.

Akker
and Boomgaard (2001) 
Fig. 50
Terminology of reservoirs (example with barrage). 

When
surface A varies with height h storage S is not proportional to height. By
measuring surfaces on different heights A(h) you get an areaelevation curve (Fig. 51). The storage on any height S(h) (capacity curve) is
the sum of these layers or integral _{}.

Akker and Boomgaard (2001) 
Fig. 51 A(h) and S(h) 

Fig. 51 left below shows dead storage,
important to avoid fish mortality, ecological damage and stench. It
makes sedimentation possible without loss of useful storage.
The time
you can deliver a desired capacity (yield) can vary from days (distribution
reservoir with small storage) to years (large storage reservoir), dependent on instream. The
maximum yield during a normative dry period is called ‘save yield’. There is
always a possibility of dryer periods then normative. So, determining save
yield requires a probability approach.
The maximum
water delivery equals instream plus accepted decrease of useful storage minus
often substantial evaporation and leakage. Increasing fluctuation of instream
increases the necessity of useful storage; constant instream would make storage
superfluous.
The choice
of reservoir capacity depends on both desired delivery capacity and accepted
risk of incidental non delivery. Irrigation systems can stand larger risks (for example 20% of time delivery below design capacity) then much
more sensible urban water supply systems
You can simulate the working of a reservoir (‘operation study’) based on runoff data of daily
(small reservoirs), monthly (normal) or yearly (very large reservoirs)
intervals in the existing river. Do not restrict to ‘critical periods’ of low runoff. Long term runoff
series give a better reliability comparison of different capacities. Fig. 55 shows the cumulative sum of input
minus output (inclusive evaporation and leakage). The graph is divided in
intervals running from a peak to the next higher peak to start with the first
peak. For every interval the difference between the first peak and its lowest
level determines the required storage capacity of that interval. The highest
value obtained this way is the required reservoir capacity.

Akker
and Boomgaard (2001) 
Fig.
52 Determining necessary storage capacity 

In 1883
Rippl introduced the ‘Rippl diagram’ (Fig.
53) summing input minus evaporation and leakage into an
increasing line. The slope is proportional to the net input. Constant water
demand is represented by straight lines. You can move them until they touch the
ultimate points of the summing curve (A, B and C; in these points the
increasing useful storage changes into decrease). Exactly where the straight
line behind such a point crosses the curved one the reservoire is full again.
The maximum vertical distance between demand line and summing curve FG is the
required capacity. The vertical distance between two successive demand lines
(BH) is discharged by emergency overfow.



Akker
and Boomgaard (2001) 
Fig. 53 Rippl diagram 
Fig. 54
Exploitation
of a reservoir 


If demand
is not constant it becomes a curved line, but the analysis remains the same. In
that case you can move the demand line vertically only to keep time of supply
and demand the same.
A summing
curve can be used to determine water delivery at given capacity as well. Then
demand lines should be moved to a vertical distance not larger then that given
capacity and crossing the summing curve somewhere later otherwise the reservoir
will never be filed up again. The slope of the demand lines represents maximum
delivery in the period concerned.
Fig. 54 shows the exploitation of a
reservoir in a given period starting with a storage S_{0} in the
beginning of the first year. After some months the content decreases up to 0,
but a large input fills the reservoir completely. The arrow has the same length
as FG from Fig.
53. From this moment until delivery is
larger than input water is discharged by emergency overflow. The vertical distance between
input and tota output does not change as long as the reservoir is full. Then a
period of decrease and increase follow until the reservoir is full again. Fig. 54 shows an empty reservoir in F because capacity was
calculated by the difference of supply and demand in this point.
To keep
summing curves manageable for ever increasing large amounts of water in periods
long enough to be reliable you can subtract an average discharge. Then the
reduced summing curve fluctuates around a horizontal line rising when input is
larger then average and descending when smaller.
Before deciding for a
capacity often more detailed studies about leakage as a function of water level
and evaporation as a function of surface are made related to one or more
periods with available data. Computer models can test the usefulness of
different strategies.
A reservoir can be used for more purposes at once, but used only to avoid
floodings downstream it is called a retention reservoir. To avoid floodings you have to
take longer periods of high input then incidental peaks into account. A
retention reservoir should be as empty as possible if you expect a high water
wave. In that case you open discharge openings as soon as possible before the
expected wave comes to increase storage capacity and to postpone emergency
overflow as long as possible. Risk = probability x consequence. To estimate the
risk a reservoir can not store runoff long enough you need to know probability
distributions of daily discharge (Fig.
55 above), regular output as a function of water level
in the reservoir, and other factors like consequences of unverifiable overflow.
Akker
and Boomgaard (2001) 
Fig. 55 Probability distribution daily discharge and exceeding probability 

Fig. 55 below shows the accumulated
probability distribution. The dotted line shows 10% probability a discharge on
vertical axis is exceeded. In practice much smaller probabilities are used, for
instance 0.1%. Simply stated it corresponds 0.1 x 365/100 = 0.365 day per year » once per 3 year if you take a day as unbroken period.
Construction of reservoirs has environmental impacts. It requires space at the expense of original functions. Losses can not only be expressed in money. Landscape and nature have emotional or intrisic value as well. Weighting advantages and disadvantages is difficult, the more so because the intended function can not be guaranteed for 100% and side effects can not be predicted. For example the Assuan dam changed Nile delta substantially. Nile transports less slugdge. So, measurements against erosion of coast became necessary. Irrigation alongside Nile increased, but bilharzia disease dispersed in a large area as well.
The storage of water in the lower parts of The Netherlands will require heavy surface claims. The 4^{th} National Plan of watermanagement policy V&W V&W (1998) (stressing environment), and its last successor ‘Anders omgaan met water’ V&W (2000) (stressing security) mark a change from accent on a clean to a secure environment, just as the 4^{th} National Plan of environmental policy VROM (2001) compared with its predecessors[2]. Several floodings in The Netherlands and elsewhere in Europe has focused the attention on global warming and watermanagement. The future problems and proposed solutions are summarized in the figures below[3]. Storage is a central item reducing risks of lowlands.
In Fig. 56 above most left, global warming, in the figure right the ground descend of the western and northern part of the Netherlands are shown. Bottom most left, different scenarios of temperature increase, right of it, the expected increase of precipitation in winter and decilne in summer are shown. 

V&W (2000) 

Fig. 56
Expected problems 
Fig.
57 Strategies: 1 care, 2
store, 3 drain 


Water
management is recognisable everywhere in the lowlands.

Das (1993) 
Fig. 58 Lowlands with spots of
recognisable water management 

Civil
engineering offices are busy with many water management tasks (Fig. 59).




01 Water structuring 
02 Saving water 
03 Water supply and purificatien 
04 Waste water management 




05 Urban hydrology 
06 Sewerage 
07 Reuse of water 
08 High tide management 




09 Water management 
10 Biological management 
11 Wetlands 
12 Water quality management 




13 Bottom clearance 
14 Law and organisation 
15 Groundwater management 
16 Natural purification 
Das (1993) 

Fig. 59 Water managemant tasks in
lowlands 





The
Netherlands are covered by maps showing
the compartments governing their own watermanagement (Waterschappen), and their drainage areas (Fig. 60 above). Overlays show hydrological
measure points (Fig. 60 below left) and the supply of surface water (Fig. 60 below right).


Rijkswaterstaat (1985) 



Rijkswaterstaat
(1984) 
Rijkswaterstaat
(1984) 
Fig. 60 Hydrological maps of Delft and
environment. 


On the first map you can find the names of compartments, pumpingstations, windmills, sluices, locks, dams, culverts, water pipes.
Akker, C. v.
d. and M. E. Boomgaard (2001) Hydrologie (Delft) DUT Faculteit Civiele
Techniek en Geowetenschappen.
Das, R.
(1993) Integraal waterbeheer werken aan water (Deventer) Witteveen + Bosch.
Huisman, P.,
W. Cramer, et al., Eds. (1998)
Water in the Netherlands NHVspecial (Delft) NHV, Netherlands
Hydrological Society NUGI 672 ISBN
9080356522 URL Euro 20.
Rijkswaterstaat
(1984) Hydrologische waarnemingspunten Rotterdam  Oost 37 (Delft) Meetkundige
Dienst.
Rijkswaterstaat
(1984) Watervoorziening Rotterdam  Oost 37 (Delft) Meetkundige Dienst.
Rijkswaterstaat
(1985) Waterstaatskaart van Nederland Rotterdam  Oost 37 (Delft) Meetkundige
Dienst.
V&W, M.
v. (1998) Waterkader Vierde Nota waterhuishouding. Verkorte versie (Den
Haag) Ministerie V&W.
V&W, M.
v. (2000) Anders omgaan met water. Waterbeleid in de 21e eeuw. (Den
Haag) Ministerie van Verkeer en Waterstaat.
VROM, M. v.
(2001) Een Wereld en een Wil. Werken aan duurzaamheid.Nationaal
Milieubeleidsplan 4  samenvatting (Den Haag) Ministerie van
Volkshuisvesting, Ruimtelijke Ordening en Milieubeheer ISBN vrom 010294/h/0901.
Urban areas
need dry crawl spaces to keep unhealthy moist out of the buildings but they
need wet foundations as long as they are made of wood. Let us say
groundwaterlevel (recognisable from open water in the area) should stay at
least 1m below ground level (Fig.
61, Fig.
62).


(Paul van Eijk) 

Fig. 61
Flooding of a canal in Delft 
Fig. 62 Deep canal in Utrecht 


Grasslands may be wetter, dryland crops should be dryer then 1m below terrain (Fig. 63).

Ankum
(2003) page 53 
Fig. 63 Crop yields for different open water levels 

Lowlands
with drainage and flood control problems cover nearly 1mln km^{2} all
over the world (Fig. 64) and nearly half world population lives there because
of water shortage elsewhere (Rijkswaterstaat (1998;
Rijkswaterstaat (1998; Rijkswaterstaat (1998)).
x1000 km2 
1 crop 
2 crops 
3 crops 
Total 
North
America 
170 
210 
30 
400 
Centra
America 

20 
190 
210 
South
America 
60 
290 
1210 
1560 
Europe 
830 
50 

880 
Africa 

300 
1620 
1920 
South Asia 
10 
460 
580 
1050 
North and
Central Asia 
1650 
520 
20 
2190 
SouthEast
Africa 


530 
530 
Australia 

310 
120 
430 




9170 
Ankum (2003), page 2 

Fig. 64 Area of lowlands with drainage
and flood control problems 


Inhabitated
or agricultural areas below high tide river or sea level (polders) have to be
drained by one way sluices using sea tides or pumping stations (Fig. 65, Fig.
67), surrounded by belt canals (boezemkanalen), protected by dikes, made
accessible for shipping traffic by locks, internally drained by races (tochten), main ditches (weteringen), ditches (sloten), trenches (greppels), and pipe drains.

Ankum
(2003), page 78 
Fig. 65 Pumping stations in The
Netherlands 

Pumping in polders with different altitudes can be done at
once from the deepest part using gravity or in compartiments separated by dikes
and weirs saving potential energy (Fig. 67).




Huisman, Cramer et al.
(1998) page 36 ; Veer (?) 
Ankum (2003), page 76 and
55 
Fig. 66 Lowland system 
Fig. 67 Drainage by one to three pumping
stations, in earlier times by a ‘row of windmills’ (‘molengang’) 


Water is
drained by one way sluices (Fig.
68) at low tide or pumped up via belts (boezems) into the river or the sea.



Ankum
(2003), page 68 and 38 

Fig. 68 The oldest one way sluice found
in The Netherlands and its modern principle 


Fig. 69 shows the belt system of Delfland.

Ankum
(2003) page 62 
Fig. 69 The belt (‘boezem’) system of
Delfland 

One way
sluices lose purpose when average sea and river level raise and ground
level drops mainly because of the subsidence of peat polders (Fig. 70). Drying peat oxidates and disappears.

Ankum
(2003) page 71 
Fig. 70 Rising outside water levels and
dropping ground levels 

Polders are optimally drained by a regular pattern of ditches (Fig. 71, Fig.
72).


Ankum
(2003) page 42 and 82 

Fig. 71
Hachiro Gata
Polder in Japan 
Fig. 72 Wieringermeer polder (Kley 1969)



The
necessary distance L between smallest ditches or drain pipes is determined by precitipation q [m/24h], the maximally accepted
height h [m] of ground water above drainage basis between drains and by soil
characteristics.


Ankum
(2003) page 36 

Fig. 73 Variables
determining distance L between trenches 
Fig. 74 Variables
determining distance L between drain pipes 


Soil is characterised by its permeability k [m/24h].
Type of soil 
Permeability k in m/24h 

gravel 
>1000 

coarse sand with gravel 
100 
1000 
corse sand, frictured clay in new polders 
10 
100 
middle fine sand 
1 
10 
very fine sand 
0.2 
1 
sandy clay 
0.1 

peat, heavy clay 
0.01 

unripened clay 
0.00001 




Fig. 75 Typical
permeability of soil types 



A simple
formula is L=2Ö(2Kh/q).
If we accept h=0.4m and several times per year precipitation is 0.008m/24h,
supposing k=25m/24h the distance L between ditches is 100m. However, the
permeability differs per soil layer. To calculate such differences more precise
we need the Hooghoudt formula desribed by Ankum (2003) page 35.
However,
plot ditches are used as property boundaries and they determine agricultural
and urban practice. Any use has its own requirements for plot division. Systems
of plot division have to take dry infrastructure into account, combining different
network systems.

Ankum
(2003) page 59 
Fig. 76 Alternative systems of plot division in polders 

We will elaborate that in 1.5
There are
many types of water level regulators elaborated by Arends (1994) (Fig. 77, Fig.
78, Fig. 79).




Schotbalkstuw 
Schotbalkstuw met
wegklapbare aanslagstijl 
Naaldstuw 
Automatische klepstuw 




Dakstuw 
Dubbele
Stoneyschuif 
Wielschuif
rechtstreeks ondersteund door jukken 
Wielschuif via
losse stijlen ondersteund door jukken 
Arends
(1994) 



Fig. 77
Types of weirs 






Uitwateringssluis
open 
Uitwateringssluis
closed 
Inlaatsluis open 
Inlaatsluis closed 




Irrigatiesluis 
Ontlastsluis closed 
Ontlastsluis flooded 
Ontlastsluis open 




Keersluis 
Spuisluis 
Inundatiesluis (military) 
Damsluis
(military) 
Arends (1994) 



Fig. 78
Types of sluices 


To allow
accessibility of shipping traffic you need locks at every transition of water level.



Schutsluis 




Dubbelkerende
schutsluis 




Gekoppelde sluis 
Sluis met verbrede
kolk 
Bajonetsluis 



Tweelingsluis 
Schachtsluis 
Driewegsluis 
Arends,
G.J.(1994) Sluizen en stuwen (Delft) DUP Rijksdienst voor de Monumentenzorg 



Fig. 79
Types of locks 


Any regulator, culvert, sluice, lock or bridge requires a structure with entrance and exit of water needing space
themselves (Fig. 80).
Ankum (2003) page 164 

Fig. 80 Samples of the ‘entrance’ and ‘exit’ of a structure 

Floodings in 1953 caused the Delta Project, the greatest coastal protection
project of The Netherlands, (Fig.
81) showing many modern constructions.


Hettema
and Hormeijer (1986) 
Fig. 81
Delta project 

Ankum, P. v.
(2003) Polders en Hoogwaterbeheer. Polders, Drainage and Flood Control (Delft) Delft University of
Technology, Fac. Civiele Techniek en Geowetenschappen, Sectie Land en
Waterbeheer: 310.
Arends, G. J.
(1994) Sluizen en stuwen. De ontwikkeling van de sluis en stuwbouw in
Nederland tot 1940 (Delft) Delftse Universitaire Pers / Rijksdienst voor de
Monumentenzorg ISBN 9062757006.
Hettema, T.
and P. Hormeijer (1986) Nederland/Zeeland (Amsterdam) EuroBook Productions.
Huisman, P.,
W. Cramer, et al., Eds. (1998)
Water in the Netherlands NHVspecial (Delft) NHV, Netherlands
Hydrological Society NUGI 672 ISBN
9080356522 URL Euro 20.
Rijkswaterstaat (1998) "Delta's
of the World. 200th anniversary of Rijkswaterstaat" Land + Water 11
Rijkswaterstaat (1998) Summary
and Conclusions (SDD '98) International conference at the occasion of 200
year DirectorateGeneral for Public Works and Water Management, Conference
(Location) Delft University Press.
Rijkswaterstaat (1998) Sustainable
Development of Deltas (SDD '98) Inetrnational conference at the occasion of
200 year DirectorateGeneral for Public Works and Water Management, Conference
(Location) Delft University Press.
Veer, K. v.
d. (?) Nederland/Waterland (Amsterdam) Eurobook productions.
Although natural drainage follows a dendritic pattern, this is crossed by a predominantly orthogonal system of dry channels with similar hierarchical orders. For various reasons, there is a tendency for the artificial drainage of flat areas to be rectangular in shape. Because of this, the following considerations apply to both wet and dry networks. Fig. 82 shows a sequence of relationships between mesh lengthand width.in rectangular meshes with a net density of 2 km per km^{2.}



Hildebrandt
and Tromba (1989) 
Fig. 82
Length (L) and
width (W) of the mesh for a given net density of (D=2) 
Fig. 83 The
formation of right angles 


Length and
width of squares are 2/d.The same density also occurs in a pattern of
roads that go infinitely in one direction every 0.5 km. Thus, when the length
and width of the mesh 1/d = 0.5 km, the ratio between length and width is at
its limit. In that case, where the net density is 2 km per km^{2 }there can^{ }be no
‘crossroads’ any
more.
This
consideration only applies to an orthogonal system. The most efficient
enclosure is made by encircling the enclosed area with a minimum length of
road. As is well known, this is the circle, but in a continuous network, this
is approximated by a hexagonal system,. This minimal ratio between periphery
and area is demonstrated three dimensionally by very many natural phenomena
where preference is given to a minimal ratio between area and content[c].
A good example is a cluster of soap bubbles. A cluster of soap bubbles forced into a thin
layer produces a twodimensional variant. The bubbles arrange themselves in
polygons with an average of six angles. If one then pulls a thread through
them, the nearest bubbles will rearrange themselves again into an orthogonal
pattern (Fig. 52). Urban developments from radial to tangential can also be
interpreted against this background. The interlocal connections pull the radial
system straight, as it were. The additional demand for straight connections
over a distance longer than that between two side roads (called a ‘stretch’ here) introduces
rectangularity. Every deflection from the orthogonal system is then less
efficient.
This can be
clarified by engaging in a thought experiment: Imagine a rectangular framework
with hinged corners that is completely filled with marbles. If one reshapes
this framework into an ever narrower parallelogram, then there will be space
for fewer and fewer marbles, so, in every case, the rectangular shape proves to
be optimal, in this respect[d].

Fig. 84 Styling wet connections, where the density
is translated into nominal orthogonal mesh widths. 

The density
in the pattern of drainage ditches shown on a topographical map, gives one a global picture of the
soil types of that area. There are no ditches on sandy soils, whereas a wide mesh of ditches is a characteristic of clay soils and a fine mesh, of peaty soils (for examples, see Fig.
84). For convenience, the breadth of each watercourse is
fixed here at 1% of the equilateral mesh width.
This
difference is caused mainly by different vertical percolation of water k expressed in metres per twentyfour hours. That percolation is
slow in peat and clay (for example 20m/24h at average in the low West Holocene
of the Netherlands) and fast in rough sand (350m/24h in the higher East
Pleistocene of the Netherlands or sand raised town areas). Density d of lowest order ditches or brooks depends further from once a year
maximum precitipation N in metres per twentyfour hours (for example 0.007 m/24h or
0.008m/24h) and the difference between ditch level and ground water level in
the area between ditches or brooks h (for example 0.4m). Then, d(k,N,h)=250Ö(2N/kh) km/km^{2} (Fig. 85)

Peat 
Clay 
Sand 
Percolation
k [m/24h] 
6 
23 
280 
Precipitation
N [m/24h] 
0.007 
0.007 
0.008 
Waterlevel
between ditches h [m] 
0.4 
0.4 
0.4 
Network
density d [km/km^{2}] 
20 
10 
3 


Fig. 85
Network density
caused mainly by soil characteristic of percolation 


Mutually
crossings of waterways seldom separate their courses vertically (Fig. 86) as motorways do (Fig.
87).


Ankum (2003) page 160 
Standaard and Elmar (?) 
Fig. 86
Crossing of
separated waterways 
Fig. 87
Crossings of
highways 


More
often their water levels are separated by locks (Fig. 79) or become inaccessible for ships by weirs or
siphons.
However,
crossings between ways and waterways have to be separated vertically in full
function anyhow. And they often occur.




Fig.
88 Rivers, canals and brooks 
Fig. 89 Superposition races 
Fig.
90 Interference with highways 
Fig.
91 Interference with highways and railways 




When one
lays different networks over each other, an interference occurs that
defines the number of crossings, and, because of this, the level of
investment in civil engineering constructions (Fig. 92).

Fig. 92 Interference between wet and dry networks. 

The
position of urban areas with respect to orders of magnitude of water and roads
dictates their character to a large extent. The elongation (stretching) of
networks reduces the need for engineering constructions when their meshes
lie in the same direction. If one bundles them together, this also helps to
prevent fragmentation. The aim of the ‘dual network
strategy’, on the other hand, is to position
water, as a ‘green network’, as far way as possible from the
roads (in an alternating manner). However, this has the effect of increasing fragmentation.
Fig. 93 shows how different dry and
wet networks in different orders cause crossings of different kinds.



Jong (2001) 
Fig. 93 Interference of dry and wet
networks in different orders causing crossings of different kinds 



Trenches
and ditches become drains or underneath roads culverts in the urban area, but
main ditches (3m wide), races (10m) and canals (30m) have to be crossed by bridges. From 9 different kinds of crossing
Fig. 93 counts 6 types (Fig.
94).

neigbourhood streets (10m wide) 
district roads (20m wide) 
city highways (30m wide) 
main
ditches (10m wide) 
2 

1 
races
(30m wide) 
3 
1 

canals
(100m wide) 
2 

1 




Fig. 94 Five types of crossings supposed
in Fig. 93 





Especially
when the canal is a belt canal with a higher level then the other waterways many complications
arise. Extra space is needed for weirs, dikes and sluices, perhaps even locks
and many slopes not useful for building. The slope the city highway gets from
crossing the high belt canal could force to make a tunnel instead of a bridge.
Anyhow, several expensive bridges will be necessary and some of them will be
dropped from the budget, causing traffic dilemmas elsewhere.


Fig. 95 Neighbourhood street crossing
canal and railroad in Utrecht 

The
slope behind the bridge in Fig.
95 is not steep enough to get a tunnel under the railway
high enough for public transport (2.60m is too low).
based on pressure 
or 
draw 



arch bridge (boogbrug) approach ramp(aanbrug) thrust (horizontale druk) deck (rijvloer) trussed arch with upper and lower chord (vakwerkboog boog met boven en onderrrand) abutment (landhoofd) 
beam bridge (balk of liggerbrug) abutment (landhoofd) overpass, underpass (bovenkruising, onderdoorgang) deck (brugdek) continuous beam (doorgaande ligger) pier (pijler) parapet (leuning) 
suspension
bridge (hangbrug) anchorage
block (ankerblok) suspension cable (hangkabel) suspender (hanger) deck (rijvloer) center span (middenoverspanning) tower (toren) side span (zijoverspanning) abutment (landhoofd) 



trough arch bridge (boogbrug met laaggelegen rijvloer) 
multiple span beam bridge (balk of liggerbrug met meer overspanningen) 
fan cable stayed bridge (waaiertuibrug) cable stay anchorage (tuiverankering) 



halfthrough arch bridge (boogbrug met
tussengelegen rijvloer) 
viaduct 
harp cable stayed bridge (harptuibrug) 



deck arch bridge (boogbrug met hooggelegen rijvloer) 
cantilever bridge (kraagliggerbrug, cantileverbrug) suspended span (zwevend brugdeel) cantilever span (uitkragende zijoverspanning) 
transporter bridge (zweefbrug) trolley (wagen) platform (platform) 



fixed twohinged threehinged arch (ingeklemde, tweescharnier~,
driescharnierboog) 
singleleaf bascule bridge (enkele basculebrug) counterweight (contragewicht) 
lift bridge (hefbrug) guiding tower (heftoren) lift span (val) 



portal bridge (schoorbrug) portal frame (portaal) pier (pijler) 
doubleleaf bascule bridge (dubbele
basculebrug) 
floating bridge (pontonbrug) manrope (mantouw) pontoon (ponton) 




Bailey bridge (baileybrug) 
swing
bridge (draaibrug) 
Standaard
and Elmar (?) 

Fig.
96 Names of Bridges and their components 


These types
of bridges could be made of steel, concrete or wood. Depending on the material
they have a different maximum span (fig. 97).
english name 
dutch name 
span in m. 
notes 

multiple span
beam bridge 
balk liggerbrug
met meer overspanningen 
unlimited 


viaduct 
viaduct 
unlimited 
oldfashioned 

ferry bridge 
pontbrug 
unlimited 


suspension bridge 
hangbrug 
2000 
windsensitive 

fan cable stayed
bridge 
waaiertuibrug 
1000 
windsensitive 

harp cable stayed
bridge 
harptuibrug 
1000 
windsensitive 

cantilever bridge 
kraagliggerbrug,
Gerberligger 
550 


arch bridge 
boogbrug 
500 
steel 

trough arch
bridge 
boogbrug met
laaggelegen rijvloer 
500 
? with draw
connection 

fixed twohinged
threehinged arch 
ingeklemde,
tweeschanier, driescharnierboog 
500 
? with draw
connection 

halfthrough arch
bridge 
boogbrug met
tussengelegen rijvloer 
500 
? 

deck arch bridge 
boogbrug met
hooggelegen rijvloer 
500 
? 

beam bridge 
balk of
liggerbrug 
250 
steel truss,
framework 

arch bridge 
boogbrug 
200 
stiffened bars 
