Designing of a hydrological rainfall-runoff scale model · 2017. 1. 2. · rainfall-runoff models...

Internship report

Designing of a hydrological rainfall-runoff scale model

Author : Edouard COUSSY

Supervisor : Mr Willem Luxemburg

General presentation

I realized this project in the end of my second year of my engineering school of water

management and the environment in Strasbourg. It means for your scholar system that I am in

the 4th year of MEng degree. In my school, each student leaves in May the school to realize

an internship abroad.

So I choose to work in the water resources section of the civil engineering faculty of Delft. I

was interested by the subject because it deals with pedagogical purposes and it is a practical

work also.

I would like to give thanks particular at Willem Luxemburg, Sander de Vree for his great help

and all the staff from Water resources section for the cordial welcome.

Contents

Introduction ................................................................................................................................ 4

Theory ........................................................................................................................................ 5

Rainfall-Runoff process ......................................................................................................... 5

Overview of rainfall-runoff process ................................................................................... 5

Theory for modelling runoff flow and groundwater flow .................................................. 6

Hydrograph analysis: factors influencing the shape............................................................... 8

Influence of rainfall ............................................................................................................ 8

Influence of topographic and geologic characteristics: ...................................................... 9

Methodology: ............................................................................................................................. 9

Problem statement .................................................................................................................. 9

The rectangular shape is a good idea because for this shape, time of concentration is

higher than for a semi-circle (refer Influence of topographic and geologic

characteristics). ................................................................................................................. 10

Material test .......................................................................................................................... 10

Rainfall simulator ............................................................................................................. 10

Material for runoff ............................................................................................................ 12

Material for groundwater flow ......................................................................................... 13

Device to measure flow: ................................................................................................... 15

Design ................................................................................................................................... 17

Size of the scale model ..................................................................................................... 17

Rainfall generator ............................................................................................................. 18

Measure of discharge ....................................................................................................... 20

Results ...................................................................................................................................... 21

Discussion ................................................................................................................................ 32

Modelling ................................................................................................................................. 33

Introduction

The application of a hydrological rainfall-runoff scale model helps to illustrate hydrological

processes better than a theoretical example on a black board. For this reason a first version of

physical hydrological scale model was designed and built. The goal will be to build a second

version which it is possible to move to be used for practical lectures and for demonstrating in

lectures of the first year of bachelor.

The objective of the scale model is firstly to show the basic concepts of rainfall-runoff like

time of concentration and to show that rainfall duration, slope and infiltration influence the

shape of the hydrograph. The other aspect is to show the separation between the overland

flow and the groundwater flow to see the delay between the both and the different

contribution of the both in a river. Moreover, such a scale model can show basic model of

rainfall-runoff relationships like rational method or unit hydrograph method or reservoir

method.

To realize such a scale model, the first issue was to find proper materials to show concepts

that happen in real scale in days in a few minutes. The second part was to check by

experiments the set-up and to discuss about results.

Theory

The theory behind the scale model is about rainfall-runoff processes. So this part is a quick

overview of generation of runoff, interflow and groundwater flow with a presentation of

rainfall-runoff models like rational method, unit hydrograph method.

Rainfall-Runoff process

Overview of rainfall-runoff process

When a rainfall event happens, it occurs firstly interception by vegetation, evaporation and

infiltration in soil and when infiltration capacity is lower than rainfall intensity, it generates

runoff. Rainfall that produces runoff is called net rainfall. The surface runoff component

consists of water that flows overland until a river. During a storm runoff is the most

component part of a hydrograph. Figure 1 shows this.

Figure 1: Component of a hydrograph

A hydrograph definition to explain what this figures shows (from Lectures Notes of

prof.dr.ir.H.H.G Savenije):

A hydrograph is the graphical representation of the discharge of a stream plotted with time. It

includes the integrated contribution from surface runoff, groundwater seepage, drainage and

channel precipitation. The shape of a hydrograph of a single storm occurring over the

drainage area follows a general pattern. This pattern shows a period of rise that culminates in

a peak, followed by a period of decreasing discharge (called recession).

This figure shows also two other components:

-subsurface flow

-groundwater flow

In general, river has a certain amount of base flow during all the time, that is to say that

groundwater contributes of discharge in the river.

Subsurface flow is considered like a part of direct runoff. It disappears with overland flow.

This figure also shows different hydrograph time:

- The rising time is the time to peak between the beginning of the runoff and the peak flow.

- The base time is the duration of runoff.

- The lag time is the time interval from the maximum rainfall rate to the peak rate of runoff.

- The time of concentration (tc) is the time between the end of net rainfall and the end of

runoff.

Time of concentration is also the time required for the farthest point to contribute runoff. And

when a net rainfall duration equal this time, the runoff is constant due to the fact all the basin

contributes to runoff.

Figure 2: Runoff from uniform rainfall in the Rational Method

It’s the assumption of rational method describe in the following part.

Theory for modelling runoff flow and groundwater flow

In this part, a quick overview of different simple model of runoff and groundwater flow is

presented.

Runoff flow modelling

Rational method

Conditions required:

- Rainfall has a uniform distribution (in space and in time)

- Rainfall intensity is constant during time of concentration

When rainfall duration exceeds the time of concentration of a basin, the flow in the channel is

constant from time of concentration until the end of the rainfall. And it assumes that the

runoff flow is:

Q=C.i.A

Where C is the runoff coefficient, i the rainfall intensity and A the area.

Unit hydrograph method

Unit hydrograph assumes that relationships are linear and constant in time. A unit hydrograph

is the hydrograph of only runoff component obtained by a unit amount of net rainfall during

unit duration.

As it deals only with runoff, a separation of hydrograph is required.

Figure 3: basic separation of base flow

Separate a hydrograph is not easy because groundwater characteristics are always missing.

The linearity assumes that if a rainfall event happens during a double time than the unit

hydrograph, the simulated hydrograph is obtained:

1st: in plotting two unit hydrographs with a time interval equal duration of unit hydrograph

2nd

: summing the two unit hydrograph to have the simulated hydrograph

To obtain a unit hydrograph, there are conditions:

-Duration of rainfall event is about 10 or 20% of time of concentration

-A suitable number of storms are needed

-Rainfall has a uniform spatial distribution over the entire basin and during the period of

rainfall

-Rainfall events occurs individually

Groundwater flow modelling

Reservoir method

Reservoir method is a common model to simulate groundwater flow. It can be used also for

overland flow.

Reservoir method assumes that ground behaviour is like drainage of reservoir. So there is a

relation between groundwater flow Q and storage S in the aquifer:

Q=K.S

Where Q is the discharge in m3/s, K a constant in s

-1 and S the storage in m

3.

K is obtained with depletion curve (refer to figure 1 to see depletion curve from groundwater

flow).

K depends on slope i.

So we can also write:

Q=K(i).S

In applied an exponential trend line on the depletion curve, K value is obtained

Q=constant*exp(-Kt)

After it is possible to simulate a hydrograph with the following method:

With balance equation:

I-Q=S

Where I is the rainfall (input), Q is discharge and S is storage.

The following equation is obtained with a increment time of dt:

S2= S1+dt*(I-K*S1)

Discharge is obtained step by step.

All of these models can be applied with this scale model:

-Rational method in applying a rainfall as long enough

-Unit hydrograph by separating overland flow and groundwater flow.

-Reservoir method in applying a trend line from depletion curve with excel for each slope.

Hydrograph analysis: factors influencing the shape

The relation between precipitation and runoff is influenced by various storm and basin

characteristics. So the effect of these parameters can be showed with a hydrograph. So in this

part, factor influencing the shape of the hydrograph are listed.

Influence of rainfall

Rainfall intensity

For a given rainfall duration, an increase in intensity will increase the peak discharge and the

runoff volume.

Rainfall duration

For a given rainfall intensity, the rainfall duration determines the peak flow and the duration

of runoff. If we put a storm long enough, all the precipitation will become runoff. Between the

beginning of surface runoff and the time when the discharge becomes constant is called time

of concentration.

Distribution of rainfall on the basin

The area distribution of rainfall can cause variations in hydrograph shape. If an area of high

rainfall is near to the basin outlet, a rapid rise, sharp peak and rapid recession of the

hydrograph usually result. If a larger amount of rainfall occurs in the upper reaches of a basin,

the hydrograph exhibits a lower and broader peak.

Direction of storm movement

Storm direction has the highest effect on elongated catchments. Storms that move upstream

tend to produce lower peaks of a longer duration than storms that move downstream.

Influence of topographic and geologic characteristics:

Size

The major effect of increasing the drainage area on the hydrograph shape is that the time base

of the hydrograph is lengthened.

Catchment shape

For a same area, rectangular or a semi-circle or cone shapes don’t give the same hydrograph.

The rectangular one that it is the most elongated delay the flow. So the time to peak is longer

than for the others shapes.

Slope

Time of concentration and time to peak is influenced by the slope. Shorter time is observed

with higher slope.

Among these parameters the following ones can be showed:

-Rainfall duration

-Slope

-Direction of storm movement (not realized)

-Rainfall distribution (not realized)

Methodology:

This part deals with issues of building such a scale model and explains the methodology to

design. Then results are presented and discussed in the following parts.

Problem statement

The first objective is to create a basin that it is possible to move everywhere, in particular in

lectures room. So the area of the basin will be about 1-2m². The second objective is the

experiment duration. It has not to take too much time because it will also use during lectures,

but also not a too small time because another problem appears: the limit time to record a

discharge.

So creating such a scale model implies to answer these questions:

- Homogeneous rainfall is required to show the concepts. Which kind of rainfall

simulator should be used?

- What are the proper materials to create overland flow and groundwater flow and

separate flows?

- What is the best way to measure discharges?

For example the first quick design is described in the following paragraph:

Rainfall could be creates by a shower. The basin could be rectangular with on the top a board

with holes. It should create runoff and holes create infiltration. This first board should be

covered by an artificial grass to delay runoff. A second board below the first one should

represent the groundwater flow. The runoff is collected in an open drain at the bottom of the

slope. A small discharge structure like a weir is required. The level is recorded in the drain

automatically with a pressure sensor. With the water level, it is possible to get discharges.

The rectangular shape is a good idea because for this shape, time of concentration is higher

than for a semi-circle (refer Influence of topographic and geologic characteristics).

Material test

Rainfall simulator

A homogeneous rainfall distribution is a prerequisite for the demonstration and application of

different techniques. Indeed it’s the assumption of rational method, unit hydrograph.

Moreover

Materials tested:

- Shower hand: Homogeneous rainfall but the intensity of rainfall is too high

- Tubes with different holes: flexible tube, PVC tube with piece of cloth.

Figure 4: Tubes with different hole

Different problems appear:

- Tube 2 and 3 are not ideal and create a straight spray

- Tube 1 is better than 3. In case 3, water reacts like it crosses a circle hole. In the case

1, water “falls” and sprays. But it is not the ideal.

- Tube 4 creates either a straight spray when pressure is high or a drop per drop when

the pressure is low.

Each hole is different. An identical setup, facilitating openings in the tube, to achieve

homogeneous rainfall distribution appears not to be feasible.

It’s too difficult to build oneself a good rainfall simulator by this way.

- Sprinklers:

Different sprinklers were obtained.

Figure 5: photo of sprinklers

It doesn’t spray in the middle, it creates just a circle.

This following sprinkler creates a full cone jet.

Figure 6: Photo of the full cone jet sprinkler

I test one sprinkler to determine homogeneously and discharge. There are three parameters to

consider:

- Water pressure that it is possible to check with a manometer

- Spray height

- Homogeneously and coverage area.

Refer to Appendix 1: Test of the full cone jet sprinkler

Conclusion:

- Spray distribution is bad in general.

-Without a pressure regulator, it’s not possible to get different discharge. So only the full

opened valve position is possible that is to say for 6 bar, the pressure required to get the better

homogeneously.

- Steady state is obtained for a full opened valve position in 2 or 3 seconds. When valve is

closing, sprinklers doesn’t sprays significantly after 5 seconds. So it is possible to apply

rainfall duration of 20 seconds at the minimum.

-A discharge above 1 m² is about 3200ml/min (about 50ml/s) for 10 sprinklers

Better sprinkler and a pressure regulator were ordered from ispray system. But unfortunately

nozzles didn’t arrive on time. So it has never been tested but results from Utrecht University

for the same type of nozzle are available.

Refer to Appendix 2: Full square jet nozzle

Material for runoff

The first layer would be the part that generates surface runoff. The minimum duration of

rainfall is 20 seconds. A rainfall of 20, 40, 60, 80 seconds will generate. The time of

concentration should be more than 80 seconds to see a hydrograph that rises and falls and not

a constant. With longer rainfall the runoff will become constant. Therefore the rainfall should

not flow to fast from the board.

So a simple wooden or plastic plate would not be sufficient. Artificial grass that keep the

water and delays flow due to its rough surface.

Test results:

A rectangular artificial grass of 2m by 60cm glued on a wood plate was tested.

Test of artificial grass with a slope of 18%:

hydrograph

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The time of concentration is 100 seconds for a slope of 18%. Time of concentration is higher

for low slope. For 10% time of concentration is 250 seconds.

So it is possible to reduce the length of the artificial grass.

Time base will be also important to improve the measurement of the discharge (filter signal

from the water level height).

Time base rainfall duration

time base

20 80

40 110

80 130

100 160

So time base is about 100 seconds.

Artificial grass is really interesting because this material is completely pervious. So it is

possible to control runoff coefficient in gluing a part of the area.

Material for groundwater flow

The second layer imitates the groundwater flow. Second layer has the same size that the first

layer. It will be contained in a box. The thickness of the layer will be about 10cm.

Condition required for the second layer:

- Saturation of the total cross sectional area is not desired because soil will swim and

goes out.

- Reaction of the second must be observed at the same time than first layer that is to say

for rainfall of 20, 40, 60, 80 seconds

- Second layer must be enough light to be able to change the slope with a simple

mechanism.

Lists of material that has been taken into consideration:

Natural material:

-sand

-coarse

Two different kind of coarse-sand was tested: 1-2mm and 2-4mm. The test was to check

permeability with a permeability device.

Figure 7: photo of the experiment

Permeability indicates the speed of the water flow when soil is saturated like in an aquifer.

But in the scale model, there is no aquifer. So permeability is just an indication.

Table: test of permeability:

type of soil Permeability in cm/s

coarse 1-2 mm 1.2

coarse 2-4 mm 3.4

Artificial material:

-porous balls: Cinematic porosity is about 80%.

-polyester balls. Polyester balls swim.

-isolated material. It doesn’t absorb water.

Test results:

The advantage of artificial material is its weight. A disadvantage is its fast response for

porous balls. Isolated material is too impervious.

Mix of sand-coarse and porous balls:

Table: test of permeability:

type of soil permeability in cm/s

mix coarse 1-2 mm and porous balls (50%-50%) 0.8

mix coarse 2-4 mm and porous balls (50%-50%) 3.2

Figure 8: photo of 1-2mm coarse-sand (left) and mix with porous balls 50-50% (right)

According to these tests only coarse and porous balls will be considered.

To know if soil will swim or not, Darcy law must be used.

Darcy law gives the discharge in function of the slope and the surface:

Q=K.i.S

Where K is the permeability in cm/s, i the slope and S the total cross-sectional area.

Table: theoretical discharge according to Darcy law: (size of the second layer is described

below the table)

type of soil permeability in cm/s Q ml/s

coarse 1-2 mm 1.2 72

coarse 2-4 mm 3.4 204

mix coarse 1-2 mm and porous balls (50%-50%) 0.8 48

mix coarse 2-4 mm and porous balls (50%-50%) 3.2 192

Figure 9: drawing of the second layer

Conclusion of the test:

Porous balls decrease permeability. Due to high porosity, it delays water flow. Permeability is

about cm/s for all the cases. So when the soil is saturated, time to get steady state is about 100

seconds. Making a mix of 50-50 coarse and porous balls has the advantage to light the layer

and slow the flow. The density is about 1.08. So weight will be about 50-100kg. Discharges

according Darcy law are at worst 48ml/s, so smaller than the capacity of rainfall generator

with 10 sprinklers.

Device to measure flow:

The fluctuation of the discharge is between 0ml/s and 50ml/s in a time of 100 seconds.

Accuracy required is 1ml/s. So we need an accurate system measuring the discharge. The

most frequently device used to measure a discharge in an open channel is a weir.

Weirs

Different types of weirs exist

A thin weir is more suitable than a broad weir. So a V-notch or a rectangular compressed

notch is more suitable.

Figure 10: Example of a V-notch

But prediction of the relation Q=f(H) is not possible because formula that it’s given in books

are true for real channel, that is to say for big channel at least a width of 90cm. It implies to

build several weirs and calibrate it.

Water level in the weir will be varied from 0cm until 10cm. Water levels could be measured

by a pressure sensor.

Refer to Appendix 3: Test of a pressure sensor and program

The problem with a pressure sensor is it’s not enough accurate. And the other problem is

where the water level is measured. Flow should be undisturbed by the weir or by the water

fall. So the sensor should be installed enough far from waterfall.

Since this methodology appeared to be to costly and time consuming, simpler methods needed

to be considered.

Measure the rising level in a bucket:

Wave height meter and float gauge

Figure 11: Wave height meter and float gauge.

The accuracy of these devices is about µm and a sample frequency higher than 1 Hz. They

can measure the water level with a wide range of 50cm at least. So it’s possible to measure a

discharge of 1ml/s in a bucket with an area about 1000cm² and with a height of 50cm at the

maximum. So volume of the bucket can be 50L. It is interesting because it is possible to

realize 20 minutes of experiments at least (with a discharge of 10 sprinklers).

Refer to Appendix 4: Wave height meter and float gauge

Pressure sensor:

A hole is required in the bottom of the bucket. It’s complicated and accuracy is about 0.5 cm.

So to measure 1ml/s, it is required to have a tube with an area of 2cm². This is not possible.

Design

Size of the scale model

A box with the following dimension was built:

Length: 125cm

Width: 57cm

Height: 13cm

The box is comply full of a mix coarse-porous balls 50-50%. This layer is the second layer. It

represents groundwater flow.

Weight is about 100kg. To change the slope a table like in figure was used:

Figure 12: photo of the table to change the slope

The box is covered by a rectangular piece of artificial grass. This layer is the first layer and it

represents the runoff. Two plates of 15cm are glued above the artificial grass.

Figure 13: photo of the plates in wood.

So impervious coefficient is about 53%

Five pieces of wood are available for the rainfall generator. But only 4 are useful as it is

explained in the following part.

Rainfall generator

The goal is to find the best way to create a homogeneous rainfall above the artificial grass.

So the test of one sprinkler is considered and two simulations are proposed.

Distribution of cups

Results for 60cm and 6 bar in gram

Figure 14: on the left: cups number, 1 is the place of the sprinkler, on the right, results in gram

for 60 cm and 6 bar (valve completely opened).

Simulation 1:

Figure 15: simulation 1, on the left distribution of the 8 sprinklers, on the right, theory results.

Standard deviation for all spray area is 15. Dry area doesn’t spread too much.

Simulation 2:

Figure 16: simulation 2, on the left distribution of the 12 sprinklers, on the right, theory

results.

Figure 17: Standard deviation for simulation 2

Standard deviation in simulation 2 is not so better than in simulation 1. There are two

possibilities: green version or red version. We have a big dry area (in red) or a big loss area

(in green). So it’s not the ideal way to distribute sprinkler.

So simulation 1 is chosen to build the rainfall simulator.

Experiment results:

Figure 18: On the left: distribution of cups (1->21 circles) between sprinklers (x)

On the right: discharge for each sprinkler.

The average for all cups of standard deviation is 10. Total discharge: 2800ml/min

approximately.

Measure of discharge

In fact, measuring the discharge is a real problem. Due to the fact, device are really sensitive

to wave, funnels are required to get an undisturbed water level.

Figure 19: Photo of funnels for artificial grass with the wave height meter in the white bucket

(on the left) and for groundwater flow with the float gauge in the yellow bucket (on the right)

Figure 20: discharge drop per drop without funnel (on the right) and discharge drop per drop

with funnel (on the left)

Moreover, this first filter is not enough. The signal is completely perturbed with funnel.

Waves are produced by water fall.

Numerical filter is required to get a smooth discharge.

Refer to Appendix 5: Presentation of Dasy Lab and explanation of numerical filters

Conclusion:

It is possible to get the discharge in ml/sec. Discharge is converted in ml/min just to present

result with the same unit than rainfall.

Results

In this part, results from different rainfall duration and different slope are presented.

Experiments:

With this scale model it is possible to change slope and rainfall duration.

So 4 slopes (4%, 8%, 12%, 16%) and 4 rainfall duration (20, 40, 60, 80 seconds) was tested

and for each slope.

Wet condition (for all slopes)

Dry condition is a dry artificial grass and a not real dry coarse but there is no drop. An

overnight separated each dry experiment.

Wet condition is realized with a artificial grass completely wet and a discharge of

groundwater flow of 200ml/min.

“Runoff” is for the discharge from the artificial grass

“Groundwater flow” is for the discharge from coarse.

Rainfall discharge is in reality always the same (1870ml/min). It is not 2800ml/min like the

total discharge of 8 sprinklers because it doesn’t spray only on the carpet. So there is

930ml/min loss.

It was determined with a rainfall of 1000 seconds

Discharge for Runoff+Groudwater flow

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Rainfall

Figure 21: Hydrograph for the both layers for a rainfall of 1000 seconds.

Results come from experiments:

For each slope:

1 rainfall event of 800-1000 seconds -> steady state.

5 rainfall events of 20 seconds (for unit hydrograph)

2 rainfall event of 40, 60, 80 seconds

Thus we can see if experiments can be repeated several times without problems:

Above, results for 8%:

5 Hydrographs for 20 seconds

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Figure 22: results for 20, 40, 60 seconds

Hydrograph

Result for each slope:

Rainfall is plot with a different discharge for each time to be able to see something.

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min

20

40

60

80

rainfall 20

rainfall 40

rainfall 60

rainfall 80

Figure 23: Runoff and groundwater flow hydrograph separated for each slope and for rainfall

duration of 20, 40, 60, 80 seconds.

Comments:

-The rising limb (from 0 to about 150ml/min) for groundwater flow is due to the filter delay

of 60 seconds. That is the reason that rainfall start always at 63 or 65 seconds.

-Groundwater flow doesn’t react with a rainfall of 20 seconds. It starts to react with 40

seconds.

-Time to peak increases with rainfall duration.

-Rising limb for runoff follows exactly the same pattern for each rainfall time (20, 40, 60, 80

seconds) but recession curve is different for each case.

-Perturbations in the hydrograph come from the numerical filter and it’s not a reaction from

the artificial grass.

-Smooth curve are obtained for 8%. There is no explanation for that all the results with 8%

gives a smooth curve.

Result for each rainfall duration

Discharge for 20 seconds

-100

0

100

200

300

400

500

600

700

0 50 100 150 200 250 300 350 400

time in seconds

dis

ch

arg

e i

n m

l/m

in

0

200

400

600

800

1000

1200

1400

1600

1800

2000

grass+coarse 4

grass+coarse 8

grass+coarse 12

grass+coarse 15

coarse 4

coarse 8

coarse 12

coarse 15

rainfall


-200

0

200

400

600

800

1000

0 100 200 300 400 500 600

time in seconds

dis

ch

arg

e i

n m

l/m

in

0

200

400

600

800

1000

1200

1400

1600

1800

2000

rain

fall

in

ml/

min

grass+coarse 4

grass+coarse 8

grass+coarse 12

grass+coarse 15

coarse 4

coarse 8

coarse 12

coarse 15

rainfall


-500

0

500

1000

1500

2000

0 50 100 150 200 250 300 350 400

time in seconds

dis

ch

arg

e i

n m

l/m

in

grass+coarse 4

grass+coarse 8

grass+coarse 12

grass+coarse 15

coarse 4

coarse 8

coarse 12

coarse 15

rainfall


-200

0

200

400

600

800

1000

1200

1400

0 50 100 150 200 250 300 350 400

time in seconds

Dis

ch

arg

e i

n m

l/m

in

0

200

400

600

800

1000

1200

1400

1600

1800

2000

rainfall in ml/min

grass+coarse 4

grass+coarse 8

grass+coarse 12

grass+coarse 15

coarse 4

coarse 8

coarse 12

coarse 15

rainfall

Figure 24: Hydrograph, coarse (groundwater flow) and artificial grass+coarse (groundwater

flow+runoff) for each rainfall duration.

Comments:

-Curve “coarse 15%” is below the others curves because I start with a groundwater discharge

of 180ml/min and not 260ml/min

-Time to peak (for runoff) for rainfall of 20 seconds and 40 seconds increases with the slope.

-Time to peak (for runoff) for rainfall of 60 seconds and 80 seconds decreases with the slope.

Exploitation

In this part, evolution of time of concentration is presented and also infiltration.

-Time of concentration

Time of concentration

0

20

40

60

80

100

120

140

160

180

200

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

Slope

Tim

e i

n s

eco

nd

s

Time of concentration

Figure 25: Time of concentration in function of the time

Time of concentration decreases with the slope.

-Infiltred volume

Runoff volume and infiltred volume are known with the voltage (voltage at the beginning of

the experiment and voltage et the end of the experiment gives the volume of runoff, infiltred

volume is Rainfall volume minus Runoff volume).

Infiltred volume for each rainfall duration: 20,40,60,80 seconds

0

200

400

600

800

1000

1200

1400

1600

1800

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

slope

Vo

lum

e i

n m

l

infiltred volume for 20 seconds




Figure 26: Infiltred volume for each rainfall duration: 20,40,60,80 seconds.

Infiltred volume increases with the rainfall duration and decreases with the slope.

-Infiltration ratio: Infiltration ratio is equal:

Infiltration ratio= Infiltred volume/Rainfall volume

Infiltration ratio for 4%

0

10

20

30

40

50

60

70

0 200 400 600 800 1000 1200

Rainfall duration in seconds

% o

f in

filt

rate

d v

olu

me

coefficient d'infiltraton


40

41

42

43

44

45

46

47

48

0 200 400 600 800 1000 1200


% v

olu

me i

nfi

ltre

d

coefficient d'infiltration


0

10

20

30

40

50

60

0 100 200 300 400 500 600 700 800 900


% i

nfi

ltre

d v

olu

me

coefficient d'infiltration


0

10

20

30

40

50

60

0 100 200 300 400 500 600 700 800 900


% f

ilte

red

vo

lum

e


Figure 27: Infiltration ratio for 20, 40, 60, 80 and more than 800 seconds and for each slope.

Infiltration ratio increases with rainfall duration. So there is interception at the beginning of

the rain and after a constant infiltration ratio is obtained with 60 seconds or 80 seconds. Case

4% and 12% shows this perfectly. So there is no more interception from 60 seconds.

Discussion

Water start to be intercepted by artificial grass and flows and after infiltrate the carpet. Figure

below shows this phenomenon. This explain why time to peak (for runoff) for rainfall of 20

seconds and 40 seconds increases with the slope and time to peak (for runoff) for rainfall of

60 seconds and 80 seconds decreases with the slope.

Figure 28: Interception by artificial grass and quick runoff

Modelling

In this part, a quick view of possibility of modelling the scale model. This work should be

considered and show the possibility of creating a practical lectures for students.

-Unit hydrograph:

The unit hydrograph considered is results from 20 seconds. 20 seconds represents 600mL

above 0.75 m². So it represents 0.8mm/m². Indeed, experiment was realized with wet

conditions. So rainfall is net rainfall (without infiltration above the impervious part)

Results:

-100

0

100

200

300

400

500

600

700

0 50 100 150 200 250 300 350 400

40 sec simulation

40 sec original

-100

0

100

200

300

400

500

600

700

800

900

0 50 100 150 200 250 300 350 400

60 sec simulation

60 sec original

-200

0

200

400

600

800

1000

0 50 100 150 200 250 300 350 400

80 sec simulation

80 sec original

Figure 29: Simulated hydrograph and original hydrograph for rainfall duration of 40, 60, 80

seconds.

So unit hydrograph doesn’t work for 60 seconds and 80 seconds because it is not 60 or 80

seconds of net rainfall but less. As it was explained, interception with runoff start firstly and

after with a longer rainfall duration, infiltration appears in the impervious part.

So a filter function is required to correct unit hydrograph

-Reservoir method:

A cascade of reservoir is proposed:

Figure 30: Cascade of reservoirs for reservoir method

Parameters like k value or dz could be calibrated by students with the original hydrographs.

(original hydrograph doing by themselves).

K values are obtained with the recession curve.

Following table presents k value for runoff and groundwater flow.

Table: k value for artificial grass in function of the slope

Artificial grass

slope K value in s-1

0.04 0.010

0.08 0.018

0.12 0.024

0.16 0.0249

Coarse

slope K value in s-1

0.04 0.0025

0.08 0.0035

0.12 0.0030

0.16 0.0038

k value for artificial grass

y = 0.1744x + 0.0033

R2 = 0.9939

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

slope

k v

alu

e i

n 1

/s

K VALUE

Linéaire (K VALUE)

Figure 31: k values in function of the slope for artificial grass

coarsey = 0.0098x + 0.0024

R2 = 0.7644

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004

0.0045

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

slope

k v

alu

e i

n 1

/s

Série1

Linéaire (Série1)

Figure 32 : k values in function of the slope for coarse.

Conclusion:

With this first version, it is possible to show more than basic concept like time of

concentration; it could be used for practical lectures to calibrate a reservoir model for

example. Another experiment could be done, with metal valve (and not plastic valve). It will

be possible to show that storms that move upstream tend to produce lower peaks of a longer

duration than storms that move downstream.

The second version with a pressure regulator will increase the possibility of the scale model.

It will become a real complex scale model with the possibility to adjust rainfall intensity,

rainfall duration, slope, rainfall distribution and effect of the direction of storm movement.

Bibliography:

Book:

-Hydrology in practice. Elizabeth M. Shaw. Second edition, Chapman and Hall. Chapter 13:

Rainfall-Runoff relationships. pages 295-321. 1988

-Introduction to hydrology. Fifth edition. Warren Viessman, Jr; Gary Lewis. Chapter 9:

Hydrographs. 2002

-Hydrology of catchment. Rivers and Deltas. Lectures notes. Prof.dr. HHG. Savenije. October

2003.

Web site :

http://hydram.epfl.ch/VICAIRE/mod_1a/chapt_8/text.htm

http://www.copernicus.org/EGU/hess/hessd/2/1717/hessd-2-1717.pdf

http://www.hydrol-earth-syst-sci-discuss.net/4/983/2007/hessd-4-983-2007.pdf

http://www.cig.ensmp.fr/~iahs/hsj/340/hysj_34_03_0277.pdf

http://www.copernicus.org/EGU/hess/hessd/2/1717/hessd-2-1717.pdf

http://www.hydrol-earth-syst-sci-discuss.net/4/983/2007/hessd-4-983-2007.pdf

http://www.cig.ensmp.fr/~iahs/hsj/340/hysj_34_03_0277.pdf

Appendices

Appendix 1: Test of the full cone jet sprinkler

Objective: To determine characteristics of the sprinkler

- Spray distribution in function pressure and spray height

- Discharge in function pressure

Water comes from the tap. A long pipe furnished water. The sprinkler is glued in a PVC pipe.

A valve is positioned to control spraying.

Spray height can be adjusted with a set-up in wood. Pressure can be adjusted with different

position of the valve.

Firstly, a simple test consists to know the spraying area. The spraying area is quite a circle

with a diameter between 30 and 40cm.

Spray distribution:

Description of the experiment:

One sprinkler was tested and 19 cups collected water around the sprinkler like in figure 1

(above the 1st cup). Each cup has a diameter of 7cm.

Figure 1: photo and draw of cups

A rainfall event of 2 minutes approximately at each experiment is applied.

All the cups are weighted after each experiment and values are written in the following tables.

I made 6 series of experiment to complete the following table:

Height spray in cm

Pressure in bar 40 50 60

4 X X X

5 X X X

6 X X X

Why these values? Because for smaller spray heights than these values (that is to say

1040cm), different spray coverage are obtained and it is not possible to have a good

distribution above an enough area. 46 bar were applied because for 14 bar sprinklers

produce bad distribution or a straight jet. So this experiment will determinate the best

configuration after this selection.

Remarks:

- The time of experiment is approximate because stopping the rain is too difficult. The

sprinkler continues to rain and less and less until it stops. Sprinkler doesn’t spray

significantly after 5 seconds. That is for this reason that the line “total” in the

following tables is not a constant.

- Different pressures are obtained in adjusting valve. 6 bars are obtained with a full

opened valve.

Table: Weight in gram of each cups at 4,5,6 bars and for 40,50,60cm:

Spray Height 40 50 60

4 bar

1 88 77 72

2 37 46 50

3 19 23 29

4 21 25 22

5 26 17 22

6 33 39 28

7 42 47 41

8 6 3 12

9 8 6 12

10 3 2 5

11 4 6 8

12 4 5 5

13 6 8 6

14 5 6 5

15 7 10 8

16 5 3 6

17 12 12 11

18 7 9 9

19 14 16 16

total 347 360 367

5 bar

1 109 114 62

2 43 67 74

3 25 40 49

4 23 29 22

5 30 31 15

6 41 38 19

7 44 50 34

8 8 14 22

9 10 15 25

10 5 7 12

11 7 9 11

12 4 5 5

13 6 8 6

14 5 7 4

15 8 11 6

16 6 8 4

17 11 12 8

18 7 9 9

19 17 18 18

Total 409 492 405

6 bar

1 115 120 66

2 41 62 52

3 40 26 28

4 24 26 17

5 33 36 20

6 44 53 34

7 43 46 51

8 12 15 13

9 11 12 13

10 7 6 6

11 4 4 6

12 3 3 4

13 3 5 6

14 5 7 5

15 6 11 9

16 8 13 9

17 11 17 14

18 8 11 11

19 16 19 18

Total 434 492 382

Analysis of values:

Spray coverage doesn’t depend on spray height and pressure for these values:

Spray coverage doesn’t change with pressure or with spray height. Indeed in the table, two

areas are separated. First area: weight>13g and second area weight<13g. These areas are

pretty much the same for each case. This is explained by the fact that the base of the cone is

like in the following figure:

Figure: full cone spray

The base of the cone is the total area of 19 cups.

Sprinkler sprays also

Homogeneity is sensitive of spray height but not of pressure for these values:

Table of the difference between same cups and average of the difference: Average of the various in gramm

40 cm 50 cm 60 cm

between 4 et 5 bar 3 7 6



Change pressure doesn’t change the behavior of the sprinkler.

Table of standard deviation for each series of measure:

For 60 cm, standard deviation is the smallest of all the series and doesn’t change with

pressure.

-To know the distribution, three areas are separated:

1st area: cup 1

2nd

area: cup 1 (2) to cup 7

3rd

area: cup 8 to cup 19

Figure: Three areas delimited in red.

Table :Value 1

Spray height 40 cm 50 cm 60 cm

4 bar 88 114 62

5 bar 109 120 66

6 bar 115 120 66

Table: Average of the values from 1 to 7


4 bar 30 33 32

5 bar 34 43 36

6 bar 38 42 34

Table: Standard deviation between 1 (2) and 7


4 bar 24 (9) 20 (13) 18 (11)

5 bar 30 (7) 30 (14) 23 (23)

6 bar 30 (8) 33 (15) 18 (15)

Standard deviation of the 6 series


4 bar 21 20 18

5 bar 25 27 20

6 bar 27 29 18

Table: Average of the values from 8 to 19


4 bar 7 7 9

5 bar 8 10 11

6 bar 8 10 10

Table: Standard deviation between 8 and 19


4 bar 3 4 4

5 bar 4 4 7

6 bar 4 5 4

The distribution is bad for all configurations. Homogeneity will be never obtained with

such a sprinkler. Best results are obtained all the time for 60cm for the second area. Indeed

standard deviation values are the lowest of all the different area and are quite still the same

with pressure.

Discharge:

Discharge is function pressure.

Table: Discharge of the sprinkler in function of pressure

P bar Q ml/min

3.9 240

4.6 260

5 280

6.6 320

With 10 sprinklers above the scale model, maximum discharge is about 2400ml/min and

3200ml/min. 10 sprinklers represents more than 1m².

Appendix 2: Full square jet nozzle

Spraying System is a firm which produces only nozzle for industrial application. It is possible

to order nozzles, pressure regulator and connector on the website

http://www.ispray.com/sc_app/default.asp?code= or by phone.

Spraying system produce full jet spray nozzle with a square spray. So it is also possible to use

it for the scale model.

Spraying system gives more information by mail. After looking for the nozzle which produce

the lowest discharge and with spray area suitable, the version 1/8 GG 3.6 SQ was chosen.

Discharge and spray coverage are presented in the following table

Figure: spray pattern

Table : Discharge in function pressure

Pressure in bar 0.3 0.5 1 2 3

Discharge in l/s 0.93 1.2 1.6 2.2 2.7

Table: Spray coverage in function the pressure and the spray height

Spray coverage D in m 3,6SQ

Pressure in bar

0.35 0.7 1.4 2.8

Spray height A in

m

0.3 18 20 20 25

1 51 58 64 66

1.5 71 91 109 122

2 97 109 127 137

Summary of test results from nozzles of Utrecht University:

Utrecht University tested different types of nozzle but the version 1/8 GG 3.6 SQ. The main

conclusion is that for at least 1 bar is required to get the best homogeneity.

Appendix 3: Test of a pressure sensor and program

A pressure sensor is sensitive of pressure. So it can give a water level. The goal of the test is

to know what the accuracy of such a device is.

Experiment:

Pressure sensor is tested with a tube. Water level is measured in the tube with a tape. The tape

starts from the pressure sensor.

Figure: set-up of pressure sensor test.

Pressure sensor is connected with a computer. Software Test Point is needed to get the signal.

Test point is not so easy to use because to get signal in volt, a program is needed (refer to ICP

test program).

With ICP test program, rating curve was obtained:

Signal is recorded in excel for a water level of 1, 2, 3cm so on.

The relation is completely linear:

Water level= 160.2934*Volt - 61.4831

Voltage is given with a accuracy of 0.0001 V.

For a water level given, signal is not constant. It varies with a rank of 0.0025V. 0.0025V is

0.4cm.

So the accuracy of the pressure sensor is 0.4cm.

Program “Water level gauge”

A program with Test Point was written to record water level with time and to plot it in a chart:

Appendix 4: Wave height meter and float gauge.

-Wave height meter

Short description:

Wave height meter measures resistance of water with two electrodes. The electric resistance

measured between the electrodes is inverse proportional to the instantaneous depth of

immersion. Its main application is for wave application. So this device can measure a level

variation around ten cm in 0.1 seconds. The electrode length is 60cm. This device need power

supply of 20 Volt. It can be connected with a computer to get the signal. Signal is in Volt. The

wide range is 5cm-50cm.

Accuracy of wave height meter:

Wave height meter was tested in a white cylinder bucket with a diameter of 38cm and a

volume of 60liters. And voltage can be read thanks to Dasy lab software.

To get the rating curve of the device and in the same time of the bucket, I weight the water

and fill the bucket with water. For different weights, there are different values of voltage.

Rating curvey = 3132.4x

R2 = 1

0

5000

10000

15000

20000

25000

0.000 2.000 4.000 6.000 8.000

voltage in V

we

igh

t o

f th

e w

ate

r in

g

volt

Linéaire (volt)

Figure: rating curve for wave height meter

Wave height meter is completely linear:

Weight in g

Voltage in V

Weight=3132*Voltage

For a given water level, signal variation is about 0.0005V. This variation is due to the fact that

water is never completely quiet. There are waves with amplitude around µm. So it means that

this device can measure an increase of 1.6g. As water has density of 1.000kg/m3, 1.6g is

1.6ml. 1.6ml equates an increase of water level of 0.0014cm or 14µm.

Accuracy of this device is about 15µm.

The wave height meter is completely linear, indeed R²=1.

So it is able to measure a discharge of 1.6ml/s.

-Float gauge

The float gauge is composed by a metal stem of 80cm. The wide range is 6-76cm. Float

position is known by induction phenomenon. This device has an accuracy A of 1 µm

according to the developer.

To be able to measure a discharge of Q=1ml/s, the maximum area S of the bucket will be:

S=Q/A

Numerical application:

S=104cm²

With the same procedure, the rating curve was plotted but with a yellow bucket of 25 liters

and a rectangular shape. Size of the bucket: length=33cm and width: 26cm. The area is

856cm²<104.

Rating curve

-3934.442x + 43359.571

0.0

5000.0

10000.0

15000.0

20000.0

25000.0

30000.0

0.000 2.000 4.000 6.000 8.000 10.000 12.000

voltage in V

weig

ht

of

the w

ate

r in

g

w eight

Linéaire (w eight)

Figure: Rating curve of the float gauge

Relation between weight in gram (and volume in ml) and voltage in Volt is linear.

Weight= 3934*Voltage +43 359

Appendix 5: Presentation of Dasy Lab and explanation of the filter

Dasy Lab is software to log data of a signal and to process the signal. Its utilisation is really

easier than Test Point.

This appendix deals with the problem to get a smooth hydrograph, that is to say, to eliminate

effect of waves. Numerical filters are required to get it.

Presentation of the numerical filter

Frequency of the hydrograph:

For runoff: time base is about 100 seconds. So frequency is about 0.005 Hz

For groundwater flow: time base is about 1000 seconds. So frequency is about 0.0005 Hz.

Frequency of waves:

The frequency of waves in the bucket is about 3Hz.

Frequency waves are 1000 or 10 000 times less than the frequency of the hydrograph.

Presentation of numerical filters:

Two parameters are required to define a filter:

-Frequency

-Order

The best type is the Bessel filter (other filter are available).

A low pass filter is required because waves have a higher frequency.

Frequency:

The filter frequency must be 10 times higher than the frequency of the hydrograph.

If filter has the same frequency, filtered signal are not true.

Moreover, even if the frequency is 10 times higher than the frequency of the original signal

filter introduces a delay.

Figure: Filter with same frequency than the signal.

The delay is so important that filtered signal cannot follow the original signal.

Order:

An order of 10 is lower than an order of 1. But smoother curve are obtained for 10 than for 1.

Frequency considered.

For runoff:

Hydrograph signal has a frequency of 0.005Hz. So filter frequency required is 0.05Hz.

A simulation with a signal generator is possible. A sinus signal was simulated to show the

effect of a filter of 0.05Hz with an order of 2:

Figure: in blue sinus signal generated and in red filtered signal (for runoff)

For groundwater flow:

Hydrograph signal has a frequency of 0.0005Hz. So filter frequency required is 0.005Hz. But

0.01 is higher and gives better results.

A simulation with a signal generator is also possible. A sinus signal was simulated to show

the effect of a filter of 0.01Hz with an order of 2:

Figure: in blue sinus signal generated and in red filtered signal (for groundwater flow)

Filter introduces a delay to get the right value.

In the following figures, a generator gives a saw signal. After signal is differentiate. So a

discharge given is simulated.

Figure: Delay for runoff (artificial grass): 12 seconds. In blue the original signal and in red the

filtered signal

Figure: Delay for groundwater flow: 58 seconds. In blue the original signal and in red the

filtered signal

Application:

So theoretical frequency is chosen, it is possible to apply filter with the real signal (from wave

height meter and float gauge).

A program was built to record for the both hydrograph: original signal (in volt), average

signal (in volt) and average discharge with filtered discharge.

Figure: Program to get discharge.

Explanation:

Frequency sample of the experiment is 5Hz. Firstly an average of 5 samples is done. It gives

with a differentiate the average discharge with a frequency of 1Hz. Secondly signal is filtered

and after differentiate. It gives the filtered signal.

Discharge for artificial grass is obtained thanks to rating curve for the white bucket:

Qgrass=3132*IN(0)*60

This formula is written in the “formula” module.

IN(0) is the voltage differentiate from the module “differentiate”

Discharge for coarse is obtained thanks to rating curve for the yellow bucket:

Qcoarse=3934*IN(0)*60

Discharge is given in ml/min (factor 60). But don’t forget that discharge is in ml/s.

Filtered signal and average signal

-300

-200

-100

0

100

200

300

400

500

600

700

800

0 50 100 150 200 250 300 350 400

time in seocnds

dis

ch

arg

e i

n m

l/m

in

Filtered signal

Average signal

Figure: Runoff hydrograph for rainfall duration of 40 seconds. In pink the average discharge

and in blue the filtered discharge.

Average and filtered discharge

-1500

-1000

-500

0

500

1000

1500

2000

0 50 100 150 200 250 300 350 400

time in seconds

dis

ch

arg

e i

n m

l/m

in

average discharge

filtered discharge

Figure: Groundwater hydrograph for rainfall duration of 40 seconds. In pink the average

discharge and in blue the filtered discharge.

Analysis

Float gauge is for groundwater flow. Average signal is completely disturbed. But filtered

discharge gives the right value. This can be explained by the fact that float gauge is really

sensitive to microwave and this device has a accuracy of µm.

Discharge was checked with a test tube and discharge is the same than the filtered discharge.

This experiment was realized several times. Success was observed with 100%.

Designing of a hydrological rainfall-runoff scale model · 2017. 1. 2. · rainfall-runoff models...

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