BFW 40103- Water Resources E i i

Ch 4

Engineering

Chapter 4:Rainfall RunoffRainfall-Runoff ModelingModeling

Prepared by: Mohd Shalahuddin Adnan, PhD,

Lesson goals

At the end of this topic student shouldAt the end of this topic, student shouldbe able to:-

Know the rainfall-runoff relationship

Apply and analysis the concept of pp y y prainfall-runoff analysis

IntroductionIn many hydrologic engineering designs, we need to predict peakdischarge or hydrograph resulting from a certain type of storm event. Forthis purpose, some kind of rainfall-runoff model is needed to translaterainfall input to produce discharge hydrograph.

Reliable estimates of stream flow generated from catchments arerequired as part of the information sets that help policy makers makeinformed decisions on water planning and management Theinformed decisions on water planning and management. Thecharacteristics of the streamflow time series that influence waterresources system modelling and planning can include the sequencing offlows on daily and longer time steps spatial and temporal variability offlows on daily and longer time steps, spatial and temporal variability offlows, seasonal distribution and characteristics of high and low flows.

A range of methods are available to estimate streamflow fromgcatchments, using observed data wherever possible, or estimating byempirical and statistical techniques, and more commonly using rainfall-runoff models.

Introduction

WatershedRainfall RunoffWatershed

Pic source; http://distributedrr.wikidot.com/

Rainfall-RunoffModel

Rainfall Runoff

Total streamflow during a precipitation event includes the baseflow existing in the basin prior to the storm and the runoff due to the given storm precipitation. Total g p pstreamflow hydrographs are usually conceptualized as being composed of: Direct Runoff which is composed of contributions Direct Runoff, which is composed of contributions

from surface runoff and quick interflow. Unit hydrograph analysis refers only to direct runoff.

Baseflo hich is composed of contrib tions from Baseflow, which is composed of contributions from delayed interflow and groundwater runoff.

Runoff Hydrograph

700.0000

u o yd og ap

500 0000

600.0000

Surface

400.0000

500.0000Response

200.0000

300.0000Baseflow

0.0000

100.0000

0.0000

0.000

00.1

600

0.320

00.4

800

0.640

00.8

000

0.960

01.1

200

1.280

01.4

400

1.600

01.7

600

1.920

02.0

800

2.240

02.4

000

2.560

02.7

200

2.880

03.0

400

3.200

03.3

600

3.520

03.6

800

Estimation of Streamflow A hydrograph is a plot of river discharge versus time. A streamflow hydrograph comprises overland flow,

i t fl d b fl t d b i it tiinterflow and baseflow generated by precipitation flows.

A hydrograph resulting from a single precipitation

Rising limb Crest Recession

A hydrograph resulting from a single precipitation storm is known as a storm hydrograph.

arge

limb Crestlimb

Dis

cha

tt KQQ 0

Qt = discharge t time units after Q0

Q0 = initial discharge at t = 0

Time

K = recession constant

Hydrographs are also described in terms of the following y g p gtime characteristics:

Time to Peak t : Time from the beginning of the rising limb to the Time to Peak, tp: Time from the beginning of the rising limb to the occurrence of the peak discharge. The time to peak is largely determined by drainage

characteristics such as drainage density, slope, channel g y proughness, and soil infiltration characteristics. Rainfall distribution in space also affects the time to peak.

Time of Concentration, tc: Time required for water to travel from the most hydraulically remote point in the basin to the basin outlet. For rainfall events of very long duration, the time of concentration is associated with the time required for the systemconcentration is associated with the time required for the system to achieve the maximum or equilibrium discharge. The drainage characteristics of length and slope, together

with the hydraulic characteristics of the flow paths, determine the time of concentration.

Lag Time t : Time between the center of mass of the effective Lag Time, tl: Time between the center of mass of the effective rainfall hyetograph and the center of mass of the direct runoff hydrograph. The basin lag is an important concept in linear modeling of The basin lag is an important concept in linear modeling of

basin response. The lag time is a parameter that appears often in theoretical and conceptual models of basin behavior. However, it is sometimes difficult to measure in real worldHowever, it is sometimes difficult to measure in real world situations. Many empirical equations have been proposed in the literature. The simplest of these equations computes the basin lag as a power function of the basin area.

Time Base, tb: Duration of the direct runoff hydrograph.

Diff t f h d h b d 1 1 i f i f llDifferent of hydrograph based on 1mm or 1 in of rainfall

Rai

nfal

l nt

ensi

ty

t

1 in. or 1 mm of net precipitation in

period tr

t Rai

nfal

l nt

ensi

ty

t

B - 2 units of net precipitationA

Runoff Rai

nfal

l nt

ensi

ty

t

1 in. or mm of net precipitation in each

period of trARunoff

B

t

Unit hydrograph

R i

tp lag

Dis

char

ge

tr tc

Unit hydrograph

R iD

isch

arge

tr

A

BRunoff

hydrograph

Unit hydrograph

R iD

isch

arge

tr

A B

Runoff hydrograph

tr

Time

D

T

Unit hydrograph

Time

D

T

Runoff hydrograph for 2 units Runoff hydrograph for 2

Time

D

T

Unit hydrograph Runoff hydrograph for 2 units of precipitation

Runoff hydrograph for 2 consecutive periods of tr duration

Unit hydrograph analysisUnit hydrograph analysis

Sherman (1932) first proposed the unit hydrograph tconcept.

The Unit Hydrograph (UH) of a watershed is defined as The Unit Hydrograph (UH) of a watershed is defined as the direct runoff hydrograph resulting from a unit volume of excess rainfall of constant intensity and uniformly distributed over the drainage area Theuniformly distributed over the drainage area. The duration of the unit volume of excess or effective rainfall, sometimes referred to as the effective duration, defines and labels the particular unit hydrograph The unitand labels the particular unit hydrograph. The unit volume is usually considered to be associated with 1 cm (1 inch) of effective rainfall distributed uniformly over the basin areabasin area.

Unit hydrograph, UH(,t)Unit hydrograph, UH(,t)

Assumptions for a UH p

The effective rainfall has a constant intensity within the effective durationeffective duration.

Effective rainfall is uniformly distributed over the whole Effective rainfall is uniformly distributed over the whole watershed.

The time base of the DRH resulting from an excess rainfall of given duration is constant.

The ordinates of all DRH’s of a common time base are directly proportional to the total amount of direct runoff.

Instantaneous Unit Hydrograph (IUH)Instantaneous Unit Hydrograph (IUH)

Instantaneous unit hydrograph is the direct runoff hydrograph resulted from an Impulse function rainfall, i.e., one unit of effective rainfall at a time instance.

Hydrograph SeparationHydrograph Separation

There are 2 common approaches to separate the b fl f th di t ffbaseflow from the direct runoff:

1. Recession curve- using the recession curve equation

2 Arbitrary approach2. Arbitrary approach- of arbitrary nature using many techniques

Example 4.1Example 4.1

A set of daily streamflow data at a site of drainage area 6500 km2 areprovided in table below. Separate the baseflow from the direct runoffp phydrograph (DRH) by the recession curve method. Determine theequivalent depth of the direct runoff.

Time (days) Flow (m3/s) Time (days) Flow (m3/s) Time (days) Flow (m3/s)1 1600 6 6500 11 18502 1550 7 5000 12 16003 5000 8 3800 13 13304 11300 9 2800 14 13005 8600 10 2200 15 1280

100000

/s)

10000

Flow

(m3 /

10000 2 4 6 8 10 12 14 16

Time (days)Time (days)

100000100000

m3 /s

)

10000

Flow

(m

10000 2 4 6 8 10 12 14 16

Ti (d )Time (days)

Time (days) Direct runoff (m3/s)

Average runoff (m3/s)

Duration (days)

Runoff Time (m3day/s)

Computation of direct runoff volume

(m /s) (m /s) (days) (m day/s)

1

2

3

0

0

3400

0

1700

6550

1

1

1

0

1700

65503

4

5

6

97003400

7020

4970

83606550

5995

4235

11

1

1

83606550

5995

4235

7

8

9

23203500

1350

18352910

1070

11

1

18352910

1070

10

11

12

790

450

240

620

345

120

1

1

1

620

345

120

13

Total

033740

606024 36

160602433740 runoff of Volume

36 m1082891 .

area drainagevolume runoff depth Runoff 6

6

1065001082891

. m4450.

Separation by Arbitrary ApproachMethod 1 - join the beginning of the direct runoff (point A) to the end of

direct runoff (point B) by a straight line. Simplest method. If point B is not well defined, draw a horizontal line from point A.

10000

12000

8000

10000

3 /s)

4000

6000

Flow

(m

0

2000 A

B

00 2 4 6 8 10 12 14 16

Time (days)

Method 2 - extend the recession curve before the storm to point C beneath the peak. Connect point C to point D by a straight line. Point D on the hydrographConnect point C to point D by a straight line. Point D on the hydrograph

represents N days after peak, given by the formula 20.aAN

where N = time (days), A = drainage area, a = 0.8 (if A is km2) or 1.0 (if A is mi2)

10000

12000 N (days)

8000

m3 /s

)

4000

6000

Flow

(m

D

0

2000

C

00 2 4 6 8 10 12 14 16

Time (days)

Method 3 - extend the recession curve backward to point E below the inflection point. C t A t E b t i ht li bit hConnect A to E by a straight line or an arbitrary shape.

12000

8000

10000

6000

8000

Flow

(m3 /s

)

2000

4000

F

FE

A

00 2 4 6 8 10 12 14 16

Time (days)

Time (days)

Hydrograph developmenty g p pA hydrograph resulting from an isolated, intense, short-duration storm of nearly uniform distribution in space and time is most satisfactory.

The duration of the unit hydrograph will be the same as the duration of the storm that had produce the storm hydrograph. The duration of the unit hydrograph can be adjusted by the technique of superposition.

The procedure to derive a unit hydrograph is:1. The hydrograph is plotted. The baseflow is separated to obtain the direct runoff hydrograph (DRH).2. The area under the DRH that represents the volume of surface runoff is computed. The volume of runoff is converted to a depth Pn using

3 Each of the ordinates of the DRH is divided by P The result is a unitAVPn where Pn = runoff depth, V = volume under the hydrograph,

A = drainage area of the basin

3. Each of the ordinates of the DRH is divided by Pn. The result is a unit hydrograph of duration equal to the duration of the storm.

The main factors affecting hydrograph shape are:

Drainage characteristics: basin area, basin shape,

g y g p p

basin slope, soil type and land use, drainage density, and drainage network topology. Most changes in land use tend to increase the amount of runoff for a givenuse tend to increase the amount of runoff for a given storm.

Rainfall characteristics: rainfall intensity, duration, and their spatial and temporal distribution; and storm motion as storms moving in the general downstreammotion, as storms moving in the general downstream direction tend to produce larger peak flows than storms moving upstream.

Drainage types and hydrograph shapeg yp y g p p

Also need to consider the storm duration and time of concentration.

Factors that influence surface runoff Physical-geographic factors (natural, non-manageable)

Climatic (meteorological):Climatic (meteorological): Precipitation

Type of precipitation (rain, snow, sleet, etc.)Th t ( t) d i t it The rate (amount) and intensity Duration of rainfall Direction of storm movement Distribution of rainfall over the drainage basin

Previous weather (e.g. precipitation that occurred earlier and resulting soil moisture)

Time of year/seasonSummer - evapotranspiration rates higher, photosynthesis in plants - at a

maximum

Physical-geographic factors (natural, non-manageable)

Characteristics of watershed Watershed area – volume and culmination of

total runoff Shape of watershed – time of concentration to Shape of watershed time of concentration to

the outlet Elevation Slope of the area Slope of the area

The steeper the slopes, the lower the rate of infiltration and faster the rate of run-off when the soil is saturated (saturated overland flow)

Strong influence on erosion and transport processes

Length of slope and length of valley – lag time to the valley and to the outlet

Physical-geographic factors (natural, non-manageable)

Geological and soil characteristics Bedrock permeability - Run-off will occur quickly where p y q y

impermeable rocks are exposed at the surface or quickly when they underlay soils (limited amount of infiltration).

Soil permeability - Soils with large amounts of clay do absorb fmoisture but only very slowly - therefore their permeability is low.

Thickness - The deeper the soil the more water can be absorbed. Infiltration capacity - Soils which have larger particle sizes (e.gp y g p ( g

those derived from the weathering of sandstones) have larger infiltration capacities.

The infiltration capacity is among others dependent on the porosityof a soil which determines the water storage capacity and affects the resistance of water to flow into deeper layers.

Initial conditions (e.g. the degree of saturation of the soil and if )aquifers)

Anthropogenic factors (manageable)

Land use (e.g. agriculture, urban development, forestry operations)Human activities - development and urbanization:

f imperviousness - natural landscape is replaced by impervious surfaces (roads, buildings, parking lots) - reduce infiltration and accelerate runoff to ditches and streams

removal of vegetation and soil removal of vegetation and soil constructing drainage networks and underground sewer increase runoff

volumes and shorten runoff time into streams -> the peak discharge, volume, and frequency of floods increase in nearby streams

Agriculture Irrigation and drainage ditches increasing the speed of water transfer contour tillage Tillage on wet land compresses the subsoil - creating a "plough pan" decreasing

water holding, infiltration and increasing run-off/erosion.

Statistic analysis of maximum rainfall eventsExtreme of rain events I

[mm/min]Return

i dStatistic analysis of maximum rainfall eventsIDF curves:• relations between intensities, duration and

frequency of rain events

period [years]

frequency of rain events Intensity – I (mm/min) Duration – D (min) Frequency – F (1/years)

• probability of different rain event intensities for D [min]• probability of different rain event intensities for different durations (5, 10, 15, 30 … minutes, … 24 hours)

• an each curve represents a certain frequency of t i t i d d 80

90

100

D [min]

occurrence or a certain return period expressed in terms of years.

N value:30

40

50

60

70

80

H1d

,N [m

m]

• the average over a number of years of observation

• Value that is exceeded ones per N years (return period)

0

10

20

30

0 20 40 60 80 100 120

N[years]period)• Rainfall depth (mm) of certain duration (e.g. 24

hours) whose probability of appearance is 1/N = Frequency (1/years)

N [years]N [years] 22 1010 2020 5050 100100

HH1d,1d,NN[[mmmm]] 36.336.3 60.660.6 70.470.4 82.682.6 92.192.1

N [years]

Extreme dischargeExtreme values - the average over a

number of years of observation

Maximum (N value) QN(m3/s):15

20

25

N (m

3 /s)

Flood frequency curve

( ) N( )• Value that is exceeded ones per N years

(return period) - statistically• Discharge (m3/s) whose probability of

0

5

10

0 20 40 60 80 100 120

N (years)

QN

probability distributions

N (years)N (years) 11 22 55 1010 2020 5050 100100

QQNN (m(m33/s)/s) 66 88 10.910.9 13.213.2 15.615.6 18.818.8 21.521.5

g ( ) p yappearance is 1/N = Frequency (1/years)

• Are required for the design of dam, spillways, nuclear power stations, major

N (years)

bridges…• important for assessing risk for highly

unusual events, such as 100-year floods. 4 0 0

5 0 0

6 0 0

Q m [l

/s]

Minimal Qm(l/s):• Value (discharge) that is exceeded m-days

per a year – statistically0

1 0 0

2 0 0

3 0 0

Dis

char

ge Q

• Important for dry seasons, ground water storage

m [day]m [day] 3030 6060 9090 120120 150150 180180 210210 240240 270270 300300 330330 335335 364364

Qm [l/s]Qm [l/s] 507507 350350 270270 218218 180180 150150 125125 104104 8585 6868 5050 4747 3535

00 1 0 0 2 0 0 3 0 0

T im e m [ d a y ]

The surface runoff process

Interception + t ti

Rainfall excess = rainfall - losses = = rainfall - interception - surface retention - infiltration

Direct runoff = surface runoff + interflow retentionDirect runoff = surface runoff + interflow

Direct runoff

Hydrograph 11.-13.8. 2002 (Polečnice catchment)Hydrograph 11. 13.8. 2002 (Polečnice catchment)

200

220 0

0.5

Rainfall Hs=133,2mm

outlet of Polečnice

160

180

0.5

1

1 5 /10m

in)

The confluence

Outlet Chvalšinský stream

Outlet Polečnice stream abovethe confluence

100

120

140

arge

(m3 /s

) 1.5

2

ainf

all (

mm

/the confluence

60

80

100

Dis

cha 2.5

3

ensi

ty o

f ra

20

403.5

4

Inte

012:45 20:45 4:45 12:45 20:45 4:45 12:45 20:45

Time (h:min)

4.5

Some Rainfall-Runoff ModelsSome Rainfall Runoff Models Phi-Index

H t E ti Horton Equation SCS Curve Number Sacramento Soil Moisture Accounting Model Sacramento Soil Moisture Accounting Model

(SAC-SMA)

Constant Infiltration RateConstant Infiltration RateA constant infiltration rate is the most simple of themethods It is often referred to as a phi-index or f-indexmethods. It is often referred to as a phi index or f index.

In some modeling situations it is used in a conservativemode.

The saturated soil conductivity may be used for theinfiltration rate.

The obvious weakness is the inability to model changesin infiltration rate.

Th hi i d l b i d f i di id lThe phi-index may also be estimated from individualstorm events by looking at the runoff hydrograph.

Exponential Decay - HortonExponential Decay Horton This is purely a mathematical function - of the following form:

kt)ec

fo

(fc

fi

f coci

fo

fi = infiltration capacity at time, t

fc = final infiltration capacity

o

fc

fo = initial infiltration capacityfc

SCS Curve Number

Soil Conservation Service is an empirical method ofestimating EXCESS PRECIPITATION

SCS Curve Number

estimating EXCESS PRECIPITATION

We can imply that precipitation minus excessprecipitation = infiltration/retention :precipitation infiltration/retention :

P - Pe = F

Determine Curve NumberDetermine Curve Number Once the hydrologic soil group has been determined, the

curve number of the site is determined by crosscurve number of the site is determined by cross-referencing land use and hydrologic condition to the soilgroup - SAMPLE

Land use and treatment Hydrologic soil groupor Hydrologic

practice condition A B C Dpractice condition A B C D

FallowStraight row ---- 77 86 91 94Straight row 77 86 91 94Row CropsStraight row Poor 72 81 88 91Straight row Good 67 78 85 89Contoured Poor 70 79 84 88Contoured Poor 70 79 84 88

Sacramento Soil Moisture Accounting Model (SAC-SMA)

The Sacramento Soil Moisture Accounting Model (SAC-SMA) is a conceptual model of soil moisture accountingthat uses empiricism and lumped coefficients to attemptthat uses empiricism and lumped coefficients to attemptto mimic the physical constraints of water movement ina natural system.

Sacramento Soil Moisture Accounting Model (SAC-SMA)

Model ObjectivesMost of the purposes of rainfall-runoff modeling relate to providing information to support decision making for some water management policy. In particular,

Model Objectives

pp g g p y pthis can involve:

i. Understanding the catchment yield, and how this varies in time and space particularly in response to climate variability: seasonally interspace, particularly in response to climate variability: seasonally, inter-annually, and inter-decadally

ii. Estimating the relative contributions of individual catchments to water availability over a much larger region, e.g. valley or basin scale.

iii. Estimating how this catchment yield and water availability might change over time in response to changes in the catchment, such as increasing development of farm dams, or changes in land-use and land managementmanagement.

iv. Infill gaps caused by missing or poor quality data in an observed data series for a gauged catchment.

v. Estimate flows for a gauged catchment for periods before the observed fl d t t d ft h th b d fl d dflow record started or after when the observed flow record ends.

vi. Estimate flows for an ungauged catchment.

Data Requirements for Models

Rainfall Data (Major Input) Soils Data (Infiltration

More Physically-based means more data

q

Soils Data (Infiltration, Runoff)

DEM – channel network (Ri ti )

means more data requirement

More Conceptual requires less data(River routing)

Vegetation Data (For ET) GWT Data (Saturated zone

less data

GWT Data (Saturated zone flow)

Historical Rainfall-Streamflow DataStreamflow Data (Calibration)

Evaporation Data (ET)