RUNOFF & FLOOD FREQUENCY ANALYSIS

(WATERSHED MANAGEMENT)

UNIT – III

Rambabu Palaka, Assistant ProfessorBVRIT

Learning Objectives1. Watershed Delineation

a) Data Collectionb) Preparation of Contoursc) Watershed Delineation

2. Runoff Computations from a Watersheda) Empirical Formulaeb) Rational Methodc) SCS-CN Method

3. Flood Frequency Analysisa) Weibull Methodb) Gumbell Methodc) Log Pearson Method

Watershed DelineationDelineation is a process of dividing the watershed into discrete land and channel segments to analyze watershed behavior.

It means drawing lines on a map to identify a watershed’s boundaries. These are typically drawn on topographic maps using information from contour lines.

Contour lines are lines of equal elevation, so any point along a given contour line is the same elevation.

Watershed DelineationSource of Data: Toposheets from Survey of India Digital Elevation Model (DEM)

DEM:It is a digital model or 3D representation of a terrain's surface created from terrain elevation data which can be obtained through

a) Land Surveying using Auto Level, Theodolite, Total Station, GPS, DGPS etc.b) Remote Sensing

a) Aerial Photographyb) LIDAR (Light Detection And Ranging) that measures distance by

illuminating a target with a laser and analyzing the reflected light.

c) Satellite Images eg. CartoDEM

LAND SURVEYING

(Total Station, GPS, DGPS)

Location

X (Longitud

e)

Y(Latitud

e)Z

(Altitude)R1 2050.118 1500 99.606

R2 2042.9871406.06

8 99.825R3 2056.467 1421.42 100.597

R4 2076.1021430.17

3 100.457

R5 2096.7151450.55

3 100.732R6 2120.572 1463.35 100.614

R7 2151.2971473.27

5 100.753

R8 2183.5261491.92

8 100.165

R9 2201.821505.58

3 101.198Data downloaded from Total

Station

Point Data

Land Surveying

Contouring by Square Method

Contours (Vector Data)

3D Digital Model

Land Surveying

REMOTE SENSING

CartoDEM (30 m resolution) – Raster Data

Cartosat-1 was launched by PSLV-C6 on 5 May 2005

from Satish Dhawan Space Centre at Sriharikota

CartoDEM (30 m resolution)

Hillshade

Elevation

Contours

Streams

Streams

3D Model

RUNOFF

Runoff ComputationsHeavy losses and huge damages taking place in a watershed due to occurrence of flood.

Flood is produced due to heavy rainfall and its estimation is dependent on Rainfall Intensity Type of soil Shape and size of watershed Conditions of watershed at the time of rainfall Slope of waterway

Runoff ComputationsMethods of Estimation of Runoff:1. Empirical Formulae2. Envelope Curve3. Physical Indication of Past Floods4. Rational Method5. Probable Maximum Precipitation (PMP) Chart6. Rating Curve7. Unit Hydrograph Method8. SCS-CN Method9. Flood Frequency Analysis

Runoff ComputationsEmpirical Formulae:1. Dicken’s formula

Q = CA3/4

Where,Q = Design Flood (m3/s)A = Area of Catchment in KM2

C = Dicken’s ConstantNorth Indian Plains 6North Indian Hilly Regions 11-14Central India 14-28Coastal Andhra & Orissa 22-28

Runoff ComputationsEmpirical Formulae:2. Ryve’s formula

Q = CA2/3

Where,Q = Design Flood (m3/s)A = Area of Catchment in KM2

C = Ryve’s ConstantAreas within 80 km from east coast 6.8Areas within 80-160 km from east coast 8.5Limited areas near hills 10.2

Runoff ComputationsEmpirical Formulae:3. Inglis formula

Where,Q = Design Flood (m3/s)A = Area of Catchment in KM2

It is based on data of watershed in Western Ghats in Maharastra

10.4AA 124Q

Runoff Computations

Major Limitation of using Empirical Formulae is the subjective decision about

the values C to be adopted

Runoff ComputationsEnvelope Curves:

Kanwarsain and Kaprov, after collecting a large amount of data from rivers of India, presented two envelop curves as shown in figure.

Runoff ComputationsPhysical Indication of Past Floods:

Ancient monuments situated near the banks of river always bear the marks or records of the past floods.

The flood discharge is obtained from the Formula, Q = A.V

Where A = Cross section of Valley during dry seasonV = Velocity of flow can be calculated from Manning’s N

Usually, factor of safety about 1.5 is used to obtain maximum flood

Runoff ComputationsRational Method:It is most effective in urban areas with drainage areas of less than 200 acres.  The method is typically used to determine the size of storm sewers, channels, and other drainage structures.

Q = (C.I.A) / 3.6WhereC = Runoff CoefficientI = Rainfall Intensity in mm/h A = Area of Catchment in KM2

Note: Rainfall Intensity (i) can be found from the Intensity–Duration–Frequency (IDF) curves corresponding to Time of Concentration and Return Period

Runoff ComputationsIf IDF curves are not available,

where,P = RainfalltR = Duration of Rainfalltc = Time of Concentration

If Time of Concentration is not known ic = P / tR

Runoff ComputationsRunoff Co-efficient (C):

Runoff ComputationsRational Method:Assumptions: The drainage basin characteristics are fairly homogeneous Rainfall duration equal to the time of concentration results in the greatest peak discharge

The time of concentration is the time required for runoff to travel from the most distant point of the watershed to the outlet.

Time of Concentration, tc = Hydraulic Length / Velocity

Runoff ComputationsRational Method:Time of Concentration can be found using

Runoff ComputationsProbable Maximum Precipitation Chart:PMP Charts have been prepared by Meteorological Department of India for some states such as Punjab, Haryana, Delhi and Rajasthan using following methods.

1. Meteorological method2. Statistical Study of Rainfall data,

PMP = Avg. Rainfall + K.σ

whereK = Frequency Factor depends on statistical distribution series, no. of years record and the return period.σ = Standard Deviation

Runoff ComputationsRating Curve:It is a graph of discharge versus stage for a given point on a stream, usually at gauging stations, where the stream discharge is measured across the stream channel with a flow meter.

Runoff ComputationsUnit Hydrograph Method:It is a linear model of the catchment which is used to find out the volume of direct surface runoff (DSR) due to 1 cm of rainfall excess. If rainfall comes to the catchment producing 2 cm of excess rainfall, the ordinates of the DSR will be twice as much as the UH ordinates and volume of DSR will be two times of the volume of unit hydrograph.

Assumptions:1. The rainfall is of spatially uniform intensity with in its specified time2. The effective rainfall is uniformly distributed throughout the whole area of

drainage basin

Runoff ComputationsUnit Hydrograph Method:

Runoff ComputationsSCS – CN Method:The curve number method was developed by the USDA Natural Resources Conservation Service, which was formerly called the Soil Conservation Service or SCS.

The curve number is based on the area's hydrologic soil group, land use, treatment and hydrologic condition.

Runoff ComputationsSCS – CN Method:

WhereP = RainfallIa = Initial AbstractionsS = Potential maximum retention after runoff begins

Hydrologic Soil Groups:HSG Group A (low runoff potential): Soils with high infiltration rates even when thoroughly wetted. (final infiltration rate greater than 0.3 inches/hour).

HSG Group B: Soils with moderate infiltration rates when thoroughly wetted. (final infiltration rate of 0.15 to 0.30 inches/hour)

HSG Group C: Soils with slow infiltration rates when thoroughly wetted. (final infiltration rate 0.05 to 0.15 inches/hour)

HSG Group D (high runoff potential): Soils with very slow infiltration rates when thoroughly wetted. (final infiltration rate less than 0.05 inches/hour).

FLOOD FREQUENCY ANALYSIS

(Estimation of Design Flood)

Flood Frequency AnalysisReturn Period:A return period, also known as a recurrence interval (sometimes repeat interval) is an estimate of the likelihood of flood or a river discharge flow to occur.

For example, a 10 year flood has a 1/10=0.1 or 10% chance of being exceeded in any one year. This does not mean that if a flood with such a return period occurs, then the next will occur in about ten years' time - instead, it means that, in any given year, there is a 10% chance that it will happen, regardless of when the last similar event was.

Flood Frequency AnalysisReturn Period is a statistical measurement typically based on historic data and is usually used for risk analysis (e.g. to decide whether a project should be allowed to go forward in a zone of a certain risk, or to design structures to withstand an event with a certain return period).

Methods:1. Weibull Method2. Gumbell Method3. Log Pearson Method

Flood Frequency AnalysisWeibull MethodIn probability theory and statistics, it is a continuous probability distribution

Most commonly used method If ‘n’ values are distributed uniformly between 0 and 100 percent

probability, then there must be n+1 intervals, n–1 between the data points and 2 at the ends.

Probability, P = m / n+1

where, m = rank

Year Rainfall (mm)

Arranged Data (mm) Rank, m Probability,

P = m/(n+1)Return Period

(Years)Tr = 1/P

2009 546 945 1 0.142857143 7.00

2010 857 857 2 0.285714286 3.50

2011 567 661 3 0.428571429 2.33

2012 661 567 4 0.571428571 1.75

2013 945 546 5 0.714285714 1.40

2014 423 423 6 0.857142857 1.17

Rainfall Frequency Analysis – Weibull’s Method

Descending order

7.00 3.50 2.33 1.75 1.40 1.170

100

200

300

400

500

600

700

800

900

1000f(x) = − 292.572925242699 ln(x) + 987.134599848554

Rainfall Frequency Analysis (Weibull's Method)

Rainfall (mm)

Return Period (Years)

Logarithmic Curve

Flood Frequency AnalysisGumbel’s Extreme Value Distribution Method:

E.J. Gumbel in 1941 was consider that annual flood peaks are extreme values of floods in each of the annual series of recorded data. Hence, floods follow the extreme value distribution.

Probability, P = 1 – e –e –y

Return Period, T = 1/P

Where y = reduced variate = [1.282 (Q – Q) / σ] + 0.577e = base of Naperian Logarithm

Flood Frequency AnalysisGumbel’s Extreme Value Distribution Method:

Flood Magnitude for a given Return Period, QT = Q + KT σ

WhereFrequency Factor,

T = Return Period

Q = Mean σ = Standard Deviation

Rainfall Frequency Analysis -Gumbel’s Extreme Value Distribution Method

Year Rainfall (mm) Reduced Variate, y Probability, P Return Period (Years)Tr = 1/P

2014 423 -0.99 0.93 1.07

2009 546 -0.20 0.71 1.42

2011 567 -0.07 0.66 1.52

2012 661 0.54 0.44 2.27

2010 857 1.80 0.15 6.58

2013 945 2.38 0.09 11.26

Mean 666.32

S.D. 198.80 Probability, P = 1 – e –e –y

1.00 10.00 100.000

100200300400500600700800900

1000f(x) = 208.099081580789 ln(x) + 459.45749455339

Rainfall Frequency AnalysisGumbel’s Extreme Value Distribution

Method

Return Period (Years)

Rainfall (mm)

Flood Frequency AnalysisLog Pearson Type III Distribution Method:

Person (1930) developed this method. In this method, it is recommended to convert the data series to logarithms and then compute the following.1. Compute Logarithms of flow log Q2. Estimate Average of log Q3. Compute Standard Deviation σ log Q4. Compute Skew Coefficient,

Cs = (N Σ (log Q – log Q)3) / (N-1)(N-2) (σ log Q)3

5. QT = log Q + K (σ log Q)where K = log Pearson Frequency Factor based on Cs & Return Period

Year Rainfall (mm) log Rainfall2014 423 2.63

2009 546 2.74

2011 567 2.75

2012 661 2.82

2010 857 2.93

2013 945 2.98

log Mean 2.81log S.D. 0.13

Rainfall Frequency Analysis -Log Pearson Type III Distribution Method

QT = log Q + K (σ log Q)

Reference

Watershed Management by

Madan Mohan DasMimi Das Saikia

PHI Learning Private Limited