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CEL251 Hydrology: SURFACE FLOW : Runoff

Runoff

Runoff means the draining of precipitation from a catchment area through a surface channel.

It is the output from the catchment in a given time. Initially a large proportion of the

precipitation contributes to surface storage and soil moisture storage. There are two types of

storage: retention and detention. Retention is storage held for a long period of time and

depleted by evaporation. Detention is short term storage depleted by flow away from the

storage location viz. unsaturated flow, groundwater flow and overland flow. Rainfall excess,

which is neither retained on the land surface nor infiltrated into the soil, moves over the land

surfaces to reach smaller channels and then bigger channel to form streamflow. The

precipitation which becomes streamflow may reach the stream by overland flow or

subsurface flow or both. Overland flow and channel flow reaching the catchment outlet is

called surface runoff. The part of the precipitation that infiltrates and joins channel at some

downstream location is known as interflow or subsurface storm flow. The amount of

interflow depends on the geological conditions of the catchment. The velocity of subsurface

flow is so low that not all of a watershed can contribute subsurface flow to a stream during a

storm. Depending upon the time delay between the infiltration and the outflow it may be

prompt inter flow or delayed interflow. Further, based on the time delay between the

precipitation and the runoff, the runoff may be (i) direct runoff, or (ii) base flow. Direct

runoff enters the stream immediately after the precipitation (surface runoff plus prompt

interflow plus precipitation on channel surface). The delayed flow that reaches a steam

essentially as groundwater flow is called base flow.

Runoff representing the response of a catchment to the precipitation reflects the

integral effects of a wide range of catchment (soil, vegetation, slope, geology, shape and

drainage density), climatic (temperature, humidity, wind velocity etc which influence

evapotranspiration), and precipitation (intensity, distribution in time and space and its

variability) characteristics. True runoff is therefore streamflow in the natural conditions

without human interventions. Such a streamflow unaffected by works of man is called virgin

flow.

Horton’s Law of Streams Ordering

Rainfall excess moves over the land surfaces to

reach smaller channels. This portion of the

runoff is called overland flow and involves

building up storage over the surface and draining

off the same. Overland flow starts as sheet flow,

as flow accumulates going down a slope its

depth increases until discharges into a stream

channel. Usually the lengths and depths of

overland flow are small and the flow is in

laminar regime. Flows from several small

channels join bigger channels and so on till the

flow reaches the catchment outlet. Horton’s laws

of Stream ordering (laws relating the number and

length of streams of different order) (1) the

smallest recognizable channels are designated

order 1; these channels normally flow only

during wet weather; (2) where two channels of order 1 join, a channel of order 2 results

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downstream; (3) in general where two channels of order i join, a channel of order i+1 results;

(4) where a channel of lower order joins a channel of higher order, the channel downstream

retains the higher of the two orders; (5) the order of the drainage basin is designated as the

order of the steam draining its outlet, the highest stream order in the basin.

Horton found that the bifurcation ratio RB is constant from one order to another for a

basin. This is known as Horton’s law of Stream Numbers. The typical range of RB is 3 to 5

while the theoretical minimum possible value is 2.

11 +==

+ iorderofchannelsofNumber

iorderofchannelsofNumber

N

NR

i

iB

Similarly there is a length ratio RL and a Horton’s law of Stream Length

iorderofchannelsoflengthAverage

iorderofchannelsoflengthAverage

L

LR

i

i

L

11 +== +

The drainage density D is the ratio of the total length of stream channels in a catchment to its

area.

catchmentofArea

ordersallofchannelssteamoflengthTotal

A

LD

ij == ∑∑

Presentation of Runoff Data

(1) HYDROGRAPH: A stream flow or runoff or discharge hydrograph is a graph or table

showing the runoff or flow rate as a function of time at a given location on the stream. The

area under a hydrograph between a time intervals is equal to the volume of runoff during that

interval. In effect the hydrograph is an integral expression of the physiographic and climatic

characteristics that govern the relationship between the rainfall and runoff of a particular

drainage basin. A hydrograph may be an annual hydrograph or a storm hydrograph.

The annual hydrograph is a plot of streamflow versus time over a year, shows the long

term balance of precipitation, evaporation and stream flow in a watershed. The total volume

of flow under the annual hydrograph is the basin yield. The basin yield of a stream is mainly

controlled by the amount of rainfall and evapotranspiration. The geology of the catchment is

significant to the extent of deep percolation losses. Annual hydrographs are of use in (i)

calculating the surface potential of a stream (ii) reservoir sizing and water release studies, and

(ii) drought studies. The annual hydrographs differ depending on the type of a stream. A

stream may be (i) perennial, (ii) intermittent, or (iii) ephemeral. A perennial stream is one

which always carries some flow. There is considerable amount of groundwater flow

throughout the year. Even during dry seasons the water table will be above the bed of the

stream. It is an effluent stream. Most of the basin yield for such a stream usually comes from

base flow, indicating that a large proportion of the rainfall is infiltrated into the basin and

reaches the stream as subsurface flow. An intermittent stream has limited contribution from

the groundwater. During the wet season the water table is above the stream bed and there is a

groundwater contribution to stream flow. However, during dry seasons the water table drops

to a level lower than that of the stream bed and the stream dries up. An ephemeral stream is

one which does not have any groundwater contribution. The annual hydrograph of such a

stream show series of short duration spikes marking flash flows in response to storms. The

stream becomes dry soon after the end of the storm flow since it is an influent stream. Basin

yield from such catchment is the result of direct runoff from large storms.

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A storm hydrograph is graph for an isolated storm. The shape of the storm hydrograph

and hence the peak flow is essentially controlled by the storm and physical characteristics of

the catchment. Evapotranspiration plays a minor role in this. Storm hydrographs are essential

in analysing stream characteristics associated with floods.

(2) FLOW DURATION CURVE: Flow duration curve is another method of studying

streamflow variability. A flow duration (or discharge-frequency) curve of a stream is a plot of

discharge against the percentage of time the flow was equalled or exceeded. The streamflow

data is arranged in a descending order of discharges. If N numbers of data points are used,

then the plotting position (Pp) of any discharge (Q) at order m is

%1001×

+=

N

mPp

Arithmetic scale paper or semi-log or log-log paper is used depending upon the range of data

and use of the plot. The flow duration curve represents the cumulative frequency distribution

and can be considered to represent the streamflow variation of an average year. The ordinate

Qp at any percentage probability Pp represents the flow magnitude in an average year that can

be expected to be equalled or exceeded Pp % of time and is termed as Pp % dependable flow.

The slope of a flow duration curve depends upon the interval of data selected. This curve is

useful in comparing the flow characteristics of different streams, in evaluating various

dependable flows in the planning of water resources projects, in the design of drainage

systems, and in flood control studies.

(3) FLOW-MASS CURVE: The flow-mass curve is a plot of the cumulative discharge

volume against time plotted in chronological order. The ordinate of the mass curve, V at any

time t from the beginning is

∫=t

dtQV0

Since hydrograph is a plot of Q vs. t,

mass curve is an integral (summation)

curve of the hydrograph; conversely

slope of the mass curve at any point

represents rate of flow (Q), i.e. ordinate

of the hydrograph, at that instant. The

slope of line joining two points on a mass

curve represents average discharge

between these two points. Mass curve is

used in calculation of storage

volume/reservoir capacity, and in

calculation of maintainable demand from

a given capacity reservoir.

Calculation of reservoir capacity: If it is

assumed that the reservoir is full at the

beginning of a dry period the maximum

amount of water drawn from the storage

is the cumulative difference between inflow and outflow/demand volumes from the

beginning of the dry season, so storage S required is

( )∑∑ −= outflowflowinS max

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The storage S which is the maximum cumulative deficiency in any dry season is

obtained as the maximum difference in the ordinate between mass curves of supply/ inflow

and demand/outflow. The minimum storage volume required by a reservoir is the largest of

such S values over different dry periods.

Calculation of maintainable demand from a given capacity reservoir: In the converse case

tangents are drawn from the ridges of the inflow mass curve across the next valleys at various

slopes. The demand line that requires just the given storage is the proper demand that can be

sustained by the reservoir in that dry period. Similar demand lines are drawn at other valleys

in the mass curve. The smallest of the various demands thus found denotes the maximum or

safe maintainable demand that can be sustained by the given storage.

It is to be noted that (i) the

vertical distance between two

successive tangents to a mass curve

at the ridges represent the water

wasted over the spillway and (ii) a

demand line must intersect the mass

curve if the reservoir is to refill.

Non-intersection of the demand line

and mass curve indicates

insufficient inflow. Further it is

necessary to account for

evaporation, leakage and other

losses from the reservoir in the

analysis of problems related to

reservoirs. These losses may either

be included in demand rates or

deducted from inflows. In the latter

method the mass curve may have negative slopes at some points.

Sequent Peak Algorithm: In storage analysis by mass curve method it is assumed that (i) if N

years data are available the inflow and demands are assumed to repeat in cyclic progression

of N year cycles; (ii) the reservoir is assumed to be full at the beginning of dry period.

Sequent peak algorithm is a variation of the basic mass curve method to facilitate graphical

plotting and handling of large data. In the sequent peak algorithm a mass curve of cumulative

net flow volume against

time (or residual mass

curve) is used. Net flow

volume = Inflow volume –

Outflow volume. For any

peak P1, the next

following peak (P2) of

magnitude greater than P1,

is called a sequent peak.

The lowest point between

P1 and P2 is called trough

T1. Then the reservoir

capacity is P1 – T1.

Likewise subsequent

sequent peaks Pi and

troughs Ti can be found and the required reservoir capacity S = Max of (Pi – Ti).

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Basin Yield or Annual Runoff Volume

The total volume of water that can be expected from a stream in a given period such as a

water year is called the yield of the stream or the catchment basin. The water year in India is

from June 1st to May 31

st since during this period a complete annual cycle of climatic change

is expected. The basin yield is invariably calculated in all water resources development

studies. The methods used are (i) hydrograph method, (ii) runoff – rainfall correlation

method, (ii) empirical equations, and (iv) watershed simulations.

Rainfall – runoff correlation: The relationship between rainfall and the resulting runoff is

quite complex and is influenced by a host of factors relating the catchment and climate. For

simplicity a linear correlation between the rainfall and runoff is adopted through regression

analysis. If the resultant correlation coefficient is near to unity, the linear relationship is

acceptable. The equation straight line regression between runoff (R) and rainfall (P) is

baPR +=

and the coefficients a and b are given by

( ) ( )( )( ) ( )22 ∑∑

∑∑∑−

−=

PPN

RPPRNa and

( ) ( )N

PaRb

∑∑ −=

where N = number of observation sets of P and R. The coefficient of correlation r is

( ) ( )( )

( ) ( )[ ] ( ) ( )[ ]2222 ∑∑∑∑∑∑∑

−×−

−=

RRNPPN

RPPRNr

The value of r may lie between -1 to +1. But rainfall and runoff have always positive

correlation and a value of correlation coefficient between 0.6 to 1.0 indicates a good

correlation. For large catchments, it is found advantageous to have an exponential

relationship as baPR = . The correlation method is adequate for preliminary studies, for

accurate results sophisticated methods are adopted.

Empirical Equations: Empirical equations are applicable only to the region in which they

were derived. These relations are essentially rainfall runoff relations with additional third or

fourth parameters to account for climatic or catchment characteristics. Simplest one is in the

form

PCR R=

where CR is runoff coefficient, which depends upon the type of catchment and nature of

monsoon rainfall. There are tabulated for different investigators for the different regions.

Watershed Simulation: This is based on the hydrologic water budget equation for the

determination of runoff for a given period as

SEPR ∆−−=

This technique of predicting the runoff, which is the catchment response to a given rainfall

input, is called deterministic watershed simulation. In this the mathematical relationships

describing the interdependence of various parameters in the system are first prepared and this

is called the model.

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Droughts

A drought is a climatic anomaly characterized by deficit supply of moisture. This may result

from subnormal rainfall over large regions causing below normal natural availability of water

over long periods of time. Drought phenomenon is a hydrological extreme like flood and is a

natural disaster. However unlike floods the droughts are of creeping kind; they develop in a

region over a length of time and sometimes may extend to continental scale. The

consequences of droughts on the agricultural production, hydropower generation and regional

economy are well known. Further during droughts the quality of available water is highly

degraded resulting in serious environmental and health problems. Meteorological drought is a

situation where there is more than 25% decrease in precipitation from normal over an area. A

year is considered a drought year if more than 20% area of a country is affected by a

moderate (rainfall is 50-75% of normal) and/or severe (rainfall < 50% of normal) drought. If

the probability of occurring a drought in an area is 20 to 40% it is a drought prone area; if this

probability is greater than 40% then it is chronically drought prone area. Meteorological

drought if prolonged results in hydrological drought with marked depletion of surface water

and ground water. The consequences are in the drying up tanks, reservoirs, streams and

rivers, cessation of springs and fall in the ground water level. Agricultural drought occurs

when the soil moisture and rainfall are inadequate during the growing season to support

healthy crop growth to maturity. Drought Management: The causes of drought are essentially

due to temporal and spatial aberrations in the rainfall, improper management of available

water and lack of conservation of runoff in surface and sub-surface storages. As such the

strategy for making drought prone areas less vulnerable to drought associated problems

should include the following measures: (1) creation of storages through water resources

development, (2) inter basin transfer of surface waters, (3) development of ground water

potential, (4) development of appropriate water harvesting practices, (5) soil moisture

conservation measures, (6) minimization of evaporation losses from water bodies, and (7)

encouraging pastures, forestry and other modes of development which are relatively less

water demanding.