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Dr. Murari R. R. VARMA
Department of Civil Engineering
Thapar University, Patiala
CE 004Hydrology and Ground Water
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Drainage basin (watershed, catchment)
- Drains surface water to a common outlet
Drainage divide - how is it defined?
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Hydrographs
A stream flow or discharge hydrograph is a graph or table
showing the flow rate as a function of time at a given
location on the stream.
OR
A hydrograph is a graph showing discharge (i.e., stream
flow at the concentration point) versus time
A hydrograph is the response of a given catchment to a
rainfall
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Types
Long term Hydrographs(Annual, Monthly, Seasonal) Calculating Surface water Potential of a stream
Reservoir Studies
Drought studies
Storm or flood hydrograph Results from an isolated storm Single-peaked skewed distribution of discharge
Comprised of all runoff components namely surface, inter flow andbase flow
Hydrographs complex multiple peaks, kinks
Simple hydrographs resulting from isolated storms used foranalysis.
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Chow, 1988
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Chow, 1988
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Chow, 1988
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Factors affecting flood hydrograph
Physiographic factors
Basin Characteristics
Size
Times base larger for larger catchments
Shape
Fan shaped (high peak and narrow hydrographs) Elongated (broad and shallow peaks)
Slope
Time base smaller - steeper recession curves higher slopes
Nature of the valley
Elevation
Drainage density Ratio of total channel length to total drainage area higher DD, higher peaks.
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Physiographic factors
Infiltration characteristics Land use and land cover
Soil type and Geological conditions
Lakes, swamps and Other storages
Channel Characteristics CS, Roughness and Storage capacity
Climatic Factors
Storm Characteristics
Precipitation, intensity, duration, magnitude and movement of storm
Initial loss
Evapotranspiration
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Chow, 1988
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Hydrograph Components Rising Limb or curve
Controlled by basin and climatic factors
Crest Segment
Recession limb or curve
Controlled by catchment characteristics
Due to depletion of Storage (surface and channel, inteflow, groundwater)
Qt = Q0 Krt Barnes (1940) or Qt = Q0 e
-at where a = ln kr
Kr =recession constant of a value less than unity
Kr= krs . Kri. Krb
Krs varies 0.05 to 0.20Kri varies from 0.5 to 0.85
Krb varies 0.85 to 0.99
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Raghunath, 2006
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Base flow Separation
Raghunath, 2006
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DRH Direct Runoff Hydrograph
The SRH Obtained after base flow Separation is DRH
ERH Effective rainfall Hyetograph or hyetograph of rainfall
excess
Area of ERH x Area of catchment = area under a DRH=volume
of direct runoff
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Unit Hydrograph
Predict the flood hydrograph resulting from aknown storm in a catchment
Sherman 1932
The Hydrograph of direct runoff resulting from oneunit depth(usually 1cm) of rainfall excess occurringuniformly over the basin and at a uniform rate for aspecified duration( D hours).
-Unit refers to depth of rainfall excess - 1cm
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Features
- UH a lumped response of the catchment to a unit
rainfall excess ofD hr duration
- It relates only direct runoff to rainfall excess.
- Volume of water contained in the Unit
Hydrograph must be equal to rainfall excess- Area ofUH is equal to volume given by 1 cm
depth of rainfall excess over the catchment.
- Rainfall is considered to have an average intensity
of 1/D cm/h for the duration D hr of the storm.- Distribution is considered to be uniform all over
the catchment
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Basic Assumptions
Direct runoff response to a given effective rainfall in acatchment is time-invariant. DRH for a given ER in acatchment is same irrespective of
when it occurs
Linear Response Direct runoff response to rainfall excess is linear.
X1(t)->
y1(t) and X2(t)->
y2(t) X1(t) + X2(t) -> y1(t) + y2(t)
X2(t) = r X1(t) then y2(t) = r y1(t)
ER in a duration D is r times the unit depth the resultingDRH will have ordinates bearing ratio r to those of
correspondingD-
h unit hydrograph. Since the area resulting DRH should increase by ratio r the
base ofDRH will be the same as that of unit hydrograph.
Enables the method called super position to derive DRH
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if two ER ofDh duration occur consecutively,
their combined effect is obtained by
superposing the respective DRHs
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Application ofUnit Hydrograph
A DRH of a catchment can be calculated if an
appropriate UH is available
IfDh UH and Storm hyetograph are available
ERH is derived
ERH divided into M blocks ofD duration
Rainfall excess in each Dh is operated upon the UH
to obtain Various DRH curves
Ordinates of this DRH are lagged suitably to obtain
proper time sequence and then are collected and
added to obtain the nett DRH.
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Determination of DRH from known UH
and ERH
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Derivation ofUnit Hydrographs A no. of isolated Storm Hydrographs caused by short
spells of rainfall excess each of approximately sameduration. (0.90D to 1.1 Dh) are selected from acontinuously gauged runoff of the stream.
Baseflow is separated for each.
A no ofUnit Hydrographs are plotted on a common
pair of axes. Various UH Will not be identical
Adopt a mean of such curves (average to peak flowsand time peak are calculated)
Curve of best fit judged by eye is drawn
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UH
Criteria for Selecting Storm Events to
Derive UHs
Storms are isolated and occur individually;
Storm coverage should be uniform over the entire
watershed - watershed area should not be too large, say
200 ha < 5000 km
2
; Storms should be flood-producing storms ER is high,
10mm < ER < 50mm is suggested;
Duration of rainfall should be approx. 1/5 to 1/3 of basin
lag;
The number of storm events should be at least 5.
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UH
Derivation of UH (For simple ERH)
1. Analyze hydrograph and perform baseflow separation.
2. Measure the total volume of DRH in equivalent
uniform depth (EUD)
3. Find the effective rainfall such that VDRH = VERH.
4. Assume that ERHs are uniform, the UH can be derived
by dividing the ordinates of DRH by VDRH
5. The duration of the UH is the duration of ERH.
6. In rainfall-runoff analysis, the times of occurrence for
DRH and ERH are commonly made identical.
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Unit Hydrograph from a complex storm
- When suitable isolated storms are not available
- Decompose ameasured composite flood hydrograph intoits component DRHs and base flow
- A common UH of appropriate duration is assumed toexist
- Inverse of derivation of flood hydrograph from UH
Ordinates of Composite DRH
Q1 = R1u1Q2=R1u2+R2u1
Q3=R1u3+R2u2+R3u1
.
Q5 =R1u5+R2u4+R3u3
Solving by optimisation schemes by matrix methods
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UH's are derived from simple isolated storms and if
their durations do differ much ~ +- 20%D groupedunder one average duration D h.
Due to lack of data- for different durations
Other duration are derived from available durations
Two methods
1. Method of Super position
2. S curve
Unit Hydrographs of different Durations
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S-Curve Analysis (1)
S-curve is a DRH (also called S-hydrograph), resulting from acontinuous effective rainfall at a constant rate for an infinite
period.
Produced by summation of an infinite series of Dh Uhs spaced
Dh apart
After D hours, the continuous rainfall producing 1 cm (or 1
inch) of runoff every D hr would reach an equilibrium
discharge, Qs.
The equilibrium discharge, Qs, can be computed as
Qs = [A/D x 10-4
] m3
/hr
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S-Curve Analysis (2)
To derive a UH of duration D-hr from the S-curve, , obtained from D-hr UH, the S-curve is shifted to the right by T-hr. Then, the difference
between the two S-curves represents the direct runoff hydrograph
resulting from a rainfall excess of T/D cm or inches. The -hr UH then
can be easily obtained by dividing the ordinates of SA-SB by T/D.
Note: The S-curve tends to fluctuate about Qs. This means that the
initial UH does not represent actually the runoff at a uniform rate over
time. Such fluctuations usually occur because of lack of precision in
selecting UH duration. That is, the duration of the UH may differ
slightly from the duration used in calculation. Nevertheless, an average
S-curve can usually be drawn through the points without too much
difficulty.
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Use and Limitations of Unit HydrographUse
Development of Flood hydrographs for extreme rainfall
use in design of Hydraulic Structures
Extension of Flood flow records based on rainfall records
Development of Flood forecastingand warning systems
Limitations
Assumptions - uniform distribution, Intensity constant for
duration of rainfall excess
Basins above 5000 Km2 and below 200ha are not
preferred.
Precipitation must be from rainfall:snowmelt cannot be
satisfactorily represented
Large storages like tanks, Ponds , large flood bank storage
affect linear reationships
Precipitation has to uniform.
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Duration of Unit Hydrograph
Should not exceed the time of rise
Should not exceed the basin lag
Time of concentration
D~ of basin lag is ideal choice
>1200 km2 above 12 hr duration preferred.
Distribution graphs
Variation of UH introduced by Bernard (1935)
A D-h UH with ordinates representing the percentage
of surface runoff occurring in successive periods of equal
time intervals ofD-h
Useful in comparing the runoff characteristics of different
catchments.
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UH
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Synthetic Unit Hydrographs
No data ungauged catchments Remote locations
Empirical equations developed from available data is
developed for a region
Relation between basin and salient hydrograph
characteristics. UHs derived thus are called Synthetic UHs.
Methods for synthesising hydrographs for ungauged areas
have been developed by Bernard, Clark, McCarthy and
Snyder. Snyders method Appalachian mountains USA
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Snyders method
3 main parameters - base width (T), peak discharge (Qp)and lag time (basin lag, tp)
Basin lag or lag time (In snyders method midpoint of unit
rainfall excess to peak of the UH)
Represents the mean time of travel of water particlesfrom all parts of catchment to the outlet during a given
storm.
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UH
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UH
Finalizing of Synthetic UH
After obtaining the parameters of from Synders method a tentative UH is drawn
An S curve is developed and Plotted As UH ordinates will bw tentative
will have kinks
Smoothened and logical pattern of S curve is sketched From this S curve a tr hr UH can be derived back
Area under th UH is checked to see if it is 1cm
Time obtained from synthetic UH will be least accurate.
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UH
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UH
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UH