m2 lecture 2 -unit hydrograph-2015
DESCRIPTION
HydrologyTRANSCRIPT
Transforming the Runoff
E J Peters 2015
• MODULE 2:Hydrograph AnalysisUNIT 2:UNIT Hydrograph (UH)OBJECTIVESThe student should be able to: Represent graphically the UH Estimate “excess rain” from a storm Separate baseflow from direct runoff on a
hydrograph Derive a UH from direct runoff data, watershed
area, and baseflow information
E J Peters 2015
Slide 2 of 65
E J Peters 2015
Unit hydrograph (UH)• Sherman (1934) originally advanced the theory of
the unit hydrograph.
• That is a basin outflow resulting from one inch, one cm, one mm etc. of runoff generated uniformly over the drainage area at a uniform rainfall during the specified period
• UH theory can be summarized as “ the hydrologic system is linear and time invariant (Dooge, 1973)
E J Peters 2015
The Basic Process
E J Peters 2015
Excess Precip. Model
Excess Precip.
Excess Precip.
Runoff Hydrograph
Runoff Hydrograph
Stream and/or Reservoir “Routing”
Downstream Hydrograph
Basin “Routing” UHG Methods
Necessary for a single basin
Unit Hydrographs
Assumptions• Rainfall excesses of equal duration produce
hydrographs with equivalent time base regardless of intensity
• Direct runoff ordinates for a storm of given duration are directly proportional to rainfall excess volumes.( 3 times the rainfall would triple hydrograph ordinates)
• Time distribution of direct runoff is independent of antecedent precipitation
• Distribution is the same for all storms of equal duration (spatially and temporally)
E J Peters 2015
Abstraction (Losses) EstimationPhi – Index Method
• Excess (effective) rainfall – Rainfall that is not retained or
infiltrated– Becomes direct runoff– Excess rainfall hyetograph (excess
rainfall vs time)
• Abstraction (losses)– Difference between total and
excess rainfall hyetographs
• Phi – Index– Constant rate of abstraction
yielding excess rainfall hyetograph with depth equal to depth of direct runoff
M
mmd tRr
1
interval time
runoffdriecttongcontributi
rainfallofintervals#
indexPhi
rainfall observed
runoffdirect ofdepth
t
M
R
r
m
d
E J Peters 2015
Phi index of 2 cm
E J Peters 2015
Graphical representation
E J Peters 2015
Step : Separate the baseflow to obtain the surface runoff
E J Peters 2015
Semi-log PlotSemi-log Plot
E J Peters 2015
1
10
100
1000
10000
100000
29 34 39 44 49 54 59 64 69 74 79 84 89 94 99 104
109
114
119
124
129
134
Time (hrs.)
Flo
w (
cfs)
Recession side of hydrograph becomes linear at approximately hour
64.
The Unit Hydrograph
E J Peters 2015
Unit Hydrograph “Lingo”Duration Lag Time Time of Concentration Rising Limb Recession Limb (falling limb) Peak Flow Time to Peak (rise time) Recession Curve Separation Base flow
E J Peters 2015
E J Peters 2015
Unit hydrographUnit hydrographE
ffec
tive
rai
n
Time
T
T
1
Su
rfac
e ru
nof
f, R Volume of surface runoff
=area under hydrograph =volume of effective rainfall
E J Peters 2015
Principle of linearity
21
0.25
E J Peters 2015
E J Peters 2015
Principle of superpositionPrinciple of superposition
T
2TT
T
R1R2
SR1
SR2
Time
Eff
ecti
ve
rain
fall
Su
rfac
e ru
nof
f
E J Peters 2015
E J Peters 2015
Obtain the surface response
E J Peters 2015
Selecting storms for deriving the Unit Hydrograph
• Storms that occur individually, simple storm structure• Storms that have uniform distribution of rainfall
throughout the period of rainfall excess• Storms that have a uniform spatial distribution over
the entire watershed• Duration of the rainfall excess should be
approximately 25-30% of the lag time t p
• Direct runoff should be between 0.5 to 1.75 cm
E J Peters 2015
Application of a unit hydrographApplication of a unit hydrographdemonstrating superposition, linearity and laggingdemonstrating superposition, linearity and lagging
T
Total surface runoff
SR1 (surface runoff due to R1)
SR2 (surface runoff due to R2)
2TT
Time2T
Su
rfac
e ru
nof
fE
ffec
tive
rai
n
E J Peters 2015
0
10
20
30
40
50
60
70
80
90
100
0 1 2 3 4 5 6 7 8 9 10 11 12Time (hours)
Su
rfac
e ru
nof
f (m
3 s-
1 )
0
0.5
1
1.5
2
Eff
ecti
ve r
ain
(cm
)
E J Peters 2015
Changing the unit Hydrograph duration
E J Peters 2015
EXAMPLE: FOR AN E
Time(hr)
Q(m3s-1) Q –BF (m3s-1) (direct runoff)
0 100 0
1 100 0
2 300 200
3 500 300
4 900 700
5 1200 1100
6 1150 1050
7 950 850
8 600 500
9 450 350
10 300 200
11 200 100
12 100 0
13 100 0
The base flow is estimated as 100 m3s-1
Subtract baseflow from column to give column (3)
The gauge readings at the station for the storm are shown n column (2)
E J Peters 2015
Unit Hydrograph summary
• The unit hydrograph results from 1cm, 1 in or 1 mm of excess precipitation (or runoff) spread uniformly in space and time over a watershed a given duration.
• The key points1unit of EXCESS rainSpread uniformly over space- evenly distributed over
the watershedUniformly in timeThere is a given duration
E J Peters 2015
Rule of thumb for using UH• Storm should be fairly uniform in nature• Excess precipitation fairly uniform in basin• Initial conditions generally similar in basin• No breaks or periods of no precipitation during
storm• Storm produces 1 unit of excess precipitation ie
area under hydrograph after correcting for base flow= 1unit
E J Peters 2015
The one-hour unit hydrograph for a watershed is given below
(a) Estimate the hydrograph from a storm of two hours duration with an excess precipitation rate of 0.5 cm/hr for the first hour and 0.3 cm/hr for the second hour.
(b) Develop a 2 hour unit hydrograph for this watershed.
Time (hr) Q (m3s) 0 0 0.5 80 1.0 120 1.5 200 2.0 100 2.5 50 3.0 0 3.5 4.0
E J Peters 2015
E J Peters 2015
SummaryUnit hydrographs• The first thing to remember when using unit hydrographs is
that they relate effective rainfall to surface runoff. If you are given total rainfall amounts, you will need to determine effective rainfall before doing anything else. In practice this can be done either by using a constant loss (e.g. phi-index) or by using Hortonian infiltration. (Refer back to infiltration lecture notes.)
• In this case you are provided with total rainfall depths, and are told that the phi-index = 0.6 cm hr -1 . So, effective rainfall is simply the total rainfall depth (in each hour) minus the infiltrated amount as given by the phi-index.
E J Peters 2015
Summary
• The unit hydrograph ordinates are multiplied by the effective rainfall to compute the surface runoff arising from that rainfall. This procedure is repeated for each individual hour of rain.
• Remember that the runoff amounts arising from rainfall falling in the second hour must be lagged by one hour, the runoff arising from rainfall falling in the third hour must be lagged by two hours and so on - this accounts for the zeroes in the middle portion of the table.
• This is the second thing to remember when dealing with unit hydrographs!
E J Peters 2015
Summary
E J Peters 2015