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Hydrologic Analysis. Dr. Bedient CEVE 101 Fall 2013. Review. A watershed- a basic unit used in most hydrologic calculations relating to the water balance or computation of rainfall-runoff Watershed Response-how the watershed response to rainfall. Several characteristics will effect response - PowerPoint PPT Presentation
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Hydrologic Analysis
Dr. Bedient CEVE 101 Fall 2013
Review A watershed- a basic unit used in
most hydrologic calculations relating to the water balance or computation of rainfall-runoff
Watershed Response-how the watershed response to rainfall. Several characteristics will effect response Drainage Area Channel Slope Soil Types Land Use Land Cover Main channel and tributary
characteristics-channel morphology The shape, slope and character of
the floodplain There is a way to plot the flow
from the outlet over a space of time. This graphical representation is called a hydrograph
Typical Graphs for Hydrologic Analysis
HydrographHyetograph
Cummulative Rainfall
HydrographsHydrograph: continuous plot of instantaneous
discharge Flow rate (cfs or cms) vs. time
Watershed factors of importance: Size and shape of drainage area Slope of the land surface and the main channel Soil types and distribution in watershed
Meteorological Factors that influence the shape and volume of runoff: Rainfall intensity and pattern Areal distribution of rainfall over the basin Size and duration of the storm event
Hurricane Ike (September 13) and FAS2 Prediction
Made by Nick FANG at the Phil Bedient Water Resources Research Group at Rice University.
Typical Hydrographs
Rising limb Crest segment Recessive curve Falling limb Base Flow
The Watershed Response Hydrograph
As rain falls over a watershed area, a certain portion will infiltrate the soil. Some water will evaporate to atmosphere.
Rainfall that does not infiltrate or evaporate is available as overland flow and runs off to the nearest stream.
Smaller tributaries or streams then begin to flow and contribute their load to the main channel at confluences.
As accumulation continues, the streamflow rises to a maximum (peak flow) and a flood wave moves downstream through the main channel.
The flow eventually recedes or subsides as all areas drain out.
Hyetograph Graph showing rainfall intensity vs time
(in./hr) Can be calculated if given cumulative rainfall
(P) or gross rainfall (I)
Example of plotting hyetographs and rainfall For the rainfall given below, plot cumulative
rainfall (P) and gross rainfall hyetograph with ∆t = 30 min.
Time (min) Rainfall (I) (in)
0 0
30 0.2
60 0.1
90 0.3
Example of plotting hyetograph and rainfall We are given gross rainfall, to find cumulative
rainfall you need to take rainfall from each time step and you add it to the previous time step’s result so 0 + 0 (I0) = 0 0+ 0.2 (I1)= 0.2 0.2 + 0.1(I2) = 0.3 0.3+ 0.3 (I3)= 0.6
The resulting table will beTime (min) Cumulative Rainfall
(P) (in)
0 0
30 0.2
60 0.3
90 0.6
To go from P to I you take your rainfall at a time step and subtract the previous time step-try it and see if you get the same results.
Example of plotting hyetograph and rainfall To plot rainfall intensity (in./hr) you take your
gross rainfall (I) and divide it by your time step (30 min = 0.5 hr) 0 / 0.5 = 0 in/hr 0.2 / 0.5 = 0.4 in/hr 0.1 / 0.5 = 0.2 in/hr 0.3 / 0.5 = 0.6 in/hr
Determining volume of runoff The volume of runoff from a watershed is
equal to the area under the hydrograph. In graph form, an approximation can be made
by which estimates the volume as a bar graph. Each individual bar is then added to give volume.
In table form, this is done by multiplying flow (Q) by the time step.
This is summarized in the next example.
Example of determine total volume of runoff Given the hydrograph, determine the total
volume of runoff for a 2600 acres-basin.
Adapted from Bedient et al, Hydrology and floodplain analysis, 4 th ed. Example 2-1
Example of determine total volume of runoff Step 1: We can determine the volume by creating a bar
graph to estimate volume as shown in the next figure:
Step 2 = Sum the bar graphs
So total volume = 9100 cfs-hr= 9027.78 ac-in
(1.008 cfs-hr = 1 ac-in)
Time (hr) Q (cfs) Volume (cfs-hr)
0-2 100 200
2-4 300 600
4-6 500 1000
6-8 700 1400
8-10 650 1300
10-12 600 1200
12-14 500 1000
14-16 400 800
16-18 300 600
18-20 200 400
20-22 150 300
22-24 100 200
24-26 50 100
Finding the volume left to infiltration Depending on the soil types, runoff will not
begin until the soil is completely saturated. There is a way to find how much water was
infiltrated into the soil during a rain event. If given an amount of rainfall and the amount
of direct runoff. Infiltration is equal to the difference between rainfall and direct runoff (evaporation is ignored)
This is summarized in the next example.
Example of finding the volume left to infiltration. Given our previous
2600-acre basin with a runoff of 9100 cfs-hr. Determine the amount of volume left to infiltration knowing that there was 4.0 in. of rainfall.
Example of finding the volume left to infiltration. Step 1: Convert cfs-hr to ac-in
9100 cfs = 9027.78 ac-in Step 2 = Divide ac-in by acres
9027.78 ac-in / 2600 ac = 3.47 = 3.5 inches- amount of direct runoff
Step 3 = Subtract direct runoff from rainfall 4.0 – 3.5 = 0.5 in was left to infiltration.
Unit Hydrographs Unit Hydrograph: The unit
hydrograph represents the basin response to 1 inch (1 cm) of uniform net rainfall for a specified duration.
Works best for relatively small subareas (1-10 sq miles)
Assumptions Rainfall excesses of equal
duration are assumed to produce hydrographs with equivalent time bases
Rainfall distribution is assumed to be the same for all storms of equal duration
Direct runoff ordinates for a storm of given duration are assumed directly proportional to rainfall excesses volumes 2X the rainfall produces a
doubling of hydrograph ordinates
Unit Hydrographs In summary
The hydrologic system is linear and time invariant. This means that complex storm hydrographs
(the hydrographs we’ve looked at) can be produced by adding up individual unit hydrographs, adjusted for rainfall volumes and added and lagged in time.
This is known as hydrograph convolution (see next example)
Timing Parameters: UH
Lag timeLag time: (L or Tp) time from the center of mass of rainfall to the peak of the hydrograph
Time of RiseTime of Rise: (Tr) the time from the start of rainfall excess to the peak of the hydrograph
Time of ConcentrationTime of Concentration: (Tc) the time from the end of the net rainfall to the inflection point of the hydrograph
Time BaseTime Base: (Tb) the total duration of the DRO hydrograph
Developing a Storm Hydrograph from a 1 hr Unit Hydrograph-Unit Hydrograph Convolution To find the storm hydrograph from the unit
hydrograph it is necessary to have the rainfall ordinates for that given storm.
The flow (U) ordinates of the Unit Hydrograph are also needed.
Then, the (U) will be multiplied by P1 then by P2 until it has been multiplied by all the rainfall ordinates.
Everytime you move to a different rainfall ordinate, you lag by one hour (since we have a 1-hr UH).
Once everything has been multiplied and lagged. For each hour, the resulting P*U for that hour are added. This gives the flow of the storm (Q) for that hour.
These steps are shown in the next example
Unit Hydrograph Convolution Deriving hydrographs from multiperiod rainfall
excess
or
Where Qn = storm hydrograph ordinate
Pi = rainfall excess
Uj = UH ordinate where j = n - i + 1
Storm Hydrograph from the Unit Hydrograph Given the rainfall excess and the 1-hr UH derive
the storm hydrograph for the watershed using hydrograph convolution. Compute the resulting hydrograph and assume no losses.
P = [0.5, 1.0, 1.5, 0, 0.5] in.U = [0,100, 320, 450, 370, 250, 160,
90, 40, 0] cfs
From Bedient et al. Hydrology and floodplain analysis. 4th Ed. Example 2-5
Storm Hydrograph from the Unit Hydrograph
Want to multiply U by each P and lag by one hour everytime you move to the next P.
Then for each hour you add your results for that following time, that will give you Q.
Time (hr) P1*U P2*U P3*U P4*U P5*U Q
0 0.5
1 0.5 1
2 0.5 1 1.5
3 0.5 1 1.5 0
4 0.5 1 1.5 0 0.5
5 0.5 1 1.5 0 0.5
6 0.5 1 1.5 0 0.5
7 0.5 1 1.5 0 0.5
8 0.5 1 1.5 0 0.5
9 0.5 1 1.5 0 0.5
10 1 1.5 0 0.5
11 1.5 0 0.5
12 0 0.5
13 0.5
P = [0.5, 1.0, 1.5, 0.0, 0.5] in.U = [0,100, 320, 450, 370, 250, 160, 90, 40, 0] cfs
Step 1
Want to multiply U by each P and lag by one hour everytime you move to the next P.
Then for each hour you add your results for that following time, that will give you Q.
Time (hr) P1*U P2*U P3*U P4*U P5*U Q
0 0.5*0 = 0
1 0.5*100 = 50 1*0 = 0
2 0.5*320 = 160
1*100 = 100
1.5*0 = 0
3 0.5*450 = 225
1*320 = 320
1.5*100 = 150
0*0 = 0
4 0.5*370 = 185
1*450 = 450
1.5*320 = 480
0*100 = 0 0.5*0 = 0
5 0.5*250 = 125
1 *370 = 370
1.5*450 = 675
0*320 = 0 0.5*100 = 50
6 0.5*160 = 80 1*250 = 250
1.5*370 = 555
0*450 = 0 0.5*320 = 160
7 0.5*90 = 45 1*160 = 160
1.5*250 = 375
0*370 = 0 0.5*450 = 225
8 0.5*40 = 20 1*90 = 90 1.5*160 = 240
0*250 = 0 0.5*370 = 185
9 0.5*0 = 0 1*40 = 40 1.5*90 = 135 0*160 = 0 0.5*250 = 125
10 1*0 = 0 1.5*40 = 60 0*90 = 0 0.5*160 = 80
11 1.5*0 = 0 0*40 = 0 0.5*90 = 45
12 0*0 = 0 0.5*40 = 20
13 0.5*0 = 0
Storm Hydrograph from the Unit HydrographP = [0.5, 1.0, 1.5, 0.0, 0.5] in.U = [0,100, 320, 450, 370, 250, 160, 90, 40, 0] cfs
Step 2
Want to multiply U by each P and lag by one hour everytime you move to the next P.
Then for each hour you add your results for that following time, that will give you Q.
Time (hr) P1*U P2*U P3*U P4*U P5*U Q
0 0.5*0 = 0 0
1 0.5*100 = 50 1*0 = 0 50
2 0.5*320 = 160
1*100 = 100
1.5*0 = 0 160+100+0=260
3 0.5*450 = 225
1*320 = 320
1.5*100 = 150
0*0 = 0 225+320+150+0 = 695
4 0.5*370 = 185
1*450 = 450
1.5*320 = 480
0*100 = 0 0.5*0 = 0 1115
5 0.5*250 = 125
1 *370 = 370
1.5*450 = 675
0*320 = 0 0.5*100 = 50
1220
6 0.5*160 = 80 1*250 = 250
1.5*370 = 555
0*450 = 0 0.5*320 = 160
1045
7 0.5*90 = 45 1*160 = 160
1.5*250 = 375
0*370 = 0 0.5*450 = 225
805
8 0.5*40 = 20 1*90 = 90 1.5*160 = 240
0*250 = 0 0.5*370 = 185
535
9 0.5*0 = 0 1*40 = 40 1.5*90 = 135 0*160 = 0 0.5*250 = 125
300
10 1*0 = 0 1.5*40 = 60 0*90 = 0 0.5*160 = 80
140
11 1.5*0 = 0 0*40 = 0 0.5*90 = 45
45
12 0*0 = 0 0.5*40 = 20
20
13 0.5*0 = 0 0
Storm Hydrograph from the Unit HydrographP = [0.5, 1.0, 1.5, 0.0, 0.5] in.U = [0,100, 320, 450, 370, 250, 160, 90, 40, 0] cfs
Step 3
UH Convolution Example Pn= [0.5, 1.0, 1.5, 0.0, 0.5] in
Un= [0, 100, 320, 450, 370, 250, 160, 90, 40, 0] cfsTime (hr)
P1Un P2Un P3Un P4Un P5Un Qn
0 0 0
1 50 0 50
2 160 100 0 260
3 225 320 150 0 695
4 185 450 480 0 0 1115
5 125 370 675 0 50 1220
6 80 250 555 0 160 1045
7 45 160 375 0 225 805
8 20 90 240 0 185 535
9 0 40 135 0 125 300
10 0 60 0 80 140
11 0 0 45 45
12 0 20 20
13 0 0
Uniform Open-Channel Flow Uniform open channel flow is
the hydraulic condition in which the water depth and the channel cross section do not change over some reach of the channel.
The total energy change over the channel reach is exactly equal to the energy losses of boundary friction and turbulence.
Strict uniform flow is rare in natural streams because of the constantly changing channel conditions. Often assumed in natural
streams for engineering calculations.
To calculate flow within a channel equations such as the Chezy eq. and Manning’s equation are used.
Manning’s Equation
Q = Flowrate, cfsn = Manning’s Roughness Coefficient (ranges from 0.015 - 0.15)S = Slope of channel in longitudinal directionR = A/P, the hydraulic radius, where:A = Cross-sectional Area of Flow (area of trapezoid or flow area)P = Wetted Perimeter (perimeter in contact with water)
P = Wetted Perimeter Pipe P = Circum. Natural Channel
Q=
1.49nAR
23 S
A AA
Note: this equation is for U.S Customary units-for the metric units 1.49 is 1
Manning’s variables for different cross-sections
Example of calculating flow Brays Bayou can be represented as a single
trapezoidal channel with a bottom width b of 75 ft and a side slope of 4:1 (horizontal:vertical) on average. If the normal bankfull depth is 25 ft at the Main St. bridge, compute the normal flow rate in cfs for this section. Assume that n = 0.020 and S = .0002 for the concrete-lined channel.
From Bedient et al. Hydrology and Floodplain analysis 4th Ed. Example 7-3
Example of calculating flow Given
y = 25 ftn = 0.02S = 0.002b = 75 ft
Manning’s Equation is used to compute Q and from the geometry provided: =
A = = 4375 ft^2 P = = 281.16 ft
Then all the values are plugged in to give Q = 28,730 cfs
Q=
1.49nAR
23 S