Excess Rainfall Reading for today’s material: Sections 5.3- 5.8
Feb 23, 2016
Excess Rainfall Reading for today’s material:
Sections 5.3-5.8
Excess rainfall • Rainfall that is neither retained on the land
surface nor infiltrated into the soil• Graph of excess rainfall versus time is
called excess rainfall hyetograph• Direct runoff = observed streamflow -
baseflow• Excess rainfall = observed rainfall -
abstractions• Abstractions/losses – difference between
total rainfall hyetograph and excess rainfall hyetograph
f-index
• f-index: Constant rate of abstraction yielding excess rainfall hyetograph with depth equal to depth of direct runoff
• Used to compute excess rainfall hyetograph when observed rainfall and streamflow data are available
f-index method
M
mmd tRr
1
f
• Goal: pick t, and adjust value of M to satisfy the equation
• Steps1. Estimate baseflow2. DRH = streamflow
hydrograph – baseflow3. Compute rd, rd =
Vd/watershed area4. Adjust M until you get a
satisfactory value of f5. ERH = Rm - ft
interval timerunoffdriecttongcontributi
rainfallofintervals#indexPhi
rainfall observedrunoffdirect ofdepth
t
M
Rr
m
d
f
ExampleTime Observed
Rain Flowin cfs
8:30 203
9:00 0.15 246
9:30 0.26 283
10:00 1.33 828
10:30 2.2 2323
11:00 0.2 5697
11:30 0.09 9531
12:00 11025
12:30 8234
1:00 4321
1:30 2246
2:00 1802
2:30 1230
3:00 713
3:30 394
4:00 354
4:30 303
0
2000
4000
6000
8000
10000
12000
7:30 PM 9:00 PM 10:30 PM 12:00 AM 1:30 AM 3:00 AM 4:30 AM 6:00 AM
Time
Stre
amflo
w (c
fs)
0
0.5
1
1.5
2
2.5
No direct runoff until after 9:30And little precip after 11:00
Have precipitation and streamflow data, need to estimate losses
Basin area A = 7.03 mi2
Example (Cont.)• Estimate baseflow (straight line method)
– Constant = 400 cfs
0
2000
4000
6000
8000
10000
12000
7:30 PM 9:00 PM 10:30 PM 12:00 AM 1:30 AM 3:00 AM 4:30 AM 6:00 AM
Time
Stre
amflo
w (c
fs)
baseflow
Time Observed Direct Runoff
Rain Flow in cfs cfs
8:30 0.15 203 9:00 0.26 246 9:30 1.33 283
10:00 2.2 828 428 10:30 2.08 2323 1923 11:00 0.2 5697 5297 11:30 0.09 9531 9131 12:00 11025 10625 12:30 8234 7834
1:00 4321 3921 1:30 2246 1846 2:00 1802 1402 2:30 1230 830 3:00 713 313 3:30 394 4:00 354 43550 4:30 303
Example (Cont.)• Calculate Direct
Runoff Hydrograph– Subtract 400 cfs
Total = 43,550 cfs
Example (Cont.)• Compute volume of direct runoff
37
3
11
1
11
1
ft10*7.839
/sft 550,43*hr5.0*s/hr3600
n
nn
nd QttQV
• Compute depth of direct runoff
in80.4ft4.0
ft5280*mi03.7ft10*7.839
22
37
AV
r dd
Example (Cont.)• Neglect all precipitation intervals that occur
before the onset of direct runoff (before 9:30)• Select Rm as the precipitation values in the 1.5
hour period from 10:00 – 11:30
)5.0*3*08.220.233.1(80.41
f
f
M
mmd tRr
in27.0tf
in54.0f
in80.4dr
Example (Cont.)
0
2000
4000
6000
8000
10000
12000
7:30 PM 9:00 PM 10:30 PM 12:00 AM 1:30 AM 3:00 AM 4:30 AM 6:00 AM
Time
Stre
amflo
w (c
fs)
0
0.5
1
1.5
2
2.5
ft=0.27
Time Observed Direct Runoff
Excess Rainfall
Rain Flow in cfs cfs in
8:30 0.15 203 9:00 0.26 246 9:30 1.33 283
10:00 2.2 828 428 1.06 10:30 2.08 2323 1923 1.93 11:00 0.2 5697 5297 1.81 11:30 0.09 9531 9131 12:00 11025 10625 12:30 8234 7834
1:00 4321 3921 1:30 2246 1846 2:00 1802 1402 2:30 1230 830 3:00 713 313 3:30 394 4:00 354 43550 4:30 303
SCS method• Soil conservation service (SCS) method is an
experimentally derived method to determine rainfall excess using information about soils, vegetative cover, hydrologic condition and antecedent moisture conditions
• The method is based on the simple relationship that Pe = P - Fa – Ia
Pe is runoff depth, P is precipitation depth, Fa is continuing abstraction, and Ia is the sum of initial losses (depression storage, interception, ET)
Time
Prec
ipit
atio
n
pt
aI aF
eP
aae FIPP
Abstractions – SCS Method• In general
• After runoff begins
• Potential runoff
• SCS Assumption
• Combining SCS assumption with P=Pe+Ia+Fa
Time
Prec
ipit
atio
n
pt
aI aF
eP
aae FIPP
StorageMaximumPotentialSnAbstractioContinuing
nAbstractioInitialExcess Rainfall
Rainfall Total
a
a
e
FIPP
PPe
SFa
aIP
a
eaIPP
SF
SIP
IPP
a
ae
2
SCS Method (Cont.)• Experiments showed
• So
SIa 2.0
SPSPPe 8.0
2.0 2
0
1
2
3
4
5
6
7
8
9
10
11
12
0 1 2 3 4 5 6 7 8 9 10 11 12Cumulative Rainfall, P, in
Cum
ulat
ive
Dir
ect R
unof
f, Pe
, in
10090807060402010
• Surface– Impervious: CN =
100– Natural: CN < 100
100)CN0Units;American(
101000
CN
S
100)CN30Units;SI(
25425400
CNCN
S
SCS Method (Cont.)• S and CN depend on antecedent rainfall
conditions• Normal conditions, AMC(II)• Dry conditions, AMC(I)
• Wet conditions, AMC(III)
)(058.010)(2.4)(IICN
IICNICN
)(13.010)(23)(IICN
IICNIIICN
SCS Method (Cont.)• SCS Curve Numbers depend on soil conditions
Group Minimum Infiltration Rate (in/hr)
Soil type
A 0.3 – 0.45 High infiltration rates. Deep, well drained sands and gravels
B 0.15 – 0.30 Moderate infiltration rates. Moderately deep, moderately well drained soils with moderately coarse textures (silt, silt loam)
C 0.05 – 0.15 Slow infiltration rates. Soils with layers, or soils with moderately fine textures (clay loams)
D 0.00 – 0.05 Very slow infiltration rates. Clayey soils, high water table, or shallow impervious layer
Example - SCS Method - 1• Rainfall: 5 in. • Area: 1000-ac• Soils:
– Class B: 50%– Class C: 50%
• Antecedent moisture: AMC(II)• Land use
– Residential • 40% with 30% impervious cover• 12% with 65% impervious cover
– Paved roads: 18% with curbs and storm sewers– Open land: 16%
• 50% fair grass cover• 50% good grass cover
– Parking lots, etc.: 14%
Example (SCS Method – 1, Cont.)
Hydrologic Soil Group
B C
Land use % CN Product % CN Product
Residential (30% imp cover)
20 72 14.40 20 81 16.20
Residential (65% imp cover)
6 85 5.10 6 90 5.40
Roads 9 98 8.82 9 98 8.82
Open land: good cover 4 61 2.44 4 74 2.96
Open land: Fair cover 4 69 2.76 4 79 3.16
Parking lots, etc 7 98 6.86 7 98 6.86
Total 50 40.38 50 43.40
8.8340.4338.40 CNCN values come from Table 5.5.2
Example (SCS Method – 1 Cont.)
• Average AMC
• Wet AMC3.92
8.83*13.0108.83*23
)(13.010)(23)(
IICNIICNIIICN
in25.393.1*8.05
93.1*2.058.0
2.0 22
SPSPPe
in93.1108.83
1000 S
8.83CN
in13.483.0*8.05
83.0*2.058.0
2.0 22
SPSPPe
in83.0103.92
1000S
101000 CN
S
Example (SCS Method – 2)• Given P, CN = 80, AMC(II)• Find: Cumulative abstractions and excess rainfall hyetograph
Time (hr)
Cumulative
Rainfall (in)
Cumulative Abstractions (in)
CumulativeExcess Rainfall
(in)
Excess RainfallHyetograph (in)
P Ia Fa Pe0 01 0.22 0.93 1.274 2.315 4.656 5.297 5.36
Example (SCS Method – 2)• Calculate storage• Calculate initial abstraction• Initial abstraction removes
– 0.2 in. in 1st period (all the precip)– 0.3 in. in the 2nd period (only part
of the precip)• Calculate continuing abstraction
in50.21080
1000101000 CN
S
a
ea IP
PSF
in5.05.2*2.02.0 SIa
aae FIPP )0.2(
)5.0(5.2)(
)(
PP
SIPIPS
Fa
aa
in34.0)0.29.0(
)5.09.0(5.2hr)(2 aF
Time (hr)
CumulativeRainfall (in)
P
0 0
1 0.2
2 0.9
3 1.27
4 2.31
5 4.65
6 5.29
7 5.36
Example (SCS method – 2)• Cumulative abstractions can now be calculated
Time (hr)
Cumulative
Rainfall (in)
Cumulative Abstractions (in)
P Ia Fa0 0 0 -1 0.2 0.2 -2 0.9 0.5 0.343 1.27 0.5 0.594 2.31 0.5 1.055 4.65 0.5 1.566 5.29 0.5 1.647 5.36 0.5 1.65
)0.2()5.0(5.2
PPFa
Example (SCS method – 2)• Cumulative excess rainfall can now be calculated• Excess Rainfall Hyetograph can be calculated
Time (hr)
CumulativeRainfall
(in)
Cumulative Abstractions (in)
CumulativeExcess Rainfall (in)
Excess RainfallHyetograph (in)
P Ia Fa Pe
0 0 0 - 0 0
1 0.2 0.2 - 0 0
2 0.9 0.5 0.34 0.06 0.06
3 1.27 0.5 0.59 0.18 0.12
4 2.31 0.5 1.05 0.76 0.58
5 4.65 0.5 1.56 2.59 1.83
6 5.29 0.5 1.64 3.15 0.56
7 5.36 0.5 1.65 3.21 0.06
aae FIPP
Example (SCS method – 2)• Cumulative excess rainfall can now be calculated• Excess Rainfall Hyetograph can be calculated
Time (hr)
CumulativeRainfall
(in)
Cumulative Abstractions (in)
CumulativeExcess Rainfall (in)
Excess RainfallHyetograph (in)
P Ia Fa Pe
0 0 0 - 0 0
1 0.2 0.2 - 0 0
2 0.9 0.5 0.34 0.06 0.06
3 1.27 0.5 0.59 0.18 0.12
4 2.31 0.5 1.05 0.76 0.58
5 4.65 0.5 1.56 2.59 1.83
6 5.29 0.5 1.64 3.15 0.56
7 5.36 0.5 1.65 3.21 0.06
aae FIPP
0 1 2 3 4 5 6 7
Excess Rainf al lRainf al l
0
0.5
1
1.5
2
2.5
Time (hour)
Rainf al l (in) Rainf al l Hyetogr aphs
Time of Concentration• Different areas of a
watershed contribute to runoff at different times after precipitation begins
• Time of concentration– Time at which all parts of
the watershed begin contributing to the runoff from the basin
– Time of flow from the farthest point in the watershed
Isochrones: boundaries of contributing areas with equal time of flow to the watershed outlet
Stream ordering• Quantitative way of studying
streams. Developed by Horton and then modified by Strahler.
• Each headwater stream is designated as first order stream
• When two first order stream combine, they produce second order stream
• Only when two streams of the same order combine, the stream order increases by one
• When a lower order stream combines with a higher order stream, the higher order is retained in the combined stream