Rainfall-runoff modeling
ERS 482/682
Small Watershed Hydrology
ERS 482/682 (Fall 2002)
Lecture 14 - 1
What are models?
• A model is a conceptualization of a system
– In hydrology, this usually involves the response
of a system to an external stimuli
rainfall
ERS 482/682 (Fall 2002)
runoff
(discharge)
Lecture 14 - 2
What are models?
• A model is a conceptualization of a system
– In hydrology, this usually involves the response
of a system to an external stimuli
• Models are tools that are part of an overall
management process
ERS 482/682 (Fall 2002)
Lecture 14 - 3
Data
collection
Management
objectives,
options,
constraints
Make
management
decisions
Model
development
and
application
ERS 482/682 (Fall 2002)
Lecture 14 - 4
Why model?
• Systems are complex
ERS 482/682 (Fall 2002)
http://water.usgs.gov/outreach/OutReach.html
Lecture 14 - 5
Why model?
• Systems are complex
• If used properly, can enhance knowledge of
a system
• Models should be built on scientific knowledge
• Models should be used as ‘tools’
ERS 482/682 (Fall 2002)
Lecture 14 - 6
Rules of modeling
• RULE 1: We cannot model reality
– We have to make assumptions
• DOCUMENT!!!!
• RULE 2: Real world has less precision than
modeling
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Lecture 14 - 7
Precision vs. accuracy
• Precision
– Number of decimal places
– Spread of repeated computations
• Accuracy
– Error between computed or measured value and
true value
error of
= field error + model error
estimate
ERS 482/682 (Fall 2002)
Lecture 14 - 8
The problem with precise models…
we get more precision from
model than is real
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Lecture 14 - 9
Fundamental model concepts
DRIVER
area
topography
soils
vegetation
land use
etc.
RESPONSE
ERS 482/682 (Fall 2002)
SYSTEM
REPRESENTATION
Q
Lecture 14 - 10
Basic model
DRIVER
Mathematical
equations and
parameters
RESPONSE
SYSTEM
REPRESENTATION
ERS 482/682 (Fall 2002)
Lecture 14 - 11
The whole
world
The model
world
Figure 9-37 (Dingman 2002)
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Lecture 14 - 12
Runoff processes to model
Table 9-8 (Dingman 2002)
Small
watershed
ASSUMPTION!
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Lecture 14 - 13
Effective water input, Weff
• Effective (excess) rainfall
– Does not include evapotranspiration or ground
water storage that appears later
Weff  Qef
ASSUMPTION!
Weff  W  ET  S c  D   
where
ASSUMPTION!
ET = event water evapotranspired during event
usually small
Sc = canopy storage during event
antecedent
D = depression storage during event
soil-water
 = soil-water storage during event
content, 0
ERS 482/682 (Fall 2002)
Lecture 14 - 14
constant
fraction
initial
abstraction
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Estimating Weff
constant
rate
infiltration
rate
Figure 9-40 (Dingman 2002)
Lecture 14 - 15
Estimating Weff
• SCS curve-number method
W  0.2Vmax 
2
Weff 
initial
abstraction
W  0.8Vmax
where Vmax = watershed storage
capacity [L]
W
= total rainfall [L]
Figure 9-42 (Dingman 2002)
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Lecture 14 - 16
Estimating Weff
• SCS curve-number method
W  0.2Vmax 
2
Weff 
W  0.8Vmax
1000
 10
where Vmax = watershed storage 
CN
capacity [inches]
W
= total rainfall [inches]
Based on land use in Table 9-12,
soil group in Table 9-11, and
soil maps from NRCS
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Lecture 14 - 17
From NRCS
soils maps
and GIS
Example 9-6
Table 9-12
Land
cover
Soil
group
Area
(mi2)
Forest
B
0.72
0.58
58
Forest
C
0.15
0.12
72
Meadow
A
0.26
0.21
30
Meadow
B
0.11
0.09
58
Given: W = 4.2 in
TW = 3.4 hr
A = 1.24 mi2
L = 0.84 mi
S = 0.08
ERS 482/682 (Fall 2002)
Fraction of Condition
total area
II CN
CN  0.5858  0.1272  0.2130  0.0958
 54
1000
Vmax 
 10  8.52 inches
54
2

4.2  0.2  8.52
Weff 
 0.57 inches
4.2  0.8  8.52
Lecture 14 - 18
Example 9-6
Table 9-13
Land
cover
Soil
group
Area
(mi2)
Forest
B
0.72
0.58
58
X 38
Forest
C
0.15
0.12
X 53
72
Meadow
A
0.26
0.21
30
X 15
Meadow
B
0.11
0.09
58
X 38
Given: W = 4.2 in
TW = 3.4 hr
A = 1.24 mi2
L = 0.84 mi
S = 0.08
ERS 482/682 (Fall 2002)
Fraction of Condition
total area
I CN
CN  35
Vmax  18.6 inches
Weff  0.012 inches
Lecture 14 - 19
SCS method for peak discharge
inches
ft3 s-1
ERS 482/682 (Fall 2002)
mi2
484Weff AD
q pk 
Tr
hr
Lecture 14 - 20
SCS method for peak discharge
484Weff AD
q pk 
Tr
Tr  0.5TW  0.6Tc
From Table 9-9
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Lecture 14 - 21
SCS method for peak discharge
Example 9-7
484Weff AD
q pk 
Tr
Tc = 0.44 hr from Table 9-9
Tr  0.53.4  0.60.44  1.96 hr
Given: W = 4.2 in
4840.57 0.57 
TW = 3.4 hr
3
q


175
ft
pk
A = 1.24 mi2
1.96
L = 0.84 mi
S = 0.08
Weff = 0.57 in for Condition II
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s -1
Lecture 14 - 22
Rational method
Q=CIA
• Assumes a proportionality between peak
discharge and rainfall intensity
q pk  u RCRieff AD
where uR= unit-conversion factor (see footnote 7 on p. 443)
proportionality coefficient
CR = runoff coefficient
ieff = rainfall intensity [L T-1]
AD = drainage area [L2]
ERS 482/682 (Fall 2002)
Lecture 14 - 23
Rational method
Q=CIA
q pk  u RCRieff AD
• Additional assumptions:
– Rainstorm of uniform intensity
over entire watershed
– Negligible surface storage
– Tc has passed
– Return period for storm is same
for discharge
ERS 482/682 (Fall 2002)
Apply to small
(<200 ac)
suburban
and urban
watersheds
Lecture 14 - 24
Rational method
Q=CIA
q pk  u RCRieff AD
• The proportionality coefficient, CR
accounts for
–
–
–
–
–
Antecedent conditions
Soil type
Land use
Slope
Surface and channel roughness
ERS 482/682 (Fall 2002)
Lecture 14 - 25
Rational method
Q=CIA
q pk  u RCRieff AD
• Approach
– Estimate Tc Table 9-9
– Estimate CR Table 9-10 or Table 10-9 (Dunne and Leopold 1978)
– Estimate ieff for return period T
• Usually use intensity-duration-frequency (IDF) curves
Figure 15.1 (Viessman and Lewis 1996)
ERS 482/682 (Fall 2002)
Lecture 14 - 26
Rational method
Q=CIA
q pk  u RCRieff AD
• Approach
– Estimate Tc Table 9-9
– Estimate CR Table 9-10 or Table 10-9 (Dunne and Leopold 1978)
– Estimate ieff for return period T
• Usually use intensity-duration-frequency (IDF) curves
– Apply equation to get qp
Viessman and Lewis (1996)
ERS 482/682 (Fall 2002)
Return period (yrs)
Multiplier for CR
2-10
25
50
100
1.0
1.1
1.2
1.25
Lecture 14 - 27
Rational method vs. SCS CN
method
• Rational method
– Small (<200 acres) urbanized watershed
– Small return period (2-10 yrs)
– Have localized IDF curves
• SCS Curve Number method
– Rural watersheds
– Average soil moisture condition (Condition II)
ERS 482/682 (Fall 2002)
Lecture 14 - 28
Adaptations
• Rational method
– Modifications for greater return periods
– Runoff coefficients for rural areas (Table 10-9:
Dunne and Leopold 1978)
– Modified rational method for Tc  TW
• SCS TR-55 method
– Applies to urban areas
– Has a popular computer program
ERS 482/682 (Fall 2002)
Lecture 14 - 29
Adaptations
• SCS TR-55 method (cont.)
– Approach
• Find the type of storm that applies from Figure 16.19
(Viessman and Lewis 1996)
• Use CN to determine Ia from Table 15.5 (Viessman
and Lewis 1996)
• Calculate Ia/P
• Find qu = unit peak discharge from figure for storm
type in cfs mi-2 in-1 (Viessman and Lewis 1996)
• Find runoff Q in inches from Figure 10-8 (Dunne and
Leopold 1978) for P
• Find peak discharge for watershed as Qp = quQA
ERS 482/682 (Fall 2002)
Lecture 14 - 30
Unit hydrograph
• Definition: hydrograph due to unit volume
of storm runoff generated by a storm of
uniform effective intensity occurring
within a specified period of time
uniform
intensity
over TW
Qef 1 unit
Assumption: Weff = Qef
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Multiply unit hydrograph
by Weff to get storm
hydrograph
Lecture 14 - 31
Unit hydrograph development
Figure 9-45
• Choose several hydrographs from storms of same duration
(~X hours) (usually most common/critical duration)
• For each storm, determine Weff and plot the event flow
hydrograph for each storm
• For each storm, multiply the ordinates on the hydrograph by
Weff-1 to get a unit hydrograph
• Plot all of the unit hydrographs on the same graph with the
same start time
• Average the peak values for all of the unit hydrographs, and
the average time to peak for all of the hydrographs
• Sketch composite unit graph to an avg shape of all the graphs
• Measure the area under the curve and adjust curve until area
is ~1 unit (in or cm) of runoff
ERS 482/682 (Fall 2002)
End result: X-hr unit hydrograph
Lecture 14 - 32
Unit hydrograph application
• Multiply unit hydrograph by storm size
• Add successive X-hour unit hydrographs to
get hydrographs of successive storms
(Figures 9-46 and 9-47)
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Lecture 14 - 33
Unit hydrograph
• Predicts flood peaks within ±25%
• Need only a short period of record
• Can apply to ungauged basins by
regionalizing the hydrograph
– Synthetic unit hydrographs
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Lecture 14 - 34
Synthetic unit hydrograph
• Unit hydrograph for ungauged watershed
derived from gauged watershed
– Example (Dingman 2002): ht   1* exp  t * 
T
 T 
– Example (Dunne and Leopold 1978):
TLP  Ct LLc 
0.3
TW  0.18TLP
C p AD
qp 
TLP
Tb  72  3TLP
ERS 482/682 (Fall 2002)
where
Ct = coefficient (1.8-2.2)
L = length of mainstream from outlet
to divide (miles)
Lc = distance from outlet to point on
stream nearest centroid (miles)
Cp = coefficient (370-440)
Tb = duration of the hydrograph (hrs)
Lecture 14 - 35
-index
Figure 8-7 (Linsley et al. 1982)
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Figure 10-7 (Dunne & Leopold 1978)
Lecture 14 - 36