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WATERSHED MANAGEMENT
RUNOFF MODELS
H Y D R O LO G Y A N D WAT E R R E S O U R C E S , R G 7 4 4
I N S T I T U T E O F S PA C E T E C H N O LO G Y
NOVEMBER 13, 2013
RUNOFF MODELS
Peak runoff models
◦ Provide only the estimates of peak discharge from the watershed
Continuous runoff models
◦ This class of runoff models provides storm hydrographs for a given rainfall
hyetograph
◦ Provide an estimate of runoff vs. time series
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PEAK RUNOFF MODELS
Rational Method
NRCS Method
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RATIONAL METHOD
 To calculate peak runoff from small watersheds
 Provides peak runoff rate from a catchment given:
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the runoff coefficient C,
the time of concentration Tc,
the area of the catchment, and
the information to calculate the input or design storm or rainfall event
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RATIONAL METHOD: ASSUMPTIONS
Catchment is small (less than 200 acres)
Catchment is concentrated
Rainfall intensity is uniform over the area of study
The runoff coefficient is catch-all coefficient that incorporates all losses
of the catchment
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RATIONAL METHOD: FORMULA
Qp = CIiA
Qp = Peak discharge (cfs)
C = runoff coefficient (function of soil type and drainage basin slope)
Ii = average rainfall intensity (in/hr) for a storm duration equal to the
time of concentration, Tc
A = area (acre)
For runoff coefficient refer Bedient Table 6-5 page 381
Obtain i from IDF curve with tr (duration) and T defined (assume tr = Tc)
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DETERMINING TC
Take Tc = 5min when A (acres) < 4.6 S (slope %)
Or use Kinematic Wave Theory (iterative process)
L = length of overland flow plane (feet)
S = slope (ft/ft)
n = Manning roughness
Ii= Rainfall intensity (in/hr)
C = rational runoff coefficient
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RATIONAL METHOD: EXAMPLE 6-6 BEDIENT
Drainage design to be accomplished for a 4 acre asphalt parking lot in
Tallahassee for a 5 yr return period. The dimensions are such that the
overland flow length is 1000 ft down a 1% slope. What will be the peak
runoff rate?
Refer Table 6-5, 4-2 & Figure 6-5
Assume tr value, for that value read rainfall intensity from IDF curve.
Calculate Tc using Kinematic wave theory. (iterate till tr = Tc)
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RUNOFF COEFFICIENT FOR NONHOMOGENEOUS
AREA
Weighted runoff coefficient based on area of each land use
Cw = ∑j=1 n Cj Aj/ ∑j=1 n Aj
Example McCuen page 381
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NOVEMBER 20, 2013
NRCS RUNOFF CURVE NUMBER METHODS
By the USA Soil Conservation Service (now called the Natural Resources
Conservation Service), division of the USDA (USA Department of Agriculture)
To predict peak discharge due to a 24-hr storm event
Empirically derived relationships that use precipitation, land cover and physical
characteristics of watershed to calculate runoff amount, peak discharges and
hydrographs
More sophisticated approach than Rational Method
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NRCS CURVE NUMBER
Curve number is a coefficient that reduces the total precipitation to
runoff potential, after “losses”
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Evaporation
Absorption
Transpiration
Surface Storage
Higher the CN value - higher the runoff potential will be
It is essential to use the CN value that best mimics the Ground Cover
Type and Hydrologic Condition
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NRCS RAINFALL-RUNOFF EQUATION
Following equation presents relationship between accumulated rainfall and
accumulated runoff
Equation 1
Where:
Q = accumulated direct runoff (in. or mm)
P = accumulated rainfall (potential maximum runoff) (in. or mm) (24-Hour Rainfall
Depth versus Frequency Values)
Ia = initial abstraction including surface storage, interception, evaporation and
infiltration prior to any runoff occurring (in. or mm)
S = potential maximum soil moisture retention after runoff begins (in. or mm)
Note: for P ≤ Ia, Q = 0
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POTENTIAL MAXIMUM RETENTION (S)
potential maximum retention (S) can be calculated using
Equation 2
Equation 2
Where:
z=10 for English measurement units, or 254 for metric
CN = Runoff Curve Number
Generally, Ia may be estimated as
Ia = 0.2 S
Substituting Ia value in Equation 1
Equation 3
Equation 4
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NRCS RUNOFF EQUATIONS
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Estimation of CN
Equation 4 (slide# 14) can be rearranged so the CN can be estimated if
rainfall and runoff volume are known (Pitt, 1994)
The equation then becomes:
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Curve Number CN
The principal physical watershed characteristics affecting the relationship
between rainfall and runoff are
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land use,
land treatment,
soil types, and
land slope.
NRCS method uses a combination of soil conditions and land uses (ground
cover) to assign a runoff factor to an area (CN)
CN indicates the runoff potential of an area
◦ Higher the CN, the higher the runoff potential
Soil properties also influence the relationship between runoff and rainfall
since soils have differing rates of infiltration
Based on infiltration rates, the NRCS has divided soils into four hydrologic
soil groups
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COMPOSITE CURVE NUMBER
When a drainage area has more than one land use
When Composite CN is used
◦ Analysis does not take into account the location of the specific land uses
◦ drainage area is considered as a uniform land use represented by the
composite curve number
◦ can be calculated by using the weighted method
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HYDROLOGIC SOIL GROUPS
Hydrologic Group is a grouping of soils that have similar runoff potential under similar
storm and cover conditions
Group A Soils: High infiltration (low runoff). Sand, loamy sand, or sandy loam.
Infiltration rate > 0.3 inch/hr when wet.
Group B Soils: Moderate infiltration (moderate runoff). Silt loam or loam. Infiltration
rate 0.15 to 0.3 inch/hr when wet.
Group C Soils: Low infiltration (moderate to high runoff). Sandy clay loam. Infiltration
rate 0.05 to 0.15 inch/hr when wet.
Group D Soils: Very low infiltration (high runoff). Clay loam, silty clay loam, sandy clay,
silty clay, or clay. Infiltration rate 0 to 0.05 inch/hr when wet.
Effects of Urbanization: Consider the effects of urbanization on the natural hydrologic
soil group. If heavy equipment can be expected to compact the soil during construction
or if grading will mix the surface and subsurface soils, you should make appropriate
changes in the soil group selected.
Antecedent soil moisture conditions: AMC I, II and III
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ANTECEDENT SOIL MOISTURE CONDITIONS-AMC
AMC is the preceding relative moisture of the pervious surfaces prior to
the rainfall event
◦ Low: when there has been little preceding rainfall
◦ High: when there has been considerable preceding rainfall prior to the
modeled rainfall event
ACM I (dry), ACM II (average) and ACM III (wet)
For modeling purposes, we consider watersheds to be
AMC II, which is essentially an average moisture condition
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CNs
A CN of 100 is to be used for permanent water surfaces
such as lakes and ponds
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EXAMPLE
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CONTINUOUS RUNOFF MODELS
Time area method
Unit Hydrograph Techniques
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TIME AREA METHOD
Develop to address non-uniform rainfall in large areas
Convert rainfall excess into hydrograph
Concept of time-area histogram is used
This method assumes that outflow hydrograph results from pure translation
of direct runoff to the outlet at uniform velocity, ignoring any storage effects
in the watershed
Watershed divided into subareas with distinct runoff translation times to the
outlet
Subareas are delineated with isochrones of equal translation time (numbered
upstream from the outlet)
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TIME AREA METHOD
If a rainfall of uniform intensity is distributed over the watershed area,
water first flows from are as immediately adjacent to the outlet
Percentage of the total area contributing increases progressively in time
Example : Surface runoff from area A1 will reach the outlet first,
followed by contributions from A2, A3, …..and so on
Qn = RiA1+Ri-1A2+…….R1Aj
Qn = Hydraulic ordinate at time n (cfs)
Ri= excess rainfall ordinate at time i (ft/s)
Aj= time-area histogram ordinate at time j (ft2)
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EXAMPLE 2-2 FROM BEDIENT PAGE 112
Time area histogram method. The following is an example of the inflow for
hour 5 using the 5 hour rainfall and 4 sub-basins. Assume constant rainfall
intensity of 0.5in/hr
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NOVEMBER 27, 2013
UNIT HYDROGRAPH (UHG) THEORY
Unit Hydrograph of a watershed is defined as the direct runoff hydrograph
resulting from a unit depth of rainfall excess (1 in or 1 cm) distributed
uniformly over a drainage area at a constant rate for an effective duration
The effective rainfall is considered uniformly distributed within its duration
and throughout the whole area of the basin
Uniquely represents storm-flow response (hydrograph shape) for a given
watershed
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UNIT HYDROGRAPH THEORY:
ASSUMPTIONS
1. The effective rainfall is uniformly distributed within its
duration
2. The effective rainfall is uniformly distributed throughout the
whole area of the basin
3. The base period of the direct runoff hydrograph produced by
effective rainfall of same duration (intensities may be
different) are also same
4. The ordinates of the direct runoff hydrographs of a common
base period are directly proportional to the total volume of
direct runoff represented by the respective hydrographs
5. For a given drainage basin the hydrograph of runoff due to a
given period of rainfall reflects the unchanging characteristics
of the basin
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UNIT HYDROGRAPH THEORY:
ASSUMPTIONS
2 Basic Assumptions:
Time Invariance
◦ Direct runoff response to a given effective rainfall in a catchment is
time invariant, i.e. direct-runoff hydrograph (DRH) for a given excess
rainfall in a catchment is always the same irrespective of when it occurs
Linear Response
◦ Direct runoff response to the rainfall excess is assumed to be linear.
Means if inputs x1(t), x2(t) cause outputs y1(t) and y2(t) respectively
then an input x1(t) + x2(t) will cause an output y1(t) + y2(t). Also if x1(t) =
r x2(t) then y1(t) = r y2(t).
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LINEAR RESPONSE
 UH is 1/2 the size but TB (time base) and TP (time to peak) are the same
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TYPICAL UNIT HYDROGRAPH
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PROPERTIES OF UNIT HYDROGRAPH
Volume under unit hydrograph is equal to 1 unit rainfall excess (1 in or
cm)
If duration of 2 rainfall excess events is equal without regard to their
respective rainfall intensities, they must result in the same hydrograph
time base
Results in a linear system whereby the direct runoff for storm of
specified duration is directly proportional to the rainfall excess amount
or volume
Rainfall distribution for all equal duration storms is identical in time and
space
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DEVELOPMENT OF UHG
Examine records of watershed for single peaked, isolated
stream flow hydrographs resulting from short duration
rainfall hyetograph of relatively uniform intensity
Determine depth of storm precipitation spread over the
watershed equivalent to the volume of water divided by
area
◦ Volume is equal to area under hydrograph
Ordinates of UHG can be calculated by dividing the
ordinates of the DRH by the storm depth
Check: recalculate area under UHG and divide it by
watershed area. That should give unit storm depth.
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EXAMPLE:
Determine the UHG ordinates for the hydrograph shown in figure. The area of
watershed is 16.2 square km
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EXAMPLE
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TABLE:
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3.5 CM DIRECT RUNOFF HYDROGRAPH
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DRG ORDINATES FROM UHG WITH VARIABLE
RAINFALL EXCESS VALUES (M PULSES OF EXCESS
RAINFALL
Discrete Convolution Equation is used to compute direct runoff hydrograph ordinates
Qn = direct runoff hydrograph ordinates, Pm= Rainfall excess, Un-m+1 = unit hydrograph ordinates,
n= direct runoff hydrograph time interval (1, 2, …N), m= precipitation time interval
M = pulses of excess of rainfall
N = pulses of direct runoff
N-M+1 = L, Number of UH ordinates
Reverse process is called ‘deconvolution’ to derive unit hydrograph given Pm and Qn
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DISCRETE TIME CONVOLUTION
EQUATIONS
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APPLICATION OF UHG TO RAINFALL
INPUT
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DECONVOLUTION PROCESS
Q n and Pm are known
Q1 = P1 * U1 (Q1 and P1 known, calculate U1)
Q2= P2*U1 + P1 *U2 (all known except U2)
And so on
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Example:
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EXAMPLE
Hard copies provided in class
Reading material on Hydrograph Analysis:
http://www.civil.pdn.ac.lk/acstaff/urrathnayake/CE_205-UR-Note1.pdf
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DECEMBER 11, 2013
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INSTANTANEOUS UNIT HYDROGRAPH
Limiting the duration of UHG to zero an Instantaneous Unit Hydrograph
is obtained
Instantaneous Unit Hydrograph is the hydrograph resulting from an
instantaneous rainfall of one unit uniformly over the basin
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SYNTHETIC UHG
When observed rainfall/runoff data for a catchment is not available to
derive UHG
Construct synthetic UHG based on empirical functions (basin’s physical
characteristics)
◦ Developing UHG for other locations on the stream in the same watershed or
other watersheds that are of similar character with known data
1.
Snyder’s Unit Hydrograph
2.
SCS Dimensionless Unit Hydrograph
3.
Clark (time area method)
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SNYDER UHG
Relates the time from the centroid of the rainfall to the peak of the UHG
to geometrical characteristics of the watershed
Important factors to be considered for a UGH are;
◦ peak flow and time of peak flow
◦ Coefficient derived from gaged watershed in the area Cp and Ct
◦ Cp = peak flow factor, and Ct = lag factor.
Basic Assumption of Synder’s Method:
◦ that basins which have similar physiographic characteristics are located in
the same area will have similar values of Cp and Ct
Therefore, for ungagged basins, it is preferred that the basin be near or
similar to gaged basins for which these coefficients can be determined
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Snyder’s UHG: Computing Ct
tp = basin lag time (hrs)
Lc= distance from outlet to a point on the stream nearest the centroid of the
watershed area -in km (miles)
L = length of main stream from outlet to the upstream divide - in km (miles)
C1 = 0.75 ( 1.0 for English units)
𝐶𝑡 =
𝐶1
𝑡𝑝
𝐿. 𝐿𝑐
0.3
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Snyder’s UHG: Computing Cp
Qp = peak direct runoff rate - in m3/s (cfs)
A = watershed area - in km2 (mi2),
qp= peak discharge/unit watershed area
C2 = 2.75 (640 for English units)
𝐴 𝐶2𝐶𝑝
𝑡𝑝
Or for a unit discharge (discharge per unit area)
𝑄𝑝 =
𝐶2𝐶𝑝
𝑞𝑝 =
𝑡𝑝
Or
𝐶𝑝 =
𝑞𝑝𝑡𝑝
𝐶2
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Characteristics of a Standard UHG
tp = 5.5 tr
----------- 1
tp = C1Ct (LLc)0.3 ----------- 2
𝑄𝑝 =
𝐴 𝐶2 𝐶𝑝
𝑡𝑝
----------- 3
tp = basin lag – time from the centroid of excess rainfall hyetograph to
the peak runoff (hrs)
Qp = peak direct runoff rate
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Snyder: Development of a Required UHG
assuming that Ct, Cp, L, and Lc are known
Required: a unit hydrograph whose associated effective rainfall pulse
duration is tR for an ungagged watershed
1.
2.
Use equation 2 to determine the lag-time, tp
If tR meets the criterion for a standard UHG (tp = 5.5 tR) then the
required unit hydrograph is a standard UHG
◦ equations 2 and 3 can be used directly to estimate the peak discharge
and the time to peak of the required unit hydrograph
3.
If tR does not meet the criterion for a standard UHG
◦ In this case, the lag-time of the required unit hydrograph, tpR, is
tpR = tp – (tr – tR)/4 ------------ 4
◦ where tp is obtained from equation 2, tr is obtained from equation 1 and tR is
given.
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Conti…
4.
The peak discharge of the required UHG, QpR, is,
QpR = Qp tp/tpR -------- 5
where Qp is obtained from equation 3
5.
Assuming a triangular shape for the UHG, and given that the UHG
represents a direct runoff volume of 1 cm (1 in), the base time of the
required UHG may be estimated by
tb = C3A/QpR -------------- 6
where C3 is 5.56 (1290 for the English system)
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Drawing Snyder’s UHG
Relationships for the widths of the UHG at values of 50% (W50) and 75%
(W75) of QpR developed by U.S. Army Corps of Engineers;
W% = Cw(QpR/A)-1.08
where the constant Cw is 1.22 (440 for English units) for the 75% width and
equals to 2.14 (770 for English units) for the 50% width
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Snyder’s Synthetic UHG
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Example: Snyder’s Method
A watershed has a drainage area of 5.42 mi2; length of the main stream is 4.45 mi, and the main
channel length from the watershed outlet to the point opposite the center of gravity of the watershed
is 2.0 mi, Using Ct = 2.0 and Cp = 0.625, determine the standard synthetic UHG for this basin. What is
the standard duration? Use Snyder’s method to determine 30 min unit hydrograph parameters.
Solution:
Given: Ct = 2.0, Cp = 0.625, Lc = 2.0 mi, L= 4.45 mi, tR= 30 mi (0.5 hr), C1 = 1, C2 = 640, C3 = 1290
Equation 2 ----- tp = C1 Ct (LLc)0.3 =1 x2 (4.45 x 2) 0.3 = 3.85 hrs
Equation 1 -------Standard rainfall duration, tr = tp/5.5 = 3.85/5.5 = 0.7 hrs, tr ≠ tR.
Equation 4 -------- tpR = tp – (tr – tR)/4 = 3.85 – (0.7 – 0.5)/4 = 3.8 hrs
Equation 3 --------- 𝑄𝑝 =
𝐴 𝐶2𝐶𝑝
𝑡𝑝
= 5.42 x 640 x 0.625/3.85 = 563 cfs
Equation 5 --------- QpR = Qp tp/tpR = 563 x 3.85/3.8 = 570.5 cfs
Equation 6 ---------- tb = C3A/QpR = 1290 x 5.42 /570.5 = 12.26 hrs
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SCS UNIT HYDROGRAPH
CLARK’S IUH
Time-Area Method (concept of isochrones)
HYDROGRAPHS
Floods 2013 in Sindh
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