# Watershed Management Hydrograph, Unit Hydrograph Theory WATERSHED MANAGEMENT RUNOFF MODELS H Y D R O LO GY 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 N OV E M B E R 1 3 , 2 0 1 3 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 2 PEAK RUNOFF MODELS

Rational Method NRCS Method 3 RATIONAL METHOD To calculate peak runoff from small watersheds Provides peak runoff rate from a catchment given:

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

4 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

5 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) 6 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 7 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) 8

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 9

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 11 NRCS CURVE NUMBER Curve number is a coefficient that reduces the total precipitation to runoff potential, after losses

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 12 NRCS RAINFALL-RUNOFF EQUATION Following equation presents relationship between accumulated rainfall and accumulated runoff

Where: Equation 1 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 13 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 14 NRCS RUNOFF EQUATIONS 15

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: 16 17

18 Curve Number CN The principal physical watershed characteristics affecting the relationship between rainfall and runoff are

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 19 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 20

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 21 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 22 CNs A CN of 100 is to be used for permanent water surfaces such as lakes and ponds

23 EXAMPLE 27 28

CONTINUOUS RUNOFF MODELS Time area method Unit Hydrograph Techniques 29 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)

30 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) 31 32

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 33

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 35 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 36 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). 37 LINEAR RESPONSE UH is 1/2 the size but TB (time base) and TP (time to peak) are the same 38 TYPICAL UNIT HYDROGRAPH

39 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 40

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. 41 EXAMPLE: Determine the UHG ordinates for the hydrograph shown in figure. The area of watershed is 16.2 square km

42 43 44 EXAMPLE

45 TABLE: 46 3.5 CM DIRECT RUNOFF HYDROGRAPH

47 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 48 DISCRETE TIME CONVOLUTION EQUATIONS

49 APPLICATION OF UHG TO RAINFALL INPUT 50 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 51 Example:

52 EXAMPLE Hard copies provided in class Reading material on Hydrograph Analysis: http://www.civil.pdn.ac.lk/acstaff/urrathnayake/CE_205-UR-Note1.pdf 53

DECEMBER 11, 2013 54 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 55 SYNTHETIC UHG When observed rainfall/runoff data for a catchment is not available to derive UHG Construct synthetic UHG based on empirical functions (basins 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. Snyders Unit Hydrograph 2.

SCS Dimensionless Unit Hydrograph 3. Clark (time area method) 56 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 Synders 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 57 Snyders 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) 58 Snyders 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) Or for a unit discharge (discharge per unit area) Or

59 Characteristics of a Standard UHG tp = 5.5 tr ----------- 1 tp = C1Ct (LLc)0.3 ----------- 2

----------- 3 tp = basin lag time from the centroid of excess rainfall hyetograph to the peak runoff (hrs) Qp = peak direct runoff rate 60 61

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. 62 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) 63 Drawing Snyders UHG Relationships for the widths of the UHG at values of 50% (W 50) 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 64 Snyders Synthetic UHG 65 Example: Snyders

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 Snyders 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 --------- = 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 66 SCS UNIT HYDROGRAPH

CLARKS IUH Time-Area Method (concept of isochrones) HYDROGRAPHS Floods 2013 in Sindh 69 70

71 72 73