Advanced/ Surface Hydrology Dr. Jagadish Torlapati Fall 2017

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MODULE 1 – RUNOFF HYDROGRAPHS

WORKSHEET 1 Watershed

A watershed is an area of land that captures rainfall and other precipitation and funnels it to a lake or stream or wetland. The area within the watershed where the rainfall event occurs is called the catchment area. In engineering applications, these terms are used interchangeably. The catchment is also called a drainage basin or a drainage area. The surface runoff from a rainfall event in a watershed is captured an outlet called catchment outlet or pour point. Precipitation Rainfall data is collected by National Weather Service (NWS) manually using a standard 8inch rain gage or an automatic-recording rain gages such as the tipping bucket rain gage. Rain gage measurements are point measurements and can be representative of a small area of 25 km2 (10 mi2). NWS uses next-generation radar (NEXRAD) to obtain areal measurement of rainfall. These weather stations are capable of measuring weather activity within 230 km radius.

In engineering design, we use historical or statistical measurement of rainfall represented in the form of Intensity-Duration-Frequency (IDF) curves. These curves express the relationship between the average intensity of a rainstorm during an average time for a probability of occurrence. An example IDF curve is shown in the Figure above. These curves are developed by using the average maximum rainfall data using statistical methods. Things to note from a IDF curve:

• The rainfall intensity increases as the duration decreases • The rainfall intensity increases as the return period increases. The probability of a rainfall

event with high intensity is low. In United States, the frequency of local rainfall distributions was published by Hershfield in 1961, this is commonly referred to as TP-40 (Technical Paper 40 published in NWS). These frequency distributions were derived from data from 4000 stations assuming a Gumbel distribution. When IDF curves are not available, we use a methodology proposed by Chen. Chen (1983) uses the three rainfall depths derived from TP-40 (𝑅""#, 𝑅%&"#, 𝑅""##) and proposed a relationship between average intensity, i (in/hr) for a rainfall of duration, t (min), by 𝑖 =

𝑎𝑡 + 𝑏" ." (1)

Advanced/ Surface Hydrology Dr. Jagadish Torlapati Fall 2017

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where a, b1, c1 are empirical functions of the three depths derived from TP-40. A typical runoff hydrograph is shown below

Rainfall excess is defined as the total rainfall minus the abstractions such as infiltration. Overland runoff occurs when the rainfall rate exceeds the infiltration capacity of the soil. Runoff models are classified as either

• Distributed parameter models – small areas such as roof, lawn streets etc • Lumped parameter models – used for large catchments where the processes are lumped

into one parameter We generally use hydrographs to understand the catchment response to a rainfall. Hydrographs show the temporal variation of rainfall at the catchment outlet (D shown in the Figure). It is possible to understand the characteristics of a catchment such as the slope, type of terrain etc by looking at the hydrograph. Hydrographs are extensively used in flood routing and storage calculations in stormwater management systems.

Advanced/ Surface Hydrology Dr. Jagadish Torlapati Fall 2017

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Time of concentration Longest travel time that it takes for surface runoff to reach the discharge point of a catchment. This is a function of effective rainfall intensity (ie), catchment length scale (L), average catchment slope, S0, the type of catchment surface (C) Different empirical methods are used to compute the time of concentration (tc) (a) NRCS method

(2)

where tc is the time of concentration in minutes, P24 is the 2-year 24-hour rainfall in mm, L is the length of the catchment in m, n is the Manning’s roughness coefficient for overland flow; and So is the ground slope

(b) Kirpich equation

(3)

where tc is the time of concentration in minutes, L is the flow length in m, So is the average slope along the flow path. This was primary developed in wooded agricultural catchments in Tennessee. Rossmiller suggested that for concrete or asphalt, the calculated tc should be multiplied by 0.4.

(c) Izzard equation

(4)

where L is the overland-flow distance in m, ie is the effective rainfall intensity (mm/h) and K is a constant given by

(5)

cr is the retardance coefficient that is determined by the catchment surface as given in the Table 10.4 of the textbook.

(d) Kerby Equation

(6)

where L is the length of flow in m, r is the retardance roughness coefficient given in Table 10.5 of the textbook and So is the slope of the catchment.

tc =5.5P24

nLSo

⎛

⎝⎜⎞

⎠⎟

4/5

tc = 0.019L0.77

S00.385

tc =530KL1/3

ie2/3 where ieL<3.9 m2 /h

K= 2.8 ×10−6 ie + cr

S01/3

tc = 1.44LrS0

⎛

⎝⎜⎞

⎠⎟

0.467

Advanced/ Surface Hydrology Dr. Jagadish Torlapati Fall 2017

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(e) Kinematic wave equation

(7)

where tc is time in minutes, ie in mm/h, L is the length of the catchment in m, n is the Manning’s roughness coefficient for overland flow; and So is the ground slope

Problem 1 An urban catchment with an asphalt surface has an average slope of 0.5%, and the distance from the catchment boundary to the outlet is 90 m. At the catchment location, the 2-year 24-hour rainfall is estimated as 50 mm. For a 20-min storm with an effective rainfall rate of 75 mm/h, estimate the time of concentration using all the empirical equations

tc =6.99ie2/5

nLSo

⎛

⎝⎜⎞

⎠⎟

3/5

Advanced/ Surface Hydrology Dr. Jagadish Torlapati Fall 2017

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The Rational Method The rational method is a widely used peak-runoff model in urban hydrology. This is used to calculate the peak runoff (Qp) for a given rainfall intensity (i) as follow

where C is the runoff coefficient, and A is the area of the catchment Assumptions:

1. Entire catchment area is contributing the runoff (duration of the rainfall is equal to the time of concentration)

2. Rainfall is distributed uniformly over the catchment 3. All catchment losses are incorporated into the runoff coefficient, C

Qp = CiA

Advanced/ Surface Hydrology Dr. Jagadish Torlapati Fall 2017

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Problem 2 A new 1.2 ha suburban residential development is to be drained by a storm sewer that connects to the municipal drainage system. The development is characterized by an average runoff coefficient of 0.4, a Manning’s n for overland-flow of 0.2, an average overland-flow length of 70m and an average slope of 0.7%. The time of concentration can be estimated by the kinematic wave equation. Local drainage regulations require that the storm-sewer pipe be sized to accommodate the peak runoff rate resulting from a 10-year rainfall event. The 10-year IDF curve is given by

where i is the rainfall intensity in cm/h and t is the duration in minutes. Location regulations further require a minimum time of concentration of 5 mins. Determine the peak runoff rate to be handled by the storm sewer.

i = 315.5t 0.81 + 6.19

Advanced/ Surface Hydrology Dr. Jagadish Torlapati Fall 2017

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Problem 3 Consider the case where the residential development described in the above problem contains 0.4 ha of the impervious area that is directly connected to the storm sewer. If the runoff coefficient of the impervious area is 0.9, Manning’s n for overland flow on the impervious surface is 0.03, the average flow length is 20 m and the average slope 0.1%, estimate the design runoff rate to be handled by the storm sewer.