HYDROLOGY WORKSHEET 1 PRECIPITATION

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1 HYDROLOGY WORKSHEET 1 PRECIPITATION 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 km 2 (10 mi 2 ). 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 1

2 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 = a t + b "." (1) where a, b 1, c 1 are empirical functions of the three depths derived from TP-40. What are some of the limitations of IDF curves? 2

3 In engineering design, return period of the design rainfall should be selected on basis on economic efficiency. For residential areas, the return period for storm sewer design is 2-15 years where for commercial or high value districts, it is about years. Probable Maximum Precipitation (PMP) is the theoretical greatest depth for precipitation for a given duration that is physically possible over a given area. This is particularly important for large water-resources projects. This considers risk factors in the location such as the failure of an embankment or a dam that could increase the extent of damage due to flood. P24 refers to the probable maximum depth for a 24-hour duration. Rainfall abstractions The processes of interception, infiltration and depression storage are referred to as rainfall abstractions. These processes are used to calculate the surface runoff. Interception is the process of rainfall disconnected from reaching the ground by vegetation above the ground. Depression storage is the rainfall that accumulates into surface depressions during storms. This does not contribute to surface runoff and will either infiltrate into the ground or evaporate. Typical depression storage values are given in Table 9.8 Infiltration is the process by which the rainfall seeps into the ground. This is most dominant process of rainfall abstraction process. 3

4 INFILTRATION Infiltration describes the entry of water into the soil through the soil surface, percolation describes he movement of water within the soil. The intensity of amount of infiltration can be conceptually calculated by the following models 1. F-index method 2. Horton s equation (1939;1940) 3. NRCS Method 4. Green and Ampt (1911) F-index method Assumes that the infiltration rate is constant throughout the rainfall event If the rainfall intensity is less than the infiltration rate, then the runoff is zero. Problem 1 Consider the rainfall hyetograph Time (hr) Intensity (in/hr) Find the total infiltration and runoff in inches if the infiltration rate is (a) 0.4 in/hr (b) 0.8 in/hr 4

5 Problem 2 Find the infiltration rate in inches/hr if the total infiltration is inches Time (hr) Intensity (in/hr)

6 Horton s Model The change in moisture content in soil with elevation is described by a soil retention curve. The change in moisture content during a rainfall event is shown in the Figure below. In this model, the infiltration potential is high at the beginning of the rainfall since the soil is dry. The infiltration process slows down until it reaches a constant value. The potential infiltration rate (f p ) as a function of time is given below f 0 = f. + (f # f. )e 567 (2) where f 0 is the initial maximum infiltration rate, f c is the asymptotic minimum infiltration rate and k is decay constant. 6

7 Problem 3 A catchment soil has Horton infiltration parameters of f 0 =100 mm/hr, f c =20 mm/hr and k = 2 min -1. What rainfall rate would result in ponding from the beginning of the storm? If the rainfall rate is maintained for 40 min, describe the infiltration as a function of time during the storm. Cumulative infiltration in Horton s Model Cumulative infiltration is the total volume of water in inches or mm, that infiltrated into the soil during the rainfall event. This is calculated by integrating the Horton s infiltration capacity equation with respect to time. Case I: Ponding is continuous In this case, the rainfall intensity is always greater than the infiltration potential. Water is always ponded on the surface and the infiltration occurs at the current infiltration potential (f p ). Therefore, F t = f. t + f # f. k 1 e 567 (3) Case II: Ponding is not continuous In this case, rainfall intensity is lower than the infiltration potential. Therefore, infiltration occurs at the rate of the rainfall. F = f. k ln f # f. + f # k f. k ln f 0 f. f 0 k (4) 7

8 Problem 4 A catchment soil is found to have the following Horton infiltration parameters: f 0 =100 mm/hr; f c =20 mm/hr, k=0.030 min -1 and the depression storage on the ground surface is estimated as 2 mm. The design storm is given by the following hyetograph Interval (min) Rainfall (mm/hr) Estimate the time at which ponding begins, the amount of surface runoff expected from this storm and the ratio of rainfall to runoff 8