Analyses of Rainfall Hydrology and Water Resources RG744 Institute of Space Technology October 05&11, 2013

Mean Rainfall Mean Annual Rainfall: determined by averaging the total rainfall of several consecutive years at a place Mean Monthly Rainfall: by averaging the monthly total rainfall for several consecutive years Mean annual rainfall: minimum of 35-40 years of continuous records is desirable. Deficit or surplus rainfall comparing with mean annual rainfall

Interception and Net Precipitation Vegetation influence on pattern of deposition and amount of precipitation reaching the soil surface Interception losses are less in arid and semiarid regions that have sparse vegetation Net precipitation is gross precipitation (measured by gauge) minus interception loss Net precipitation is the amount available either to replenish soil water deficits or to become surface, subsurface, or ground water flow.

Effective Rainfall Rainfall component causing perceptible change in the stream flow That is only a portion of the total rainfall recorded over the catchment Rainfall that does not infiltrate the soil and moves into the stream as overland flow Infiltration capacity: High in dry soil No overland flow if precipitation is lower than infiltration capacity (but interflow may occur). With persistence precipitation , the soil becomes wet and infiltration rate decreases causing runoff. 4

Flood/Storm Frequency Flood frequency: number of times a particular flood/storm can be expected in a river/watershed in a given number of years Example: 100 year flood – a flood that can be expected once in 100 years. (usually worked out by extrapolating the observed data) Frequency is the percentage of years, during which a storm of a given magnitude may be equaled or exceeded Recurrence interval/return period: Time interval after which a similar flood can be forecasted or expected. Return Period: Time interval after which a storm of given magnitude is likely to recur.

Frequency Analysis Objective: to develop a frequency curve Precipitation frequency curves can be developed to evaluate maximum events Used for planning water resources structures Relationship between the magnitude of events and either the associated probability or the recurrence interval Weather systems vary year to year and hence magnitude of future events can not be predicted accurately Have to rely on statistical analyses of rainfall amounts over certain period Frequency distribution of past events Probability or likelihood of having certain events occurring over a specified period is estimated Source: Hydrology and the management of watersheds By Kenneth N. Brooks

Recurrence Interval of a Storm Number of years within which a given storm may equal or exceed once - Also known as return period Means this precipitation value or more than that occurs m times in n years Ranking: The serial number of a specific value of precipitation in the descending order . Source: Hydrology Principles

Probability of Exceedance The probability of occurrence of a flood (having a recurrence interval T-year) in any year, Probability: Reciprocal of the return period p = 1/ T Example source: Elementary Engineering Hydrology By Deodhar M. J. Frequency: Inverse of return period multiplied with 100 and expressed as %.

Frequency Frequency: Probability expressed in terms of percentage Frequency of a rainfall of a given magnitude = the number of times the given event may be expected to be equaled or exceeded in 100 years Example source: Elementary Engineering Hydrology By Deodhar M. J. Frequency: Inverse of return period multiplied with 100 and expressed as %.

Example: Example source: Elementary Engineering Hydrology By Deodhar M. J.

Hydrology and Management of Watershed by Kenneth. Frequency curve of daily rainfall for a single station The probability of having a 24 hr rainfall event of 100mm or more in any given year is about 0.02 (or a 50 year recurrence interval)

Prob (no occurrence in N years) = (1-p)N Once the frequency curve is developed, the probability of exceeding certain rainfall amount over a specified period can be determined The probability that an event with probability p will be equaled or exceeded x times in N years is determined by: If x=0 (no occurrence in N years) then Prob (no occurrence in N years) = (1-p)N Therefore; Prob (at least 1 occurrence in N years) = 1-(1-p)N Example: the probability of having a 24 hr rainfall event of 100mm or greater over a 20 year period is determined by (see solution in the end)

The percentage probabilities of floods (or rainfall) of different recurrence intervals (T) to occur in particular periods (N) are given in Table 8.4 Source: Hydrology Principles

Intensity Duration Analysis Study of intensity and its duration is called Intensity Duration Analysis Usually most intense storms last for shorter duration As intensity reduces duration increases

Intensity Duration Curve Graph of duration vs. intensity for an area Normally follows the following equation Where; I = intensity in mm/hr t = duration in minutes C, a, b = constants for the specific area Also known as intensity duration graph. Source: Elementary Engineering Hydrology By Deodhar M. J.

Intensity Duration Curve Intensity Duration Curve prepared for a specific study

Example: A storm occurred over a catchment area as under: Time (min) Precipitation (mm) 0 0 10 19 20 22 30 7 40 20 50 23 60 33 70 28 80 8 90 6 Plot maximum duration intensity curve?

Intensity Frequency Duration Analysis When sufficient data (say 50 years) for a catchment area is available Analyze data for each storm Analyze for: Intensity Frequency Duration Different graphs for different catchment areas depending on their hydrologic character

Intensity-Frequency-Duration Curve Source: Hydrology by Das and Saikia To know rainfall intensities of different duration and different return period

Isopluvial Maps Combined map for large area for maximum rainfall depth for various combination of a return period and duration These are Isohyets shown on regional rainfall map

Source: Engg Hydorlogy,3E  By Subramanya

Depth-Area-Duration (DAD) Analysis Average depth of storm and its duration for a specific area Also called DAD study Horton’s Equation Pa =Poe-(KA)^n Areal spread of rainfall within watershed. Amount of high rainfall that may be expected over the catchment. Frequency analysis discussed before is based upon rainfall characteristics at a point or a specific location. The design of storage reservoir and other water resources related structures required that the watershed area to be taken into account. Because rainfall is usually not uniform, increasing the area of watershed the depth of rainfall with a certain probability will decrease. Every storm has a center having maximum precipitation. Po= maximum precipitation at the center of storm. Pa=Average Precipitation over a specific area. (Po-Pa) is positive value and its value increases with bigger catchment and decreases with smaller catchment. K & n are regression constants varies with duration of storm.

DAD Curve Based on records of several storms on an area Maximum areal precipitation for different durations corresponding to different areal extents Source: Hydrology Principles

Depth-Area-Duration (DAD) Curve Based on records of several storms on an area Maximum areal precipitation for different durations corresponding to different areal extents

Index of wetness Ratio of rainfall in a given year and average annual precipitation When it is Less than 1 - bad year/deficient year/ dry year More than 1 – good year / surplus year / wet year Equal to 1 – normal year Source: Deodhar chapter 4

Probable Extreme Rainfall Events (Standard Design Storms) Probable Maximum Precipitation Standard Project Storm Frequency based storm Important for water resources engineering

Probable Maximum Precipitation (PMP) Assumed physical upper limit of rain that will fall over a specified area in a given time (that’s physically possible) Rainfall for a given area and duration that can be reached or exceeded under known meteorological conditions Used to provide an estimate of the Probable Maximum Flood (PMF) hydrographs For design of major structure with the threat of loss of life PMP is used (where no risk of failure accepted) Source: usf Amount of rainfall over a region that can not be exceeded over at that place. The greatest depth that can occur in a given duration at a given location Higher in hot humid regions. PMP is obtained by studying all the storms that have occurred over the region and maximizing them for the most critical atmospheric conditions (assuming maximum air moisture and maximum air inflow occurs simultaneously) . PMF estimated after appropriate adjustment for infiltration losses.

Standard Project Storm (SPS) Storm which is reasonably capable of occurring over the basin under consideration (actually occurred) The heaviest rain storm occurred in the region during the period of rainfall records Used for design project with economic considerations and low risk SPS or SPF - Standard Project Flood

Frequency Based Storm i: Frequency analysis of long term stream flow data at a site of interest Or ii: Frequency analysis of rainfall data coupled with rainfall- runoff model to get design flood (if flow data is not available) ii) When i data is not available

Solution to example Source: Hydrology and the Management of Watersheds by Brooks