Precipitation Analysis PDF

PRECIPITATION ANALYSIS  ANALYSIS OF RAINFALL RECORDS Double mass analysis is a commonly used data analysis approach for investigating the behavior of ❑Missing Rainfall records made of hydrological Data or meteorological data...

PRECIPITATION ANALYSIS  ANALYSIS OF RAINFALL RECORDS Double mass analysis is a commonly used data analysis approach for investigating the behavior of ❑Missing Rainfall records made of hydrological Data or meteorological data at a number of locations. It is used to determine whether there is a need for corrections to the data to account for changes ❑ Inconsistency in in data collection procedures or other local conditions. Such changes may result from a variety Rainfall Record of things including changes in instrumentation, changes in observation procedures, or changes in gauge location or surrounding conditions. Double mass analysis used for checking consistency of a hydrological or meteorological record and is considered to be an essential tool before taking it for analysis purpose. DOUBLE MASS CURVE The double mass curve is obtained by plotting: ▪X-axis - Average accumulated precipitation of nearby stations ▪Y-axis - Accumulated precipitation of the station under consideration DOUBLE MASS CURVE Steps: All data lying after the deviation point from the Arrange the data (recent to straight line requires past) correction Determine cumulative rain To determine correction fall of the subjected station factor calculate the slope of and of the nearby stations the curve before and after Draw double mass curve the point of deviation Part of the curve which lies in straight line requires no correction  𝑺𝒂 cf = 𝑺𝒐 Where; Pa =Adjusted precipitation Po =Observed precipitation Sa =Slope prior to the break in the curve So =Slope after the break in the curve EXAMPLE: Check consistency of the data and correct if inconsistent. RAINGAUGE NETWORK Network density – is defined as the ratio of the total area of catchment to the total number of gauges in the catchment. The WMO laid out the following norms for minimum network density: Region Description Network Density Minimum Tolerable I Flat region of temperate, 1 guage for 600 to 900 1 guage for 900 to Mediterranean and tropical zones km2 3000 km2 II Mountaneous areas of temperate, 1 guage for 100 to 250 1 guage for 250 to Mediterranean and tropical zones km2 1000 km2 II Arid and Polar zones 1 guage for 1500 to 10000 km2 CALCULATION OF OPTIMUM RAIN GUAGE STATION (N) 𝒄𝒗 𝟐 N= [ ] 𝒑 Where; Cv = coefficient of variation of the rainfall values of existing stations. 𝑆𝑥 = 𝑥 100 Sx = standard deviation 𝑥 x = mean of rainfall values of existing stations p = desired degree of error values of estimating mean rainfall EXAMPLE 1: A catchment has five raingauge stations. In a year, the annual rainfall recorded by the gauges are 78.8 cm, 90.2 cm, 98.6 cm, 102.4 cm, and 70.4 cm. For a 6% error in the estimation of the mean rainfall, determine the number of gauges needed. Solution: 78.8+90.2+98.6+102.4+70.4 x = 1/n σ 𝑥𝑖 = = 88.08 cm 5 σ(𝑥𝑖 −𝑥)2 𝑠𝑥 2 = 𝑛−1 =((78.8 − 88.08)2 + (90.2 − 88.08)2 + (98.6 − 88.08)2 + (70.4 − 88.08)2 )/4 = 179.732 sx = 13.41 Hence, Cv = 15.22 N = 6.43 = 7 PRESENTATION OF RAINFALL DATA 1. Hyetograph method A hyetograph is a bar graph showing the intensity of rainfall with time as shown in the figure. PRESENTATION OF RAINFALL DATA 2. Mass curve of Rainfall method A mass curve of rainfall is a plot of cumulative depth of rainfall against time, as shown in the figure below. The steepness of the curve indicates the intensity of rainfall. A horizontal portion of the curve indicates that there was no rainfall during that period. PRESENTATION OF RAINFALL DATA 3. Point Rainfall Method The rainfall of the station is known as point rainfall or station rainfall. The point rainfall data is presented graphically as plots of magnitude vs. time in the form of bar diagram. Point Precipitation data are used collectively to estimate the areal variability of rainfall. It is also used in deriving the intensity-duration-frequency curves. INTERPRETATION OF RAINFALL DATA Generally, the precipitation may be required under the following headings: Intensity (i) Frequency (f) Duration (t) Areal extent INTENSITY OF RAINFALL The intensity of rainfall (i) is defined as the The intensity rainfall is classified rate at which rainfall occurs, and expressed into the following three types: as cm/h or mm/h. light intensity rainfall The non-recording type rain gauge, however, measures only rainfall depth (P) in a day, or in = 2.5 mm/h a duration (t) of the rainfall. Moderate intensity rainfall = 2.5 – 7.5 mm/h Therefore, the intensity of rainfall is given by: Heavy intensity rainfall 𝒑 𝒊= = > 7.5 mm/h 𝒕 Where; p = the rainfall amount (cm or mm) t = the duration of rainfall (min or hr) EXAMPLE 2: Time Cumulative Rainfall Rainfall in successive Rainfall intensity 15 min (mm/h) The ordinates (in mm) of a rainfall mass curve interval for a storm, which commenced at 6:30 hours, (mm) recorded by self recording rain gauge at 15 minutes interval are as under: 0, 12.4, 22.1, 6:30 0 -- -- 35.1, 52.7, 63.7, 81.9, 109.2, 123.5, 132.6, 6:45 12.4 12..4 49.6 143.3, 146 and 146. 7:00 22.1 9.7 38.8 Construct the hyetograph of this storm for a 7:15 35.1 13 52 uniform interval of 15 minutes. 7:30 52.7 17.6 70.4 7:45 63.7 11 44 8:00 81.9 18.2 72.8 Solution: 8:15 109.2 27.3 109.2 First, solve for the rainfall intensity. Show the 8:30 123.5 14.3 57.2 result in a tabular form. 8:45 132.6 9.1 36.4 9:00 143.3 10.7 42.8 9:15 146 2.7 10.8 9:30 146 0.0 0.0 Then, plot the data using hyetograph. RECURRENCE INTERVAL/RETURN PERIOD The recurrence interval is the interval For the frequency analysis, in years for occurrence of the event various events are arranged in of the same magnitude. It is the descending order of magnitude, reciprocal of the frequency. and each event is assigned an Frequency of rainfall is the number of order number m, with m=1 for the time that a given magnitude of first entry, m=2 for the second rainfall may occur in a given period. entry and so on, till last entry (event) has m = N = number of The recurrence interval or also known years of record. as return period given by: 𝟏 𝐓= 𝐏𝐨 where Po is the probability of occurrence. The probability Po of an event is given Example 3: by the following formulae: The values of annual precipitation at a rain gauge station in mm per year, in chronological sequence from 1972 to 1981 are indicated below: California formula 475; 377; 731; 1066; 361; 305; 926; 628; 409; 236; 𝐏𝐨 = 𝒎 𝒐𝒓 𝑻 = 𝑵 337 and 853. 𝑵 𝒎 Estimate the value of precipitation which has recurrence interval of six years using the probability method. Hazen formula 𝟐𝐦 −𝟏 𝟐𝐍 𝐏𝐨 = 𝐨𝐫 𝐓 = Given: N = 12 years; T = 6 𝟐𝐍 𝟐𝐦 −𝟏 Solution: Ranking of storm = m = N/T Weibull formula 𝒎 𝑵+𝟏 = 12/6 = 2 𝐏𝐨 = or 𝐓 = 𝑵+𝟏 𝒎 Hence, we should pick the second severest storm. From the records the 2nd severest storm is 926 mm. Hence the value of precipitation which has reccurence interval of 6 years is 926 mm.  INTENSITY-DURATION ANALYSIS It has generally been observed that the greater the intensity of rainfall, the shorter is the length of time it continues. As the duration of storm increases, the maximum intensity of storm decreases. EXAMPLE 4. From the storm in example 2, compute the maximum rainfall intensities for duration of 15, 30, 45, 60, and 120 minutes and plot the intensity duration graph. Solution: In the above table, the bold figures denote the maximum rainfall depth for the respective durations. Thus, the maximum rainfall depth of 15 min, 30 min, 45 min, 60 min, 90 min, and 120 min. durations are 27.3, 45.5, 59.8, 74.1, 101.4, and 123.5 respectively. max. intensity for 15 min. duration i15 = 27.3/0.25 = 109.2 mm/h max intensity for 30 min duration i30 = 45.5/0.5 = 91 mm/h max intensity for 45 min duration i45 = 59.8/0.75 = 79.7 mm/h max intensity for 60 min duration i60 = 74.1/1 = 74.1 mm/h max intensity for 90 min duration i45 = 101.4/1.5 = 67.6 mm/h max intensity for 120 min duration i45 = 123.5/2 = 61.75 mm/h  INTENSITY-DURATION-FREQUENCY RELATIONSHIP It is observed that a storm of any given duration will have larger intensity if its return period is large. This means that for storm of given duration, storms of higher intensity in that duration are rarer than storms of smaller intensity. EXAMPLE 4: Given rainfall data, for rains of duration of 5 min.,10 min, 20 min, 30 min, 60 min, 90 min, and 120 min, at a certain station, available for a period of three decades were analyzed and ten worst storms of each of these durations are shown in their decreasing order in the table below. Plot the IDF curves for storms of return periods of 10,2, and 1 years. Use California formula. SOLUTION: Solve for the return period (T). The next step would be solving for the rainfall intensity, during each duration/storm, for the required return periods. INTENSITY-DURATION-FREQUENCY (IDF) CURVE  DEPTH-AREA RELATIONSHIP For a rainfall of a given duration, the average depth of rainfall decreases from the maximum (or highest) values as the considered area increases. EXAMPLE: Using depth-area curve, estimate the average precipitation that may be expected over an area of 1800 km2 due to a storm of 15th July 1992, lasting for 24 hours, assuming the storm to be located at the center of the area. The isohyetal map for the storm gave the following areas eclosed between different isohyets:  SOLUTION: In order to plot the depth area curve, let us first compute the equivalent uniform depth (EUD) of rainfall (mean depth of rainfall) over increasing area of the basin. DEPTH-AREA CURVE The figure shows the plot between mean depth of rainfall and area enclosed between the isohytes and boundary of the basin. From the above depth-area curve, we obtain average depth of precipitation = 24.1 mm for an area of 1800 km2.  MAXIMUM AND MINIMUM RAINFALL Procedures for determination of maximum The magnitude of maximum rainfall rainfall: and minimum rainfall within specified time period can be determined by 1. arrange the rainfall data in descending order the use of frequency formula given and assign rank number (m) to each rainfall by Hazen: event, the total number of event being equal to 𝐓= 𝟐𝐍 = 𝐍 N. 𝟐𝐦 −𝟏 𝐦 −𝟎.𝟓 Where; 2. compute recurrence interval (T) for each event. T = recurrence interval within which the event is either equal to or greater 3. Plot a graph between recurrence interval (T) than the specified amount. as the abscissa and corresponding rainfall as the m = rank number assigned to the ordinate. event 4. Determine the expected maximum rainfall magnitude for any desired value of T from this graph. MAXIMUM AND MINIMUM RAINFALL (CONTD.) Procedures for determination of minimum rainfall: 1. Arrange the rainfall data in ascending and assign rank number (m) to each rainfall event, the total number of events being equal to N. 2. Compute recurrence interval (T) for each event. 3. Plot a graph between recurrence interval (T) as the abscissa and corresponding rainfall as the ordinate. 4. determine the expected minimum rainfall magnitude for any desired value of T from this graph. EXAMPLE: The rainfall data recorded at a rain gauge station are given below: Year Rainfall (cm) Year Rainfall 1951 61 1961 54 1952 50 1962 70 1953 75 1963 34 1954 32 1964 63 1955 36 1965 68 1956 30 1966 82 1957 46 1967 78 1958 52 1968 58 1959 72 1969 56 1960 40 1970 65 A. Computation for maximum rainfall From this curve, the maximum precipitation at T= 15 is 79 cm. B. Computation of minimum rainfall From this curve, the minimum rainfall at T = 15 is 31 cm