GRD Journals | Global Research and Development Journal for Engineering | Emerging Research and Innovations in Civil Engineering (ERICE - 2019) | February 2019
e-ISSN: 2455-5703
Estimation of Annual One Day Maximum Rainfall using Probability Distributions for Waghodia Taluka, Vadodara 1Pranav
B. Mistry 2T. M. V. Suryanarayana Research Scholar 2Associate Professor 1,2 Department of Water Resources Engineering and Management Institute 1,2 The Maharaja Sayajirao University of Baroda, Samiala-391410, India 1
Abstract Rainfall is an infrequent and an important hydrological parameter on the earth. In the design of irrigation and other hydraulic structures, evaluating the magnitude of extreme rainfall for a specific probability of occurrence is of much importance. For the present study daily rainfall data from 1968-2010 for Waghodia Taluka is collected and analysed for Annual One Day Maximum Rainfall (AODMR) using various five commonly used probability distribution viz., Gumbel’s distributions, Normal distributions, Lognormal, Log Pearson type III and Generalized Extreme distribution to determine the best fit probability distribution. The expected values were compared with the observed values using goodness of fit were determined by chi square (γ2) test. The chisquare values for Normal, Log-Normal, Log- Pearson type-III, Generalized Extreme distributions and Gumbel’s distributions and were 29.98, 29.68, 48.58, 8.40 and 4.06 respectively which shows that the Gumbel’s distribution was the best fit probability distribution to forecast annual one day maximum rainfall for different return periods. Also, expected Annual One Day Maximum Rainfall using Gumbel’s distribution for return period of 2, 5, 10, 25, 50 and 100 were 122.65mm, 177.75mm, 214.24mm, 260.34mm, 294.54mm and 328.49mm respectively. The comparisons between the observed and predicted maximum value of rainfall clearly shows that the developed model can be efficiently used for the prediction of rainfall. The results of this study would be useful for agricultural scientists, decision makers, policy planners and researchers for agricultural development and constructions of small soil and water conservation structures, irrigation and drainage systems in Gujarat, India. Keyword- AODMR, Probability Distributions, Chi-Square Test __________________________________________________________________________________________________
I. INTRODUCTION Analysis of rainfall data strongly depends on its distribution pattern. It has long been a topic of interest in the fields of meteorology in establishing a probability distribution that provides a good fit to daily rainfall. Several studies have been conducted in India and abroad on rainfall analysis and best fit probability distribution function such as normal, lognormal, Gumbel, Weibull and Pearson type distribution were identified by Sharma and Singh (2010). Frequency analysis of rainfall is an important tool for solving various water management problems and is used to assess the extent of crop failure due to deficiency or excess of rainfall. Probability analysis of annual maximum daily rainfall for different returns periods has been suggested for the design of small and medium hydraulic structure (Bhatt et al, 1996). Rainfall modelling is an important area of hydrologic studies and is one in which research is still being actively carried out. Probability analysis can be used for prediction of occurrence of future events from available records of rainfall with the help of statistical methods (Kumar and Kumar, 1989).
II. LITERATURE REVIEW Sabarish et al (2017) studied an extreme value analysis of rainfall for Tiruchirapalli City in Tamil Nadu and best-fit probability distribution was evaluated for 1, 2, 3, 4 and 5 days of continuous maximum rainfall. The goodness of fit was evaluated using Chisquare test. The results of the goodness-of-fit tests indicate that log-Pearson type III method was the overall best-fit probability distribution for 1-day maximum rainfall and consecutive 2-, 3-, 4-, 5- and 6-day maximum rainfall series of present study. Similarly Bhakar et al. (2008) studied the variation of rainfall pattern using Weibull’s (extreme value type III) method and weekly rainfall was predicted at various probability levels. Gumbel distribution was found to be fitted well for prediction of weekly and monthly maximum rainfall. Rahman et al. (1997) used trend analysis to study the changes in monsoon rainfall of Bangladesh and observed no significant changes. Ahmed (1989) estimated the probabilistic rainfall extremes in Bangladesh during the pre-monsoon season.
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Estimation of Annual One Day Maximum Rainfall using Probability Distributions for Waghodia Taluka, Vadodara (GRDJE / CONFERENCE / ERICE - 2019 / 059)
Karmakar and Khatun (1989) repeated a similar study on rainfall extremes during the southwest monsoon season. However, both the studies were focused only on the maximum rainfall events for a limited period. May(2004) reported that the frequency of wet days has noticeably increased over the tropical Indian Ocean who predicted that intensity of heavy rainfall events in Bangladesh will be increased in future. Immerzeel (2007) predicted accelerated seasonal increases in rainfall in the 21st century with strongest increase in monsoon in the Brahmaputra basin. Shah and Suryanarayana (2014) estimated daily rainfall data of 30 years (1961-1990) and analyzed to determine the annual one day maximum rainfall of devgarhbaria situated near panam dam. Also, Shah and Suryanarayana (2014) used probability distributions such as normal, lognormal and gamma distribution to determine the best fit probability distribution for annual one day maximum and two to seven consecutive days’ maximum rainfall series by comparing observed values with tabulated Chisquare value for Panam dam. In this present study, annual one day maximum rainfall (AODMR) of Waghodia Raingauge station for (1962-2010) years estimated. The area selected for the present study is one of the raingauge stations in the Vadodara district, which is located in central part of Gujarat state.
III. STUDY AREA AND DATA COLLECTION Vadodara district with 7548.50 Sq. km area, is located central part of mainland Gujarat, lies between 21°49”19” and 22°48”37” North Latitude and 72°51”05”and 74°16”55” East Longitude.
Fig. 1: Map of Vadodara District
Vadodara district area, in general, being located south of Tropic of Cancer and in transition zone of heavy rainfall areas of South Gujarat and arid areas of North Gujarat plains, have sub-tropical climate with moderate humidity. The various season of the year are (a) monsoon - middle of June to October, (b) winter - November to February, and (c) summer – March to June. For the present study daily rainfall data of Waghodia Taluka from 1968-2010 viz., 43 years is selected and analysed.
IV. RESULTS AND ANALYSIS In present study area the region Vadodara and in that particular Waghodia Taluka is falls under semi-arid climate having hot summer (40o - 44o C) and cold winter (10 o C -16 o C) with monsoon rains occurring from June to September more than 80% of rain is received from South-West monsoon during four months period June to September and the rainfall of rainy season is significantly different from that dry season. The statistical analysis of rainfall is calculated and it is shows that maximum amount of rainfall occurring in month of July with 450.34 mm which is shown in below Table 1. Also, from the daily rainfall data it is observed that in Waghodia Taluka the highest average rainfall occurred in the year of 1973 with amount of 1464.59 mm which includes 166.10 mm in month of June 417.49 mm in month of July 366.00 mm in month of August and 515.00 mm in month of August. So, 1973 year has been found to be the rainiest year of the decade with total annual rainfall of 1464.59 mm mm whereas 2009 had received the lowest amount of rainfall in the entire decade 296.50 mm. Year June July August September (1968-2010) Total 188.83 450.34 364.80 207.35 Average 4.39 10.47 8.48 4.82 Table 1: Statistical Analysis of Monsoon Season Rainfall
Statistical analysis of annual one day maximum rainfall (AODMR) recorded at Waghodia (1968-2010) with corresponding date were analysed and have been presented in below Table 2. The highest and lowest values of AODMR were
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Estimation of Annual One Day Maximum Rainfall using Probability Distributions for Waghodia Taluka, Vadodara (GRDJE / CONFERENCE / ERICE - 2019 / 059)
found to be 273 mm on 11th September 1969 and 29 mm on 22nd July 2009, respectively. The year 1984, 1985, 1986, and 1987 are successive rainfall deficit years in present study area. Below Figure 2 shows the variability of total annual rainfall with mean Âą SD which shows that maximum range with 195.13 and minimum 70.47 and most of the years comes under that range except some years. Year AODMR Month Year AODMR Month 1968 136.5 6th July 1991 110.5 24th July 1969 273 11th September 1992 67 3rd September 1970 119 11th July 1993 75 11th July rd th 1971 79 23 July 1994 192 7 September 1972 88.8 7th July 1995 200 27th July 1973 140 31st August 1996 183 28th July 1974 47 13th July 1997 100 25th August 1975 111 13th August 1998 235 7th July 1976 206 11th July 1999 75 19th June 1977 137 27th June 2000 150 13th July th 1978 241 29 August 2001 76 17th June th 1979 94 11 July 2002 77 25th June 1980 85 27th July 2003 232 24th August 1981 132.7 17th August 2004 178 31st July th 1982 60 8 August 2005 240 23rd Sept. 1983 98 18th August 2006 195 31st July 1984 119.4 11th August 2007 82 2nd July th 1985 111 18 July 2008 122 12th August th 1986 168 25 June 2009 29 22nd July 1987 79 29th June 2010 102 5th August 1988 132 22nd July Table 2: Annual One Day Maximum Rainfall (AODMR) for the period 1968-2010
Fig. 2: Variability of Total Annual Rainfall
Various statistical parameters of AODMR were determined and have been summarized in below Table 3. The average AODMR for the time duration mentioned above was found as 132.89 mm with a standard deviation of 62.33 mm, coefficient of variation (Cv) 63.07% and coefficient of skewness (Cs) 0.66%. The positive value of Cs indicates that the distribution is slightly right tailed and the mass of the distribution (here AODMR) is concentrated towards the left i.e. towards the initial years of the decade. Parameters Maximum Value (mm) Minimum Value (mm) Average of One Day Maximum Rainfall (mm) Standard deviation (mm) Coefficient of Variation Coefficient of Skewness
Values 273.00 29.00 132.89 62.33 63.07 0.66
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Estimation of Annual One Day Maximum Rainfall using Probability Distributions for Waghodia Taluka, Vadodara (GRDJE / CONFERENCE / ERICE - 2019 / 059)
Table 3: Statistics of Waghodia Taluka (1968-2010)
A. Probability Analysis of AODMR The return period of AODMR for 1968-2010 was calculated using Weibull method for different probability distribution such as Normal, Log Normal (LN), Log Pearson Type III, Gumbel and Generalized Extreme Value distributions (GEV) were calculated for the return periods such as 1.05, 1.1, 1.33, 1.42, 2, 2.2, 4, 6.29, 11 and 22 years. Also, it is generally recommended that 2 to 100 years is sufficient return period for soil and water conservation measures, construction of dams, irrigation and drainage works so estimated rainfall is also calculated for 2, 5, 10, 25, 50 and 100 years. The expected AODMR for the different probability distributions have also been graphically presented in Figure 3. From the Figure, it can be observed that the estimated AODMR for the various five different probability distribution functions follow the nearly same trend as observed rainfall. Return Period 2 5 10 25 50 100
Normal Distributions Generalized Extreme Distributions Gumbel’s Log Pearson Type III 123.74 122.65 123.18 121.56 177.52 177.75 184.72 181.27 205.71 214.24 225.47 220.32 235.73 260.34 276.95 268.57 255.07 294.54 315.14 303.69 272.45 328.49 353.05 337.81 Table 4: Expected Annual Rainfall for Various Frequency Distributions Method
Log Normal 118.58 180.28 224.41 283.39 329.51 377.27
Fig. 3: Estimated AODMR for different return periods
The expected AODMR for different probability distributions such as normal, log-normal, log-Pearson type-III, Gumbel and Generalised Extreme distribution were calculated for various probabilities and return period which is shown in below Table 5. Expected Rainfall, (mm) Probability (%) 04.55 09.09 15.91 25.00 45.45 50.00 70.45 75.00 95.45
Return Period, T (Years) 22.00 11.00 06.29 04.00 02.20 02.00 01.42 01.33 01.05
Observed Rainfall (mm)
Gumbel
GEV
Normal Distributions
263.00 269.85 253.99 231.89 240.00 230.91 219.12 209.15 206.00 198.46 190.05 187.56 183.00 170.93 165.40 166.81 122.00 130.47 129.17 131.00 119.00 123.18 122.65 123.74 085.00 92.52 95.19 90.10 079.00 85.55 88.94 81.74 047.00 42.01 49.96 26.02 Table 5: Expected AODMR using Probability distributions
LP III
Log Normal
258.09 195.61 190.63 158.67 124.84 121.56 57.07 50.75 35.22
270.47 227.92 190.76 156.78 121.93 118.58 60.19 54.17 39.05
In the present study all five probability distribution functions were compared by goodness of fit i.e., chi-square test and then selecting the function that gave the smallest chi-square value determined the best probability distribution function for Waghodia Taluka. The chi-square values for Normal, Log-Normal, Log- Pearson type-III, Generalised Extreme distributions and Gumbel’s distributions and were 29.98, 29.68, 48.58, 8.40 and 4.06, respectively which is shown in below Table 5. Gumbel’s distributions distribution gave the lowest calculated chi-square value among the four probability distributions. Hence, Gumbel’s distribution has been found the best probability distribution for predicting AODMR for Waghodia Taluka of Vadodara district. The chi-squared values for the different probability distributions have been presented in Table 5. The analysis revealed that Gumbel distribution to be the one with the lowest chi-squared value with 4.06 amongst the other four distributions tested for goodness of fit data and hence the best probability distribution for predicting AODMR. The second, third and fourth good-fit distributions were GEV, LN, Normal and Log Pearson type III with 8.4, 29.68, 29.98 and 48.58 respectively. Which shows that Gumbel’s distribution is selected for estimation of AODMR in present study. Also, from results of Gumbel distribution, it can be
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Estimation of Annual One Day Maximum Rainfall using Probability Distributions for Waghodia Taluka, Vadodara (GRDJE / CONFERENCE / ERICE - 2019 / 059)
expected that a maximum and minimum rainfall of 263.00 and 47.00 mm can be expected with 4.55% and 95.45% probability and a return period of 22 years to 1.05 years and corresponds to that expected rainfall is 269.85 mm and 42.01 mm. Chi-Square Values Return Period, Gumbel's GEV Normal Distributions LP III Log Normal T (Years) 22.00 0.17 0.32 4.17 0.09 0.21 11.00 0.36 1.99 4.55 10.07 0.64 06.29 0.29 1.34 1.81 1.24 1.22 04.00 0.85 1.87 1.57 3.73 4.38 02.20 0.55 0.40 0.62 0.06 0.00 02.00 0.14 0.11 0.18 0.05 0.00 01.42 0.61 1.09 0.29 13.67 10.23 01.33 0.50 1.11 0.09 15.73 11.38 01.05 0.59 0.17 16.92 3.94 1.62 Total 4.06 8.40 29.28 48.58 29.68 Table 6: Chi-Square Values using for Different Probability distributions at Various Probability P (%) 04.55 09.09 15.91 25.00 45.45 50.00 70.45 75.00 95.45
V. CONCLUSIONS Rainfall is highly variable in space and time and subject to variability with natural and anthropogenic causes. The frequency analysis of annual one day maximum rainfall for identifying the best fit probability distribution was done by using five probability distributions viz. Normal distributions, Log Normal, Gumbel’s and Log Pearson Type-III and Generalised Extreme distributions. The results of the study revealed that the average value of annual one day maximum rainfall was 273mm with standard deviation 62.33 mm and the coefficient of skewness was observed to be 0.66%. The July month received the highest amount of one day maximum rainfall 450.34mm followed by August 364.80mm, September 207.35mm and June 188.93mm during study period. The expected Annual One Day Maximum Rainfall using Gumbel’s distribution for return period of 2, 5, 10, 25, 50 and 100 were 122.65mm, 177.75mm, 214.24mm, 260.34mm, 294.54mm and 328.49mm respectively. It was observed that two probability distribution functions Gumbel’s distribution and Generalised Extreme value distributions fitted significantly except other. Gumbel’s distribution was found to be the best fitted to AODMR data by Chi-square test for goodness of fit. The results from the study could be used as a rough guide by engineers and hydrologists during the design and construction of drainage systems in the catchment area any dam site and computation of drainage co-efficient.
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