Madras Agric. J., 105 (4-6): 182-185, June 2018

Trend Analysis of Rainfall Intensity in District of Tamil Nadu

A. Indhuja1* and U. Arulanandu2 1Department of Physical Science and Information Technology, Tamil Nadu Agricultural University, Coimbatore. 2Department of Social Sciences, ADAC and RI, Tiruchirappalli.

Rainfall is the dynamic weather parameter having a significant role in the agriculture livelihood. Growth in agriculture and other related sectors depends mainly on the adequate amount and timely availability of rainfall. Variability in precipitation exerts a huge impact on human beings and agriculture. This variation gives the necessity to study the regular pattern of rainfall. The present study aims at analysing the trends in rainfall intensity across various blocks of using daily rainfall data for the period 1990 to 2017. Non-parametric tests such as Mann- Kendall test and Sen’s slope estimator were employed for this purpose. Results revealed that two blocks showed statistically significant increasing trends (95% confidence level) and one block showed significant decreasing trend (95% confidence level) and the remaining eleven blocks showed no significant trends.

Key words: Rainfall, Trend, Mann-Kendall, Sen’s slope.

Rainfall is one of the important weather parameters (MK) test and Sen’s slope estimator. They observed that having greater effect on the livelihood of majority a decreasing trend in some of the months and an of individuals in all over the world. Growth in increasing trend in few other months. The study agriculture and other related sectors depends on also revealed an overall change in precipitation adequate amount and timely availability of rainfall. Of trend during South-west monsoon. (Rai et al., 2014) all the climatic factors, rainfall is of greatest concern conducted a study on climate change, variability to the farmers in rainfed agriculture. The variation of and rainfall probability for crop planning in a few annual and monsoonal rainfall in space and time are districts of central India. They obtained initial and well known and this variability of monsoonal rainfall conditional rainfall probability of getting 10 mm and has considerable impact on agricultural production. 20 mm rainfall per week and concluded that 25th The term variability refers to the deviation from the Standard Meteorological Week (SMW) in Damoh long-term average. In the context of rainfall, variability district is suitable for seed bed preparation and 27th is the extent to which rainfall amounts vary across an SMW (2-7 July) in Sagar district is most suitable for area and over time. sowing operation. With this background the current study is concerned with trend analysis of rainfall in Monitoring of real time rainfall distributions on Tiruchirappalli district of Tamil Nadu. daily basis is required to estimate the progress and status of monsoon and to commence necessary Material and Methods action to control flood/drought situation. This uplifts a Study area question that whether the variability is purely random or is there any identifiable pattern in these variations. Tiruchirappalli district is situated in central south- Information on temporal and spatial variations is eastern India, almost at the geographic centre of the very essential for understanding the hydrological Tamil Nadu surrounded by a Perambalur district in balance on a regional/global scale. The distribution the north, Pudukkotai district in the south, Karur and of rainfall is also significant for water management Dindigul districts in the west and Thanjavur district in in agriculture and monitoring of drought. (Kwarteng the east. It lies between the coordinates 10o47’40.56” et al., 2009) analysed 27 year rainfall data in the N latitude and 78o41’6”E longitude. The topology of Sultanate of Oman using Mann-Kendall test and Tiruchirappalli is almost flat, with an altitude of 78 reported that the yearly rainfall over Oman was quite metres above mean sea level. The district has an variable and irregular. (Kumar et al., 2010) observed area of about 4,404 sq.km. It belongs to Cauvery long term rainfall trends in India using non-parametric delta zone, which receives an average annual rainfall Mann-Kendall test and concluded that no significant of about 842.6 mm. trend was detected in the whole of India in annual, Data collection seasonal or monthly rainfall. (Babar and Ramesh, 2014) analysed the trends in south west monsoon Daily rainfall data for the period from 1990 to rainfall over Nethravathi basin using Mann-Kendall 2017 was obtained from the Disaster Management and Mitigation Department, Revenue Administration, *Corresponding author’s email: [email protected] 183

Government of Tamil Nadu. This consisted of If, Z is positive and p < 0.05, then it is said to be secondary data on daily rainfall of 14 blocks in in increasing trend; Tiruchirappalli district. If, computed probability p > 0.05, then there is Tools of analysis no trend. Mann-Kendall trend test Sen’s slope estimator The non-parametric Mann-Kendall test (Mann The magnitude of the trend in the seasonal and

1945, Kendall 1975 and Gilbert 1987) is commonly annual( 𝑠𝑠 data− 1) series was estimated using a non- 𝑆𝑆 > 0 parametric √𝑉𝑉𝑉𝑉𝑉𝑉(𝑠𝑠) method known as Sen’s estimator (Theil, used to identify monotonic trends in climate data or 𝑍𝑍 = 0 𝑆𝑆 = 0 (𝑠𝑠 + 1) hydrological data. The null and alternative hypothesis 1950). This method 𝑆𝑆 < 0 can be used when the trend is is an indicator function that results{ in√𝑉𝑉𝑉𝑉𝑉𝑉 the(𝑠𝑠) values -1, 0, or 1. Based on the sign are given by If, Z is negative andassumed p < 0.05, then it is saidto to be in decreasing linear, trend ;that is: If, Z is positive and p < 0.05, then it is said to be in increasing trend; 𝑗𝑗 𝑘𝑘 H : There𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆( is𝑋𝑋 no− trend𝑋𝑋 ) in the series. If, computed probability p > 0.05, then there f(t) is no trend.= Qt + B 0 of where j >k, the function is calculated as follows. Sen’s slope estimator Where, Q - slope, H1: There is a negative or positive trend. (𝑋𝑋𝑗𝑗 − 𝑋𝑋𝑘𝑘) The magnitude of the trend in the seasonal and annual data series was estimated using Temporal variation of rainfall across 14 Blocksa non of-parametric method known as Sen’s estimator (Theil, 1950).B This - method constant can be used and the district would be analysed by using Mann-Kendallwhen the trend is assumed to be linear, that is: t - time. test. The is anpositive indicator sign function indicates that results a constant in the values increase -1, 0, or 1. Based on the sign 𝑗𝑗 𝑘𝑘 1 𝑖𝑖𝑓𝑓(𝑖𝑖𝑡𝑡) 𝑥𝑥= 𝑄𝑄𝑄𝑄 +−𝐵𝐵  𝑥𝑥 > 0 in𝑗𝑗 trend𝑘𝑘 over time and the negative value indicatesWhere, Q - slope, To get the slope Q in the above equation, we 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆of (𝑋𝑋 − 𝑋𝑋 where) j >k, the function is calculated as follows. 𝑗𝑗 𝑘𝑘 𝑗𝑗 𝑘𝑘 a constant decline in trend. The larger𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 the(𝑋𝑋 Mann-− 𝑋𝑋 B -) constant= and[ first 0 calculate𝑖𝑖𝑖𝑖𝑥𝑥 − 𝑥𝑥 the= slope0] of all data value pairs using 𝑗𝑗 𝑘𝑘 t - time. 𝑗𝑗 𝑘𝑘 (𝑋𝑋 Kendall− 𝑋𝑋 ) is anstatistic, indicator function stronger that results the in the trend values -1,(magnitude 0, or 1. Based on isthe sign −the1 formula:𝑖𝑖𝑖𝑖𝑥𝑥 − 𝑥𝑥 < 0 To get the slope Q in the above equation, we first calculate the slope of all data value pairs 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆(proportional𝑋𝑋𝑗𝑗 − 𝑋𝑋𝑘𝑘) Test tostatistic strength).: The first step is to find the of where j >k, the function is calculated as follows. using the formula: where i=1,2,…k ; j>k sign of difference between consecutive 1 𝑖𝑖𝑖𝑖𝑥𝑥𝑗𝑗 − data𝑥𝑥𝑘𝑘 > 0points. 𝑗𝑗 𝑘𝑘 (𝑋𝑋 − 𝑋𝑋 ) 𝑗𝑗 𝑘𝑘 𝑗𝑗 𝑘𝑘 X and X are the data values at time j and k 0 𝑖𝑖𝑖𝑖𝑥𝑥 − 𝑥𝑥 = 0 j 𝑗𝑗 𝑘𝑘 k is an indicator 𝑠𝑠function𝑠𝑠𝑠𝑠𝑠𝑠(𝑋𝑋 that− results𝑋𝑋 ) = in [the values -1, 0, or 1. Based] on the sign 𝑥𝑥 − 𝑥𝑥 𝑗𝑗 𝑘𝑘 𝑄𝑄𝑖𝑖 = respectively.𝑗𝑗 − 𝑘𝑘 𝑗𝑗 𝑘𝑘 −𝑗𝑗 1 𝑘𝑘 𝑖𝑖𝑖𝑖𝑥𝑥 − 𝑥𝑥 < 0 where i=1,2,…k ; j>k 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆(𝑋𝑋 − 𝑋𝑋 ) j >k 1 𝑖𝑖𝑖𝑖𝑥𝑥 − 𝑥𝑥 > 0 Testof statistic :where , the function is calculated as follows.𝑗𝑗 𝑘𝑘 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠(𝑋𝑋𝑗𝑗 − 𝑋𝑋𝑘𝑘) = [ 0 𝑖𝑖𝑖𝑖𝑥𝑥 − 𝑥𝑥 = 0] 𝑛𝑛−1and 𝑛𝑛are the data values at time j and k respectively. 𝑗𝑗 𝑘𝑘 𝑗𝑗 𝑘𝑘 If there are ‘n’ values Xj in the time series, we (𝑋𝑋 − 𝑋𝑋 ) −1 𝑖𝑖𝑖𝑖𝑥𝑥 − 𝑥𝑥 < 0 𝑥𝑥𝑗𝑗 is𝑥𝑥𝑘𝑘 an indicator function that results in the values -1, 0, or 1. Based on the sign Test statistic : is isan anindicator indicator function function that results that in the results valuesIf there - 1,are ‘0,n’ valuesor 1. Basedinget the time as on series themany, we signget as many as as N = slopeslope estimates estimates . Q. The Sen’s 𝑗𝑗 𝑘𝑘 𝑛𝑛(𝑛𝑛−1) i 𝑗𝑗 𝑗𝑗 𝑘𝑘 𝑖𝑖 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆(𝑋𝑋 − 𝑋𝑋 ) j >k𝑥𝑥 2 𝑄𝑄 in the values𝑗𝑗 -1,𝑘𝑘 0, or 1. Based on𝑗𝑗 the𝑘𝑘 sign of𝑆𝑆of = The∑ Sen’s where slope∑ estimator ,slope 𝑠𝑠the is𝑠𝑠𝑠𝑠𝑠𝑠 the fun medianction (estimator𝑥𝑥 of is these −calculated N 𝑥𝑥values) of isas follows.. theThe N valuesmedian of are of these N values of 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆of (𝑋𝑋 − 𝑋𝑋 where) j >k, the𝑛𝑛− fun 1 1 ction𝑛𝑛𝑖𝑖𝑖𝑖𝑥𝑥 is− calculated𝑥𝑥 > 0 as follows. 𝑗𝑗 𝑘𝑘 𝑘𝑘=1 𝑗𝑗=𝑘𝑘+1 𝑖𝑖 𝑖𝑖 where j >k, the𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 function(𝑋𝑋𝑗𝑗 − 𝑋𝑋𝑘𝑘) = is[ calculated0 𝑖𝑖𝑖𝑖𝑥𝑥 − 𝑥𝑥 = as0] follows.(𝑋𝑋𝑗𝑗 −ranked𝑋𝑋𝑘𝑘) in ascending orderQ and .the The Sen’s estimator N values is given by, of𝑄𝑄 Q are ranked𝑄𝑄 in ascending order 𝑛𝑛−1 𝑛𝑛 𝑗𝑗 𝑘𝑘 i i 𝑗𝑗 𝑘𝑘 𝑆𝑆 = ∑−1 ∑𝑖𝑖𝑖𝑖𝑥𝑥𝑗𝑗𝑠𝑠−𝑠𝑠𝑠𝑠𝑠𝑠𝑥𝑥𝑘𝑘 (<𝑥𝑥0− 𝑥𝑥 ) (𝑋𝑋where− 𝑋𝑋 ) j = 1,2,3,…,𝑘𝑘=1 𝑗𝑗= 𝑘𝑘n+-11 and k = j+1, j+2, j+3, ……………..and the Sen’s estimator n. is given by, Test statistic: 𝑗𝑗 𝑘𝑘 Test statistic:𝑆𝑆 = ∑ ∑ 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠(𝑥𝑥 − 𝑥𝑥 ) 1 𝑖𝑖𝑖𝑖𝑥𝑥𝑗𝑗 − 𝑥𝑥𝑘𝑘 > 0 where j = 1,2,3,…, n-1 and k = 𝑘𝑘j+=11𝑗𝑗,= 𝑘𝑘j++12, j+3, …………….. n. 𝑗𝑗 𝑘𝑘 𝑗𝑗 𝑘𝑘 where j = 1,2,3,…, n-1 and k = j+1, j+2, j+3, …………….. n. 1 𝑖𝑖𝑖𝑖𝑥𝑥𝑗𝑗 − 𝑥𝑥𝑘𝑘 > 0 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠To(𝑋𝑋 obtain− 𝑋𝑋 ) = [the 0 constant𝑖𝑖𝑖𝑖𝑥𝑥 − 𝑥𝑥 = 0 B] in the equation, N values 𝑗𝑗 𝑘𝑘 𝑗𝑗 𝑘𝑘 −1 𝑖𝑖𝑖𝑖𝑥𝑥 − 𝑥𝑥 < 0 𝑛𝑛−1 𝑛𝑛 𝑗𝑗 𝑘𝑘 of differences X - Qt are found. The median of these 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠(𝑋𝑋 − 𝑋𝑋 ) = [ 0 𝑖𝑖𝑖𝑖𝑥𝑥Test− statistic𝑥𝑥 = 0: ] j k, j > k i i where and where are the annual and values in are years the j and annual k, j > k, valuesrespectively𝑗𝑗 𝑘𝑘 in years and , respectively where and are the annual values in years j and k,𝑗𝑗 j > k𝑘𝑘, respectively−1 𝑖𝑖𝑖𝑖 𝑥𝑥 − 𝑥𝑥 < 0 𝑆𝑆 = ∑ ∑ 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠(𝑥𝑥 − 𝑥𝑥 ) values gives an estimated of B. The Mann Kendall Zc 𝑗𝑗 Test𝑘𝑘 statistic: 𝑘𝑘=1 𝑗𝑗=𝑘𝑘+1 𝑥𝑥𝑗𝑗 𝑥𝑥𝑘𝑘 𝑗𝑗 𝑘𝑘 and Sen’s slope estimation were done using XLSTAT where 𝑥𝑥j = 1,2,3,…,𝑥𝑥 n-1 and k = j+1, j+2, j+3, …………….. n. ForFor large large Samplewheres s j = 1,2,3,…,𝑥𝑥 𝑥𝑥n-1 and k = j+1, j+2, j+3, ... n. 𝑛𝑛−1 𝑛𝑛 For large Samples 17 Software package. 𝑆𝑆 = ∑ ∑ 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠(𝑥𝑥𝑗𝑗 − 𝑥𝑥𝑘𝑘) where andwhere are the x annual and values x arein years the j and annual k, j𝑛𝑛 >−1 k, respectively𝑛𝑛 values in years 𝑘𝑘=1 𝑗𝑗=𝑘𝑘+1 Case I (no ties): For largej sample (aboutk n>8) S is normally distributed with Results and Discussion n where j = 1,2,3,…, n-1 and k = j+1, j+2, j+3, …………….. n. Case Ij (no𝑥𝑥and𝑗𝑗 ties): 𝑥𝑥k,𝑘𝑘 jF or> klarge, respectively sample (about >8) S is normally distributed𝑗𝑗 𝑘𝑘 with 𝑆𝑆 = ∑ ∑ 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠(𝑥𝑥 − 𝑥𝑥 ) For large Sample s 𝑘𝑘=1 𝑗𝑗=𝑘𝑘+1 Results of the non-parametric Mann-Kendall For large Samples where and n are the annual values in years j and k, j > k, respectively 𝐸𝐸(𝑆𝑆) = 0; whereC asej = 1,2,3,…, I (no n -ties):1 and k =F j+or1 , largej+2, j+ 3sample, …………….. (about n. >8) Stest is normally on rainfall distributed at the 95 per with cent significance are Case I (no ties): For large sample (about n>8) S is normally distributed with 𝑗𝑗 𝑘𝑘 Case I (no ties): For large sample (about n𝑥𝑥>8) 𝑥𝑥 presented in Table 1. 𝐸𝐸(𝑆𝑆) = 0; For large Samples 𝑛𝑛(where𝑛𝑛 − 1) (2 𝑛𝑛and+ 5 ) are the annual values in years j and k, j > k, respectively  𝑉𝑉𝑉𝑉𝑉𝑉 (S𝑆𝑆) =is normally distributed with 18 Table 1. Values of Mann-Kendall test and Sen’s Case II (tied observations)𝑗𝑗 : In 𝑘𝑘case of ties, the variance of S is 𝐸𝐸(𝑆𝑆) = 0;E𝑛𝑛(S𝑛𝑛)− =𝑥𝑥1 )0;(2𝑛𝑛𝑥𝑥+ 5) Case I (no ties): For largeslope sample (about Estimator n>8) S is normally distributed with 𝑉𝑉𝑉𝑉𝑉𝑉(𝑆𝑆) = For large Samples 𝐸𝐸(𝑆𝑆) = 0; 18 Mann Sen’s Probability Trend Case II VAR(tied𝑛𝑛( observations)𝑛𝑛 − 1)(2𝑛𝑛 + 5) : In case of ties, the variance of S is 𝑉𝑉𝑉𝑉𝑉𝑉(𝑆𝑆) = 1 𝑔𝑔 Blocks Kendall Slope value Case I18 (no ties): For large sample𝑝𝑝=1 𝑝𝑝(about𝑝𝑝 n>8)𝑝𝑝 S is normally𝐸𝐸(𝑆𝑆) distributed= 0; with (Z ) (Q) Case II (tied (observations)𝑆𝑆) = 18 [𝑛𝑛(𝑛𝑛: −In1 case)(2𝑛𝑛 of+ ties5),− the∑ variance𝑡𝑡 (𝑡𝑡 of− S1 )is( 2𝑡𝑡 + 5) ] c where, n is the number of data points Andanallur 0.73 8.027 0.46 No trend VAR  1 𝑛𝑛(𝑛𝑛 − 1)(2𝑛𝑛 + 5) 𝑛𝑛(𝑛𝑛 − 1)(2𝑛𝑛 + 5) g is the VARnumber of tied group( ) 𝑔𝑔 𝑉𝑉𝑉𝑉𝑉𝑉(𝑆𝑆) = -0.9285 -6.57 0.353 No trend 𝑉𝑉𝑉𝑉𝑉𝑉18 𝑆𝑆 = 𝑝𝑝=1 𝑝𝑝 𝑝𝑝 𝑝𝑝 18 (𝐸𝐸𝑆𝑆()𝑆𝑆=)1= 0[;𝑛𝑛(𝑛𝑛 − 1)(2𝑛𝑛 + 5𝑔𝑔 ) − ∑ 𝑡𝑡 (𝑡𝑡 − 1)(Case2𝑡𝑡 +II (tied5)] observations): In case of ties, the variance of S is Case II (tied observations):th 𝑝𝑝=1 𝑝𝑝18𝑝𝑝 In case𝑝𝑝 of ties, the Manachanallur 2.192 13.24 0.028 Increasing trend where, is the n numberis the(𝑆𝑆) number=ofCase 18data[𝑛𝑛 (points𝑛𝑛 ofII− 1 data (tiedin)( 2the𝑛𝑛 points+ p 5 observations))group− ∑ 𝑡𝑡 (𝑡𝑡 − 1)(2𝑡𝑡: I+n5 )case] of ties, the variance of S is where,variance n is the number of ofS data is points 𝑡𝑡𝑝𝑝 -3.062 -24.699 0.003 Decreasing trend g is the number of tied 𝑛𝑛group(𝑛𝑛 − 1)(2𝑛𝑛 + 5) VAR g is the number𝑉𝑉𝑉𝑉𝑉𝑉 of (tied𝑆𝑆) =group 1 Manikandam 𝑔𝑔0.9089 5.402 0.363 No trend where, n is the 18number of data points 𝑝𝑝=1 𝑝𝑝 𝑝𝑝 𝑝𝑝 Case II (tied observations): In case of ties, the variance of S is (𝑆𝑆) = 18 [𝑛𝑛(𝑛𝑛 − 1)(2𝑛𝑛 + 5) − ∑ 𝑡𝑡 (𝑡𝑡 − 1)(2𝑡𝑡 + 5)] is is the the numberg is of the of data data numberpoints points VAR in the in ofpth the grouptied pth group where, n is the number of dataMarungapuri points 0.7309 6.298 0.465 No trend 𝑝𝑝 1 th 𝑔𝑔Musiri -1.0866 -4.97 0.277 No trend 𝑝𝑝𝑡𝑡 tp is the number of data points in the p ggroup is the number of tied group 𝑡𝑡 VAR 𝑝𝑝=1 𝑝𝑝 𝑝𝑝 𝑝𝑝 1 18 𝑔𝑔 Pullambadi 1.955 10.198 0.049 Increasing trend (𝑆𝑆) = [𝑛𝑛(𝑛𝑛 − 1)(2 is𝑛𝑛 the+ number5) −of data∑ points 𝑡𝑡in the(𝑡𝑡 pth group− 1 )(2𝑡𝑡 + 5)] (𝑆𝑆) = 18 [𝑛𝑛(𝑛𝑛 − 1)(2𝑛𝑛 + 5) − ∑𝑝𝑝=1 𝑡𝑡𝑝𝑝(𝑡𝑡𝑝𝑝 − 1)(2𝑡𝑡𝑝𝑝 + 5)] where, n is the number of data points Thathaingarpet 0.889 4.937 0.374 No trend where, n is the number of data points 𝑡𝑡𝑝𝑝 (𝑠𝑠 − 1) Thiruverumbur -1.244 -5.772 0.228 No trend g is the number of tied group 𝑆𝑆 > 0 g is the number√𝑉𝑉𝑉𝑉𝑉𝑉 (of𝑠𝑠) tied group Thottiam -1.679 -6.83 0.101 No trend is the𝑍𝑍 number= of data points0 in the p th group 𝑆𝑆 = 0 -1.244 -7.871 0.228 No trend (𝑠𝑠 + 1) th 𝑡𝑡𝑝𝑝 is the number of data 𝑆𝑆 points< 0 in the p group Uppiliyapuram 0.8759 12.25 0.381 No trend If, Z is negative{ √and𝑉𝑉𝑉𝑉𝑉𝑉 p( <𝑠𝑠 )0.05, then it is said to be Vaiyampatty -0.2173 -1.274 0.859 No trend If, Z is negative and p𝑝𝑝 < 0.05, then it is said to be in decreasing trend; in decreasing𝑡𝑡 trend; If, Z is positive and p < 0.05, then it is said to be in increasing trend;

If, computed probability p > 0.05, then there is no trend.

Sen’s slope estimator

The magnitude of the trend in the seasonal and annual data series was estimated using a non-parametric method known as Sen’s estimator (Theil, 1950). This method can be used when the trend is assumed to be linear, that is:

𝑓𝑓(𝑡𝑡) = 𝑄𝑄𝑄𝑄 + 𝐵𝐵  Where, Q - slope,

B - constant and

t - time.

To get the slope Q in the above equation, we first calculate the slope of all data value pairs using the formula:

𝑥𝑥𝑗𝑗 − 𝑥𝑥𝑘𝑘 𝑄𝑄𝑖𝑖 = 𝑗𝑗 − 𝑘𝑘 where i=1,2,…k ; j>k

and are the data values at time j and k respectively.

𝑥𝑥𝑗𝑗 𝑥𝑥𝑘𝑘 If there are ‘n’ values in the time series, we get as many as N = slope estimates . 𝑛𝑛(𝑛𝑛−1) 𝑥𝑥𝑗𝑗 𝑄𝑄𝑖𝑖 The Sen’s slope estimator is the median of these N values of . The2 N values of are

𝑖𝑖 𝑖𝑖 ranked in ascending order and the Sen’s estimator is given by, 𝑄𝑄 𝑄𝑄 184

a.

Fig. 1. Trend of Zc for individual blocks for b. 28 Pullambadi years block The annual mean rainfall is Fig.subjected 1 Trend to the of Mann- Zc for individual blocks for 28 years Kendall test at each block. Table 1 summarizes the significant decreasing and increasing rainfall trends and Sen’s Slope estimate (Q) for finding magnitude of each block during the study period 1990-2017.

c. Manapparai

Fig. 2 Annual Fig. rainfall 2. Annual trends rainfall using Sen’s trends slope using method Sen’s slope method The results exposed that there was both statistically significant (95 % confidence level) positive and a. Manachanallur block negative trends in the mean annual rainfall intensity in the wider area of Tiruchirappalli district. Among the 14 blocks, two blocks viz., Manachanallur and Pullambadi showed statistically significant increasing trend (at 5% level), whereas the Manapparai block showed statistically significant decreasing trend (at 5% level). The other blocks showed insignificant

trends. The Zc values for Andanallur, Manikandam, Marungapuri, Thathaingarpet and Uppiliyapuram blocks showed an insignificant increasing trend, while Lalgudi, Musiri, Thiruverumbur, Thottiam, Thuraiyur and Vaiyampatty showed an insignificant decreasing trend (Fig. 1). Following the Mann Kendall test, Sen’s slope estimator was employed to find out the change b. per unit time of trends and the results are presented in Table 1, where the negative sign indicates a

c. Manapparai

Fig. 2 Annual rainfall trends using Sen’s slope method 185 downward slope and the positive sign represents an decreasing trend (95% confidence level) found in upward one. Manapparai and no significant trends in rest of the blocks. The outcomes of the Sen’s Slope test appear Sen’s estimator value was minimum (4.937 mm/ to be similar to those attained from the Mann-Kendall year) at Thathaingarpet block and maximum (13.24 test. Data reduction techniques such as Principal mm/year) at Manachanallur block for the positive Component Analysis can be used to see the spatial trends. On the other hand, for the negative trends, and temporal variation. the highest slope value was present for Vaiyampatty block (-1.274 mm/year). The estimated Sen’s References slope (Q) showed ascending magnitude in seven Babar, S. and H. Ramesh. 2014. Analysis of extreme blocks (Andanallur, Manachanallur, Manikandam, rainfall events over Nethravathi basin. ISH Journal of Marungapuri, Pullambadi, Thathaingarpet and Hydraulic Engineering. 20(2): 212-221. Uppiliyapuram) and descending slope magnitude Gilbert, R.O. 1987. Statistical Methods for Environmental in seven blocks (Lalgudi, Manapparai, Musiri, Pollution Monitoring, John Wiley and Sons, NewYork, Thiruverumbur, Thottiam, Thuraiyur and Vaiyampatty). p. 336. Fig. 2a, b & c shows the annual rainfall trends using Jain, S. K. and Kumar, V. (2012). Trend analysis of rainfall Sen’s Slope method for the three blocks that had and temperature data for India. Current Science. shown a significant increasing and decreasing trends 102(1): 37-49. in Mann Kendall method. The outcomes of the Sen’s Kendall, M.G. 1975. Rank Correlation Methods, 4th edition, Slope test appear to be similar to those obtained Charles Griffin, London. from the Mann-Kendall test. Jain and Kumar (2012) Kumar, V., Jain, S. K. and Y. Singh. 2010. Analysis of long- studied trends in rainfall, rainy days and temperature term rainfall trends in India. Hydrological Sciences over India. Magnitude of the trend has been estimated Journal. 55(4): 484-496. by Sen’s estimator of the slope, while statistical Kwarteng, A. Y., Dorvlob, A. S. and G.T.V. Kumara. 2009. significance was evaluated by Mann-Kendall test. Analysis of a 27-year rainfall data (1977-2003) in Results indicated that there were both positive and the Sultanate of Oman. International Journal of negative trends in the area. Sen’s slope estimate also Climatology. 29(4): 605-617. gave results corresponding to the MK test values. Mann, H.B. 1945. Non-parametric tests against trend. Econometrica. 13: 163-171. Conclusion Rai, S. K., Kumar, S., Rai, A. K. and D.R. Palsaniya. 2014. Climate Change, Variability and Rainfall Probability Rainfall intensity trend analysis with Mann- for Crop Planning in Few Districts of Central India. Kendall test showed that statistically significant Atmospheric and Climate Sciences. 4(3): 394-403. increasing trends (95% confidence level) appear Theil, H. 1950. A rank-invariant method of linear and in Manachanallur and Pullambadi, significant polynomial regression analysis. Proc. Kon. Ned. Akad. v. Wetensch. A53: 386-392.

Received : May 16, 2018; Revised : June 25, 2018; Accepted : June 30, 2018