TREND DETECTION OF THE RAINFALL AND AIR TEMPERATURE DATA IN TAMIL NADU

Transcription

1 TREND DETECTION OF THE RAINFALL AND AIR TEMPERATURE DATA IN TAMIL NADU *Stella Maragatham R. Department of Mathematics, Queen Mary s (Autonomous) College, Chennai-04 *Author for Correspondence ABSTRACT The present study is mainly concerned with the changing trend of rainfall and temperature of southern part of India viz., Tamil Nadu. This phenomenon has a time depending complex dynamics and hence, needs an integrated long time study. In this study, trend detection of these variables was used in annual and seasonal time scales in five Districts of Tamil nadu namely, Chennai, Coimbatore, Nagapattinam, Vellore, Kanyakumari using data pertaining to 30 years period ( ). Parametric tests including t- test and linear regression and Non parametric tests of Mann Kendall, Mann Whitney and Spearman s rho was used for trend detection in the time series of data. Results indicated that there are not any linear and nonlinear significant trends among rainfall time series both annual and seasonal scale in districts of Tamil nadu State. But there are linear (results of t-test and linear regression) and nonlinear significant trends (results of Mann Kendall, Mann Whitney and Spearman s rho tests) in the most time series of selected stations. These trends in air temperature are mainly positive and show increase in air temperature in the study area. Thus it is required to have a comprehensive study of impact assessment in this region especially its impacts on the water supply systems and agriculture sector. Keywords: Time Series, p-value, Trend, Non Parametric INTRODUCTION Climate change is one of the main challenges in the world that is being studied by scientists and researchers. This phenomenon has impact on human life both directly and indirectly. Scientific research has shown that surface air temperature increased about 0.2 till 0.6 C during last century (Abaurrea and Cerian, 2001) and studies indicate that this parameter may increase about 1.5 to 4.5 C by 2100 (IPCC, 2004). It should be considered that this rate may vary in different geographical regions (Colin et al., 1999). Global warming can affect land ecosystems especially water cycle. Rainfall is a key input in management of agriculture and irrigation projects and any change in this variable can influence on sustainable management of water resources, agriculture and ecosystems. Mainly, studies of climate change science are focused on the probable changes in the annual series of a variable such as rainfall or temperature and variability of these is important. There are physical and empirical methods for climate change detection. Physical methods use climate model for change detection whereas a statistical method uses empirical approach. There are numerous studies that use trend analysis for climate change and global warming. Climate data may be used directly (Van Belle and Hughes, 1984; Xie and Cao, 1996; Zhao and Dirmeyer, 2003; Yue and Hashino, 2003) or indirectly (Douglas et al., 2000; Knowles et al., 2007). Proedrou et al., (1997) in a study of winter air temperature in Creek found that this variable had decreasing trend during 1951 till 1993 but showed upward trend in the summer seasons. Kampata et al., (2008) have evaluated trend analysis in the rainfall of Zam bezi river basin in Zambia using Mann Kendall test using data from 5 rain gauges. Results indicated that there is a slow decrease in this variable that it is not statistically significant. A study on the trend condition of rainfall in Vellore and Chennai districts showed that drought intensity has decreased in the central region compared with the past during 1980 till Also variability of annual rainfall in study area is related to some large scale fluctuations of annual rainfall (Lebel and Ali, 2009). Mann Kendall test for trend detection in monthly, seasonal and annual scale of rainfall in the Kerala state of India for data obtained during 1871 till 2005 showed that there is a significant descent in Copyright 2014 Centre for Info Bio Technology (CIBTech) 1

2 monsoon rainfall in the northwest region but it got an upward direction after this phenomenon. Also there was not any trend in the winter and summer seasons (Krishnakumar et al., 2009). Kumar and Jain (2010) studied trend detection in seasonal and annual rainfall and rainy days using Mann Kendall test in Kashmir valley. Results imply that there was an upward trend of rainfall and rainy days in one station but other stations showed decreasing trend for both variables. Annual and monthly data of rainfall and temperature in England was evaluated by Perry (2006) in a grid net of 5 km resolution for data obtained from 1914 to He indicated that there was a significant trend in the rainfall. Summer rainfall has decreased but winter rainfall has increased in the north and western parts of the study area t-test method for trend detection was used by Ghahreman (2006) who used this test for trend detection of mean annual air temperature in 34 stations of Iran and found that 50% of stations showed positive trend while 41% of station had negative trend. Local and temporal changes in rainfall of Iran were studied by Asakerh (2007) who noted that 51.4% of Iran area was faced by rainfall changes that has high rate changes in mountains area and western part of Iran. Minimum of this change is mm in Sarab station and its maximum is 29.6 mm in the Kouhrang station. Tamil Nadu is located in the southern part of India and has an important role in the socio economic development of India which is one of the major rice producers of the country. This region is prone to drought phenomenon. In the other words, this region can be confronted by water supply stress. Thus for better management and programming, suitable studies related to rainfall and temperature are necessary for this region. These results can be used for local and regional programming of water resources sections and helps governors for selecting optimum strategies related to water management. In fact the goal of the study is determining trend of rainfall and temperature series that results is suitable of water supply organizers for better water management in the State. MATERIALS AND METHODS Study Area Tamil nadu is located in the southern part of arid lands of India with area of 4334 km 2. There are some mountainous regions in the west (Western Ghats) but plains and playas are the main feature of the geomorphology in the east section. So there is not a unit climate in this area. The average annual of precipitation in this area is over 1000 mm with high variability coefficient. There are 5 climatology stations taken into account that have longer period of data record; that was used in this study. The time period for this study is considered 30 years from 1980 to 2009.The rainfall data and the temperature for 5 districts month wise is given in tables 5 and 6.Average temperature for different seasons and annually are calculated and average rainfall of different seasons is also calculated for comparisons. Methods In this study, statistical method was used for trend detection in the rainfall and temperature series. Parametric tests of t-test and linear regression and nonparametric tests of Mann Kendall, Spearman s rho, Kendall s tau and Mann Whitney were used for trend detection in the time scales of annual and seasonal. t-test In the parametric test such as t student, a linear regression is considered between random variable of (Y) during time of (X). Regression coefficient of b1 (Pearson correlation coefficient) is calculated by data and t statistics is determined by the following equation: (1) In this equation, t-student distribution has freedom degree of n-2 that n is sample size, s is residual standard deviation and SS x is sum square of dependent variable (time in trend analysis). Null hypothesis (H 0 : ρ = 0 (or β 1 = 0)) and H1 hypothesis (H 1 : ρ 0 (or β 1 0) are determined in the significant level of α. ρ and β1 are correlation coefficient and regression coefficient respectively. Lack of trend hypothesis can reject when the calculated t is more than its critical amount (t α/2) or p-value is lower than significant level (for example 0.01%) (Yue and Pilon, 2004). Copyright 2014 Centre for Info Bio Technology (CIBTech) 2

3 Linear Regression Linear regression is a parametric test and it assumes that data has normal distribution and it evaluate existence of linear trend between time variable (X) and desire variable (Y). Slop of regression line is calculated by following equation: (2) (3) And S statistics can calculate by: S = b/δ S statistics has freedom degree of n-2 and it assumes data with normal distribution and errors are independent with the same distribution (normal) and has mean of zero: (4) Mann Kendall Test A single variable statistics of Mann Kendall is defined for a special time series (Z k, K = 1, 2,..., n) by following relation: And (5) If there is not relationship between variables and the series has not trend, it would have (Onoz and Bayazit, 2003): E (T) = 0 and Var (T) = n (n-1) (2n+5)/18 Spearman s Rho Test This is a sequential nonparametric test. For data sets of {Xi, i = 1,2, n} the null hypothesis is assumed that all Xi are independent and have the same distribution. But H0 hypothesis is assumed that Xi decrease or increase corresponding to I and it means there is a trend in the data series. Test statistics of D is defined as: (6) where, R (X i ) is i th order of X i observed data and n is sample size regard to null hypothesis, D has normal distribution symmetrically and its average and variance are (Sneyers, 1990): E (D) = 0 V (D) = 1/n-1 Copyright 2014 Centre for Info Bio Technology (CIBTech) 3

4 Mann-Whitney Test This is a kind of nonparametric test that is used for trend detection in data and can compare two independent and accidental variables. U statistics is calculated as following: Where n 1 and n 2 are sample size of two variables and R i is their rank. (7) RESULTS AND DISCUSSION Results Plots of data series versus time are represented in Figure 1 and in Figure 2. Data sets should have normal distribution in the parametric test, thus normality test was carried out using Kolmogrov Smirnov method. Kolmogrov Smirnov test is a nonparametric test that can use for detection normal distribution of data. This test compares the observed cumulative distribution function for a variable with a specified theoretical distribution like normal distribution. The power of this test is detection departures from the hypothesized distribution. For using data in parametric tests, data should have normal distribution and we can check type of data distribution for these kinds of test using Kolmogrov Smirnov test. All data distribution was controlled by this test. Table 1: Results of t-test for data of rainfall and temperature data set Station Period p-value Chennai Annual 0.31 Winter 0.06 Pre monsoon 0.12 Monsoon 0.01 Post monsoon 0.99 Vellore Annual 0.03 Winter Pre monsoon 0.02 Monsoon 1.11 Post monsoon 0.03 Nagapattinam Annual 2.56 Winter 2.31 Pre monsoon 2.10 Monsoon 2.3 Post monsoon 0.05 Kanyakumari Annual Winter 0.38 Pre monsoon Monsoon 0.89 Post monsoon 0.76 Coimbatore Annual 0.78 Winter Pre monsoon Monsoon 0.83 Post monsoon 0.66 Copyright 2014 Centre for Info Bio Technology (CIBTech) 4

5 Table 2: Results of linear regression test for the rainfall and temperature data Station Period b a S Chennai Annual Winter Pre monsoon Monsoon Post monsoon Vellore Annual Winter Pre monsoon Monsoon Post monsoon Nagapattinam Annual Winter Pre monsoon Monsoon Post monsoon Kanyakumari Annual -o Winter o.84 Pre monsoon Monsoon Post monsoon Coimbatore Annual Winter Pre monsoon Monsoon Post monsoon Linear Regression Method Results of regression test indicate that the statistic S has maximum of 3.89 and minimum of Though there are fluctuations the comparability of rainfall with temperature does not show any significant trend.both are positive or negative simultaneously or in other words they are positively proportionate to each other conforming Mann-Kendall s test. Copyright 2014 Centre for Info Bio Technology (CIBTech) 5

6 Table 3: Results of Mann-Kendall s test and Sen s slope estimator of rainfall and temperature data set Station Period Rainfall Rainfall Temp Temp p-value MK Stat p- value MK Stat Sen s slope (RF) Chennai Annual Winter Pre monsoon Monsoon Post monsoon Vellore Annual Winter Pre monsoon Monsoon Post monsoon Nagapattinam Annual Winter Pre monsoon Monsoon Post monsoon Kanyakumari Annual Winter Pre monsoon Monsoon Post monsoon Coimbatore Annual Winter Pre monsoon Monsoon Post Monsoon Sen s slope(temp) Copyright 2014 Centre for Info Bio Technology (CIBTech) 6

7 Table 4: Results of Spearman s rho and Kendall s tau for data set of rainfall and temperature Station Period SP Test Kendall s tau test Chennai Annual Winter Pre monsoon Monsoon Post monsoon Vellore Annual Winter Pre monsoon Monsoon Post monsoon Nagappattinam Annual Winter Pre monsoon Monsoon Post monsoon Kanyakumari Annual Winter Pre monsoon Monsoon Post monsoon Coimbatore Annual Winter Pre monsoon Monsoon Post monsoon Copyright 2014 Centre for Info Bio Technology (CIBTech) 7

8 Table 5: Results of Mann-Whitney test for the data set Station Period P-Value Chennai J-F 0.31 MAM 0.26 J-S 0.96 O-D 0.34 ANNUAL 0.76 Vellore J-F 0.90 MAM 0.96 J-S 0.39 O-D ANNUAL Nagapattinam J-F 0.49 MAM J-S 0.35 O-D 0.01 Kanyakumari ANNUAL 0.24 J-F 0.19 MAM 0.32 J-S 0.15 O-D ANNUAL 0.02 Coimbatore J-F 0.96 MAM 0.88 J-S 0.44 O-D ANNUAL 0.35 Discussion This study was focused on the trend detection of annual and seasonal time series of rainfall and temperature at 5 stations in the Tamil Nadu, viz. Chennai, Vellore, Nagapatinam, Kanyakumari and Coimbatore for a 30 years period. Parametric tests of t-test and linear regression were used for linear trend detection and non parametric tests of Mann Kendall, Mann-Whitney and spearman s rho were used for nonlinear trend of date sets. Plots of rainfall data show irregular fluctuations in different time scale, but these fluctuations are smaller with clear trends in temperature time series. Results of different test are presented as follows: t-test Method Normality test of data indicated that all data have normal distribution with confidence level of 95%. t-test was performed for two separated groups with 30 sample sizes and each significant difference means existence of trend in data. Results indicated that there is no significant trend for both seasonal and annual scales with confidential level of 95 %.From the above table, though there are significant trends in some seasons over all the risk of removing them to null hypothesis is less than that it has to be counted. In other words, in the seashore regions, they are directly proportional and in the offshore regions it slightly differs. But this change is not of a considerable amount. Linear Regression Method Results of regression test indicate that the statistic S has maximum of 3.89 and minimum of Though there are fluctuations the comparability of rainfall with temperature does not show any significant trend.both are positive or negative simultaneously or in other words they are positively proportionate to each other conforming Mann-Kendall s test. Copyright 2014 Centre for Info Bio Technology (CIBTech) 8

9 Mann-Kendall Test In the non-parametric Mann Kendall test, trend of rainfall and temperature for 30 years in 5 districts of Tamilnadu has been calculated for annual and the four Indian seasons together with Sen s slope estimation for these period. Results of Mann-Kendall test and Sen s slope estimator are shown in Table 1. Minimum value of Mann Kendall statistic for rainfall and temperature are (in winter, Chennai), (annual, Nagapattinam) (in winter, Chennai) respectively. There is an evidence of rising trends in rainfall in Chennai during winter (J-F), pre monsoon(mam), in Vellore during annual (J-D), pre monsoon (MAM), post monsoon (O-D), in Nagapattinam during pre monsoon (MAM), in Kanyakumari during annual, pre monsoon, and post monsoon and in Coimbatore during all the seasons. In other seasons it is negative. There is an evidence of raising trend of temperature in Chennai during annual and all seasons, in Vellore there is no positive trend, in Nagapattinam during winter (J-F), in Kanyakumari during winter (J-F) and in Coimbatore during winter (J-F) and monsoon (J-S). As far as, for a healthy trend, the trend with respect to rainfall and temperature should be uniform i.e. if both are negative or positive then it is balancing otherwise the cause for rising trend may be global warming. The cause of rise in rainfall may be due to due to different geographical conditions that influence the variation. Sen s slope is also calculated for the same five districts in Tamilnadu.Its values are also presented in Table 1 from the table there is no change for the winter season of Vellore is identified i.e., 0 otherwise the Sen s slope results are not significant with the Mann-Kendall s. The places or seasons showing different trends with respect to rainfall and temperature are Chennai winter, Pre monsoon, post monsoon seasons Vellore annual, Pre monsoon, post monsoon seasons Nagapattinam winter, pre monsoon seasons Kanyakumari annual, winter, monsoon, Pre monsoon, post monsoon seasons Coimbatore - Pre monsoon, post monsoon seasons If both the trends move simultaneously ie., either increasing or decreasing then the climate will be normal. The variations may be due to air pollution, glaciers melting on poles, green house gases etc. Therefore we can conclude that there is evidence of some change in the trend of precipitation in the specific regions in 30 years period. Hence, further study in this region finding the cause and other aspects may help better irrigation in the State. Mann-Whitney Test Nonparametric test of Mann-Whitney was performed on the rainfall and temperature series of 5 districts of Tamil Nadu for the period of 30 years. Results in Table 3 indicate that the rainfall and temperature are closely related to each other i.e. in test the risk of rejecting the null hypothesis is lower than 10 % in each case. Hence, it emphasises that the rainfall and the temperature are influencing each other. During winter seasons, a positive trend exists in almost all the places. Spearman s Rho Test The Spearman s Rho test and Kendall s Tau test for different seasons of 5 districts of Tamil Nadu are shown in table 2.Results of Spearman s rho test indicate there is no significant trend in many seasons. In Chennai during monsoon and post monsoon seasons, it is negative. In Vellore during monsoon it is negative. In Kanyakumari during post monsoon, in Nagapattinam during monsoon the negative trend occurs. The result of Kendall s tau simulates almost the same trends as in Spearman s rho test. Stability of rainfall variables and lack of positive trend in annual and seasonal scales in Chennai and in Vellore, it is expected that evaporation rate has increased due to warming of study area and this can cause stress on the water supply systems and limits agriculture practices. Matouq (2008) mentioned in his work that increasing air temperature caused increasing of evaporation. Increasing of air temperature and diminishing rainfall can influence a lot on water systems (Yasin, 2009). Also this positive trend of temperature can influence on the hydrologic cycle and it can impact on change of snowmelt time of Copyright 2014 Centre for Info Bio Technology (CIBTech) 9

10 upstream region and it may initiate problems in water supply system and extended irrigation networks in the downstream of this basin. Thus it is necessary that policy makers make an attempt to solve this problem and introduce proper programs in the regional and local scales toward diminishing negative impacts of the global warming. Table 6: Monthly Rainfall data of 5 districts in Tamil Nadu CHENNAI year JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC VELLORE year JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC Copyright 2014 Centre for Info Bio Technology (CIBTech) 10

11 NAGAPPATINUM year JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC KANNIYAKUMARI year JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC Copyright 2014 Centre for Info Bio Technology (CIBTech) 11

12 COIMBATORE year JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC Copyright 2014 Centre for Info Bio Technology (CIBTech) 12

13 Table 7: AVERAGE MONTLY TEMPERATURE DATA OF TAMIL NADU CHENNA I YEAR JAN FEB MA R AP R MA Y JUN JUL AUG SEP OCT NOV DE C VELLOR E YEAR JAN FEB MA AP MA JUN JUL AUG SEP OCT NOV DE Copyright 2014 Centre for Info Bio Technology (CIBTech) 13

14 R R Y C COIMBATORE YEAR JAN FEB MA AP MA JUN JUL AUG SEP OCT NOV DEC R R Y Copyright 2014 Centre for Info Bio Technology (CIBTech) 14

15 KANYAKUMARI YEAR JAN FEB MA AP MA JUN JUL AUG SEP OCT NOV DEC R R Y Copyright 2014 Centre for Info Bio Technology (CIBTech) 15

16 NAGAPPATTIN UM YEAR JAN FEB MA AP MA JUN JUL AUG SEP OCT NOV DEC R R Y Copyright 2014 Centre for Info Bio Technology (CIBTech) 16

17 Specified Districts in Tamil Nadu In this study to access better results and comparison of the tests, not only Mann Kendall test that used by some researchers (Kampata et al., 2008; Krishnakumar et al., 2009; Kumar and Jain, 2010) but also other Copyright 2014 Centre for Info Bio Technology (CIBTech) 17

18 linear and nonlinear tests was used. Also some researchers have indicated that Mann Kendall test is a suitable test for trend detection (Montazeri and Ghayour, 2009; Yue and Pilon, 2004) but some work suggest other test like t-test, regression method, Spearman s rho, Kendall s tau are also can be used but Mann Kendall test is the best for trend detection and they indicated that the t-test has less power than the non-parametric test when the probability distribution is skewed. Conclusion Results above show that generally, t -student and linear regression are suitable parametric tests for linear trend detection and nonparametric tests of Mann Kendall, Man Whitney and Spearman rho have good capability for nonlinear trend detection especially in the climatology data series. It is recommended that several statistical tests are used for trend detection for a data series and it can decrease uncertainty of incorrect detection and interpretation compared with using a single test. REFERENCES Abaurrea J and Cerian AC (2001). Trend and variability analysis of rainfall series and their extreme events. Available: Colin P, Silas M, Stylianos P and Pinhas A (1999). Long term changes in diurnal temperature range in Cyprus. Atmospheric Research Douglas EM, Vogel RM and Kroll CN (2000). Trends in floods and low flows in the United States: Impact of spatial correlation. Journal of Hydrology Hajam S, Khoshkhou Y and Shamsodin R (2008). Trend detection of annual and seasonal rainfall of some stations in the central basin of Iran. Geographical Research Journal IPCC (2004). IPCC Workshop on Describing Scientific Uncertainties in Climate Change to Support Analysis of Risk and of Options. IPCC, Colorado, USA. Kampata JM, Parida BP and Moalafhi DB (2008). Trend analysis of rainfall in the headstreams of the zambezi river basin in Zambia. Physics and Chemistry of the Earth Krishnakumar KN, Rao GSLHVP and Gopakumar CS (2009). Rainfall trends in twentieth century over Kerala, India. Atmospheric Environment Kumar V and Jain SK (2010). Trends in seasonal and annual rainfall and rainy days in Kashmir Valley in the last century. Quaternary International Matouq M (2008). Predicting the impact of global warming on the Middle East region: Case study on Hashemite Kingdom of Jordan using the application of geographical information system. Journal of Applied Sciences Onoz B and Bayazit M (2003). The power of statistical tests for trend detection. Turkish Journal of Engineering and Environmental Sciences Sneyers R (1990). On the Statistical Analysis of Series of Observations. World eteorological Organization, Geneva, Switzerland 192. Soltani E and Soltani A (2008). Climate change of Khorasan, north east of Iran, during Research Journal of Applied Sciences Van Belle G and Hughes JP (1984). Nonparametric tests for trend in water quality. Water Resources Research Yasin AA (2009). Application of analytical hierarchy process for the evaluation of climate change impact on ecohydrology: The case of azraq basin in Jordan. Journal of Applied Sciences Yazdani Mohammad Reza, Khoshal Dastjerdi Javad, Mahdavi Mohammad and Sharma Ashish (2011). Trend Detection of the Rainfall and Air temperature Data in the Zayandehrud Basin. Journal of Applied Sciences Yue S and Hashino M (2003). Long term trends of annual and monthly precipitation in Japan. Journal of the American Water Resources Association Yue S and Pilon P (2004). A comparison of the power of the t test, mann-kendall and bootstrap tests for trend detection. Hydrology Science Journal Copyright 2014 Centre for Info Bio Technology (CIBTech) 18