Analysis of Long Term Temperature Trend for Madhya Pradesh , India ( 1901-2005 )

The paper examines the impact of climatic change on the mean temperature time series for Pre-monsoon (Mar-May), Monsoon (Jun-Sept), Post-monsoon (Oct-Nov), winter (Dec-Feb) and Annual (Jan-Dec) at 45 stations in the state of Madhya Pradesh, India. Impact detection is accomplished by using the Mann-Kendall method to find out the monotonic trend and Sen’s slope is method is to identify the grandeur of trend for the period 1901 to 2005 (105 years). Prior to the trend analysis prominence of eloquent lag-1 serial correlation are eradicated from data by the pre-whitening method. In addition, shift year change has also been examined in the study using Pettitt’s test. From 45 stations, most of the station show symbolic hike trend at 5% significance level in the mean temperature time series for Madhya Pradesh region. During peak summer months the maximum temperature touches 40°C in the entire Madhya Pradesh. The magnitudes of annual increase in temperature in the majority of the stations are about 0.01°C.The analysis in the present study indicated that the change point year of the significant upward shift changes was 1963 for annual mean temperature time series, which can be very useful for water resources planners in the study area. The finding of the study provides more insights and inputs for the better understanding of regional temperature and shift behavior in the study area. keywords: Monotonic trend analysis, Sen’s slope, Mann-Kendall test, Pettit’s test, serial correlation, Temperature.


INTRODucTION
After precipitation, the temperature is found to be an essential meteorological parameter of climate.It is also considered as a good indicator to understand the global climate as it signifies the exchange of energy process over the surface of the earth with proper accuracy (Shukla et al., 2015 andJhajharia &Singh., 2011).In 2007, Intergovernmental Panel on Climate Change (IPCC) stated the growing tendencies of temperature is about 0.74°C of mean temperature in past 100 years from 1906 to 2005 in several areas of the world with respect to space and time.Reiter et al. (2012) observed an increase in temperature in the Upper Danube basin with a rise of 0.8°C /decade during summer.Even in spring and winter temperatures have also shown a constant increase.In the past 500 years, the month wise surface temperature in Europe has never been as warmer as is growing in 21 st century (luterbacher et al., 2004).In past 53 years, the annual average temperature in Canada has increased by 1.2°C (Vincent et al., 2007).According to IPCC 2007, upwards trends have also been detected across the 7 subregions of Asia.In Russia the rise in mean yearly temperature is observed to be 2 to 3°C (Savelieva et al., 2000;Peterson et al., 2002), 0.7°C in Northwest part of China (Shi et al., 2002), 1.0°C in Japan (Ichikawa, 2004), 1.8°C in main towns of Mongolia (Batima et al., 2005).
A few studies have been carried out in India as well on temperature changes and their alliance with climate change.A temporal and spatial change of annual and seasonal temperature was conducted in India by researchers including Shukla, R., and Khare, D., (2013), Mishra et al., (2013) Darshana et al., (2012) reported that the average annual precipitation variation was (694 mm, Westnimar) to (1416 mm, Mandla).The annual precipitation showed a maximum reduction (-11.99%,Balaghat) and minimum (-8.52%,Shahdol) district.For annual precipitation year, 1978 was found to be the most probable year of change.Alteration in mean percentage of 1901-1978 over the period of 1979-2002 has also been found showing the decrease in precipitation virtually in whole stations.Also in 102 years in Madhya Pradesh, the decrease in annual precipitation was 2.59%.During the period 1901-1978 west part of MP was observed with more rise in yearly precipitation as compared to east part of MP.Revadekar et al., (2011) conducted the observational analysis by taking 121 stations spread all over India showed that widespread warming through an increase in intensity and occurrence of warm events and also by a decrease in the occurrence of cold actions.
Indrani Pal et al., (2009) reported that the long period trends in variations of the highest and lowest values of monthly temperatures and their effects on seasonal fluxes in various regions in India.The trends magnitude and statistical significance were determined by least square regression techniques and the varia tions were regulated by the relevant coefficient of variations.The outcomes is that the monthly maximum temperature raised, though unevenly, over the 20 th century.The minimum temperature changes were more variable than maximum, both temporally and spatially, with lesser significance results.This study showed good pointers of Indian climate changeability over the 20 th century.Jhajharia et al., (2009) examine the year wise average temperature variation (5 to 30°C) and the average relative humidity between (70 to 85%) for the many part in north-east India.In 2010, (Jhajharia and Singh) finds the decreasing trends in Diurnal Air Temperature (DTR) at 4 stations in northeast for every timescales.Instead, the DTR trends were significant at annual, seasonal (pre-monsoon and monsoon), & monthly (May, June, August, September, and November).Major rising trends in DTR are detected at 3 stations in october month as well as in post-monsoon & monsoon seasons.The 4 sites showed significant rising trends for T mean at post-monsoon seasons.For post-monsoon, the T max and T min are found to be more than monsoon in the seasonal cycle.Significant declining trends during sunshine hours were observed on the basis of winter, pre-monsoon and monthly timescales.Bhutiyani et al. (2007) demonstrated that the existence of possible variation between the precipitation and temperature in the late-1960s century.However, post-1970, these connections appear to have grown weaker.This points out the presence of other climatic factors (rise of greenhouse gasses etc.), which could be playing an important role.
The present study involves monotonic trend analysis of mean temperature of the state of Madhya Pradesh of India.Temperature trend analysis carried out with Mann-Kendall (MK) test in 45 different districts on annual, for 1901 to 2005 (105 years).This study will help the agricultural planners and managers dealing with the water resources of the area.

Study Area
Madhya Pradesh is situated in the center of India covering 443,000 km 2 of area.Being at the center, the state is surrounded by many other states like Chhattisgarh, Uttar Pradesh, Rajasthan, Gujarat, and Maharashtra.The state is dissected by a major river system, the Narmada which is the lifeline of the state together with Tapti, Mahanadi, Wainganga etc.The area of the state stretches from 21°17' N to 26°36' N latitude and from 74°02' E to 82°26' E longitude.There are 45 districts in the state and the major crops of the region include rice, wheat, jawar, soybean etc. MP has a sub-tropical type of climate with hot dry summer and cool dry winter thus it experiences the extreme climatic conditions.Temperature rises to as high as 40°C or more particularly in the southern part in the districts of Khandwa, Khargone etc.In Bhopal, the minimum temperature remains around 25 0 C and maximum around 40°C through summer.During winter, the minimum and maximum temperature vary from 10°C to 25°C respectively.The position of the 45 meteorological stations in the state of Madhya Pradesh has been shown in Fig. 1.

Analysis of climatic changes over Madhya
Pradesh was based on the evalu ation of available meteorological and hydrological time series using the statistical method (Mann-Kendall method).In the present study testing of the hypothesis, the result shows that the observed historical climatic trends in the central part of India reflected a signficant change in climate.

Serial correlation effect
The existence of negative or positive autocorrelation affects the trend in a series (Hamed and Rao, 1998).The autocorrelation (also known as serial correlation coefficients) test was performed to check the randomness and periodicity if any in the time series of all data (Madarres and Silva, 2007).If randomness is found, or in other words, if lag-1 serial correlation coefficients are statistically insignificant then, Mann-Kendall (MK) test is used without altering the authentic data.Otherwise, Modified Mann-Kendall (MMK) test is applied after eliminating the effect of serial correlation (randomness) from the time series (Karpouzos et al., 2010).The autocorrelation coefficient r k of a discrete time series for lag-k is estimated as follows: ... (1) Where, r k is the lag-k serial correlation coefficient of the series.The hypothesis of serial independence is then tested by the lag-1 autocorrelation coefficient as H 0 : r 1 = 0 against H 1 : |r 1 |> 0 using the test of significance of serial correlation (Yevjevich, 1971)  Where, (r k ) tg is the normally distributed value of r k , t g is the normally distributed statistic at g level of significance.The value of t g is 1.645, 1.965 and 2.326 at a significance level of 0.10, 0.05 and 0.01 respectively.If |r k | > (r k ) tg , the null hypothesis about serial independence is rejected at the significance level a (here 0.05).For the non-normal series, MK test is an appropriate choice for the trend analysis (Yue andPilon, 2004, Basistha, et al., 2008).Therefore, the MK test has been used wherever the autocorrelation is not significant at 5% significance level.

Pre-whitening
The method of Pre-whiting is applied to remove the effect of Serial correlation on the non-parametric test.lettenmaier et al., (1994) suggested that the effects of serial correlation upon trend tests in such applications could be assumed negligible; concern about the potential impacts of autoregressive processes upon trend analysis nevertheless appears to be gaining momentum.

...(3)
Where PW X is the whitened data to be used in the subsequent trend analysis and c is the lag-1 serial correlation coefficient as determined directly from the data using Equation 3. Pre-whitening is utilized only if observed r is greater than some critical value, C criti taken to be 0.1 by von Storch (1995).This method is known as single-stage pre-whitening.

Analysis of trend
The following sections describe the nonparametric (Mann-Kendal) methods used to assess trends over Madhya Pradesh.

Mann-Kendall method
Trend analysis has been executed by using non-parametric Man-Kendall test.It is a statistical method used for analyzing the temporal trends and spatial variation of hydro-climatic series.Smith (2000) mentioned that a non-parametric test is given priority over the parametric one because it can avoid the issue raised by data skew.Man-Kendall test is favored when various stations are tested in the same study (Hirsch et al., 1991).Mann-Kendall test was drafted as a non-parametric test by Mann (1945) for trend detection and test statistic distribution was given by Kendall (1975) for a testing turning point and non-linear trend.The Mann-Kendall statistic S is formulated as ...( 4) The application of trend test is done to a time series x i which is ranked from i = 1,2,………n-1 and x j is ranked from j = i+1,2,……….n.Each of the data point x i is considered as a reference point which is correlated with all the rest of the data point's x j so that ... (5) The variance statistic is computed as ... (6) Where t i represents the number of ties up to sample i.The test statistics Z c is estimated as ... (7) In which Z c follows a standard normal distribution.A positive (negative) value of Z indicates where a denotes the significance level, then the trend is significant.

Sen's Slope estimator Test
The magnitude of the trend is estimated with the help of Sen's estimator.In this case, the linear trend is present and hence the true slope is estimated by this method.Here, the slope (T i ) of all data pairs is first computed as (Sen, 1968) ... (8) In which x j and x k are represented as data values at time j and k (j>k) correspondingly.The median of these N values of T i is considered as Sen's estimator of slope which is given as ...( 9) The sen's estimator is calculated as Q med =T(N+1)/2 if N is odd, and it is computed as Q med =[T N/2 +T (N+2)/2 ]/2 if N is even.lastly, Q med is estimated by a two-sided test at 100 (1-a)% confidence interval and then a true slope can be derived by the non-parametric test.Q i with a positive value indicates an upward or increasing trend and a negative value of Q i signifies a downward or decreasing trend in the time series.

Mann-whitney-Pettitt method (MwP)
The time series {X1, X2…, Xn} with length n is taken.t was taken as the time of the most expected change point.Two samples {X1, X2, …, Xt} and {Xt+1, Xt+2, …, Xn} then can be obtained by dividing the time series at t time.The Ut index was obtained in the following way: ...( 10 The approximated significant probability p(t) for a change point (Pettitt, 1979) is represented as: ...(13) When probability p(t) surpasses (1a), then the change point becomes significant statistically at time t with the significance level of a.

ReSuLTS AND DIScuSSION
lag-1 Serial correlation coefficients of the Annual and seasonal Average Temperature series for entire Madhya Pradesh are represented in Table 1.The annual temperature series almost for all station had a positive lag-1 serial correlation coefficient.As revealed earlier, the existence of positive serial correlation will increase the risk of rejecting the null hypothesis of no trend in the MK test.
Temperature trend in the region for the period 1901 to 2005 (105 years) showed a significant increasing trend in mean temperature at 5% significance level.During peak summer months the maximum temperature touches 40°C in the entire Madhya Pradesh.Amongst 45 most of the station showed significant increasing trends in mean    3. The results showed that the monotonic trends in average temperature time series were positive for all stations of Madhya Pradesh.The spatial percentage change in the trends of mean temperature is given in Fig. 3.However, the change percentage in trends (increasing) in the case of mean temperature is uniform in larger parts of the state.Homogeneity test has been performed to find the shifting year when a considerable change in the climate was witnessed in the region.Pettitt test is widely used to detect the change year for different series of mean temperature.The magnitudes of the significant increasing warming trends in the annual average temperature series were found in the majority of the stations are about 0.01 o C respectively.

AckNOwLeDGMeNT
The authors, thankfully, acknowledges the India Water Portal (Indian Meteorological Agencies) for providing rainfall station data and Department of Science and Technology (DST), New Delhi for providing financial funding during the study period.Due to which quality analysis of average temperature series has been made achievable.
following Rai et al., (2010), ...(2) of U t value against t in a time series will results in a continuously increasing value of |U t | with no change point.Yet, if there is a change point (even a local change point), then |U t | will increase up to the change point level and then will begin to decrease.The major significant change point t gives the point where the value of |U t | remains highest: ...(12)

Table 2 : Values of slope b (°c/year) for the Annual and seasonal mean temperature series (1901-2005)
an upward (downward) trend.A significance level á is also used to test for either an upward or downward monotone trend (a two-tailed test).If Z c is greater than Z a/2

Table 3 : Shows Z value obtained by Mann-kendall Test (1901-2005)
*Bold value indicate significant trend at the 95% of confidence level.

Table 4 : Pettitt's test
Table 4 presents series-wise change year for different stations, the tests indicate shifting in the mean categories of temperature were the frequency of occurring years more among 45 stations is the year of 1963.Thus, change point year is 1963 for mean temperature time series for entire Madhya Pradesh, India.cONcLuSIONS 1 The annual mean temperature time series almost for all 45 station had a positive lag-1 serial correlation coefficient.On another hand, seasonal basis the post-monsoon and winter season also shows the positive correlations were in the premonsoon season most of the station showing a negative trend but in monsoon season only the station betul shows negative correlations among all the station.