Journal of Computer and Mathematical Sciences, Vol.10(6),1236-1243 June 2019 ISSN 0976-5727 (Print) (An International Research Journal), www.compmath-journal.org ISSN 2319 - 8133 (Online) Rainfall Trend Analysis for Karnataka State with Spatial Distribution G. Nanjundan, Nanjundappa Gari Keerthy* and Sadiq Pasha Department of Statistics, Bangalore University Bengaluru 560 056, INDIA. email:[email protected]* (Received on: March 12, 2019) ABSTRACT The aim of this paper is to understand and find talukwise rainfall climatic trends with spatial distribution based on 57 years of rainfall data for all the 175 taluks of Karnataka State. It is important to study the degree and direction of the rainfall trend for planning and understanding the climatic phenomena in local scale with spatial variation and distribution. Sen’s slope and Mann-kendall non parametric test employed. The observed trend are classified and the results are represented in maps. Keywords: Rainfall Trend, Spatial distribution, Sen’s Slope, Mann-kendall statistics. 1. INTRODUCTION Karnataka is one of the southern state of India having geographical area of 1, 92,000 sq.km. Though it has a cultivable area of 1, 03,810 sq.km,only 20% of it is under irrigation. The climate of the State is determined mainly by the geographical location with respect to the sea, monsoon winds and physiography. Karnataka State has very moist monsoon climate on the West Coast, semi-arid climate in the Western Ghats and arid (very warm) climate in central and northern districts. The year is divided into three season’s viz., Pre Monsoon season from Jan to May; South-West monsoon from June to September; North East monsoon season from October to December; Karnataka State is divided into four regions. Which are south interior Karnataka, North interior Karnataka, Malnad and Coastal Karnataka. The rainfall received in an area is an important factor in determining the amount of water available to meet various demands, such as agricultural, industrial, domestic water supply and for hydroelectric power generation. Global climate changes may influence long- term rainfall patterns impacting the availability of water, along with the danger of increasing occurrences of droughts and floods. The southwest (SW) monsoon, which brings about 71% 1236 G. Nanjundan, et al., Comp. & Math. Sci. Vol.10 (6), 1236-1243 (2019) of the total precipitation over the State, is critical for the availability of freshwater for drinking and irrigation. Changes in climate over the Karnataka region, particularly the SW monsoon, would have a significant impact on agricultural production, water resources management and overall economy of the State. The heavy concentration of rainfall in the monsoon months (June–September) results in scarcity of water in many parts of the country during the non- monsoon periods. In view of the above, a number of studies have attempted to investigate the trend of rainfall for district and State level. Present study has looked at the trends on the State level, District level and taluk level for 57 years of monthly data from 1960-2017. And also spatial distribution is also is very important tool to understand the spatial variation over the state. All the talukwise results are shown in spatial Map No.6 to 9 for comparing and understanding the spatial variability between taluks. Districts, regions and state results are shown in Table No.1. 2. DATA AND METHODOLOGY The historical data of 167 taluks for the period from 1960 to 2016 have been taken into analysis. The data for the remaining 8 taluks have been considered based on availability of the data in different years. These taluks along with data availability period are list below. 1 Bangalore South (1963-2016) 6 Haliyal (1970-2016) 2 Hagaribommanahalli (1969-2016) 7 Supa (1964-2016) 3 Basavakalyan (1966-2016) 8 Yellapur (1970-2016) 4 Gadag (1967-2016) 5 Sulya (1970-2016) It is to mention that results of Bangalore South taluk has been considered to represent the Bengaluru East taluk newly created in 2009 of Bengaluru Urban district. Taluks Map is given in Map1. The magnitude of the trend in the time series was determined using Sen’s estimator (Sen, 1968). This method has been widely used for determining the magnitude of trend in hydro-meteorological time series, and details are available in Lettenmaier et al. (1994); Yue & Hashino (2003) and Partal & Kahya(2006). The statistical significance of the trend in seasonal and annual series was analysed using the non-parametric Mann-Kendall (MK) test(Mann, 1945; Kendall, 1975). The MK test has been employed by a number of researchers (e.g. Yu et al., 1993; Douglas et al., 2000; Yue et al., 2003; Burn et al., 2004; Singh et al., 2008a,b) to ascertain the presence of statistically significant trend in hydrological climatic variables, such as temperature, precipitation and stream flow, with reference to climate change. The MK test checks the null hypothesis of no trend versus the alternative hypothesis of the existence of increasing or decreasing trend. Trends are obtained for seasonal and annual. Trend slope are tested by using the Mann- kendall test and increasing are decreasing trend of slope is obtained by Sen’s method (Sens- 1968). Significance level is taken at 5% trend Slope. The Mann–Kendall statistic is given by 1237 G. Nanjundan, et al., Comp. & Math. Sci. Vol.10 (6), 1236-1243 (2019) 푛 푖−1 푆 = ∑ ∑ 푠푖푔푛(푥푖 − 푥푗), 푖=2 푗=1 Where n is the length of the data set, 푥푖푎푛푑푥푗 are two generic sequential data values. The function 푠푖푔푛(푥푖 − 푥푗) assumes the following values: +1, 푖푓(푥푖 − 푥푗) > 0 푠푖푔푛(푥푖 − 푥푗) = { 0, 푖푓(푥푖 − 푥푗) = 0 −1, 푖푓(푥푖 − 푥푗) < 0. Under the hypothesis of independent and randomly distributed variables when n≥8, the statistic S is approximately normally distributed with zero mean and the Variance Var(S) as follows. 1 Var(S) = [푛(푛 − 1)(2푛 + 5)], 18 Where n is the length of the times-series. The standardized test statistic Z is given by 푆 − 1 , 푖푓푆 > 0 √푉푎푟(푆) 푍 = 0, 푖푓푆 = 0 푆 − 1 , 푖푓푆 < 0. {√푉푎푟(푆) The presence of a statistically significant trend is evaluated using the Z value. This statistic is used to test the null hypothesis such that no trend exists. A positive Z indicates an increasing trend in the time-series, while a negative Z indicates a decreasing trend. In this study, if Z > +1.96 or Z < –1.96, the null hypothesis (Ho) is rejected at the 95% significance level. The estimate for the magnitude of the slope of trend b is calculated using non-parametric Sen’s method, which is the median of slopes of all data value pairs. (푋푗−푋 ) 푏 = 푚푒푑푖푎푛 [ 푖 ] ,for all i < j, (푗−푖) Where b is the slope between data points 푥푗푎푛푑푥푖measured at times j and i respectively. 3. Results and discussion Basic statistics i.e., talukwise mean rainfall of seasonal and annual is shown in Map No.2 to 5.Results of talukwise seasonal and annual trend with classification of Decreasing, Increasing, Significantly increasing at 95%, Significantly decreasing at 95% and No trend based their slope and statistical P-Value are spatially represented from Map No.6 to 9. District, region and State trend results are tabulated in Table-1. 1238 G. Nanjundan, et al., Comp. & Math. Sci. Vol.10 (6), 1236-1243 (2019) Map No.1: Map shows list of taluks in Karnataka state 1239 G. Nanjundan, et al., Comp. & Math. Sci. Vol.10 (6), 1236-1243 (2019) Map No 2-5: Seasonal and annual talukwise mean rainfall (1960-2016). 1240 G. Nanjundan, et al., Comp. & Math. Sci. Vol.10 (6), 1236-1243 (2019) Map No 6-9: Seasonal and annual talukwise rainfall trend(1960-2016). 1241 G. Nanjundan, et al., Comp. & Math. Sci. Vol.10 (6), 1236-1243 (2019) Table-1: District, region and state seasonal slope value Southwest Northeast Pre_Monsoon Annual Monsoon Monsoon District\Region\State (Jan- (Jan-Dec) (June-Sep) (Oct-Dec) May)(mm/year) (mm/year) (mm/year) (mm/year) Bangalore Urban District 1.0918 0.0648 -1.0375 0.2612 Bangalore Rural District 0.4005 -0.3216 -0.6403 -0.5594 Ramanagara District 0.8414 0.3538 0.0005 1.3141 Kolar District 1.2029 1.2142 0.0472 2.2367 Chikballapur District 0.7535 0.5717 -0.5157 0.2625 Tumkur District 0.362 1.5673 -0.7167 0.9046 Chitradurga District 0.6574 1.739 0.2307 2.8494 Davanagere District 0.0919 0.425 -0.2074 0.1042 Chamarajanagar District -0.6007 -0.4012 -0.7815 -1.7015 Mysore District -0.482 0.3834 0.0541 0.8173 Mandya District -0.2002 0.6424 0.2353 1.1552 Bellary District 0.4775 0.413 -0.1396 0.9074 Koppal District 0.63 -0.2269 -0.1765 0.5592 Raichur District 0.5084 -1.0142 -0.4774 -0.8793 Kalaburagi District 0.4276 -2.3528 -0.2624 -2.1606 Yadgir District 0.1983 -3.3715 -0.2152 -3.776 Bidar District 0.4691 2.12 0.1448 2.6892 Belgaum District -0.6909 -0.1916 -0.2679 -1.7118 Bagalkote District 0.0381 -0.8811 -0.8696 -1.6691 Bijapur District 0.0775 -1.0585 -0.5971 -2.1804 Gadag District 0.4252 -0.2743 -0.4058 0.1514 Haveri District 0.2462 0.3587 -0.4251 0.1273 Dharwad District -0.0217 -0.9243 -0.5015 -1.3107 Shimoga District 0.0019 2.2578 -0.2235 1.9347 Hassan District 0.1508 1.3453 -0.8498 0.9408 Chikmagalur District 0.4265 -0.8512 0.2217 0.1063 Kodagu District -0.3305 -4.2565 -0.1967 -4.7122 Dakshina Kannada District 0.5041 -11.581 0.3515 -10.23 Udupi District -0.2826 -5.6341 1.3647 -5.0524 Uttara Kannada District 0.0412 -0.1273 -0.3354 -0.4178 South Interior Karnataka Region 0.2387 0.664 -0.3367 1.039 North Interior Karnataka Region 0.0504 -0.4041 -0.5062 -0.6997 Malnad Region 0.074 0.5624 -0.3236 0.9094 Coastal Region 0.092 -4.2009 -0.0267 -3.2766 State 0.0654 -0.0953 -0.2388 0.1508 Bold Value indicates statistically significant at 95%.