Correlation analysis of climatic dynamics of Jammu and Kashmir using wavelet methods 1.

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1 Int. Journal of Applied Sciences and Engineering Research, Vol. 3, No. 2, Copyright 2014 by Authors Licensee IJASER Under Creative Commons License 3.0 Research article ISSN Correlation analysis of climatic dynamics of Jammu and Kashmir using wavelet methods 1. Mudassar Rashid Lone 2.Zaheer Abbas 3 A.H.Siddiqi 1,2 Department of Mathematical Sciences Baba Ghulam Shah Badshah University, Rajouri (J&K) 3 College of Engineering &Technology Gautam Budha University,Noida (UP) Doi: /ijaser Abstract: Wavelet analysis is a powerful tool that is already in use throughout science and engineering. The versatility and attractiveness of the wavelet approach lie in its decomposition properties, principally its timescale localization. The applications of wavelet analysis are systematically increasing in the Meteorology. In the present paper, we study correlation between time series of five meteorological parameters of Jammu and Kashmir for the period using wavelet methods. We also obtain the wavelet spectrum and compute the cross-correlation coefficient between the two same meteorological parameters, of the two different locations using statistical methods. In general, for all pairs of stations the time series for temperature and rainfall data were adjudged to be highly correlated, whereas wind speed, pressure and relative humidity comparatively less correlated. Keywords: Wavelet analysis; Correlation; Wavelet spectrum. 1. Introduction In meteorology, the applications of wavelet analysis are systematically increasing and in spite of the initial efforts required for the proper formalism, currently the wavelet transform has turned out to be a very useful tool in time series analysis of meteorological signals and hence creating an encouraging new horizon to the research activities. Also, the atmospheric correlations play a significant role in determining the climate trends which are crucial in understanding the short and long-term trends in climate. The climate changes, so experienced today are mainly due to over ambitious strategies and actions of human being on the eco-system. Moreover, the rapid growth in human population and depletion of non-renewable sources of energy are also contributing to the major changes in the climatic scenario of the earth; thus, resulting in the desertification and uncertain fluctuations in the climatic parameters like wind speed, barometric pressure, temperature and rainfall. The climate of a location is mainly studied with the help of temperature and rainfall trends of that location. There has been a major investigation almost all over the world to study the climatic changes and hence to extract relevant information from the data so available. Although, there are several modern time series analysis methods, the wavelet analysis has been extensively used to investigate a signal in time-frequency domain and in particular for non-stationary signals as the length of the data set increases the wavelet analysis becomes an important tool due to its self affine properties. Wavelet transform is used to analyze heart rhythm, chest volume and blood oxygen saturation data. The usefulness of wavelet transform is demonstrated by studying dispersion of Yanai waves. The trends, periodicities and variations in time series are being analyzed by the wavelet methods in a successful way and. Lau Weng analyzed climatic parameters using wavelet methods and highlighted the climatic features of the signal. Several investigation have been performed for the correlation between climatic parameters, biomedical signals and wind predictions This study utilizes the meteorological data to study five parameters daily means of temperature, pressure, relative humidity, wind speed and daily totals for precipitation of nine different locations selected strategically, spreading over the entire state of Jammu and Kashmir for a period of 16 years ranging from 1995 to Strategic location and data account of the study area 1 Corresponding author ( mudassir2lone@gmail.com) Received on February 2014; Accepted on March 2014; Published on April

2 Jammu and Kashmir is the northern most state of India situated between N to N North Latitudes and E to E East Longitudes. Geographically the State is divided into three distinct climatic regions; Humid subtropical region of Jammu, Temperate Kashmir valley and Cold arid desert areas of Ladakh. Geographically, the State has three distinct regions: Jammu, Kashmir and Ladakh. Jammu region comprises the plains, hills and mountains. Jammu region comprises of 10 districts; Kathua, Jammu, Udhampur, Doda, Rajouri, Poonch, Reasi, Ramban Samba and Kishtawar. In Jammu region, Jammu District shares its border with Rajouri, Udhampur and Kathua in the North, in the East and in the South East respectively. Jammu is the hottest region with highest temperature experienced in June. Doda is entirely hilly and shares its border with Anantnag District of Kashmir valley and chamba district of Himachal Pradesh. The northern part of the Rajouri district consists of hilly terrain and shares a long border with Pakistan occupied Kashmir (PoK) in the West. Ramban is North to Udhampur and Banihla is on its North. River Chenab passes through the District. The climate of Rajouri, Doda and Ramban like Kashmir valley is subjected to snowfall and a severe winter. Table 1: Meteorological stations used in the study. Station Latitude Longitude Elevation(m) Period Records Srinagar Jammu Rajouri Pulwama Leh Kargil Qazigund Banihal Doda Kashmir is an ancient lake basin 140 km long and 32km wide. Average elevation of the valley is 5300ft above sea level. Kashmir region comprises of 10 districts; Srinagar, Kulgam, Shopian, Pulwama, Bandipore, Ganderbal, Baramulla, Anantnag, Budgam and Kupwara. In Kashmir region Srinagar District is surrounded by by the Hurmukh mountain(16903 ft) in the East, Tosh Maidan 4000ft in the North and Snony Kazi Nag(12125ft ) in the North-west and also the Mahader Mountain. Pulwama is situated in the South eastern part of the valley and shares its border with Srinagar and Badgam in the North-West and by Anantnag in the South East. Anantnag, Southern most District of the valley shares its boundaries with District Pulwama in the west and from south to east is attached to Rajouri, Udhampur and Doda District respectively and borders Kargil in the North. Ladakh region constitutes the Eastern most part of the State of Jammu and Kashmir. Ladakh region comprises of 02 districts; Kargil and Leh and includes Karakoram range and upper Indus river valley. Kargil and Leh constitute the Northern as well as the Eastern most part of the Jammu and Kashmir, where Kargil shares the LoC with Pakistan occupied Kashmir (PoK) in the North and Leh is bordered by International Border (IB) or Line of Control (LoC) with China in the North. Both of these areas are characterized by severe dry cold in winter with mercury dipping to -40 degree centigrade. Average altitude of Ladakh region is ft and hardly gets rain. The State of Jammu and Kashmir, therefore, lies between the hot plains of the Jammu province and coldest dry table-land of Ladakh. These territories are, as such, transitional in climate. Weather conditions are different at different places. The temperature in these regions varies spatially. Leh is the coldest (-36 degree centigrade avg.) while Jammu is the hottest. Mean monthly temperature is lowest in January and highest in July except in Jammu, where highest temperature is experienced in June. Mean monthly temperature in January varies from -27 degree centigrade at Drass in Ladakh to 11 degree centigrade at Jammu; Kargil and Leh being other stations of below freezing average. The climate of Jammu and Kashmir varies greatly owing to its rugged topography. In the south around Jammu, the climate is typically monsoonal, though the region is sufficiently far west to average 40 to 50 mm (1.6 to 2 inches) of rain per month between January and March. In the hot season, Jammu city is Lone R. Mudassar et al. 547

3 very hot and can reach up to 45 C whilst in July and August, very heavy though erratic rainfall occurs with monthly extremes of up to 650 millimetres (25.5 inches). In September, rainfall declines, and by October conditions are hot but extremely dry, with minimal rainfall and temperatures of around 29 C (84 F). Kashmir receives as much as 635 millimeters (25 in) of rain from Arabian Sea, with the wettest months being March to May with around 85 millimetres (3.3 inches) per month. Annual rainfall of the valley recorded is about 75 cms. August is the warmest month with temperature rising to 35 deg. centigrade and January is the coldest month with temperature falling down to below zero. The climate of Ladakh is extremely dry and cold. Annual precipitation is only around 100 mm (4 inches) per year and humidity is very low. In this region, almost 3,000 meters (9,750 ft) above sea level, winters are extremely cold. In Ladakh, the average January temperature is 20 C with extremes as low as 40 C. In summer in Ladakh, days are typically warm 20 C. 3. Definitions and mathematical formulation 3.1Cross-correlation coefficient The cross-correlation co-efficient, given by is a measure of strength of linear association between two variables with. 3.2 Auto-correlation A data set exhibits autocorrelation if value at time is correlated with a value at time where d is some time increment in the future. In a long memory process the auto-correlation decays over time following a power law where is a constant and is the autocorrelation function with lag k. For a given at time the k-lag auto correlation function is defined as,,where. It is to be remarked here that unlike cross-correlation, the autocorrelation results in a correlation coefficient indicating the degree of similitude between two values of same variable at time and. 3.3 Wavelet transform If satisfies, then is called the basic wavelet and relative to every basic wavelet, the continuous wavelet transform of a function on is given by. where and such that, called dilation parameter and, called translation parameter. A wavelet transform decomposes a signal into several groups (vectors) of coefficients. Different coefficient vectors contain information about characteristics of the sequence at different scales. 3.4 Wavelet spectrum The wavelet spectrum denoted by defines the energy of wavelet coefficient for scale by power law the power of. and is defined as Here is exponent, the value of which is decided by Lone R. Mudassar et al. 548

4 3.5 Wavelet cross correlation coefficient is defined as where * is complex conjugate and the relation between correlation coefficient and wavelet correlation coefficient is given by. 4. Meteorological data analysis using statistical cross-correlation In section 3.1, we introduced the concept of cross correlation and wavelet correlation coefficient. In Tables 4.1 to 4.4 we present cross correlation coefficients between pairs of Jammu region, Kashmir region, Ladakh region and finally between the pairs of the three regions meteorological data respectively. As seen from the table 4.1 the temperature and relative humidity of locations of Jammu region experienced strong correlation while surface pressure, wind speed and total rain experienced comparatively low degree of correlation in some pairs of the region like Jammu-Banihal and Jammu-Doda. Table 2: Cross-correlation coefficients between pairs of Jammu region meteorological data collection stations. Cross-Correlation Coefficients Station Pairs Surface Pressure Air Temperature Relative Humidity Wind Speed Total Rain Jammu-Rajouri Jammu-Banihal Jammu-Doda Rajouri-Banihal Rajouri-Doda Banihal-Doda It is observed that strong correlation exist for meteorological parameters of the pair Banihal-Doda and a perfect correlation is noticed for the temperature of Banihal-Doda. For the Kashmir and Ladakh region a higher degree of correlation seems to exist among all the pairs of the locations for all the meteorological parameters except total rain and pressure that have lower value of correlation coefficients for the pair Srinagar-Pulwama, Srinagar-Qazigund and Srinagar-Pulwama respectively. All the correlation coefficients for the rest of pairs are shown in table 4.2 and 4.3 respectively. Table 3: Cross-correlation coefficients between pairs of Kashmir-region meteorological data collection stations. Cross-Correlation Coefficients Station Pairs Surface Pressure Air Temperature Relative Humidity Wind Speed Total Rain Srinagar Qazigund Srinagar Pulwama Qazigund- Pulwama Table 4: Cross-correlation coefficients between pairs of Ladakh region meteorological data collection stations. Cross-Correlation Coefficients Station Pairs Surface Pressure Air Temperature Relative Humidity Wind Speed Total Rain Leh-Kargil Lone R. Mudassar et al. 549

5 Table 5: Cross-correlation coefficients between pairs of three (Jammu, Kashmir and Ladakh) regional meteorological data collection stations. Cross-Correlation Coefficients Station Pairs Surface Pressure Air Temperature Relative Humidity Wind Speed Total Rain Jammu-Srinagar Jammu-Qazigund Jammu-Pulwama Rajouri-Srinagar Rajouri-Qazigund Rajouri-Pulwama Banihal-Srinagar Banihal-Qazigund Banihal-Pulwama Doda-Srinagar Doda-Qazigund Doda-Pulwama Jammu-Leh Jammu-Kargil Rajouri-Leh Rajouri-Kargil Banihal-Leh Banihal-Kargil Doda-Leh Doda-Kargil Srinagar-Leh Srinagar-Kargil Qazigund-Leh Qazigund-Kargil Pulwama-Leh Pulwama-Kargil In case of pairs of all the three regions viz. Jammu, Kashmir and Ladakh it is observed from the table 4.4 that for all the pairs of these three regions the temperature is strongly correlated with the highest value of correlation coefficient as 1 and lowest as The relative humidity shows strong correlation behavior for the pairs from the locations of Jammu region and Kashmir region where as a poor behavior for the combination of locations with that of Ladakh region. Also a negative correlation is noticed for the relative humidity of Jammu-Leh pair. Again a similar behavior is observed for the pressure time series having negative correlation for the pairs Jammu-Leh, Jammu-Kargil, Rajouri-Leh and Pulwama-Leh( , , , ) with the exceptions having a poor correlation between Doda-Kargil and Srinagar- Kargil with coefficient values and respectively. The rainfall and wind speed time series exhibit almost same behavior for all the pairs of the locations taken from the three regions as both of the time series are strongly correlated for the pairs of the locations of Jammu region and Kashmir region having coefficient values more than 0.70 and only exception of pairs Jammu- Srinagar, Jammu-Qazigund for wind speed with correlation coefficient 0.52 and 0.59 and pair Jammu- Srinagar for total rain with coefficient value For the pairs of locations combined with the stations from Ladakh region, wind speed and rainfall time series are positively correlated having lower degree of correlation with the exception of the pair Jammu-Leh showing poor correlation with the correlation coefficient having value and for wind speed and rainfall respectively. 5. Correlation analysis of meteorological data using continuous wavelet method The complexity of climate variability on all time scales requires the use of several refined tools to unravel its primary dynamics from observations. Wavelet Analysis of a time series is the study of previously mentioned Lone R. Mudassar et al. 550

6 properties of time series (signal), by breaking up of the signal (time series) into shifted and scaled version of the original (mother) wavelet. Being a signal s time-scale analysis method, wavelet transform is better than Fourier transform due to its high-resolution features, good localization both in time and scale domains and its capacity of analyzing signals at multi time scales. Unlike Fourier analysis that yields an average amplitude and phase for each harmonic in a dataset, the wavelet transform produces an instantaneous estimate or local value for the amplitude and phase of each harmonic. This allows detailed study of non-stationary spatial or time-dependent signal characteristics. In order to analyze the correlation between several pairs of stations selected among the combinations of nine different stations located strategically over different parts of Jammu and Kashmir we use here continuous wavelet analysis method. We compute and draw graphs of wavelet correlation and wavelet spectrum for all the 36 pairs of stations of all the three regions but in this paper we have selected only three stations Jammu, Srinagar and Leh one from each of the three regions and from Figure 1 to Figure 20, presented the graphs corresponding to temperature, pressure, relative humidity, rainfall and wind speed time series for the wavelet correlation and wavelet spectrum for the station pairs Jammu-Srinagar and Srinagar-Leh respectively. The scale depicts whether the parameters are correlated, strongly correlated or uncorrelated. Figure1: Wavelet correlation coefficient for average temperature. Figure2: Wavelet correlation coefficient for pressure. Figure3: Wavelet correlation coefficient for relative humidity. Figure4: Wavelet correlation coefficient for rainfall. Lone R. Mudassar et al. 551

7 Figure5: Wavelet correlation coefficient for wind speed. Figure6: Wavelet spectrum of temperature for Jammu-Srinagar. Figure7: Wavelet spectrum of pressure for Jammu-Srinagar Figure8: Wavelet spectrum of relative humidity for Jammu-Srinagar. Figure9: Wavelet spectrum of rainfall for Jammu-Srinagar. Figure10: Wavelet spectrum of wind speed for Jammu-Srinagar. Lone R. Mudassar et al. 552

8 Figure11: Wavelet correlation coefficient of average temperature. Figure12: Wavelet correlation coefficient of pressure. Figure13: Wavelet correlation coefficient of relative humidity. Figure14: Wavelet correlation coefficient of rainfall. Figure15: Wavelet correlation coefficient of wind speed. Figure16: Wavelet spectrum of temperature for Srinagar-Leh. Lone R. Mudassar et al. 553

9 Figure17: Wavelet spectrum of pressure for Srinagar-Leh. Figure18: Wavelet spectrum of relative humidity for Srinagar-Leh. Figure19: Wavelet spectrum of rainfall for Srinagar-Leh. Figure20: Wavelet spectrum of wind speed for Srinagar-Leh. From the graphs we observed that the wavelet correlation coefficient of all the meteorological parameters exhibit the same behavior as first an increase and then a decrease is observed up to the scale 5000 and then there is an increase up to the scale 20,000.The wavelet correlation coefficient for average temperature and rainfall (Figure 1, Figure 4, Figure 11, Figure 14) behave slightly different by remaining constant up to some scale before following the trend. In case of wavelet spectrum an interesting fact is observed that two maxima and one minima exist up to the scale 5000 and both the maxima and minima for all the station pairs are achieved at the same scale for all the meteorological parameters except for Jammu-Srinagar rainfall (Figure 9) which shows slight variation. 6. Observation From the wavelet analysis of the data so obtained we observed that the time series of climatic parameters; pressure, air temperature, relative humidity, wind speed and rainfall showed mixed behavior regarding correlation between different pairs of stations as some of the stations of Jammu region have hot and humid climate and the other have cold climate resembling to that of Kashmir region as noticed from the pairs of stations like Banihal-Qazigund, Banihal-Pulwama, Doda-Qazigund and Doda-Pulwama. Lone R. Mudassar et al. 554

10 Stations of Kashmir region are strongly correlated with the lowest correlation coefficient as and highest as Ladakh region exhibits a totally different climatic attitude with the behavior slightly matching the stations of Kashmir region. In general, for all pairs of stations the time series for temperature and rainfall data were adjudged to be highly correlated, whereas wind speed, pressure and relative humidity comparatively less correlated particularly in the pairs of stations in combination with the locations of Ladakh region. Acknowledgement We wish to pay our gratitude to the Sher-e-Kashmir University of Agricultural Sciences and Technology Kashmir (SKUAST-K) for providing the meteorological data of Jammu and Kashmir. 6. References 1. Abahussain AA. et al., Desertification in the Arab region: analysis of current status and trends, J Arid Environ, 51, pp Arnell NW, The effect of climate change on hydrological regimes in Europe: a continental perspective, Global Environ Change, 9, pp Balling Jr RC et al.,198.7 The impact of rapid urbanization on pan evaporation in Phoenix, Arizona. Journal of Climatol, 7, pp Bhardwaj R., Wavelet & Correlation Analysis of Weather Data, International Journal of Current Engineering and Technology, 2 (1), pp Chang CC, The potential impact of climate change on Taiwan s agriculture. Agric Econ, 27, pp Elagib NA et al., Climate variability and aridity in Bahrain, Journal of Arid Environmental, 36, pp Elagib NA et al., Recent trends and anomalies in mean seasonal and annual temperatures over Sudan, of Arid Environmental, 45, pp Figliola A. et al., Analysis of Physiological Time Series Using wavelets, IEEE Engineering in Medicine and Biology, 1, pp Hadhrami et al., Continuous and Discrete Wavelet Transforms Based Analysis of Weather Data of North Western Region of Saudi Arabia, World Journal of Science, Technology and Sustainable Development, 7 (4). 10. Hunt K. et al., Wind Speed Modelling and Short-term Prediction using Wavelets. 11. Jose AM et al., A study on impact of climate variability/change on water resources in the Philippines, Chemosphere 33, pp Kipkorir EC. et al.,2002. Analysis of rainfall climate on the Njemps flats, Baringo District, Kenya. J Arid Environ, 50, pp Lau KM. et al.,1995. Climate signal detection using wavelet transform: How to make a time series sing., Bulletin of the American Meteorological Society, 76, pp Lazaro R et al., J. Analysis of a 30-year rainfall record ( ) in semi-arid SE Spain for implications on vegetation, of Arid Environmental, 48, pp Meyers S.D. et al., An Introduction to Wavelet Analysis in Oceanography and Meteorology: With Application to the Dispersion of Yanai Waves, American Meteorological Society, Moonen AC et al., Climate change in Italy indicated by agro-meteorological indices over 122 years, Agric Forest Meteorology, 111,pp Partal T. et al., Long-term trend analysis using discrete wavelet components of annual precipitations measurements in Marmara region (Turkey), Physics and Chemistry of the Earth 31, pp Pimenta MT et al., A Susceptibilidade a Desertificacao, Revista Florestal, 11, pp Pisoft P. et al., Cycles and trends in the Czech temperature series. 20. Rehman S. et al., Wavelet based correlation coefficient of time series of Saudi Meteorological Data, Chaos, Solutions and Fractals, 39, pp Samuel S R. et al., Study on Correlation between Southwest and Northeast Monsoon Rainfall over Tamil Nadu, Universal Journal of Environmental Research and Technology, 1(4), pp Schwalm CR et al., Climate change and site: relevant mechanisms and modeling techniques, Forest Ecology Management, 150, pp Lone R. Mudassar et al. 555

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