INTERNATIONAL JOURNAL OF GEOMATICS AND GEOSCIENCES Volume 3, No 1, 2012

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1 INTERNATIONAL JOURNAL OF GEOMATICS AND GEOSCIENCES Volume 3, No 1, 2012 Copyright by the authors - Licensee IPA- Under Creative Commons license 3.0 Research article ISSN Markov Chain Model for probability of weekly rainfall in Orathanadu Taluk, Thanjavur District, Tamil Senthilvelan.A 1, Ganesh.A 2, Banukumar.K 3 1-Assistant Professor, Department of Geography, Government Arts College (Autonomous), Kumbakonam 2- Professor, Department of Geography, Bharathidasan University, Tiruchirappalli. 3- Assistant Professor, Department of Geography, Periyar EVR College (Autonomous), Tiruchirappalli kbanukumar@gmail.com ABSTRACT It is necessary to know the sequence of dry and wet periods for successful agricultural management and planning of soil and water conservation measures. Probability analysis is a very useful tool for making important decisions in agricultural operation. In this study, Markov Chain Model has been extensively used to study spell distribution. For this purpose a week period was considered as the optimum length of time. The present study has been carried out to find the probabilities of occurrence of wet week (W), wet week preceded by wet week (W/W) at different threshold limits of 10 and 20 mm. On the basis of the analysis the following conclusions are made: (a) the 3 and 3 1/2 month varieties are best suited for Vettikkadu region; (b) 3 1/2 and 4 months paddy varieties can be successfully grown in Neivasal Thenpathi area and (c) 4 and 4 1/2 months paddy varieties are favourably grown in Orathanadu region. 1. Introduction The yield of crops particularly in rainfed condition depends on the rainfall pattern. Simple criteria related to sequential phenomena like dry and wet spells could be used for analyzing rainfall data to obtain specific information needed for crop planning and for carrying out agricultural operations (Srinivasa Reddy et al.,). Markov Chain probability model has been recognized as a suitable model to explain the long term frequency behaviour of wet or dry weather spells. In this model, the conditional probability has been accepted as fully justified in the analysis of weekly rainfall data. Several research scholars have demonstrated its practical utility in agricultural planning for both long and short term periods. This model enables to determine the probability of occurrence of dry and wet weather during a particular week (5, 10, and 13). The agriculture is the mainstay of the economy of the people of Orathanadu Taluk. It is one of the major paddy growing taluks of Thanjavur District, Tamil (Figure 1). It is located between N and N latitudes and between E and E longitudes. The total geographical area of the study area is Km 2. Many authors have used Markov chains to model the daily occurrence of precipitation. Gabriel and Neumann analyzed the occurrence of rain at Tel Aviv, Israel, by fitting a twosate, first-order Markov chain. The two states corresponded to rain and no rain. They used Markov chain probability model to study the data of daily rainfall occurrence at Tel Aviv. Submitted on May 2012 published on July

2 This accounts for the form of distribution of dry and wet spells. Further aspects of rainfall occurrence patterns are derived. In particular, the distribution of the number of rainy days per week is obtained. The fitting and the use of models for daily rainfall observation are discussed by Stern and Coe. They found that the non-stationary Markov chains are fitted to the occurrence of rain, gamma distribution with parameters vary with time of year, are fitted to rainfall amount. They also concluded that numerical methods are used to derive results from these models that are important in agricultural planning. A rainfall simulation model based on a first-order Markov chain has been developed to simulate the annual variation in rainfall amount that is observed in Bangladesh by Sayedur Rahman. Markov chain models have been used to evaluate probabilities of getting a sequence of wet and dry weeks during South-west monsoon period over the districts Purulia in West Bengal and Giridih in Bihar state and dry farming tract in the state of Maharashtra of India by Pabitra Banik. Srinivasa Reddy, et.al employed Markov chain model to analyze probability of dry and wet weeks for agricultural planning at Bangalore. An application of stochastic process for describing and analyzing the daily rainfall pattern at Aduthurai is presented by Samuel Selvaraj, et.al. They suggest that first order Markov chaining with two parameters gamma distributions were found to be adequate to generate daily rainfall sequences at Aduthurai. Pandharinath (10) applied Markov Chain model in Andhra Pradesh, India and identified the wet and dry weeks during monsoon period. He considered 20mm/week as the threshold limit, to distinguish between dry and wet weeks. Rajendram and Sivasamy applied Markov Chain model at 10,20,40 and 80mm threshold levels to analyse probability of weekly rainfall and its agro-climatic implications to paddy crop over Batticaloa, Sri Lanka. Figure 1: Study area map 192

3 2. Data and Methodology The daily rainfall data have been collected for three stations of Orathanadu Taluk, Thanjavur District, viz., Neivasal Thenpathi, Vettikkadu and Orathanadu from the Department of Economics and statistics, Chennai. Daily rainfall data for Neivasal Thenpathi and Vettikkadu stations were available for 30 years ( ) whereas Orathanadu station has 18 years of data ( ). The long term mean and its maximum and minimum, standard deviation and coefficient of variation of the rainfall in meteorological standard weeks have been calculated (Table 1). For the purpose of agricultural planning, Reddy applied Markov Chain model in Combolcha station, Ethiopia by choosing 10,20,40 and 80mm/week as threshold limits. These threshold levels were considered as adequate for the crop activities such as land preparation (10mm), crop planting or sowing (20mm), and application of fertilizer and/or weeding (40mm). According to Reddy, in a given week i of a given year received more than 20mm/week at more than 50%(W/W) threshold level, then week i is the right time for planting. If weeding/fertilizer application is to be carried out in week i then the week should have at least 75%(W/W) probability at 40mm/week. if the interest is when not apply fertilizer/pesticides, then one can use the probability estimate at 80mm/week. If fertilizer and/or insecticides/pesticides are applied on week i then W should not exceed 25% probability level at 80mm/week. Rajendram and Sivasami applied the same threshold limits to estimate the weekly rainfall probabilities over Batticaloa, Sri Lanka. In the present study, Markov Chain model has been used and the same threshold limits have been employed for estimating the weekly rainfall probability. With the following notations, the initial and conditional probabilities for the above said threshold limits have been computed using the following formula. Under initial probabilities, the probability of a given week as wet or dry is estimated, whereas in the case of conditional probabilities, if a given week i is wet, then the chances of (i+k) th period as wet, wet/wet or dry/dry are estimated. A period is said to be wet when the parameter of that period exceeds a threshold limit and to be dry when under the limit. P(W) = F(W)/n P(W/W) = F(W/W)/F(W) P(W) Probabilities of the week being wet P(W/W) Conditional probability of wet week preceded by a wet week n= number of years of data F(W) Frequency of wet weeks F(W/W) Frequency of wet weeks preceded by another wet week 3. Rainfall probabilities of Orathanadu Taluk The major crops cultivated in Orathanadu Taluk are paddy, pulses, groundnut and sugarcane. Paddy is the principal crop growing in three seasons, viz., kuruvai (Sornavari), samba/ Thaladi (Pishanam) and Kodai (Navarai). The first crop is known as kuruvai, the short term crop with a duration of days from June/July to October/November. The paddy crop cultivated after harvesting the kuruvai crop is called Thaladi, which has a duration of days from October/November to February/March. The more important season for paddy crop in the study area is samba season. Samba is a long term crop with a duration of 135 days to 150 days from August /September/October to Jan/Feb/March. 193

4 Table 1: Descriptive Statistics on weekly rainfall (mm) for Vettikkadu ( ) Week Month Date Total Mean Max Min SD CV W23 June W W W W27 July W W W W W32 August W W W W36 September W W W W40 October W W W W W45 November W W W W49 December W W W Table 2: Descriptive Statistics on weekly rainfall (mm) for Neivasal Thenpathi ( ) Week Month Date Total Mean Max Min SD CV W23 June W W W W27 July W W W W W32 August W W W W36 September

5 W W W W40 October W W W W W45 November W W W W49 December W W W It is pointed out that the definite dates of opening and closing of Mettur Dam water for irrigation is not known. This reflects in planning cropping sequence of farmer s choice. This constraint not only affects kuruvai, thaladi and samba rice growing seasons, but also has an impact on the growing of the summer season crops. The torrential rain during Northeast monsoon hinders both kuruvai harvest as well as Thaladi transplanting. It also causes larger patches of low lying lands inundated. So, it is essential to know the probability of receiving rainfall at a particular week for sowing operation. According to Reddy (18), at 20mm/week threshold limit, the conditional probability (W/W) of a given week i is >50% (under k=1), then week i is appropriate for sowing/planting. If not, i is not the right time for planting. Table 3: Descriptive Statistics on weekly rainfall (mm) for Orathanadu ( ) Week Month Date Total Mean Max Min SD CV W23 June W W W W27 July W W W W W32 August W W W W36 September W W W W40 October W W W W

6 W45 November W W W W49 December W W W Figure 2: Conditional probabilities of wet week preceded by wet week P (w/w) at 10 mm threshold limit 196

7 Figure 3: Conditional probabilities of wet week preceded by wet week P (w/w) at 20 mm threshold limit 3.1.Vettikkadu: The weekly mean rainfall and its descriptive statistics for this station are shown in table 1. The mean monthly or weekly rainfall data gives only trends of certain climatic pattern. They can be useful tool to indicate agro-climatic homogenous zone. But they do not give any information on the temporal rainfall variability. The maximum rainfall of 620mm has been recorded during the study period for the standard meteorological week 46, which comes under Samba crop season. The samba season is a major rice growing season in Vettikkadu. The estimation of co-efficient of variation (CV) of rainfall is more suited for agricultural purposes. The higher the CV, the lesser the dependability of rainfall and vice versa. In orathanadu taluk, the planting/sowing of Kuruvai crop depends on the opening of Mettur Dam for irrigation. Because the planting is done in the month of June/July which falls during the standard weeks of 23 rd -26 th week /27 th -30 th week. During the Kuruvai season the co-efficient of variation of rainfall ranges from % to % which reflect the higher 197

8 variability of rainfall during this period. The initial and conditional probabilities occurrences of wet week and wet week followed by wet week at 10 mm and 20 mm threshold limits for the same period also shows less than 50%. Therefore rainfed crops cannot be successfully grown during Kuruvai crop season. The planting/sowing Samba crop starts in the month of August/September/October. The coefficient of rainfall during the sowing period of Samba crop varies from 98.79% to %. According to the crop planning-climate Atlas (2003), the threshold limit for Co-efficient of Variation for weekly rainfall should be less than 150%. During the Samba crop season the CV is less than threshold limit of 150 percent (except week no. 32). This indicates higher dependability of rainfall during this period. Hence, agricultural operations like planting/sowing can be undertaken successfully during this period. The initial and conditional probabilities of rainfall during the Samba crop season at 10 mm and 20 mm threshold limits have been shown in Tables 4 and 5 for this station. During this season particularly between week 32 and week 44, the occurrence of probability of wet week ranges from 13 percent to 67 percent at 20mm/week limit. The probability of occurrence of a wet week preceded by a wet week (W/W) is ranging from 13 percent to 74 percent during the same season Neivasal Thenpathi: The mean weekly rainfall and other statistics of this station have been shown in Table 2. The maximum rainfall of 549mm has been received in week 51. The Samba crop season is the major paddy growing season in this area also. The Co-efficient of Variation of rainfall for Kuruvai season varies from percent to percent which clearly indicate higher variability of rainfall during this crop season. The values of rainfall variability are higher than the threshold limit of 150 percent. Therefore, rainfed crops cannot be grown in this period. The probability of occurrence of wet week at 10mm threshold limit for the same season varies from 20 to 37 percent. So, it is highly impossible for farmers to undertake land preparation activities during Kuruvai season. The Co-efficient of variation of rainfall for Samba season varies from percent to percent. The variability of rainfall is less than 150 percent during the sowing period of this season (except week 32). The initial and conditional probabilities of rainfall during the Samba crop season at 10 mm and 20 mm threshold limits have been shown in Tables 4 and 5 for this station.the probability of occurrence of wet week during the sowing period of Samba season (i.e., from week 34 to week 44) ranges from 33 percent to 70 percent at 20mm/week threshold limit. The conditional probability of W/W at 20mm/week during the same season varies from 31 percent to 71 percent. So, the week having 50 percent probability level should be carefully chosen for planting. In this analysis, even though the samba crop season starts in the month of August (week 32), the standard week 40 has the conditional probability of 65 percent and the consecutive weeks also has the level of probability above the threshold limit of >50 percent. Hence, planting/sowing of rainfed crops can be successfully undertaken from 40 th week Orathanadu: The descriptive statistics of this station is given in Table 3. The maximum rainfall recorded during the study period was mm in week 48. The major paddy growing season for this area is Samba crop season. The Co-efficient of Variation of rainfall during kuruvai season varies from % (week 24) to % (week 25). The variability is above the threshold limit of 150 percent except for week 24. It indicates the dependability of rainfall during the season is lesser. The probability of occurrence of wet week for the kuruvai crop season at 10mm/week threshold limit varies 7 percent to 33 percent. It is also less than 50 percent at 20mm/week threshold limit. The initial and conditional probabilities of 198

9 rainfall during the Samba crop season at 10 mm and 20 mm threshold limits have been shown in Tables 4 and 5. for this station. Therefore agricultural activities like land preparation, sowing/planting cannot be taken up during this season. The Co-efficient of Variation of rainfall during the Samba sowing period (August/September/October) varies from 89.99% (week43) to % (week40). The lesser variability of rainfall during this season indicates higher dependability of rainfall. The probability of occurrence of wet week during samba season varies from 10% to 50% at 20mm/week threshold limit. The conditional probability of W/W at the same threshold limit is ranging from 13 percent to 87 percent (Table 13 and Fig.11). Therefore the week having the conditional probability of 50 percent and above at 20mm/week threshold limit should be carefully chosen for samba crop planting/sowing. In present analysis, 35 th week records 75 percent probability level and the consecutive weeks also have the conditional probability above the threshold limit of 50 percent and above. Therefore rainfed agricultural activities can be initiated starting from 35 th standard week Spatial Distribution of Rainfall Probabilities in Orathanadu Taluk The spatial distribution map of rainfall probability has been prepared using spline method, one of the interpolation techniques of the spatial analyst tools in Arc GIS environment. The conditional probabilities of wet week preceded by wet week P(W/W) at 10 mm and 20 mm threshold limit have been summarised in tables 4 and 5 respectively. The resultant map ( figures 2 & 3) shows that the north, northeast, east, southeast and northwestern part of the study area experience percent probability at 10mm threshold level in 34 th, 35 th and 39 th standard meteorological weeks whereas the entire Orathanadu taluk enjoys the same probability level in 36 th,38 th and 40 th meteorological weeks. It is concluded from fig.3 that the conditional probability of 50 percent and above can be identified in 35 th and Table 4: Conditional probabilities of wet week preceded by a wet week P(W/W)at 10mm threshold limit Rainfall Stations Weeks Neivasal Vettikkadu Thenpathi Orathanadu W W W W W W W W W W W W W W W

10 W W W W W W W W W W W W W W W Table 5: Conditional probabilities of wet week preceded by a wet week P(W/W)at 20mm threshold limit Rainfall Stations Week Neivasal Vettikkadu Thenpathi Orathanadu W W W W W W W W W W W W W W W W W W W W W W W W W W

11 W W W W th weeks in the entire Orathanadu taluk. The same probability level is experienced in almost entire study area in 36 th week except Vettikkadu area. 4. Conclusion The initial crop activities start with the land preparation. According to Reddy (20), the initial and conditional probabilities at 10mm/week threshold limit is considered for the land preparation. The conditional probability of occurrence of rainfall at 20mm/week threshold limit can be adopted for the crop sowing/planting. The following conclusions emerge from the above analysis. (a) Vettikkadu: The initial and conditional probabilities at 10mm/week threshold level is calculated as more than 50% in the 40 th week (W = 67% and W/W = 80%). Therefore, land preparation can be taken up in 40 th standard week and can be extended up to 43 rd week. The chances of occurrence of 20mm/week is above 50% in 43 rd week which is the optimum time for planting 3 months paddy varieties and 42 nd week for sowing 3 1/2 months varieties. Considering the above probabilities, it is found that the 3 and 3 1/2 month varieties are best suited for this area. (b) Neivasal Thenpathi : The initial and conditional probabilities at 10mm/week threshold limit is reported as above 50 percent in the 38 th week (W = 57% and W/W = 65%). Hence, land preparation can be initiated from 38 th to 40 th week. The likelihood of occurrence of 20mm/week is more than 50% in 40 th week which will be the favourable time for sowing 4 months paddy varieties and 3 1/2 months varieties can be sown in 42 nd week. It is concluded that 3 1/2 and 4 months paddy varieties can be successfully grown in this region. (c) Orathanadu : The initial and conditional probabilities for land preparation is estimated at more than 50% in the 36 th week (W = 61% and W/W = 73%). So, the land preparation can be undertaken from 36 th to 39 th week. The conditional probability of occurrence of rainfall for planting is above 50% in 39 th standard week (W/W = 70%) which is best suited for sowing 4 1/2 months paddy variety. The 4 month variety can also be sown in 40 th week. It is therefore concluded that 4 and 4 1/2 months paddy varieties are favourably grown in this area. 5. References 1. Alaguraja P. Nagarathinam S.R. et al (2010), Rainfall Distribution Study in Coimbatore District Tamil Using GIS, I.K International Publication, New Delhi, 5, pp Banukumar.K, Aruchamy.S, (2007), Climatic Types of Tamil, India,, Journal of Spatial Science, 1(1&2), pp Banukumar K., Rajamanickam G.V., and Aruchamy, S, (2005), Study of Drought Prone Areas in Pudukkottai Taluk, Tamil -A 201

12 Hydrogomorphological Approach, Indian Journal of Geomorphology, 10(1&2), pp 4. Chandler E. Richard and Howard S. Wheater (2002), Analysis of Rainfall Variability using generalized linear models: A case study from the west of Ireland, Water Resources Research, 38(10), Chaudhary J.L. (2006), Rainfall Analysis using Markov Chain Modeling for Bastar, Geographical Review of India, 60(1), pp Dhar, O.N et.al. (1982), Trends and fluctuations of seasonal and annual rainfall of Tamil, Proceedings of Indian Academy of Science,(Earth Planet Science), 91(2), pp Di Giuseppe, E. et.al. (2005), Analysis of dry and wet spells from 1870 to 2000 in four Italian sites, Geophysical Research Abstracts, 7(6). 8. Kirupalani, R.H. and Aswini Kulkharni (1997), Rainfall Variability over South East Asia Connections with Indian Monsoon and ENSO Extremes: New Perspectives, International Journal of Climatology, 17, pp Maria Mimimou (1983), Daily precipitation occurrences modeling with Markov Chain of seasonal order, Hydrological Sciences, 28, pp Nicholson, S.E. (1999), An Analysis of Recent Rainfall Conditions in West Africa, Including the Rainy Seasons of the 1997 El Niño and the 1998 La Niña Years, Journal of Climate, Article: pp Pabitra Banik, et.al., (2000), Markov Chain Analysis of Weekly Rainfall data in determining drought proneness, Discrete Dynamics in Nature and Society, 7, pp Raghavendra Ramanan. S (2006), Water Balance Modeling of Rain fed crops: A study of sorghum and groundnut in Salem and Namakkal Districts, Unpublished Ph.D., Thesis, Department of Geography, University of Madras, Madras. 13. Rajeevan, M. et.al. (2006), High Resolution daily gridded rainfall data for the Indian Region: Analysis of break and active monsoon spells, Current Science, 91,3, pp Rajendram, K and Sivasami, K.S. (2005), Markov Chain Model for Probability of Weekly Rainfall and its Agro-Climatic Implications to Paddy Crop over Batticaloa, Sri Lanka,The Indian Geographical Journal, 79(2),pp Ramamurthy. K (1943), A Study of Rainfall Regime at Vellore, Indian Geographical Journal, 18, pp Ramamurthy. K (1948), Some aspects of the Regional Geography of Tamilnad, Climate, Indian Geographical Journal, 23, pp Ramamurthy. K (1972), A Study of Rainfall Regimes in India, Text Book, University of Madras, Madras. 202

13 18. Rao, S.S. (1992), Upland cultivation in Bastar (Constraints-Solutions), Technical Bulletin No. 14, ZARS, Jagdalpur, M.P., India. 19. Robertson, G.W. (1976), Dry and wet spells, UNDP/FAO, Tan Razok Agri. Res. Center. Project Field Report, Agrometeorology, A-6, pp Samuel Selvaraj, R. and Tamil Selvi, S. (2010), Stochastic modeling of daily rainfall at Aduthurai, International Journal of Advanced Computer and Mathematical Sciences, 1(1), pp Sayedur Rahman, M. (1999), A Rainfall Simulation Model for Agricultural Development in Bangladesh, Discrete Dynamics in Nature and Society, 5, pp Srikanthan, R and McMahon, T.A. (2001), Stochastic generation of annual, monthly and daily climate data : A review, Hydrology and Earth System Sciences, 5(4), Srinivasa Reddy, G.V. et.al., (2008), Markov Chain Model Probability of Dry, Wet Weeks and Statistical Analysis of Weekly Rainfall for Agricultural Planning at Bangalore, Karnataka journal of agricultural sciences, 21(1),pp Stern, R. D. and R. Coe (1982), Fitting Models to Daily Rainfall Data, Journal of Applied Meteorology, 21(1), pp Stern, R. D. and R. Coe (1984), A Model Fitting Analysis of Daily Rainfall Data, Journal of the Royal Statistical Society. Series A (General), 147(1),, pp Subramaniam, A. R. and Sanjeeva Rao, P. (1989), Dry spell sequences in South coastal Andhra, Mausam, 40(1), pp Yukiko Hirabayashi, et.al., (2008), A 59-year ( ) global near-surface meteorological data set for land surface models. Part I : Development of daily forcing and assessment of precipitation intensity, Hydrological Research Letters 2, pp