Weekly Rainfall Analysis and Markov Chain Model Probability of Dry and Wet Weeks at Varanasi in Uttar Pradesh
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1 885 Environment & Ecology 32 (3) : , July September 2014 Website: environmentandecology.com ISSN Weekly Rainfall Analysis and Markov Chain Model Probability of Dry and Wet Weeks at Varanasi in Uttar Pradesh R. S. Singh, Chandrabhan Patel, M. K. Yadav P. K. Singh, K. K. Singh Received 23 January 2014; Accepted 24 February 2014; Published online 10 March 2014 Abstract Knowledge of sequence of dry and wet periods along with onset and withdrawal of helps in good crop management and planning of soil and water conservation measures. In this study Markov Chain Model has been used to know the dry and wet spell distribution. For this purpose a week period was considered as the optimum length of time. The present study on weekly analysis of rainfall data has been carried out to find the probabilities of occurrence of dry and wet weeks, onset and withdrawal of rainy at Varanasi. The successive dry weeks hint for the need of supplemental irrigations and moisture conservation practices whereas, successive wet weeks gives an idea of excessive runoff water availability for rainwater harvesting and to take up suitable measures to control soil erosion. Higher values of Coefficient of Variation (CV) of weekly rainfall indicate the erratic distribution of rainfall. The average annual rainfall over BHU campus, Varanasi was found to be mm with CV of 20.7%. The data on onset and withdrawal of indicated that the monsoon starts effectively from 25 th SMW (18 th 24 th June) and remains active up to 39 th SMW (24 th 30 th September). During the probability of occurrence of wet week is 40% except during 24 th SMW. During the mean weekly rainfall is found to be highest (about 80.0 mm) during 29 th SMW (16 th 22 nd July) and more than 40 mm during 26 th 39 th SMW and found to be 20 mm during entire (11 th June30 th September) including 24 th and 25 th SMW. The results through analysis have been used for agricultural planning and agrometeorological advisory in Varanasi and surrounding districts of Uttar Pradesh. Keywords Markov chain model, Rainfall, Onset of Monsoon, Withdrawal of monsoon, Water balance. R. S. Singh, Chandrabhan Patel, M. K. Yadav* Department of Geophysics, Banaras Hindu University, Varanasi , India P. K. Singh, K. K. Singh Agromet Service Cell, IMD, New Delhi , India manojagro@gmail.com *Correspondence Introduction Crop productivity particularly from dryland and rainfed agriculture is always uncertain and largely depends on the rainfall amount and distribution. 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 [1]. Re-
2 886 Table 1. Characterization of the at Varanasi ( ). Mean week of onset of rainy Jun season Earliest week of onset of rainy May season Delayed week of onset of Jul Mean week of withdrawal of Sep Earliest week of withdrawal of Aug Delayed week of withdrawal of Oct Mean length of 98 days Duration of Longest 17 weeks (119 days) Shortest 09 weeks (63 days) cently, Markov Chain Model has been used to study the probability of dry and wet spells by some researchers [2, 3]. Another aspect useful for crop planning is forward and backward accumulation of rainfall to determine the onset and withdrawal of. The onset and the withdrawal of monsoon largely determine the success of rainfed agriculture. Pre-monsoon showers help in land preparation and sowing of kharif crops. Late onset of monsoon delays sowing of crops leading to poor yields. Similarly, early withdrawal of rains affects the yield due to severe moisture stress especially when the kharif crops are at critical growth stages of grain formation and grain development [4]. The annual and seasonal analysis of rainfall will give general idea about the rainfall pattern of the region, whereas the weekly analysis of rainfall will be of much use in agricultural planning. Materials and Methods Daily rainfall data recorded at the Meteorological Observatory of Ozone unit, Department of Geophysics, Banaras Hindu University, Varanasi (Uttar Pradesh) (25 o 01 N, 83 o 30 E and 076 m from sea level) for a period of 36 years ( ) were used for the present study. Weekly rainfall values have been worked out from daily values and were used for the present analysis. The dry and wet spell analysis was carried out using weekly rainfall based on Markov Chain Model considering less than 25 mm rainfall in a Table 2. Probability of onset and withdrawal of at Varanasi. SMW = Standard week, P = Meteorological probability in percentage. (a) Onset SMW % P (b) Withdrawal SMW % P week as a dry week and 25 mm or more as a wet week [2]. The different notations followed in this analysis are given below. (a) Initial probability P D = F D /n...1 P W = F W /n...2 (b) Conditional probabilities P DD = F DD /F D...3 P WW = F WW /F W...4 P WD = 1P DD...5 P DW = 1 P WW...6 (c) Consecutive dry and wet week probabilities 2D = P DW 1 P DDW W = P Ww 1 P WWw D = P DW 1 P DDw2 P DDW W = Pw W 1 Pww W2 Pww w Where, P D Probability of the week being dry, P W Probability of the week being wet, F D Number of dry weeks, F W Number of wet weeks, n Number of years of data, P DD Probability (conditional) of a dry week preceded by a dry week, P WW Probability (conditional) of a wet week preceded by a wet week, P WD Probability (conditional) of a wet week preceded by a dry week, P DW Probability (conditional) of a dry week preceded by a wet week, F DD Number of dry weeks
3 887 Table 3. Weekly climatic water balance and rain water harvesting potential (surplus water) over BHU, Varanasi under various rainfall and field capacity conditions. PPT = Precipitation, PET = Potential Evapo-transpiration, AET = Actual Evapotranspiration, DEF = Deficit water, SPL = Surplus water. Rain water harvesting potential SMW PPT Normal AET DEF Surplus water (SPL) Year no. (mm) PET (mm) (mm) (mm) SPL (mm) Duration i.e. SMW no. Normal ( ) Good monsoon , 32, 33, 37 & 38 year 2011 Poor monsoon year 2009 preceded by another dry week, F WW Number of wet weeks preceded by another wet week, 2DProbability of 2 consecutive dry weeks starting with the week, 2WProbability of 2 consecutive wet weeks starting with the week, 3DProbability of 3 consecutive dry weeks starting with the week, 3WProbability of 3 consecutive wet weeks starting with the week, PD W1 Probability of the week being dry (first week), PDD W2 Probability of the second week being dry, given the preceding week dry, PDD W3 Probability of the third week being dry, given the preceding week dry, PW W1 Probability of the week being wet (first week), Pww W2 Probability of the second week being wet, given the preceding week wet, Pww W3 Probability of the third week being wet, given the preceding week wet. Onset and withdrawal of was computed from weekly rainfall data by forward and backward accumulation methods respectively. In this method weekly rainfall was summed by forward accumulation ( weeks) until a certain amount of rainfall was accumulated. Accumulation of 75 mm rainfall has been considered as the onset time for the growing season of dry seeded kharif crops and land preparation. The withdrawal of was determined by backward accumulation of rainfall ( weeks) data. Rainfall accumulation of 20 mm was chosen for the end of, which is sufficient for ploughing of fields after harvesting the crops [5], [6]. The percent probability (P) of each rank was calculated by arranging them in ascending order and by selecting highest rank allotted for particular week. The following Weibull s formula has been used for calculating percent probability: m P = N + 1 Where, m is the rank number and N is the number of years of data used. The weekly mean, maximum, minimum, standard deviation, coefficient of variation and percentage contribution to annual rainfall were also computed and tabulated. Weekly climatic water balance [7] has been carried out quantify the different component of water balance as well as rain water harvesting potentials and its probable duration under different rainfall situations. Results and Discussion The data on onset, withdrawal and duration of the (difference between onset and withdrawal time) are presented in Table 1. Weekly rainfall data of 36 years ( ) indicated that the monsoon starts effectively from 25 th SMW (18 th 24 th June) and remains active up to 39 th SMW (24 th 30 th September). Therefore, mean length of was found to be 14 weeks (98 days). The earliest and delayed week of onset of were 21 st SMW (21 st 27 th May) and 29 th SMW (16 th 22 nd July), respectively. Similarly the earliest and delayed week of cessation of were 34 th SMW (20 th 26 th August) and 43 rd SMW (22 nd 28 th October), respectively. The probabilities of onset and withdrawal of rainy
4 888 Table 4. Weekly rainfall, initial, conditional and consecutive probabilities of rainfall at Varanasi ( ). SMW=Standard Meteorological Week, SD=Standard deviation, CV=Coefficient of variations, % of ARF=Percentage contribution of weekly rainfall towards average annual rainfall. P (W)=Probability of Wet weeks, P (D)=Probability of dry weeks, P (W/W) = Probability of preceding wet week / wet week, P (D/W) = Probability of preceding dry week/wet week, P (D/D) = Probability of dry week / dry week, P (W/D) = Probability of wet week / dry week. Probabilities (%) Rainfall (mm) Conditional Consecutive % Initial P P P P P P P P SMW Mean Max Min SD CV ARF P (W) P (D) (W/W) (D/W) (D/D) (W/D) (2D) (2W) (3D) (3W)
5 889 Table 4. Continued. Probabilities (%) Rainfall (mm) Conditional Consecutive % Initial P P P P P P P P SMW Mean Max Min SD CV ARF P (W) P (D) (W/W) (D/W) (D/D) (W/D) (2D) (2W) (3D) (3W) season was calculated by using Weibull s formula and results are presented in Table 2. The results reveal that there is a 75% chance that the onset of rainy season and cessation of will occur during 26 th and 40 th SMW respectively. The longest and shortest length of was 19 and 09 weeks, respectively. Analysis of water balance and rainfall harvesting potentials are presented in Table 3. It has revealed that the region has considerable amount of rain water harvesting potential which normally varied between 170 and 260 mm in each monsoon season. The most probable period for rain water collection starts from 31 st SMW and ends by 39 th SMW (August and September). This amount of rain water if harvested and stored properly during monsoon season can be reused as supplemental irrigation water during mid season/terminal drought period or during rabi season. The weekly rainfall attributes showing mean, maximum, minimum, standard deviation, coefficient of variation and percentage of weekly rainfall contribution towards annual rainfall are presented in Table 4. The results reveal that, there are, total of 16 weeks (24 th 39 th SMW) where rainfall exceeds more than 20 mm. During the mean weekly rainfall is found to be more than 40 mm during 26 th 38 th SMW and found to be less than 40 mm during 24 th, 25 th SMW and 39 th SMW. The coefficient of variation during vary from 56.0% (29 th SMW) to 169.5% (38 th SMW). The weekly contribution of rainfall is found to be more than 60% and more than 80% during 28 th 37 th SMW and during 24 th 39 th SMW, respectively accounting towards annual average rainfall over Varanasi. The results pertaining to initial and conditional probabilities of dry and wet weeks in Table 3 for all the 52 standard meteorological weeks but, the results are discussed in relevance with (23 th SMW43 th SMW) only. The results from Table 3 reveal that, during the probability of occurrence of wet week is 40% except during 24 th SMW. The probability of occurrence of dry week preceded by another dry week during monsoon season is more than 50% during 24 th, 25 th 27 th, 32 th and 38 th SMW. The probability of occurrence of wet week preceded by another wet week during the kharif crop growing season is 70% continuously for 12 weeks starts from 26 th SMW to 37 th SMW. Consecutive probabilities of dry and wet weeks are presented in Table 3. It is interesting to mention here that the probability of two and three consecutive dry weeks starting from 27 th SMW (2 nd 8 th July) to 37 th SMW (10 th 16 th September) are below 20% and below 10%, respectively indicating very low chances of occurrence of water stress to rainfed crop grown in the region during the peak rainy months/season. In contrast, the probability of two and three consecutive wet weeks is more than 40% for the period starting from 27 th SMW to 36 th SMW and from 27 th SMW to 32 nd SMW, respectively indicating fair to good chances of successfully harvesting of rainfed crops having life cycles up to 70 to 80 days duration in the region. Conclusion The significant contribution of weekly rainfall (>60 mm) during 32 th 37 th SMW has great relevance and importance towards soil erosion measures to be taken up for soil erosion control. The area has considerable potential for harvesting of rain water ( mm) during the above wet weeks which can met the supplemental irrigation water requirement of the crop grown
6 890 in the Varanasi and surrounding districts of Uttar Pradesh. Even in the event of mid season consecutive dry weeks, mulching and other moisture conservation practices will help in reducing soil evaporation and conserve moisture in top layers of the soil. References 1. Singh RS (2012) Rainfall record and climatic water balance over BHU, Varanasi in the eastern Uttar Pradesh region. A monograph/report, AMFU, BHU, Varanasi, pp Pandharinath N (1991) Markov chain model probability of dry, wet weeks during monsoon period over Andhra Pradesh. Mausam 42 : Bhargava AK, Singh PK, Mitra V, Prasad A, Jayapalan M (2010) Rainfall variability and probability pattern for crop planning of Roorkee region (Uttarakhand) of India. Mausam 61 : Dixit AJ, Yadav ST, Kolate KD (2005) The variability of rainfall in Konkan region. J Agromet 7 : Babu PN, Lakshminarayana P (1997) Rainfall analysis of a dry land watershed-polkepad : A case study. J Ind Water Res Soc 17 : Panigrahi B, Panda SN (2002) Dry spell probability by Markov chain model and its application to crop planning. Ind J Soil Cons 30 : Thornthwaite CW, Mather JR (1955) Water balance. Publications in climatology. Drexel Inst Technol Centerton, New Jersey 8 :
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