Dry and wet spell probability by Markov chain model for agricultural planning at Palghar district, Maharashtra

Introduction

Palghar district is the most North-Western district of the state of Maharashtra on the Arabian Sea coast. The district has a total 8 talukas, Jawhar, Mokhada, Talasari, Vasai, Vikramgad, Palghar, Dahanu and Wada. The Arabian Sea forms the western boundary, while net sown area of the district is 109291 which is 14.00% of the total geographical area of the district. Paddy is major crop grown in the district. While Nagali & Warai are the other cereals grown in the district. The total area under cereals was 90.00%. The total area under pulses is 7.00%. The Major pulses grown are green gram, black gram, red gram & bengal gram. Area under Oil seeds very low in compared to other districts. Topographically it has much diverse condition.ie. Hilly zone, saline zone, plateau zone and characterised by high iritic rainfall. In varied agricultural zones rainfall variability analysis aids to take farm decisions on times of sowing, inter culture operations, fertilizer application etc. Many studies have reported the advantages of working out weekly rainfall probabilities for a station or for an agroclimatic region (Subbulakshmi et al., 2005 and Nemichandrappa et al., 2010) [27,18] . Probability analysis can be used for predicting the occurrence of future events of rainfall from the available data with the help of statistical methods (Kumar and Kumar, 1989) [13] . Chattopadhyay and Ganesan (1995) [4] attempted to study the variability of annual and seasonal rainfall and its probability and suggested suitable cropping pattern for Tamil Nadu. Prakash and Rao (1986) [21] have suggested use of weekly rainfall data to predict the occurrence of rainy events and its amount for crop planning in Kota. Gupta et al. (1975) [12] suggested that the rainfall at 80 per cent probability can safely be taken as assured rainfall, while that of 50 per cent probability is the medium limit for taking dry risk. In order to stabilise the crop production at certain level, it is essential to plan agriculture on a scientific basis in terms of making best use of rainfall pattern of an area. This necessitates studying the sequences of dry and wet spells of an area so that necessary steps can be taken up to prepare crop plan in rainfed regions (Reddy et al. 2008) [22] . Prediction of wet and dry spell analysis for proper crop planning and agricultural operations may prove useful to farmers for improving productivity and cropping intensity. Markov chain probability model has been used previously for finding out the frequency of wet spells in Greece (Tolika and Maheras 2005) [28] , dry spells in Croatia (Cindrić et al. 2010) [5] and computation of probability of occurrence of daily precipitation. Previous researchers (Pandarinath 1991; Banik et al. 2002; Barron et al. 2003; Deni et al. 2010) [19,1,2,8] have used Markov chain model to study the probability of dry and wet spell analysis in terms of the shortest period like week and also demonstrated its practical utility in agricultural planning. Rainwater management and its optimum utilisation is a prime issue of present-day research for sustainability of rainfed agriculture. Increased climate variability has made rainfall patterns more inconsistent and unpredictable (Kumar et al. 2005) [14] . To meet the future food demands and growing competition for water among various sectors, a more efficient use of water in rainfed agriculture will be essential. Kothari et al. (2007) [15] opined that on the basis of water harvesting, water can be utilised for saving of crops during severe moisture stress. In order to address the issue, detailed knowledge of rainfall distribution can help in deciding the time of different agricultural operations and designing of water harvesting structures for providing round the year full irrigation (Srivastava 2001; Srivastava et al. 2009) [25,26] . For sustainable crop planning, rainfall was characterised based on its variability and probability distribution by previous researchers (Mohanty et al. 2000; Bhakar et al. 2008; Jain and Kumar 2012) [17,3,9] for different regions of India. Manikandani et al., 2014 [16] analysed that the chance of getting 25 mm weekly rainfall with 50 per cent probability was noticed from 39th to 46th standard week covering eight weeks. Drought resistant short duration pulses and sorghum can be grown within the growing period from 39th to 46th standard weeks. Direct sowing of rabi crops just after harvest of kharif crops may also be tried to realize the advantage of residual moisture. Reddy et al., (2008) [23] studied on Markov Chain Model probability of dry, wet weeks and statistical analysis of weekly rainfall for agricultural planning at Bangalore. In this study Markov Chain Model has been extensively used to study spell distribution. Hence, present study has been undertaken to suggest the cropping plan for Palghar district of Maharashtra considering the rainfall amount at different probability levels.

Materials and Methodology

The daily rainfall data of Palghar district from 1998-2023 (26 years) were collected from Department of Agriculture, Maharashtra State (maharain.maharashtra.gov.in). The daily rainfall was grouped as week, month, seasonal and annual, and the statistical parameters like average (x), standard deviation (σ) and coefficient of variation (CV) for all groups were worked out. The daily rainfall was aggregated into weekly and used for analysis. Two types of probabilities i.e., Initial and Conditional probability indices were used for the study. Initial and conditional probabilities (Markov-Chain Model) simple criterion related to sequential phenomenon like dry and wet spell was used for analysing rainfall data to obtain specific information needed for crop planning and for carrying out agricultural operations. For the purpose of agricultural planning, we have applied Markov Chain model by choosing 10, 20, 40, and 80 mm/week as threshold limits. In this study, weekly rainfall values have been used to estimate consecutive dry and wet spell analysis based on "Markov Chain probability model". Initial, conditional probabilities and consecutive dry and wet spell analysis for 52 Standard meteorological weeks (SMW) are made by using equations from 1-8.

Initial probability

Where, P(D) = probability of the week being dry F(D) = frequency of dry weeks P(W) = probability of the week being wet F(W) = frequency of wet weeks N = total number of years of data being used.

Conditional probabilities

Where, P(DD) = probability of a week being dry preceded by another dry week F(DD) = frequency of dry week preceded by another dry week P(WW) = probability of a week being wet preceded by another wet week F(WW) = frequency of a wet week preceded by another wet week P(WD) = probability of a wet week preceded by a dry week P(DW) = probability of a dry week preceded by a wet week.

Consecutive dry and wet week probabilities P(2D) = P(DW1) × P(DDW2) (Eq. 7) P(2W) = P(WW1) × P(WWW2) (Eq. 8) Where, P(2D) = probability of 2 consecutive dry weeks starting with the week P(DW1) = probability of the first week being dry P(DDW2) = probability of the second week being dry, given the preceding week being dry P(2W) = probability of 2 consecutive wet weeks starting with the week P(WW1) = probability of the first week being wet P(WWW2) = probability of the second week being wet, given the preceding week being wet

Results and Discussion

Variability in monthly, seasonal and annual rainfall

Mean, Standard Deviation (S.D.) and Coefficient of Variation (C.V.) for monthly, seasonally and annual rainfall over the study area, were calculated and are presented in (Tables 1). Table 1 shows that July was the wettest month having average rainfall of about 1001.8 mm with SD & CV was 306.8 mm and 30.6%

Weekly rainfall probabilities

The initial {P (W)} and conditional probability {P (W/W)} approach would be relatively good method for rainfall analysis, especially in the regions like Palghar, it comes under heavy rainfall region but it found erratic or short dry periods can be expected during monsoon & post-monsoon season. The initial rainfall probability {P (W)} of wet week getting 10 mm rainfall per week was >40% during 23 SMW (Table 2) at Palghar district and hence, field preparation should be done during this period. The initial probability {P (W)} as well as conditional probability of wet week followed by wet week {P (W/W)} of getting 10 mm rainfall was more than 50% during 23 to 26 SMW (Table 2). Therefore, nursery sowing of rice can be planned during this period. Further delay in sowing may cause very low productivity and even crop failure. 5). Farmers whose adapt rainfed rice based cropping system, they should prefer to grow early & medium duration rice varieties. They should harvest rain water during 31 st , 32 nd and 38 th SMW, So, it may useful as protective life saving irrigation from harvested rain water.

Consecutive dry and wet week probabilities

During monsoon season, the probability of dry week (PD) getting 10 mm rainfall is more than 50% was observed during 37th and 39th to 42 nd SMW and also chance of dry week preceded by another dry week (PDD) were more than 40% during 40 th , 41 st and 42 nd SMW. Therefore, during those dry weeks especially at the end of main rainy season, supplementary irrigation and moisture conservation practice such as mulching need to be undertaken. 43th SMW (22 Oct -28 Oct) & 45 th to 52 nd SMW was observed that chance of dry week preceded by another dry week (PDD) more than 90% for getting10 mm.

Therefore, growing of high value rabi crops without supplementary irrigation would be very high risk during 45 th to 52 nd SMW. Probability of dry week preceded by another dry week regarding getting 20 mm was found during 39 th (24 Sep -30 Sep) & 41 st SMW (08 Oct -14 Oct). Farmers should make arrangement of irrigation for fruit crops which are in vegetative growth stage.

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