Introduction

India’s economy is mainly dependent on agriculture, which is based on monsoon rainfall and its distribution. Fluctuation in rainfall directly influence the growth, development and yield of crops. India ranks first among the countries that practice rainfed agriculture both in terms of extent (86 mha) and value of production (Sharma et al., 2010). 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. The most important factor for low yield is the lack of assured water supply (Panigrahi and Panda, 2002). Increased climate variability has made rainfall patterns more inconsistent and unpredictable (Kumar et al., 2005). The demand of water in other sectors especially to meet the increasing demand for rapid growing industrialisation and urbanisation will dwindle the share of water available for agriculture in the future. Further, depletion of groundwater and reduced stream flows (Khan et al., 2008) affect drinking water supplies, health and rural livelihoods (Meijer et al., 2006); for instance, in India, the implications for social equity for the poor and groundwater-dependent communities for drinking and irrigation are quite large (EPW, 2007). Rainwater management and its optimum utilisation is a prime issue of present-day research for sustainability of rainfed agriculture. Kothari et al. (2007) 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). For sustainable crop planning, rainfall was characterised based on its variability and probability distribution by previous researchers (Mohanty et al., 2000; Sharda and Das, 2005; Bhakar et al., 2008; Jain and Kumar, 2012) for different regions of India.  For successful agricultural management and planning of soil water conservation measures, information about occurrence of dry and wet periods along with onset and withdrawal of rainy season is important. Panigrahi and Panda (2002) and Kar (2003) applied Markov Chain method for calculating initial and conditional probability of dry and wet spells of different duration for various climatic situations and have evaluated its practical importance in crop planning. Researchers (Pandarinath, 1991; Banik et al., 2002; Barron et al., 2003 and Deni et al., 2010) 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.

The onset and withdrawal characteristics of monsoon largely determine the success of rainfed agriculture. Late onset of monsoon delays sowing of crops leading to poor yields. Similarly, early withdrawal of rains adversely affect the yield due to severe moisture stress especially when the kharif crops are at critical growth stages of grain formation and grain development (Dixit et al., 2005). In the present study an attempt has been made to analyze the probable week of onset and withdrawal of monsoon, initial and conditional probability of dry and wet spells and also the probability of 2 and 3 consecutive dry and wet spell weeks using Markov chain model for Parbhani district of Maharashtra.

Materials and Methods

2.1.  Study area

The study was conducted in the Department of Agricultural Meteorology, Vasantrao Naik Marathwada Agricultural University (VNMKV), Parbhani, Maharashtra, India situatedat 17⁰ 36’ N latitude and 76⁰ 47’ E longitude with an elevation of 406 m amsl. The Parbhani has uneven, erratic rainfall.Weekly rainfall values for a period of 42 years (1971–2012) have been computed from daily values and were used for the present analysis.

Rainfall data were categorised into four seasons, viz. pre-monsoon (March–May), monsoon (June– September), post-monsoon (October–December) and winter (January–February) season. Monthly effective rainfall was calculated using Eqs. 1 and 2 following the USDA Soil Conservation Service method. This method is being widely used in India for calculation of monthly effective rainfall. The same method has been used for calculation of effective rainfall for rainfed districts of India by Sharma  et al., 2010.

P_e=P_t (125-0.2P_t )/125   (When P_t <250 mm)               (1)

P_e=(125+0.1P_t )/125   (When P_t ≥ 250 mm)                  (2)

Where P_e=Monthly effective rainfall (millimetres) and P_t = total monthly rainfall (millimetres).

2.2.  Computation method for the onset and withdrawal of rainy season

Onset and withdrawal of rainy season was computed from weekly rainfall data by forward and backward accumulation methods respectively. In this method weekly rainfall was summed by forward accumulation (20+21+…+52 weeks) until a certain amount of rainfall was accumulated. Seventy five millimetres of rainfall accumulation has been considered as the onset time for the growing season of dry seeded crops and land preparation (Babu and Lakshminarayana, 1997; Panigrahi and Panda, 2002). The withdrawal of rainy season was determined by backward accumulation of rainfall (48+47+46+…+30 weeks) data. Twenty millimetres of rainfall accumulation was chosen for the end of rainy season, which is sufficient for ploughing of fields after harvesting the crops (Babu and Lakshminarayana, 1997). For determining the probability of onset and withdrawal of monsoon in particular week, the forward and backward accumulated rainfall were noted as per case and assigned with rank number.The following Weibull’s formula has been used for calculating percent probability:

P=m/(N+1)×100                                                       (3)

Where, m is the rank number and N is the number of years of data used.

2.3.  Computation of dry and wet spells using Markov chain probability models

The dry and wet spell analysis was carried out using weekly rainfall based on Markov Chain Model considering less than 20 mm rainfall in a week as a dry week and 20 mm or more as a wet week (Pandharinath, 1991). Markov chain is a stochastic process to predict the succeeding situation of day solely based on situation of previous day. The different notations followed in this analysis are given below.

a) Initial probability

P_D=F_D/N                                                                 (4)

P_W=F_W/N                                                                (5)

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 and N=total number of years of data being used.

b) Conditional probabilities

P_DD=F_DD/F_D                                                             (6)

P_WW=F_WW/F_W                                                 (7)

P_WD=1-P_DD                                                     (8)

P_DW=1-P_WW                                                    (9)

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 wet week preceded by another wet week, P_WD=probability of a wet week preceded by a dry week and P_DW=probability of a dry week preceded by a wet week.

c) Consecutive dry and wet week probabilities

P_2D=P_DW1×P_DDW2                                      (10)

P_3D=P_DW1×P_DDW2×P_DDW3                           (11)

P_2W=P_WW1×P_WWW2                                   (12)

P_3W=P_WW1×P_WWW2×P_WWW3                      (13)

Where P_2D =probability of two 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_3D=probability of three consecutive dry weeks starting with the week; P_DDW3=probability of the third week being dry, given the preceding week dry; P_2W =probability of two consecutive dry 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; P_3W =probability of three consecutive wet weeks starting with the week; and P_WWW3=probability of the third week being wet, given the preceding week wet.

Results and Discussion

3.1.  Average rainfall, effective rainfall, distribution over seasons and analysis of rainy days

Total annual rainfall in the Parbhani region ranged between 517.6 mm (the lowest during the year 1972) and 1711.0 mm (the highest during the year 1990). The average annual rainfall is around 928.4 mm with 47 rainy days (32.8% coefficient of variation). If rainfall received in a year was equal to or more than the average rainfall plus standard deviation for 42 years of rainfall (i.e. 928.4+304.2=1232.6 mm), it was considered as excess rainfall year (Sharma and Kumar, 2003). During eight years i.e. 1975, 1983, 1987, 1989, 1990, 1998, 2005 and 2010, this region received rainfall of more than 1233 mm and considered as excess rainfall years. Only 19% of total years of analyses under this study received rainfall of more than 1233 mm. Out of 42 years, 17 years recorded annual rainfall in excess of average or normal (928.4 mm) while 25 years (i.e. 59% of the total years of rainfall record) recorded below normal rainfall (Figure 1). Monthly average and effective rainfall of the Parbhani region for 42 years are presented in Figure 2.

Figure 1: Annual variability of annual rainfall over normal at Parbhani (1971-2012)

Figure 2: Average monthly rainfall and effective rainfall for the study area, Parbhani; ER is the effective rainfall

Considering monthly rainfall distribution, it was revealed that mean rainfall of August was 235.7 mm, which was the highest and its contribution was 25.4% annual average rainfall. July rainfall was slightly lower than that in August (i.e. 23.4% of annual average rainfall). December was the lowest rainfall month. Total annual effective rainfall (ER) was 668.6 mm which was 72.0% of the total annual rainfall. It was also observed that 259.8 mm of rainfall water was lost in the form of surface runoff, deep percolation and evaporation.

The distribution of rainfall for different seasons showed that the normal southwest monsoon, which delivered 83.6% of annual rainfall, extended from June to September (Table 1).

Table 1: Rainfall distribution in the Parbhani region over different seasons (data of 42 years for the period 1971–2012)

This is also the main season (rainy season) for cultivation of rainfed crops. Winter season contributes only 1.3% of the total annual rainfall; 3.7 and 11.4% of the total annual rainfall occurred during pre- and post-monsoon season, respectively with the lowest coefficient of variation during monsoon(36.3%) followed by post-monsoon (82.7%) , pre-monsoon (93.5%) and winter (150%). The occurrence of rainy days were categorized into four groups viz. 0-40, 41-50, 51-60 and 61-70 days (Table 2). The analysis showed that maximum numbers of rainy days were observed under 41-50 days category followed by 0-40 and 51-60 days. Numbers of rainy days under 61-70 days category were found only 7.1%.

Table 2: Number of years under different magnitude of rainy days

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 3. Data revealed that, there were total of 18 weeks (23^rd to 40^th SMW) where rainfall exceeded more than 20 mm. During rainy season the mean weekly rainfall was found to be more than 40 mm during 24^th - 27^th, 30^th -32^nd, 34^th–36^th and 38^th SMW and found to be less than 20 mm during 41^st–43^rd SMW. The coefficient of variation during rainy season varied from 95.8% (24^th SMW) to 262.3% (43^rd SMW).

Table 3: Weekly rainfall attributes at Parbhani (1971–2012)

3.2.  Analyses of rainfall for onset and withdrawal of monsoon season The results of forward and backward accumulation of weekly rainfall for onset and withdrawal of effective monsoon are presented in Table 4.

Table 4: Characterisation of rainy season at Parbhani (1971–2012)

Weekly rainfall data (1971–2012) indicated that the monsoon started effectively from the 24^th SMW (11^th–17^th June) and remained active up to the 43^rd SMW (22^nd–28^th October). Therefore, mean length of rainy season was found to be 20 weeks (140 days). The earliest and delayed onset of rainy season was 21^th SMW (21^th–27^th May) and 27^th SMW (2^nd–8^th July), respectively. Similarly, the earliest and delayed week of cessation of rainy season was 39^th SMW (24^th - 30^th September) and 48^th SMW (26^th November–2^nd December), respectively. The probabilities of the onset and withdrawal of rainy season were calculated by using Weibull’s formula considering forward and backward accumulation of weekly rainfall (Table 5).

Table 5: Probability of onset (Forward accumulation from 21st week) and withdrawal of effective monsoon (Backward accumulation from 48th week)

The results forward accumulation starting from 20^th week revealed that there was 95% chance onset of effective monsoon i.e. probability of getting cumulative rainfall ≥75 mm in 27^th week. Similarly, the 93% chance of withdrawal i.e. the probability of getting cumulative rainfall ≤ 20 mm in 48^th SMW, considering backward accumulation of weekly rainfall into account starting from week 48^th.

3.3.  Markov chain model

The results of initial and conditional probabilities of dry and wet weeks and consecutive dry and wet weeks are presented in Table 6 and 7 respectively for all the 52 standard meteorological weeks. The results showed that the probability of occurrence of dry week was high until the end of the 23^rd SMW. The initial probability of dry week (P_D) and conditional probability of dry week preceded by another dry week (P_DD) varied between 30.9 -100% and 30.8–100% respectively during 1^st–52^nd SMW. Similarly the initial probability of wet week (P_W) and conditional probability of wet week preceded by another wet week (P_WW) varied between 0.0 - 69.1% and 0.0–84.2% respectively during1^st–52^nd SMW. For main rainy season (24^th - 43^rd week), the initial probability of dry week (P_D) and conditional probability of dry week preceded by another dry week (P_DD) ranged from 30.9–85.7% and 30.8–90.0% respectively. At the first week of main rainy season i.e. 24^th week, the chance of occurrence of dry week (P_D) and conditional probability of dry week preceded by another dry week (P_DD) were 38.1 and 44.5% respectively, similarly at the end of main rainy season (43^rd week), dry week (P_D) and conditional probability of dry week preceded by another dry week (P_DD) had chance of 85.7 and 90.0% occurrences respectively.

For main rainy season, the initial probability of wet week (P_W) and conditional probability of wet week preceded by another wet week (P_WW) varied from 14.3–69.1% and 25.0–84.2% respectively. At the first week of main rainy season, the chance of occurrence of wet week (P_W) and conditional probability of wet week preceded by another wet week (P_WW) were 61.9 and 73.4% respectively, similarly at the end of main rainy season, wet week (P_W) and conditional probability of wet week preceded by another wet week (P_WW) had chance of 14.3 and 25.0% occurrences respectively. It is clear from results that, probability of occurrence of wet week is more than 35% during 23-24^th  SMW (4^th June–17^thJune) and average weekly rainfall ranges from 27.4 to 41.9 mm, this rain can be utilized for summer ploughing and initial seed bed preparations. The mean onset of rainy season was found to be 24^th SMW. So, during 24^th  SMW(11^th  June–17^th  June), the sowing operations can be taken up since, the probability of wet week is more than 50% and average weekly rainfall  is 41.9 mm. Sowing operations taken at 24^th SMW helps for good germination of seeds and helps in avoiding moisture stress for germination period during 25^th –28^th  SMW. In the event of delayed start of rainy season, the sowing operations can be taken up latest by 27^th SMW (2^nd July–8^th July) and further delay in sowing may cause very low productivity and crop failure. Since, mean length of rainy season was observed to be 20 weeks (140 days), during kharif, short duration crops of groundnut, pigeon pea, maize, sorghum, green gram, soybean, sunflower, field bean, cowpea and other low water required crops which have high return value can be taken up. Another advantage of growing short duration cereals, pulses and oilseeds in first fortnight of June is that these can be harvested by the end of September (39^th SMW) and short duration rabicrops can be sown during 40^th-43^rd SMW (1^st-28^th October). Since, winter rainfall is uncertain and erratic than south west monsoon also it contribute only 11.4% of total rainfall. Therefore growing of high value rabi crops without supplementary irrigation would be very high risky during rabi season.

During main rainy season, the probability of dry week (P_D) being more than 50% were observed during 29^th, 37^th and 40^th to 43^rd SMW and also chance of dry week preceded by another dry week (P_DD) were more than 50% during 28^th, 29^th and 37^th to 43^rd SMW. Therefore during those dry weeks especially at the end of main rainy season, supplementary irrigation and moisture conservation practice need to be undertaken. The significant contribution of weekly rainfall i.e. 42.2% of total annual rainfall during 30^th–36^th  SMW and  high consecutive wet week probability during 30^th–35^th SMW, indication for potential scope of harvesting excess runoff water for future supplemental irrigations and also drives attention towards soil erosion measures to be taken up for soil erosion control. The analyses of consecutive dry and wet spells (Table 6) revealed that there were 28.6 to 100% chances that two consecutive dry weeks (P_2D) would occur within the first 23 weeks of the year.

Table 6: Initial and conditional probabilities of dry and wet spells of rainfall at the study site, Parbhani region

Table 7: Analyses of consecutive dry and wet week probabilities of rainfall at the study site, Parbhani

Similarly, the probabilities of occurrence of three consecutive dry weeks (P_3D) were also very high (10.7–100%) in the first 23 weeks of the year. The corresponding values of two and three consecutive wet weeks (i.e. P_2W and P_3W) from the 1^st to 23^rd SMW were very low with values ranging from 0 to 26.2% and 0 to 15.1%, respectively. From the 24^th to 38^th SMW, the chances of occurrence of two and three consecutive dry weeks were only within 7 to 30.9% and 2.8 to 24.5%, respectively. Similarly, there were chances of 28.6 to 42.9% and 14.9 to 29.6% that the weeks from the 24^th to 38^th SMW would be getting sufficient rain with two and three consecutive wet weeks, respectively.

Conclusion

During rainy season probability of dry week (P_D) being more than 50%  was observed during 29^th, 37^th and 40^th to 43^rd SMW. Therefore during those dry weeks especially at the end of main rainy season, supplementary irrigation and moisture conservation practice need to be undertaken. The significant contribution of weekly rainfall i.e. 42.2% of total annual rainfall during 30^th–36^th  SMW, hints for potential scope of harvesting excess runoff water for future supplemental irrigations.

Reference

Babu, P.N., Lakshminarayana, P., 1997. Rainfall analysis of a dry land watershed-Polkepad: A case study. Journal of Indian Water Resources Society, 34–38.

Banik, P., Mandal, A., Sayedur, Rahman, M., 2002. Markov chain analysis of weekly rainfall data in determining drought-proneness. Discrete Dynamics in Nature and Society 7, 231–239.

Barron, J., Rockström, J., Gichuki, F., Hatibu, N., 2003. Dry spell analysis and maize yields for two semi-arid locations in east Africa. Agricultural and Forest Meteorology 117, 23–37.

Bhakar, S.R., Mohammed, I., Devanda, M., Chhajed, N.,  Bansal, A.K., 2008. Probability analysis of rainfall at Kota. Indian Journal of Agricultural Research 42,3, 201–206

Deni, S.M., Suhaila, J., Wan Zin, W.Z., Jemain, A.A., 2010. Spatial trends of dry spells over Peninsular Malaysia during monsoon seasons. Theoretical and Applied Climatology 99, 3–4, 357–371.

Dixit, A.J., Yadav, S.T., Kokate, K.D., 2005. The variability of rainfall in Konkan region. J. Agrometeo7, 322–324.

EPW, 2007. Half-solution to groundwater depletion. Economic Political Weekly, 42, 40, 4019–4020.

Jain, S.K., Kumar, V., 2012. Trend analysis of rainfall and temperature data for India. Current Science 102(1), 37–49.

Kar, G., 2003. Initial and conditional probabilities of rainfall and wet and dry spells for red and laterite zone of West Bengal using Markov Chain model.Indian Journal of Soil Conservation 31(3), 287–290.

Khan, S., Mushtaq, S., Hanjra, M.A., Schaeffer, J., 2008. Estimating potential costs and gains from an aquifer storage and recovery program in Australia. Agricultural Water Management 95(4), 477–488.

Kothari, A.K., Jat, M.L., Balyan, J.K., 2007. Water balanced based crop planning for Bhilwara district of Rajasthan. Indian Journal of Soil Conservation 35(3), 178–183.

Kumar, R., Singh, R.D., Sharma, K.D., 2005. Water resources of India. Current Science 89(5), 794–811.

Meijer, K., Boelee, E., Augustijn, D., Molen, I., 2006. Impacts of concrete lining of irrigation canals on availability of water for domestic use in southern Sri Lanka. Agricultural Water Management 83(3), 243–251.

Mohanty, S., Marathe, R.A., Singh, S., 2000. Probability models for prediction of annual maximum daily rainfall for Nagpur. Journal of Soil and Water Conservation 44(1&2), 38–40.

Pandarinath, N., 1991. Markov chain model probability of dry and wet weeks during monsoon periods over Andhra Pradesh. Mausam 42(4), 393–400.

Panigrahi, B., Panda, S.N., 2002. Dry spell probability by Markov Chain model and its application to crop planning. Indian Journal of Soil Conservation 30, 95–100.

Sharda, V.N., Das, P.K., 2005. Modeling weekly rainfall data for crop planning in a sub-humid climate of India. Agricultural Water Management 76, 120–138.

Sharma, B.R., Rao, K.V., Vittal, K.P.R., Ramakrishna, Y.S., Amarasinghe, U., 2010. Estimating the potential of rainfed agriculture in India: prospects of water productivity improvements. Agricultural Water Management. 97(1), 23–30.

Sharma, D., Kumar, V., 2003. Prediction of onset and withdrawal of effective monsoon dates and subsequent dry spells in an arid region of Rajasthan. Indian Journal of Soil Conservation 31(3), 223–228.

Sharma, M.A., Singh, J.B., 2010. Use of probability distribution in rainfall analysis. New York Science Journal 3(9), 40–49.

Srivastava, R.C., 2001. Methodology for design of water harvesting system for high rainfall areas. Agricultural Water Management 47, 37–53.

Srivastava, R.C., Kannan, K., Mohanty, S., Nanda, P., Sahoo, N., Mohanty, R.K., Das, M., 2009. Rainwater management for smallholder irrigation and its impact on crop yields in eastern India. Water Resources Management 23, 1237–1255.