Markov Chain Rainfall Probability Model and Rainy Season Length in Kendrapara District, Odisha for Efficient Crop Management Strategies

Systematic information on rainfall patterns and distribution is essential for crop selection, adopting improved agronomic practices, designing rainwater harvesting structures, and conserving rainwater. This study analyzed the probabilities of rainfall occurrence to know the rainfall onset, withdrawal, and rainy season length for different blocks of Kendrapara district, Odisha. The rainfall analysis showed that the kharif season shares 75-78% of annual rainfall with July and August being the wettest. Seasonal rainfall showed a significant increase during kharif season while the decreasing trend was observed during the rabi and summer seasons. Markov chain analysis showed that the weekly probability for 20-mm rainfall and consecutive two weeks is more than 70% during SMW 25-38. During the June-October period, assured rainfall at 80% probability is greater than 800 mm in four blocks, while in other blocks it ranged between 610-779 mm. Assured rainfall during the rabi and summer season is uncertain, however, a 105-126 mm rainfall is received in May in many blocks, useful for summer ploughing and green manure crops. Rainy season length analysis at an 80% probability level revealed that only in 14-16 weeks’ rain occurs, thereby, only short-duration paddy can be grown with lower risk. By utilizing October rainfall and conserved soil moisture, short-duration pulses/oilseeds could be grown in all the blocks. However, kharif paddy must be sown/transplanted at the optimum time


Introduction
Rainfed agriculture has a prominent role in India's agriculture and economy.Globally, India has the largest cultivable area under rainfed condition to the tune of 71.1 M ha and value of produce out of rainfed ecosystem. 1,2The study area of the present investigation is the Kendrapara district of Odisha state where more than 70% of farmers are dependent on agriculture and allied activities.Venkateswarlu and Prasad 3 opined that the rainfed agro-ecosystem plays key role in Indian agriculture with an enormous type of crops, cropping systems, and agro-forestry.However, inter-annual variability of the Indian summer monsoon due to the prevalence of El Nino/ENSO activities also brink a high risk to rainfed agriculture and it was found that a negative correlation exists between sea surface temperature anomaly and southwest monsoon rainfall over Odisha state. 4Rainfall is highly variable weather element both spatially and temporarily and Panda et.al., 5 reported that any variation in rainfall directly affects the livelihood of the farming community of Kendrapara district where 94% population lives in rural areas.Farm output would get affected owing to dry spell in critical crop growth stages during good rainfall years too.Hence, systematic information on rainfall patterns, their variability and probability paves the way for crop selection, adoption of better agronomic practices, and designing of different rainwater storage structures 6,7,8,9,10,11,12 and conservation of excess rainwater in storage structures to utilize during dry spells. 13,14For instance, the characterization of rainfall like weekly, monthly, inter-and intra-seasonal distribution of rainfall, the dates of onset, cessation, and rainy season length is very important for reaping a good harvest in the challenged rainfed agroecosystem. 15Most importantly monsoon onset dates of crop growing season enable the farmers to take better crop management decisions. 15,16,17,18any researchers have characterized the rainfall through probability, trend, heavy rainfall events and length of rainy season analysis for different districts of Odisha state. 19,20However, studies on weekly rainfall probability and the start of rainy season and planning a cropping pattern at the block level for the district of Kendrapara is limited.Hence, in order to fulfill this gap, the present investigation was conducted to determine better crop planning for different blocks of Kendrapara, Odisha using weekly, monthly and seasonal rainfall probability analysis and also by working out start, end and duration of rainy season.

Description of the Study Site
The Kendrapara district is located in the central coastal plain and hills agro-climatic zone of Odisha with a total geographical area of 2640 km 2 .The district spreads between 22º 21' N to 20º 47' N latitude and 86 º 15 'E to 87 º 03' E longitudes on the eastern coast of Odisha.The district is endowed with water resources due to the rivers viz, the Mahanadi, the Brahmani, the Baitarani, the Kharasrota, the Luna, and the Karandia.In addition to these major rivers, around 19 small rivers (locally known as nallas, joras or gullias) also flow through the nine blocks of the district, and floods are quite common during monsoon season due to high-intensity rainfall, saucer shape topography, and tidal ingression.The nine blocks of the Kendrapara district are shown in Fig. 1.Rice is the main crop during the kharif season while pulse and oilseed crops are cultivated during the rabi and summer seasons with residual soil moisture or supplemental irrigation.As per the District Irrigation Plan of Kendrapara, Kendrapara and Pattamundai blocks are having 100% irrigation facilities followed by Derabis (92%), Marshaghai (85%), and Aul (72%) during the kharif season. 21he least area under irrigation is noticed in the Rajnagar block (20%) followed by Mahakalpara (25%) and Rajkanika (35%).

Rainfall Data
To carry out rainfall analysis, daily rainfall data of all nine blocks of Kendrapara district for 26 years (1994  -2019) were collected from the website of Odisha Rainfall Monitoring Mission (https://rainfall.nic.in/login.asp).Daily rainfall data has been converted to weekly, monthly, seasonal [Kharif (June-Oct), Rabi (Nov-Feb), Summer (Mar-May)] and annual basis.The methodology followed in this study is presented in the flow chart (Fig. 2).MAKESENS (Microsoft-EXCEL template) was employed for computing Mann-Kendall test. 22

Initial and Conditional Probability
Wet and dry weeks probability was computed based on Markov chain probability procedure. 23n present study, wet week was referred as a week which received ≥ 20 mm rainfall and if the weekly rainfall ≤20 mm it was considered as a dry week.Following formula (Eqns 1& 2) was used to find out the probability for a wet week.
where, P (W) = Initial probability of the week being wet, F (W) = frequency of wet weeks and N = total number of years considered for analysis.
P w/w= F(w/w)/ F(W) ... (2)   where, Pw/w =conditional probability of a wet week preceded by a wet week, F (W/W) = frequency of wet week preceded by a wet week, F (W)=frequency of wet weeks

Dependable Rainfall Probability
Weibull's formula was employed (Eq 3) to work out dependable rainfall at different probability level.
where P is % probability, m = rank number and N = number of years of data used.Monthly and seasonal rainfall of each year was arranged in ascending order, assigned with a rank and then percent probability (P) was estimated.
In the present study, monthly and seasonal (Kharif, Rabi and Summer) rainfall probability at 20, 50 and, 80% were worked out and it is referred to as high, medium, and low risk.Bhakar et.al., 24 reported that rainfall at 80% probability can be safely considered as dependable rainfall while, likelihood rainfall at 50% probability level is the highest for taking any risk, respectively.

Computing the Start, End and Duration of the Rainy Season
As per the procedure proposed by Kothari et al., 25 weekly rainfall data was utilized to find out the onset, cessation and duration of rainy season.Weekly rainfall up to 75 mm was added by forwarding accumulation (20+21+…+ 52 week).Starting week of rainy season was identified whenever a week receives 75 mm rainfall because this much rainfall amount is needed for land preparation and sowing of crops. 25,26The soil must have reached its wilting point due to the prevalence of prolonged dry spells in the hot summer season.Land preparation and rainfed crops sowing would be easy once a week receives 75 mm rainfall and hence previous researchers have chosen this onset criterion.Mandal et.al., 27 also used weekly rainfall of 75 mm to find out starting week for sowing if rainfed rice in Sagar Island of West Bengal.Backward accumulation of 20 mm rainfall in a week (52+51+50+…..+35 week) was considered to find out the withdrawal of rainy season.
For monsoon withdrawal, 20 mm of accumulated rain was deemed necessary, which is enough to prepare fields for the post-rice crops. 28Rainy season length was found by subtracting the week during which the season ends from the week during which the season starts.Additionally, the rainy season onset week, end week, and length in weeks were estimated at different probability levels.

Variability of Rainfall in Different Blocks
Average monthly rainfall in different blocks indicated that July and August were the wettest months of the year.These two months are contributing 16-20 percent of annual rainfall individually followed by September (15-18%), June (11-15%), and October (11-13%).It was noticed that in the Garadapur block, 18 percent of annual total rainfall was received in September month which was higher than in July (16%).In the remaining months, a low amount of rainfall in the range of 20-60 mm was experienced across the blocks except in May (Table 1).
Significant rainfall amount of 105 mm (Garadapur block) to 126 mm (Derabis block) was received during May owing to convection activity or a lowpressure system in the Bay of Bengal.This rainfall can be efficiently utilized for summer ploughing and to raise green manure crops to improve the soil's physical, chemical and biological properties.Rautaray et.al. 29 found that mid-May to mid-June is optimum for sowing Sesbania green manure crop before growing the lowland rice crop and it would help the farmers to reduce inorganic fertilizer and to counter soil health deterioration and environmental degradation over eastern parts of India.Kharif is a major crop growing season, which receives 75-78% of annual rainfall (AR).The highest amount of rainfall was observed in the Kendrapara block (1221 mm) followed by the Rajnagar block (1196mm) and the lowest in Garadapur (1080 mm) and Mahakalpara (1095 mm) blocks.Rabi season is the driest season of the year which receives 8-10% of annual rainfall while it was 12-15% for the summer season.

Monthly and Seasonal Rainfall Trend
Mann-Kendall trend test revealed that no significant trend was observed in any of the blocks of Kendrapara district during April, May, June, October and November (Table 1).However, a significant increasing trend was noticed during July-September months and significant declining trend was seen during December-March months in many blocks of Kendrapara district.Pattamundai showed significant increasing trend during kharif season (Fig. 3).Increasing tendency in rainfall during kharif season months gives an opportunity to harvest and store excess rainwater in storage structures and can be effectively utilized during dry period/months as rabi season showed significant decreasing rainfall trend.

Initial and Conditional Probability of Weekly Rainfall
Percentage probability for receiving ≥ 20 mm rainfall in a week and two weeks in a row for all the nine blocks of the Kendrapara district is furnished in Hence, sowing operation may be started during these weeks and it would help in better germination and establishment because the weekly rainfall probability for ≥ 20 mm was between 50 and 70% from 24 to 25 SMW.After the onset of the monsoon, the probability -for a wet week and two wet weeks consecutively rose to 70% from SMW 25 to SMW 38 in different blocks of the district.During these weeks, excess rainwater through runoff can be stored in farm ponds and utilized for supplemental irrigation during dry spells.Again, the wet week probability dropped 50% from SMW 41 onwards due to the cessation of the southwest monsoon and reached 0% at the end of the year.Dependable rainfall at various probability levels for different blocks is presented in the table 2.
Kharif seasonal rainfall at 20% probability indicates that all blocks of the district receive more than 1400 mm rainfall which is more than sufficient to grow even long-duration paddy crops.However, this amount of rainfall may be expected for only 2 out of 10 years only and hence, there exist a high risk.
Rainfall at a 50% probability level was above 1000 mm in all blocks of the Kendrapara district except Garadapur (961 mm).Assured rainfall at an 80 percent level is considered optimum for agricultural crop planning.Gupta et.al., 30 4).At the same time, there is upsurge in area (+13502 ha) under pulse during the rabi season and decline in area (-321 ha) under pulse during kharif season.The cropped area under rabi oilseed crops also decreased by 2799 ha in recent period (2011-2019) when compared to 2000-2010.The schemes launched by the Government of Odisha like Targeting Rice Fallows in Eastern India 31 and multipronged strategies of Odisha University of Agriculture and Technology in collaboration with line departments to improve the pulse research and extension in Odisha state could be the reasons for the rise in rabi pulse acreage in recent years.

Crop Planning and Management Strategies
The present analysis indicated that under rainfed conditions, direct sowing/nursery sowing of paddy crop may be taken in SMW 24 (June 11-17) for a short duration drought tolerant paddy (90-120 days) like Kamesh and Satyabhama, especially in Rajnagar, Mahakalpara and Rajkanika blocks as these blocks have the least area (20-35%) under canal irrigation.This would help in the effective utilization of the rainwater during the entire kharif season and the critical phases of the crop like panicle development, flowering, and grain development fall during August and September.Under delayed sowing conditions, farmers have to go for direct sowing by SMW 26 (June 25-July 1) with extra shortduration (90-100 days) varieties (Shabhagidhan and Vandhana) to harvest the crop at the cessation of the southwest monsoon.The district is prone to both floods as it is in the vicinity of the Bay of Bengal and drought due to the vagaries of the monsoon.To cope with this situation, farmers should have a plan for water harvesting structures to drain and conserve the excess rain/flood waters during the flood as well as the cultivation of drought-tolerant varieties.
Blocks like Kendrapara, Pattamundai, Derabis, Marshaghai and Aul had more than 70% net sown area under irrigation, medium (Satabdi, Rajalakshmi, Ajay, Satyakrishna, improved Lalat) and longduration (Pooja, Reeta, CR Dhan 300, CR Dhan 701) cultivars of paddy can be grown.In this case, also, it is optimal to go for sowing by SMW 24/transplanting by SMW 28 which would facilitate the farmers to fully utilize the rainwater up to September/October, and thereafter irrigation requirements can be met from canal water.Das 32 clearly stated that sowing upland rice and rice transplanting under irrigated conditions beyond SMW 29 (July 16-22) affect productivity badly even with proper crop management practices.Further, he reported that paddy is transplanted three to four times and continues even in September month due to recurrent floods in this part of the state which led to the poor yield of 0.5-1.0t/ha.Subash et.al., 33 also opined that rice productivity would reduce by 50%, if it is planted beyond August in the Bihar state.Varieties like Swarna Sub-1, Reeta, Sarala, and Durga are suggested for the blocks where shallow low land/semi-deep water-logged ecosystem is existing as well as against to withstand water stagnated conditions for week/two weeks.
Rainfall analysis showed that ample opportunities exist to cultivate pulse/ oilseed crops after kharif season paddy as around 37,000 ha of land are under rice fallow in Kendrapara district. 34Sowing/ transplanting of kharif paddy in time and cultivation of short/extra short-duration cultivars is one of the strategies for the successful cultivation of rabi pulse crops, especially in Rajnagar, Mahakalpara, and Rajkanika blocks.Short-duration pulse crops (60-80 days) like green gram (OUM11-5, OBGG 52, IPM 02-3) and black gram (Prasad, Ujala, and PU 31) can be taken up 34 utilizing the stored soil water after the cessation of the southwest monsoon as well as rain in October to harvest the good crop and to enhance the farm income.It is highly possible to cultivate rabi pulse and oilseed crops like groundnut in other blocks of the district looking into the available irrigation sources.The potential use of groundwater in all the blocks is another option as the stage of overall ground water development of the district is only 53% and their status is safe in all the blocks. 35owever, conjunctive use of canal and groundwater can be utilized wherever saline water issue is noticed.Above all, ensuring the crops under Pradhan Mantri Fasal Bima Yojana is a conscious option to safeguard in the event of crop failure due to flood/ drought or any other natural disasters.

Conclusions
The rainfall analysis (month, season and annual scale) for the different blocks of Kendrapara district indicated that July and August are the wettest months and contribute 16-20% of annual rainfall while, kharif season rainfall shares about 75-78%.Among the blocks, Kendrapara and Garadapur receive the highest and lowest rainfall during the kharif season.Markov Chain initial and conditional probability analysis showed that the probability for 20 mm rainfall in a week and consecutive two weeks also is more than 70% during SMW 25-38.Assured rainfall at an 80% probability is more than 800 mm during the June-October period in Kendrapara, Rajnagar, Marshaghai, and Derabis blocks while in other blocks it ranged between 610 mm and 779 mm only.Mann-Kendall trend test indicated a significant increasing trend in the kharif season while a significant decreasing trend was observed during rabi and summer seasons.Hence, it is highly possible to store runoff water in water harvesting structures during excess rainfall period to arrest flooding water and utilize it during recurrent dry spells during the cropping season and also for life-saving irrigation for Rabi crops.Though, assured rainfall during the rabi and summer seasons was very uncertain, a significant amount of rainfall (105-126 mm) is being received in May in different blocks which could be used for summer ploughing and growing green manure crops like Sesbania sp.
Length of the rainy season analysis revealed that at an 80% probability level it was 14-16 weeks only and it is understood that under rainfed conditions, long-duration paddy (150 days) can be cultivated at high risk; medium duration paddy (125-135 days) at medium risk while short-duration paddy (90-105 days) is at lower risk.Short-duration paddy (90-120 days) can be sown by SMW 24 in Rajnagar, Mahakalpara, and Rajkanika blocks as these blocks had the lowest irrigation sources.This would help for efficient utilization of available rainwater during the kharif season and protect the crop after the cessation of rainy season from the soil moisture stress.In other blocks, where other irrigation sources are available, medium and long-duration paddy sowing and transplanting activity are to be completed by SMW24 and SMW 28 to avoid yield loss due to delayed planting.Cultivation of short-duration pulses like green gram, black gram, and oilseeds like groundnut in all the blocks of Kendrapara district is possible by utilizing rainfall during October and conserved soil moisture.However, kharif season paddy must be sown/ transplanted at an optimal time to reap a good harvest.

Fig. 3 :
Fig. 3: Average (a) kharif(b) rabi and (c) summer seasonal rainfall and its trend in different blocks of Kendrapara district (D-Decreasing trend; I-Increasing trend; * and ** Significant at p<0.05 and p<0.01 level, respectively)

Fig. 4 .
Fig.4.In general, the chance was very low from 1 st Standard Meteorological Week (SMW) and slowly it picked up to 50% during SMW 20-23 owing to the occurrence of convective rainfall/ low pressure-induced pre-monsoon rainfall.Hence, sowing operation may be started during these weeks and it would help in better germination and establishment because the weekly rainfall probability for ≥ 20 mm was between 50 and 70% from 24 to 25 SMW.After the onset of the monsoon, the probability -for a wet week and two wet weeks consecutively rose to 70% from SMW 25 to SMW 38 in different blocks of the district.During these weeks, excess rainwater through runoff can be stored in farm ponds and utilized for supplemental irrigation during dry spells.Again, the wet week probability dropped 50% from SMW 41 onwards due to the cessation of the southwest monsoon and reached 0% at the end of the year.

Fig. 4 :
Fig. 4: Initial and conditional probability for 20 mm in a week in different blocks of the Kendrapara district

Table 2 : Dependable rainfall (mm) during different seasons at different probabilities in different blocks of the Kendrapara district Name of the block
in all blocks of the district.It is inferred from the duration of the rainy season that the rainy season extends up to 23/24 weeks (161-168 days) at a 20 percent probability.It is expected that 19/20 weeks

Change in the Area Under Major Crops in Kendrapara District from 2000-2010 to 2011-2019
In general, two main cropping seasons are practiced in the Kendrapara district with rice as the main crop during the Kharif season and rice/ pulse/ oilseed crops during the Rabi season.As per the IRRI 31 report, there is a decline in crop diversification in Odisha; and 80, 10 and 10 % of the cropped area is covered by rice, pulses and other food crops, respectively by 2014-15.Crop area statistics (Odisha Agriculture Statistics, Dept. of Agri.& Farmer's Empowerment, Govt. of Odisha) of Kendrapara district indicated that rice acreage reduced by 4573 and 2681 ha during kharif and rabi seasons, respectively during 2010 and 2019 (Table