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Trend and climate change were
studied in annual rainfall data for the period of 62 years (1949-2010) of Sagar
and 65 years (1945-2010) of Damoh districts of Bundelkhand region of central India.
The analysis of weekly rainfall probability was also carried out at both the
locations for field operations and crop planning in rainfed agricultural system
for improving the farmer’s livelihood. Mean annual rainfall was 1233.8 mm with
32.6% variability for Sagar and 1225.1 mm with 30.3% variability for Damoh
region. Sagar and Damoh region exhibited significant decreasing trend in the total
amount of annual rainfall in the last 15 years (1996 to 2010). Also, both
locations showed significant long-term decreasing trend in annual rainfall.
Climate of both the regions have changed as in the recent 15 years annual
rainfall had decreased by 156.4 and 310.7 mm at Sagar and Damoh from their long
period average (LPA), respectively. The Initial
and conditional rainfall probability analysis at Damoh reinforced
that Initial probabilities {P (W)} of getting 10 mm rainfall per week was 76%
during 25^{th} (18-24 June) SMW. Thus, the seed bed preparation could
be initiated during this week. Initial as well as conditional probability of
wet week followed by wet week {P(W/W} of getting 20 mm rainfall was more than
80% during 27^{th} SMW (2-7 July) in Sagar district. Therefore, this
week is most suitable for sowing operation in this district.

Climate from geological epoch has been changing with time and it is reasonable to assume that it will change. Recently, the severe drought conditions have disrupted human societies in Bundelkhand region of central India and got the attention of India on reality of climate variability and its significance. The information on annual and seasonal rainfall of a region is useful to design water harvesting structure for agricultural operations, field preparation, seeding, irrigation, fertilizer application and overall in field of crop planning [^{th} century which increased by three times during the period 1968 to 2000 and in last 10 years, region have witnessed five drought years [

Weekly rainfall data for the period 1949 or 1945 to 2010 i.e., for 62/66 years pertaining to Sagar (23˚5'N, 78˚5'E, 594 m msl), and Damoh (25˚5'N, 79˚29'E, 595 m msl), respectively were obtained from India Meteorological Department (IMD), Pune, India. Weekly, annual and seasonal rainfall distribution patterns were critically examined and analyzed adopting procedure suggested by Panse and Sukhatme [

Then computed,

Now, let

Defining:

We computed:

The statistic

Trends were examined using Mann-Kendall rank statistic (t), Spearman rank statistic (r_{s}) and Gaussian low-pass [_{i} were replaced by their ranks k_{i} such that each term was assigned a number ranging from 1 to N that reflects its magnitude relative to the magnitude of all other terms. Then statistic P for the series was computed, which is accomplished as follows. Count up the number of later terms whose values exceed k_{1}, and denote this number by n_{1}. Then compare the value of the second term that exceed k_{2}, and denote this by n_{2}. Continue this procedure for each term of the k_{i} series with X_{N}_{−1} and its corresponding number n_{N}_{−1}, then P is given by the sum:

where, as:

Spearman rank statistic (r_{s}): The calculation r_{s} requires that the series x_{i} under investigation first be transformed to its rank k_{i} as described above. The each term of rank series k_{i} should be subtracted by i to compute d_{i} (where “i” ranges from 1 to N).

Then compute,

where, as:

For N larger than 8, the value of r_{s} can be tested for significance by solving for “t” with the equation given below and comparing this with probability points of student’s t-distribution for (

t =

An initial and conditional probability of weekly rainfall at different threshold limits (10, 20 and 40 mm) were computed using first order Markov chain process [

where, Pr is the plotting percentage, N is the total numbers of years and “m” is the rank of observed values of weekly rainfall, when rainfall in descending order of magnitude.

The mean annual rainfalls for both the locations are more than 1200 mm with a standard deviation (SD) of more than 371 mm and coefficient of variation (CV) of more than 30.3%. The coefficient of variation indicates that the rainfall was highly variable at these two locations. The average annual rainfall varied from 491.7 mm (1981) to 2167.1 (1991) and 234.8 (1989) to 2387.3 mm (1956) at Sagar and Damoh, respectively (

The annual and monsoon (23^{rd} - 39^{th} SMW) rainfall series were normally distributed. About 90% of annual rainfall is received from the southwest monsoon during monsoon season. Average rainfall during the monsoon season is 1104.5 mm and varied from 440.6 to 1896.3 mm with SD of 320 mm at Sagar. The annual rainfall contribution was 2.5%, 4.4% and 3.5% to the pre-monsoon (10^{th} - 22^{nd} SMW), post monsoon (42^{nd} - 50^{th} SMW) and winter (51^{st} - 9^{th} SMW) season rainfall, respectively. The CV (more than 100%) indicated that the rainfalls during these seasons are highly variable. The rainfall ranged from zero to 201.5 mm, zero to 246.0 mm and zero to 196.2 mm for respective seasons, respectively. Coefficient of skewness and coefficient of kurtosis showed that rainfall series in all the three seasons were not normally distributed. At Damoh, similar pattern of rainfall during monsoon season was observed as at Sagar.

In monsoon season, the highest (1953.4 mm) and lowest (219 mm) rainfall was recorded during the year 1956 and 1989, respectively (_{1}/SE(g_{1}) and g_{2}/SE(g_{2})) were computed to test the normality at 95% level of significance. It is evident from the

The average of these sub-periods along with Crammer’s t_{k} test is given in

. Statistical parameters of annual and seasonal rainfall in Sagar & Damoh districts of central India

Rainfall | Sagar | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Mean | SD | CV (%) | Highest (mm) | Lowest (mm) | % C | CS | CK | g_{1}/ SE(g_{1}) | g_{2}/ SE(g_{2}) | |||

Annual | 1233.8 | 386.2 | 32.6 | 2167.1 | 491.7 | - | 0.56 | 0.02 | 1.67 | 1.20 | ||

Monsoon | 1104.5 | 320.0 | 29.0 | 1896.3 | 440.6 | 89.5 | 0.60 | 0.10 | 1.85 | 0.16 | ||

Pre-monsoon | 30.5 | 37.1 | 121.7 | 201.5 | 0 | 2.5 | 2.41 | 7.81 | 7.4^{*} | 12.00^{*} | ||

Post-monsoon | 54.4 | 66.0 | 121.3 | 246 | 0 | 4.4 | 1.46 | 1.38 | 4.5^{*} | 2.1^{*} | ||

Winter | 44.4 | 40.2 | 90.4 | 196.2 | 0 | 3.6 | 1.50 | 3.04 | 4.6^{*} | 4.6^{*} | ||

Damoh | ||||||||||||

Annual | 1225.1 | 370.8 | 30.3 | 2387.3 | 234.8 | - | 0.51 | −0.84 | 1.6 | −1.29 | ||

Monsoon | 1100.4 | 329.5 | 29.9 | 1953.4 | 219 | 89.9 | 0.17 | 0.80 | 0.51 | 1.23 | ||

Pre-monsoon | 30.6 | 35.0 | 114.3 | 158.9 | 0 | 2.5 | 1.76 | 3.57 | 5.4^{*} | 5.4^{*} | ||

Post-monsoon | 46.4 | 60.9 | 131.2 | 260.8 | 0 | 3.8 | 1.53 | 1.76 | 4.72^{*} | 2.7^{*} | ||

Winter | 47.0 | 52.0 | 110.5 | 280.1 | 0 | 3.8 | 1.93 | 5.76 | 5.9^{*} | 8.8^{*} | ||

^{*}Frequency distribution rainfall series are not normal at 95% level, %C: Contribution in annual rainfall (%), CS: Coefficient of skewness, CK: Coefficient kurtosis, g_{1}/SE(g_{1}) and g_{2}/SE(g_{2}): Fisher statistics.

. Annual rainfall during different period at Sagar & Damoh locations of Central India

Distract/Sub-Period | Sagar | Distract/Sub-Period | Damoh | ||
---|---|---|---|---|---|

Mean (SD) in mm | Crammer t_{k}_{ }test | Mean (SD) in mm | Crammer t_{k }Test | ||

1949-1970 | 1237.4 (332.4) | 0.01 | 1945-1970 | 1307.7 (363.9) | 2.05^{*} |

1971-1995 | 1185.2(472.2) | −0.90 | 1971-1995 | 1181.9 (392.2) | 0.86 |

1996-2010 | 1077.4 (216.1) | −2.2^{*} | 1996-2010 | 914.4 (308.9) | −2.70^{**} |

^{*}, ^{**} Significant at 5 and 1% probability level.

differed from the long period average (LPA) of 1233.8 mm. However, the average annual rainfall (1077.4 mm) during the recent period (1995-2010) was significantly (P < 0.05) lower than the LPA at Sagar. Rainfall had decreased by 156.4 mm during the recent period as compared to LPA. At Damoh, the I sub-period (1945-1970) average (1307.7 mm) was higher and differ significantly from their long period average (1225.1 mm). However, the II sub-period rainfall did not differ significantly (

To understand the nature of trend, the annual series was subjected to “Gaussion low pass filter” (GLPF) analysis” i.e., a 9-point Gaussian low pass filter/weights (WMO, 1966) was used to give a smoothed curve [^{2} = 40.0%) in annual rainfall series during the recent sub-period (1995-2010) with a rate of 42.3 mm/year. Similarly, at Damoh annual rainfall series exhibited significantly decreasing trend (Y = −24.941x + 1139.5 R^{2} = 16.6%) during the recent period (1995-2010) with a rate of 24.9 mm/year. However the magnitude of decrease at Damoh was lower than Sagar.

The Mann-Kendal rank (t) and Spearman Rank Statistics (r_{s}) revealed a significant (P < 0.05) decreasing trend in annual and kharif (26^{th} - 41^{st} SMW) (^{nd} - 15^{th} SMW) season rainfall showed slight decreasing trend but not statistically significant. However, rabi season rainfall at Damoh showed a significant decreasing trend.

The initial rainfall probability {P (W)} of getting 10 mm rainfall per week was 67% and 69% during 25^{th} and 26^{th} SMW, respectively at Sagar district (^{th} SMW. Therefore, this week is more suitable for sowing of crops. The top dressing of urea may be done during 32^{nd} SMW as the {P (W/W)} of getting 20 mm rainfall during this period is more than 95% (^{th} (27 August-2 September) SMW (

Gaussian low pass filter curves of annual rainfall at Sagar

Gaussian low pass filter curves of annual rainfall at Damoh

. Mann-Kendal rank (t) and Spearman Rank Statistics (r_{s}) of annual and seasonal rainfall

Rainfall Series | Sagar | Rainfall Series | Damoh | ||
---|---|---|---|---|---|

t | r_{s} | t | r_{s} | ||

Annual | −0.22^{*} | −2.1^{*} | Annual | −0.24^{*} | −3.10^{*} |

Kharif | −0.24^{*} | −2.4^{*} | Kharif | −0.21^{*} | −2.62^{*} |

Rabi | −0.02 | −0.2 | Rabi | −0.20^{*} | −1.96^{*} |

^{*}, Significant at 5% probability level.

The initial and conditional rainfall probability analysis at Damoh revealed that initial probabilities {P (W)} of getting 10 mm rainfall per week was 76% during 25^{th} (18-24 June) SMW (^{th} SMW, since an amount of 10 mm rainfall per week can be taken as the minimum requirement for seedbed preparation and even sowing in already tilled fields for rainfed kharif crops. However, sowing can be done during 26^{th} SMW as the conditional probability of wet week followed by wet week of getting 20 mm rainfall was 76% - 94% during 26^{th} - 27^{th} SMW. More than 50% probability of 20 mm rainfall during a week is considered as the wet week and is ideal for the crop sowing operation [^{th} to 37^{th} (10-16 September) SMW was ranged between 56% to 80% (Fig- ure 4), hence, proper drainage provisions should be made in deep and medium black soils. The top dressing of

Initial and conditional probabilities of weekly rainfall at different threshold limits at Sagar

Initial and conditional probabilities of weekly rainfall at different threshold limits at Damoh

urea may be done during 32^{nd} (6-12 August) and 33^{rd} (13-19 August) SMW as the {P (W/W)} of getting 20 mm rainfall during this period is more than 90% [^{th }(20-26 September) and 39^{th} (24-30 September) SMW, respectively, and hence, pesticides may be sprayed to control insects, pests and diseases in all the affected crops. Since the conditional probability of getting 10 mm rainfall is less than 20% during the crop season, therefore, intercultural operations may be planned as and when sunny days appears for 2 - 3 days.

The chances of taking rainfed rabi crops are more at Sagar in comparison to Damoh as the conditional probability of wet followed by wet is more than 60% during second week of January. However, at both the locations with the advancement of time, probability of getting rainfall is reducing and it was recorded that from 38^{th} (17- 23 September) SMW, the initial probability of getting rainfall of 20 mm reduced to 40%, clearly indicating that supplemental irrigation is required for long duration varieties. The study also shows long-term rainfall probability studies may be important parameters for varietal selection to achieve assured production in a particular region. Short duration varieties of rainfed crops should be selected in the above mentioned regions, where, rainfall starts receding within 38^{th} SMW. Therefore, ICRISAT bred chickpea cultivars, such as, ICCV-96029 (matures within 75 days), ICCV-2 and ICCV-93929 (both matures within 85 days) and IARI bred mustard cultivars like Pusa Agrani, Pusa Mahak, Pusa Tarak, Pusa Mustard 25 and Pusa Mustard 27 (all maturing between 100 - 110 days) should be selected for this region so that terminal droughts may be escaped.

The minimum weekly rainfall amount expected at 60%, 70% and 80% probability level is presented in ^{th} SMW is above 80%, and farmers can initiate their field preparation operations from 26^{th} week and in subsequent weeks i.e., 27^{th} (July 2-8) onwards probability of receiving more the 20 mm rainfall is more than 70%, which is ideal week for sowing of kharif crops in the region. The 30^{th} and 31^{st} SMW are also ideal time for the crop fertilization based upon the rainfall pattern and intensity. At Damoh, the expected amount of rainfall is 16 mm at 70% probability level during 25^{th} SMW, sowing of kharif crops can be initiated for early duration crop varieties. Proper drainage network is essential for black soil dominant Damoh district as the expected amount of rainfall at 70% probability level is more than 60 mm during 30^{th} to 33^{rd} SMW. Long duration crop varieties can be taken at Damoh in comparison to Sagar as the rainy days are two week more at Damoh. Moreover, chances of taking double cropping are also more at Damoh by taking short duration crop varieties during kharif and early sowing of rabi crops.

. Expected weekly rainfall amount at different probability levels

SMW | Date and Month | Probability level (%) | |||||||
---|---|---|---|---|---|---|---|---|---|

Sagar | Damoh | ||||||||

Mean | 60 | 70 | 80 | Mean | 60 | 70 | 80 | ||

24 | June, 11-17 | 15.6 | 3 | 1.3 | 0.5 | 18.6 | 6.9 | 1 | 0 |

25 | June, 18-24 | 40.1 | 12 | 9.7 | 7.2 | 44.5 | 28.5 | 16 | 10.6 |

26 | June, 25-1 | 53.7 | 18.9 | 11.4 | 3 | 68.8 | 28.2 | 21 | 11.8 |

27 | June 2-8, July | 84.5 | 38.2 | 29 | 8.9 | 70.9 | 64.2 | 44.8 | 38.1 |

28 | July, 9-15 | 81.9 | 43.4 | 21.4 | 10.2 | 79.0 | 52.8 | 32.2 | 25.4 |

29 | July, 16-22 | 76.6 | 39.2 | 31.8 | 14.6 | 92.8 | 65.4 | 53.2 | 36.5 |

30 | July, 23-29 | 82.6 | 46.8 | 39.4 | 17.2 | 86.4 | 78.8 | 60.9 | 38.5 |

31 | July, 30-5, Aug | 123.3 | 66.7 | 41.7 | 30 | 130.0 | 108.9 | 79.2 | 56.7 |

32 | Aug, 6-12 | 112.5 | 50.3 | 41.8 | 28.6 | 109.1 | 88.7 | 65.9 | 57.6 |

33 | Aug, 13-19 | 97.0 | 54.6 | 41.8 | 22.5 | 88.7 | 69.6 | 55.6 | 48.6 |

34 | Aug, 20-26 | 76.1 | 39.7 | 25.6 | 12.6 | 85.2 | 56.4 | 37 | 25.4 |

35 | Aug, 27-2, Sep | 80.4 | 31.4 | 14 | 4.4 | 74.4 | 55.2 | 39.9 | 24.5 |

36 | Sep, 3-9 | 71.7 | 26.7 | 11.4 | 2.4 | 71.0 | 58.8 | 39.2 | 22.9 |

37 | Sep, 10-16 | 55.2 | 16.6 | 5.5 | 0.3 | 57.1 | 38.4 | 19.2 | 8.9 |

38 | Sep, 17-23 | 39.4 | 1.5 | 0 | 0 | 30.9 | 11.1 | 6 | 2.2 |

39 | Sep, 24-30 | 20.9 | 3 | 1.3 | 0.5 | 11.8 | 3.3 | 0 | 0 |

At both the location, rainfall in the range of 18.9 to 79.2 mm is expected from 26^{th} to 37^{th} week (June 18-September16). Overall expected rainfall days are more than 84 at both the locations suggesting that medium duration varieties of various crops can be ideal in the region. However, at Damoh the expected amount of rainfall at 70% probability level was 16 mm during 25^{th} ( June 18-24) SMW, suggesting that sowing can be done one week prior in comparison to Sagar. The intermittent rains of more than 20 mm rainfall was also expected at 70% level during 36^{th} to 37^{th} SMW, but thereafter probability of getting even 20 mm rainfall per week is not 70%, suggested that long duration varieties may be more suitable with supplemental irrigation.

The prevalent kharif season crops of the region include green gram, black gram, sorghum and maize depending upon the soil type. In view of the above studies, it is suggested that the kharif rainfed crops such as groundnut, black gram, green gram and sesamum should be sown during 27^{th} SMW in both Sagar and Damoh region. The ideal combination of crops of the regions can be sorghum for the grain purpose intercropped with cowpea for the fodder purpose. Livestock integrated with the agricultural/food production systems is the cornerstone for rural economy of the farmers, therefore, the current suggested cropping systems integrating food-fodder system with rainfall probabilities may fetch an additional green fodder of 150 - 200 q·ha^{−1} to the farmers apart from the sorghum grain yield and improve their livelihood. Therefore, overall the current study reveals that past rainfall record analysis may be a handy tool for future rainfall probability projections, which alternatively can be of immense importance in the crop and other field operation planning in rainfed agricultural system as well as improving their livelihood.

The overall mean annual rainfall was 1233.8 mm with 32.6% variability for Sagar and 1225.1 mm with 30.3% variability for Damoh region. Mann-Kendall rank and spearman rank statistics revealed that there is a significant long-term decreasing trend in annual, kharif and rabi season rainfall at both locations. However, in the past 15 years (1996 to 2010), both regions exhibited significant decreasing trend in total amount of annual rainfall. Climate of both the regions has changed as in the recent 15 years annual rainfall has decreased by 156.4 and 310.7 mm at Sagar and Damoh from their long period average. Therefore, overall the current study reveals that past rainfall record analysis may be a handy tool for future rainfall probability projections, which alternatively can be of immense importance in the crop and other field operation planning in rainfed agricultural system as well as in improving their livelihood.