S1: Mann-Kendall Test and Sen S Slope

Exploring climate change perceptions, rainfall trends and barriers to adaptation in a drought prone region in Odisha, India

Architesh panda [email protected]

S1: Mann-Kendall test and Sen’s slope To avoid the presence of positive and negative autocorrelation effects, before applying the MK test, the data series was tested for serial correlation. If the lag-1 autocorrelation (r1) was found to be non-significant at 95% confidence level, then the MK test was applied to the original data series, otherwise the MK test was applied to “pre-whitened” series obtained as (x2-r1x1,x3- r1x2,……., xn-r1xn-1). (von Storch, H. (1995), Zhang et la 2001)

The Mann-Kendall test statistic for a series R1, R2…..Rn… is given by Generally if a dataset displays a consistently increasing or decreasing trend, S will be positive or negative respectively, with a larger magnitude indicating the trend is more consistent in its direction.

Variance of Mann-Kendall statistic is

Where, n is the number of data points

The test statistic Z is calculated as follows:

The hypothesis of no trend is rejected , where Z is taken from the standard normal distribution table and α is level of significance (Barnard 1947). This means that there is a probability α that a trend is falsely identified. In hypothesis testing, the significance level is the criterion used for rejecting the null hypothesis. Experimenters have used either the 0.05 level (sometimes called the 5% level) or the 0.01 level (1% level), although the choice of levels is largely subjective. The lower the significance level, the more the data must diverge from the null hypothesis to be significant. In the present study of rainfall variability analysis, we used 0.05 level as it is more conservative than the 0.01 level.

The Sen's Slope estimator is a nonparametric, linear slope estimator that works most effectively on monotonic data. Unlike linear regression, it is not greatly affected by gross data errors, outliers, or missing data. The Sen’s Slope technique is used to determine the magnitude of the trend line. The approach involves computing slopes for all the pairs of ordinal time points using the median of these slopes as an estimate of the overall slope (Gilbert, 1987). Sen's method proceeds by calculating the slope as a change in measurement per change in time.

( 5) where, Q = slope between data points and ; = data measurement at time i’; = data measurement at time i; i’ = time after time i.

Variance for Sen’s slope is determined by

where, n = number of data points; tp = the number of ties for the pth value; q = the number of tied values.

Sen’s Estimator of Slope (Q’)

Where N = number of calculated slopes To estimate the range of ranks for the specified confidence interval of ranks

The ranks of the lower (M1) and upper (M2) confidence limits are given by After calculating the slopes corresponding to M1 and M2 as the lower and upper confidence limits, respectively, the median slope is then defined as statistically different from zero (for the selected confidence interval), if the zero does not lie between the upper and lower confidence limits. The Sen’s method uses a linear model to estimate the slope of the trend and the variance of the residuals should be constant in time. When hypothesis of no trend is rejected by Mann-Kendall test (positive value of test statistic indicates the increasing trend and negative value indicates the negative trend), the Sen's Slope is used to quantify the trend.

t-test This method tests whether the means in two different periods are different. The test assumes that the data are normally distributed. The test proceeds as follows:

where x and y are the means of the first and second periods respectively, and m and n are the number of observations in the first and second periods respectively, and S is the sample standard deviation (of the entire m and n observations). S2: Table 1: Trends in rainfall: Month wise and season wise rainfall trends of Balangir station from 1958 to 2005 and Komna station from 1951 to 2002

Month Mean SD CV (%) Slope MK P-Value Sen’s Slope

Jan 8.38 15.86 189.24 0.02 -0.987 0.16 0

Feb 18.57 29.18 157.20 -0.09 -0.108 0.45 0

Mar 17.10 26.23 153.36 -0.05 0.988 0.83 0

Apr 26.17 25.34 96.84 0.06 -0.257 0.39 -0.04

May 35.66 36.55 102.49 0.17 1.671 0.95 0.40

Jun 192.18 122.82 63.91 0.11 0.648 0.74 0.48

Jul 392.07 148.32 37.83 0.23 -0.684 0.24 -1.45

Aug 356.17 165.91 46.58 0.15 0.986 0.83 1.57

Sep 206.77 119.28 57.69 0.11 -1.164 0.12 -1.43

Oct 61.70 65.81 106.67 0.12 -0.622 0.26 -0.34

Nov 15.32 30.63 199.94 0.13 0.105 0.54 0

Dec 6.67 15.05 225.71 0.10 -0.607 0.27 0

Annual 1336.76 367.16 27.47 1.46 0.364 0.64 4.64

Winter 26.95 32.52 120.69 0.235 -0.106 0.45 0.00

Pre-Monsoon 78.93 52.12 66.04 0.11 1.537 0.93 0.68

Monsoon 1147.19 331.32 28.88 0.59 -0.222 0.41 -0.67 Post-Monsoon 83.69 82.09 98.09 0.02 -0.479 0.31 -0.30

Month Mean SD CV (%) Slope MK P-Value Sen’s Slope

Jan 10.07 17.56 174.34 0.13 0.117 0.54 0

Feb 12.97 19.95 153.82 -0.08 -0.024 0.49 0

Mar 21.64 33.09 152.91 -0.12 -1.35 0.08* -0.07

Apr 27.42 30.77 112.19 0.05 2.022 0.02** 0.33

May 34.99 43.57 124.51 0.10 0.878 0.81 0.16

Jun 194.62 91.53 47.03 -0.05 0.86 0.80 0.82

Jul 348.38 138.27 39.69 0.13 -0.875 0.19 -0.91

Aug 338.03 250.20 74.02 -0.05 0.307 0.62 0.42

Sep 197.06 117.22 59.48 0.07 -2.17 0.01*** -2.06

Oct 51.00 50.17 98.36 0.03 -0.402 0.34 -0.09

Nov 11.58 27.08 233.83 0.15 0.425 0.66 0.00

Dec 5.55 16.31 294.05 0.11 0.121 0.54 0.00

Annual 1253.32 368.43 29.40 1.64 -0.355 0.36 -0.884

Winter 23.04 25.69 111.47 0.20 0.293 0.61 0.00

Pre-Monsoon 84.05 64.28 76.47 -0.10 0.56 0.71 0.30

Monsoon 1078.09 334.44 31.02 1.27 -0.733 0.23 -1.97

Post-Monsoon 68.13 66.42 97.49 0.01 0.078 0.53 0.02 Notes: *, **, ***, Significant at 10%, 5 % and 1% level respectively,

S2: Table 2: Traditional weather Perdition System among the farmers

Indicator Scope If the leaves and fruits of Neem tree (Azadirachta indica) fall and start decomposing in the soil then good rain will come that season. Seasonal If in a particular year the production of Chahar (Buchanania lanzen Spreng), Mahul (Madhuca Indica J.F. Gmel, Kendu (Diospyros melanoxylon) and Mango is good then, rain will be good that year Yearly If parrots eat Jamun (Syzygium cumini) half, then there will be half rain, if they will eat it full, then good rain in that season. Seasonal If cloud is in north and south it will rain, if it is on east and west it won’t rain. Weekly A particular type of snake will hang itself in the tree, if it will make more sound more rain and less sound less rain. Weekly Ants going in a queue before the likely rainy days mean there will be more rain. Few days If in the month of June Kum (Gmelina arborea) tree gets more fruit then more rain or vice versa. Seasonal If the Bharatiya bird builds his nest in north side rain will come, nest in south rain won’t come. Seasonal If the Cobra snake is seen climbing the tree then rain will come definitely within fewday. Few days Honeybee making new house means rain will come. Weekly The year with more winter is generally the year with more rain. Yearly Coughing of cows before rain. Few days In the good rainy years the leaves of the Sahaj (Terminalia alata Heyne ex Roth) tree will get black. Yearly Crow nesting in dry trees. Weekly Sound of the Rabbit, if it is three times continuously then rain will come if irregular then rain will be irregular Few days

Source: Compiled by author through FGDs

S2: Table 3 Common perception among farmers on Monsoon rain and the Local Calendar

1. No seasonal rainfall only low pressure rain.

2. Geographical disparity in distribution of rain.

3. Less rain during planting of rice 4. Sudden and untimely rain

5. Upland paddy cultivation is not doing well.

6. Reduced pulses production due to less rain

7. Paddy showing window has shifted from 8 June-21 June (Mrigasira) to Punarvasu (6-19 July) and Pushya (20 July-2 August).

8. Less rain in Aslesa (3-16 August) leading to dryness in the land when water actually needed from rain.

9. Due to less rain in Makha (17-30 August) in the last 30 years the frequencies of pest attacks have increased in rice production.

10. Pubbha (31 August-12 September) and Uttara (13 September-26 September) are supposed to be bring the last good rain for rice. However, due to less rain, the cost of water pumping has increased significantly and also affecting Rabi crops production.

Traditional Local calendar

Nakshatra Duration Ashwini 13 April-26 April Bharani 27 April-10 may Kritika 11 May-24 May Rohini 25 May-7 June Mrigashira 8 June-21 June Ardra 22 June-5 July Punarvasu 6 July-19 July Pushya 20 July- 2 August Aslesha 3 August-16 August Makha 17 August- 30 August Pubba 31 August-12 September Uttara 13 September-26 September Hasta 27 September-9 0ctober Chitta 10 October-23 October Swathi 24 October-5 November Vishaka 6 November-18 November Anuradha 19 November-2 December Jyeshta 3 December-15 December Moola 16 December-18 December Purvashada 29 December-10 January Uttarashada 11 January-23 January Sravana 24 January-5 February Dhanishta 6 February-18 February Shatabhisha 19 February-3 March Poorva Bhadra 4 March-17 March Uttara Bhadra 18 March-30 March Revati 31 March-12 April

Table 4: Barriers to adaptation

1. Changing 1. Lack of availability and marketing facility for cultivating traditional millets which were Crops/variety drought resistant due to short growing periods.

(FGDs: 1,2,3,4) 2. Growing more vegetables and pulses is constrained by lack of water facility and lack of labor.

3. Land is not suitable and lack of information on which land suitability of crops.

4. Lack of drought resistant crops and seeds.

2. Water Storage and 1. Small landholding and lack of land Conservation practices 2. Lack of monetary resources and knowledge on practices.

(FGDs: 1,3,4) 3. Lack of government support 4. Lack of renovation of available water bodies.

3. Soil Conservation 1. High prices and lack of availability of organic manure due to decreasing livestock. practices 2. Lack of labor. (FGDs: 2,3,4) 3. Lack of credit for soil conservation practices.

4. Lack of scientific knowledge and new techniques.

4. Diversification of 1. Lack of grazing land. livestock 2. Lack of labor. (FGDs: 1,2, 3,4) 3. Lack of credit facility for purchasing livestock.

4. Not profitable

5. Crop insurance 1. Complicated process

(FGDs: 1,3,4) 2. Lack of property rights.

3. Not beneficial

4. Lack of knowledge on the government programmes.