Analysis of Time Series data on Rainfall for Coonoor

Written by Balachander T
01
Aug

Analysis of Time Series data on Rainfall for Coonoor (v0.1 dtd 06-03-2014)

Dataset: Monthly rainfall in mm

Period: Jan 1935 to Dec 2013

Source and Credit: UPASI, Coonoor. Obtained as hard copy.

Raw data

Data entered in Excel Sheet as two column (Data, rainfall in mm) and then saved as csv. The matrix format is for ease of viewing.

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

1935

0

0

0

0

0

28.5

65

143.5

53.1

272.8

238

113.5

1936

35.8

277.9

268.7

9.1

69.6

118.9

57.9

67.8

148.1

327.7

329.9

101.1

1937

26.7

172.5

160.8

206.3

70.4

89.7

73.4

59.7

63.5

302.5

257.1

73.1

1938

0

192

215.4

124.5

35.8

30

88.4

137.9

141

250.4

68.8

315.5

1939

104.4

18

39.4

246.1

84.3

116.1

40.6

62.2

137.4

259.8

241.5

46.2

1940

1.5

34

9.7

245.6

181.1

133.6

24.6

119.1

99.3

211.8

516.6

62.2

1941

101.9

116.1

0

90.9

129

127

39.1

62

141.7

123.9

265.7

92.5

1942

0

0

0

117.3

184.9

49.5

68.1

88.4

85.3

185.9

167.9

300.5

1943

296.4

77.5

15.7

149.1

62

78.2

49.3

121.4

80.5

293.6

241.1

80.3

1944

135.6

169.2

124.2

74.2

63

113

35.8

123.7

121.2

340.4

550.4

155.5

1945

30.5

20.6

0

136.7

55.6

29.5

115.1

98

45.2

318.3

592.3

11.2

1946

66.8

26.2

82.5

184.4

77.5

48.5

46.2

101.6

160.3

266.9

450.9

309.6

1947

223.3

27.7

160.5

272.8

72.6

36.3

7.4

125

79.5

106.7

70.1

306.3

1948

148.3

94.2

11.2

46.2

119.4

33.8

63.3

55.1

34.5

293.1

792.7

284.2

1949

0

0

0.3

144

81.5

29.5

157

56.4

82

297.9

333.8

0.5

1950

0

157.5

81.8

29.5

113.5

41.4

83.1

107.9

31

126.7

248.7

34.3

1951

103.1

3.1

171.5

280.7

103.1

23.9

79.3

42.4

231.1

67.8

423.2

36.1

1952

52.1

285

5.3

116.1

9.9

45.5

40.9

47.7

81.3

103.9

36.1

417.1

1953

141.7

82.5

134.9

99.3

60.5

100.1

139.7

86.9

70.4

399

89.7

46

1954

220

47.2

209.8

116.3

157.7

24.4

72.9

100.3

22.1

275.3

33.5

111.8

1955

122.9

7.1

52.6

129.3

110

24.4

45.5

27.4

183.4

280.4

153.4

160.3

1956

60.5

26.4

0.8

93.5

35.3

111

27.2

73.9

93.2

281.9

424.2

142.7

1957

0

88.1

96.3

72.6

354.8

114.3

53.9

65.5

67.8

548.6

459.7

172

1958

0

107.4

108.4

193.1

263.6

10

33.3

55.5

66.4

119.4

303.1

69.4

1959

10.8

40.4

3.6

108.7

162.3

102.7

113.9

89.1

115.9

274

444.6

173.4

1960

44

1

387.5

327.4

125.4

54.2

192

29.2

97.1

430.2

502

52

1961

10.6

76.4

0

300.3

124.1

64.4

142.5

64.8

193.2

348.3

452

43.1

1962

53.8

186

52.2

27.8

123

53.8

55.8

119.4

137.4

480.8

133.4

263.2

1963

130.1

63.4

235.7

113.9

49.8

80.8

58.2

17

95.5

243.8

487

192.8

1964

0

39

109.5

24.2

72.6

64.2

159.2

167.6

77.8

132.6

237.6

373.2

1965

20.8

204.6

66

152.2

58.8

7.2

64.8

188.2

27.2

90

315.6

417.2

1966

332

44.2

69.2

129.4

40.8

35.6

93.2

107

108.2

481

524.2

175.8

1967

123.4

0

4.2

6.2

103

59.6

67.6

47.4

48.4

295.4

164.8

174

1968

16.2

268.2

201.8

143.4

89.6

54.8

70.2

84.2

113.6

166

215.2

145.2

1969

0.6

49.6

2.2

210.2

59.6

137.4

79.4

354.6

20.8

321

308.4

227.2

1970

42.8

39

146.6

190

92.6

17.6

77

97.8

41.8

230.6

291.4

39.8

1971

50

14.6

280.6

55.2

147

12

59.2

113.4

156.2

311.4

196.6

318.4

1972

4.6

0.6

0

25.8

143.8

75.2

40.2

17.4

232.8

415.4

418.4

344

1973

0

4

20.4

21.2

134.2

114.8

139

87.8

82.6

604.2

247.4

224.9

1974

2.8

5.6

28.4

86

122.1

40.6

87

47.9

279.2

120.6

56.4

40.2

1975

51.6

26.6

131.6

76.8

132.4

106

145.4

74.2

264.8

112.2

140

30

1976

0

0

62.4

164

29

47.6

66

167

78

318

342

148

1977

0

100.2

49.2

172

257.2

28

43.8

76.8

244.6

602

864.6

6

1978

123

210

27

238

94

54

69

33

113

417

832

488

1979

7

178

157

42

22

36

83

58

266

475

1348

281

1980

0

2

59

147

85

48

36

48

85

237

534

34

1981

43

0

94

71

111

47

65

60

164

324

123

174

1982

8

0

2

78

92

67

97

46

95

359

339

31

1983

35

0

8

37

95

58

54

93

150

363

91

482

1984

298

285

395

53

44

54

92

20

264

238

150

142

1985

118.8

0

0.1

215.7

75.3

107.2

81.1

69.7

174.4

113.9

249.6

309.1

1986

74.8

224.2

99.8

75.8

30.3

55.1

52.5

23.4

167.5

234.2

112.9

315.9

1987

56.4

36.1

55.5

16.6

122.1

41.2

8.7

61

106.4

357

340.3

536.4

1988

16.6

24.3

26.4

162.5

105.9

15.6

204.4

112.6

182.5

97.5

193.3

192.9

1989

16.6

0

204.6

140.6

34.4

45.7

131.4

41.2

164

147.4

292

171.8

1990

233

0

70.4

43

84.9

25.1

41.6

76.8

47

807.7

375.1

125.7

1991

124.4

5.3

61.4

55.2

22.2

176.1

101.8

93.6

158.6

280.6

536.3

21.3

1992

47.1

0

0

104.8

94.5

106.7

48.6

71.1

104.4

176.8

936.4

65.1

1993

0

0

82.8

6.9

75.6

74.8

102.8

109.6

33.2

309.8

1060.2

265.3

1994

52.5

86

31.2

176.6

70.7

35.8

80

38.8

128.5

497.4

593.2

54.3

1995

193.1

11.1

195.4

137.5

78.4

50.7

110.4

148.7

62.5

209.4

179

8

1996

8.1

99.4

49.1

162

79.7

67.5

83.8

90.9

182.2

423.2

255.3

553.6

1997

119.2

0

39

33.6

151.8

81

114

74.6

133.1

680.2

528

279.6

1998

51.2

11.7

3.2

36.5

55

58.3

107.7

201.1

87.8

169.3

214.4

667.5

1999

1.9

264.1

11.1

113.8

47.4

21.6

80.4

54.6

106.7

603.4

431.3

150.8

2000

47.9

243.7

0

72.6

114.9

40.7

22.7

162

242.5

140

419.9

153.1

2001

54.1

8.6

6

326.3

62.1

69.4

49.8

106.2

131.4

185.3

502

372.9

2002

41.9

19.2

14.2

55.4

136.9

15.4

75.2

63

51.5

530.2

547.7

51.8

2003

0

49.3

246.1

197.9

65.2

68.8

122.6

93.7

51.5

386.3

365.2

33.5

2004

118.9

52.9

4

78.9

646.2

47

96.2

36.9

391.1

654.2

505.9

10.9

2005

24.2

25.7

107

233.6

45.2

92.2

137.5

56.7

117.6

228.7

558.4

103.9

2006

79.9

0

142.8

111.8

109.8

55.3

36.3

67.5

160.2

755.1

578.6

91.4

2007

26.6

140.4

45

68.9

86.1

111.4

85.4

145.4

121.4

392.8

107

284.4

2008

13.1

396.9

391.2

104.1

86.1

81.7

109.7

232.1

27

541.6

109

75.6

2009

5.3

0

160.1

40.7

99.9

34.7

93

178.6

33.4

131.5

1164.3

190.6

2010

65.9

2.2

0

36.5

170.2

79.3

151.8

76.9

166.7

217.3

499.3

188.5

2011

30.2

195.7

16.7

219.8

62.6

106.7

80.4

100.3

110.1

625.3

442

117.6

2012

36.5

6

70.1

95

44.9

53.1

29.5

109.9

35.6

750.2

0

0

2013

6.2

48.8

126

106.7

134.7

52.2

51.6

67.5

173.9

211.4

272.5

119.5

This was converted into a single column list of only rainfall data (rain_list_full.csv) which was used for analysis.

Code in R

rf <- read.csv(“rain_list_full.csv”)

rfts <- ts(rf, start=c(1935,1), end=c(2013, 12), frequency=12)

plot(rfts)

rfstl <- stl(rfts[,1], s.window = “periodic”)

plot(rfstl)

str <- StructTS(rf[,1],frequency = 5, type =“level”)

str

tsdiag(str)

Graphs and Interpretation

Graph 1 – Raw Data

Graph 2: stl output

The above output shows that the seasonality component is not very strong although there seems to be a regular pattern in it. The trend component is even less significant. The remainder seems to explain a lot of the variation in the rainfall data (It is significant). (Is there some method to examine the remainder to decompose it further? How do we find El Nino type of larger time scale events in this. From a planning point of view, how do we understand the variation in rainfall over time?)

Graph 3: structTS output

Need help in interpreting this. At the commandline the structTS yielded this output

 

Call:

StructTS(x = rf[, 1], type = “level”)

 

Variances:

level epsilon

3.925e-01 2.328e+04