Analysis of Time Series data on Rainfall for Coonoor

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

Tagged Payment for Ecosystem Services, PES