5. Data and Analysis

Continuous periodogram power spectral analyses (Jenkinson,1977 References ) was done for the climatological datasets listed in Table 2.

 

Table 2

Details of climatological data sets used in the study

No

Parameter

Region

Period / Duration (years)

Reference

1

Rainfall Annual and Seasonal:JJAS

All - India

1871 - 1994 / 124

Parthasarathy et. al. (1995)

2

,,

Homogeneous India

,,

,,

3

,,

Core monsoon India

,,

Parthasarathy (Private communication)

4

,,

Northwest India

,,

,,

5

,,

West Central India

,,

,,

6

,,

Central Northeast India

,,

,,

7

,,

Northeast India

,,

,,

8

,,

Peninsular India

,,

,,

9

Rainfall : Annual

England and Wales

1766 - 1980 / 215

Wigley and Jones (1982)

10

SOI : Seasonal

Tahiti - Darwin

1852 - 1984 / 133

Wright(1989)

11

Surface Temp.: Annual and Seasonal

Arctic

1957 - 1981 / 25

Kelly and Jones(1981)

12

Surface Temp.: Annual and Seasonal

Antarctic

1957 - 1983 / 27

Rapier(1983)

 

 

 

The power spectra were plotted as cumulative percentage contribution to total variance versus the normalized standard deviation t given as (Equation 9).

where L is the period in years and T50 the period up to which the cumulative percentage contribution to total variance is equal to 50. The phase spectra were plotted as cumulative(%) normalized(normalized to total rotation) phase .The variance and phase spectra alongwith statistical normal distribution for the data sets(Table 2) are shown in Figures 7 - 9.

FIGURE 7

FIGURE 8

FIGURE 9

The cumulative percentage contribution to total variance and the cumulative (%) normalized phase (normalized w. r. t. the total rotation) for each dominant waveband is computed for two representative data sets and shown in Figure 10 to illustrate Berry's phase, namely the progressive increase in phase with increase in period and also the close association between phase and variance(see Item d, Section 4.2 ).

FIGURE 10

Table 3 gives the following results of continuous periodogram analyses for the data sets : (1) The period T50 upto which the cumulative percentage contribution to total variance is equal to 50 . (2) The dominant peak periodicities in wavebands 2 - 3, 3 - 4, 4 - 6, 6 - 12, 12 - 20, 20 - 30, 30 - 50, 50 - 80. These wavebands include the model predicted(Equation 5) dominant peak periodicities 2.2, 3.6, 5.8, 9.5, 15.3, 24.8, 40.1, and 64.9 years for values of n ranging from -1 to 6 .

 

 

Table 3

Periodogram estimates

Region

T50

Peak periodicities in dominant (normalised variance > 1.0) wave bands(years)

Duration in years

years

2 -3

3 - 4

4 -6

6 - 12

12 - 20

20 - 30

30 - 50

50 - 80

All India (Annual) 124

3.733

2.075,2.151,2.352 2.460,2.652,2.774 2.887

3.096,3.210,3.374 3.515,3.688,3.846

4.573, 4.793, 5.670

6.450,6.815 7.517,10.806

12.886 16.009

21.653

34.027

65.375

Homogeneous (Annual)

124

3.641

2.028,2.092,2.149 2.347,2.455,2.665 2.774,2.881,2.972

3.075,3.197,3.327 3.699,3.850

4.798, 5.704

6.768,7.509 8.492,10.656

12.669 16.300

21.893

35.063

68.043

Core-Monsoon (Annual)

124

3.987

2.090,2.294,2.453 2.673,2.779,2.878 2.969

3.071,3.197,3.354 3.501,3.685,3.835 3.987

4.788, 5.054, 5.704

6.754,7.472 10.646

12.720

21.762

36.677

70.962

North West (Annual)

124

3.453

2.034,2.086,2.149 2.199,2.349,2.445 2.684,2.776,2.884 2.966

3.174,3.344

4.154, 4.783, 5.692

6.863,7.472 8.307

12.381 16.513

21.653

31.790

 

West Central (Annual)

124

4.298

2.096,2.147,2.347 2.462,2.652,2.774 2.972

3.087,3.203,3.324 3.846

4.582, 4.798, 5.715

6.640,7.547 10.678

13.055 15.850

22.201

35.700

65.180

Central North (Annual)

124

3.722

2.086,2.160,2.244 2.359,2.472,2.801

3.102,3.216,3.381 3.515,3.688,3.854

4.385, 4.573, 4.783, 5.019, 5.681

6.075,6.444 7.524,11.304

12.707

22.695

 

57.120

Northeast (Annual)

124

3.858

2.051,2.092,2.287 2.342,2.472,2.689 2.765,2.904

3.115,3.284,3.398 3.522,3.663,3.823

4.500, 4.722, 5.591, 5.960

6.808

12.063 13.751 18.600

 

 

64.596

Peninsular (Annual)

124

3.916

2.059,2.145,2.193 2.460,2.540,2.646 2.776,2.872,2.972

3.140,3.255,3.411 3.637,3.854

4.028, 4.200, 4.764, 5.203, 5.854

7.502

12.233 15.381 18.452

All India

(Seasonal JJAS)

124

3.384

2.024,2.103,2.151 2.359,2.462,2.670 2.768,2.878

3.084,3.200,3.388 3.526,3.688,3.952

4.217, 4.568, 4.779, 5.014, 5.698

6.057,6.768 7.383,8.874 10.678

12.580 16.830

21.395

 

65.835

Homogeneous (Seasonal JJAS)

124

3.213

2.030,2.096,2.149 2.347,2.460,2.673 2.768,2.872,2.969

3.071,3.190,3.321 3.505

4.213, 4.788, 5.039, 5.710

6.087,6.761 7.390,8.698 10.678

12.393 16.563

21.438

 

67.908

Core-Monsoon (Seasonal JJAS)

3.467

2.000,2.094,2.149 2.294,2.455,2.571 2.678,2.771,2.963

3.065,3.190,3.367 3.501,3.972

4.424, 4.783, 5.054, 5.704

6.075,6.754 7.353,10.688

12.443 16.662

21.246

 

71.247

North West

(Seasonal JJAS)

124

3.405

2.000,2.036,2.096 2.151,2.199,2.352 2.448,2.550,2.684 2.771,2.872,2.966

3.068,3.181,3.371 3.512

4.179, 4.783, 5.721

6.111,6.863 7.464,8.458

12.282 16.464

21.545

 

76.642

West-Central (Seasonal JJAS)

3.252

2.026,2.100,2.347 2.411,2.465,2.584 2.665,2.765,2.969

3.194,3.311

4.242, 4.587, 4.788, 5.024, 5.704

6.069,6.700 7.280,8.812 10.720

12.443 16.729

21.610

 

65.441

Central Northeast (Seasonal JJAS

124

4.200

2.000,2.092,2.242 2.307,2.368,2.421 2.475,2.545,2.660 2.807

3.210,3.401,3.901

4.226, 4.564, 4.779, 4.999, 5.244, 5.698

6.044,6.822

12.555 16.480

22.604

 

55.542

Table 3 (Contd.)

Northeast (Seasonal JJAS)

124

4.028

2.044,2.088,2.287 2.342,2.510,2.673 2.754,2.890

3.029,3.127,3.268 3.388,3.526,3.666

4.109, 4.487, 4.712, 4.954, 5.978

6.342,6.829 9.837,10.937

12.148 13.751 18.032

22.514

 

69.418

Peninsular (Seasonal JJAS)

124

3.442

2.020,2.139,2.193 2.364,2.462,2.532 2.676,2.771,2.861

3.425,3.558,3.804

4.217, 4.559, 4.798

6.587,7.309 8.467

17.067

 

 

 

England And Wales (Annual)

215

3.572

2.000,2.088,2.122 2.143,2.219,2.294 2.349,2.380,2.445 2.617,2.684,2.763 2.852,2.963

3.035,3.140,3.271 3.391,3.601,3.770 3.952

4.221, 4.623, 4.870, 5.140, 5.308, 5.931

6.981,7.273 7.585,8.307 9.227,9.817 11.014

12.835 13.945 17.204

21.140 26.740

49.906

SOI (DJF)

133

4.247

2.040,2.354,2.416 2.485,2.540,2.596 2.774,2.884

3.174,3.378,3.508 3.785

4.023, 4.230, 4.555, 4.779, 5.779

6.450,9.385

12.631 14.256 16.073 19.185

25.949

SOI (MAM)

133

4.255

2.057,2.122,2.167 2.210,2.296,2.700 2.881

3.187,3.384,3.565 3.835

4.238, 4.698, 5.140, 5.382, 5.860

6.548,9.292 10.321 11.270

12.631 16.202 19.730

26.079

35.771

SOI (JJA)

133

4.192

2.069,2.113,2.158 2.347,2.540,2.594 2.765,2.867

3.265,3.394,3.537 3.839

4.032, 4.217, 4.527, 4.764, 5.100, 5.866

6.266,7.186 9.264 10.571

12.455 16.251

20.290 27.253

SOI (SON)

133

3.995

2.053,2.109,2.156 2.255,2.359,2.530 2.697,2.774,2.881

3.181,3.391,3.515 3.866

4.032,4.200 4.532,4.798 5.854

6.304,9.209 11.304

13.862

20.971 26.079

Arctic (Winter)

25

3.964

2.139,2.636

3.381

4.097

6.124,9.604

24.487

Arctic (Spring)

25

2.893

2.000,2.623

4.642

6.727

27.582

Arctic (Summer)

25

4.040

2.188,2.824

3.337

7.494

13.520

Arctic (Autumn)

25

2.757

2.000,2.428,2.771

3.681

5.313

10.352

22.402

Arctic (Annual)

25

3.778

2.000,2.342,2.665

3.558

4.407

6.836,10.720

24.316

Antarctic (Winter)

27

3.928

2.197

3.432

4.226

9.135

42,612

Antarctic (Spring)

27

4.779

2.107

3.242

4.464,5.919

9.181

19.968

Antarctic (Summer)/ 27

4.994

2.053,2.328,2.788

3.242

4.755

31.192

Antarctic (Autumn)/ 27

3.297

2.000,2.361,2.724

3.137

4.302

12.282

Antarctic (Annual)/ 27

5.009

2.000,2.182

3.324

4.793

8.484

33.120

T50 is the period up to which the cumulative % contribution to total variance is equal to 50.

Dominant peak periodicities significant at or less than 5% level are given in bold letters.

 

The following analyses was done to illustrate the two important results: (a) superimposition of dominant peak peridicities contribute to the observed departure from mean for the time series, (b) projection into the future for times of occurrences of dominant peaks helps predict near future trend in departure from mean. Two representative data sets used for the study were taken from All India monsoon (JJAS) rainfall for the 19-years periods 1952-1971 and 1967-1986. Periodogram estimates of number of positive and negative dominant peaks for half-year preceding each year was computed for all the years in the two series and also the projected values for the following two major rainfall deficit years 1972 and 1987 and shown in Figure 11.

FIGURE 11

There is a close association between the observed departures and frequency of occurrence of dominant peaks for the two data sets and the projected values indicate the observed negative departures.