Visits since 6 July 1998


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, 2.776,2.88 4 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
Peninsul ar (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
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
SO(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 upto 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.


Back to Table of Contents


This page hosted by GeoCities Get your own Free Home Page

Hosting by WebRing.