Possible association between Indian monsoon rainfall and solar activity
Abstract
[1] Over the 120 y period (1871–1990) for which reliable Indian rainfall statistics are available, solar activity parameters exhibit nonstationarity. Taking this fact into account, we present here the results of an analysis of four solar activity indices and seven major Indian monsoon rainfall time series, over two distinct test periods respectively of low and high solar activity, each comprising three complete solar cycles. It is found that the average rainfall is higher in all seven rainfall indices during periods of greater solar activity, at confidence levels varying from 75% to 99%, being 95% or greater in three of them. Using wavelet techniques it is also found that the power in the 8–16 y band during the period of higher solar activity is higher in 6 of the 7 rainfall time series, at confidence levels exceeding 99.99%. These results support existence of connections between Indian rainfall and solar activity.
1. Introduction
[2] Increasingly strong evidence for possible association between solar processes and terrestrial climate indices [Beer et al., 1990; Lassen and Friis-Christensen, 1995; Haigh, 1996, 1999, 2001; Labitzke and van Loon, 1997; Mehta and Lau, 1997] has accumulated in recent years. In a recent study by Neff et al. [2001], strong coherence between solar variability and the monsoon in Oman in the period between 9 and 6 ky B.P. has been reported. Doubts about effects on shorter time scales (of the order of 10 to 100y) seem however to remain. Earlier studies of possible connections between Indian monsoon rainfall and solar activity [Jagannathan and Bhalme, 1973; Jagannathan and Parthasarathy, 1973], using correlation and power spectral analysis of the rainfall distribution in 48 meteorological stations spread all over India, reported presence of the 11-year sunspot cycle at significance levels of 95% or higher in only 5 of them.
[3] Reliable data on Indian rainfall are available for a period of 120 y (1871–1990). The solar activity over this period is clearly not a stationary process (see Figure 2 below, showing relatively low activity during 1875 to 1915). If, ignoring this nonstationarity, we compute a conventional correlation coefficient between all India summer monsoon rainfall and sunspot numbers, we get a value of, for example, only 0.11 (95% confidence band −0.07 to 0.29, using an equal-tails test). To test for possible connections between rainfall and solar activity, one therefore needs to take into account the phase of such multidecadal variation. A similar point has been made in a different context by Labitzke and van Loon [1997]. We tackle this problem by (i) comparing averages over periods of about the same duration over which solar activity is respectively low and high, and (ii) analysing the multidecadal variations of both solar and rainfall time series through wavelet techniques. Wavelet methods have earlier been used to analyse Indian rainfall by Torrence and Webster [1999], Torrence and Compo [1998], and Narasimha and Kailas [2001].
[4] The idea that the tropics can amplify a small radiant flux signal to a relatively large and dynamic climate change elsewhere in the world as well [Haigh, 2001; Visser et al., 2003], serves to provide further motivation for the present work.
2. The Data Analysed
[5] Seven annual area-weighted Indian rainfall time series for the period 1871–1990 have been considered for the analysis. These comprise the 6 homogeneous regions of northeast India (NEI), northwest India (NWI), central northeast India (CNEI), west central India (WCI), peninsular India (PENSI) and a so-called homogeneous Indian monsoon (HIM) region, and an overall time series called the all India summer monsoon (AISM) rainfall [Parthasarathy et al., 1995].
[6] We have performed the analysis also over the spatially finer scale provided by the data in each of the 28 meteorological subdivisions of India [Parthasarathy et al., 1995], but will not discuss this in detail as the overall conclusions from an analysis of the 7 major rainfall time series are not thereby significantly altered. However some striking features of the results for some subdivisions will be cited.
[7] The range of scales over which these rainfall data can provide useful information on temporal variability is limited by the relatively short length of data. For the present study we have found annual rainfall to be the most appropriate rainfall index to use. The solar indices under study are sunspot number index, group sunspot number, solar irradiance and sunspot area. The sunspot index data have been obtained from Rai Choudhuri [1999] and Fligge et al. [1999], and the data for group sunspot number from the NOAA ftp site ftp://ftp.ngdc.noaa.gov/STP/SOLAR_DATA. The data for the time series of annual mean solar irradiance has been obtained from Lean [2004] [see also Lean et al., 1995] available at the online resource of the World Paleoclimate Data Center website, although some reservations have been recently expressed over irradiance estimates [see Foukal et al., 2004]. We will in the main cite results using the sunspot number as the primary index of solar activity, as the other indices do not lead to significantly different conclusions.
[8] One important difference between rainfall and sunspot data is that the former are cumulative, the latter are not: individual sunspots live typically for several days, and all monthly data of sunspots are usually compiled by taking averages of daily data over a month. The monthly average sunspot number plotted against time does not appear very smooth [see, e.g., NASA, 2004]. As our aim here is to study possible connections between the rainfall and solar processes with time scales of order years to decades, it is adequate to use yearly sunspot numbers.
3. Results
[9] To display visually and illustrate the nature of the variations we propose to analyse, we show in Figure 1 the ‘wavelet map’ or scalogram for NEI rainfall and sunspot number over the 8–16 y scale band. Striking similarity between the slightly meandering row of wavelet coefficient maxima is clearly seen. The average time interval between neighbouring maxima in wavelet coefficients is 10.7 y for sunspots and 10.4 y for the rainfall; note that the meander of these local maxima extend over the whole 8–16 y band.
[10] Figure 2 shows the time series of three solar activity parameters. All three show a nonstationary character over the duration of the data stretch. To test for possible connections between solar activity and rainfall, especially over multi-decadal scales, it seems appropriate to select two periods, of approximately the same duration, over which the contrast in solar activity is as high as possible. Furthermore, to allow for cumulative effects of solar activity on the rainfall, it is preferable to choose consecutive complete solar cycles (considering the period from one minimum to the next as one complete cycle) in each of the two test periods. Based on these considerations the most appropriate choice turns out to be the two intervals 1878–1913 and 1933–1964 respectively; each comprises three complete cycles, and has neighbouring cycles at either end of higher and lower amplitudes respectively. For comparison, brief results will be cited also for the sub-optimal test periods 1878–1933 and 1934–1986, each comprising five complete cycles. Longer full-cycle test periods will clearly overlap.
[11] The rainfall time series are illustrated in Figure 3 by plots of data for three homogeneous regions and the Konkan subdivision (on the west coast). While the solar indicators have a clearly cyclic character, the rainfall time series appear irregular and random, but one can already notice the marked difference in average rainfall between the two test periods, especially for the Konkan time series. (Incidentally such marked differences are seen all along the west coast.)
[12] Next we compare the mean rainfall over the two periods. Table 1 lists the annual rainfall means μ1 and μ2 respectively for the two periods for all the homogeneous regions considered; both the test periods and the corresponding means are shown on Figure 3. The null hypothesis that the difference in mean annual rainfall between these two periods is zero is rejected at the maximum confidence levels listed in Table 1 using a one-tailed z-test [Crow et al., 1960]. Thus the mean annual rainfall during 1933–1964 (higher solar activity) is everywhere higher than that during the period 1878–1913 (lower solar activity). However the confidence level is 95% or higher in 3 cases out 7, including AISM and HIM, and reaches 99% in WCI. At the other extreme, it is a low 75% in NEI and NWI. Also listed in the table are the percent differences in mean rainfall over the two test periods as compared to the respective annual mean rainfall.
| Region | μ1,a mm | μ2,b mm | % Confidencec | ( )%d |
% Power Rainfalle |
|---|---|---|---|---|---|
| AISMR | 853.5 | 883.0 | 95 | 3.5 | 16 |
| HIM | 858.6 | 916.5 | 96.8 | 6.7 | 22.5 |
| WCI | 1067.2 | 1145.7 | 99 | 7.3 | 19.7 |
| PENSI | 1140.5 | 1183.2 | 85 | 3.6 | 19.6 |
| CNEI | 1204.2 | 1235.4 | 80 | 3.0 | 11.3 |
| NWI | 542.0 | 565.1 | 75 | 5.0 | 25.2 |
| NEI | 2071.8 | 2100.2 | 75 | 1.4 | 11.6 |
- a Mean rainfall over three cycles of low solar activity, 1878–1913.
- b Mean rainfall over three cycles of high solar activity, 1933–1964.
- c Confidence level at which μ1 − μ2 differs from zero by the z-test.
- d
% difference in mean rainfall over the two test periods with respect to the annual mean rainfall
.
- e Contribution to total power from 8–16 y band.
[13] These percentages as well as the percentage confidence level for the z-test considered are depicted on a map of India in Figure 4. It appears from this figure that the sunspot-rainfall association is strong over much of India but weak over the northwest and northeast. The west coast subdivisions of Konkan, Kerala and Coastal Karnataka as well as West Madhya Pradesh show highly significant results (96.3% to 99.9%).
[14] For the five-cycle solar activity test periods 1878–1933 and 1934–1986 the mean rainfall in 6 of the 7 rainfall time series in the second test period is again higher, but at lower confidence levels, varying from 62.5% (PENSI) to 92.5% (WCI).
[15] The standard F-test [Crow et al., 1960] shows that the variances in test period 1 are greater than those in test period 2 in 19 out of 29 subdivisions, 15 of which are generally in the western half of the country. Confidence levels vary from 50% to 99.9%.
[16] In order to investigate whether a more direct association between solar activity and rainfall can be established, we now present a wavelet analysis in the form of colour-coded contour maps of wavelet power spectra as functions of time and Fourier period (henceforth referred to as period) as shown in Figures 5 and 6. The individual wavelet power spectra for HIM rainfall and sunspot number are respectively shown in the top and bottom panels of Figure 5. It is seen that the 8–16 y period band exhibits predominantly the highest wavelet power in the case of sunspot number. (Although the sunspot cycle is normally considered to have a period of about 11.6 y, different numbers are quoted in the literature. Solar cycle lengths vary over the range of 9 to 13 y [Lassen and Friis-Christensen, 1995]. The value 11.6 y is close to the geometric mean of the ends of the 8–16 y band. For these reasons, and to take account of the ‘meander’ seen in Figure 1, we take the 8–16 y band as representative of solar activity.) Now, HIM exhibits most power in the 2–7 year band, but substantial power in the 8–16 y period band also, thus indicating strong connections with solar activity. In order to make a quantitative comparison, we compute the wavelet power over the dyadic period bands 2–4, 4–8, 8–16, 16–32, and 32–64 y for each case. The results are shown in Figure 6 which reveals contributions in the 8–16 y band varying over the range 11.3% to 25.2% among the rainfall time series considered (the highest being in NWI and HIM). To further study the implication of the presence of relatively high power in the 8–16 y band, we make a comparison of the mean wavelet power in the band over the two three-cycle test periods. In all cases except NEI the power is higher in the period of higher solar activity compared to that in the low activity period, at confidence levels exceeding 99.9% by the z-test.
[17] As may be expected, the confidence levels on a similar test vary more widely at the subdivisional level, from high values over the west coast (Kerala, Coastal Karnataka and Konkan—reaching 99.9% at the last region) to 50% (in Gangetic West Bengal).
[18] As compared with classical correlation/power spectral density methods, the present results demonstrate the advantages of the wavelet approach, which (i) permits analysis of nonstationary processes and enables identification of epochs during which correlations at different significance levels may have prevailed, (ii) allows us to take account of slight variations in the effective period or scale (‘meandering’) of the effect of a given forcing, such meandering being presumably the result of the nonlinear interactions between different modes of the system.
4. Conclusions
[19] The present study has actually involved four solar index time series and a total of thirty five Indian rainfall time series, but not all results have been presented as the major conclusions can be derived by considering rainfall in the homogeneous zones and sunspot number. The present statistical analysis, over the identified test periods of high and low solar activity, leads to the following conclusions: (1) Greater solar activity is associated in all cases with greater rainfall, although at significance levels that are distinctly high (exceeding 95%) in 3 out of 6 homogeneous cases studied, and greater than 75% even in the other 3 cases. (AISM rainfall does not represent a homogeneous region, and for this reason it is not the best case for studying solar/rainfall associations; but even here the confidence level is 95%.) (2) In 9(15) out of 29 subdivisions, rainfall is higher during the high solar test period at z-test confidence levels exceeding 90%(80%) respectively. (3) The strongest connections between solar activity and rainfall are observed along the west coast and in central India, and the weakest in northwest and northeast India. (4) The contribution to the wavelet power from the 8–16 year band is substantial across all the homogeneous rainfall regions, varying from 11.3% in CNEI to 25.2% in NWI.
[20] We believe the present results are robust because (i) although there are regional variations, many independent rainfall time series show strong effects over geographically contiguous and climatologically coherent zones (including the west coast, not separately identified as a homogeneous zone in the analysis of Parthasarathy et al. [1993]; (ii) 3- and 5-cycle test periods lead to mutually reinforcing conclusions; and (iii) wavelet power in the 8–16 y band is higher during the higher solar activity period at confidence levels of 99.9% or greater in 6 of the 7 major rainfall time series of Parthasarathy et al. [1993] (the exception being the northeast).
[21] It is outside the scope of the present paper to discuss the possible mechanisms that may be responsible for the rainfall/solar activity associations analysed here. Nevertheless we may note that the regional variations revealed by the present analysis are not inconsistent with the simulations of Haigh et al. [2005], which suggest that a major effect of higher solar activity may be a displacement in the Hadley cell. Such a displacement of coherent circulation patterns, depending on its magnitude, can have different effects on rainfall in different regions.
Acknowledgments
[22] The authors would like to thank Prof. A Rai Choudhuri, of the Physics Department of Indian Institute of Science, for his help on the solar data. The authors are grateful to the Centre for Atmospheric and Oceanic Sciences of the Indian Institute of Science for their continued hospitality.
