A wavelet cross-spectral analysis of solar/enso connections with Indian monsoon rainfall

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1 A wavelet cross-spectral analysis of solar/enso connections with Indian monsoon rainfall Subarna Bhattacharyya, Roddam Narasimha Jawaharlal Nehru Centre For Advanced Scientific Research (JNC), Bangalore India Acknowledgement: Dr. Vanessa George, LASP, Univ. of Colorado 1

2 Outline Data Analysed ENSO-Solar-Rainfall Connections Using Time Domain Analysis Wavelet Power Spectral Analysis Wavelet Cross-Spectral Analysis With Monte Carlo Methods Conclusions 2

3 Data analysed (ENSO) global SST ENSO index (henceforth referred to as ENSO) uses the eastern equatorial Pacific SST index as an ENSO index over (20N--20S) minus (20N--90N,20S--90S) over the longitude grid 0 deg E-358 deg E. The anomalies are in hundredths of a degree Celsius and are measured with respect to the period Nino 3 SST anomalies: The Nino 3 Region is bounded by 90W-150W and 5S-5N. Monthly means were computed for each time series for the period Also at NOAA Climate Prediction Center Nino3.4 SST anomalies: 120W-170W and 5S-5N ftp://ftp.cgd.ucar.edu/pub/cas/tni\_n34. 3

4 Data analysed (contd) SST anomaly tendency affects the AISM rainfall to a larger extent than the SSTs or the SST anomalies themselves (e.g. Rajeevan et al. 2005). Nino 3.4 Tendencies: The anomalies in SST over the months December, January and February are subtracted from those over the succeeding months March, April and May to get the SST anomaly relevant to the rainfall of the monsoon season beginning in May--June. A positive SST Nino 3.4 anomaly tendency represents a strong El Nino over the Pacific, which in turn results in weakening of the monsoon circulation over Asia. Similarly, a negative implies weakening of the El Nino over the Pacific and strengthening of the monsoon over Asia. 4

5 Data Analysed (Rainfall) HIM HIM region covers the central and north western parts of India amounting to 55 % of the total land area of the country. HIM is considered to be the most characteristic index of the component of Indian rainfall dominated by the dynamics of the south west monsoon. All India Summer Monsoon (AISM) Rainfall is also studied Homogeneous rainfall region map 5

6 Data analysed (Solar Activity) Solar cycle processes: Sunspot number Group sunspot number Solar Irradiance Source: NOAA ftp://ftp.ngdc.noaa.gov/stp/solar_data 6

7 Solar-rainfall connections: previous results SB & RN, Geophys. Res. Lett Mean rainfall is higher in test-periods of higher solar activity at confidence levels varying from 75% to 99% Strong regional variations: AISMR misleading indicator; NEI behaves radically differently than rest of homogeneous regions Over the two test-periods of high and low solar activity, the average cross power for rainfall and solar activity index exceeds that between noise and solar activity index at confidence levels of 99.99% or higher at the 8-16 y, 9-13 y and y bands using the z-test. SB, PhD Thesis, JNC,

8 ENSO AISM Solar Irradiance Over TP1 and TP2 solar activity exhibits maximum contrast. Test Period 1 (TP1): Test Period 2 (TP2): Rainfall, Solar process in phase ENSO, Rainfall out of phase ENSO, Solar processes out of phase % confidence levels (using z-test) shows, for significant difference between means for the two 8test periods

9 Nino 3, Nino 3.4 SST Nino 3, Nino 3.4 SST anomalies are out of phase with rainfall and solar processes over the two test periods, although the confidence levels for the differences in these cases are low. 9

10 Continuous Wavelet Transform Let x n = x(nt), n=0..n-1. Continuous Wavelet Transform of x n is W n (s) P N 1 n 0 =0 x n 0 ª? (n0 n)±t s 3 7 5, (1) where for a Morlet wavelet ª( )=¼ 1=4 exp (i! 0 )exp µ 2=2, ^Ã(s! µ k )= 2¼s 1=2 ^Ã0 (s! ±t k ); ª? = Complex conjugate of ª. R1 1 j ^Ã0 (! 0 ) j 2 d! 0 =1: (2) (3) (4) 10

11 Wavelet Power Spectrum Local wavelet power spectrum: W n (s) W? n(s) Wavelet power: j W n (s) W? n(s) j. (5) (6) Global wavelet power: ¹W(s) = 1 N P N 1 n= 0 j W n (s) W? n(s) j (7) 11

Contours in green and blue mark regions where the cross

12 ENSO AISM Solar Irradiance Wavelet cross power spectra using Morlet continuous wavelets. Contours in green and blue mark regions where the cross spectrum exceeds the reference spectrum at 90% and 95% confidence levels respectively. 12

ENSO AISM Solar Irradiance Torrence & compo (1998) Test: Global wavelet cross power spectrum between (a) ENSO index & solar irradiance, (b) AISM rainfall & solar irradiance, (c) ENSO

13 ENSO AISM Solar Irradiance Torrence & compo (1998) Test: Global wavelet cross power spectrum between (a) ENSO index & solar irradiance, (b) AISM rainfall & solar irradiance, (c) ENSO index & sunspot number, (d) AISM rainfall & sunspot (e) ENSO & AISM. ENSO-AISM cross power shows lowest confidence levels (70%), ENSO-IRRAD shows highest confidence levels (97.5%). 13

14 ENSO Monsoon Sunspot: Spatial Variation Wavelet cross power averaged over different period bands as percentages of the total wavelet cross power. Band (1): 1--2 y, (2): 2--4 y, (3): y, (4): y, (5): y, (6): Note here SN denotes Sunspot Numbers y. High cross power in band 4 for Nino 3.4 and SN 14

15 Nino 3.4 T Monsoon Sunspot Nino3.4T & AISM rainfall show high cross power in the 8-16 y band whereas Nino 3.4 T & AISM show scattered cross power over 2-8 y band. 15

16 Nino 3.4 T Monsoon For all the homogeneous rainfall regions, Nino 3.4 T & RF shows high cross power scattered over the 2-8 y band, and even over test period 1, and also over test period 2 in case of PENSI. 16

17 Consolidated results on ENSO % Contribution to wavelet power in 2-7 y and 8-16 y bands. NEI in phase with Nino3, Nino3.4, Nino3.4 T over both bands; global ENSO in opposite phase with all of the above. 17

18 Consolidated results on ENSO % Contribution to wavelet cross power in 2-7 y and 8-16 y bands. Note high cross powers for Nino 3.4 Tendency and HIM in both 2-7 and 8-16 y bands. 18

19 Consolidated results on ENSO Strongest contributions are in the pairs sunspot-rainfall, Nino 3.4 tendency-rainfall, sunspot-nino 3.4 and sunspot-nino 3.4 tendency; Contributions to ENSO-rainfall cross spectra from the 8-16 y band are not substantially less than from the 2-7 y band. On the 2-7 year time scale, an increase in solar activity increases the ENSO index & decreases the monsoon rainfall over all regions. (There are regional variations in the magnitude of such a decrease.) On the 8-16 year time scale, an increase in solar activity is associated with a decrease in the ENSO index and increase in the rainfall. 19

20 Consolidated results on ENSO The net effect of solar activity on rainfall therefore appears to be the result of counteracting influences on the two bands i.e. on short and long periods; scale-interactions therefore appear to be important. The effect of positive Nino 3.4 SST tendencies on the monsoon rainfall is to decrease the rainfall. The link between monsoon rainfall and solar activity emerges as having the strongest evidence; the ENSO-solar activity connection is stronger than for the ENSO-monsoon connection. 20

21 Consolidated results on ENSO The evidence for multi-decadal connections between Indian rainfall and solar activity, directly and mediated through ENSO, is thus strong, as tested by two different procedures: time-domain analysis (which uses sunspot numbers only to select periods of greatest contrast in solar activity) wavelet cross spectra (band-averaged and otherwise, which use quantitative solar activity data to analyse effects in different period bands). 21

22 Criticism of time domain results The time domain analysis showed that rainfall was higher in the more solar--active period. However, apart from a secondary role in identifying the test periods, no quantitative indicator of solar activity takes direct part in that analysis. This leaves open the possibility (however improbable) that some other parameter (such as ENSO, for example) may be responsible for the differences observed in rainfall between the two test periods. To overcome this limitation, we perform wavelet cross power analysis using synthetic noise signals simulating the spectrum and pdf of rainfall and ENSO. WN-white noise,sn-noise with HIM/ENSO spectrum, ANnoise with HIM/ENSO pdf 22

23 Monte Carlo and statistical comparison of band averages We introduce the following notations for comparing averages statistically: Average over a band b : R b SN (t) Average over ensemble : R b SN (t). Average over test-period : [R b SN (t) ] k=1,2. An average over the 9-13 y band, as well as over the ensemble for test period 1, will be denoted by [ R 9-13 SN (t) ] 1 which is just one number. Further, we study the cumulative distribution functions of these averages. We evaluate the confidence levels to which the differences in the CDFs are significant in each case. 23

24 Monte Carlo Results on ENSO-Rainfall-Sunspot Triad Typical % conf. obtd. in 8-16 band avg. crosspower N34T-HIM & N34T-SN is 97.5 % over TP1, 99.5% over TP2 SS-HIM & SS-SN is 99.99% over TP1 & TP2 24

25 Conclusions ENSO-RAINFALL-SUNSPOT TRIAD Confidence levels at which the hypothesis that the two crossspectra are the same is rejected: For 8-16 band avg. cross-power N34T-HIM & N34T-SN : 97.5 % over TP1, 99.5% over TP2 SS-HIM & SS-SN : 99.99% over TP1 & TP2 For band avg. cross-power SS-N34T & SS-SN : 99.5% over TP1 and TP2 SS-HIM & SS-SN : 99.99% over TP1 & TP2 For 2-7 y band avg. cross power N34T-HIM & N34T-SN : less that 50% over TP1, 95% over TP2. Spatial Variations MULTIDECADAL CONNECTIONS 25

26 Conclusions * Rainfall sunspot connections are strong (99.5% confidence level between sunspot and HIM rainfall) * ENSO rainfall connections are much weaker (for example 70% confidence level between ENSO and AISM rainfall) * ENSO and solar activity connections are stronger than ENSO rainfall connections (for example 95% confidence level between sunspot and Nino 3.4 tendency) 26

Seasonal Climate Outlook for South Asia (June to September) Issued in May 2014

Ministry of Earth Sciences Earth System Science Organization India Meteorological Department WMO Regional Climate Centre (Demonstration Phase) Pune, India Seasonal Climate Outlook for South Asia (June