Examining causality relationships between sunspot cycles and global climate
John Moore1,2 Aslak Grinsted1,3 Svetlana Jevrejeva4 1Arctic
Centre, University of Lapland, Rovaniemi, Finland 2Thule Institite, University of Oulu, Finland 3Niels Bohr Institute, University of Copenhagen, Denmark 4Proudman Oceanographic Laboratory, Liverpool, UK
How not to do it “Instead of wading through hundreds of papers for evidence of the Sun’s influence on terrestrial climate, all you have to do is look at this graph.”
“All the major climate minima are evident in the Be10 record, and the cold period at the end of the 19th century. This graph alone demonstrates that the warming of the 20th century was solar-driven.” David Archibald: http://wattsupwiththat.com/2009/03/17/beryllium-10-and-climate/
Motivation • Solar cycle irradiance variations may affect the whole planet’s climate • the Quasi-Biennial Oscillation (QBO) • and Arctic Oscillation (AO) • Impacts seen in global sea level The 11-12 year solar sunspot cycle produces rather weak (0.1%) changes in solar energy output, and this is unlikely to directly to be sufficient to produce changes in weather and climate. Amplification factors have been proposed due to the higher variability of solar energy at UV wavelengths which may induce changes in stratospheric ozone and temperature, which can then propagate down to the troposphere (e.g. Baldwin and Dunkerton 2005; Labitzke 2005).
Challenge • Examining causal links between time series of sunspot number and indices of QBO, AO, ENSO activity and global sea level
1. QBO/AO link? 2. Sunspots/AO link? 3. Sunspots/ENSO link?
4. TSI-sea level cycles
Causality • Correlation is not causality, indeed correlation is not appropriate for a non-linear system, however: • A variable X is said to Granger-cause a variable Y if it can be shown that time series values of X provide significantly improved predictions of future values of Y than predictions based on Y alone would. • It is however, possible that both variables X and Y may be “caused” by another parameter .
Proposition • solar cycle irradiance variations may affect the whole planet’s climate ? – ENSO & sea level • e.g. • via the stratosphere Arctic Oscillation (AO) • Quasi-Biennial Oscillation (QBO) • Or by cloud processes (not tested here) • So things are correlated but are they caused by solar variability?
Test • Examining causal links between time series of sunspot number and indices of global sea level, QBO, AO and ENSO activity
Verification • Detection of weak cause and effect link between Southern Oscillation Index (SOI) and Arctic oscillation (AO)
Data • Monthly AO [Thompson and Wallace, 1998.] • QBO http://www.cdc.noaa.gov/Correlation/qbo.data. • ENSO - Monthly SOI [Ropelewski and Jones, 1987] Niño 3.4 SST index [Smith and Reynolds, 2004] • Solar cycle (SC) - Monthly International Sunspot http://sidc.oma.be/DATA/monthssn.dat
• Total solar irradiance, [Lean; Fligge & Solanki 2000; Solanki and Krivlova, 2003]
• Global sea level [Jevrejeva et al., 2006] • Removed the annual cycle from all series
Basic idea: • Putative causal driving forces should always lead the responding variables. • Isolate ~11yr variability from climatic and solar time series and examine whether the variations are significantly phaselocked.
Methods • • • •
Wavelet coherence (WTC) Mean phase coherence (ρ) Average mutual information (I) Wavelet lag regression
WTC, ρ, I :Basic Ideas WTC phase angle shows the relative phase of the two time series as a function of period and time. Mean phase coherence is a measure of the synchronization of the phase angle difference between the series Mutual information can be interpreted as the difference between the uncertainty of x and the remaining uncertainty of x after observing y. In other words, it is the reduction in uncertainty of x gained by observing y. Here x and y are the phases of the timeseries
The methods we use rely on filtering the data using the Continuous Wavelet Transform. • A wavelet is effectively a band-pass filter. • We stretch the wavelet in time, thus varying its ‘scale’ and characteristic period of the filter.
0 ( )
1 / 4 i0
e
e
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Useful for the wavelet coherence as scales are similar sizes in period and time
2m i m ! 0 ( ) (1 i ) ( m1) (2m)! Useful for broad-band filtering. (AMI, phase coherence and wavelet lag regression tests.) ω0 is dimensionless frequency and η is dimensionless time, and m is the order, here set = 4
The CWT of a time series X, {xn, n=1,…,N} with uniform time steps δt, is defined as the convolution of xn with the scaled and normalized wavelet.
W ( s) X n
t s
N
t x n n n 0 s n1
The complex argument of WXn(s) can be interpreted as the instantaneous phases of X: {φ1…, φn}
Wavelet Coherence •
,
WTC is a measure of the intensity of the covariance of the two series, X and Y in time-frequency space, unlike the cross-wavelet power which is a measure of the common power.
Coherence
R ( s, t ) 2
1
S s WXY (s, t )
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S s 1 WX (s, t ) S s 1 WY (s, t ) 2
2
where S is a smoothing operator
we use Monte Carlo methods with red noise to determine the 5% statistical significance level of the coherence. The 5% statistical significance level of the coherence seems to be constant (0.78) across all scales except where Sscale is influenced by domain boundaries
Mean Phase Coherence, ρ 6
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1 cos(t t ) sin(t t ) N t 1 t 1 N
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ρ(φ,θ) is a measure of ‘how constant’ the instantaneous phase difference φ-θ is.
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We will search for the optimum relative lag Δ between the two series by finding the Δ which maximizes the phase coherence ρ(φ,θ) or the AMI I(φ,θ).
Results
Wavelet Coherence QBO-AO links
Although the QBO and the Arctic Oscillation both have significant power at the biannual period, the coherence shows no relationship between the two series, and they are not simply related.
Verification: Wavelet Coherence
Squared wavelet coherence between the standardized AO and Maximum extent of sea ice in the Baltic Sea (BMI) time series. The 5% significance level against red noise is shown as a thick contour. All significant sections show anti-phase behavior. Grinsted, Moore & Jevrejeva Nonlinear Processes in Geophysics (2004) 11: 561–566
Average Mutual Information, I Mean phase coherence, ρ I ρ
The peak in AMI and relative phase strength suggests a 3 month delay between SOI an Nino3.4. That is atmosphere drives sea surface temperatures – as expected.
Average Mutual Information, I Mean phase coherence, ρ ρ I
The linkage between the AO found by wavelet coherence is confirmed: note the peak in AMI around 2 years, the same phase delay as found earlier [Jevrejeva et al., GRL, 2004] for 14 year signals.
Average Mutual Information, I Mean phase coherence, ρ I ρ Paul wavelet filtered with centre frequency λ, As a function of the lag (Δ) between the series for a) SOI and Niño3, b) AO and SC, c) AO and Niño3,
d) SOI and SC and e) Niño3 and SC
Mean phase coherence, ρ between sunspot number and Sea Surface Temperatures
Black contour is 95% significance level against red noise
Global Sea Surface Temperatures (ERSSTv2), no phase lag
Transport of ENSO signals to the polar regions. 14 year signal transmitted by oceanic waves and stratosphere.
Correlation coefficient.
Phase angle
Maps of vector sum of SST correlated with the 13.9 year SOI cycle and with its quadrature, 95% significance is black line, and its relative phase angle (degrees). Jevrejeva, Moore and Grinsted, (2004), Geophys. Res. Lett.
X is red noise with a first order regressive coefficient of 0.8, mean of zero and unit variance, and series Y and equal to 5X plus white noise (zero mean, unit variance). X is then lagged by 4 time units relative to the Y, so that it our sense it Y leads and hence is causative of X.
Wavelet Lag Coherence - Example
Y = 1.9X + 0.61
Wavelet lag coherence plot showing values of mean phase coherence (ρ) and its 95% confidence interval.
Sensitivity, m, in the equation WY(λ,t+Δ) = m WX(λ,t).
Arrows point to the right at a lag of -4 indicating that is when X and Y are in phase at all λ.
The confidence interval shown is that for ρ, as this is where the values of m have true predictive value.
Value of m =5 at a lag of -4 for all λ.
No causative link between solar irradiance and tropical climate
This method examines all of lag-period space regression parameters.
Moore, Grinsted & Jevrejeva (2008), Evidence from Wavelet Lag Coherence for Negligible Solar Forcing of Climate at Multi-year and Decadal Periods, 20 Years of Nonlinear Dynamics in Geosciences, A. Tsonis & J.B. Elsner (Eds.), Springer.
Tide gauges Following Douglas 1993: • Only long records no data gaps • Geologically stable regions.
Figure credits: Robert A. Rohde / Global Warming Art
The PSMSL has more than a thousand Revised Local Reference (RLR) tide gauge records in its data base. It must be possible to make a better GSL reconstruction utilizing more of this data.
Regional Datacoverage
‘Virtual station’ Stacking: Minimizing spatial bias wpacific
• Stations close to each other should be weighted less than isolated stations.
height = 14
Binomial tree to illustrate the ‘virtual station’ stacking method. Top-node represents the regional average, bottom nodes the tide gauge records, and rest of nodes are virtual stations.
Our GSL reconstruction Published in JGR oceans 2006: Jevrejeva, et al, “Nonlinear trends and multiyear cycles in sea level records”
A recent acceleration?
Time series of sea level with linear trends Observed Sea Level GSL MSL+TSL
MSL TSL
Melting of Greenland Antarctica & glaciers
Thermosteric hydrographic data
Unexplained residuals (GSLTSL-MSL) = 0.41 mm/yr Jevrejeva et al., J.Geophys. Res., 2008
24 long duration tide gauge stations from Douglas, 1997 Idea that sea level cycles record global heat content on 11-year scales is valid IF sea level rise is dominated by thermosteric effect Of course warming also melts ice on land raing sea level, but at time scales >> 11 years
Shaviv, 2008
48 month smoothed data
Virtual station gsl curve using all data in all months: >1000 stations Note larger error bars in 19th century due to stations being located only in Europe and N. America
Results: Seems to be large significant region of causality But mainly that gsl drives TSI (!)
Similar for Lean or S&K TSI
However....
TSI (Lean) spectra vs AR1
An AR1 realization
AR1 and TSI(Lean)
Red or white noise is very poor representation of TSI
An FFT realization Better not to assume a noise background but take it from randomizing phase in FFT
No significant region when using a better noise model for significance tests
Conclusions • No simple causative relationship between sunspot numbers and multi-year to decadal signals in the large circulation systems that define in large planet’s climate. • Even weak indirect links seem to be ruled out as the methods do detect the 5% variance 14 year period signal easily • When testing significance of quasimonochromatic signals (e.g. Sunspot number), appropriate noise models must be used
Inferences • Non-linear, non-stationary system interrelationships should be investigated by phaseaware methods not simple correlations • The 11 year signal often found may be actually the significant 5.5-5.7 year signal detected in e.g. SST fields that is amplified by red noise processes – or alternatively becomes significant in inapproriate noise tests • The 13.9 year signal is strongly obsevered in both tropical and polar climate fields and may be mistaken for an 11 year period in short time series.
Acknowledgements • Financial support came from the Thule Institute and the Academy of Finland.
Questions Please ??? No need to be shy Moore, Grinsted & Jevrejeva 2006, Is there evidence for sunspot forcing of climate at multi-year and decadal periods? Geophysi. Res. Lett. L17705, Moore, J. C., A. Grinsted, A., and S. Jevrejeva 2008, Gulf Stream and ENSO increasing the temperature sensitivity of Atlantic tropical cyclones, Journal of Climate 21 (7) 1523–1531.
Moore Grinsted & Jevrejeva (In Press), Evidence from John Moore eating porridge on Lomonosovfonna 2002. Photo: Björn Sjögren.
Wavelet Lag Coherence for Negligible Solar Forcing of Climate at Multi-year and Decadal Periods, 20 Years of Nonlinear Dynamics in Geosciences, A. Tsonis & J.B. Elsner (Eds.), Springer.
Using SSA to extract quasi-periodic signals. The original time series are resolved in components whose time evolution can be studied. NAO,AO SAT BMI AO BMI
Riga BMI BMI
E.g. these 95% level 8 year significant components show the increasing importance of the 14 year and QB components in the 14 Baltic region, and decline of year 4-5 year periods. QQ, QB
From Jevrejeva and Moore, Geophys. Res. Lett. 2001
How do oscillations look compared with global SST ?
The ERSSTv2 has monthly values of SST for each position (at 2o by 2o resolution) from 1854-present. I’m interrested in yearly anomalies. So for each point in the original dataset i subtract the mean for each month and do a yearly average.
So for each point of the globe i have a yearly timeseries with a SST anomaly.
I now look at each point on the globe to see if i can find the same 13yr cycle we found in SOI (i call that signal soi13).
In other words i find the correlation between the soi13 and the SST anomaly timeseries.
However, if the SST anomaly lags with 90 degrees the correlation coef would be zero. Therefore i look at both the correlation with soi13 and soi13 rotated 90 degrees (dsoi13/dt).
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Here’s what i actually do ... (This is almost my matlab code).
R1=corrcoef( soi13 , sstanomaly ); R2=corrcoef( dsoi13/dt , sstanomaly );
Strength of correlation: R=sqrt(sqr(R1)+sqr(R2));
Phase of correlation: phase=atan(R2,R1);
We further calculate the 95% significance level to be R>~.17 (and 99%: R>~.20) .... 95% level is shown in the figures as a black line...
Corrcoef 0.45 80
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Transport of ENSO signals to the polar regions. 14 year signal transmitted by oceanic waves and stratosphere, multiannual signals only via stratosphere.
Maps of vector sum of SST correlated with the 13.9 year SOI cycle and with its quadrature, 95% significance is delineated by the black line (a), and its relative phase angle (degrees) (b). From Jevrejeva, Moore and Grinsted, (2004), Geophys. Res. Lett.
