Solar influence
Solar activity and global
Does the Sun alone control the temperature of Earth? Rasmus E Benestad
presents data that show the extent of the solar influence on our climate.
T
heories about sunspots influencing
Earth’s climate can be traced about 200
years back in time to the astronomer
William Herschel, who suggested that there
was a correlation between wheat prices and
sunspots (Herschel 1801). Most of these
sunspot theories have been based on statistical
relationships, although the occurrence of the
ice ages seen in reconstructed temperature
records suggest preferred timescales of around
22 000, 41 000 and 100 000 years which may
be connected to variations in Earth’s axial precession, obliquity of the ecliptic, and Earth’s
eccentricity respectively (Peixoto 1992) and
hence variations in incoming solar radiation.
A physical explanation for how small variations in the solar energy output (0.1%) can
cause such large fluctuations in temperature as
observed on Earth has until recently been elusive. Svensmark (1998) proposed that the solar
activity modulates the galactic cosmic-ray
(GCR) flux into Earth’s atmosphere and that
this flux in turn affects Earth’s cloud cover by
changing the aerosol chemistry or influencing
the transition from the vapour to liquid phase
of water. Variations in the planetary cloud
cover may have profound effects on global surface temperature. One conclusion of Svensmark’s paper was that nearly all of the terrestrial warming between 1975 and 1989 may be
due to this GCR mechanism, which may imply
that the contribution from anthropogenic
sources, such as an increase in greenhouse gas
concentrations, was insignificant.
As early as in 1896, Swedish physicist Arrhenius proposed that the presence of atmospheric
greenhouse gases may result in warmer surface
temperatures on Earth than a simple radiative
balance would imply. A comparison between
measured surface temperatures and estimated
effective temperatures (assuming the planets
behave like black bodies and are at radiational
equilibrium) of the planets in our solar system
has later revealed that planets with thick atmospheres, such as Venus and Earth, have a
warmer surface than a simple radiation equilibrium can explain (Houghton 1991). The high
surface temperature can be attributed to the
greenhouse effect proposed by Arrhenius,
whereby the atmosphere absorbs the long-wave
radiation. Since the industrial revolution,
human activity has resulted in an increase in the
concentrations of atmospheric greenhouse
gases such as CO2, and most of the global
3.14
warming since 1860 has traditionally been
attributed to the greenhouse effect (IPCC 1990).
The sunspot counts described here are observations made according to a standard set by
the Swiss astronomer Johann Rudolph Wolf in
1848 for daily measurements of the sunspot
number (see box, “Data and methods”). The
method for obtaining the sunspot count
involves the addition of the total number of
sunspots and the number of groups into which
these spots cluster multiplied by 10. The daily
sunspot estimate is a weighted average of
observations made from a network of cooperating observatories, where each observation
may vary due to different interpretations of
sunspot groups, atmospheric disturbances, and
the Sun’s rotation. The sea-surface temperatures (SSTs) were obtained from the UK Meteorological Office (GISST2.2) and were based
on historical ship observations. The SSTs have
been corrected for biases associated with different bucket types and quality controlled. The
global mean surface temperatures were
obtained from the Climate Research Unit at
University of East Anglia and included both
land and sea-surface temperatures.
Hypothesis
Although there can be little doubt that variations in solar activity have some influence on
Earth’s climate (Friis-Christensen 1991, Reid
1987, Wigley 1998, Lassen 1995, Lean 1998),
there are many aspects of the solar hypothesis
that need clarification. One important question
which will be discussed here is how much of
Earth’s climate variability can be accounted for
by variations in solar activity. Svensmark
(1998) proposed that nearly all of the increase
in the global mean temperature between 1975
and 1989 was due to changes in solar activity.
This hypothesis is re-examined here, both in
terms of long-term warming and decadal variability, by rephrasing it as two simpler
hypotheses that are more easily tested:
1. Fluctuations in global temperatures are predominantly caused by variations in solar activity.
2. The recent long-term global-warming trend is
mainly due to slow changes in solar activity.
The time series were separated into a part
showing a linear trend and the rest – called the
de-trended series – prior to the analysis. All the
time series discussed here had zero mean value.
Regression analysis aims to minimize the RMS
errors between two data series, and as a
hypothesis proposing that
variations in the Sun’s activity
can account for most of the recent
global warming on Earth has received
some attention. Friis-Christensen and
Lassen suggested that the level of
solar activity is manifested in the
length of the sunspot cycle (FriisChristensen and Lassen 1991, Reid
1987). They found an apparent match
between sunspot cycle length and
the northern hemispheric
temperatures on Earth. Here, the
relationships between sunspot cycle
length and global mean land and seasurface temperatures are objectively
re-examined in order to quantify the
relationship between global mean
terrestrial temperatures and solar
activity. A significant correlation
between sunspot cycle length and
terrestrial global mean temperatures
is found. However, the results of this
study do not support the claim that
most of the recent warming is due to
the Sun’s activity. Global mean land
and sea-surface temperatures are
reconstructed using sunspot cycle
length estimated from 1760 to 1994.
A
consequence will always find a trend which
gives the optimal RMS fit between the two
curves. Such a best-fit trend may not necessarily represent a physical link, but may just as
well be due to coincidence and can therefore
lead to invalid conclusions. In this case, it was
crucial to remove linear trends before regressional analysis, as the purpose of this study
was to resolve the issue of how much of the
recent observed warming can be accounted for
by variations in solar activity. If there is a real
(and linear) relationship between the two
quantities, then a regression model based on
the de-trended series should also capture the
relationship between their respective trends.
In simple mathematical terms, the time series
can be expressed as the sum of a de-trended part
and a linear trend: x(t) = xd(t) + xt(t), where xtt
June 1999 Vol 40
Solar influence
sea-surface temperatures
The Sun affects our climate, but how and how much?
(Courtesy of SOHO/EIT consortium. SOHO is a project of
international cooperation between ESA and NASA.)
describes the linear trend in x(t) and xd(t) is the
de-trended part with no linear trend. Hence the
linear model y(t) = ax(t) implies that
yd(t) + yt(t) = a(xd(t) + xt(t)) and that the coefficient a is the same for the de-trended records
and the linear trends. Experiments with regression on time series with and without trends gave
significantly different results. The presence of a
linear trend in the two data sets gave a good fit
between the two curves, but regression with detrended series did not produce such a good
match. Correlation analysis on time series with
non-zero trends may also give a higher (anti)correlation than similar analysis on de-trended
data. The close fit between the short sunspot
cycle lengths and global mean temperature
record in Friis-Christensen and Lassen’s paper
(1991) may have been artificially enhanced by
June 1999 Vol 40
the presence of a trend in both data series.
The results
Although the sunspot cycle lengths (SSCLs)
were correlated with the global mean SST, they
could not account for all SST variability, as
only 38% of the global SST variability could
be reproduced by the SSCL regression model
(shown in figure 1).
The correlation between global mean SST
predictions based on sunspot counts (SSCs)
and the observed global mean SSTs was statistically insignificant according to a simple
(Monte-Carlo) resampling test. The regression
coefficient for the SSC model was 0.01 and the
prediction could only account for 4% of the
global mean SST variance (not shown).
The linear trend of the reconstructed global
mean SST described a warming which was less
than 0.1 °C since 1903 (figure 2). The global
mean SSTs, on the other hand, indicated a
warming of about 0.25 °C over the same period, although a rapid warming of 0.4 °C took
place after the mid-1970s. Only about a third of
the recent long-term SST increase could therefore be attributed to variations in solar activity.
The modelled global mean temperatures
warmed by less than 0.1 °C from 1860 to
1984, whereas the increase in the observed
global mean temperature was about 0.5 °C.
These results suggest that the long-term variations in solar activity can only account for a
maximum of 20% of the recent global warming. Since 1980, the reconstructed global mean
temperatures dropped, in contrast to the observations which indicated a continual warming.
3.15
Solar influence
14
r = 0.58 (95% conf = 0.47)
0.3
13
global mean SST
sun spot cycle length (years)
prediction
0.2
global mean temperature
SSCL
12
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11
0.1
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+
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+
+
+
+
+
0
+
10
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°C
+
–0.1
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9
–0.2
B = –0.0856 +– 0.0060 Var = 38.1% window length: 61 months
8
1902
1912
1922
1932
1942
1952
time
1962
1972
1982
1992
1 The plot shows the 61-month, low-pass filtered and de-trended global mean SST (red line with
circles), global mean temperatures (green line), predicted global mean SST from a cross-validation
analysis, using a regression model based on SSCL (orange line with crosses), SSCL (blue line), and
global mean temperatures (green line). The global mean SST predictions, based on a linear regression
with SSCL, could account for 39% of the (low-pass filtered) observations. The correlation coefficient
between the predicted series and the global mean SSTs was 0.58, which was statistically significant
above the 95% confidence level. The regression coefficient, B, was negative, in agreement with the
Svensmark hypothesis. All curves have been de-trended and the SSCLs shown here were estimated
by the min-min-max-max method.
The solar model produced smaller amplitudes in global mean SST and global mean
temperatures after 1860 compared to the
1760–1860 period. This non-stationary behaviour may either be a result of errors in the
sunspot record, caused by limitations of the
solar model (the solar–terrestrial link may for
instance be non-stationary or the solar–terrestrial relationship may be nonlinear), or suggest
that the variability in the global temperatures
really was stronger in the earlier period. There
was no significant linear trend in the reconstructed records from 1760 to 1990 due to the
presence of two large peaks at the beginning of
the reconstructions and at around 1830. It is
interesting to note a correspondence between
warm anomalies in the Central England Temperature (CET) and the reconstructed global
mean SSTs, although the CET peak in 1830
lead the predictions by a few years. These
results may suggest that some of the past climate variability could have been influenced by
variations in solar activity.
Discussion and conclusions
In
3.16
summary,
a
statistically
significant
correlation between global mean SST and the
length of the sunspot cycle was found. These
results therefore support the hypothesis of a
solar influence on Earth’s climate, as proposed
by Svensmark. However, this analysis did not
suggest that Earth’s climate was predominantly forced by variations in solar activity as
Svensmark suggested. Less than 40% of the
global mean SST variability can be accounted
for by changes in the solar activity over the
1907–1985 period, not taking into account the
high frequency variability and the linear trend
for the same period. Hypothesis 1 must therefore be rephrased: variations in solar activity
have some influence on Earth’s climate. The
number of sunspots, on the other hand,
appeared to have little significance for Earth’s
global mean temperatures.
The implications of these results are that part
of the terrestrial climate variability may have
explanations other than being directly related to
solar forcing. The planetary cloud cover may for
instance vary due to internal changes in the
atmosphere, and may in turn alter the planetary
albedo and hence the global mean temperatures.
It is also possible that changes in atmospheric
chemical composition, aerosol concentration,
the biosphere, Earth’s landscape (Couzin 1999),
surface processes, cryosphere (snow and ice
cover), and the ocean surface may have affected
the global mean temperatures.
The fact that our linear regression model did
explain 35–40% of the de-trended global mean
temperature variability in a cross-validation
analysis nevertheless indicates that the model
could be used to describe the solar–terrestrial
climate link proposed by Friis-Christensen and
Lassen. The contribution of long-term changes
in the Sun to the long-term global warming on
Earth could be assessed by applying the same
model to an SSCL record that also included the
long-term solar variations.
The results obtained here are inconsistent
with the proposition made by Svensmark that
most of the recent global warming is due to
long-term variation in solar activity. Little of
the warming since 1960 was captured by the
predictions based on solar activity, and
hypothesis 2 can therefore be rejected.
Svensmark’s conclusion (Svensmark 1998)
about the Sun accounting for 0.3–0.5 °C temperature rise between 1975 and 1989 was
based on the assumptions that a 3% reduction
in the global cloud cover between 1987 and
1990 was entirely due to a decrease in the cosmic-ray flux, the rise in the global temperatures was entirely due to a reduction in the
global cloud cover, and that the global temperature sensitivity to solar forcing is 0.7 to
1 °C/W m–2. Svenmark’s analysis was based on
a composite cloud coverage from four satellite
missions, all of which excluded continental
regions and only covered part of the globe.
Two of the satellites’ observations did not
include the tropics, and hence regional satellite
observations were assumed to be representative of the planetary cloud cover. The cloudcover record was furthermore short and there
was an unexplained jump in the cloud cover
index in 1993.
Internal variability in the climate system was
neglected, and the Svensmark hypothesis also
assumed that the cosmic-ray measurements
from Climax, Colorado, and Cheltenham/Fredericksburg/Yakutsk were representative of the
global mean cosmic-ray flux. The 11-year average of the Climax and Yakutsk measurements
showed opposite trends after 1987 (Svensmark
1998), which puts a question mark over this
last assumption. The disagreement between the
results from this study and those of Svensmark’s, suggest that the assumptions on which
hypothesis 2 is based were unjustified. FriisChristensen and Lassen (1991) estimated the
long-term change in the solar constant to be
1%, based on the observed change in the solar
cycle length between 1968 and 1978. If their
method for estimating SSCL gave typical errors
of 4–5 months (Mursula and Ulich 1998) then
June 1999 Vol 40
Solar influence
The solar data were based on monthly mean
sunspot counts obtained from the National
Geophysical Data Center’s Internet site
(Waldmeier 1961) in the USA, which were
low-pass filtered using a 37-month, sliding
Gaussian window to smooth the time series
before identifying sunspot maxima and minima, and the end points were removed. The
true sunspot cycle lengths (SSCLs) are difficult to compute (Mursula and Ulich 1998),
and two different methods were therefore
employed here to compute the SSCLs. The
first method (hereafter referred to as the
“min-min-max-max” method) was based on
estimating SSCL empirically from the time
between successive peaks (max-max) and successive minima respectively (min-min). Mursula and Ulich (1998) argued that both the
min-min and max-max methods are associated with typical errors of 4–5 months. The
SSCLs were therefore also computed using
the Median method proposed by Mursula
and Ulich. The choice of SSCL calculation
method did not matter for the conclusions of
this study. For both methods, the SSCL values
were defined at the mid-point between the
two dates that were used for cycle-length esti-
this estimate is highly uncertain.
Further work is needed to identify which
physical mechanisms may be involved in the
relation between the length of the sunspot
cycle and the global temperatures on Earth.
The next step may be to represent this solar
forcing in General Circulation Models (GCMs)
that describe Earth’s climate. ●
mation. The min-min-max-max method
therefore gave two SSCL estimates for every
sunspot cycle, whereas the Median method
only yielded half as many data points. Since
the SSCL estimates were distributed unevenly
in time, no filtering was applied to the SSCL
record as this would introduce a variable filter window length emphasizing larger values
of SSCL.
The SSTs were obtained from the GISST2.2
data set (Rayner 1996), provided by the UK
Meteorological Office, and covered the period from 1903 to 1994. The global mean SSTs
were estimated according to:
∑iδAiTi
T ∑iδAi
The Central England Temperature (CET)
record was obtained from the Hadley Centre
Data Internet site (Manley 1974, Parker
1992), and the global mean temperatures
were obtained from the Climate Research
Unit at the University of East Anglia (Jones
1994, Parker 1994). The latter record included both temperatures over oceans as well as
land and dated back to 1856. The CET
observations started in 1659 and were used
as a crude proxy in this study for the early
global temperatures when no other data were
available.
Since the estimates of the sunspot cycle
length is a measure of the average solar intensity over the solar cycle, variations in solar
activity on shorter timescales were not
included in this analysis. A 61-month, lowpass Gaussian filter was applied to the global mean SSTs in order to remove highfrequency noise and emphasize the lowfrequency correlation. When the solar cycle
length was estimated twice during each solar
cycle, the effective time resolution of the
SSCL record corresponded to a half solar
cycle length, however, other window lengths
and filters were also tried and the main conclusions did not depend on window width or
filter type. The 61-month window length
yielded the highest correlation score and variance of all the trials with different window
lengths. Although the Median method gave
high correlation scores, the results were all
lower than the 95% significance level due to
the small number of data points. The analysis in this study was based on regression and
correlation, where the correlation scores and
root mean square errors were estimated from
a cross-validation analysis (Wilks 1995).
M = 0.0063 °C/decade. Window length: 61 months
temperature (°C)
Data and methods
reconstruction
0.4
0.2
0
–0.2
global mean SST
–0.4
CET
Rasmus E Benestad, Klimaavdelingen, Det Norske
Meterologiske Institutt, PO Box 43, 0313 Oslo,
Norway.
1807
1779
1834
1861
1889
time
1916
1943
1971
1998
June 1999 Vol 40
temperature (°C)
M2 = 0.0047 °C/decade. Window length: 61 months
References
Arrhenius 1896 Philosopical Magazine and Journal of Science
236–276.
Couzin J 1999 Science 283 317–319.
Friis-Christensen E and Lassen K 1991 Science 254 698.
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835–845.
Manley G 1974 Q. J. Royal Met. Soc. 100 389–405.
Mursula K and Ulich T 1998 Geoph. Res Let. 25 1837–1840.
Parker D E et al. 1992 Int. J Climatology 12 317–342.
Parker D E et al. 1994 JGR 99 14 373–14 399.
Rayner N A et al. 1996 Version 2.2 of the global sea-ice and sea
surface temperature data set, 1903–1994. Climate Research
Technical Note 74 Hadley Centre, Meteorological Office, Bracknell.
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Svensmark H 1998 Phys. Rev. Let. 81(22) 5027–5030.
Waldmeier M 1961 The sunspot-activity in the years 1610–1960
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Wigley T M L et al. 1998 Science 282 1676–1679.
Wilks D S 1995 Statistical Methods in the Atmospheric Sciences
Academic Press, Orlando, Florida, USA.
0.4
reconstruction
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0
–0.2
–0.4
global mean temperature
CET
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time
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1971
1998
2 The reconstruction of global mean SST (upper panel) and global temperatures (lower panel) from
1760 to 1990 using a regression model based on both SSC and SSCL. The regression models were
calibrated using de-trended SSC, SSCL, and global mean SST (temperature) records. The trends were
then added back to the SSC and SSCL records before these were used to reconstruct the global mean
SST (temperatures). Also shown are the CET (orange line), global mean SSTs and temperatures (green
line), and the estimated linear trends from 1903 (1860) to 1990 (red line). The linear trends from 1870
described a 0.0110 °C per decade increase in the global mean SST and 0.0130 °C per decade global
mean warming. The SSCL shown here were estimated by the min-min-max-max method, and the
predictions shown here were made using ordinary linear regression analysis (no cross-validation).
3.17