Journal of Environmental Protection, 2010, 1, 111-116
doi:10.4236/jep.2010.12014 Published Online June 2010 (http://www.SciRP.org/journal/jep)
Spectral Analysis of Solar Variability and their
Possible Role on the Global Warming
Mohamed Ali El-Borie1, Eman Shafik2, Aly Abdel-moneim Abdel-halim2, Shady Youssri El-Monier2
1Physics Department, Faculty of Science, Alexandria University, Alexandria, Egypt; 2Arab Academy for Science & Technology and
Maritime Transport, Alexandria, Egypt.
Received March 28th, 2010; revised April 25th, 2010; accepted April 29th, 2010.
ABSTRACT
Our understanding of the indirect effect of changes in solar output and feedbacks in the climate system is minimal.
There is much need to refine our understanding of key natural forcing mechanisms of the climate, including solar ir-
radiance changes, in order to reduce uncertainty in our projections of future climate change. Through the recent years,
the conflict between researchers about whether global warming is a human-generated phenomenon or a result of solar
variability has raised many question marks. The aim of this work is to try to answer some of these questions by studying
the possible role of some solar variability parameters such as the geomagnetic index (aa) and the sunspot number (Rz)
in global temperature changes. Here, we present a correlative study of the possible contributions for the two compo-
nents that may be closely associated with the climate, throughout the last 130 years (1880-2008). We compared the
correlation analysis and the power spectral density (PSD) of the Rz and aa with that of the continuous records of the
GT in order to get a closer look at a possible connection between them. Our results displayed that the correlations be-
tween both (aa & GST) and (Rz & GST) are +0.66 and +0.38, respectively when both parameters Rz and aa precedes
by 2-3 yrs. The correlation of GST-aa is two times higher than that of GST-Rz. The GST spectrum reflected significant
periods at 21.3-yr, 10.7-11.6 yr variations that observed in the considered geomagnetic and sunspot spectra.
Keywords: Global Rurface Temperature, Geomagnetic Indices, Solar Variability
1. Introduction
The debate concerning global warming has been the
concern of researchers for a long time. Global warming
is a term used to describe an increase over time of the
average temperature of the Earth’s atmosphere and
oceans. It plays an important role in the ongoing public
debate concerning global warming and the risk of
man-made climate change. Where the global surface
temperature has increased by factor 0.8 ℃± 0.02℃ is
observed in the last 150 yr [1]. Researchers have attrib-
uted the increase in global surface temperature to the rise
in greenhouse effect caused by the increase of carbon
dioxide emitted by man made [2], others attributed global
warming to the decrease of the sulfate aerosols. Climate
models, driven by estimates of increasing CO2 and to a
lesser extent by generally decreasing sulfate aerosols,
predict that temperatures will increase (with a range of
1.4 ℃to 5.8 ℃for the years between 1990 and 2100).
There are many other parameter that effect on the
global surface temperature similar solar activity. The
effect of solar cycle lengths upon global temperature
changes has also been the concern of researchers [3,4].
Other [5] demonstrated a strong correlation between so-
lar cycle lengths and Northern Hemisphere temperatures
over the period 1860-1990. Following studies [3-6] have
taken an update data of the same results.
Indices of geomagnetic disturbances measure the re-
sponse of energetic solar eruptions that actually affect the
Earth. Geomagnetic activity aa seems to be the possible
link through which the solar activity controls the Earth’s
climate [1,7]. Near-Earth variations in the solar wind,
measured by the aa geomagnetic activity index, have
displayed good correlations with global temperature [1].
Study of [8] found that the total magnetic flux, leaving
the Sun and driven by the solar wind, has risen by a fac-
tor 2.3 since 1901, leading to the global temperature has
increased by 0.5℃. In addition, the solar energetic erup-
tions, which dragged out or/and organized by the ob-
served variations in the solar wind, are closely correlated
with the near-Earth environment [9,10].

Spectral Analysis of Solar Variability and Their Possible Role on the Global Warming
112
After work of [4], they found that the approximately
1.1℃ increase in global mean temperature since 1877 is
unlikely to be entirely a product of internal climate vari-
ability. Nearly 40% of the variation in global surface
temperature could be accommodated by concurrent al-
terations in geomagnetic aa and solar activity indices.
Climate commitment studies predicted even if levels of
greenhouse gases and solar parameters are to remain
constant, the global climate is committed to 0.5℃ of
warming over the next one hundred years due to the lag
in warming caused by the oceans. There are many other
parameters expel from Sun which have a high effect to
changes in the global surface temperature as the ultra-
violet radiation affect the ozone in the upper atmosphere,
as well as the solar modulation effect on cosmic rays
which in turn may affect the cloud cover and in turn lead
temperature changes [11].
In the present work, we investigate the possibility role
of some solar indices on climatic variable represented by
changes of global surface temperature. Indices of solar
disturbance measure the near-Earth variations in the solar
wind, have been studied. Here, we present a correlative
study of the possible contributions for the two compo-
nents that may be closely associated with the climate,
throughout the last 128 years (1880-2008). The two pa-
rameters are geomagnetic activity aa and the sunspots
number Rz.
2. Data and Analysis
The yearly of GT, aa, and Rz for the period 1880-2008
have been used in the present work. Data for the global
surface temperature over the period 1880-2008 are avail-
able (http://data.giss.nasa.gov/gistemp/tabledata/GLB.Ts.
txt). In addition, the sunspot numbers Rz were provided
via the National Geophysics and Solar Terrestrial Data
Center (http://www.ngdc.noaa.gov/stp/GEOMAG/aastar.
shtml), as well as the geomagnetics aa were taken from
the (http://www.wdcb.rssi.ru/stp/data/geomagni.ind/aa/aa/
AA_MONTH). Linear regression has been used to de-
termine the degree of similarity between two signals with
zero lag. If the signals are identical, then the correlation
coefficient is 1; if they are totally different, the correla-
tion coefficient is 0, and if the phase is shifted by exactly
180º, then the correlation coefficient is –1. Secondly, the
running cross-correlation was applied to find the similar-
ity between two signals with lag time (τ). Thirdly, a se-
ries of power spectral density (PSD) have been per-
formed to yield the power spectral density (PSD). The
results were smoothed using the Hanning window func-
tion. This is necessary since most of the disturbed fea-
tures will completely disappear, while the significant
peaks are clearly defined. Nevertheless, the particular
window chosen dose not shifts the positions of the spec-
tral peaks. Next, each spectrum is independently normal-
ized to the largest peak in the complete spectrum. This
restriction was chosen in order to avoid spurious
strengths often associated with peaks near the start and
end of the data set. This normalization dose not intro-
duces any errors into our identification of the peaks be-
cause it changes only the relative amplitude and not the
position of the peak spectrum.
3. Results and Discussion
The Sun expels several products of its activity to the inter-
planetary medium, namely electromagnetic radiation, ener-
getic particles, solar wind and transient ejecta with a frozen
in magnetic field. The solar radiation is the fundamental
source of energy that drives the Earth’s climate and sus-
tains life. The variability of this output certainly affects our
planet. The solar wind is pumped up with intense magnetic
fields that extend far out into interplanetary space, blocking
more cosmic rays that would be arrived the Earth. The
resulting decrease in cosmic rays mean that fewer energetic
particles penetrate to lower atmosphere where there may
help produce cloud, particularly at higher latitudes where
the shielding by Earth’s magnetic field is less. The reduc-
tion of clouds that reflect sunlight, would explain why the
global surface temperature gets hotter when the Sun is
more active. Also, the variability in ultraviolet radiation
expels from the Sun affects the ozone in the upper atmos-
phere and thus may lead to a temperature change. Thus,
solar variability provides a reasonable match to the detailed
ups and downs of the temperature record [12]. The longest
historical record of the solar variability is the sunspot num-
ber. It is the number of the dark spot that appear in photo-
sphere and it reflects the magnetic activity of the Sun. Fol-
lowing, the aa index, the time series characterizing the
geomagnetic activity disturbances, provides the longest
data set of solar proxies which goes back to 1868 [13]. The
role of geomagnetic activity in the climate change became
a topic theme of many recent studies. Close relations during
the last 60 years were found between the geomagnetic ac-
tivity and surface air temperature [14].
Figure 1 shows the 5-year running averages of annual
global surface temperature (GST), geomagnetic indices
(aa) and sunspot number (Rz). Plot 1a shows the varia-
tion of the global surface with time series from 1880-
2008. The considered period has been divided into three
sub-periods. The first (1880-1940) named as the first
warming period in which we can see that the annual
mean temperature showed a sustained warming of about
+0.36℃ (+0.06℃/decade). A second period (1940-1970)
called global cooling period where there was a cooling of
about –0.13℃ (~ –0.04℃/decade). The third period is
the second warming period (1970-2008) which we can
see that the annual mean temperature showed a sustained
warming of about +0.76℃ (+0.19℃/decade). The in-
crease in GST for the recent year (1970-2008) was faster
and smoother than the first period (1880-1940).
Plot 1b (solid line) shows the cyclic variation for geo-
magnetic activity aa, where it has an increasing trend in

Spectral Analysis of Solar Variability and Their Possible Role on the Global Warming 113
(a)
(b)
Figure 1. Yearly variations of GST, aa, and Rz with time series (1880-2008)
both minima and maxima of solar cycles. In some cycle
the geomagnetics activity aa have two peaks structure
(double peaked modulations), the first peak near the
maxima of solar activity period and the other in de-
scending phase [7,15,16]. It is believed that the first peak
is caused by coronal mass ejections, whereas the second
peak is caused by geomagnetic disturbances due to the
coronal-hole fast streams, which are more frequent in this
part of each solar cycle [17]. Dashed line shows the cy-
clic variation for sunspot number Rz, where it has an ir-
regular variation in both minima and maxima.
3.1 Cross Correlation
Figure 2 shows a strong correlation between the solar
activity and geomagnetic activity after 1-2 yrs lag time,
the correlation coefficient between them is r ~ +0.8. Re-
gression analyses have carried out between the consid-
ered parameters (GT-Rz and GT-aa). Figure 3 shows the
scatter plots of the 5-year means of the global tempera-
ture with the geomagnetic activity aa (solid line) and the
sunspot number Rz (dashed line). The straight line fit
indicates correlation between Rz and GST with magni-
tude +0.33, indicating that any change in Rz may lead to
a remarkable effect to change of the GST. On other hand,
the straight-line fit has indicated a good correlation be-
tween geomagnetic activity and GST, the correlation co-
efficient is = 0.64, indicating that any change in aa may
be led to a change in GST. Previous work [18] displayed
that the geomagnetic activity aa have a high effect to
change GST with lag time of 5-7 years.

Spectral Analysis of Solar Variability and Their Possible Role on the Global Warming
114
aa & Rz
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
-10 -50510
correlation
lag (Years)
Figure 2. Running cross-correlation (based on the annual
averages between the aa and Rz)
In order to find a causative parameter in solar variabil-
ity that may be responsible for the observed climatic
change, the running cross-correlation was applied in
Figure 4 for aa-GT (solid line) and Rz-GT (dashed line).
The 12-year lag time (τ) has been considered. For these
correlations, τ is the lag, usually recommended to be of
maximum 30% of the data length. Both curves showed
similar short term variations and seemed to be on the
increase after with short lag time. At zero time, positive
correlations were obtained between aa & GST of +0.64
and between Rz & GST equal +0.33. The highest correla-
tion coefficients appear between both (aa & GST) and
(Rz & GST) to reach +0.66 and +0.38 respectively when
both parameters Rz and aa precedes by 2-3 yrs. It’s ob-
vious that the correlation coefficient for the GST and
aa is approximately two times higher than the correla-
tions for GST and Rz. These results are consistent with
previous study [14], which showed the same result.
3.2 Power Spectrum Density
To assess the solar climate link it is important to know
the periodicities involved and their possible interactions
with climate. A series of power spectral density (PSD)
have been performed for the 5-year running averages
(1880-2008). The results were smoothed using the Han-
ning window function and each spectrum is independ-
ently normalized to the largest peak in the complete spec-
trum. The power spectrum density is calculated for the
wide range of frequencies (3.9 × 10-2-0.5 c/y), which
corresponding to a range from 2 to 25.6 years.
Figure 5 shows the spectral analysis of global surface
temperature (GST), geomagnetic indices (aa) and sunspot
number (Rz). Plots show that there are no significant
peaks observed in the high-frequency region correspond-
ing to the period from ~ 2-4.7 yr. A flat spectrum for the
short-term fluctuations is observed. At the selected fre-
quencies (> 5 yr) the spectral density is high and it shows
significant variations frequency. Table 1 shows the sig-
nificant peak for global surface temperature (GST), geo-
magnetic indices (aa) and sunspot number (Rz) with the
confidence levels.
Significant peaks are observed (plot 5a) for GST at
21.3, 14.2, 11.6, 9.1, 7.5 and 6.4 yr, while plot 5b of aa
displayed peaks at wavelengths 21.3, 14.2, 10.7, 9.14 and
7.5. Furthermore, the significant peaks for sunspot num-
Figure 3. Scatter plot of 5-year nunning averages of GST with aa (solid line) and Rz (dashed lime) the correlation values are
noted

Spectral Analysis of Solar Variability and Their Possible Role on the Global Warming115
aa & GST (solid line)
Rz & GST (dashed line)
0
0. 1
0. 2
0. 3
0. 4
0. 5
0. 6
0. 7
-15 -10-5051015
Lag (Years)
Correl ation
Figure 4. Running cross-correlation (based on the annual
averages) between the GST with (solid line) and Rz (dashed
line)
Table 1. The significant peak for aa, Rz, and GST with con-
fidence level (90%, 95%, and 99%)
Main Period existence significant
Period/Year
Aa(%) Rz(%) GST(%)
5.3-6.4 +< 95 +< 95
7.5-8 +< 99 +< 95 +< 99
9.1 +< 99 +< 99
10.7 +< 99 +< 99 +< 99
14.2-16 +< 99
21.3 +< 99 +< 99 +< 99
Figure 5. The power spectrum density (based on the annual averages) for GT, aa, Rz. The PSD of each Parameter is normal-
ized to maximum peak
ber at 21.3, 10.7 and 8 yr. In plot 5b, the geomagnetics
aa spectrum displayed a remarkable peak at 10.7 yr with
higher amplitude, this peak was found in Rz spectrum.
There are a similar fluctuations of 21.3, 10.7-11.6, 9.1,
7.5 between aa and GST. Also, other similar peaks 21.3,
10.7, 8-9.1 are appeared between Rz & GST. The spec-
trum of GST showed peak of 21.3 yr that related to the
solar magnetic cycle polarity (Hale cycle). The 21.3 was
observed in aa spectrum with large significant magnitude
rather than Rz spectrum, in this concern one can say that
aa is more effective on global surface temperature than
solar activity. Finally the global surface temperature are
strongly sensitive to the 21.3-yr, 10.7-11.6 yr variations
that observed in the considered geomagnetic and sunspot
spectra.
4. Conclusions
The aim of this paper is to find out the relation in the
long time (1880-2008) between changer of global surface
temperature (GST), and solar-geomagnetic activist repre-
sented by sunspot number (Rz) and geomagnetic indices
(aa), and to what degree they are connected.
1) Regression analysis revealed that the correlation co-
efficient between geomagnetic activity (aa) and fluctua-
tion of (GST) is = 0.64, while the correlation between Rz
and (GST) is = 0.33 at zero lag.
2) The running correlation analysis displayed that the
higher correlations between aa and GST is r = 0.66, and
between Rz and GST is r = 0.34 at time lag of 2-3 yrs.
The correlation of aa-GST is near two times higher than
that of Rz-GST.
3) Results of spectral analysis revealed strong 21.3 yr
peak in GST than the 11.6 yr peak. It is related to the
changes in the polarity of main solar magnetic field. The
interplanetary magnetic field (IMF) effect is more pow-
ered on GST than the solar activity cycle. Significant
peak at 10.7 yr are appear in both aa and Rz series which
is the most established cycle of solar activity.
4) We also found that 21.3 year peak in aa series is
larger than the same peak in Rz series this indicate the
geomagnetic activity predominate over the solar activity
in GST.
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