On the Coherence between Dynamics of the World Fuel
Consumption and Global Temperature Anomaly
L.B. Klyashtorin & A.A. Lyubushin
VOLUME 14 No. 6 2003
MULTI-SCIENCE PUBLISHING CO. LTD.
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ON THE COHERENCE BETWEEN DYNAMICS OF THE
WORLD FUEL CONSUMPTION AND GLOBAL
Federal Institute for Fisheries and Oceanography (VNIRO), 107140 Moscow, Bolshaya
Krasnoselskaya, 17, Russia. e-mail: email@example.com
Institute of the Physics of the Earth, Russian Academy of Sciences, Moscow, Russia. 123995,
Moscow, Russia, Bolshaya Gruzinskaya, 10; e-mail: firstname.lastname@example.org
Analysis of the long-term dynamics of World Fuel Consumption (WFC) and the
Global Temperature anomaly (dT) for the last 140 years (1961-2000) shows that
unlike the monotonously and exponentially increasing WFC, the dynamics of
global dT against the background of a linear, age-long trend, undergo quasi-cyclic
fluctuations with about 60 a year period. No true linear correlation has taken place
between the dT and WFC dynamics in the last century.
Spectral analysis of reconstructed temperature for the last 1420 years and
instrumentally measured for the last 140 years global dT shows that dominant
period for its variations for the last 1000 years lies in the 50-60 years interval.
Modeling of roughly 60-years cyclic dT changes suggest that the observed
rise of dT will flatten in the next 5-10 years, and that we might expect a lowering
of dT by nearly 1-0.15°C to the end of the 2020s.
Keywords: global warming, fuel consumption, global climate variations, spectral
analysis, time-frequency analysis.
Development of the world energy status is directly attributed to the consumption of
fossil fuel (oil, gas, and coal). Resulting in the large-scale atmospheric emission of
carbon dioxide and some other so-called “greenhouse” gases, which are known to
hinder the Earth thermal irradiation to outer space, i.e., affect the normal temperature
balance on the planet. The infrared irradiation absorbed by the earth’s atmosphere is
believed to cause gradual increase in the surface air temperature at the global scale.
This phenomenon is known as “Global Warming” and has variable (mainly negative)
consequences (Schneider, 1990, 1992, IPPC, 1990, 1996, 2001).
774 Energy & Environment • Vol. 14, No. 6, 2003
The purpose of this work is to provide a comparative analysis of general dynamics
of Global temperature anomaly (dT) changes and World Fuel Consumption (WFC) for
the entire period of instrumental measurements (140 years, since 1861 to the present).
The main index of climate change on the global scale is the Global dT, time series
of measured instrumentally for the last 140 years. Annual values of Global dT are very
variable, and a reliable climatic trend can be revealed only after a considerable
smoothing of the time series.
We use time series of land and sea air surface Global temperature anomaly (dT)
from published sources (i.e. Bell et al., 2000, Lawrimor et al., 2001 and Jones et al.,
1999, 2001) (http://www.cru.uea.ac.uk)
World Fuel Consumption (WFC) for the period 1850-1996 expressed in “tons of
nominal fuel” taken from Makarov (1998) and update to 2000 – via personal
communication of author (Institute of Energetic Problems, Russian Academy of
Sciences). Time series of annual air surface temperature for the last 1420 years
reconstructed by analyzing heavy isotope of oxygen (O18) from Ice Cores of Greenland
Ice Sheet was kindly provided by Geophysical Isotope Laboratory University of
Copenhagen, Denmark through Dr. V.I. Nikolaev (Institute of Geography Russian
Academy of Sciences)
RESULTS AND DISCUSSION
Since the middle of the 19th century, the WFC curve exhibits roughly exponential
virtually permanent growth at a rate of about 2.3% per year, i.e., roughly doubling
every 30 years (Figure l). Total WFC in the middle of 19th century was as low as 550
million tons, and by the late 20th century this value increase by a factor of 25.
The dT curve has the age-long linear trend increasing by +0.059°C every 10 years.
By the end of 20th century, the global dT increased by 0.6-0.8°C compared to the early
20th century (Sonechkin, 1998). The WFC and global dT dynamics have two key
differences as follows:
1) The age-long increase in WFC is approximated by an exponent, while the agelong
increase in global dT exhibits a linear trend.
2) Unlike monotonously and exponentially increasing WFC, the dynamics of global
dT with the background of a linear, age-long trend undergoes quasi-cyclic
fluctuations with a period about 60 years. (Figure 1).
Each of the observed dT cycles could be divided in two 20-30-year phases of
ascending or descending smoothed dT curve. Relationship of dT and WFC dynamics
in each of these phases are presented in the Table.
On the Coherence between Dynamics of the World Fuel Consumption and Global Temperature Anomaly 775
Figure 1. Comparative dynamics of the World Fuel Consumption (WFC) and Global
Temperature Anomaly (dT) 1861–2000. Thin line – annual dT; Bold line –
13-years smoothing; Dashed line – WFC (mill. tons of nominal fuel).
Table. Correlation between Global dT and World Fuel Consumption (WFC) in
the different time phases of the 1860-2000s.
Phase of changing Period of Observation Correlation Coefficient .
Global dT (years) Between dT and WFC . ___________________________________________________________________________________________________________________
Ascending 1861-1875 +0.92 .
Descending 1875-1910 –0.71 .
Ascending 1910-1940 +0.28 .
Descending 1940-1975 –0.88 .
Ascending 1975-2000 +0.94 .
Descending (?) 2000-2030 ? .
Between 1861-1875, both WFC and dT exhibited simultaneous, well-correlated
growth. During 1875-1910, the dynamics of these indices were different. WFC
continues to grow, while global dT decreases, which reflects in negative correlation
between the indices. The next period, from 1910 to 1940, is of particular interest in
this context. For these 30 years WFC shows virtually no increase because of the global
economic crisis of 1920-30-s. However, dT in the same period increased by more than
0.4°. During the subsequent 35-years (1940-1975), WFC increased by a factor of 2.5
(from 3 to 7 billion tons.). For the same period, global dT did not increase, but
decreased roughly by 0.12°C and negative correlation between the WFC and dT
dynamics is characteristic of this time period.
776 Energy & Environment • Vol. 14, No. 6, 2003
In the recent 25-year period (1975-2000), in accordance with the ascending phase
of an alternate dT fluctuation (see Figure 1 and Table 1), a close positive correlation
takes place between the dynamics of WFC and dT.
Thus, on the background of monotonous increase in WFC during the last 140
years, global dT dynamics exhibited alternating 25-30-year periods of lowering or
raising (with the corresponding alternation of positive or negative correlation between
the WFC and dT trends).
What changes in the dynamics of WFC and Global dT can we expect in the near
future, between 2000-2030?
Proceeding from the hypothesis of cyclic dynamics of global dT with a period of
50-60 years, we assume that the current “increasing” phase started in 1975 reached its
maximum by 2000, then the gradual decrease in dT will start in the nearest few years
and continue up to the 2030s.
It should be mentioned that the 50-60-year period of the dT fluctuations has been
derived from the time series of the instrumentally measured temperatures for the last
140 years “by eye” (Figure 1). This time period includes only 2.5 roughly 60-year
cycles, and it is insufficient from an analytical perspective for a statistically rigorous
conclusion on the cyclic character of the fluctuations and analysis of much longer time
However, polar glaciers contain paleo-climatic information in the form of the
isotopic composition of the oxygen as described by deviation of the heavy oxygen
isotope O18 concentration in the ice from that of Standard Mean Ocean Water. The
most suitable location to perform global paleo-temperature reconstruction using this
method is the central region of the Greenland ice sheet, where the conditions for snow
and ice accumulation are believed to have remained stable over the last 2000 years.
(“Nowhere else in the world is it possible to find a better combination of a reasonable
high accumulation rate, simple ice flow pattern, high ice thickness and
meteorologically significant location close to the main track of North Atlantic
cyclones” (Dansgaard et al., 1975).
Ice drilling undertaken by the joint American-Danish-Swiss expedition in the
1970s resulted in obtaining intact ice cores to the depth of 404m. Average thickness of
the annual ice layers in this region of Greenland is about 30 cm, which made it
possible to reconstruct the annual average temperatures for the last 1500 years with
high accuracy. Reconstruction of temperature in the ice cores is based on the so-called
“isotopic effect”. Some proportion of water molecules are known to contain heavy
oxygen isotope O18 instead of “usual” O16. These molecules are about 9% heavier
compared to common molecules and evaporate somewhat slower. Therefore, the
proportion of heavy molecules in water vapor is lower than in oceanic water, but
increases as the temperature increases. Water evaporated from the vast surface of the
North Atlantic was transferred by the atmospheric streams into the Greenland region
where precipitated as snow and then turned into ice layers. Concentrations of heavy
isotopes O18 in the ice specimens can be determined with a high accuracy using the
The time series of instrumentally measured (1861-2000) and reconstructed (554-
1974) temperature overlap for 113 years giving us an opportunity to compare results of
reconstructed and instrumental data of temperature changes (Fig 2).
On the Coherence between Dynamics of the World Fuel Consumption and Global Temperature Anomaly 777
Figure 2. Comparative dynamics of instrumentally measured global temperature
anomaly (dT) and reconstructed (by O18 in Greenland Ice Cores) temperature
for period of 1861-1973 years. Dashed line – annual Global dT values; Bold
line – the same smoothed by 13-years averaging; Thin line – smoothed by 15
years averaging annual reconstructed temperature.
As one can see the smoothed temperature curves reconstructed from O18 Greenland
Ice Cores temperature and Global dT practically coincide, confirming that
reconstructed Ice Cores temperature series reflect similar series of Global dT very
The 10-years averaged temperatures reconstructed from the O18 concentration in
the Greenland ice cores and spectral characteristics of the corresponding time series
are presented in Figure 3(a.).
One can see that the relatively abrupt increase of global temperatures observed in
the early 20th century is not unique event. Similar and possibly even more distinct
temperature increases were observed in 500-900 years, the epoch of very mild climate
in Atlantic-European region when Norsemen colonized Iceland and Greenland.
(Dansgaard et al., 1975).
Figure 3. Reconstructed by O18 in Ice Cores temperature (a) and its power spectra (b)
a) thin line: 10-years smoothed annual Ice Core temperature. bold line: the
same smoothed 50 years moving window b) power spectra reconstructed
778 Energy & Environment • Vol. 14, No. 6, 2003
The estimate of the power spectra of the time series on Fig3(b) shows clear peaks
on periods 33, 42, 54 and 223 years. The spectral estimate was made for 10-years
averaged lime series of reconstructed temperature (having 144 samples) by Burg’s
method of maximum entropy with auto-regression order 20 (Marple (Jr.), 1987)
However this spectral estimate is static, obtained by information from all time
series at once and it is of special interest how this spectral maxima are distributed in
time. Results of analysis of temporal dynamics of reconstructed temperature by
Greenland Ice Cores are presented in Figure 4.
Figure 4. Temporal dynamics of the power spectra of temperature reconstructed from
Greenland Ice Cores for time period 553-1973 years AD. Power estimates
were obtained in the time window of the length 640 years. Decimal
logarithmic scale for power spectra is used.
We have taken sixty-four ten year time-window readings (representing 640 years),
and made spectral estimates of maximum entropy with AR-order 10. It should be
understood that the time marks on the diagram on Figure 4 correspond to right side of
To evaluate power spectra dynamics of in time, using a moving time-window, it is
noticed that the low-frequency rhythm with period about 200 years occurs at the initial
interval of time series only – between 550AD and 1400AD. Thereafter it disappears,
but in Figure 3(b) it is present as a peak with period 223 years. Further, from 1100 until
the late 1900s the spectral peak at a frequency of 50-60 years is dominant, and for the
last 400 years the recurrence of this periodicity especially well expressed (Figure 4).
The most recent modes of behavior of global dT are characterized by intensive
harmonics with periods 50-60 years.
EVALUATION OF CYCLIC CHANGE OF GLOBAL DT FOR THE LAST 140
YEARS AND APPROACHES TO PREDICTION.
To evaluate the main regularities of evolution global dT for the last 140 years it is
necessary to consider general linear trend, within the background of these 50-60 years
and higher-frequency fluctuations with small amplitudes. These observations provide a
basis for the prediction of behavior of low-frequency variations of global dT for the
near-future decadal lime intervals. Let’s select its length equal to 30 years
(approximately half of period of the dominant harmonic). First, we evaluate parameters
On the Coherence between Dynamics of the World Fuel Consumption and Global Temperature Anomaly 779
of the linear trend for the last 140 years and then subtract them from an analyzed time
series of dT. From residual (after subtraction of linear trend) we then fit the best
harmonics with some period (our dominant cyclic trend) and finally, we calculate its
values for the time period 2000-2030. When this is done, we return the eliminated
general linear trend to the whole. The standard deviation of the residual after
subtraction of linear and cyclical trends will set the intervals of errors of the forecast.
In this sequence of operations the main problem is a choice of period τ of a cyclic
trend. It would be possible to put it equal to 54 years, as follows from Figure 3(b). But
it is necessary to take into account that this value of a period is a result of averaging of
the contributions of harmonics for all period of observations, i.e. for 1500 years. At the
same time, as it can be seen in Figure 4, the spectral structure is rather non-stationary.
As we are interested in the prediction for only a rather short interval of time (30 years),
it is more logical to select a value of τ which in the best way reflects cyclic dynamics
of dT just for recent (1861-2000) period of instrumental observations.
For a determination of τ the following approach was used. We set some interval of
probe values of τ. It is possible to find harmonics for each period of a cyclic trend
from this long time interval. The best way is through fitting variations of dT after
removing of general linear trend. The residual after removing a cyclic trend with a
given period will be characterized by some standard deviation dependent on values for
the entire period. We then select period τ by setting the condition of using the period
providing minimum of the residuals standard deviation. The best value τ=64.13 years
was found, for the dT time series after removing the general linear trend and searching
for τ in an interval of values between 20-200 years. This value lies well within the
limits of the frequency band of dominating roughly 60-years harmonics of Greenland
Ice Cores reconstructed temperature at least for the last 1000 years (Figure 4.)
The results of using the above method of dT trend prediction for τ=64.13 years is
presented in Figure 5.
Figure 5. The dynamics of instrumentally measured and modeled Global dT trend,
1861-2030s Thin line— annual global dT; Bold line – cyclic modeled trend
with period of 64.13 years; bold line with error bars – modeled predicted
trend for 2000-2030s
780 Energy & Environment • Vol. 14, No. 6, 2003
The bold line with vertical bars of standard deviations is the forecast of a lowfrequency
behavior of global dT for the next 30 years, is represented in Figure 5 by a
thin black line. The bold line presents values of a cyclic trend for the interval of
Thus, this model indicates that the maximum of the average value of global dT will
level off in the next 5-10 years. Subsequently, one can expect a lowering of its value
roughly by 0.1-0.15°C until the end of the 2020s.
The simultaneous increases of global dT and WFC trends in the last 1975-2000s
period might well be the result of cyclic roughly 60-year oscillations of global dT and
alternating positive or negative correlation between phases of WFC and dT runs as
observed in the past 140 years period of instrumental observations. The ongoing
alternative phase period 2000-2030s as one might expect should be characterized by
negative correlation between dT and WFC run (Figure 1, Table)
ESTIMATING CONNECTION BETWEEN DT AND WSC BY THE “BLACK
For additional confirmation of our suggestion of independence variations of dT on
WFC global fuel consumption the following evaluation was made.
We consider a global climatic system as a “black box”, to which the annual
increments of global consumption of fuel are added, with an output of annual
increments of global dT. We have estimated linear frequency transfer properties of this
“black box”, namely, the squared module of a spectrum of coherence and an
amplitude-frequency transfer function, using standard techniques of time-series
processing (Brillinger, 1975; Marple(Jr.),1987), by averaging periodograms and crossperiodograms.
For the length of time series 140 samples we obtained 128 frequency
values. We then perform a rather deep (for such length of time series) averaging by the
moving frequency window of a radius 10 frequency values. The result of such data
processing is presented in Figure 6(a, b).
Figure 6. (a) Squared coherence spectra estimate between annual increments of WFC
and annual increments of Global dT (b) Estimate of amplitude frequency
transfer function from annual increments of WFC to annual increments of
On the Coherence between Dynamics of the World Fuel Consumption and Global Temperature Anomaly 781
As shown in Figure 6, some relationship exists within main variations with periods
of less than 10 years, but this is extremely insignificant as from the point of view of
squared coherence (Fig 6(a)) and from the value of response (Figure 6(b)), providing
independent confirmation of the suppositions made at the beginning of “Results and
Unlike the monotonously and exponentially increasing of WFC, the dynamics of
global dT against the background of an age-long linear trend, undergo quasi-cyclic
fluctuations with a period about 60 years.
No true linear correlation exists between the Global dT and WFC dynamics for the
last 140 years.
Spectral analysis of reconstructed temperature for the last 1400 years and
instrumentally measured (for the last 140 years) global temperature anomaly dT shows
cyclic 50-60 year variations for the last 1000 years.
Modeling of roughly 60-years cyclic dT changes suggest that observed rise of dT
will level off in the next 5-10 years, when we might expect the lowering of dT by
nearly 0.1-0.15°C to the end of 2020s.
This work was supported by U.S. National Research Council, Research
Associateship Programs, TJ 2114 (Exchange Visitor Program No. P-l-2628). We thank
Dr. Gary Sharp (Center for Climate/Ocean Resources Study, Monterey, CA) for
revision of the manuscript and useful comments.
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ABOUT THE AUTHORS
Leonid B. Klyashtorin (Doctor of Sciences in Marine Biology & Fisheries) was born
1934. Since 1958-1965 he worked in Institute Oceanology Ac. Sci. Russia) on the
Primary Productivity of the Ocean. Since 1968 up to now he works in Federal Institute
for Fisheries and Oceanography (VNIRO): 1968-1980, Research on of Marine and
Fresh- Water Fish Respiration. 1980-1990- Research on Salmon Ranching and Natural
Salmon Stock dynamics. Since 1990 up to now: Research on the relations between
Climate and Long-Term Fish Stock dynamics. Published 120 papers in scientific
journals. Main recent publications: 1998, “Long-term climate change and main
commercial fish production in the Pacific and Atlantic” Fisheries Research, vol.37,
115-125; 2001, Climate change and long term fluctuations of commercial catches: the
possibility of forecasting. FAO Fisheries Technical Paper No 410, pp 86
Alexey A. Lyubushin (Doctor of Sciences in geophysics) was born 1954. He
graduated from the Moscow Physical Technical Institute. Since 1984 up to now he is
working in the Institute of Physics of the Earth, Ac. Sc., Russia and since 1994 – also
in the International Institute of Earthquake Prediction Theory and Mathematical
Geophysics, Ac. Sc. Russia). He is a professor of Moscow State Geological
Prospecting Academy, Department of High Mathematics and Mathematical Modeling.
Research interests: multidimensional signal processing, wavelet analysis, point process
statistics, artificial neural networks, geophysical monitoring, earthquake prediction,
seismic hazard assessment. Published 81 papers in scientific journals.
On the Coherence between Dynamics of the World Fuel