Link Between Atmospheric CO2 and Temperature: Does it Signal an Approaching Runaway Greenhouse Effect?
Wendell Tangborn
HyMet Inc.
13629 Burma Rd SW
Vashon Island , WA
98070
Summary
Daily temperature
departures based on observations of maximum and minimum temperatures from 1933
to 2005 at 74 weather stations in the
Introduction
Analysis
of global temperature departures in an earlier study indicated that since the
early-1980s, the timing of positive departures at multiple weather stations is
increasingly synchronized, especially during the January-March season (1). The number of
stations synchronized (have positive temperature departures on the
same day) increased so that by 1990 approximately 95 % of the stations in the
study had positive departures on a single day (January 13, 1990). Subsequently the synchronized number exceeded
90% throughout the 1990s. There is a high probability that the cause of such an
unprecedented, worldwide phenomenon is related to the rising concentration of
greenhouse gases in the earth’s atmosphere that is causing a simultaneous
change in the earth’s surface temperature patterns.
Linking Seasonal Variations in Carbon Dioxide and Temperature Index
The
1958 – 2005 record of mean monthly concentrations of atmospheric carbon
dioxide, adjusted to the 15th of each month and based on daily
observations collected at
Daily
values of atmospheric carbon dioxide are converted from the observed monthly
means by 3-point interpolation. The concentration for each day of a specific
month is determined by weighting the observed monthly concentrations for the
previous, current, and the subsequent month, based on the number of days to the
15th of that month. For example, to determine the daily CO2
concentration on July 10,
the June monthly mean would be weighted by 25 days, the July
monthly mean by 3 days and the August monthly mean by 37 days.
Figure 1. Daily averages of the
concentration of atmospheric
carbon dioxide derived from monthly means observed at
Figure
1 is the mean daily concentration of CO2 averaged for the 1958-2005
period, based on daily CO2 values determined by the conversion from
monthly observations.
Figure 2a. Daily change in the concentration of
atmospheric carbon dioxide averaged for two 24-year periods, 1958-1981 and
1982-2005.
Figure
2A shows the mean daily change in CO2
averaged for two 24-year periods, 1958-81 and 1982-2005. The
daily change in CO2 is more positive during the winter season for
the later 1981-2005 period and more negative during the summer season when
vegetation growth removes carbon dioxide from the atmosphere (6).
These differences indicate that the bio-mass in the Northern Hemisphere has
increased about 10% between the two periods, possibly due to enhanced growth
produced by the 21% increase in the concentration of atmospheric CO2
from 1958 to 2005.
Modified Diurnal Temperature Range
The diurnal temperature range, the difference between the daily maximum and minimum temperature observation, has been beneficially but not frequently applied for climate analysis. The diurnal temperature range was used to detect climatic aberrations caused by volcanic eruptions (7) and the 3-day period of airline grounding following 9/11 (8). It has also been used as a proxy for solar radiation and cloud-cover observations, in snow and ice ablation algorithms, and as a means to estimate the temperature lapse-rate (9). Long-term changes in the temperature range have been used to demonstrate significant changes in the global climate. (10, 11)
Seasonal
fluctuations in atmospheric concentrations of carbon dioxide are compared with
seasonal variations in temperature using a modified diurnal temperature range
index. Daily maximum and minimum temperature departures for each weather
station are first calculated for the 1958-2005 period based on daily averages
for the 1933-57 period. A 74-station average is
produced for both the daily maximum and daily minimum temperature departures.
The diurnal temperature range departure, which is the difference between the
daily maximum and minimum observed temperature departures
is modified by the addition of two coefficients. Optimum values for the
coefficients are determined for each 5-day interval by regressing the daily
change in the concentration of atmospheric carbon dioxide against the modified
temperature range for the full period of record (48 years).. Therefore, 73
values each of two coefficients are determined using 17, 520 pairs of change in
atmospheric CO2 and temperature departures.
The
modified temperature range on day (i) and year (n) is calculated from measured
maximum and minimum daily temperature departures.
dTm (i,n) = k1 (i) (dTx(i,n) ) – k2 (i) (dTn
(i,n))
(1)
Where:
dTm (i,n) = modified temperature
range departure
dTx(i,n) = maximum temperature
departure from the 1933-1957 average
dTn
(i,n)= minimum temperature departure
from the 1933-1957 average
k1
(i), k2 (i) = coefficients determined by
calibration for the 1958-2005 period
Each coefficient is held constant for 5-day
increments to reduce the total number from 730 to 146 and minimize a degree of
freedom conflict. It
is emphasized that dTm is an index only as k1 and k2
are not considered physically real parameters and are free to reach values that
produce the best fit between the temperature index and CO2. For this
reason the cumulative temperature departures can be very large and where shown
in the figures, are scaled down by 1/1000.
Daily
averages of dTm for two periods, 1958-81 and 1982-2005, shown in
Figure 2b, reveal a striking similarity to averages for the same periods of the
daily change in atmospheric CO2 shown in
Figure 2a.
Figure 2b. Daily modified temperature range departure (dTm
) averaged for two 24-year periods, 1958-1981 and 1982-2005. Note similarity to the daily change in
atmospheric CO2 averaged for the same periods shown in Figure 2a.
The
average mean temperature and average temperature range shown in Figure 3 do not
display similarity to either the total CO2 or the CO2
change distributions shown in Figures 1 and 2a, but the temperature range
departure index in Figure 2b closely resembles the CO2 change
pattern shown in Figure 2a.
Figure 3. Daily mean temperature and diurnal
temperature range averaged for the 1958-2005 period, for 74-weather station
records in the
The
temperature range index is more sensitive to the daily change in the
atmospheric concentration of CO2 than it is to total concentration.
The daily change in CO2 concentration is found by.
dC(i)
= C(i) – C(i-1).
(2)
Both the daily change in atmospheric CO2
and the temperature range index are summed for 48 years from the beginning of
each year:
n
= 48 i = 365
SdC(i,n) = Σ Σ
dC(i,n)
(3)
n=1 i = 1
n=48 i = 365
SdTm(i,n)
= Σ Σ dTm(i,n)
(4)
n=1
i = 1
A
linear regression for the full 1958-2005 period is run to determine optimum
values for k1 and k2 (equation
5).
SdTm(l)
= α (SdC(l)) + β
(5)
Figure 4a. Coefficients k1
and k2 are optimized by fitting daily changes in atmospheric carbon
dioxide versus a temperature range departure index (dTr) that is determined by
k1 (dTx) – k2 (dTn)
For
the 1958-2005 period, the R-squared for regressing the cumulative daily
modified temperature range, SdTm(l),
versus the daily change in concentration of atmospheric carbon dioxide, SdC(l) (17,560 pairs) is 0.77.
Optimum values of
k1 and k2 are found by
minimizing the regression error produced from equation (5). A value of 1.0 is
assigned to k1 and k2 prior to
optimization so that initially equation (1) is simply:
dTm =dTx – dTn (6)
Figure 4a
demonstrates how the optimized values of k1 and k2
vary throughout the year. There appears
to be a distinctive pattern for these two coefficients. In general, both tend to be randomly negative
throughout most of the year, but are strongly positive in July and August.
Figure 4b Relationship between optimized coefficients k1 and k2
Figure 4b shows the dependency of k2
on k1. It is likely more than
coincidental that maximum positive values for both occur during the 5-day
interval Jul 27-31,when maximum temperatures occur in
the Northern Hemisphere.
A
cumulative plot of SdTm(l) and SdC(l) from 1958 to 2005, shown in Figure 5a,
compare the daily temperature
index and seasonal fluctuations in carbon dioxide.
Figure 5a. Daily averages of cumulative
atmospheric carbon dioxide and modified
temperature range index from 1958-2005.
The
same variables, shown in Figure 5b for 1958-1967, and
Figure 5c for 1996-2005, demonstrate definite improvement with time in the fit
between atmospheric CO2 and the temperature index.
Figure 5b. Daily averages of cumulative
atmospheric carbon dioxide and modified
temperature range index from 1958-1968.
Figure
5c. Daily averages of cumulative
atmospheric carbon dioxide and modified
temperature range from 1996-2005.
Figure
6a is a scatter plot of daily SdTm(l) and
(SdC(l)) for 1958-66 the first deacde of the period, and Figure 6b for the last
decade, 1996-2005. The R2 for these two regressions is 0.70 and 0.95,
indicates that the temperature response to seasonal changes in atmospheric CO2
has significantly increased.
Figure
7 shows the R2 for fitting SdTm(l)
versus (SdC(l)) for each year of the
1958-2005 period. The equation for a linear fit of R2 versus year
is: r2 = .0071 (n) + 0.5604, which suggests that the r2 will
equal 1.0 in 15 years. Such a prediction is disquieting
because it implies a critical threshold in the earth’s climate system will be
reached in 2020. Should we then expect the unpleasant surprises in the climate
that were predicted in 1987?(12)
Figure 6a. Daily averages of cumulative
atmospheric carbon dioxide versus
temperature range for 1958-67.
Figure 6b. Daily averages of cumulative
atmospheric carbon dioxide versus the temperature range index for 1996-2005.
Figure 7. R2 of regression fit of cumulative
daily change in atmospheric carbon dioxide and cumulative temperature range
departures for each year of the 1958-2005 period
Discussion
The sensitivity of the response of surface temperatures to seasonal changes in the concentration of atmospheric carbon dioxide appears to be increasing. The seasonal daily changes in CO2 and in the temperature departure index shown in Figures 2a and 2b provide a partial explanation. Between approximately May 15 and October 15 both CO2 changes and the temperature range departure index are negative. The CO2 change is negative due to vegetation growth in the Northern Hemisphere removing carbon dioxide from the atmosphere. The temperature range index is negative because nighttime (minimum) temperature departures are becoming significantly larger than daytime (maximum) departures. Minimum temperatures are increasing more rapidly than daytime maximums because heat generated during the day is trapped at night by the increasing concentrations of CO2. Therefore, in equation (1) the term (k2 (dTn)) exceeds (k1(dTx)) and (dTm), the modified temperature range departure, is predominantly negative .
Radiative forcing, a measure of the influence that a factor has in altering the balance of incoming and outgoing radiation, increased by 20 percent from 1995 to 2005 (12), the decade that also shows the highest correlation between CO2 and temperature departures. However, the concentration of atmospheric CO2 increased just 5% during the same period, suggesting an additional forcing component other than increasing carbon dioxide is present. As carbon dioxide is removed from the atmosphere by vegetation during the NH summer and autumn there is an increase in atmospheric water vapor due to greater evaporation from the oceans and land areas. Water is many times more potent than carbon dioxide as a greenhouse gas with a powerful feedback. (13) Thus there is an added component of radiative forcing produced by water vapor that helps explain the negative departures in the temperature range index during the summer.
However, there are still inexplicable results shown in this study, such as negative temperature departures coinciding with decreasing atmospheric CO2 during the summer and autumn season. Some of these may be due to an imbalance in the atmosphere-ocean system caused by the high rate that carbon dioxide is being added to the atmosphere. The world’s oil, coal and gas deposits were formed from decaying vegetation during the Carboniferous and Permian Periods, from about 250 to 350 million years ago. In the past 100-150 years humans have converted more than half of these fossil fuels back into carbon dioxide at a rate that is a million times greater than they were deposited. The rapid influx of carbon dioxide to the earth’s atmosphere, and indirectly to its oceans and soils, produces instability in the atmosphere/ocean system, which can only adjust slowly to changes. We might now expect the unpleasant surprises in the climate that were predicted in 1987?(14)
Conclusions
The synchronization of positive temperature departures worldwide is likely caused by the concentration of atmospheric carbon dioxide reaching a threshold level in the 1990s. To quantify a carbon dioxide-temperature link, a modified temperature range index based on daily temperature departures at 74 weather stations in the United States is regressed against the daily change in atmospheric carbon dioxide for 1958-2005. Based on a 48-year trend, the correlation between atmospheric carbon dioxide and temperature is steadily increasing, when annual intervals are considered separately, and will reach 1.0 in approximately 15 years. It can be concluded that earth’s surface temperatures will then be predominantly forced by the concentration of carbon dioxide in the atmosphere and a runaway greenhouse effect will be initiated.
Acknowledgements
The late Edward R. LaChapelle was instrumental in introducing me to the intricacies of climate change in the 1970s, and also encouraged me to continue working on climate problems.(15) Funding was provided by HyMet Inc..
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