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Cycles and Trends in
Average Global Temperature
and Their Projection

Consider the record of annual average global temperature from a reputable source such as the National Oceanic and Atmospheric Administration (NOAA). In meteorology and climatology anomaly just means the deviation from some base level, usually a long term average.

In the graph there appears to be several episodes of increasing or decreasing temperature. These episodes appear to be linear. Furthermore the slopes of the upswings appear to be more or less equal. Likewise the slopes of the downswings appear to be equal. The periods of the upswings appear to be longer than the periods of the downswings. Underlying the upswings and downswings there seems to a long term trend. The extent of this long term trend can be discerned by plotting the averages for the various episodes, as is shown below.

A bent line can be fitted to the data using regression analysis. Such a regression function so fitted explains 88.06 percent of the variation in the average global temperature over the period 1880 to 2008. In this regression the slopes of the lines for the various episodes can be of any values.

The possibility of an accelerating trend was tested for by including a quadratic term in the regression. The coefficient for the quadratic term was not significantly different from zero at the 95 percent level of confidence. (Its t-ratio was 0.8.)

The values of the slopes for the two upswings are close, as are the values for the slopes of the two downswings.

The Regression Coefficients
for the Various Episodes of
Global Average Temperature

The difference in the slopes for the upswings is not significantly different from zero and likewise for the slopes for the downswings. For the upswings the ratio of the difference in the slopes to the standard deviation of the difference is 0.107. For the downswings this ratio is 0.364. Thus neither of these differences in slope is significantly different from zero at the 95 percent level of confidence. Since the differences are not significantly different from zero it is appropriate to do another regression in which the slopes are exactly equal for the upswings and also for the downswings.

Thus the more interesting regression is the one in which the slopes for all of the upswings have to be the same and likewise for the slopes of the downswings. As noted above, visually and numerically this appears to be the case. The graph of the data along with the regression estimates is shown below.

The coefficient of determination (R²) for this regression is 87.98 percent, nearly as high as the value for the unconstrained regression. This means the correlation between the regression estimate and the actual temperature anomaly is 0.938.

The measure of the statistical significance of the cycle is the t-ratio for the coefficient for the cyclic variable. The t-ratio is the regression coefficient estimate divided by the standard deviation. The value of that t-ratio for the cyclic variable is 13.2. (The t-ratio for the long term trend is 5.0.) The t-ratio has approximately a normal distribution for the 126 degrees of freedom for the data set. The probability of getting a t-ratio as large or larger from a situation in which its true value is zero is so infinitesimally small it is hard to describe it. In other words there is virtually no chance whatsoever that the 128 year cycle pattern arose just from chance.

Note the downturn for the last few years. If the cyclic pattern of the last 128 years continues, and there is no evidence that it will not, there will be a period of about 32 years during which the average global temperature will decline. The decline will be about 0.12°C over that period. The data and the projection of the long term trend along with the cycle are shown below.

There is a long term trend. Its value is found by computing the slope of the line between two low points in the cycle or two high points. That value is 0.005°C per year. This is equivalent to 0.05°C per decade and 0.5°C per century.

The slopes for the two types of episodes are the sums of the cycle trend and the long term trend. Thus the slope during an upswing is 0.0195 which is the sum of 0.005 for the long term trend and 0.0145 for the cycle trend. Thus the cycle trend slope is nearly three times as large the long term trend. The slope for a downswing is -0.004 which is the net result of a slope of -0.009 for the cycle trend and +0.005 for the long term trend.

The projection on the basis of the past cycle in global average temperatures is then a downswing from now until about 2038 when the global temperature will be 0.12°C below the 2008 level. From 2038 the temperature will rise until about 2070 when the temperature anomaly will be about 0.969°C, about 0.35°C above the 2005 level. From 2070 the temperature will decline and by 2100 the temperature will be only about 0.25°C above the 2005 level. The computation of a margin of error for the projections would be complicated, but it can be said that the standard error σ of the estimate for the regression equation is 0.087°C, so ±2σ is ±0.174°C.


Backcasts for the model are easily constructed. The first turning point was 1916. Going back 32 years puts the previous turning point at 1884. The annual increment for an upswing episode is then deducted from the regression estimate for 1884. The results are as shown.

NOAA declined to publish data for the years prior to 1880, probably because of questions of accuracy. Other organizations, such as the Climate Research Unit at the University of East Anglia, have published that data. Thus a comparison can be made of the backcasts with the display below.

Source: Climate Research Unit at the University of East Anglia, U.K.

As can be seen the backcasts fit the temperature trend that existed before 1880. The temperature anomalies for the NOAA data and the Hadley CRU data are shifted by about 0.1°C so the backcast value for 1855 of about −0.6°C based on the NOAA anomalies corresponds quite well to the −0.5°C of the Hadley CRU anomaly data. For an analysis of the Climate Research Unit data see Hadley CRU. For an analysis of the data from NASA'S Goddard Institute of Space Science see GISS.

But What about the Billions of Dollars
of Climate Projection Models?

Fundamentally the two dozen or so climate models adopted by the Intergovernmental Panel on Climate Change (IPCC) as devices for seeing into the future suffer from tunnel vision. They focus on the greenhouse effect of carbon dioxide to the exclusion of phenomena that do not fit in with that perspective. They do so because they are funded by governments with an agenda for world government control of energy use.

The climate modelers are always careful to say that their results are projections rather than forecasts. A projection is a forecast contingent upon certain assumptions. Those assumptions include such things as that there will be no major volcanic eruptions during the forecast period. But what the modelers do not say is that the number one, eight-hundred-pound-gorilla assumption is that the model is valid. The climate models have not been proven valid.

Climate models can be validated by honest backcasting; i.e., using the model to compute past values from current values using no more data for the backcast than are used for the forecast. The models for which there have been published backcasts with some semblance of honesty have insignificant correlations with actual past temperatures and thus were invalidated.

Some models claim to be able to reproduce the past global temperature record but the reproduction is fudged. The future projections for the models are smooth exponential-like curves. Honest backcasts would have the same character; i.e., smooth exponential-like curves. Instead the supposed backcasts have the ups and downs of the actual temperature data thus indicating that they are based on information from the past that would not be available for future projections. Even with this fudging they do not do all that well in terms of actual correlation.

There is of course generally a major problem of intellectual honesty with the global warming alarmist movement. When the models forecast events x, y and z and x and y do not occur but z does so, the proponents of catastrophic global warming do not say, "Oh, the theory is not adequate. It is incomplete and apparently we left out some essential processes." No, they say, "Event z proves our theory and we will find some way to dismiss the nonoccurrences of x and y."

So instead of developing adequate models the scenario went something like this: The modeling community said to governments, "Some of our models say 2+2=5, some say 2+2=5.1 and other say 2+2=4.9. Obviously 2+2=5.0±0.1. Give us a million dollars and we will show that 20+20=50±0.01. Give us a billion dollars and we will show that 200+200=500±0.001."

When non-climatology scientist see that the models are based only on well established scientific principles such as thermodnamics and fluid mechanics they think that fact guarantees that the models are science, It does not because the models are in error not from what they contain but because what they leave out.

What essential elements were left out of the models? Most but not all have to do with clouds and water vapor. Consider the difference in temperatures on winter's nights with and without clouds. Everyone knows from experience that the clear night is much colder than the cloudy night. Yet the greenhouse effect is essentially the same with or without the clouds. The crucial difference is that the undersides of clouds reflect back to the Earth's surface about 80 percent of the Earth's thermal (infrared) radiation.

The greenhouse effect can at most radiate back to Earth 50 percent of its thermal radiation and usually it is far less than 50 percent. The greenhouse effect is far less powerful than the reflectivity of the underside of clouds.

Even concerning the greenhouse effect the models leave out the effect of increased water vapor in the atmosphere from irrigation, landscape watering, swimming pools, canals and the exhausts of motor vehicles. (There are as many or more water molecules produced in the burning of hydrocarbon fuels as there are carbon dioxide molecules.) The models do include effect of increased water vapor in the atmosphere from higher temperatures. That positive feedback fits in with the agenda of proving the effect of increased carbon dioxide.

But surface temperatures can be affected by other processes besides the greenhouse effect and the reflectivity of clouds. Consider two parked cars sitting in the noonday sun; one with its windows rolled up and one with them rolled down. The two cars are getting the same radiation from the Sun and the same greenhouse effect from the atmosphere. But without doubt the car with its windows rolled up will be hotter, much hotter, than the car with its windows down. The crucial difference is that the car with its windows rolled down has convection and the other one doesn't.

Consider also the surface of the Moon. The Moon does not have an atmosphere so there is no greenhouse effect at all. Its temperature in the daytime is 225°F, hotter than boiling water. The reason is the lack of convection. (At night the Moon's surface temperature falls to -240°F so the average temperature is something like -10°F.)

Most importantly the models leave out a naturally occurring phenomenon called the Multidecadal Pacific Oscillation, a sort-of big brother of El Niño. There may also be what is called the Mid-Pacific Thermal Vent that acts like a thermostat for the Earth.

Moreover when a theory or model predicts something and it doesn't happen Science rejects that version and tries to modifiy the theory and make it complete. Science works but what is politically declared to be Science does not work and its proponents refuse to accept the fact that the model's predictions failed to materialize. Instead the proponents of such politically declared Science resort to linguistic subterfuges like shifting the terminology to Climate Change rather than Global Warming. Or they talk about global warming deniers when the real issue is noncatastrophic global warming versus catastropic global warming.

There is a great danger that when global temperatures start declining that people will think that Science cannot be depended upon when that is not true. It is only what is politically declared to be Science that cannot be depended upon.

The human race has received very little in return from the investment in climate models. In fact, there has been the negative return of disinformation. This is largely because they were created to demonstrate that there would be catastrophic effects from increased carbon dioxide which constitutes less than 0.04 of 1 percent of the atmosphere and less than 10 percent of the greenhouse gas content of the atmosphere. The data on the carbon dioxide content of the atmosphere is widely available, but the time series on the total greenhouse gas content of the atmosphere is not available. Likewise the data series on average global cloud cover and humidity is not available. This is a strange lack of basic information if the greenhouse effect is supposed to be so important for weather and climate. What has been demonstrated instead is that governments can create a quasi-religious political movement, masquerading as science, which is invulnerable to logic and facts.

Recently (2009) the most prominent geologist in Australia, Ian Plimer, published a book entitled Heaven and Earth: global warming -- the missing science. In it, on page 23, Plimer summarizes his conclusions concerning climate change:

(a) The Earth's climate has always changed with cycles of warming and cooling long before humans appeared on Earth. Numerous overlapping cycles range from 143 million years to 11.1 years. These cycles can be greatly affected by sporadic unpredictable processes such as volcanoes.
(b) Measured global warming in the modern world has been insignificant in comparison with these natural cycles.
(c) Although man-made increases in atmospheric CO2 may theoretically make some contribution to temperature rise, such links have not been proven and there is abundant evidence to the contrary.
(d) Contrary to nearly two dozen different computer models, temperature has not increased in the last decade despite an accelerated input of CO2 into the atmosphere by human activity.
(e) Other factors such as major Earth processes, variable solar activity, solar wind and cosmic rays appear to have a far more significant factor on the Earth's climate than previously thought. The IPCC has not demonstrated that the Sun was not to blame for recent warmings and coolings.
(f) Humans have adapted to live at sea level, at altitude, on ice sheets, in the tropics and in deserts. As in the past, humans will again adapt to any future coolings and warmings

The French climatologist, Marcel Leroux wrote a critique of what might be called tabloid climatology.


The NOAA data show a cycle and long term trend for average global temperature that goes back 128 years. The backcasting shows that the cycle and trend goes back an additional 25 years. The long term trend is about 0.5°C per century. The cycle consists of upswings and downswings each of about thirty years in length. The projection of the trend and cycle to the year 2100 indicates a moderate, noncatastrophic increase in global temperature.

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