Warming up a little or a lot

Our world is not getting hot any time soon. Where it’s getting hot is under the collars of those who thought up global warming. Al Gore and the UN Intergovernmental Panel on Climate Change were awarded the 2007 Nobel Peace Prize for thinking up global warming. The almost US president and his UN think tank do think it’s getting warmer. So, it’s got to be so! They are telling tall tales and crafting cool books. A few worked up a frenzy worrying it doesn’t get warm soon enough. Others upped the odds by predicting it does so at an alarming rate. That sort of scare works so long as nobody knows the standard rate of warming for a little planet like ours.

Al Gore’s Inconvenient Truth is a tour de force in child psychology. It shows a polar bear on an ice floe drifting at some cool spot somewhere in our world. It’s scene that pulls a child’s heartstring just as much as does a puppy under a Christmas tree. Our offspring may be around long enough to witness that what goes up must come down if only because the sun is beyond control of church and state. And that’s just as well. Nobody worries much that the sun itself is running out of hydrogen at an astounding rate. The good news is that its hydrogen will last some 10 billion years. The bad news is that it's numerically a lot less than IMF’s trillion dollars.

Apollo’s Blue Marble photograph

NASA satellites transmit more than stunning photographs. Massive sets of temperatures have been transmitted ever since this famous photograph was shot in December 1972. It took me aback that annual temperatures in the lower troposphere display spatial dependence. Until I was told that long term cycles in ocean currents do impact lower troposphere temperatures. That’s why it makes scientific sense to verify spatial dependence in our own sample space of time. By inverse logic, it is a scientific fraud to assume spatial dependence without proof.

Bad luck had it awhile back that a NASA satellite failed to deploy. This one was to measure carbon dioxide concentrations in the troposphere. Geoscientists might have found out some 30 years later how carbon dioxide concentrations drive the greenhouse effect. That’s why patience is as much a virtue in the study of climate change as is a good grasp of statistics. Geostatistical data analysis is a catch-22 in the sense that interpolation between measured values creates an appearance of spatial dependence where it doesn’t exist.

Much of the USA and most of Canada is missing in the Apollo photograph. The USA may not have felt like showing a lot below the 49^th Parallel in those days. Canada’s vastness stretches from the Atlantic ocean to the Pacific ocean, and winds up into the arctic where Northern Lights shimmer when the sun takes leave during long winters. Canada’s vastness twists and turns into a multitude of different climate zones. Environment Canada (EC) manages a treasure trove for those who take the study of climate change seriously.

EC’s Adjusted Historical Canadian Climate Data Base gives temperatures for a large number of locations dating back to the 1930s. I was given permission to access EC's database. I downloaded temperatures for the international airports at Calgary, Alberta, at Ottawa and Toronto, Ontario, and at Vancouver and Victoria, British Columbia. I also downloaded temperatures for Coral Harbour, Territory of Nunavut. I did so at different times and for different reasons. Excel 2007 spreadsheet templates give the statistics for each set, a plot of the annual means, and a chart with the sampling variogram. The most relevant statistics are summarized below.

Summary of statistics for six locations in Canada

For the Toronto Lester B Pearson International Airport the difference of 2.30 centigrade between the first annual mean of 6.00 in 1940 and the last annual mean of 8.30 centigrade in 2008 is statistically significant at 95% probability. Higher annual temperatures do account for the observed difference of 2.30 centigrade. Observed differences at other locations are not significant. Randomly distributed variations in measured temperatures account for those observed differences.

Annual means at Toronto Lester B Pearson International Airport

A plot of annual differences in a chart shows a distinct trend toward higher temperatures. Such a trend also indicates spatial dependence between annual temperatures in the ordered set. A sampling variogram is a chart in which the variance terms of the ordered set are plotted against the variance of the set and the lower limits of its asymmetric 95% and 99% confidence ranges. It shows where orderliness at the selected location in our sample space of time dissipates into randomness.

Toronto Lester B Pearson International Airport

The sampling variogram for annual temperatures measured at the Toronto Lester B Pearson International Airport displays a significant degree of spatial dependence. The question is then why geostatisticians like to assume spatial dependence rather than verify it by applying Fisher’s F-test to the variance of the set and the variance terms of the ordered set. The mining industry is pleased to krige and smooth from here to eternity. Professional engineers and geoscientists with provincial securities commissions, too, do krige and smooth with the best. But here's the cinch! NASA and NOAA are not about to krige and smooth because the mining industry says so. What should the Harper Government do when the rules of statistics are rigged? Goverments do not sort out abuse of statistics. Good grief! It's the Great Lake Study where sound statistics will resurface. Come cold or warm water!