One of the concerns for alarm has been the melting of the polar ice caps. The arctic ice cap is floating ice and its melting will not add one bit to the level of the oceans. However, the melting of the ice in the Arctic Ocean would, on balance, be a great boon to global shipping and to the climate of the high latitude land. The statistics on the area of the arctic sea ice might seem to give some credence to the belief that global warming, although amounting to only a sixth of a degree Centigrade per decade, could have dramatic effects, perhaps even catastrophic effects.

The statistics for the extent of the arctic sea ice from 1979 to 2001 are given below. They are from the World Meteorological Organization by way of John Christy's article, "Temperature Changes in the Bulk Atmosphere: Beyond the IPCC," which was publiced in Shattered Consensus: The True State of Global Warming, edited by Patrick J. Michaels (Rowman & Littlefield Publishers, 2005).

The statistics are given, as is the convention in climatology, in terms of deviations from the average. Such deviations are usually called anomalies in climatology as though anything that differs for the average is an anomaly. As can be seen, there appears to be a downward trend. The IPCC took this as a confirmation of the consequences of global warming.

Worse than the misinterpretation of trends has been the use of the sharp decline in arctic sea ice from 1994 to 1995 as evidence for global warming. As can be seen from the statistics that was an anomaly and the sea ice soon returned to near average levels.

However it is generally a mistake to interpret what is happening to one part of a system as evidence for what is happening to the system as a whole. For example, consider the statistics for sea ice in the Antarctic region.

This appears to be an upward trend. By IPCC's logic this would be evidence of global cooling, but the divergence of the sea ice at the two poles means that the supposed trends are not evidence for any global change. Putting the statistics together shows that globally there is no evidence of a trend.

The National Oceanic and Atmosphere Administration (NOAA)also provides data from satellites on the sea ice. This time series is shown below:

Over the thirty year period there is slight downward trend for Arctic sea ice and a slight upward trend for Antarctic sea ice, for a very slight downward trend for the to total sea ice. For the more recent years the trend is downward for both regions but extrapolating from a five year period is of doubtful validity. The amount of sea ice is the cumulative sum of the annual changes. The statisitcs for such variables always appear to have trends even when there is no underlying trend. For such statistics it is more appropriate to look at the first differences, the annual changes. These statistics for the total sea ice are shown below.

In this display there is no indication that there was any significant shift in the structure of the variable in recent years. A regression analysis of the change on time gives a negative coefficient but the t-ratio for that coefficient is only 1.5 and not statistically significant at the 95 percent level of confidence. The coefficient of determination (R²) for the regression is only 0.078. This indicates that there is no reason to say there is a trend in the annual change in the global sea ice. However there average value for the annual changes over the period is negative and the t-ratio for that average value is 2.9, which is statistically significant at the 95 percent level of confidence. For more on the statistical problems see Statistics.

Some would like to focus on the Arctic ice alone, but if the problem is global there is no more justification for looking only at the Arctic seaice than to look only at the Antarctic sea ice. When the evidence is selected then there is no objective test of a hypothesis.

When a quantity is the sum of terms which have a stochastic component (random variations) then it appears to have trends and cycles even if the underlying phenomena has no trends or cycles. The change in the volume of sea ice is proportional to the net heat energy inflow so the volume of sea is such a variable. The fact that the volume of global sea ice appears to be trending downward is not necessarily evidence for a downward trend. Consider the following simulation for sea ice volume. For the simulation a set of 60 random numbers from a distribution have an expected value of zero. These are summed and the sums plotted.

The preceding analysis pertains only to the sea ice. There is a good chance that what is happening to the sea ice in each polar region is also occurring for the total ice in the regions. Most of the arctic ice is floating and its melting would not add to the volume of the oceans whereas most of the antarctic ice is resting on land its increase would deduct water from the oceans.