This material deals with the trend in the temperature in the Greenland region. This is an important topic concerning climatology but it immediately raises statistical questions concerning the objective establishment of trends. Consider the temperature record for the Greenland region.

Empirical climatologists looking at this record say that there is a trend of declining temperatures in the region over the past thirty years. Global warming alarmist looking at the same data will assert that the declining trend ended about 1980 and since then there is an increasing trend that is due to the burning of fossil fuels in industrial countries. It is obvious that one cannot identify a short term change in temperature as trend rather than simply an expected fluctuation. The question is what objective analysis can be applied to temperature record to establish whether there has been a shift in the trend.

If we look at the year-to-year changes in the annual average temperatures for the Greenland region it is not obvious that anything changed around 1980.

Let us consider a purely statistical model in which the value of a variable is the past value incremented by some increment u[t] which is a random variable with expected value of zero ; i.e.,

y[t] = y[t-1] + u[t]
 

This roughly corresponds to what is involved in regional temperature. The temperature is the past temperature plus the temperature change generated by the current surplus or deficit energy flow for the region.

Here is such a time series when the random variable has a uniform distribution over an interval centered at zero. A sample of 60 random values is drawn to generate the values of y. Each time the screen is refresh a new sample of 60 random values is drawn. (If the image is not clear click on the REFRESH button.)

Although generally for a sample there appears to be trends the statistical process has no trends in either direction. The apparent trends over intervals is strictly a matter of chance.

Here is the same sort of simulation model but with a larger variance for the changes.

Almost always there appears to be some trend pattern in the graph but in actuality there is no trend to the variable. This points out the difficulty of objectively determining trends from statistical data.

(To be continued.)