February 11, 2007, 5:00 am News


The mean daily temperature at the vast majority of meteorological stations, and  is obtained by taking the average of the maximum and minimum temperature, usually on a special thermometer.

Although many richer countries have recently installed automatic equipment for temperatue measurement it is not known how many have done so, for how long, or whether the method of measurement of mean daily temperature has changed.

Any elementary textbook on statistics begins by showing how to obtain an average. You should have as many observations as possible, you should assemble them into a distribution curve in their order of magnitude, and if it is symmetrical, and sufficiently resembles the Gaussian or "Bell" curve, you can use the simplified mathematics that this entails to calculate the mean and its confidence limits. The procedure for this is on every "scientific" calculator and computor spread sheet.

What you should not do, is to take the average of the largest and the smallest. This is because the outliers often do not obey the Gaussian equation. We are always hearing of the frequent "100 year floods" that result from this fallacy.

Those reported measurements which are obtained by the average of  the maximum and minimum temperature are therefore subject to an unknown bias, and there is no statistical method which could be used to determine it, or to assign a mathematically determined figure for their reliability.

This may not matter much for local weather forecasts as they are often wrong anyway, and the consequences of bias are probably small.

It is a different matter when the measurements are amalgamated by a complex procedure to provide a supposed record of annual global temperatures, which is then used as evidence for the supposed influence of increased greenhouse gas emissions and a whole series of economically damaging attacks on our way of life.

In order to try and find out how great was the bias involved in measuring the average of maximum and minimum instead of an average of a temperature series I put "mean daily temperature" into "Google.

To my amazement it directed to the NIWA website item


which is apparently intended as a student exercise. It consists of two Excel spreadsheets, each consisting of daily temperature readings at 24 New Zealand weather stations, one for summer and one for winter. The student is invited to calculate the error involved in assuming that the mean daily temperature is the average of the maximum and minimum, by comparing it with the average of 24 hourly readings.

The results amazed me.

For the summer series the mean error was 0.9ºC with a range between 2.6ºC and 0.4ºC

For the winter series the mean error was +0.3ºC with a range between 7.6ºC and Minuis 6.9ºC.

Try it for yourself!

The above figures are for New Zealand. Just imagine the possibilities of bias for sites in Russia where temperatures can range between 40ºC and minus 40ºC!

Surely this means that for the vast majority of readings of mean daily temperature the figures are so biased, that the amalgamated version which claims we are being harmed by an increase of 0.7ºC since 1850 or 0.5 degrees since 1950 is without any sense.

In order to derive the "global mean annual surface temperature anomaly record" the following steps must be taken. The mean monthly temperature is obtained from the average of the mean daily temperatures. You then take the average of these from chosen weather stations in a latitude/longitude box. You then find the average of all the available boxes on the globe, You then average the monthly figures to get the global figure. You then subtract it from the average of all these over a reference period, and you come up with the annual global temperature anomaly.

Each of these operations is subject to a variety of errors, and the whole edifice is built upon the mean daily temperature fallacy.

There were 200 weather stations in the year 1850. It grew to 6000 in 1980 and then fell to 2500 today.  The above figures show that the bias involved in calculating wrongly varies wildly from one site to another, even on a single day. It varies with the seasons, and presumably over the years. Every time a station closes or moves in the whole system it chalks up an unknown bias, which for an individual day could be over 7 degrees or more.

There are a very few longstanding sites with fairly reliable records where any bias my not change much. They should therefore give some guidance on possible temperature trends. Many of these are on John Daly's website at

You may note that most of them show no warming for the past 100 years. They include Christchurch, New Zealand, for which the maximum temperature since 1910 was in 1917.

I have even wondered whether the comparative stability of global average temperatures for the past eight years might be associated with correct measurement of daily mean temperature by many of the world weather stations instead of the usual biased ones.

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