Suppose you wanted to measure whether the total number of ants on earth has been increasing. The number of ants at any given place depends on location and on season. Let’s assume that today there are 10,000 botanists at fixed locations across the world diligently measuring the number of ants passing through each square meter. The daily average population at each location can then be estimated as the sum of the maximum daytime population plus the minimum nighttime population divided by two. Unfortunately though 100y ago there were only 30 such botanists at work and they used pen and paper to record the data. How can we possibly hope to determine whether the global ant population has been increasing since then? The only way is to do that is to assume that **changes** in ant population are the same everywhere because it is a global phenomenon – for example it depends on oxygen levels. Our botanists sample this change at random fixed places. Then as far as possible we should remove any spatial biases inherent in this ever changing historical sampling coverage. We can only do this by normalising at each location the population time series relative to its ‘**average’** value within say a standardised 30 year (seasonal) average. Then we can subtract this normal value to derive the ant population differentials (**anomalies**). Next we form a ‘spatial’ average of all such disparate ant anomalies (essentially differentials) for each year in the series. What we can then deduce are annual global ant population ‘anomalies’ , but in doing so we have essentially giving up hope of ever knowing what the total number of ants alive on earth were at any given time.

Measuring global temperatures is rather analogous because they too are based on the same assumptions, namely that a) temperatures change coherently over vast areas and b) these changes are well reflected by stochastic sampling over the earth’s surface. The global temperature** anomaly** is a spatial average over all measurements of localised monthly temperature **differentials** relative to their average over a fixed period.

Figure 1 shows the decadal smoothed results from GHCN V3/HadSST3. The big picture shows there are four phases:

- 1880-1910 Falling or flat
- 1910-1945 Increasing
- 1945-1975 Falling or flat
- 1975-2015 Increasing

The individual station anomalies for Tav, Tmin and Tmax have each been computed using their respective seasonal averages between from 1961-1990. Note how all the series get zeroed together at the fixed normalisation period. This is an artefact of the choice of baseline period. We can also observe the following apparently odd effects in Figure 1b.

- Tav ‘warms’ faster than both Tmin and Tmax after 1980.
- Tmin warms faster than Tmax after 1970. There is other evidence that nights warm faster than days
- Oceanic temperatures were warmer than global temperatures before 1910 and then again between 1930 to 1972, but have since lagged behind land temperatures. This appears to be a cyclic phenomenon.

The zeroing effect in differences is again an artefact of using temperature **anomalies. ** However, if one looks at these trends dispassionately one must conclude that there is an underlying natural oceanic cycle of amplitude ~0.3C and wavelength ~90y which drove global temperatures until ~1930. Since then a slow but increasing CO2 induced warming effect has emerged which has now distorted this natural cycle. This has resulted in an underlying global warming of about 0.8C.