The mean of the 12 monthly global averages does not equal the annual average. Why not?
We calculate the global annual average from a gridded data set. The gridded data set breaks the earth’s surface into ‘squares’ whose sides are 5 degrees in longitude and 5 degrees in latitude. We have observations of temperature in some of the grid squares, but in others we have no observations. To calculate a monthly average we take a weighted mean of all those grid-squares that contain data that month. In other words we multiply the temperature anomaly in each grid square by the area of the grid square and add them all together, then we divide this by the total area of grid squares that contain data. We do this separately for the northern and southern hemispheres, then take the mean of the two. This stops the global average from being dominated by the better observed northern hemisphere. To calculate an annual average we first calculate the annual average for each grid square. We then take a weighted mean of all those grid-squares that contained data that year (the method is the same
