# How to divide timeseries into normal periods in meteorology and climatology?

When analyzing hydrological and climatological timeseries/observations it is a common practice to compare statistics made on normal periods. As WMO calls them: "WMO Climatological Normals".

These periods consist normally of 30 years of data. If you want to compare two normal periods with each other, let's say for example the periods 1951-1980 and 1981-2010.

Now if we take averages for all the seasons in the period 1951-1980, the last month is December in this period. If we regard December, January, and February as a complete season/winter, it means that we have an incomplete winter at the end of the period 1951-1980. Now taking December to represent a whole winter, would be inaccurate. The monthly variations of a climatic parameter can vary greatly, and multiplying the December values by 3 wouldn't yield a result based on actual observations. Also making December the whole winter of 1980, would underestimate the real winter average. This would in turn affect the overall 30-year mean, by lowering it and giving a wrong picture of the actual seasonal mean in that normal period.

Same goes for the beginning of the period 1981-2010, here we have January and February as an incomplete winter.

Now in order to get complete seasons in the intersections between the normal periods, wouldn't it be best to split the periods as follows: 1951-1980.11.30 and 1980.12.01-1990.

Also it would be best to cut out December completely at the end of the period: 1980.12.01-1990.

So that it becomes: 1980.12.01-1990.11.30.

The same goes for the last normal period: 1951-1980.11.30.

Where we would cut out January and February of 1951 so that we get: 1951.03.01-1980.11.30.

In this way we make sure we have complete seasons in both normal periods. So if we also do comparisons of monthly averages: JAN-FEB-MAR..., we would still split up the periods in the same manner, in order to use the exact same periods for exact comparison with the seasonal averages.

However when we have split up the periods as follows: 1951.03.01-1980.11.30 and 1980.12.01-1990.11.30. Is it still normal in academic papers to say that we are comparing the normal periods 1951-1980 and 1981-2010, when there is actually a small overlap in the last?

If this is not the normal procedure, what is the way to get around this? What do researchers normally do in this case?

In addition cutting of seasons/months in this manner yields an unequal number of months/seasons. The analysis might have data from a higher number of the month February compared to January. So the statistics from February are more reliable. Also a disadvantage of cutting out actual observation data, yields a loss of valuable observation data, which lowers the reliability of the statistics.

• If you would just cut the timeseries from exactly when year changes you will still have 30 Decembers and 30 Januarys etc. and I would suggest you to do so. Your whole logic begins from an assumption that these three months somehow perfectly cover the winter (and one winter must be fully represented each time it occurs). No and no on both assumptions. Feb 26 '18 at 10:52
• It meteorology it is common to regard december, januar and february as a complete winter. So in research papers when finding mean values for seasons, december, januar and february would be winter. Now my question for averaging is how to include data from the last december in the first normal period. How should that last december be weighted when calculating the average, what is common practice? I agree with you when doing monthly averages.
– Anna
Feb 26 '18 at 14:00
• Or would one simply take the average of december 1980, january 1980 and february 1980, which would represent the average for winter 1980?
– Anna
Feb 26 '18 at 14:17
• Yes exactly. Unless you have a very specific reason to for example study each winter as a whole. For example if I would want to study how each winter affects the subsequent winter. Feb 26 '18 at 14:35