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## Calculating the mean sea levels

Definition and calculation of the mean sea levels

Mean sea level is a vague notion that needs to be clearly defined to have a good understanding of the signals contained in the series of values and to interpret the variations (temporal mean? spatial mean? in what extension?).

The definition adopted in SONEL corresponds to the definition of the Permanent Service for Mean Sea Level, the PSMSL, and of the Global Sea Level Observing System GLOSS to which SONEL contributes. The means are temporal averages at the tide gauges (point on the coast), over daily, monthly and annual periods.

There are, however, different ways to calculate these means. They are briefly summarised below:

Annual values: arithmetic means of monthly means weighted for the number of days actually observed during the month. The value is calculated if at least 11 monthly values are actually available (cf. rules of the PSMSL).

Monthly values : arithmetic means of daily means. However, the value is not calculated if more than 15 days are missing (cf. rules of the PSMSL).

Daily values: the choice of an arithmetic mean over a 24h period has the disadvantage that it does not adequately filter the signals from periods of less than one day, particularly those from tides for which a period of 24h50 would be more suitable. Filters have been designed to do this (Doodson, Demerliac). Pugh (1987) reexamined the different filters and concluded that the differences were minimal for the monthly means at Newlyn (1-2 mm). We have adopted the Demerliac filter for historical reasons, but the Doodson filter is proposed to the users as well. Click on the link to find out more about filters.

File format

The daily, monthly and annual heights are expressed in millimetres.
The dates are in decimal years (centred on the 15th day of the month for monthly values and at midday for daily values).