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**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).

Sea level observations are traditionally recorded as hourly heights. Subsequently, the mean sea level is derived using a linear combination of these heights (Bessero, 1985).

**Fig. 1 : Mean sea level computation formulae, where M=2n+1, ∆ is the sampling, a _{k} is a sequence of real coefficients. **

Several such linear filters exist to compute the daily mean sea levels. Theoretically, the longer is the vector a_{k}, the more efficient is the filter for the reduction of the tidal effects (it takes into account more observations), but the more limited will be its application in the case of tide gauge observations containing gaps. The Demerliac filter is a good trade-off recommended by the French hydrographic agency (SHOM). It uses a 71 elements symmetric vector a_{k} (see the table below)

k | Avergae of 25 heights 25*a _{k} | Doodson filter 30*a _{k} | Munk "Tide Killer" filter 10^7*a _{k} | Godin filter 14400*a _{k} | Demerliac filter 24576*a _{k} |
---|---|---|---|---|---|

0 | 1 | 0 | 395287 | 444 | 768 |

1 | 1 | 2 | 386839 | 443 | 766 |

2 | 1 | 1 | 370094 | 440 | 762 |

3 | 1 | 1 | 354118 | 435 | 752 |

4 | 1 | 2 | 338603 | 428 | 738 |

5 | 1 | 0 | 325633 | 419 | 726 |

6 | 1 | 1 | 314959 | 408 | 704 |

7 | 1 | 1 | 300054 | 395 | 678 |

8 | 1 | 0 | 278167 | 380 | 658 |

9 | 1 | 2 | 251492 | 363 | 624 |

10 | 1 | 0 | 234033 | 344 | 586 |

11 | 1 | 1 | 219260 | 323 | 558 |

12 | 1 | 1 | 208050 | 300 | 512 |

13 | 0 | 195518 | 276 | 465 | |

14 | 1 | 180727 | 253 | 435 | |

15 | 0 | 165525 | 231 | 392 | |

16 | 0 | 146225 | 210 | 351 | |

17 | 1 | 122665 | 190 | 325 | |

18 | 0 | 101603 | 171 | 288 | |

19 | 1 | 85349 | 153 | 253 | |

20 | 72261 | 136 | 231 | ||

21 | 60772 | 120 | 200 | ||

22 | 47028 | 105 | 171 | ||

23 | 30073 | 91 | 153 | ||

24 | 13307 | 78 | 128 | ||

25 | 66 | 105 | |||

26 | 55 | 91 | |||

27 | 45 | 72 | |||

28 | 36 | 55 | |||

29 | 28 | 45 | |||

30 | 21 | 32 | |||

31 | 15 | 21 | |||

32 | 10 | 15 | |||

33 | 6 | 8 | |||

34 | 3 | 3 | |||

35 | 1 | 1 |

**Tab. 1 : Coefficients used for different linear filters. For each filter, a _{k}=a_{-k}.**

Source : Bessero (1985)

**Some useful links:**

R Script of the Demerliac filter

R script of the Doodson filter

R software website

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**References:**

Bessero G. (1985). Marées. SHOM, Fascicule 2, chap. IX à XV.

Help us to have the most complete and updated database

SONEL aims at providing high-quality continuous measurements of sea- and land levels at the coast from tide gauges (relative sea levels) and from modern geodetic techniques (vertical land motion and absolute sea levels) for studies on long-term sea level trends, but also the calibration of satellite altimeters, for instance.

SONEL serves as the GNSS data assembly centre for the Global Sea Level Observing System (GLOSS), which is developed under the auspices of the IOC/Unesco. It works closely with the PSMSL and the University of Hawaii Sea Level Center (UHSLC) by developing an integrated global observing system, which is linking both the tide gauge and the GNSS databases for a comprehensive service to the scientific community. It also acts as the interface with the scientific community for the French tide gauge data.