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> Filters for the daily mean sea level computation

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.