# Mean sea level, instant mean level, nominal mean level, mean ocean surface

## Mean sea level

The term "mean sea level" is ambiguous. Intuitively one would assume it to be constant. However, it is fundamentally variable since it depends on the period for which it was calculated. Though it is indeed a mean, it is obtained using the following formula where t1 and tN are the start and end dates of the observations and h (tn ) is the measured sea level height at time tn. The origin of the height measurements is fixed and the time interval between measurements is generally constant and short compared to the interval between successive high and low tides.  In practice, the term "mean sea level" is not the strict mean level observed, but the result of a digital filtering (of which the mean is only one particular case).

## Instant mean sea level

The "instant mean sea level" is obtained by subtracting the astronomical tide from the heights measured.

The instant mean sea level can, for statistical purposes, be considered as a random variable which is the height of the free surface in the absence of periodic oscillations due to astronomical effects. The average of N instant mean levels gives a more accurate result than the simple average height because it minimizes the residual periodic components, which are low over long periods, so it is usually from the instant mean level that the mean sea level is calculated over long periods. The difficulty is that, regardless of the time scale, even fairly long (a few years), this random variable is not stationary because the average depends on the sample considered.

The mean sea level (which should be accompanied by at least start and end dates of the calculation method) and the instant mean sea level relative to a terrestrial reference are a function of time. Neither value can be considered a vertical reference, because one of the fundamental criteria, stability, is not respected.

## Nominal mean sea level

For tidal predictions, we use the mean sea level calculated over the longest possible period that is set relative to the land and terrestrial reference frames. This is called the "nominal mean sea level". This calculation is performed for sites where there are long term tidal observations, if possible several years. These sites are referred to as reference ports.

## Mean sea surface

The mean sea surface (MSS) is calculated using satellite altimetry. The ellipsoidal height of the sea surface is averaged at each point of the track (after various adjustments to eliminate the astronomical tide). After interpolation to fill in the regions not covered between the tracks, the result is the mean surface representative of the mean level at each point (with the resolution permitted by the gaps between the satellite tracks) during the observation period.

MSS cannot currently be measured near the coast by satellite, and the resolution is lower than 20 km, which further limits its use in hydrography.

To find out more:

Reference

• Simon B. (2007). La Marée - La marée océanique et côtière. Edition Institut océanographique, 434pp.

Last updated: 12/12/2012