# What is the right geoid for calculating current sea depth from ECEF position and sea depth soundings

Let's say that I have an ECEF position (derived from GNSS, IMU, and barometric data) which is accurate to +-10cm. Let's also say that I have a chart of sea floor soundings, which, as unrealistic as it may be, we'll assume to be accurate to +-1cm.

I'd like to use the two to calculate the current water depth. The missing link is finding the local sea level datum in ECEF coordinates. Is there an appropriate geoid which captures the worldwide mean sea level to an accuracy of tens of cm (or better)? If not, what is the best fallback approach?

A water-line position in ECEF gives you an absolute position relative to the centre of the Earth but, by itself, no information on the relationship with depth or indeed orthometric height.

A chart with sea floor soundings typically gives you the depth of water below Chart Datum. The definition of Chart Datum varies depending on the local hydrographic authority. For example, in the UK Chart Datum is generally defined as close to Lowest Astronomical Tide (LAT); this is considered the lowest tidal level under normal circumstances. In the US the tidal level Mean Lower Low Water (MLLW) is the datum used.

Consequently, given the ECEF position:

1. Convert current ECEF into lat/lon/ellipsoidal height.
2. Determine the relationship between Chart Datum and the ellipsoid = N
3. Then, current water depth = current ellipsoidal height - N + sounding depth

The crux of course is determining (2) - the relationship between Chart Datum and the ellipsoid - this is not a simple problem.
Examples of existing solutions to the relationship between Chart Datum and the ellipsoid: In the UK and Ireland - use the VORF model. In the US - Vdatum. In France - Bathyelli.

A UK-centric high level view of the challenges involved: UKHO/UCL Vertical Offshore Reference Frame

• Thanks for the examples, and the very clear rephrasing. I had thought that the point of the geoid was to capture the water height (assuming no tides or weather which would locally and temporarily affect it). Is my understanding of the geoid wrong? Jun 11, 2021 at 23:34
• your general understanding of the geoid is correct. The issue is that for Safety of Life at Sea (SOLAS) applications the geoid is not an appropriate datum. This is why lowest tidal levels are used for chart soundings - not the geoid.
– JimT
Jun 11, 2021 at 23:37
• Gotcha. So I think what you're saying is that, while the geoid could in theory be used, in practice what I will find is that the datums are not referenced to the geoid, but instead to WGS84. And so the issue becomes the logistical challenge of finding the definitive local reference for any arbitrary country/body of water. Is this about right? Jun 12, 2021 at 4:13
• Yes - you need an ellipsoidally-modelled chart datum surface for relating GNSS observations with the charted depths. There is no global model as it will vary depending on the governing hydrographic authority.
– JimT
Jun 12, 2021 at 7:05

cool problem.

Most Datums used the mean sea level as their reference surface, and as such all heights (AHD as an example) are measured with reference to this datum - mean sea level. So whilst their probably isn't a suitable world datum (as this would be far too generalised and not 10cm accuracy) WGS84 is the global datum. There are localised datums which are more suitable for local areas (eg: In Australia we use GDA94) Have a read of this article for more info about local datums. https://en.wikipedia.org/wiki/Geodetic_datum