We (@mengel , @sitreu) have now come to the following conclusion:

It is standard to reference the bathymetry to a mean state of the sea level (including dynamic effects). In merged topography datasets (e.g. *ETOPO1*) with topography over land and over ocean, the part over the ocean is referenced to a mean state of the ocean (e.g. *mean sea level (MSL)*) and referenced to the geoid over land. There is a discontinuity at the cost (because the geoid of course does not include dynamic ocean effects) which is handled in some way (I don't know how exactly). Geoclaw assumes that the topography is referenced this way and therefore the *sea_level* parameter is only a constant offset of the mean state of the ocean.

We have agreed now that we will go a slightly different path for simplicity. We use the geoid as reference for the topography over land and over the ocean. The mean state of the ocean is then added via the constant *sea_level* parameter. However we will use the most resent geoid *GOCO06s* as reference which has a much better resolution compared to the outdated *EGM96* and is much closer to the mean sea level. The *sea_level* parameter defined as the mean value (or center as currently) of the mean sea level above geoid over a lat-lon-box varies much less for the choice of *GOCO06s* as geoid compared to *EGM96* which was used so far.

Please also look at issue #2 on the variance of sea level above geoid and the sensitivity of the *sea_level* parameter for different choices of the geoid.

I prefer option 1 because it seams to be the easiest to implement. We should however check how "bad" the local assumption of constant sea level effects is for our model domains.

I think we have three options:

- Reference
**B**and the DEM to GOCO05s and approximate difference between the sea surface and the geoid by a constant value*sea_level*. This means that we need to change the reference system in the current code but the rest remains the same. - Reference
**B**to MHW and the DEM to GOCO05s, approximate the offset between MHW and GOCO05s+ additional effects such as sea level rise by a contsant value*sea_level* - Change geoclaw to accept sea_level to be a spatially varying vector field instead of a scalar value. Then any reference system can be used.

We need a common vertical reference system for bathymetry and DEM in our set up. Therefore referencing bathymetry to MHW is not working for us as this is not possible for the DEM.

However if the vertical reference system for bathymetry is not MHW the mean dynamic topography and mean tidal effects, which are spatially varying, must be reflected in the *sea_level* parameter of geoclaw. The flaw is that this is a scalar value in geoclaw. The best we can do in this case is to choose a high resolution geoid such that the mean dynamic topography and tidal effects have less spatial variability locally such that it can locally be approximated by a constant offset from the geoid.

It seems this definition above is not fully reflected in the data we currently provide as bathymetry to GeoClaw. Rather, we provide a "classic" bathymetry

B'of topography referenced against a Geoid (EGM96 currently).

I would not say that we provide a "classic" bathymetry. The standard is rather to specify bathymetry relative to the sea surface.

What is here called bathymetry

Bdoes not only include the depth of the ocean floor relative to a fixed georeference (typically Geoid), but also all the spatial (and for GeoClaw time constant) variation of the sea surface water, so mean dynamic topography and mean tidal effects.

Geoclaw mentions that a typical reference for **B** is the mean high water level (MHW). This is also a georeference but includes as you rightly say mean dynamic topography and mean tidal effects. However it does not change the definition of **B** which is the position of the sea floor relative to a vertical reference system. It is just a different reference system.

As pointed out above this reference system is however not defined over land and therefore it is unclear how to reference the topography over land consistently with the bathymetry.

I try to put it in different words.

The core problem is that in geoclaw *sea_level* is defined as a scalar value and not a spatially varying field.
The thickness of the fluid modeled in geoclaw: *h*, is calculated as the difference between the sea surface and the bathymetry * B*.

*h* = *sea_level* - **B**

If *sea_level* and * B* were both spatially varying fields with the same vertical reference datum, this reference datum would cancel out for

But in geoclaw the sea surface is defined as a scalar value *sea_surface*. When calculating *h* = *sea_level* - * B* there is an implicit assumption that both

This is the reason why it matters which vertical datum we choose. It must be a vertical datum that is as similar to the actual sea surface as possible.

- The geoclaw documentation argues that a common choice for the vertical reference of bathymetry is the tidal maximum over a long (i.e. 19 years) time period, i.e. the Mean High Water (MHW). In this case, the assumption that the sea surface is parallel to the vertical reference is true and a temporal difference to the MHW level like sea level rise can be added as a scalar offset. The problem with this choice of a vertical datum is that MHW is only defined over the ocean. It is therefore not possible to use this reference for the topographic data over land, i.e. the DEM. Discontinuities at the coasts can not be avoided in this case.
- We currently use the geoid model
*EGM96*as reference for the bathymetry, the DEM, and the satellite altimetry used to calculate the scalar value*sea_level*which is taken as the value at the center of the simulation domain.*EGM96*is often used as reference for DEM data. However it is a relatively coarse geoid model and differs from the newer*GOCO05s*by up to*6m*locally. The assumption that the sea surface is parallel to this vertical datum is not good. In*Figure 1*we show the average sea surface over the years 1993-2012 referenced to the*EGM96*for the simulation domain of storm 2004319N10134. The standard deviation of this sea surface over the simulation domain is 0.65m and the largest difference is 3.57m. - An alternative approach would be to reference everything to the higher resolution and state of the art GOCO05s geoid. The sea surface referenced to this geoid has much less variation with a standard deviation of 0.09m and a maximum difference of 0.31m (see
*Figure 2*). In this case we do not have a discontinuity to the DEM but we are also further away from the true sea surface compared to the MHW reference system

**Figure 1**: Mean sea level in the period 1993-2012 referenced to the EGM96 geoid

**Figure 2**: Mean dynamic topography in the period 1993-2012 referenced to the GOCO05 geoid

Source_code for producing the figures and statistics described above

**Simon Treu**
(af1daf23)
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at
16 Nov 14:33
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Update number of epochs in training loop from 50 to 2

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... and
2 more commits
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**Simon Treu**
(e379af65)
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at
09 Nov 15:47
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Fixed bugs in the basic model architecture