'zeta' in ROMS

[feroda]

Recently, I am looking at altimeteric data, which contains both anomaly and absolute value. At that point, a doubt came to my mind --
If the model starts from rest state, WHAT does 'zeta' mean in ROMS (SSH anomaly or absolute SSH)? Thanks!

[wilkin]

ROMS zeta is "absolute SSH" in the sense that it includes time mean and time varying SSH with respect to a datum (i.e. zeta=0) that is a geopotential surface, i.e. if zeta=constant there is no associated pressure gradient force.

Altimetrists do not say "absolute" SSH so let me clarify:

In altimetry the equivalent quantity to ROMS zeta is close to the sum of mean dynamic topography (MDT) and sea level anomaly (SLA).

MDT is the height of the long-term time mean sea level with respect to a geopotential surface (the marine geoid). This is different from the Mean Sea Surface which has huge slopes in it because of variations in gravity due to the uneven distribution of the earth's mass. These geoid slopes are not relevant to ocean dynamics so MDT+SLA is the most ROMS-like quantity because the slope of MDT+SLA is almost equivalent to the slope of zeta.

Why do I say "almost"? Well there are some subtleties here.

Note that tides are usually removed from altimeter SLA, though you can choose to leave them in depending on how you are acquiring your altimeter data. ROMS has tides so remember that.

The inverse barometer effect is usually removed from altimetry BUT ALSO absent from ROMS (so no problem there).

Other high frequency sea level variability is not removed from SLA so just keep that in mind (coastal trapped waves for example).

But where we cannot immediately reconcile altimetry and ROMS is the steric effect associated with thermal expansion of the water column. This is real and observed by altimeters, so included in SLA. But ROMS is a Boussinesq model so this effect is neglected. On a seasonal time scale the steric effect might be significant in SLA but it always has long wavelengths so is seldom relevant to coastal dynamics. In our experience, mesoscale SLA variance is much larger and the steric effect disappears in the noise. But strictly speaking one should make some allowance for this missing dynamics in ROMS if it's relevant to the problem you are studying.

John.

[susonic]

Dear code developer and users,

Recently I was told that there is a branch of ROMS which can add steric effect.
That model is developed by Song and it is not a open source code.
These days the climate variability is becoming more important and I think that it is necessary to consider the steric height for calculating long term variability such as 100 years or so.

I'm wondering whether we can add non-boussinesq code in Rutgers ROMS.

[mengqingjun]

ROMS zeta is "absolute SSH" in the sense that it includes time mean and time varying SSH with respect to a datum (i.e. zeta=0) that is a geopotential surface, i.e. if zeta=constant there is no associated pressure gradient force.

Altimetrists do not say "absolute" SSH so let me clarify:

In altimetry the equivalent quantity to ROMS zeta is close to the sum of mean dynamic topography (MDT) and sea level anomaly (SLA).

MDT is the height of the long-term time mean sea level with respect to a geopotential surface (the marine geoid). This is different from the Mean Sea Surface which has huge slopes in it because of variations in gravity due to the uneven distribution of the earth's mass. These geoid slopes are not relevant to ocean dynamics so MDT+SLA is the most ROMS-like quantity because the slope of MDT+SLA is almost equivalent to the slope of zeta.

Why do I say "almost"? Well there are some subtleties here.

Note that tides are usually removed from altimeter SLA, though you can choose to leave them in depending on how you are acquiring your altimeter data. ROMS has tides so remember that.

The inverse barometer effect is usually removed from altimetry BUT ALSO absent from ROMS (so no problem there).

Other high frequency sea level variability is not removed from SLA so just keep that in mind (coastal trapped waves for example).

But where we cannot immediately reconcile altimetry and ROMS is the steric effect associated with thermal expansion of the water column. This is real and observed by altimeters, so included in SLA. But ROMS is a Boussinesq model so this effect is neglected. On a seasonal time scale the steric effect might be significant in SLA but it always has long wavelengths so is seldom relevant to coastal dynamics. In our experience, mesoscale SLA variance is much larger and the steric effect disappears in the noise. But strictly speaking one should make some allowance for this missing dynamics in ROMS if it's relevant to the problem you are studying.

John.

Hi John, I am comparing the results of ROMS oupput using the AVISO data,as you said ,I used ADT,which has the reference surface of teh geoid. But the value of ADT is somehow bigger than the 'zeta'(free surface) in ROMS .I am wondering is the reference surface used in ROMS the same that used in ADT ? Thank you for reply !

[wilkin]

But the value of ADT is somehow bigger than the 'zeta'(free surface) in ROMS .I am wondering is the reference surface used in ROMS the same that used in ADT ?

There is no simple answer to that question. The reference surface in ROMS is whatever you mean it to be when you conceive your model configuration, and choose the geographic extent, the bathymetry and the coastline. If you have digital bathymetry data from some geodetic service then that will have a defined datum. Navigation data is frequently with respect to MLLW (mean lower low water) in which case when depth h=0, and zeta=0 (i.e. you are at the edge of the water) then the tide is actually dead low water. In ROMS you would want dead low water to occur when zeta = minus the tide amplitude. So what to do ...

Consider your model set-up and ask: if everything were stationary and zeta became flat what value would I want it to have? Because you can quite legitimately initialize ROMS at rest with zeta = non zero constant. That is well posed.

So a starting point would be to calculate the average of AVISO MDT in your domain and set average initial zeta in ROMS to be the same. This is not quite right because locally the MDT is in balance with the mean velocity. And depending on what you do at open boundaries you may get a rapid adjustment back to your open boundary data.

Even so, if you are taking AVISO ADT as open ocean boundary condition data and downscaling to some coastal domain, then at the coast your model dynamics will give a different MDT because of the mean flow you set-up. You should not expect your new coastal MDT to match AVISO - that's the whole point of downscaling.

I suggest you compare your model mean zeta to AVISO MDT in deep water (where AVISO is valid - it is not good on many continental shelves) and if it seems to be typically offset by a constant then just add/subtract that constant from your initial zeta.

You read more about vertical datum at
http://oceanservice.noaa.gov/facts/vdatum.html
and
http://vdatum.noaa.gov/about.html

[lmp4]

I have been thinking about this alot recently; and to go off topic slighly I want to talk about the steric signal. All previous studies that have used AVISO SSH data have removed the steric signal. However I am really not sure how to do this myself...

This paper http://www.geo.utexas.edu/courses/387H/ ... jgr_04.pdf has been quoted as the 'willis database' a means to remove the signal but I simply can't understand it and how to proceed from here.

[susonic]

I also agree with Luke's opinion.
I have been trying to find a way to remove the steric signal from SSH.
But since I'm a novice user of ROMS, I do not know how to do it.
Are there any recommendation or tips to do it?
Any answer would be appreciated.

JH

[lmp4]

Hi, Sorry I forgot to follow up on this! I'd try contacting Willis (the author of the paper I linked to) directly The database is actually a mat-lab file containing steric height corrections.

[susonic]

Hi Luke,

How can I get the matlab script?
Sould I contact to Willis or
Would you send the script to my e-mail or upload to this post?
ocean0510@gmail.com

-JH

[lmp4]

I'd contact Willis and ask him.