Steric SSH changes

[julia-neme]

I've been calculating steric changes here as:

This integrates the departure of density from a reference density. I didn't know what value to assign to the reference density, so I chose it to be the time mean, that is it depends on (x, y, z). I had done it only for the upper and lower 100m, will do for the entire column now.

[julia-neme]

Total steric contribution to SSH in control, up and down:

Up and down anomalies with respect to control:

Looking at Figure 2 it doesn't seem that changes at the end of the simulation come from steric contributions, since they are approx one order of magnitude less... although someone might want to check my script :)

[StephenGriffies]

@julia-neme is the density here the in situ density? That is what it should be for computing steric effects. I ask since some folks mistakenly use potential density.

[julia-neme]

Hi stephen! Yes, its in-situ density calculated using gsw.rho (Gibbs SeaWater toolbox).

[StephenGriffies]

Sounds good.

[julia-neme]

As per our discussion today, in the calculation I replaced the reference density by a constant value (1035) instead of using the time mean for each experiment. I think it is what we wanted:

Should I still calculate it using density from control and dz from the perturbation?

[adele-morrison]

Nice, yes, so changing the reference density just aligned the starting points. We're still off by a factor of 2-4.

Yes I think it would still be good to do the control density with dzt from WIND+ to see how much of that change is coming from dzt vs rho.

[adele-morrison]

@StephenGriffies we have a question for you. We're struggling to reconcile the net sea level changes over the continental shelf with the Ekman effect (i.e. the change from the zonal wind only experiment) plus the steric effect (calculated above from in situ density change).

Is there anything else obvious that we're missing? Could the fact that we have more sea ice formation and export out of the shelf region be contributing to reducing sea level around Antarctica?

[julia-neme]

Dashed blue line in this plot is using density from control and dzt from WIND+. This confirms that all the changes are coming from density changes right?

But true, this is half of what the total changes in SSH show..

[StephenGriffies]

Hi. I will try to look at this asap. Sorry for my delay.

[StephenGriffies]

Hi @julia-neme and @adele157

Two suggestions. One trivial and the other more fundamental.

1/ Does the sea level you are plotting include the inverse barometer effect from sea ice? Using MOM5 lingo: are you plotting "sea_level" or "eta_t"? The sea_level diagnostic removes the inverse barometer, whereas eta_t is the actual position of the model's free surface top interface. For sea level studies such as in CMIP, we want sea_level. But when interested in model development, eta_t can be more important. Note that if "max_ice_thickness = 0.0", then eta_t = sea_level, since in this case the weight of sea ice does not affect the ocean free surface. This might be the setting in ACCESS, but unsure.

2/ When studying regional sea level patterns, it is useful to decompose sea level changes into local steric changes plus mass changes. Steric changes to sea level result from changes to density as integrated over the total depth of a column. As such, steric effects are typically more important for sea level over the deep ocean, where there is more water to integrate over. That then leaves the shelves as regions where mass changes can be more visible, with mass changes revealed by bottom pressure changes. So my guess is that you are missing the bottom pressure term in your diagnostics, and that can play a big role in some shelf regions.

For the physics and maths of what I am talking about, see Appendix B of Griffies et al (2014): http://dx.doi.org/10.1016/j.ocemod.2014.03.004

One modest qualifier: bottom pressure changes in a Boussinesq model can be a bit tricky given that Boussinesq models do not conserve mass but instead they conserve volume. Griffies and Greatbatch (2012) talk about the way to correct for this term in Section D.3.3 of http://dx.doi.org/10.1016/j.ocemod.2012.04.003

My recommendation for your shelf analysis is to ignore this Boussinesq correction for now. I suspect it is not important for your purposes. Rather, it is important for studies of the angular momentum budget as in

Bryan, F. O. (1997). The axial angular momentum balance of a global ocean general circulation model. Dynamics Of Atmospheres And Oceans, 25, 191-216 pp. doi:10.1016/S0377-0265(96)00477-0

I hope this helps.

[julia-neme]

Thanks @StephenGriffies! Lets see if I got this right.. Regarding:

1. I am using sea_level, and I think that max_ice_thickness = 0.0, but maybe @adele157 can confirm that. Therefore we are not including the inverse barometer effect due to sea ice, and we "shouldn't" worry about that?

2. I am not including mass changes. I thought that we could recover mass changes simply by looking at the decrease that would come from X amount of freshwater export from the study region, but that doesn't bring us closer to fully explaining sea level changes at the end of our simulation by steric+mass changes effects.

   Including only steric effects explains about half of the full sea level changes (see Figure 2 here only up to the year 2158.) However, if you look at Figure 8c, and considering that the total area of our study region is ~5e12 m2, that doesn't amount to the ~0.3cm change we need.

I will take a look at the Boussinesq correction, maybe discuss in our next hackathon and come back to this soon. I hope I have interpreted you answer correctly :)

[StephenGriffies]

1. With max_ice_thickness = 0.0 then sea_level = eta_t. So do not concern yourself with the sea ice inverse barometer as it is absent from this simulation. It does not affect the computed sea level in the model.

2. How are you computing the freshwater export? And are you including the net mass input arising from E-P+R through top of the ocean. Note that I am looking at equation (48) in Griffies et al (2014), where you see that bottom pressure changes arise from E-P+R as well as convergence of depth integrated mass transport. That is, are you sure you have a closed mass budget (really a closed volume budget since model is Boussinesq) for the shelf region?

I do not think the Boussinesq correction is needed. Recall the model is Boussinesq, so this correction term is not what the model will include when computing its free surface. Instead, I think the answer sits with the mass budget.

[julia-neme]

I calculated the mass term now, as the average over our study region of bottom pressure divided by g and rho_0 = 1035, following equation (48) in Griffies et al (2014). Here you can see both terms, mass changes and steric changes:

And here you can see their sum:

Almost there but not quite matching our Figure 2, where at the end of the simulation WIND+ shows ~+-.75cm and WIND- ~-1cm.

[adele-morrison]

Thanks Julia! And thanks @StephenGriffies for the references and info. Julia, do you think you could add the raw sea_level anomaly time series to this for comparison? Figure 2 has some complicated things going on, if I remember right, we subtracted the control climatology and applied a 12 month rolling mean.

[julia-neme]

I had a unit conversion error that @adele157 spotted. Corrected figures below:

It's not a perfect match.. but quite close. From what I gather that the mass contribution is more significant than steric changes actually for what we see in the last years of the simulation..