ROMS Radiation Boundary condition (RadNud)

[stan_martyanov]

Dear all!

After reading the paper by Marchesiello et al., 2001 "Open boundary conditions for long-term integration of regional ocean models" and several other ROMS-related articles, as well as almost all related topics here on the Forum, I still don't have a complete understanding of the RadNud boundary condition option implemented in ROMS. I hope that experienced ROMS-users can easily help me with my question.

As follows from Marchesiello et al. 2001, the condition is based on the 2D radiation scheme (oblique radiation) proposed by Raymond & Kuo (1984)+weak nudging, with the addition of strong nudging to the external data in case of inward wave direction.

My question concerns the fact that the RadNud condition, as it follows from the very idea of this condition and the paper by Marchesiello et al. 2001, must deal only with wave-like motions (external mode, fast gravitational waves - tides, storm surges, etc) because we compute the phase velocity and use it to radiate out the internal information (ssh, ubar, vbar). The complete equation is as follows, where Cx, Cy are phase speed components:


But in practice this condition is also used for 3D variables (uvel, vvel, temp, salt, tracers).

How can radiation condition RadNud which utilizes the long-wave speed be used for, say, advection of tracers through the boundary (outward direction) when the external fast waves are absent or already dealt with by this or another BC (e.g. Flather+Chapman)? I mean, in this case we should use advection velocity (uvel, vvel) and not the phase speed (Cx, Cy). When the direction of the flow is inward (information coming into domain) the strong nudging deals with the boundary condition easily and there is no phase speed to consider (C=0). Nevertheless, even in this case to bring some information into the domain, we should use the value of incoming field (say, S) at the boundary and advection velocity.

But when the flow is outward, I really have some difficulties in understanding how to advect out tracers (or uvel, vvel) using long-wave phase speed... Maybe I miss something and in this case the actual speed that is used in this BC is not a phase speed but rather the advection speed (using upwind scheme or something)?

Kind regards,
Stan

[kate]

For each field using RadNud, the phase speed is computed locally, at each point on the boundary. If you look, that phase speed can be quite noisy, in time and space. You could try using ambient velocity instead, but the point is that you are trying to radiate away waves, which don't necessarily move with the ambient velocity.

One could add a temporal filter to the phase speed, but one would have to do extra work to get perfect restarts.

[stan_martyanov]

Thank you for your reply, Kate!

I did not provide the corresponding formulas used to compute the phase velocity, but I know that phase velocities Cx and Cy are computed separately for each variable along all open lateral boundaries. And that RadNud condition is applied separately for each variable, it is clearly mentioned in the paper by Marchesiello.

The thing I still cannot fathom (and which I could not find in the corresponding paper) is why (in the default ROMS RadNud condition) we use phase velocity for all situations and do not use advection velocity for 3D variables. I understand that using the phase speed deals with radiation of the information out of the domain by internal (baroclinic) long waves. The radiation of information (namely, ssh, ubar, vbar) by external mode is implemented by Flather+Chapman or another RadNud condition for these variables. This is what I understand. Could you please confirm if I am correct at this point?

But how does it help to transport the information (say, uvel, vvel, T or S) through the boundary by means of ordinary currents and not the wave-motion? Say, I have a domain with 3 open boundaries. And there is a significant non-stationrary (and strongly alternating in time, depth and direction) flow though the boundaries, and this flow is not due to tides or other long waves, but it is due to ocean currents (advection with speed app. 30-50 cm/sec). How to deal with such situation using the default RadNud condition?

[wilkin]

A radiation condition for 3-D variables is potentially sensible if you have 3-D wave motions emanating from the model interior, such as internal gravity waves, that might reflect at the boundary. This was the general idea behind the original Orlanski (1976) paper that inspired this approach.
https://www.sciencedirect.com/science/a ... 9176900231

But as Kate points out, if you actually go in and inspect the computed phase velocities they are very noisy and do not paint a picture of coherent wave fronts impinging on a boundary.

These are very imperfect boundary conditions, but that is almost always the case in regional modeling. The guidance I always give is ... "if you care about your solution near where the boundary is, don't put a boundary there."

[stan_martyanov]

Thank you for the reply, John!

Yes, the computed phase speed estimation and its resemblance to the white noise near the open boundaries was also reported by Treguier et al. (2001), so it is a really well-known issue, and still one of the causes of critique imposed on modelers from mathematicians-theoretists .

But, I'm still interested in situation I described earlier: almost no long waves, transport of information through the open boundaries is mainly due to currents. So, I suspect, that the implicit answer to my question is: RadNud condition as it is implemented in ROMS cannot appropriately handle such situation. Is it correct?

As I understand, in this case, due to almost chaotic fluctuation of phase speed near the boundary, the actually remaining part of the RadNud condition for such situation will be the (clamped+nudging) condition. It may be OK if we speak about inflow because the nudging is strong in this case. But what about outflow due to currents? Due to small nudging and actual absence of phase speed, how can information be transported by currents through the boundary during the inflow period?

Maybe in this case the better option is to set the Clamped BCs explicitly in ROMS? Yes, it will lead to problems in long-waves travel and their reflection etc, but it will handle transport due to currents. Am I correct in this?

PS: what I'm trying to do by asking all these annoying questions is not to criticize the available tools implemented in ROMS, but to find out what is the more or less best practice to use ROMS and particularly its OBCs options in situation I described.

[arango]

Except periodic boundary conditions, all the open boundary conditions in ROMS are ill-conditioned from the purest mathematician point of view. The only thing that we can do is minimize its errors. There are several strategies that are available, as you found out. In my experience, we need to first control the open boundary conditions for the vertically-integrated equations (ubar, vbar, and zeta) because of the fast-dynamics of the system. If those are wrong, your 3D solutions will be contaminated and in trouble.

Then, we do the 3D equations. You have several alternatives but pay attention to the tracers (temperature and salinity) first because they govern the other equations via the density. You can use radiation plus nudging and determine the time scales. If there is still noise, add a sponge with higher diffusivity and viscosity. Also, you can add a nudging term to tracer equations that only operates in the sponge around the open boundaries to control inflows. You will need to activate the climatology options.

If after all these, you are having issues then your regional grid is not optimal. Open boundaries should stay away from major bathymetry features and circulation variability. That's where the ocean modeler experience is an asset.

[kate]

If you feel that using the local velocity would be better in your situation than the phase speed, you should try coding it up and seeing how it behaves. I expect that was tried at some point and found wanting, but we only had a limited number of domains when trying this stuff.

[wilkin]

Clamping and nudging won't help you if you have an advection dominated outflow because the exterior conditions know nothing of the interior solution that is propagating out along characteristics of the current. They will act as a wall.

You might be better off simply using gradient conditions, which extrapolate what is reaching the boundary one more grid cell to the perimeter.

For example, I am working right now with a simple idealized estuary for a class I am teaching. In the case plotted below, a river plume exits the estuary, turns right, and tries to flow out the open boundary. In both plots the 2D OBC are Chapman/Flather.

But in the top panel u,v,T,S have Gradient conditions on the "southern" boundary, while in the bottom panel the 3-D variables are Radiation. With radiation the outflow is impeded and partially wraps up into the domain.

I think of Gradient conditions as effectively setting the outflow phase speed to delta-y/delta-t because it propagates the solution exactly one grid cell. Maybe this is what you want.

[stan_martyanov]

It looks like it is getting clearer to me now about possible ROMS configuration in my case (I believe I forgot to mention - I'm building a high-res Kara Sea regional model).

Based on what I've heard here, I'll start with Flather+Chapman for ubar, vbar and zeta, and with RadNud for 3D variables with more or less strong nudging for both inflow and outflow (but still keeping Tau(in) << Tau(out) of course).

If it doesn't work, I'm going to try clamped condition for 3D variables still keeping Flather+Chapman for vertically-integrated equations. Also, the use of a nudging layer looks attractive in both cases. But I'm not sure about using the sponge layer since it will suppress the variability I'm trying to introduce through the open boundaries.

I really want to thank all of you for your kind assistance and helpful suggestions!

Kind regards,
Stan

[stan_martyanov]

Clamping and nudging won't help you if you have an advection dominated outflow because the exterior conditions know nothing of the interior solution that is propagating out along characteristics of the current. They will act as a wall.

You might be better off simply using gradient conditions, which extrapolate what is reaching the boundary one more grid cell to the perimeter.

For example, I am working right now with a simple idealized estuary for a class I am teaching. In the case plotted below, a river plume exits the estuary, turns right, and tries to flow out the open boundary. In both plots the 2D OBC are Chapman/Flather.

But in the top panel u,v,T,S have Gradient conditions on the "southern" boundary, while in the bottom panel the 3-D variables are Radiation. With radiation the outflow is impeded and partially wraps up into the domain.

I think of Gradient conditions as effectively setting the outflow phase speed to delta-y/delta-t because it propagates the solution exactly one grid cell. Maybe this is what you want.

Oh, thank you very much! I'm also working with the estuary dominated region and these results seem very helpful! It looks like my hypothesis about clamped condition is not good.

But in the top panel u,v,T,S have Gradient conditions on the "southern" boundary

Based on these figures, It looks really good. What do you use on the northern boundary for 3D variables then? Also gradient condition? Do you have any inflow from the north or east?

UPD: as I understand, gradient condition will not help if there is also an incoming current-related flow through the same boundary where I want to release riverine waters (say, in the eastern part of your southern boundary). In other words, inflow+outflow can not co-exist at the same boundary in gradient condition.

[patrickm]

Bonjour

I'd like to make two points:
1- OBCs are designed to handle both physical and numerical modes, and are probably more useful for the latter. This is probably why, in all our long-term simulations, Orlansky-type radiation conditions (in the active/passive approach) outperformed all others in terms of transparency and solution control, despite (or thanks to) the noisy aspect of the calculated radiation velocity.
2- Short-term and long-term performance are very different. In PE equations, and especially in discretized equations, OBCS are ill-posed, and there is always a trade-off between underspecification and overspecification, i.e. between transparency and solution control. With underspecification (gradient conditions, for example), the solution appears very continuous and may be suitable for short-term study, but in the longer term, this would lead to solution drift. The set of solutions presented in our 2001 article mainly concerns realistic long-term regional simulations.

Patrick

[stan_martyanov]

Hello Patrick!

Thank you very mush for this information, it really helps because after reading your article (2001) the question about dealing with current-related inflow/outflow in ROMS is, in fact, the only one that remained in my understanding, all other aspects of the model setup and OBCs' features were clearly described.

Based on what you told:

This is probably why, in all our long-term simulations, Orlansky-type radiation conditions (in the active/passive approach) outperformed all others in terms of transparency and solution control, despite (or thanks to) the noisy aspect of the calculated radiation velocity.

and

The set of solutions presented in our 2001 article mainly concerns realistic long-term regional simulations.

will it be correct to suppose that the RadNud condition you designed and used in the paper, although mathematically constructed to deal with wave-like motions, still can handle relatively slow current-related flows through the open boundaries due to (thanks to?) a noisy behavior of the calculated phase speed?

Two posts earlier John Wilkin demonstrated the problems with RadNud condition in advection-dominated region.

Did you try to take into account the advection speed through the open boundaries to advect the 3D variables in/out the domain? There is no information about it in the paper.

Thanks in advance!

Stan