Issues with tides in COAWST Estuary_Test2

[stevenmiguelfigueroa]

Hi all.

I'm doing some research with the Estuary_Test2 grid from the COAWST repository. The bathymetry and OBC are:

est_test2.png (211.36 KiB) Viewed 2746 times

! W S E N
! e o a o
! s u s r
! t t t t
! h h
!
! 1 2 3 4

LBC(isFsur) == Cha Clo Gra Clo ! free-surface
LBC(isUbar) == Red Clo Cla Clo ! 2D U-momentum
LBC(isVbar) == Red Clo Cla Clo ! 2D V-momentum
LBC(isUvel) == Gra Clo Gra Clo ! 3D U-momentum
LBC(isVvel) == Gra Clo Gra Clo ! 3D V-momentum
LBC(isMtke) == Gra Clo Gra Clo ! mixing TKE

LBC(isTvar) == Cla Clo Cla Clo \ ! temperature
Cla Clo Cla Clo ! salinity

I would like to research a shallow, funnel shaped estuary which has the tidal characteristics of 1) tides go to zero in the eastern boundary (river), 2) 90 degree phase difference between elevation and current, and 3) flood-dominance.

When I plot the results I see the current goes to zero, but the elevation does not in the eastern boundary:

Alongchannel_zeta_ubar.png (23.26 KiB) Viewed 2746 times

When I plot elevation vs. current for selected points along the channel, I see the tide transforms rapidly from a 90 degree phase difference in the western ocean boundary (ellipse with a vertical semi-major axis) to one with about 45 degree phase difference (ellipse with tilted semi-major axis), then back to 90 degree phase difference at the eastern boundary (note here X distances are distance from western OB):

Furthermore, the currents are ebb-dominant (not shown).

My interpretation is that there is a standing wave in the eastern boundary. I have tried many combinations of boundary conditions, but the results are similar. Ideally I want to apply high friction so the tides dissipate before reaching that boundary, or have the tides radiate out from that boundary, but I have not had success with either of these. When I ran a strongly stratified simulation, I found that the freshwater couldn't escape the western boundary. But when I applied the western OBC from the Estuary_Test (different test case), it worked. But I still am unsure about the eastern OBC. To radiate them out makes the most sense, but it doesn't seem to work. Is it related to the nudging/relaxation setting or OBCFAC (factor between outflow and inflow)?

The mixed progressive-standing wave like character is the main thing which I have not been able to solve. I have tried several OBC, bathymetries, bottom roughnesses, and external forcing to no avail. I was hoping Estuary_Test2 would behave as a shallow, funnel shaped estuary, for which analytically the behavior is known to have a phase difference of 90 degrees (i.e., Friedrichs, 2010). I'm hesitant to continue building the model if it has a mixed progressive-standing character, as I typically expect a ~90 degree phase relation for estuaries. And later when I decompose the sediment fluxes, I expect it will result in more tidal pumping or Stokes drift than is typically the case in nature. My interpretation as to why, is that the width convergence length for Estuary_Test2 is about 4 km, which is very high convergence. So, I'm wondering if this mixed tidal character is a property of the Estuary_Test2 grid. Is there any way to get a 90 degree phase difference on it?

Lastly, I was able to solve the tidal asymmetry. Based on my research, reducing the width of the shoals converts Estuary_Test2 from ebb-dominance to flood-dominance.

To summarize my questions:

1) Can you recommend a way to dissipate the tides before reaching the eastern OB, or which eastern OBC and related settings to use to radiate the tides out?
2) Can you recommend a way to have a 90 degree phase difference between elevation and current in Estuary_Test2? (Or alternatively provide explanation for the mixed tides.)

Thank you.

Edit: I may be biased toward short estuaries which tend to be standing-like. According to Li and O-Donnell (2005), short estuaries tend to be standing-like, and long estuaries tend to be progressive-like. Could Estuary_Test2 be an in-between situation?

Friedrichs, C.T., 2010. Barotropic tides in channelized estuaries. Contemporary issues in estuarine physics, pp.27-61.
Li, C. and O’Donnell, J., 2005. The effect of channel length on the residual circulation in tidally dominated channels. Journal of Physical Oceanography, 35(10), pp.1826-1840.

[jcwarner]

Looks like you are digging in deep to the estuary test 2. I think Hans Burchard and I made up this case (mostly him) to have something different than the straight standard case we had before. To get the system to be the way you want, will require some tests. But here are some suggestions.
the eastern end is clamped and if you look in the Projects folder for estuary test 2 there is ana_m2obc with code:

#if defined ESTUARY_TEST2
ramp=TANH((tdays(ng)-dstart)/1.0_r8)
IF (LBC(ieast,isUbar,ng)%acquire.and. &
& LBC(ieast,isVbar,ng)%acquire.and. &
& DOMAIN(ng)%Eastern_Edge(tile)) THEN
my_area=0.0_r8
my_flux=0.0_r8
DO j=Jstr,Jend
cff=0.5_r8*(zeta(Iend ,j,knew)+h(Iend ,j)+ &
& zeta(Iend+1,j,knew)+h(Iend+1,j))/pn(Iend,j)
my_area=my_area+cff*umask(Iend+1,j)
END DO
my_flux=-1000.0_r8*ramp <--------------------------------------you can adjust this value to get a stronger river flow.
DO j=Jstr,Jend
BOUNDARY(ng)%ubar_east(j)=my_flux/my_area
BOUNDARY(ng)%vbar_east(j)=0.0_r8
END DO
END IF

also, you can try Fla for the east obcs for ubar and vbar. that will help to radiate the tide out, but then you may not get exactly the same transport as specified with the ana_m2obc. You will have to try some tests.

-j

[stevenmiguelfigueroa]

Dr. Warner, thank you for your helpful reply.
I'm curious whether there are any publications based on Estuary_Test2, or was research limited to the salt intrusion test featured in the COAWST manual?
For my application, I am using my own .nc river input file.

Your suggestion to try Fla for the east OBC did indeed radiate the tide out. Now the OBCs I'm using are symmetrically:

! W S E N
! e o a o
! s u s r
! t t t t
! h h
!
! 1 2 3 4

LBC(isFsur) == Cha Clo Cha Clo ! free-surface
LBC(isUbar) == Fla Clo Fla Clo ! 2D U-momentum
LBC(isVbar) == Fla Clo Fla Clo ! 2D V-momentum
LBC(isUvel) == RadNud Clo RadNud Clo ! 3D U-momentum
LBC(isVvel) == RadNud Clo RadNud Clo ! 3D V-momentum
LBC(isMtke) == Gra Clo Gra Clo ! mixing TKE

LBC(isTvar) == RadNud Clo RadNud Clo \ ! temperature
RadNud Clo RadNud Clo ! salinity

(However I may need to rework the eastern OBC considering that I am using river point sources which are not on the edge of a mask. It results in a persistent salinity column on the rho-points behind my river point sources).

I furthermore tried the new OBC with different bottom roughness heights. The along-channel zeta and ubar turned out as:

EastFlather_roughnesscompare.png (70.95 KiB) Viewed 2596 times

Looking at zeta vs ubar for selected points along-channel turned out as:

So, setting east OBC to Fla resulted in no standing wave there. Instead the tidal character was progressive (like a classical long, rectangular channel with weak friction). Considering the entire channel, this time the tide transformed from a phase difference between elevation and current of -90 deg, to -45 deg, to 0 deg. I suspected that the -45 deg was indicating a situation with a diffusive wave (long, shallow, nonconvergent case in Friedrichs, 2010). So I did a 2D momentum diagnostic run, and plotted the tidally averaged terms along the channel:

For the diffusive case, friction dominates acceleration of momentum. It ended up that the diagnostic didn't seem to support such a diffusive wave to explain the -45 deg phase difference in the central part of the channel.

Thank you again for your instruction. Your comment has certainly improved the tides for my version of Estuary_Test2.


Tarpley, D., Harris, C.K., Friedrichs, C.T. and Sherwood, C.R., 2019. Tidal variation in cohesive sediment distribution and sensitivity to flocculation and bed consolidation in an idealized, partially mixed estuary. Journal of Marine Science and Engineering, 7(10), p.334.

[stevenmiguelfigueroa]

I worked on this some more, and I thought I would post in case it is relevant for another researcher in the future.

A Flather condition in the east radiated the tides out, but it doesn't seem to jive with river discharge points, as they should be on land/sea or closed boundaries.
You can actually do it, but during floods the freshwater leaves to the east out of the domain.
As an alternative, extending the estuary length to until the tides dissipate and using a closed eastern boundary seems to suffice.
This approach had been mentioned briefly by Ganju and Schoellhamer (2009).


Ganju, N.K. and Schoellhamer, D.H., 2009. Calibration of an estuarine sediment transport model to sediment fluxes as an intermediate step for simulation of geomorphic evolution. Continental Shelf Research, 29(1), pp.148-158.