## Dependence of water levels on sigma parameters

### Dependence of water levels on sigma parameters

I am running the ROMS in Cook Inlet, AK which is tidally very active and am doing so in a fully three-dimensional baroclinic mode (i.e. SOLVE3D is defined) but with T=const. (15C) and S=const. (35 PSU) to validate (first) the water levels/elevations and the currents. The only forcing in the simulation is tides (no river, surface or T/S open boundary forcing, etc.). Once, I get the water levels and currents correct, I will then repeat the computation by also including T, S, river forcing, surface forcing and lateral open boundary forcing, non-tidal water level, etc.. For the vertical eddy-viscosity formulation, I am using the MY2.5 scheme (to begin with). The bottom friction formulation I am using is the quadratic one with Cd=0.003-0.008 and I have also coded up a spatially variable bottom friction formulation as an ana_*.h module which I have used.

I find that the water level predictions from ROMS are sensitive to the parameters I use in the vertical sigma grid formulation (i.e. theta_s and theta_b) and some combinations (e.g. theta_s=4.5, theta_b=0.95, Tcline=10) give relatively better water elevation predictions than other values (e.g. theta_s=6.5, theta_b=1.0, Tcline=10) - when I compare with the known harmonic consitituents at certain locations.

The simulation I am doing is effectively barotropic because T, S are constant and I was therefore quite surprised by why the water levels are sensitive to the sigma grid formulation parameters - after all, are not the water levels predicted by the barotropic equations which are 2D and hence "independent" of the vertical sigma grid distribution?

Could someone please let me know why this is so? In particular, is it due to a model formulation issue?

I find that the water level predictions from ROMS are sensitive to the parameters I use in the vertical sigma grid formulation (i.e. theta_s and theta_b) and some combinations (e.g. theta_s=4.5, theta_b=0.95, Tcline=10) give relatively better water elevation predictions than other values (e.g. theta_s=6.5, theta_b=1.0, Tcline=10) - when I compare with the known harmonic consitituents at certain locations.

The simulation I am doing is effectively barotropic because T, S are constant and I was therefore quite surprised by why the water levels are sensitive to the sigma grid formulation parameters - after all, are not the water levels predicted by the barotropic equations which are 2D and hence "independent" of the vertical sigma grid distribution?

Could someone please let me know why this is so? In particular, is it due to a model formulation issue?

### Re: Dependence of water levels on sigma parameters

what type of bottom friction r u using?

### Re: Dependence of water levels on sigma parameters

I am using the ROMS Quadratic bottom friction formulation (UV_QDRAG) and have tried Cd=0.003-0.010 (constant) values.

### Re: Dependence of water levels on sigma parameters

For the quadratic stress the model uses the velocity from the lowest sigma level and multiplies that with the rdrg2 value. As you change the number of levels, the bottom level will get closer to the seafloor and the velocity magnitude will most likely decrease and thus give a net smaller bottom drag for the same rdrg2 value. You might want to use a logdrag since it assumes a log profile in the region between the middle of the bottom cell and the seafloor. in this case, as you change number of sigma levels the velocity will also chnage but its vertical location will be accounted for in the log(z/z0) type of computation.

-j

-j

### Re: Dependence of water levels on sigma parameters

In the water level sensitivity studies I did, I always kept the number of vertical model levels, Nz constant and the quadratic drag coefficient, Cd constant also and only varied the theta_s, theta_b values. But I guess this then changes the height of the first rho-point in the vertical above the model ocean bottom and hence also the u and v velocity components at this location and thus the bottom friction value from the formula : stress u = Cd*u*sqrt(u*u+v*v). So this might be the reason why the water levels are sensitive to the vertical sigma grid formulation stretching coefficients?

### Re: Dependence of water levels on sigma parameters

possibly yes.

- drews
**Posts:**35**Joined:**Tue Jun 19, 2007 3:32 pm**Location:**National Center for Atmospheric Research-
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### Re: Dependence of water levels on sigma parameters

Cd=RDRG2=0.003 is the ROMS default. Can you tell me what RDRG2=0.010 means physically? A lot of rocks on the bottom? A lot of seaweed? What would be a reasonable maximum value?I am using the ROMS Quadratic bottom friction formulation (UV_QDRAG) and have tried Cd=0.003-0.010 (constant) values.