I'm having problems with pressure gradient errors over an idealized continental slope application. My initial field is just flat stratification, with an N2 profile derived from a climatological dataset. I have baroclinic (barotropic) velocity errors of 10 cm/s (4 cm/s) after a steady-state is reached, when a clear along-slope jet develops (attached).

The horizontal resolution is ~1.65 km in both xi and eta directions. The number of vertical levels is 50, and the coarsest vertical resolution is 80 m, near the bottom (attached). Vtransform = 2, Vstretching = 4, Tcline = theta_s = theta_b = 0. Sponge layers that ramp the harmonic viscosity and diffusivity coefficients up to 5 times their inner values are set along all 3 open boundaries.

Boundary conditions are: Chapman explicit for the free-surface, Shchepetkin for the normal 2D velocities, Gradient for the TKE field and Radiation + Nudging for the tangential 2D velocities, 3D velocities and tracers. All nudging is done towards the initial conditions at the boundaries, that is, flat T and S profiles, and zero everywhere for all velocities and the free-surface, reflecting the initial state of rest.

The Beckmann and Haidvogel number (rx0) is 0.075, and the Haney number (rx1) is 3.7, which I understand are conservative values. The current values for the harmonic viscosity and diffusivity coefficients is 200 m2/s. I experimented with 50 m2/s, and the error is only about 1 cm/s larger. With a biharmonic viscosity of 4.5e+07, the error is about the same. With biharmonic viscosity and biharmonic diffusivity though, the error oscillates violently between 10 cm/s and 100 cm/s.

The CPP options I'm using are:

UV_ADV, UV_COR, UV_QDRAG, DJ_GRADPS, SOLVE3D

UV_U3HADVECTION, TS_U3HADVECTION

UV_C4VADVECTION, TS_C4VADVECTION

UV_VIS2, TS_DIF2

CURVGRID, SPHERICAL, MASKING

MIX_GEO_UV, MIX_GEO_TS, VISC_GRID, DIFF_GRID, MY25_MIXING, SPONGE, RADIATION_2D, ANA_SMFLUX, ANA_STFLUX, ANA_BTFLUX, T_PASSIVE, ANA_BPFLUX, ANA_SPFLUX

Talking to the author of this post (viewtopic.php?f=17&t=3323), we believe this might be a pressure gradient noise issue similar to the one he reported there. I implemented many of his useful suggestions, which brought improvements to the solution, but

**the pressure gradient errors are still much larger than what I would expect for my conservative values of rx0 (0.075) and rx1 (3.7)**. In fact, this paper (http://www.sciencedirect.com/science/ar ... 0302000033) compares different pressure gradient algorithms in a steep seamount test case, and shows baroclinic velocity errors of O(0.1 cm/s), with rx0 = 0.07 and rx1 = 2.7 and using the same pressure gradient algorithm I have been using (the parabolic splines density jacobian, CPP option DJ_GRADPS) and a similar maximum bottom slope.

**Also, their vertical resolution is 225 m, much coarser than my 80 m.**

The things I have already tried so far are: Playing with the vertical stretching curve, increasing the vertical resolution, increasing the horizontal resolution, changing the mixing coefficients between harmonic and biharmonic (and their values), decreasing the actual slope of the continental slope (currently the maximum slope is 0.03), capping the topography at 2000 m (it was 4000 m before), using time-dependent horizontal mixing coefficients (UV_SMAGORINSKY and TS_SMAGORINSKY options), changing the rotation of the viscosity/diffusivity tensors between along S-surfaces and along geopotential surfaces (MIX_S_TS, MIX_GEO_TS, MIX_S_UV and MIX_GEO_UV options), changing the boundary conditions, putting the sponge on and changing the pressure gradient algorithm (which showed that the DJ_GRADPS is the algorithm that produces the smallest error for my application. This agrees with the result obtained for the study I mentioned above for the seamount test case, which has similar values of rx0 and rx1). Most of these changes have had small beneficial effects.

I have also checked for errors in the initial field itself, but it is pretty flat, as it should be, only with very small-scale sawed features that always appear in the areas of maximum bottom slope due to interpolation errors (attached).

Any suggestions on ways to decrease the errors on the 3D velocity field to an acceptable level (I think, lower than perhaps 1.0 cm/s) is greatly appreciated.

Thank you all for your time,