SSH incorrect

[cbegeman]

Bug in the definition of SSH:

The following example is provided for a Polaris test case E3SM-Project/polaris#435, ocean/single_column/vmix_stable, with bottomDepth = 400m, nVertLayers = 100, and ssh = 0 throughout the simulations (resulting in time-constant layerThickness = 4m +/- mach precision).

• SshCell is incorrect. Consistent with -bottomDepth + layerThickness(k), which for these tests is -396. Its dimensions also include NVertLayers
• ZMid output from Omega is not consistent with the geometric zMid, ranges from ZMid(k=0) = 9.8 to ZMid(k=nVertLayers) = -397.9
• ZInterface ranges from ZInterface(k=0) = 10.25 to ZInterface(k=nVertLayersP1) = -BottomDepth for a case with no mass flux

[vanroekel]

@cbegeman I've taken a look at this and the ZMid and ZInterface code are correct. the Polaris test is providing geometric thickness but that code expects PseudoThickness. Even though the density correction is small, integrated over 400m it adds up to a ~10m top level interface.

the SSH code is definitely wrong for the 3d ocean as @mwarusz pointed out. I will move that to the computeZHeight routine and correct it.

There is a broader question about what Polaris should provide to omega. I'll post a separate discussion about this point.

[cbegeman]

@vanroekel and @mwarusz Thanks for looking into this further! I edited the title and description to reflect the fact that only SSH appears to be incorrect.

[vanroekel]

update, I think I have this fixed. I overwrote layerThickness in the init.nc file with pseudoThickness calculated in python and here is ZMid

ZMid =
  -2, -6, -10, -14, -18, -22, -26, -30, -34, -38, -42, -46, -50, -54, -58, 
    -62, -66, -70, -74, -78, -82, -86, -90, -94, -98, -102, -106, -110, -114, 
    -118, -122, -126, -130, -134, -138, -142, -146, -150, -154, -158, -162, 
    -166, -170, -174, -178, -182, -186, -190, -194, -198, -202, -206, -210, 
    -214, -218, -222, -226, -230, -234, -238, -242, -246, -250, -254, -258, 
    -262, -266, -270, -274, -278, -282, -286, -290, -294, -298, -302, -306, 
    -310, -314, -318, -322, -326, -330, -334, -338, -342, -346, -350, -354, 
    -358, -362, -366, -370, -374, -378, -382, -386, -390, -394, -398,

Here is ssh

 SshCell =
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

I'll run the barotropic channel next to confirm and then make the PR