[MITgcm-support] non-hydrostatic momentum budget

[Andrea Cimatoribus]

Dear all,
I am trying to compute the budget of momentum in my non-hydrostatic 
configuration. First of all, thanks to all those who contributed in the 
past on this topic, it certainly saved me huge amounts of time and 
head-scratching.

I put here the recipe from JMC for reference:
[du/dt] = - gravity * ( ETAN(i) - ETAN(i-1) ) / DXC
         + Um_dPHdx
         + Um_Advec   (+ Um_Cori : but only if using CD-Scheme )
         + Um_Diss    (+ Implicit vertical viscosity tendency)
         + Um_Ext
         + AB_gU

The problem:
the recipe above works beautifully (relative error <<1e-3) in the 
hydrostatic case, with only some issues near the boundary, I guess 
because of my cheap ETA derivatives. However, in the nonhydrostatic 
case, the above budget gives relative errors around 10% in many places 
(10% of the "truth" diagnosed via TOTUTEND/TOTVTEND).

What term am I missing? Could it be that TOTUTEND does not have all the 
terms in the NH case? I tried looking into mom_vecinv.F, but I could not 
reach any conclusion. I also tried playing with ADVrE_Um/ADVrE_Vm fluxes 
(treating it as the implicit vertical viscosity term), but that didn't 
help either (I thought the vertical advection was missing).

Thank you for your insights,
Andrea


PS: I attach the data file and a figure for the curious ones, it shows 
the relative error of the diagnosed acceleration (magnitude of vector) 
with respect to the one directly produced via TOTUTEND/TOTVTEND. There 
seems to be some correlation (not perfect, though) between the relative 
error and the advective term.

-- 
Andrea Cimatoribus
postdoctoral researcher
EPFL ENAC IIE ECOL
https://people.epfl.ch/andrea.cimatoribus
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# Model parameters
# Continuous equation parameters
 &PARM01
 tRef=5.4,
 sRef=0.03,
# Horizontal viscosity / diffusivity
# see http://mitgcm.org/pipermail/mitgcm-support/2010-January/006439.html
 viscAh=1.0E-6,
 diffKhT=2.0E-7,
 viscC2Smag=0.3,
 viscA4Grid=0.01,
 usejamartwetpoints=.TRUE.,
 vectorInvariantMomentum=.TRUE.,
 highOrderVorticity=.TRUE.,
###
# Vertical viscosity / diffusivity
 viscAz=5.0E-5,
 diffKzT=2.0E-7,
###
 f0=1.05e-4,
 beta=0.E-11,
 selectCoriMap=0,
 useEnergyConservingCoriolis=.TRUE.,
#tAlpha=2.E-4,
#sBeta =0.,
 gravity=9.81,
# free surface
 rigidLid=.FALSE.,
 implicitFreeSurface=.TRUE.,
 exactConserv=.TRUE.,
 nonHydrostatic=.TRUE.,
 hFacMin=0.2,
 hFacInf=0.2,
 hFacSup=2.0,
 nonlinFreeSurf=0,
 select_rStar=0,
 useRealFreshWaterFlux=.FALSE.,
# for avoiding dumping of surface waves
# unconditionally stable
# http://mitgcm.org/sealion/online_documents/node40.html
 implicSurfPress=0.5,
 implicDiv2DFlow=0.5,
###
 implicitViscosity=.TRUE.,
 implicitDiffusion=.TRUE.,
# drag
 allowFreezing=.FALSE.,
 no_slip_sides=.TRUE.,
 no_slip_bottom=.TRUE.,
 bottomDragQuadratic=2.5E-3,
#sideDragFactor=2,
 eosType='MDJWF',
 readBinaryPrec=64,
# SOM, see Hill 2012
 tempAdvScheme=81,
# do not use salt for now
 saltStepping=.FALSE.,
 staggerTimeStep=.TRUE.,
# IO configuration
 useSingleCpuIO=.TRUE.,
 globalFiles=.FALSE.,
 &

# Elliptic solver parameters
 &PARM02
 cg2dMaxIters=1000,
 cg2dTargetResidual=1.E-8,
 cg3dMaxIters=1000,
 cg3dTargetResidual=1.E-8,
 &

# Time stepping parameters
 &PARM03
 nIter0=0,
 endTime=2592000.0,
 deltaT=6.0,
 abEps=0.1,
 pChkptFreq=864000.0,
 chkptFreq=0.0,
 dumpFreq=0,
 monitorSelect=1,
 monitorFreq=43200.,
 &

# Gridding parameters
 &PARM04
 usingCartesianGrid=.TRUE.,
 delX=560*113.0,
 delY=196*113.0,
 delZ= 0.30, 0.54, 0.78, 1.02, 1.26, 1.50, 1.74, 1.98, 2.22, 2.46,
       2.70, 2.94, 3.18, 3.42, 3.66, 3.90, 4.14, 4.38, 4.62, 4.86,
       5.10, 5.34, 5.58, 5.82, 6.06, 6.30, 6.54, 6.78, 7.02, 7.26,
       7.50, 7.74, 7.98, 8.22, 8.46, 8.70, 8.94, 9.18, 9.42, 9.66,
       9.90,10.14,10.38,10.62,10.86,11.10,11.34,11.58,11.82,12.06,
 &

# Input datasets
 &PARM05
 bathyFile='lemanbathy.bin',
 hydrogThetaFile='temp_2016-06-05T1200.bin',
 hydrogSaltFile='',
 uVelInitFile='',
 vVelInitFile='',
 zonalWindFile=,
 meridWindFile=,
 &
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