[MITgcm-support] Spurious internal buoyancy minima in long runs

[Christopher L. Wolfe]

Hi Modelers,

I'm having a bit of a strange problem the MITgcm. I'm running at coarse resolution (80 km) in a simple domain (a 2000 km by 8000 km by 2000 m box) with a linear equation of state, GM/Redi eddies, and a "mixed layer" modeled by specifying a large diffusivity near the surface which smoothly decays into the interior. I'm forcing it with smooth winds, temperature restoring (9 days) to a fixed profile, and a fixed and balanced surface salt flux. 

The problem is that I keep ending up with bottom water which is denser than any water found at the surface. Both the temperature and salinity fields are bounded by their surface values, which is expected since both tracers satisfy advection-diffusion equations with extremum principles which state that any extrema are found at the surface. With a linear equation of state, the buoyancy satisfies a similar advection-diffusion equation with a similar extremum principle, yet the buoyancy of the bottom water is persistently lower than any water found at the surface. This is a serious problem, since I'm trying to study deep stratification and it's hard to draw any useful conclusions with a huge volume of my domain filled with an "impossible" water mass.

I don't think this is a problem with my initial conditions, since I've integrated the model for almost 17,000 years with an interior diffusivity of 8e-5. I've tried using different advection schemes (2, 7, and 81) and en/disabling the "Smolarkiewicz hack" without any change in the results. For the nonlinear advection schemes, I've also varied the horizontal diffusivity from 0 to 100 with no effect.

I'm very much bothered by this problem and have run out of things I can think of trying. If anyone here has any suggestions/explanations, I'd be extremely grateful to hear them. I'm enclosing my data file below for reference.

Thanks,
Christopher

# ====================
# | Model parameters |
# ====================
#
# Continuous equation parameters
 &PARM01
 sRef=20*35,
 tRef=20*0.0,
 viscAh=10E3,
 viscAz=0.25E-3,
 no_slip_sides=.TRUE.,
 no_slip_bottom=.FALSE.,
 diffK4S=0.0,
 diffKhS=0.0,
 diffKzS=0.0,
 diffK4T=0.0,
 diffKhT=0.0,
 diffKzT=0.0,
 f0=-1.3683e-04,
 beta=3.4208e-11,
 tAlpha=2.E-4,
 sBeta =7.4e-4,
 gravity=10.,
 rhoConst=1000.,
 rhoNil=1000.,
 rigidLid=.FALSE.,
 implicitFreeSurface=.TRUE.,
 saltAdvection=.TRUE.,
 saltForcing=.TRUE.,
 saltStepping=.TRUE.,
 tempAdvection=.TRUE.,
 tempForcing=.TRUE.,
 tempStepping=.TRUE.,
 eosType='LINEAR',
 nonHydrostatic=.FALSE.,
 momAdvection=.TRUE.,
 implicitViscosity=.TRUE.,
 implicitDiffusion=.TRUE.,
 ivdc_kappa=10.,
 readBinaryPrec=64,
 writeBinaryPrec=32,
 tempAdvScheme=81,
 saltAdvScheme=81,
 staggerTimeStep=.TRUE.,
 bottomDragLinear=1.1135E-3,
 debugLevel=-1,
 useJamartWetPoints=.TRUE.,
 useSingleCpuIo=.TRUE.,
 diffKrNrS=4.069423e-03,
   3.808919e-03,
   2.924517e-03,
   1.608878e-03,
   5.410003e-04,
   1.345410e-04,
   8.147859e-05,
   8.000402e-05,
   8.000000e-05,
   8.000000e-05,
   8.000000e-05,
   8.000000e-05,
   8.000000e-05,
   8.000000e-05,
   8.000000e-05,
   8.000000e-05,
   8.000000e-05,
   8.000000e-05,
   8.000000e-05,
   8.000000e-05,
 diffKrNrT=4.069423e-03,
   3.808919e-03,
   2.924517e-03,
   1.608878e-03,
   5.410003e-04,
   1.345410e-04,
   8.147859e-05,
   8.000402e-05,
   8.000000e-05,
   8.000000e-05,
   8.000000e-05,
   8.000000e-05,
   8.000000e-05,
   8.000000e-05,
   8.000000e-05,
   8.000000e-05,
   8.000000e-05,
   8.000000e-05,
   8.000000e-05,
   8.000000e-05,
 &

# Elliptic solver parameters
 &PARM02
 &

# Time stepping parameters
 &PARM03
 nIter0=0006205000,
# 5000 years
 nTimeSteps=1825000,
 deltaTMom=3600,
 deltaTtracer=86400,
 abEps=0.1,
# write out every 50 years
 pChkptFreq=1.5768e10,
 chkptFreq=1.5768e9,
 dumpFreq=1.5768e9,
 monitorFreq=1.5768e7,
 tauThetaClimRelax=764400.,
 cAdjFreq=0,
 pickupStrictlyMatch=.FALSE.,
 &

# Gridding parameters
 &PARM04
 usingCartesianGrid=.TRUE.,
 usingSphericalPolarGrid=.FALSE.,
 dXspacing=80.e3,
 dYspacing=80.e3,
 delZ=  12.0505,  14.9159,  18.4328,  22.7337,  27.9692, 
        34.3067,  41.9245,  51.0025,  61.7057,  74.1598, 
        88.4181, 104.4189, 121.9376, 140.5412, 159.5568, 
       178.0710, 194.9769, 209.0770, 219.2372, 224.5642,
 &

# Input datasets
 &PARM05
 bathyFile='topo_two.bin',
 thetaClimFile='TSurf.bin',
 zonalWindFile='windx.bin',
 saltFluxFile='SaltFlux.bin',
 &