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ALTERNATE FORMULATION for the PRESSURE GRADIENT in HYCOM

ALTERNATE FORMULATION for the PRESSURE GRADIENT in HYCOM. V. Garnier, M. Iskandarami and E. P. Chassignet RSMAS/MPO, University of Miami (vgarnier@rsmas.miami.edu). Hybrid coordinates: isopycnal, z, s s in coastal area ?. Wind / atmospherical fluxes z/ s. Tides z /s/r.

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ALTERNATE FORMULATION for the PRESSURE GRADIENT in HYCOM

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  1. ALTERNATE FORMULATION for the PRESSURE GRADIENT in HYCOM V. Garnier, M. Iskandarami and E. P. Chassignet RSMAS/MPO, University of Miami (vgarnier@rsmas.miami.edu)

  2. Hybrid coordinates: isopycnal, z, ss in coastal area ? Wind / atmospherical fluxes z/s Tides z/s/r Coastal density dynamics / river discharges z/s Coastal circulation Large scale influence z/s/r Realistic topography Pressure gradient error over steep/roughly topography ? • s coordinates: • Time evolution of density • Refinement of vertical resolution • (surface,bottom)

  3. The Seamount Problem H=H0 (1-A exp(-(x/L)2), H0=4500m, A=0.6, L=50km Dx = 8 km T=5+15 exp(-z/1000) S=35 psu T = 0h : no horizontal gradient of density, no forcing, no viscosity, no diffusivity, no bottom friction… s =|DH|/2H = 0.07 r = | sDH/HDs| = 2.7 > 1 Small hydrostatic inconsistency HYCOM Vmax=2.62 m/s ! The seamount problem reveals that my modification of the Flux Limiters in the continuity equation to conserve the mass exactly is not accurate at all and amplifies the error…

  4. After 10 days: POM and HYCOM errors are similar and still increasing ROMS’s error is ~30 times smaller (0.24 cm s-1) Pattern of error differ for POM and HYCOM Seamount: HYCOM/POM/ROMS POM t = 10 j HYCOM t = 10 j

  5. FCi+1/2,k+1 FXi+1,k+1/2 FXi,k+1/2 FCi+1/2,k Pressure Gradient Force Pressure Jacobian Density Jacobian Pseudo-flux form (Shchepetkin & Mc Williams, 2003)

  6. FCi+1/2,k+1 FXi+1,k+1/2 FXi,k+1/2 FCi+1/2,k Pressure Gradient Force

  7. Montgomery/Pressure Gradient Baroclinic part

  8. Validation of the implementation T = 0h T = 2h L = 64 km H = 1000 m Dx = 500 m Dz = 50 m Dr = 5.468 kg/m3 (tanh) HYCOM original HYCOM T = 2h T = 2h HYCOM original HYCOM HYCOM original HYCOM DH/DX = 640 m / 64 km = 1% DH/DX = 200 m / 64 km = 0.3%

  9. Seamount: HYCOM/POM/ROMSNew Pressure gradient HYCOM behaves similarly to ROMS using the more accurate pressure gradient scheme available in ROMS Errors are not sensitive to time step, advection scheme… ROMS t = 10 j HYCOM t = 10 j

  10. Conclusion • Numerical experiments explore the limitation of the use of s-layers in HYCOM. In case of steep slopes, limitations come from computational errors in the horizontal pressure gradient formulation. • Pressure gradient errors are estimated over a seamount as motion induced in an ocean initially at rest, uniformly stratified and unforced. • In full s-coordinates, the current Montgomery gradient scheme has errors comparable with POM Pressure gradient scheme (a few cm/s) • A cubic formulation (Shchepetkin & Mc Williams, 2003) of the Pressure gradient has been implemented to replace the current Montgomery gradient scheme in HYCOM : errors are now comparable with ROMS ones (a few mm/s). • Other experiments are required to confirm these encouraging results. • How to perform with null layer thicknesses encountering with the use of hybrid coordinates ?

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