Assessment of a wetting and drying scheme in the HYbrid Coordinate Ocean Model (HYCOM)

1. Assessment of a wetting and drying scheme in the HYbrid Coordinate Ocean Model (HYCOM) Sébastien DENNEULIN Eric Chassignet, Flavien Gouillon, Alexandra Bozec

2. Outline • Introduction • Problem statement • Standard HYCOM limitations • Analytical solution • Numerical solution • Conclusions

3. (Oey, 2006) Introduction Numerically, wetting and drying means that a grid point can be considered either land or sea.

4. Problem statement • To have a better understanding and resolution of coastal ocean model dynamics (tides, storm surges, tsunami, etc.) • Better resolution of coastal ocean dynamics may in turn improve large scale ocean model dynamics.

5. HYbrid Coordinate Ocean Model: HYCOM • Primarily based on shallow-water equations (Bleck et al., 2002) • Generalized coordinate ocean model, i.e., the vertical coordinate is selected by the user. Default configuration: z-coordinate in the mixed layer, isopycnal coordinate in the interior, and terrain-following (sigma) in coastal areas.

6. Time splitting “The split-explicit scheme requires that prognostic variables be separated into their barotropic (i.e depth-independent) and baroclinic components.” from Bleck and Smith, [1990] Baroclinic components Barotropic components Pressure variables are also split into barotropic/baroclinic components

7. Limitations of the standard version of HYCOM p = (1+)p’ ; = /H <<1 everywhere p = p’ p = (1+)p’ ; = /H p = p’ + p’

8. ANALYTICAL SOLUTION: SLOSHING WATER IN A PARABOLIC BASIN

9. Thacker analytical solution Bowl topography

10. Thacker analytical solution ∞ ∞ Parabolic channel topography

11. Thacker analytical solution Thacker assumes that V = 0 U = U0(t) =>

12. Thacker analytical solution Parabolic bathymetry The general solution for the sea surface elevation is a straight line defined by

13. Thacker analytical solution and C and D are constants. where

14. NUMERICAL SOLUTION

15. Numerical solution vs. analytical solution Parabolic channel Red: Numerical solution wetting and drying Black:Analytical solution • Barotropic ocean • Parabolic channel 160 km x 200 km • Mean level of water is 10m • dx =1 km 0 m 10 m 20 m 0 km 80 km 200 km

16. Error estimates of sea surface elevation Error (meters) Red : Middle point Black :Left point green :Right point TIME (hours)

17. 16 periods T = 7.06 hr Analytically T= 7.0500 hr Estimation of the attenuation • U velocity time series of the point A (red). • Almost 0.15 m s-1 of dissipation in 5 days. • The total adjustment will be reach after ~31 days

18. Conclusion • We have run the wetting and drying HYCOM in a parabolic channel and a bowl. • Comparison with analytical solution (Thacker) shows that the model is working well. • Some numerical dissipation and wall effect attenuate the oscillation, but it is very weak. Now it is working for the analytical solution, we could run this version in more realistic case

19. The End

20. Result Considering the velocities in the parabolic channel, this experiment are a barotropic case.

21. Discussion • The same configuration as before but with the FVCOM. (Finite Volume Coastal Ocean Model).

22. Numerical experiments HYCOM