1. Assessment of a wetting and drying scheme in the HYbrid Coordinate Ocean Model (HYCOM) Sébastien DENNEULIN Summer 2007 Internship at COAPS Eric Chassignet, Flavien Gouillon, Alexandra Bozec

2. 1. Introduction 2. Problem statement 3. Standard HYCOM limitations 4. Analytical solution 5. Numerical solution 6. Conclusions Outline

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

4. Problem statement Why do we need this scheme ? - 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 On the barotropic component 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 The equations of motion in 2D: Bowl topography From Thacker, 1981 ζ = sea surface elevation h = bathymetry defined by

10. The bathymetry becomes The equations of motion in 1D: Parabolic channel topography From Thacker, 1981 ∞ ∞ Thacker analytical solution

11. The equations of motion in 1D Thacker assumes that V = 0 U = U 0 (t), thus, => Thacker analytical solution

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

13. whereand C and D are constants. Analytical solution Thacker analytical solution

14. NUMERICAL SOLUTION

15. Numerical solution vs. analytical solution 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 Parabolic channel 0 km80 km 200 km 0 m 20 m 10 m

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

17. 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 16 periods T = 7.06 hr Analytically T= 7.0500 hr

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. Thanks

20. Considering the velocities in the parabolic channel, the Figure proves we are dealing with a barotropic case.

21. Same configuration as before but with the FVCOM. (Finite Volume Coastal Ocean Model). http://www.coaps.fsu.edu/~ddmitry/bowl/bowl_10km.mov