Modeling the M2 and O1 Barotropic and Baroclinic Tides in the Gulf of Mexico Using the HYbrid Coordinate Ocean Model (HYCOM)

Flavien Gouillon1; B. Vanniere2; A. Bozec1; E. P. Chassignet1; (gouillon@coaps.fsu.edu) 1 Center for Ocean-Atmospheric Predictions Studies, Florida State University, Tallahassee, FL, USA

2 Ecole Normale Supérieur de Lyon, Lyon, France

1)Objectives of the study• Validation of the M2 and O1 barotropic tidal model implementation in the

Gulf of Mexico using the HYbrid Coordinate Ocean Model (HYCOM)• Investigate the importance of the tidal conversion process as a

contributor to the barotropic tidal dissipation for a realistic stratified

ocean

2) Model and Experiment Setup• HYCOM is used to conduct all numerical experiments.• It is run in fully isopycnal mode to avoid spurious diapycnal mixing.• The model domain is shown in Figure 1.• The horizontal resolution is 1/25°.• The barotropic tides in a semi-enclosed basin are originating from a local

tidal potential (celestial forces) described by Newton’s theory and also

from the model open boundaries, by tidal barotropic transport and

velocities derived from the Egbert and Ray model (2005).• Flather (1979) conditions are applied at the model boundaries.• The model is run 8 days after spin-up. Output are saved every hour.• For the barotropic case, the model is run as a 1-layer model.• For the baroclinic case, we use a mean GDEM3 climatology for the Gulf

of Mexico from the month of January with 25 layers.

Figure 1: Model Domain. Open boundaries are the dashed line, solid

black line denotes the location of cross-vertical sections.

5) The baroclinic simulation of the M2 tide

• The same configuration is run with a realistic stratification (Figure 4).• The tidal signal is very similar to the barotropic configuration.

7) Conclusion

• The M2 and O1 barotropic tides in the Gulf of Mexico are

accurately simulated using HYCOM.• Over the whole basin, the baroclinic tidal energy is

negligible.• Baroclinic energy can be locally important (i.e. West

Florida Shelf, Yucatan Peninsula).

6) The M2 Baroclinic Energetics

• The basin baroclinic power is computed from Khatiwala (2003):

P corresponds to 1/30,000 of the basin barotropic total power.• Baroclinic energy is negligible.• Internal wave structures exist in a stratified Gulf of Mexico (Fig. 5).• The baroclinic velocities at the West Florida Shelf can reach 1 m.s-1.• Baroclinic energy cannot be neglected in some locations.• The tidal conversion is computed following Llewellyn Smith and

Young (2001):

• The black solid dots in Figure 6 denote where C is maximum and

topography is rough.• Figure 6 shows the signature of the internal wave propagation within

the Gulf of Mexico.

xdhUpC B2

0

Figure 5: Cross-Vertical sectionof zonal/meridional baroclinic velocities

Figure 6: Depth integrated vertical velocity and max tidal conversion locations

Figure 3: Barotropic tidal amplitudes and phases for M2 a) and c), and O1

b) and d) for HYCOM (left panel) and GOT99 (right panel)

3) Validation of the barotropic M2 and O1 tides using tidal

gauges• ~60 tidal gauges located along the Gulf

of Mexico coast are used.

• Tidal amplitudes compare well against observations.

• A circular statistic approach is used in order to compare the phases.

• Circular correlation coefficients (ρ) are computed and are shown in Figure 2b.

Figure 2: Scatter plot of the tidal amplitudes a) and histogram of the circular distances and phase bias b)

Figure 4: M2 Baroclinic tidal amplitudes and phases

Internal wave beam

Internal wave beam

4) Validation of the barotropic M2 and O1 tides using GOT99

• A comparison against GOT99 (observation by satellite altimetry

measurements) is shown in Figure 3.• The modeled barotropic tides compare well against the realistic ones.

• The M2 modeled tidal amplitudes are slightly overestimated.

• The O1 modeled tidal amplitudes are well simulated.

• Tidal phases are close to the observations however:

• The modeled M2 tide leads the observed tide

• The modeled O1 tidal wave is late compared to observation

• The dissipation that occurs through bottom friction at the shelf compares

well with previous studies (~1.1 GW, Gouillon et al, 2008).• Tidal energy fluxes at the open boundaries agree with previous studies:

300 m isobath

dttUdxdx

dhtzxpP )()),,((

2

0/2

0

'0

With h the bathymetry, p’ the baroclinic pressure, U

the baroclinic velocity, ω0 is the tidal frequency

With pB the baroclinic pressure, U the baroclinic velocity, ω0 is the tidal frequency, ρ0 the reference densityTidal Constituent Gouillon et al. (2008) (GW) This study (GW)

M2 2.45 2.52

O1 0.72 0.21