Pierre and Marie Curie University

Ocean, Atmosphere, Climate and Spatial Observations

M2 OACOS

Practical Work in Coastal Oceanography-

Numerical Modeling Mini-Project

Artemis Ioannou & Maxime Marin

March 14, 2016

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1 Introduction

The main purpose of the project is to analyze simulations of the coastal circulation model ”RegionalOcean Modelling System” (ROMS). This Model was co-developed by the IRD and the University ofCalifornia Los Angeles and is widely used in scientific community as its usage is facilitated by pre-processing tools (included grid and forcing). ROMS is built on the Navier Stokes equations as well asthe conservation of various variables such as mass, heat and salinity. The model also takes into accountthe hydrostatic and Bousinessq approximations. The discretisation of the model is made using the finitedifferences method on the C type grid. The C grid is such as each value is defined at the centre of thegrid cell except for the horizontal and vertical velocity components which are defined at the boundaryof the grid cells.The grid contains 20 vertical layers organised in sigma coordinates, following the seabedtopography. In this report, we will first focus our interest on the description of the tidal forcing bythe global model TPXO and the resulting tidal signal observed, before looking at the residual currentand its geostrophic characteristics. The observation of Lagrangian particules trajectories will be usedto link those two physical processes. Finally, the influence of density stratification will be explored andespecially the impact of the tides on such stratification resulting in the genesis of internal waves.

2 Description of the Model Forcing

2.1 Bottom Topography

The analysis focuses on the Western coast of France, near Brittany, France. The local bottom to-pography used for model simulations, displayed in Fig. 1, is specific to coastal areas as we observe thecontinental shelf gradually getting deeper offshore. The maximum depth is approximately 130m, mean-ing that the area of interest only captures the continental shelf part of the Atlantic ocean. The currenttopography is used by the regional model for the simulation of the flow.

Figure 1: Bottom topography.

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2.2 Tidal Forcing from the global model imposed on the regional model’sopen boundaries

In order to evaluate the tidal forcing from the global model, the temporal variations of sea level arevisualized for all the different tidal frequencies illustrated in Table 1. For these 8 different tidal forcesthe sea level variations were compared in two points of the domain with different phase and amplitude.The 2 points coordinates are point1: x = 2.6W and y = 47.5N near the coastal region and point 2: x= 4W and y=47.2N at offshore region, respectively. In Fig. 2a and Fig. 2b the phase and amplitudefor the tidal frequency M2 and S2 are depicted. We can observe that the sea level variation of the 2different points of the domain have no important differences between the offshore and coastal region.This is mainly expected as the grid resolution of the global model is not able to capture the coastlinedetails in order to precisely assess the impact in the tides. For that purpose a regional model is used inorder to simulate the tides with higher resolution.The regional model uses the global model outputs asboundary conditions.

2.3 Tidal signal in the interior of the regional model

A first simulation is performed using the regional model. It is forced by the tidal forcing from theglobal model. Barotropic currents are imposed at the open boundaries. The water column is homogeneous(constant temperature and salinity, simulating winter well-mixed conditions). In Fig. 3 the differencebetween the regional and the global model is illustrated. The larger differences are observed as expected inthe coastal region because in the global model the details of the coastline were not represented accurately.The global model grid resolution (δx, δy) is 15km x 15km. The difference observed in the offshore regioncan be related to the difference of the simulated bottom topography between the global and regionalmodel. This could create different dynamics which are not captured by the regional model creating bigerror in that offshore region.

Table 1: Different Tidal Forcing frequencies.

Name Reason Period AmplitudeSemi-diurnal

M2 Lunar Principal 12h25 100%S2 Solar Principal 12h00 46.5%N2 Major lunar elliptic 12h40 19.1%K2 Lunar- solar declination 11h58 12.6%

DiurnalO1 Lunar Principal 25h49 41.5%K1 Lunar – Solar Declination 23h56 58.4%P1 Solar Principal 24h04 19.3%Q1 Major Lunar elliptical 26h52 7.9%

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(a) Amplitude and Phase of M2 tidal frequency.

(b) Amplitude and Phase of S2 tidal frequency.4

Figure 3: Difference of Global versus RegionalModel.

Figure 4: Sea surface elevation time series forthe TPXO(black) and the ROMS(red) models.

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3 Modeling tides in an unstratified ocean

3.1 Tides variability

Fig 5 shows the variability of the tides at high frequency. Over the period of 37 hours, the flowtide intensity (represented by the vectors) stays relatively constant. Moreover, the sea surface elevationdisplays similar patterns throughout the time steps. On the contrary, the variability of the tides ata lower frequency increases significantly as showed in Fig. 6. Indeed Weekly patterns of sea surfaceelevation are highly different as well as the velocity vector fields, indicating that the tides variabilityis more important at low frequency than high frequency. Such variability is highlighted by Fig. 4as it displays the amplitude evolution of the sea surface elevation at 2.8W;47.45N. Despite the highfrequency quasi-diurnal frequency variability leading the alternating high and low tides, their amplitudeonly varies on a relatively low frequency. More precisely, the dominating variability frequency appearsto be approximately of the order of 15 days, highlighting the comments made previously.

Figure 5: Sea surface elevation and velocity vectors during the flow tide at different times (12h frequency).

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Figure 6: Sea surface elevation and velocity vectors during the flow tide at different times (weeklyfrequency) .

3.2 Residual current

Averaging the current through a long period of time cancels the impact of the tidal currents. Fig. 7ashows the resulting residual currents over the area of interest. This current is mostly due to the secondorder terms of the momentum equations : ~v∇(~v)Such current is particularly important near coastal areas and seems to be meandering. It can also berelated to the relative important gradient of sea surface elevation near the coast. In order to know if sucha residual current is related to the gradient of elevation observed, we can study its relative geostrophy.Geostrophic currents are defined as flowing parallel to isolines of pressure (i.e. elevation) and keepinghighest pressure on its right as described in the following geostrophic equilibrium equation:{

Ug = − gf ∂yP

Vg = gf ∂xP

To study whether the velocity vector is parallel to the isolines of pressure, the scalar product of thetwo vector is computed as well as the cross product so that the direction of the current is also takeninto account. Fig. 7b shows a measure of the geostrophy of the residual current, with values equal to 0representing a perfectly geostrophic current. When focusing on the area where the residual current is the

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strongest (i.e. close to the shore), the residual current appears to be highly non-geostrophic, supportingthe impact of the non linear terms of the momentum equations on the residual current. Only a smallpart of the current seems to be geostrophic, especially around 2.6W,47.2N and on the southern coast ofBelle-Ile. This suggests that the residual currents is must be forced by baroclinic processes coming fromriver discharges or friction with the bottom topography (non linear terms on the right of the momentumequations).

(a) Residual current velocity mapped with contours of mean sea surface elevations. Nor-malised velocity vectors were overlayed;

(b) Measure of the geostrophy of the residual currents. The scalar and cross product ofthe velocity and pressure gradient vectors were combined to derive such measure. Lowvalues tend towards geostrophy. The resiudal current velocity vectors were overlayed.

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3.3 Virtual Trajectory floats

The tidal forcing is evaluated for specific fluid parcels. For that purpose virtual Lagrangian floats arelaunched in the model domain and transported by the tidal flow. This allows the visualization of theirtrajectories corresponding to the advective pathways of the water masses. 56 floats were launched at8 different locations and 7 different depths around the Belle-Ile island. We focus the analysis only insurface float points. Fig. 8 displays the trajectory evolution of 4 different initial float positions (purplecircles). Their displacement in time evolution captured every hour for 20 days period and is shown withthe different colors - purple = 0h,red= 480h(20days). The mean current within the 20 days period isillustrated in vectors. The float trajectories are advected by the mean current as they tend to followthe vector lines pathways. In order to better represent the tidal effect in comparison with the residualcurrent we focus on the specific float point of the Fig 9. In that case the float trajectories are displayedevery 5 days period for a total time of 20 days. The impact of tides on the fluid parcels is illustrated inthe upper diagrams where the fluid parcels move away and towards the shore.The above displacementflood and ebb tide indicates that the tidal force is strong and comparable with the magnitude of theresidual current causing such a displacement.

Figure 8: Float trajectories of 4 different positions against residual current of 20 day period.

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From the upper right diagram, we could deduce that the fluid parcels need 5 days to be displacedapproximately 10km towards the shore corresponding to a mean tidal current of 2.3cm/s. The weaktidal current may relates to the low tidal cycle of that period - 5-10 January between the flood and theebb tide. For the 2 float points shown in Fig. 8 (2 lower diagrams) there is not significant tidal effect.The fluctuation of their trajectories is weak a fact that could be related to their relatively high distancefrom the shore where the tidal effect is less strong.

Figure 9: Float trajectories of float parcel near Belle ile.

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4 Influence of density stratification

4.1 Without tidal forcing

The model is now forced by vertical stratification on the boundaries as well as freshwater and heatfluxes at the surface. In the case where the tidal forcing is omitted, vertical stratification of the watercolumn differs highly depending on the season. Indeed, Fig. 10a & 11a show that there is no verticalstratification of the water column in winter meaning that the water column is fully mixed. There existsonly a gradient of temperature and salinity from the coast to offshore, with fresher and colder waterscloser to the shore. However, in summer, the water column is not mixed anymore as a vertical gradientof temperature and salinity develops. Moreover, the shallowing of the thermocline close to the shore ischaracteristic of the presence of an upwelling, bringing colder waters at the surface. The surface velocityfields also differs significantly from winter to summer as the surface currents get much faster. Therefore,an increased advection of fresher waters from the south-east is simulated by the model.

Figure 10: Averaged surface salinity and vertical profile of averaged salinity over the mapped transectin winter(top) and summer(bottom) without tidal forcing

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Figure 11: Averaged surface temperature and vertical profile of averaged salinity over the mappedtransect in winter(top) and summer(bottom) without tidal forcing

4.2 In the presence of tidal forcing

When the tidal forcing is included in the model, only little modifications of the mean state are observed.This is to be expected as when averaging over a long period of time, only the residual currents areobserved, and such currents are not affected by the tides (see previously). However, the addition ofthe tidal forcing increases the intensity of the coastal upwelling. In Fig. 12a the increase of the verticalcomponent of velocity can reach 0.035cm/s. The values of vertical velocity when the tidal forcing isomitted only reach 10−4cm/s, therefore the upwelling is significantly dependent on the tides. Suchconcept is supported by the observations from Fig. 12b, showing that the addition of the tidal forcing,decreases the coastal temperature of approximately 0.1 degrees throughout the water column.

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Figure 12: Vertical velocity (top), temperature (left) and salinity (right) modifications from tidal forcing.

The enhancement of the coastal upwelling due to tidal forcing can be explained by the creation oftide-induced internal waves. Indeed, when the tidal current meets a particular topography such as aseamount or a continental slope vertical velocity anomalies will be likely and could in turn perturbthe thermocline structure, especially during summer when the stratification is stronger. Fig. 13 showsthe propagation of such a wave through time at a particular location. Moreover, the amplitude of thedeformation is increasing as we get closer to the shore. This indicates that the upwelling is likely to beenhanced as we get closer to the shore, once again supporting the results previously observed.

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Figure 13

A better representation of the wave through time can be accessed realising an Hovmoller representationas seen on Fig 14. From this figure, the direction of propagation can easily be retrieved in addition to thephase speed. In this case, the propagation is towards the coast as the deformation tends to be parallelto the coast. Moreover, the approximation of the Phase speed gives a value of 38km/day or 0.43m/s

Figure 14: Hovmoller Diagram.

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5 Conclusion

This report attempted to evaluate the impact of tidal forcing onto the local dynamic of south Brittany,France. The tidal forcing in the regional model ROMS is taken from the global model TPXO. The regionalmodel does incorporate a more detailed bathymetry and therefore has a better resolution of tide solvingespecially close to the coast were the tide amplitudes is the highest. Moreover, the computed tides havea weak high frequency variability whereas their low frequency variability is dominant. This is due to thenature of the tidal forcing incorporating a few tidal modes. When looking at the average current overa long period of time, the tidal component is neglected and only the residual current can be studied.The residual current was most important close to the coast supporting the fact that this current ismostly due to second order terms of the moment equations. Indeed, the measure of geostrophy showedthat the residual current was largely ageostrophic. Lagragian floats provide tidal forcing informationas the position of the floats allows the estimation of the intensity of the tides at each time steps,while being advected by the residual current. However only the impact of the tides were forcing themodel, and neither the wind nor freshwater inputs were taken into account which could highly influencefloats trajectories especially at the surface. Finally, the analysis of the model outputs showed that thetides were in important factor in enhancing vertical velocities and more especially the summer coastalupwelling. Tidal flow onto shallowing topography induces internal waves propagating towards the coastwith increasing intensity, and eventually breaking the thermocline, encouraging mixing. Overall, thisreport highlights the importance of model forcings and boundary conditions for the representation ofthe state. Modelers have to be careful when deciding what is the processes they want to emphasise andchoose their model conditions accordingly.

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