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Journal of Coastal Research 20 3 893–912 West Palm Beach, Florida Summer 2004

A Set of 3-D Nested Models for Tidal Propagationfrom the Argentinean Continental Shelf to the Rıo dela Plata Estuary—Part I. M2

C.G. Simionato1,2,*, W. Dragani2,3,4, M. Nunez1,2 and M. Engel5

1Centro deInvestigaciones delMar y la Atmosfera

(CIMA/CONICET-UBA)Argentina

2 Departamento deCiencias de laAtmosfera y losOceanos

FCEN, Universidad deBuenos Aires

Argentina

3Servicio de HidrografıaNaval (SHN)

Argentina

4Consejo Nacional deInvestigacionesCientıficas y Tecnicas(CONICET)

Argentina

5Institut furMeereskunde (IfM)

Universitat HamburgGermany

ABSTRACT

SIMIONATO, C.G.; DRAGANI, W.; NUNEZ, M., and ENGEL, M., 2004. A set of 3-D nested models for tidal propa-gation from the Argentinean Continental Shelf to the Rıo de La Plata Estuary—Part I M2. Journal of Coastal Research,20(3), 893–912. West Palm Beach (Florida), ISSN 0749-0208.

As a contribution to the UNDP/GEF project ‘Environmental Protection of the Rıo de la Plata and its Maritime Front’,the three-dimensional primitive equation Hamburg Shelf Ocean Model is being implemented for forecasting purposes.As a first step a study of the tidal propagation was done. Data for the estuary were gained through a set of threeone-way nested models. Simulations were started with a large-scale model covering the Argentinean and Uruguayanand part of the Brazilian continental shelves. This model provides boundary conditions to a smaller scale model ofthe Rıo de la Plata and adjacent continental shelf, which in turn is used to force a small-scale high-resolution modelof the Rıo de la Plata estuary. Model sensitivity to different boundary conditions and to model parameters wasinvestigated. Solutions are not sensitive to the two different boundary conditions tested, derived from global dataassimilating models. It results also not sensitive to lateral diffusion but to bottom friction. M2 tidal wave propagatesnorthwards as a Kelvin wave, with amplitudes reaching almost 4 m in Southern Patagonia and a few centimeters atthe Rıo de la Plata estuary. Simulation results for the M2 component propagation were validated using all tidal gaugedata available and several currents observations, resulting in a very good agreement. These simulations have per-mitted, therefore, the construction of more reliable model derived cotidal, corange and tidal currents charts. The non-linear transfer of energy from semidiurnal to higher order harmonics was mapped. It can reach very high values atsome locations of the Patagonian coast. Tidal energy dissipation derived from the simulations shows that it constitutesan important amount of the globally estimated one.

ADDITIONAL INDEX WORDS: Estuaries, tides, models, tidal currents, Patagonian Shelf, Argentinean ContinentalShelf, Rıo de la Plata, 56.5–23.58 S, 69.5–45.58 W.

INTRODUCTION AND BACKGROUND

The Rıo de la Plata is a shallow and extensive estuary lo-cated on the eastern coast of South America at approximately358 S. It has a NNW–SSE general orientation and is formedby the confluence of two of the most important rivers of SouthAmerica. These are the Parana and Uruguay rivers whosemean discharges are of 16000 m3 s21 and 6000 m3 s21 respec-tively (NAGY et al., 1997). The estuary has a funnel shapeapproximately 300 Km long that narrows from 220 Km at itsmouth to 40 Km at its upper end (BALAY, 1961). The estua-rine area is 35000 Km2 and the fluvial drainage area is3.13106 Km2. The Rıo de la Plata ranks 5th and 4th world-wide in fresh water discharge and drainage area respectively(FRAMINAN et al., 1999). This system substantially contrib-

Received and accepted in revision 8 March 2004.* Corresponding author address: Centro de Investigaciones del

Mar y la Atmosfera (CIMA/CONICET-UBA), Ciudad Universitaria,Pab. II, 2do Piso, (1424) Ciudad Autonoma de Buenos Aires, Argen-tina. Fax: (54)(11)4-788-3572, e-mail: [email protected]

utes to the nutrient, sediment, carbon and fresh water bud-gets of the South Atlantic Ocean (FRAMINAN et al., 1999 andreferences therein). It affects the hydrography of the adjacentcontinental shelf, impacts important coastal fisheries, and in-fluences coastal dynamics up to more than 400 Km north onthe Brazilian shelf (CAMPOS et al., 1999; FRAMINAN et al.,1999; PIOLA et al., 2000). The Rıo de la Plata has huge socialand economical importance for the countries on its shores,Argentina and Uruguay. The most important cities and har-bors, including both capitals (Buenos Aires and Montevideorespectively) and many of the industrial centers and resortsof these countries are placed on its margins. The estuary isalso the most important source of fresh water for the millionsof inhabitants and it is an area of spawning and nursery formany coastal species (COUSSEAU, 1985; BOSCHI, 1988). Hav-ing become the most developed basin of southern SouthAmerica, the system is clearly being impacted by antropo-genic actions.

The coincidence of large or even moderately high tides andlarge meteorologically induced surges, has historically caused

894 Simionato et al.

Journal of Coastal Research, Vol. 20, No. 3, 2004

catastrophic floods in many coastal areas, threatening andclaiming human lives and producing major economic and ma-terial damages. Some low-lying parts of Argentinean coastsare vulnerable to this phenomenon. It is the case of the cityof Buenos Aires and its surroundings, located on the upperright margin of the Rıo de la Plata estuary. Since recordsbegan in 1905, the maximum water level at Buenos Aires wasregistered in 1940. Enhanced by strong south-easterly winds,it reached 4.44 m above the Tidal Datum, being the tidalheight overcome by 3.18 m. More recently, in 1989 and 1993,extreme floods were also experienced at the city. Water levelsreached 4.06 m and 3.95 m above the Tidal Datum, being thetidal heights overcome by 3.25 m and 2.49 m, respectively(D’ONOFRIO et al., 1999). Even though the events are not al-ways so extreme they are frequent, taking place several timesevery year. Besides the large discharge, flooding is mainlydue to combination of tides and surge (D’ONOFRIO et al.,1999).

Nowadays, the Servicio de Hidrografıa Naval of Argentina(SHN) maintains a warning system based on a statistical pre-dictive method that combines astronomical tide and surge.Nevertheless, a reliable operational numerical model for fore-casting the Rıo de la Plata is not available yet. Such a modelis essential not only for storm surge prediction but also forgeneral coastal management purposes in a strongly humanmodified system.

As a contribution to the UNDP/GEF project ‘Environmen-tal Protection of the Rıo de la Plata and its Maritime Front’,and as the result of a co-operation, the construction of a use-ful prediction tool is under development by the Centro deInvestigaciones del Mar y la Atmosfera (CIMA) and SHN,Argentina, and the Oceanographic Institute of the Universityof Hamburg (IfM), Germany. The three-dimensional primi-tive equation Hamburg Shelf Ocean Model (HamSOM) de-veloped at the University of Hamburg by BACKHAUS (1983,1985) is being applied for this purpose. This model has beenapplied to many shelf seas worldwide (see, for example,BACKHAUS and HAINBUCHER, 1987; RODRIGUEZ et al., 1991;STRONACH et al., 1993; SIMIONATO et al., 2001) having shownthat the model is very robust in studying the shelf sea dy-namics.

Given that our model is being constructed with predictionpurposes, realism must be an inherent feature of our simu-lations. One of the first steps in that sense is an adequaterepresentation of the tidal propagation. Even though severalmodeling attempts were done for the area, only three of themhave been registered in refereed literature. Two of them, theworks by O’CONNOR (1991) and VEIRA and LANFREDI (1996),were very simple approaches for understanding the causes ofthe surge and the tides characteristics, not built with theintention of being used as a forecasting tool. In a set of pa-pers, GLORIOSO and SIMPSON (1994), GLORIOSO and FLATH-ER (1995, 1997) and GLORIOSO (2000), (hereafter referencedas G-MOD), studied the tidal propagation in the Patagonianshelf by means of 2-D and 3-D barotropic models. Their mod-els included marginally the Rıo de la Plata, but as the estuarywas very close to the boundary condition, their solution for itis not very reliable.

Even though TOPEX/POSEIDON satellite data assimilat-

ing models have substantially improved the quality of theglobal tide simulations (LE PROVOST et al., 1995, 1998), andsome of them are freely available to the scientific community,their resolution is usually of around 18. This is clearly notenough not only to provide information about the tides at theestuary, but also to provide accurate boundary conditions toa relatively small-scale model for the Rıo de la Plata and theadjacent Continental Shelf. Particularly, the southern bound-ary of such a model should cross the Patagonian Shelf, knownto be one of the most important regions of the World Oceanfor tidal resonance and dissipation (ANDERSEN et al., 1995;GLORIOSO and FLATHER, 1997).

The use of observed data in order to force model boundariesis not possible either, because data are only available atcoastal stations and interpolation would not represent thelarge variations that previous models show that occur at theintermediate deeper points (O’CONNOR, 1991; VIERA andLANFREDI, 1996).

Therefore, as a first step on our simulation attempts, astudy of the tidal propagation at the Rıo de la Plata was done.This kind of simulations allows not only complementing theobservations in order to obtain a better picture of the tidalpropagation but also provides the tidal currents and otherderived quantities.

Given that the global tidal models do not supply adequateboundary conditions near the Rıo de la Plata itself, it wasdecided to start with a very large scale model. It covers thewhole Argentinean Continental Shelf and provides boundaryconditions to a smaller scale model of the Rıo de la Plata andthe adjacent Continental Shelf. This model in turn givesboundary conditions to a small-scale high-resolution modelfor the Rıo de la Plata. Sensitivity experiments to two differ-ent boundary conditions coming from global models of RAY etal. (1994) and ZAHEL (1997) as well as to the model param-eters were done. The simulation results for every of the threemodels were validated by using all of the available tidalgauge data and most of the current meter observations. Re-sults of these analyses show that the model results are invery good agreement with observations. In this sense, oursimulations have permitted constructing more reliable modelderived cotidal and corange as well as tidal currents charts,mapping the non-linear transfer of energy from semidiurnalto higher order harmonics and deriving tidal energy flux anddissipation charts. This information is very useful to comple-ment the few coastal data available in extensive and compli-cated areas as the Argentinean Continental Shelf and the Rıode la Plata. For paper length reasons, only the propagationof the M2 component will be discussed here. The other com-ponents will be shown in an accompanying paper to be sentin the next future.

DATA

The locations along the Argentinean and Uruguayan coastwhere sea level has been measured are shown Table 1. Geo-graphical position of stations in the table can be found inFigure 1 by their associated indexes. These data were usedto compute part of the harmonic constants presented in thispaper. Tidal records were measured at standard tidal sta-

895A Set of 3-D Models for Tidal Propagation


Table 1. Location of sea level gauge and duration of the series analyzedto obtain harmonic constants. Indexes in brackets refer locations to Figure 1.

Station (index) Latitude Longitude Type of DeviceNo.

Days

Martın Garcıa (2)Colonia (3)Buenos Aires (4)La Plata (5)Montevideo (6)

348 119 S348 289 S348 349 S348 509 S348 559 S

588 159 W578 519 W588 239 W578 539 W568 139 W

FloaterFloaterFloaterFloaterFloater

2920730

14965365

1460Punta del Este (7)Torre Oyarvide (8)Par Uno (9)San Clemente (10)Pinamar (11)

348 589 S358 069 S358 109 S368 219 S378 079 S

548 579 W578 089 W568 199 W568 239 W568 519 W

FloaterFloaterPressure sensorFloaterFloater

3654745330730

1460Mar del Plata (12)Puerto Belgrano (13)San Blas (14)San Antonio–E (15)Punta Colorada (16)

388 029 S388 539 S408 339 S408 489 S418 469 S

578 319 W628 069 W628 149 W648 529 W658 009 W

NGWLMSFloaterTide poleTide poleFloater

1823013840

271Puerto Madryn (17)Santa Elena (18)Cdro. Rivadavia (19)Puerto Deseado (20)San Julian (21)Punta Quilla (22)

428 469 S448 319 S458 529 S478 459 S498 159 S508 079 S

658 029 W658 229 W678 299 W658 559 W678 409 W688 259 W

FloaterTide poleFloaterFloaterTide poleNGWLMS

1350531

182573045

180Rıo Gallegos (23)Punta Vırgenes (24)Ba. San Sebastian (25)Rıo Grande (26)Bahıa Thetis (27)Ushuaia (28)

518 369 S528 309 S538 109 S538 479 S548 389 S548 499 S

698 019 W688 289 W688 309 W678 399 W658 159 W688 139 W

FloaterTide poleTide poleFloaterTide poleNGWLMS

7293861

180139182

tions at sixteen locations, where sea levels were gathered bya basic tide gauge with a floater and counterweight inside avertical tube (UNESCO, 1985).

The National Oceanic and Atmospheric Administration,USA (NOAA) and the SHN of Argentina installed three NewGeneration Water Level Measurement System (NGWLMS) atMar del Plata, Punta Quilla and Ushuaia tidal stations. TheNGWLMS tide gauge uses a dual system based in an acousticand a pressure sensor. The acoustic sensor sends a shock ofacoustic energy down a PVC sounding tube and measures thetravel time for the reflected signals from a calibration refer-ence point and from the water surface. The sensor controllerperforms the calculations to determine the distance to thewater surface. The other system is based in a traditionalpressure sensor to measure hydrostatic pressure of the watercolumn at a fixed point and convert the pressure into a level.

Harmonic constants from eight places were calculated fromtide pole measurements taken every 30 minutes or one hour.A pressure sensor (water level recorder Aanderaa modelWRL-7) was installed in Par Uno at 8 m depth, 30 km southof Montevideo. This instrument was programmed with an in-terval sampling of 30 minutes.

Finally, harmonic constants values from the AdmiraltyTide Tables (HYDROGRAPHER OF THE NAVY, 2000) were usedto validate the model at the Brazilian locations Porto Belloand Rıo Grande (indexes 0 and 1 in Figure 1) and at theMalvinas Islands station Port Stanley (index 38 in Figure 1).

The positions of current meters whose data are employedin this paper can be found in Table 2 and identified in Figure1 by their associated index.

NUMERICAL SIMULATIONS

Model Description

The model used for the numerical investigations is theHAMSOM (HAMburg Shelf Ocean Model), developed byBACKHAUS (1983, 1985) at the Institut fur Meereskunde(IfM) in Hamburg, Germany. Even though this model hasbeen described at many publications (BACKHAUS, 1983, 1985;BACKHAUS and HAINBUCHER, 1987; RODRIGUEZ and ALVA-REZ, 1991; RODRIGUEZ et al., 1991; STRONACH et al., 1993;ALVAREZ et al., 1997), a brief description of the main equa-tions solved and parameterization used is given in what fol-lows. It is a three dimensional multi-level (z coordinate) finitedifference model, on the Arakawa C grid, based, on its bar-otropic version, on the following set of Reynolds equations:

]u ]u ]u ]u 1 ]p1 u 1 v 1 w 1

]t ]x ]y ]z r ]x

2 2] u ] u ]tx5 fv 1 A 1 1h 2 2[ ]]x ]y ]z

]v ]v ]v ]v 1 ]p1 u 1 v 1 w 1

]t ]x ]y ]z r ]y

2 2] v ] v ]ty5 2fu 1 A 1 1 (1)h 2 2[ ]]x ]y ]z

where u and v are the vector velocity components; t the time;P the pressure; r the water density; f the Coriolis frequency;tx and ty the components of the stress vector and Ah is thehorizontal eddy viscosity.

Following the approach of ALVAREZ et al. (1997), who usedthe same model to study the tidal propagation in the Spanishcoast, the astronomical forcing is neglected. Even thoughsome authors handle the self-attraction and loading of theocean tide by a simple scalar multiplier of the elevations inthe momentum equations (ACCAD and PEKERIS, 1978), thisis only a crude approximation, and it is particularly poor innear-coastal areas (FRANCIS and MAZZEGA, 1990).

The formulation is completed with the continuity and hy-drostatic equations:

]u ]v ]w ]p1 1 5 0 5 2rg (2)

]x ]y ]z ]z

where g is the acceleration due to gravity.HamSOM is written in Cartesian coordinates. In order to

account for the convergence of the meridians due to thespherecity of the Earth, all distances in the horizontal axisare computed as a function of latitude and the cell volume soconsidered is distorted for mass conservation purposes.

The code uses a two time level numerical scheme (presentand future). To avoid instabilities, some terms of the equa-tions are treated semi-implicitly (pressure gradient and ver-tical diffusive stress) and the remaining ones explicitly. TheCoriolis term is treated following the approach of WAIS

(1985).In order to derive and solve the discretized model equations

first the momentum equations are vertically integrated ineach layer; this way an expression for layer transports isfound, which contains the unknown surface elevation (mak-



Figure 1. Map of the study area, showing the domain of every of the three models (A, B and C) and the location of the tidal gauge and current meterstations used for model validation. The names and exact location of the stations indicated by the indexes can be found in Tables 1 and 2.

Table 2. Location of current meters and duration of the series analyzed to obtain the tidal ellipses. Indexes in brackets refer locations to Figure 1.

Station(index) Latitude Longitude

AnalyzedDays Depth

InstrumentDepth Instrument

PF-RDP (29)CN-RDP (30)QBO-RDP (31)PPP-RDP (32)B-RDP (33)

348 329 S348 459 S348 499 S358 169 S358 529 S

578 519 W568 529 W578 199 W568 509 W558 379 W

71666960

117

5 m10 m6 m6 m

20 m

3 m5 m3 m1 m

10 m

rotorrotorrotorrotorrotor

ER-BB (34)B-GSM (35)B-GN-3 (36)CN-TF (37)

398 239 S418 379 S438 159 S528 529 S

618 289 W638 409 W638 489 W688 089 W

3612

26910

15 m25 m81 m38 m

3 m12 m27 m18 m

rotorrotoracousticrotor



ing the equation for the first layer to be non-linear) and ver-tical diffusive stresses. By vertically integrating again alongthe water column, the vertical diffusive stresses are canceledout and an expression for the vertically integrated transportis obtained. When this expression is substituted into the ver-tically integrated continuity equation (applied to a cell vol-ume), an elliptic equation system for the increment of thewater level is got. This last equation is solved by means ofan iterative over relaxation technique, which is combinedwith a direct elimination algorithm in order to speed up theconvergence. This way, after the parameterization of the dif-fusive and bottom stress terms, the equations for the layervelocities can be solved by direct elimination. Following theeddy viscosity analogy, the vertical diffusive stresses are pa-rameterized as functions of the layer velocities; the verticaleddy mixing coefficients are updated using a mixing lengthexpression (POHLMANN, 1996) that accounts for turbulent ef-fects in a local equilibrium way. The bottom stress is param-eterized by means of a quadratic law in terms of the currentvelocity:

5 CbuWL zuWbzWtb (3)

where uWb stands for the horizontal velocity vector at the bot-tom layer of the model and uWL is the vertically averaged hor-izontal velocity in a frictional layer close to the bottom. Cb isthe nondimensional drag or bottom friction coefficient. Forstability reasons, this term is treated semi-implicitly, beinguWb computed in the future time and uWL in the present.

In order to avoid large jumps in the values of friction inareas where the depth of the bottom layer is very thin, bot-tom transport is computed in a layer of constant thickness(30 m) always that the total depth is higher than this value(RODRIGUEZ and ALVAREZ, 1991).

Simulations Description

Given that global tidal models cannot provide adequateboundary conditions for a small-scale model of the Rıo de laPlata estuary, it was necessary to start our simulations witha very large-scale model. The Rıo de la Plata estuary wasreached through a set of three one-way nested models. Thelargest scale ‘‘Model A’’ covers an area spanning from 56.58S to 23.58 S and from 69.58 W to 45.58 W (Figure 1). Thehorizontal resolution is of 209 in the zonal direction and 159in the meridional one, what represents 27 Km approximately.Ten layers are employed in the vertical, whose bottoms areat 10, 20, 30, 60, 100, 200, 500, 1000, 3000 and 6000 m. Thisvertical discretization was selected to provide a good resolu-tion in the upper layers and, therefore, solve properly thewind driven circulation in future modeling. The minimum al-lowed depth is 5 m. Given the fact that ETOPO5 bathymetrydata display unrealistic very shallow features over the Ar-gentinean Continental Shelf, the topography has been builtby combining this last data set with data provided by theServicio de Hidrografıa Naval of Argentina (SHN, 1986) fordepths shallower than 200 m. The so obtained bathymetry isshown in the left panel of Figure 2, in which the most rele-vant features of the broad Argentinean shelf can be appre-ciated.

Model A provides boundary conditions to a higher resolu-tion model of the Rıo de la Plata—adjacent Continental Shelf(Model B, Figure 1). This model spans the region between 428S and 31.48 S, and 61.58 W and 51.58 W, with horizontal res-olutions of 6.669 and 59, approximately 9 Km, respectively. Inthis case 13 vertical levels were used, with bottom at 4, 6, 10,15, 20, 40, 60, 100, 200, 500, 1000, 3000 and 6000 m. Mini-mum allowed depth is 4 m in this case. The depth of the firstlayer is too high to properly resolve the shallow region of theRıo de la Plata. Nevertheless, it has been set deep enough toproperly solve the first layer at the south-westernmost areasof model domain, where the tidal amplitudes are known tobe large. Given that the model is a z-coordinate one, the firstlayer depth has always to be kept larger than the maximumtidal amplitude.

Finally, Model B provides boundary conditions to the high-est resolution Model C (Figure 1) of the Rıo de la Plata. Thiscovers the region between 36.58 S and 34.08 S and 59.08 Wand 54.58 W, with horizontal resolutions of 1.89 and 1.59, ap-proximately 3 Km, respectively. This model has 13 layerswith bottom depths at 1, 2, 3, 4, 5, 6, 7, 10, 15, 25, 35, 45 and55 m. The election of these levels allows for a good verticalresolution even at the very shallow areas of the upper Rıo dela Plata estuary.

High-resolution bathymetry data for models B and C wereprovided by the SHN and come from digitalization of charts(SHN, 1992, 1993, 1999a, 1999b). The corresponding bottomtopographies are shown in the right upper and lower panelsof Figure 2 respectively. The large bathymetry gradients pre-sent in the region of interest are evident in the figure. Eventhe relatively small scale Model B has bottom depths thatvary from centimeters at the upper estuary to 5500 metersat the outer shelf.

Model forcing was introduced by imposing tidal elevationat the open boundaries. In order to test the sensitivity of thesolution to the boundary conditions, data derived from twodifferent global models were used to force Model A. A bilinearinterpolation routine was used to convert ZAHEL (1997) andRAY et al. (1994) 18 resolution models outputs into amplitudesand phases at 209 3 159 resolution at the boundaries of ModelA. Validation indicates that the solution forced with valuescoming from Zahel’s model provides slightly better results.Nevertheless, it must be pointed out that even though a com-parison between both global model outputs exhibits a slightdifference in the amplitudes and phases at the southern partof the domain, our solutions do not result highly sensitive toit. For that reason, only the solution obtained with Zahel’sboundary conditions will be shown along this paper.

The simulation time step for Model A was 5 minutes (300seconds). With this relatively small time step, stability andabsence of numerical damping and phase lags, which mayoccur at long time steps (KOWALIK and MURTY, 1993) areensured.

In order to test model sensitivity to the horizontal eddyviscosity, different experiments for values of this parameterranging from 100 to 600 m2 s21 were done. As long as thesolutions do not exhibit sensitivity to the parameter thesmaller value was selected for the solutions shown in thispaper.



Figure 2. Bathymetry (isobaths in meters) for every of the three model domains. Note that the contour interval is neither regular nor the same fordifferent figures.

Model A was run for the equivalent to 12 months startingfrom rest. After approximately 10 days of simulation most ofthe transients due to the spin up of the model are dissipated.In order to ensure the stability of the solution the analysiswas done by using only the last 8 months of the simulationwith semi-hourly data. The analysis was done by means of atidal analysis routine that follows the FOREMAN (1977, 1978)approach to convert the simulated sea surface elevations intoM2 wave amplitudes and phases. Higher order harmonics likeM4 are also analyzed to study the non-linear sub modes gen-eration at the shelf.

Once the amplitudes and phases were obtained for ModelA, interpolation routines were used to get boundary condi-tions for Model B. Results do not exhibit sensitivity to vari-ations between 50 and 200 m2 s21 of the horizontal eddy vis-cosity. Therefore, a value of 50 m2s21 was chosen for the pa-rameter in this case. The time step was 5 minutes (300 sec-

onds), small enough to ensure stability and absence ofnumerical problems.

Finally, amplitudes and phases obtained from Model B areused to force Model C. For this last high-resolution modelhorizontal eddy viscosity was set to 50 m2s21; results, oncemore, do not show sensitivity to variations of this parameter.The time step in this case was of 2.5 minutes (150 seconds).

Models B and C were also run for the equivalent to 12months and the analysis to derive the harmonic constantswas developed using the last 8 months of the simulation.

Modeled Amplitudes and Phases

The amplitudes and phases of the M2 tidal component ob-tained by harmonic analysis of the numerical simulation per-formed with the lower resolution Model A are shown in theupper left and upper right panels of Figure 3, respectively.The plots show the tide propagating as a Kelvin wave, with



Figure 3. Upper panels: Corange (amplitudes in meters) and cotidal (phases in degrees) maps of the M2 constituent from Model A. Lower panels: Scatterplots of modeled vs. observed amplitudes and phases for Model A simulation; the full line indicates the perfect fit.

amplitudes growing towards the coast, after entering into thedomain from the south and southeast in a general good agree-ment with what is known about the tidal propagation in thearea (G-MOD).

The highest amplitudes, over 4 m, occur at around 508 S.Amphidromic points are observed, from south to north, south-ward Malvinas Islands (at around 528 S), southeastward SanJorge Gulf (at approximately 488 S) and between San Matıas



Table 3. Observed and simulated M2 harmonic amplitudes and phases for every of the three models. ‘‘–’’ sign is used for locations that are not solvedbecause of model resolution. Differences between observed and modeled amplitudes and phases are shown as ‘Ampl. Dif.’ and ‘Phase Lag’ respectively.

Station (index)

Observed

Ampl.(m)

Phase(deg)

Model A

Ampl.(m)

Phase(deg)

Ampl.Dif.(m)

PhaseLag

(min)

Model B

Ampl.(m)

Phase(deg)

Ampl.Dif.(m)

PhaseLag

(min)

Model C

Ampl.(m)

Phase(deg)

Ampl.Dif.(m)

PhaseLag

(min)

Porto Belo (0)Rio Grande (1)Martın Garcıa (2)Colonia (3)Buenos Aires (4)

0.220.040.190.150.27

156345350287302

0.190.06———

154328———

10.0320.02

———

24.14235.19

———

0.08—

0.090.11

335—

275339

10.04—

20.0620.16

220.70—

124.84275.59

0.290.150.28

11289304

10.100.00

10.01

141.4014.1414.14

La Plata (5)Montevideo (6)Punta del Este (7)Torre Oyarvide (8)Par Uno (9)

0.230.140.060.320.18

243119347146103

0.230.130.08—

0.17

244121350—

103

0.0010.0120.02

—10.01

12.0714.1416.21

—0.00

0.220.140.090.270.15

245144344166114

20.010.00

10.0320.0520.03

24.14251.7516.21

241.40222.77

0.250.150.080.330.19

239115346152101

10.0210.0110.0210.0110.01

28.2828.2822.07

112.4224.14

San Clemente (10)Pinamar (11)Mar del Plata (12)Puerto Belgrano (13)San Blas (14)

0.360.320.361.090.82

11306304234159

0.370.350.350.280.27

1432731528

125

20.0120.0310.0110.8110.55

16.21143.47118.63

1318.78270.38

0.390.340.361.040.75

14327318240157

10.0310.02

0.0020.0520.07

26.21243.47228.98212.4214.14

0.42 12 10.06 12.07

San Antonio–E (15)Punta Colorada (16)Puerto Madryn (17)Santa Elena (18)Cdro. Rivadavia (19)

3.142.841.891.632.06

7263

320269220

3.232.781.771.731.96

8478

328262221

20.0910.0610.1120.1010.10

216.56131.05116.56214.4912.07

3.36 85 10.22 226.91

Puerto Deseado (20)San Julian (21)Punta Quilla (22)Rıo Gallegos (23)Punta Vırgenes (24)

1.792.833.743.853.20

1397552457

1.713.153.773.903.43

13876553511

10.0820.3220.0320.0520.23

22.0712.0716.21

220.7018.28

Ba. San Sebastian (25)Rıo Grande (26)Bahıa Thetis (27)Ushuaia (28)Puerto Stanley (38)FS1 (39)

3.292.621.270.560.430.36

352333299239277281

3.042.581.400.590.440.36

359340300233281283

10.2510.0420.1320.0320.01

0.00

114.49114.4912.07

212.4218.2814.14

Gulf and Bahıa Blanca (near 408 S). The position of thesepoints as well as the general pattern of the cotidal and cor-ange isolines are similar to the ones obtained by G-MOD.Those authors find one more amphidromic point at the Rıode la Plata, located near Punta del Este, which is absent inour solution. O’CONNOR (1991) presents theoretical argu-ments, which will be discussed below, according to which thatamphidrome should not occur. Direct observations supportthese arguments (D’ONOFRIO, personal communication).

Table 3 shows a comparison between modeled amplitudesand phases and observations at the coastal and island loca-tions of Figure 1. In order to simplify the interpretation ofthe results, the lower panels of Figure 3 display scatter plotsof the modeled vs. observed values of amplitude (left panel)and phase (right panel); the solid line represents the ideal fit.Table 3 and Figure 3 indicate that the model has a very goodagreement with observations at most of the locations. Theexceptions are San Blas and Bahıa Blanca, where modeledvalues are lower than the observed ones and the modeledphases are not correct. A similar problem was in part over-come by GLORIOSO and FLATHER (1997) by reducing the bot-tom friction coefficient one order of magnitude north of Pen-ınsula de Valdes at every point where the depth is shallowerthan 50 meters. Sensitivity experiments carried out withHamSOM show that such a reduction of the coefficient pro-

duces an increase in the local tidal amplitudes, making themmore similar to the observed ones. Nevertheless even underthese conditions model is not able to properly locate the am-phidrome in front of San Blas, which should be far away fromthe coast in order to reproduce the observed phases. For thatreason, the results shown in Figure 3 derive from a run donewith a classical value of the coefficient of 2.5 3 1023. Ourexperiments show, as well, that the position of the amphid-romes is sensitive to the variation of this parameter. Whensimilar conditions to the ones taken by GLORIOSO andFLATHER (1997) are imposed to our model we also obtain theamphidromic point they observe at the Rıo de la Plata.

Modifications in model parameters, like bottom friction andeddy viscosity, do not improve the solution between BahıaBlanca and San Blas. It suggests that a higher resolution isnecessary to solve the complicated processes that occur inthis shallow region. Beyond this area, agreement between ob-served and simulated values is very good, with differences inamplitudes generally lower than 10%. The solution does notdisplay a systematic trend to overestimation or underesti-mation of amplitudes. Phases are generally well reproduced,with phase lags lower than 25 minutes.

The barotropic set of equations that constitute the Ham-SOM model contains three non-linear terms: the bottom fric-tion, the advection of momentum terms and the continuity



Figure 4. Corange (amplitudes in meters) and cotidal (phases in degrees) maps of the M4 constituent from Model A.

equation vertically integrated for the first layer. One of theeffects of these terms is the generation of shallow water con-stituents, which can become important when performing aharmonic analysis or a storm surge prediction. The shallowwater constituent M4 was extracted from our simulation by

means of a harmonic analysis technique. Results for the Pa-tagonian Shelf, where this component is most important, areshown in Figure 4, together with scatter plots of observed vs.simulated values for the amplitudes and phases. The ampli-tude of this component can reach according to our model sim-



Figure 5. Idem figure 3 for Model B.

ulation very large values (larger than 0.20 m) at some loca-tions of the Patagonic coast, like the San Matıas Gulf or theBahıa Grande area, in agreement with observations. Eventthough the scatter plot suggests that the model tends to un-derestimate the amplitudes, the component is important,with values larger than 0.10 m at most of the many gulfs andbays of the coast, indicating the importance of non-linear pro-cesses in the shelf.

The results of the simulation between Bahıa Blanca andSan Blas were highly improved when the higher resolutionModel B was applied. The simulated amplitude and phase ofM2 as reproduced by Model B one-way nested to Model A areshown in the upper left and upper right panels of Figure 5,respectively. Sensitivity studies to the bottom friction coeffi-

cient were done in this case as well. Best results were ob-tained when this coefficient was set to 5 3 1024 south of 398at every point where the depth is shallower than 50 m. It hasbeen argued (O’CONNOR, 1991) that in regions with muddybottom that reduction better represents the propagationcharacteristics. It is known that between Bahıa Blanca andSan Blas the bottom is muddy and also characterized by thepresence of large tidal flats. In contrast to the case of ModelA, in this case both, amplitudes and phases, reach the ob-served values when that parameter is modified. The positionof the amphidrome results to be very sensitive to the change.

It can be seen in Figure 5, that the largest amplitudes cor-respond to the northern part of the San Matıas Gulf, withvalues exceeding 3.3 m. The amphidromic point is displaced



Figure 6. Idem figure 3 for Model C.

eastward with respect to Model A simulation results, locatednow at approximately 418 S and 618 W. At the Rıo de la Platathe pattern for amplitudes and phases is similar to the larg-est scale model ones.

A comparison of simulated vs. observed values at the lo-cations of Figure 1 is shown in Table 3. Scatter plots of mod-eled vs. observed values together with a perfect fit line areshown in the lower panels of Figure 5. Model displays a slighttendency to overestimate the phase.

Even a higher resolution is necessary to properly simulatethe propagation of the tide at the very shallow regions of theupper Rıo de la Plata estuary. This resolution is reached withModel C. A set of sensitivity experiments to the bottom fric-tion coefficient was done for this case as well. Similarly toO’CONNOR (1991), results show that the best agreement withobservations is obtained when the bottom friction coefficientis reduced to 3/5 of the exterior value (2.5 3 1023) at everypoint where the depth is shallower than 10 m.

The simulated amplitudes and phases obtained from theharmonic analysis of the sea surface elevations provided by

the simulation are shown in the upper panels of Figure 6.Results are highly consistent with what is known about thetidal propagation in the region.

The tidal dynamics in the interior part of the estuary havebeen described by BALAY (1956, 1961) and simulated byO’CONNOR (1991) and VIEIRA and LANFREDI (1996). Theseauthors results show that the range between the maximumand minimum of the tide is 0.8 m. The normal range of thetidal amplitude is around one meter on the Argentinean side,but only one third of this value on the Uruguayan side. Thisis not only a result of the fact that the tide is higher at thesouth than at the north of the estuary mouth, but also of theCoriolis effect. The wave propagates as a free external gravitywave along the estuary, with a phase velocity of ÏgH (whereH is the water depth). It takes the wave approximately 12hours to propagate from one extreme to the other one. As thisperiod is almost similar to the period of the tide, it can co-exist two maximums or two minimums at the same timewithin the estuary. This last feature is very clear in the sim-ulated phases plot (Figure 6, upper right panel).



Figure 7. Comparison of measured (solid line) and computed (dotted line) M2 tidal ellipses at different locations at the Argentinean Continental Shelf.The depth of the model layer at which the instrument was located is indicated.

The progression of the wave, northward and with the coastto the left, and the decay of the amplitude offshore are con-sistent with a response of Kelvin waves to the forcing at theshelf. The dynamics of the tides in terms of Kelvin waves isdescribed by GILL (1982) and discussed for the particular caseof the Rıo de la Plata by O’CONNOR (1991). The Rossby radiusof deformation is a scale of the decay offshore of the ampli-tude; taking as a representative depth of the estuary H 5 10m, it results ÏgH /z f z 5 115 Km, which is narrower than thesize of the estuary on its outer and medium parts. This fact,added to the importance of the dissipation in shallow watersensures that there would not be an amphidromic system in-side the estuary.

All of these features are well described by Model C simu-lation, which displays a very good agreement with observa-tions. Table 3 shows a comparison between observed and sim-ulated amplitudes and phases at locations of Figure 1. Theerrors for the amplitudes are of a few centimeters (lower than2 cm at all but one point) and the phase lags are lower than10 minutes excepting Oyarvide, where it is of around 13 min-utes. The model only fails in reproducing the observed valuesat Martın Garcıa. This location corresponds to an island atmouth of the Uruguay River that cannot be properly solvedwith a 3 Km resolution model. The scatter plots of modeledvs. observed amplitudes and phases for this simulation areshown in the lower panels of Figure 6. Here simulated phases



Figure 8. Comparison of measured (solid line) and computed (dotted line) M2 tidal ellipses at different locations at the Rıo de la Plata estuary. Thedepth of the model layer at which the instrument was located is indicated.



Figure 9. M2 tidal current ellipses derived from Model A (left panel) and a zoom over the Patagonian Continental Shelf (right panel). Shaded zonesindicate counterclockwise rotation of the ellipses.

follow closely observations, whereas the model seems to over-estimate slightly the amplitudes.

Tidal Currents

In order to validate the currents resulting from the simu-lations, M2 HamSOM-generated tidal ellipses were comparedwith direct measurements at the locations 29 to 37 of Figure1, whose characteristics are given in Table 2. Five of theseobservations correspond to the Rıo de la Plata estuary andthe other four to locations on the continental shelf. Simulatedvelocities were interpolated to the current meter depth,which does not usually coincide exactly with model layerdepth, and analyzed through a harmonic analysis routine inorder to be compared with measured ellipses. Results of thiscomparison for stations 34–37 at the shelf are shown in Fig-ure 7. Figure shows a general agreement between modeled(dotted line) and observed (full line) currents in both, speedand phase. Observations indicate speeds of almost 1 m s21 atB-GSM and CN-TF (Table 2) that are properly reproduced by

the simulations. In stations ER-BB and B-GN phase is sat-isfactory reproduced, but model tends to overestimate thespeed in the first of these stations.

Observed and modeled tidal ellipses for the Rıo de la Plataestuary at stations 29–33 are displayed in Figure 8. It is ob-served that Model C tends to overestimate the zonal velocitycomponent, meanwhile it reproduces well the meridional oneand the phase. Largest differences between observed andmodeled currents are obtained at PF-RDP (index 29). Sincethe water density was set equal to a constant in the simu-lations and there is no simulated wind stress, only frictionalstresses contribute to vertical variability. As a result, verticalstructure is not significant in our simulations. Unfortunately,there are no observations of current’s profiles at the Conti-nental Shelf to provide an indication of the importance of thisvertical structure. The only observed currents profiles at theRıo de la Plata estuary, gathered at its intermediate part,were recently analyzed by DRAGANI et al. (2002). Their re-sults show that, due to the important salinity and therefore



Figure 10. M2 tidal current ellipses derived from Model B. Shaded zonesindicate counterclockwise rotation of the ellipses.

Figure 11. Idem figure 10 for Model C.

density gradients, vertical variations of the currents can beextremely large in this region and that velocity vectors caneven reverse with depth. We conclude, therefore, that thelack of thermohaline structure in our simulations could be,at least in part, responsible for the model failures in repro-ducing the observed currents in this region.

Modeled tidal ellipses for the largest integration domain(Model A) are shown in Figure 9, together with a zoom overthe Patagonian Shelf. Shaded zones indicate counterclock-wise rotation. Largest currents are observed in the followingareas: along the coast from eastern Tierra del Fuego to south-ern San Jorge Gulf; over the Burdwood Bank; northwesternMalvinas Islands and at the San Matıas Gulf mouth. Theseresults compare well with G-MOD ones, except in the regionbetween Bahıa Blanca and San Blas, where our simulationprovides much lower velocities.

In the case of Model B largest tidal velocities (Figure 10)are obtained in the San Matıas Gulf, whereas they are small-er between Bahıa Blanca and San Blas, in agreement withModel A results. Nevertheless it should be pointed out thatmodels A and B solutions differ in the sense of rotation of theellipses between those two locations, due to the difference inthe amphidrome position in both simulations (Figures 3 and5). For Model B, besides the San Matıas Gulf, largest veloc-ities are related to the Rıo de la Plata Estuary. A detail ofthis last area derived from the highest resolution Model C isdisplayed in Figure 11. Maximum speeds are obtained at thenorthernmost and southernmost tips of the SamborombonBay, Punta Piedras and Punta Rasa, while in the interior ofthe Bay values are much smaller. This last region displays arotational feature, but at the upper and central estuary thecurrents tend to be more unidirectional.

Tidal EnergeticsAdditional important quantities that can be calculated

from our simulations are the energy flux and the dissipation

by bottom friction. Given the good correspondence betweensimulated and observed harmonic constants of sea level andtidal currents, it is expected that a good estimation of thesequantities will derive from model results. Besides, no esti-mation of these parameters is available in literature for theRıo de la Plata area.

The energy flux can be computed as (PUGH, 1987):

1WF 5 (F , F ) 5 rgHA(U, V)cos[(g 2 g ), (g 2 g )] (4)x y A U A V2

where FW 5 (Fx, Fy) is the energy flux vector, H is the waterdepth, A is the amplitude of the elevation and gA its phase.(U,V) and (gU,gV) are the amplitude and the phase of the ver-tically averaged current components in the zonal and merid-ional direction respectively, as calculated from harmonicanalysis of the time series derived from the model.

This formula was used by G-MOD to estimate the energyflux over the Patagonian shelf from tidal simulations for themost important tidal constituents. They concluded that inthis region energy flux due to M2 dominates, being two ordersof magnitude larger than the ones due to the other constit-uents. M2 energy flux on the Patagonian Shelf as derivedfrom model A is shown in the left panel of Figure 12. Ourpicture presents an aspect qualitatively similar to the onederived by G-MOD even though some differences are found.The energy enters the model domain mainly from the southand reaches the shelf through the region between Tierra delFuego and the Burdwood Bank. Another flux branch reachesthe Malvinas Islands from the northeast. Westward the is-lands this branch turns to the west and joins the main fluxat approximately 528 S. It then flows northwards and dissi-pates along the coastline reaching the San Matıas Gulf. Themost relevant differences with respect to G-MOD simulationsare the flux incoming from the northeast to the Malvinas is-lands and a maximum of the flux over the Burdwood Bank,both features absent in G-MOD.

M2 flux diminishes to the north reaching very small valuesnorthern the San Matıas Gulf, indicating that energy is dis-sipated along the continental shelf. In order to identify themost important areas for dissipation and quantify its mag-



Figure 12. M2 tidal energy flux vectors in W m21 (left panel) and contours of M2 tidal energy dissipation by bottom friction rate in W m22 (right panel)derived from Model A. Note that contour interval is not regular.

nitude, the mean rate of energy dissipation per unit area bythe bottom friction (Eb) was derived. It has been shown (DA-VIES et al., 1985) that an accurate expression for estimatingthis dissipation from numerical simulations is:

T12 2 3/2E 5 c r (u 1 v ) dt (5)b b E b bT 0

where the integration period T was chosen to be a M2 tidalperiod. Results for the Patagonian shelf (right panel of Figure12) are mostly consistent with G-MOD derivation. Dissipa-tion in the region is large and highly localized in four mainregions: over the Burdwood Bank, eastward Tierra del Fuego,southward San Jorge Gulf and at the San Matıas Gulf mouth.Secondary dissipation areas are found northward San JorgeGulf and around Malvinas Islands. The main difference withthe former computation by G-MOD is the lack in our resultsof dissipation between San Blas and Bahıa Blanca. Never-theless, this feature is consistent with the low energy fluxobserved over the area in both, G-MOD and our, simulations.

An integration of the M2 energy dissipation by bottom fric-tion over the model domain gives a result of 117 GW (1 GW5 109 W). Our estimation is similar to total energy dissipa-tion at the Patagonian shelf calculated by MILLER (1966) of130 GW, but around a half of the computations by CART-WRIGHT and RAY (1989) and GLORIOSO and FLATHER (1997),of 245 GW and 218 GW respectively. In any case, dissipationin the region constitutes an important amount of the esti-mated total global value (2400 GW).

M2 energy flux derived from Model B is given in the leftpanel of Figure 13, where the change in the scale of the ar-rows between San Matıas Gulf and the rest of the domainmust be noted. This change was adopted because energy fluxin San Matıas Gulf is one order of magnitude larger than inthe other areas of Model B. Most of energy enters the domainfrom the east. At the inner continental shelf, at approxi-mately 37.58 S the westward incoming flux splits into twobranches. One of them turns to the north and enters the Rıode la Plata estuary from the south, keeping itself close to the



Figure 13. Left panel: M2 tidal energy flux vectors in W m21 for Model B; note the change in the scale of the arrows between San Matıas Gulf and therest of the domain. Right panel: M2 tidal energy dissipation by bottom friction rate in W m22 (right panel) derived from Model B; note that contourinterval is not regular.

Figure 14. M2 tidal energy flux vectors in W m21 (left panel) and contours of M2 tidal energy dissipation by bottom friction rate in W m22 (right panel)derived from Model C.

coast. The other one deflects to the south flowing along thecontinental shelf break up to the southernmost portion of thedomain. There it seems to turn around the amphidromicpoint at 418 S–618 W (Figure 5, upper right panel) and toreinforce the northward flux parallel to the coast which iscoming from the Patagonian Shelf.

Energy dissipation by bottom friction in this domain (Fig-ure 13, right panel) has its maximum at the San Matıas Gulf,where the velocities are very intense (Figure 7, upper rightpanel and Figure 10). A secondary maximum is present atthe Rıo de la Plata estuary.

The left panel of Figure 14 shows the energy flux derived

from the simulation for the Rıo de la Plata Model C. Improvedresolution allows for a better definition of the details insidethe estuary. Energy flows mainly along the Argentineancoast, whereas values are very small on the Uruguayan coast.Maximums in this flux occur coincidentally with the maxi-mum currents (Figures 8 and 11) at Punta Piedras and PuntaRasa. When reaching the upper portion of the estuary, fluxhas strongly attenuated. This suggests that most of the dis-sipation takes place in the extremes of Samborombon Bay.This is in effect observed when the energy dissipation by bot-tom friction is computed. It is shown in the right panel ofFigure 14, which also indicates that dissipation occurs as well



along the deep channels of the middle part of the estuary andat its upper part. A secondary maximum in dissipation ataround 568 W is observed, coincident with the presence of theRouen Bank. It is interesting to note that there is almost nodissipation inside the Samborombon Bay. It should be noted,nevertheless, that the energy flux and the energy dissipationmight be overestimated, since both the amplitude of the el-evation and specially the currents are overestimated by themodel (Figure 8).

SUMMARY AND CONCLUSIONS

A set of three 3-D nested models based on HamSOM codefor tidal propagation from the Argentinean Continental Shelfto the Rıo de la Plata estuary has been developed. The set ofmodels was constructed as a first step of the development ofa warning and management system. In that sense they werebuilt in a very realistic manner, representing an importantadvance with respect to previous works.

In this paper the propagation and amplification of M2, byfar the most important tidal constituent of the region, is an-alyzed. Model results have been validated by using all of theavailable tidal gauge data and several current meter obser-vations. A good agreement between observations and modelresults is observed for both, harmonic constants and tidalcurrents. For the Rıo de la Plata estuary, errors in modeledamplitude are lower than 2 centimeters for all but one point,where it reaches 6 cm. Phase lags are lower than 13 minutesin all of the cases. It is observed that our model tends tooverestimate the magnitude of the currents, even thoughtheir phase is well captured. Therefore, we are confident thatthe validity of the data obtained by the simulations could beextended to other areas where no tidal gauge and/or currentmeters are present and that the set of three one-way nestedmodels can constitute the base of a useful management tool.

Simulations have allowed the construction of a more reli-able and higher resolution model derived M2 cotidal, corangeand tidal current charts for the Argentinean ContinentalShelf and the Rıo de la Plata estuary. Non-linear generationof the higher order harmonic was analyzed. M4 was found tobe important, with values larger than 0.10 m, at most of themany gulfs and bays of the Patagonian coast. Maximumswere found at the San Matıas Gulf and the Bahıa Grandearea, in good agreement with observations.

Energy flux and energy dissipation by bottom friction werecomputed for each of the three domains. Results indicate thatdissipation at the Patagonian Shelf constitutes an importantamount of the total globally estimated one. An important dif-ference with respect to the former computation by GLORIOSO

and FLATHER (1997) is a smaller dissipation amount betweenBahıa Blanca and San Blas. Nevertheless, low dissipation inthis area is consistent with the low energy flux observed inboth, the former and our, simulations. The comparison be-tween modeled and observed currents indicates that our mod-eled velocities could be overestimated in this last region. Itsuggests that energy flux, and ergo energy dissipation, at theBahıa Blanca/San Blas zone could be even smaller than theestimation presented in this paper.

High-resolution simulations for the Rıo de la Plata estuary

and the adjacent Continental Shelf have allowed the first es-timations of the tidal energy flux and the energy dissipationby bottom friction at the estuary. Results indicate that energyflux to the Rıo de la Plata comes from the east and entersthe estuary from the south-westernmost portion of its mouth.Energy flow concentrates mainly along the Argentineancoast, whereas values are very small on the Uruguayan one.Consistently, most of the dissipation takes place in the ex-tremes of Samborombon Bay. Dissipation occurs as well alongthe deep channels of the middle part of the estuary and atits upper part. A secondary maximum coincident with thepresence of the Rouen Bank is observed at the exterior partof the estuary. Nevertheless, energy flux and energy dissi-pation produced with our simulations might be overestimat-ed, since that our model tends to overestimate the currents.

In the near future ADCP and drifters measurements willbe collected in the context of the UNDP/GEF project ‘‘Envi-ronmental Protection of the Rıo de la Plata and its MaritimeFront’’. These measurements will be very valuable to furthervalidate our model results.

ACKNOWLEDGMENTS

This work was partially supported by SETCIP of Argentinaand BMBF of Germany through the Co-operation Project AL/A98-UVII/15. Part of the research has been supported byUBA Grant X072 and BID-PICT 99-6215. Useful discussionwith scientists of other institutions have resulted of cooper-ative work promoted by the UNDP/GEF project ‘‘ProteccionAmbiental del Rıo de La Plata y su Frente Marıtimo’’ con-ducted by the Consortium CARP/CTMFM.

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M RESUMEN M

El Rıo de la Plata es uno de los sistemas estuariales mas importantes del mundo y la cuenca mas desarrollada del este de Sudamerica. El estuario esta expuesto afrecuentes crecidas que causan danos significativos producidas por la combinacion de la marea con ondas de tormenta. Aunque el Servicio de Hidrografıa Naval deArgentina (SHN) mantiene un sistema de alarma basado en un metodo estadıstico de prediccion, aun no se dispone de un modelo numerico operacional confiablepara pronostico y gestion costera del Rıo de la Plata. Como una contribucion al Proyecto PNUD/GEF ‘Proteccion Ambiental del Rıo de la Plata y su Frente Marıtimo’,y como resultado de un proyecto de cooperacion, una herramienta de pronostico de este tipo esta siendo desarrollada por el CIMA y el SHN de Argentina y el IfMde Alemania. Con este fin se esta aplicando el modelo tridimensional en ecuaciones primitivas HamSOM (Hamburg Shelf Ocean Model). Como un primer paso serealizo un estudio de la propagacion de la marea. Dado que ni los datos disponibles ni los modelos globales pueden proporcionar condiciones de contorno adecuadascerca del Rıo de la Plata, los datos para el estuario fueron obtenidos a traves de la aplicacion de un conjunto de tres modelos anidados unidireccionalmente. Lassimulaciones se comenzaron en un modelo de gran escala que cubre las plataformas continentales argentina y uruguaya y parte de la brasilena. Este modeloproporciona condiciones de contorno a un modelo de menor escala de Rıo de la Plata y la plataforma continental adyacente, que a su vez se utiliza para forzar un



modelo de pequena escala y alta resolucion del Rıo de la Plata. Se investigo la sensibilidad de la solucion a dos diferentes condiciones de contorno provenientes demodelos globales que asimilan datos (ZAHEL, 1997 and RAY et al., 1994) ası como a varios parametros del modelo. Aunque una comparacion entre las soluciones delos modelos globales muestra diferencias en la parte austral del dominio del modelo de mayor escala, nuestras soluciones no exhiben sensibilidad a las mismas. Lassoluciones tampoco resultan sensibles a la difusion lateral, pero sı a la friccion de fondo. Las simulaciones muestran la onda de marea M2 propagando hacia el nortecomo una onda de Kelvin, con amplitudes que alcanzan los 4 m en la parte sur de la Patagonia y valores mucho menores, de solo unos pocos centımetros en elestuario del Rıo de la Plata. En este primer trabajo se validaron resultados de la simulacion de la propagacion de la componente M2 en cada uno de los tres dominiosutilizando todos los datos de mareografos disponibles y varias observaciones de corrientes. Las simulaciones muestran buena concordancia con las observaciones. Eneste sentido, estas simulaciones han permitido la construccion de cartas derivadas de modelo de lıneas cotidales, de isoamplitud y de corrientes de marea masconfiables. La transferencia no lineal de energıa de la componente semidiurna a harmonicos de mayor orden fue asimismo mapeada. Esta puede alcanzar valoresmuy altos en algunos lugares de la costa patagonica. La disipacion de energıa de marea fue derivada de las simulaciones. Esta constituye una porcion importantede las estimaciones para la disipacion global. Esta informacion, obtenida de nuestras simulaciones, es muy util para complementar los pocos datos costeros disponiblesen regiones tan extensas y complejas como la Plataforma Continental Argentina y el Rıo de la Plata.

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