Nonlinear tide-surge interactions in the Río de la Plata Estuary
Introduction
The nonlinear tide-surge interaction (NTSI) has historically been studied by many authors (e.g., Proudman, 1955a, Doodson, 1956, Rossiter, 1961, Godin, 1972, Wolf, 1981, Murty, 1984, Bijlsma, 1986, Flather, 2001, Bernier and Thompson, 2007, Jones and Davies, 2008). In deep regions of the ocean, the tide is unaffected by the surge; however, in shallow coastal regions there is significant modification of tidal elevations and currents due to that interaction (Jones and Davies, 2008). Those interactions have been extensively studied in intertropical regions, because during hurricanes or tropical storms they can have large effects on the sea level and floods (e.g., Sinha et al., 1996, at Hooghly Estuary, India; Paul et al., 2016, along the coastal of Bangladesh; Khalilabadi, 2016, at the Persian Gulf, the Strait of Hormuz and the Gulf of Oman; Feng et al., 2018 at the Bohai Sea, China; Xiong et al., 2019, at the Yellow Sea; Pandey and Rao, 2019, at Bay of Bengal; Sebastian et al., 2019, along the eastern coast of India; Wankang et al., 2019, at the Tieshan Bay, China). In extratropical regions, where winds rarely reach speeds of the magnitude of hurricanes, or under conditions when winds are not so extreme, the subject has been less studied. The pioneer study of Rossiter (1961) showed that NTSI can significantly affect the amplitude and timing of the storm surges in the Thames River. More recently, several authors demonstrated that in diverse parts of the world NTSI is strong and, therefore, the magnitude of surges can only be predicted accurately if those interactions are taken into account (Sindhu and Unnikrishnan, 2013). For instance, Bernier and Thompson (2007) and Zhang et al. (2010) found that NTSI accounts for about 30% of the total water level on the eastern coast of Canada and the Taiwan Strait, respectively; Idier et al. (2012) and Quinn et al. (2014) reported that the interaction can account for a large portion of the water level at the English Channel, accounting for up to 50%. With a theoretical approach, [75] investigated the main sources of nonlinear NTSI and found that the second-order (nonlinear) solution includes the contribution of three different effects related to the three nonlinear terms of the equations of motion: shallow waters, horizontal advection, and nonlinear bottom friction. Nevertheless, the relative importance of the different effects depends upon the site, its geometry, bathymetry, etc. Zenghao and Yihong (1996), Bernier and Thompson (2007), Zhang et al. (2010) and Spicer (2019), for instance, showed that at the Shangai coast, the eastern coast of Canada, the Taiwan Strait and the coasts of Maine, respectively, the dominant contribution to the interaction comes from the nonlinear bottom friction. Idier et al. (2012), instead, found that at the English Channel it mainly comes from the shallow water effect, even though in some portions of that channel the bottom friction can also become important. Lyddon et al. (2018) showed that in the tide-dominated Severn Estuary (south-west England) the maximum surge elevation increases exponentially up-estuary due to the shallow water effect. It has been demonstrated that the nonlinear interactions can also have a climatological effect on the long term water level means. For instance, Arns et al. (2019) found that NTSI can significantly reduce high water levels; moreover, they found evidence that changes in NTSI might have the potential to counteract the increasing flood risk associated with sea level rise, tidal and/or meteorological changes alone. Thus, NTSI can have a variety of effects and the sources of those interactions can be more than one and depend upon the site. The examples highlight, therefore, the need to carry out specific studies for every particular region of interest in order to understand the underlying dynamics and the eventual needs for an accurate forecasting.
The Río de la Plata (RdP, Fig. 1), located on the eastern coast of southern South America at approximately 35 S, one of the largest and most populated estuarine systems of the world (Shiklomanov, 1998). Its width varies from almost 50 km at its upper end to 230 km at its mouth, and has a length of 320 km (Balay, 1961). Because of its dimensions, the system behaves more as a semi-enclosed basin than as typical estuary (Simionato et al., 2004a). Positive storm surges, known as Sudestadas and associated with strong and persistent southeasterly winds, are relatively frequent in the region (Seluchi and Saulo, 1996, Gan and Rao, 1991). This phenomenon has historically caused catastrophic floods in the RdP coasts, threatening and claiming human lives and producing major economic and material damages (D’Onofrio et al., 1999). The Metropolitan Area of Buenos Aires City (AMBA, 1), site of the Capital of Argentina, with a population of more than 16 million people, is regularly affected by those events. For instance, in 2010 and 2012 extreme surges reached 3.25 m and 2.40 m over the Tidal Datum (Diario-Clarín, 2010, Diario-Clarín, 2012), being 1.90 m the emergency alert level (Balay, 1961). The maximum event recorded took place on April 15, 1940, when the observed level reached 4.44 m above the Tidal Datum (D’Onofrio et al., 2012). On the other hand, negative extreme surges in the RdP are associated with winds that have a dominant and persistent north westerly to westerly component, which are less frequent in the region (D’Onofrio et al., 2008). Nevertheless, when they do occur, they inhibit the access to the principal harbours of the region and impair the drinking water intakes of the most important city of southern South America. Even though both the positive and negative surges are not always so extreme, they are relatively frequent, taking place several times per year; moreover, observations suggest that the number and strength of the events have been increasing with time (D’Onofrio et al., 2008, Meccia et al., 2009).
The RdP is a microtidal system and the tidal regime is mixed, dominantly semidiurnal. The principal lunar semi-diurnal M is the most significant constituent; however, there are significant diurnal inequalities, mostly caused by the principal lunar diurnal constituent O (D’Onofrio et al., 1999). The maximum amplitude at Buenos Aires can reach 1 m, whereas the mean is 0.6 m. At Punta Rasa, the maximum amplitude reaches 1.43 m and the mean is of 0.76 m (SHN, 1987). The tide propagates inside the RdP as a Kelvin wave forced at the estuary mouth, leaving the coast to the left in the Southern Hemisphere; therefore, tidal amplitudes are larger and currents are stronger along the Argentinean (southern) coast than along the Uruguayan (northern) one (Glorioso and Flather, 1995, Glorioso and Flather, 1997, Simionato et al., 2004a). Owing to the effect of depth reduction on the phase speed and wavelength, and to the considerable length of the estuary, semidiurnal constituents have the unusual feature of nearly complete a wavelength within the estuary at all times (C.A.R.P., 1989). Tidal amplitudes are generally not amplified towards the upper part; the estuary is long and converges only at its innermost part, where it is extremely shallow and bottom friction plays a fundamental role controlling the wave amplitude (Framinan et al., 1999, Simionato et al., 2005a).
Even though tides and storm surges in the RdP and its adjacent shelf have been widely studied independently (e.g., O’Connor, 1991, Simionato et al., 2004a, Simionato et al., 2005a, D’Onofrio et al., 2008, Meccia et al., 2009, D’Onofrio et al., 2012), their interaction has not received attention from the scientific community yet. Due to the geographical setting of the estuary (extremely wide, long and shallow) and the features of tidal propagation and the surges, interactions are expected to occur and to be significant. It is an interesting problem not only from the theoretical point of view; also from an operational perspective, a better understanding of NTSI in this highly populated area is fundamental to aid in building an appropriate forecast system of water level (e.g., Horsburgh, 2014, Jones and Davies, 2008, Sindhu and Unnikrishnan, 2013).
The aim of this paper is, in this sense, to study NTSI in the RdP Estuary. For that, direct observations and numerical simulations are used to identify and characterize the areas where those interactions occur, to understand the involved physical processes and to quantify their importance. The paper is organized as follows. In Section 2, the observations, the numerical model, and the methodology are presented. In Section 3, water level observations are statistically analysed with a novel objective technique (surrogates) to test the possibility of occurrence of nonlinear interactions; then, numerical simulations are run to quantify and understand their sources. Finally, the results are discussed (Section 4) and subsequently conclusions are drawn (Section 5).
Section snippets
Data
Hourly water level observations in the RdP have been collected by the Servicio de Hidrografía Naval (SHN) of Argentina and the Servicio Oceanográfico, Hidrográfico y Meteorológico de la Armada (SOHMA) of Uruguay. In this paper the six stations shown in Fig. 1 (white squares) and Table 1 were used: Mar del Plata, Oyarvide, Palermo, Colonia, Montevideo and Punta del Este. Many of the series span relatively short periods of time, whereas Palermo and Oyarvide are the only stations with observations
Nonlinearity test for the observations
Fig. 2 shows the hourly water level () for every analysed station (Fig. 1 and Table 1) during a relatively strong Sudestada event occurred on December 23th, 2002, when simultaneous observations at the six stations were available. The central plot shows the surface wind for the moment of the peak of the storm, represented by vectors, and contours of the atmospheric sea level pressure (SLP) from the ERA5 reanalysis (Copernicus Climate Change Service (C3S), 2017). The water level time series show
Discussion
The analysis of observations discussed in Section 3 revealed that NTSI in the RdP are statistically significant, and suggested that they would increase upstream and that they would be stronger along the southern coast than along the northern one (Fig. 4). The results of the numerical simulations confirmed those hypothesis and indicated, moreover, that the interactions are independent of the magnitude of the surge and of its sign (Fig. 5), i.e., of the wind speed and direction.
The numerical
Conclusions
The aim of this paper has been to investigate the occurrence of nonlinearity tide-surge interactions (NTSI) in the Río de la Plata (RdP) and to understand its sources, using both data analysis and numerical modelling. The novel surrogate analysis was applied to direct observations collected at several locations of the estuary coast. The statistical analysis objectively indicates that water level within the estuary has a significant nonlinear component; it also suggests that interactions would
CRediT authorship contribution statement
Matías G. Dinápoli: Conceptualization, Methodology, Software, Formal analysis, Writing - original draft, Writing - review & editing. Claudia G. Simionato: Conceptualization, Writing - original draft, Writing - review & editing, Supervision, Project administration, Funding acquisition. Diego Moreira: Methodology, Data curation, Writing - original draft, Writing - review & editing.
Acknowledgements
This study was funded by the National Agency for Scientific and Technological Research of Argentina (ANPCyT) PICT 2014-2672 Project, the Programa de Investigación y Desarrollo para la Defensa del MINDEF (PIDDEF) 14-14 Project, and the UBACYT, Argentina 20020150100118BA directed by Claudia G. Simionato. Matías G. Dinápoli participation was possible thanks to ANPCyT and CONICET Ph.D. fellowships.
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