Modeling an arrested salt-wedge estuary subjected to variable river flow

Highlights

• We validate a three-dimensional hydrodynamic model of a salt wedge estuary.

• Vertical grid resolution, bottom friction, background eddy viscosity are adjusted.

• Longitudinal salinity structure is well reproduced.

• It predicts the overall measured phenomena and the effects of the flash flood event.

Abstract

In this study we present an approach to calibrate a three-dimensional hydrodynamic model of a salt-wedge estuary, the Araranguá Estuary, southern Brazil, based on the Delft3D-FLOW model. The calibration was carried out in four steps to predict the vertical salinity structure along the estuary in an efficient and effective way. Skill assessment was used to evaluate the calibration quality. The model is forced by water-level elevation along the offshore open boundary and river-discharge inflows from the two major tributaries. The hydrodynamic model was calibrated using field observation of water level, currents and longitudinal salinity structure. Calibration was performed adjusting vertical grid resolution, bottom-friction coefficient and background eddy viscosity. The model achieves high skill values at water level and currents variations during a 113-day period (in 2008) covering a wide range of river discharge and tidal forcing. Water surface fluctuations obtained from the model are in good agreement with the field data. Modeled depth-averaged currents reproduce the temporal pattern of observed data. Longitudinal salinity structure is also well reproduced, although the vertical structure is more diffusive than the observations. Results also demonstrate that the model predicts the overall measured phenomena and the effects of the flash-flood event, with the discharge affecting water level, currents and salinity.

Introduction

Estuaries are transitional environments between continents and the coastal oceans. Estuarine conditions depend on fluvial, tidal, wind and baroclinic forcing and on the dynamics of the adjacent continental shelf. The relative balance among these factors defines estuarine characteristics such as salinity intrusion length, stratification, and dispersion and exchange mechanisms (Ralston et al., 2010a). Estuaries can be classified as salt wedge, highly stratified, partially stratified or well mixed according to their vertical salinity structure (Pritchard, 1955, Cameron and Pritchard, 1963). This classification ultimately reflects the competition between buoyancy forcing from river discharge and mixing from tidal forcing (Valle-Levinson, 2010). Salt-wedge estuaries are usually associated with microtidal regime and relatively large river discharge in relation to the tidal prism (e.g., the Mississippi River, USA (Wright and Coleman, 1971); Rio de la Plata River, Argentina (Acha et al., 2008); Itajaí-Açu River, Brazil (Schettini et al., 2006); Ebro River, Spain and Rhone River, France (Ibañez et al., 1997). Being a relative control, salt-wedge estuaries can also be formed with lower river discharge but subjected to small tidal ranges, such as the Rječina (Krvavica et al., 2017) and Jadro (Ljubenkov, 2015) rivers, in Croatia, the Strymon River, Greece (Zachopoulos et al., 2020) and the Araranguá River, Brazil (D’Aquino et al., 2010) The examples above can be set as ‘arrested salt-wedge estuaries’, since the marine waters lingers in the estuarine basin for periods of time much longer than the tidal cycle. In the ‘tidally forced salt wedges’, the salt wedge advances and retracts almost entirely during a tidal cycle, with relatively small mixing with freshwater. Examples of such systems are Fraser River, Canada (Geyer and Farmer, 1989), Merrimack River, USA (Ralston et al., 2010a, Ralston et al., 2010b) and the São Francisco River, Brazil (Paiva et al., 2020).

The vertical salinity distribution characterizes the degree of stratification and affects the vertical mixing process and also plays a fundamental role in the salt balance (Geyer, 2010, Wang et al., 2011) and transport of other scalars such as sediments, nutrients and pollutants. Understanding the structure and variability of the salinity distribution in an estuary is important to many ecological and engineering management decisions (Ralston et al., 2008). In this sense, numerical modeling has been established as an effective tool to understand physical processes in estuarine and coastal waters, being able to reproduce and predict its processes. Modeling highly-stratified estuarine flows are especially challenging (Ralston et al., 2017). One reason for that is the nature of mixing. In well mixed estuaries, mixing is mainly due to the bottom stress and bottom generated turbulence. In highly stratified flows, mixing is also generated from baroclinic instabilities at the pycnocline, resulting in upwards salt flux by entrainment. Further, stratification works as a vertical barrier for momentum and scalar fluxes, what must in some way be encompassed by turbulent closure schemes (Nunez Vaz and Simpson, 1994).

The success of the model application depends on adjustments in their main parameters, considered here as the model calibration procedure. In the modeling literature there is no standard procedure for model calibration and verification (Cheng et al., 1991). It is common sense that to calibrate and validate a numerical model requires a good and sufficiently broad set of data to include the most important variations of natural phenomena (e.g., tide variations and river discharge fluctuations). All available field data can be used in model calibration (Cheng et al., 1993). However, a series of factors need to be considering the comparison of model outputs with measurements. These include measurements accuracy (instruments calibration and reliability) and the horizontal and vertical measurement location, which may not be the same as the model grid point.

Model calibration and validation appears in various forms, dependent on the available data, characteristics of the water body, and the perceptions and opinions of modelers (Hsu et al., 1999). Usually, the model calibration is considered by comparing time-series of the field data and modeled results. When possible, studies have addressed the model calibration as the adjustment of model parameter values and validation/verification as the subsequent testing of the calibrated model, for which two sets of data are required (e.g., Dias and Lopes, 2006, Fossati and Piedra-Cueva, 2013, Hasan et al., 2013, Hsu et al., 1999, Huang, 2007, Ji et al., 2007, Liu et al., 2007, Seiler et al., 2020, Xu et al., 2008).

Numerical models that adequately reproduce the vertical stratification are required for salt wedge and strongly stratified estuaries, and it is important that the model is able to adequately simulate the spatial and temporal salinity distribution. Therefore, three-dimensional (e.g. Warner et al., 2005, Ralston et al., 2010a, Ralston et al., 2010b, Simons et al., 2010, Funahashi et al., 2013, Putra et al., 2015) or two-layer shallow-water models (e.g. Ljubenkov, 2015, Krvavica et al., 2017, Krvavica et al., 2021) have been successful in reproducing salt-wedge dynamics. Initial conditions for salinity have been imposed in different ways in order to evaluate the salinity structure in the calibration procedure. For example, Warner et al. (2005) impose a horizontal salinity gradient at the seaward open boundary based on the current value of salinity. In their study, the first 10 days of simulations was to provide dynamic adjustment of the density field. Salinity at open boundary was based on depth-dependent time-varying from observations data (Ralston et al., 2010a, Ralston et al., 2010b). Simons et al. (2010) created an initial salinity condition by introducing a longitudinal linear salinity field (0 to the upstream to 25 at the open boundary) and then run a 10-day simulation. Funahashi et al. (2013) set constant salinity conditions at the boundaries and run the model for one month with a constant river discharge to reach a steady state representative for salinity distribution. A multi-station of salinity profile was developed by Putra et al. (2015) as an unconventional calibration mechanism for a 3D salinity model. Another way to initialize the salinity field is along-channel vertical profiles of salinity interpolation (Chua and Fringer, 2011). Although there is no pattern in the calibration process, an alternative approach can be considered. Krvavica et al. (2021) modeled the Neretva River estuary, a microtidal salt-wedge estuary in Croatia. In their numerical experiments, a two-layer numerical model reproduced the salt-wedge dynamics, highlighting the importance of the river discharge in controlling its dynamics.

In this study we present the approach adopted to set up a three-dimensional hydrodynamic model of a salt-wedge estuary, the Araranguá Estuary, Brazil. Our goal is to describe the implementation, calibration and validation steps, in order to have a robust tool for further assessments in this estuary. The model results were assessed through comparisons with observed data. The measurements extend over a 113 days period with several spring neap cycles and large variations in river discharge, associated to pulses in river discharge. The field data includes water level and currents time series, and along-estuary salinity distribution.