This paper describes the development of a two-dimensional water quality model that solves hydrodynamic equations tied to transport equations with reactions mechanisms inherent in the processes. This enables us to perform an accurate assessment of the pollution in a coastal ecosystem. The model was developed with data drawn from the ecosystem found in Mexico’s southeast state of Tabasco. The coastal ecosystem consists of the interaction of
The concern for water environmental pollution by heavy metals has recently increased due to the negative effects it might have in human beings [
Metals are naturally present in small concentrations or traces in earth’s crust; many of them are essential for the growth and development of plants, animals, and human beings. The geo-available origin of these metals occurs from the mother rock to the soils after being released by weathering. In contrast, the presence of high concentrations of metals with respect to the ecological norms is an indicator of anthropogenic activities, such as hazardous wastes derived from industrial activities, mining, and agriculture.
As rivers serve as a medium for transport of dissolved and particulate matter from continents to the ocean, nowadays, interest in the pollution of rivers by metals has increased along with the exponential increment of industrialisation, urbanisation, and agriculturisation of coastal areas. This has substantially increased the concern and level of awareness in this problem [
In coastal waters, heavy metals are distributed through the water column (particulate and dissolved) and the bottom sediments. This occurs during the mixing of fresh and marine water, which causes flocculation and sedimentation of organic matter, nutrients, and trace elements from rivers. Actually, dissolved metals come into the particulate phase due to processes as flocculation, water pH, sediment mineralogy, and others during estuarine mixing [
In this work, it is assumed that the partition coefficient does not depend on the concentration of the sorbing solids, according to Thomann and Mueller [
Flocculation plays a key role in the dynamics of estuarine and coastal environments, controlling the transport of fine-grained cohesive sediments and particulate contaminants throughout these systems [
For the above reasons, strategies and tools to mitigate the pollution of heavy metals are required [
Most common methods to evaluate heavy metals pollution in water bodies are based on quality indexes, which generally use correlation or fuzzy methods for their estimation [
Water quality models (WQM) have increased in number and have improved in recent years, focusing on the study of the water quality as well as pollutant transport in shallow water ecosystems. The behaviour and transport of toxic substances, such as metals and/or hydrocarbons, have been deeply studied on shallow aquatic systems during this century [
The most popular numerical WQM are AQUATOX, Branched Lagrangian Transport Model (BLTM), One-Dimensional Riverine Hydrodynamic, Water Quality Model (EPD-RIV1), QUAL2Kw, Water Quality Analysis Simulation Program (WASP), Water Quality for River-Reservoir Systems (WQRRS), ROMS-ICS [
In recent decades, there has been a boom in the development of hydrodynamic models with coupled water quality models; here we can also mention the POM model, MIKE3, COHERENS, ROMS, and MOHID model.
The MOHID three-dimensional model has the ability to simulate complex estuarine and coastal flows in numerous applications dealing with mesomalar coastal lagoons, tidal channels, and estuarine systems [
MIKE 3 model is a general three-dimensional hydrodynamic model for flow simulation in estuaries, bays, and coastal and oceanic areas [
ROMS model (Regional Ocean Modeling System) has been used to simulate the water circulation in different regions of the world’s oceans at different scales (local and basin) [
COHERENS model is a multipurpose three-dimensional model based on finite differences. This model allows the coupling with different submodels that simulate physical and biological processes, as well as the transport and transformation of sediments and pollutants [
Most of these last models are commonly used today, but most of them do not focus their strength on the solution of toxic substances transport such as heavy metals; they are more focused on hydrodynamic ocean domain than interaction of coastal-lotic-lentic water bodies.
Although there are available WQM as discussed above, it is common to find models developed by particular researchers that include effects or processes specific to their case of study, such as the MINEQL [
Despite the existing WQM, the aim of this work is to develop a water quality module, which can be coupled to a hydrodynamic numerical model, applicable to the study of hydrodynamics and water quality in coastal ecosystems. The hydrodynamic model adopted in this work is self-developed for research purposes and has been previously used in different research applications, including the hydrodynamic-hydrological modelling in flood zones [
The water quality module developed herein takes into account many parameters, including the advection-diffusion-reaction mechanism. The required parameters cannot be found in a specific existing WQM. These parameters were adopted from Ambrose Jr et al. [
In this area, several studies have been carried out in the last decade, related to the study of the dynamics of the river-lagoon-sea interaction [
This paper begins by a detailed presentation of the coastal ecosystem in Section
The coastal ecosystem under study is located at the east of Tabasco State, in the southeast of Mexico. The lagoon is located between LAT 18° 10’ and 18° 12’ N and between LONG 94° 02’ and 94° 00’ W (Figure
Location of study zone and control points (C.P.) in the coastal ecosystem. The centre of lagoon is located at W 94° 01’ 12” N 18° 11’ 6”.
For hundreds of years, the main activities in the zone have been agriculture, cattle farming, and fishing. Nevertheless, oil field
In the last 20 years, important changes in hydrology and water quality have occurred, changing the productivity and reducing the number of endemic species. These changes have had social, economical, and commercial impacts for native population. This area is currently under industrial development, where two kinds of activities stand out: oil (extraction and production) and livestock farming, which together account for almost 90% of the productive sectors of Tabasco State [
The predominant climate in the region is warm and humid, with abundant rainfall through the whole year, particularly during autumn. Its annual thermal regime oscillates between 25.8°C and 27.8°C; the highest average temperature occurs in May with 29.4°C, while the minimum is registered in January with 23.1°C. September/October is the most rainy period with an average precipitation of 400 mm, while June features the minimum precipitation with an average value of 43.3 mm [
For
In this zone of the Gulf of Mexico, tide presents a mixed type with diurnal influence, whose oscillations are not greater than 30-60 cm. The surge is moderate in E-W direction, with a maximum height of 2 m in normal meteorological conditions.
The WQM developed herein consists essentially of two parts: a hydrodynamic module and a water quality module. The later one is in charge of transporting heavy metals through the water body by using the hydrodynamic module results, which has been calibrated and tested previously [
In measurement campaigns, water and sediment samples were collected following the guidelines of the Standard Methods for the Examination of Water & Wastewaters methodology [
For heavy metals in water, 500 ml of sample was taken at each point using a van Dorn water sampler. The samples were filtered (0.45
For heavy metals in sediments, samples of 100 g were collected from the surface layer of the bottom sediments (max. 5 cm) with an Ekman dredger. These samples were stored in sterile polyethylene bags and kept at 4.0°C for transport. Particulate and dissolved concentrations of metals were also obtained in sediments.
All the samples were collected in duplicate to determine the precision of tests and sample handling. In order to minimise the effect of hydrological input from rivers, the sediment and water sampling were performed during mornings from 8:00 to 12:00 hours in low tide conditions when there is little penetration from the sea to Chicozapote river and El Yucateco lagoon.
The chemical analyses of heavy metals in water and sediments were performed using atomic absorption spectrophotometry, with spectrophotometer (Shimadzu, Mod. AA 6800).
According to previous
Measured data and the chemical analyses of these parameters served to specify boundary and initial conditions to the numerical model developed herein. They also aided in validating the model for the field site.
The numerical model used in this work is self-developed, strongly based on the proposal of Casulli and Cheng [
Simulation process flowchart for hydrodynamic module.
Simulation process flowchart for water quality module.
The hydrodynamic module used in this work is based on the two-dimensional shallow water equations, which can be derived from the Reynolds-averaged Navier-Stokes equations [
The equation to calculate the free surface elevation (
As mentioned above, in order to achieve more realistic hydrodynamics, mechanical dispersion phenomenon is also considered through the introduction of a model of turbulence. Due to the nature of the water body treated herein, the following mixing-length model is used [
The wind shear stress terms in
The numerical solution scheme of the hydrodynamic module is based on a second-order finite difference formulation in both time and space. The solution method is an adaptation of the semi-implicit Eulerian-Lagrangian scheme proposed by Casulli and Cheng [
A 2D mesh is used for the numerical simulations, based on a staggered cell arrangement, as shown in Figures
Discretization cell. Top view.
Vertical mesh arrangement.
In Figure
The solution of the system of (
The WQM consists of two parts, the one in charge of transport and the one in charge of the reaction mechanisms to which the substance is subject. Within the quality module, the Advection-Diffusion-Reaction equation is solved as
The WQM is initialized considering no reaction (
Depiction of reaction metal model parameters for a completely mixed lake. 1 stands for water column and 2 for sediment layer.
In (
A description of the processes underlying the parameters in (
For the decay of the dissolved substances, the most important mechanisms in the degradation rate of the dissolved toxic substance (
The overall exchange rate (
Henry’s (
The sediment diffusion rate
To determine both settling and resuspended velocities, a particle characterisation in the region under study is required. In this work, such characterisation was made with sediment samples taken from field campaigns, where organic matter, particle sizes, porosity, humidity, and so forth were quantified as follows: the organic matter was obtained by the wet oxidation technique using exothermic heating and oxidation of organic carbon of the sediment sample [
In coastal ecosystems, a good approximation to the settling velocity
For the resuspended velocity
In estuarine and coastal environments, usually characterised by muddy bottoms, flocculation plays a key role [
The hydrodynamic characteristics of water bodies such as coastal lagoons are governed by a slight balance between tidal forces, currents flow, wind stresses, and density, which induce pressure and friction forces at the bottom [
The forcing boundary conditions of the sea-
Wind rose used in the hydrodynamic module for dry season.
Wind rose used in the hydrodynamic module for wet season.
Forcing boundary conditions used in the study domain for dry season: (a) tide condition; (b) hydrological flow, and for wet season; (c) tide condition; (d) hydrological flow. The gauging stations where the hydrological flow and the tide condition were taken are shown in Figure
Bathymetry and mesh of the domain.
Bathymetry of the study zone, measured relative to the mean sea level, in metres (m). Arrows indicate gauging stations of hydrological flow and tide boundary conditions
Mesh configuration for the study zone
The bathymetry shown in Figure
The area under study was discretised through a structured mesh. A variable-spacing grid was used to make the model more efficient in zones of interest, with
In order to assess the quality of the numerical solution with respect to field measured data, the Root Square Mean Error
A value of RMSE = 0 indicates a perfect fit. Some suggested values for decision-making related to the data produced by the RMSE are presented in Table
Criteria for the qualitative evaluation of goodness of fit for RMSE.
RMSE | Fit |
---|---|
> 0.70 | Not satisfactory |
| |
0.60-0.70 | Satisfactory |
| |
0.30-0.60 | Good |
| |
0.00-0.30 | Very good |
Considered time spans for wet and dry seasons.
Season | Initial date | Duration (days) |
---|---|---|
Dry | June, 1st | 50 |
| ||
Wet | September, 1st | 30 |
For NSE coefficient, the range
Tabasco State is the region of Mexico where the climate is very rainy, so seasons of the year are not highly differentiated, with abundant precipitations throughout the whole year. Thus, it is important to differentiate between the typical characteristic climate periods in the study area, such as summertime and wintertime, because the dynamics can significantly change [
In this work, metals concentrations were measured in four control points (C.P.). Two sampling points are located within the lagoon (C.P. 1 and 2) and two in the river (C.P. 3 and 4) (see Figure
The validation process of the WQM consists in finding the values involved in the considered reaction mechanism (see Section
In order to start the validation process, initial conditions are required. Such values are introduced to the computational domain on each control point at the beginning of the simulation. The initial parameters were imposed based on EPA recommendations. Then, a numerical simulation carried out forcing with measured concentrations in C.P. 1, C.P. 2, and C.P. 3 of Figure
WQM parameters for the considered heavy metals that resulted from the validation process.
Variable | Value | |||
---|---|---|---|---|
Cd | Cr | Ni | Pb | |
| Initialised from measured data in C.Ps. | |||
| ||||
| 0.01 | |||
| ||||
| 0.2 | |||
| ||||
| 1.85 | 1.90 | 1.90 | 1.85 |
| ||||
| From hydrodynamic module | |||
| ||||
| 0.0074 | 0.0124 | 0.0114 | 0.0049 |
| ||||
| 0.1 | |||
| ||||
| By Control Point | |||
| ||||
| 1.5 | |||
| ||||
| 0.8 | |||
| ||||
| 0.9 | |||
| ||||
| 0.00035 | 0.00015 | 0.00015 | 0.00035 |
| ||||
| 0.0042 |
It ought to be noted that the values of the system coefficients lie within the typical values reported for them in the literature [
In order to perform the hydrodynamic simulation, the hydrodynamic module has already been calibrated with the parameters shown in Table
Calibrated parameters of the hydrodynamic module [
Variable | Value |
---|---|
| 9.81 |
| |
| 0.09 |
| |
| 0.41 |
| |
| 0.6 |
The hydrodynamic simulations were performed using a time step of
(a) Dry season, day 50 snapshot. (b) Wet season, day 30 snapshot.
According to results obtained from field measurements, it is possible to observe that, for dry season, there is an intense recirculation in the lagoon due to the influence of sea. Nevertheless, for wet season, river flow is higher, tide penetration almost does not exist, and lagoon’s behaviour presents lack of recirculation.
Figures
Root Mean Square Error (RMSE) and Nash-Sutcliffe efficiency coefficient (see (
Error | C.P. 1 | C.P. 2 | C.P. 3 | C.P. 4 |
---|---|---|---|---|
RSME | 0.0011 | 0.0006 | 0.0005 | 0.0019 |
| ||||
NSE | 0.3699 | 0.6818 | 0.4036 | 0.2820 |
Root Mean Square Error (RMSE) and Nash-Sutcliffe efficiency coefficient (see (
Error | C.P. 1 | C.P. 2 | C.P. 3 | C.P. 4 |
---|---|---|---|---|
RSME | 0.0011 | 0.0011 | 0.0017 | 0.0032 |
| ||||
N-S | 0.3699 | 0.8224 | 0.8230 | 0.2718 |
Simulated distribution of Cadmium at the end of the dry season (day 50th snapshot).
Behaviour of Cadmium concentration
Simulated distribution of Cadmium at the end of wet season (day 30 snapshot).
Behaviour of Cadmium concentration
Figures
Root Mean Square Error (RMSE) and Nash-Sutcliffe efficiency coefficient (see (
Error | C.P. 1 | C.P. 2 | C.P. 3 | C.P. 4 |
---|---|---|---|---|
RSME | 0.0026 | 0.0008 | 0.0023 | 0.0103 |
| ||||
N-S | 0.4121 | 0.7291 | 0.9647 | 0.3132 |
Root Mean Square Error (RMSE) and Nash-Sutcliffe efficiency coefficient (see (
Error | C.P. 1 | C.P. 2 | C.P. 3 | C.P. 4 |
---|---|---|---|---|
RSME | 0.0107 | 0.0116 | 0.0031 | 0.0022 |
| ||||
N-S | 0.6948 | 0.6378 | 0.2016 | 0.2026 |
Simulated distribution of Chromium at the end of dry season (day 50 snapshot).
Behaviour of Chromium concentration
Simulated distribution of Chromium at the end of wet season (day 30 snapshot).
Behaviour of Chromium concentration
Figures
Root Mean Square Error (RMSE) and Nash-Sutcliffe efficiency coefficient (see (
Error | C.P. 1 | C.P. 2 | C.P. 3 | C.P. 4 |
---|---|---|---|---|
RSME | 0.0058 | 0.0031 | 0.0551 | 0.0335 |
| ||||
N-S | 0.4649 | 0.4906 | 0.3573 | 0.2003 |
Root Mean Square Error (RMSE) and Nash-Sutcliffe efficiency coefficient (see (
Error | C.P. 1 | C.P. 2 | C.P. 3 | C.P. 4 |
---|---|---|---|---|
RSME | 0.0020 | 0.0035 | 0.0089 | 0.0198 |
| ||||
N-S | 0.9320 | 0.8155 | 0.0163 | 0.0984 |
Simulated distribution of Lead at the end of dry season (day 50 snapshot).
Behaviour of Lead concentration
Simulated distribution of Lead at the end of wet season (day 30 snapshot).
Behaviour of Lead concentration
Figures
Root Mean Square Error (RMSE) and Nash-Sutcliffe efficiency coefficient (see (
Error | C.P. 1 | C.P. 2 | C.P. 3 | C.P. 4 |
---|---|---|---|---|
RSME | 0.0024 | 0.0015 | 0.0155 | 0.0156 |
N-S | 0.3289 | 0.3101 | 0.4473 | 0.0619 |
Root Mean Square Error (RMSE) and Nash-Sutcliffe efficiency coefficient (see (
Error | C.P. 1 | C.P. 2 | C.P. 3 | C.P. 4 |
---|---|---|---|---|
RSME | 0.0024 | 0.0015 | 0.0155 | 0.0155 |
| ||||
N-S | 0.3289 | 0.3101 | 0.4473 | 0.0619 |
Simulated distribution of Nickel at the end of dry season (day 50 snapshot).
Behaviour of Nickel concentration
Simulated distribution of Nickel at the end of wet season (day 30 snapshot).
Behaviour of Nickel concentration
The numerical simulations presented above were performed for wet and dry seasons. The hydrodynamic results show that, for dry season, tidal reversing currents occur affecting the whole ecosystem, favouring the formation of vortices within
The metals transport simulations show that, for both season scenarios, dry and wet, the concentration of metals maintains a stable behaviour, which is perturbed by oscillations due to hydrodynamics. The oscillations are greater for dry season, where the hydrodynamics are driven by tides. For the wet scenario, metals concentrations show very slight disturbances, maintaining an almost constant behaviour during the simulation period. In general, the concentrations are higher at control points located in
On the other hand, as it can be observed from the structure of the model presented herein, it is of great importance to possess enough information to feed the numerical model with the necessary data in order to validate it and to obtain the results that better reproduce the pollutant transport. In other words, the use of numerical modelling does not exempt the in-depth acquaintance of the dynamics of the system under study. This implies several numerical simulations to achieve the best agreement with field measured data.
This in-depth acquaintance means to know, besides the initial concentrations of the toxicants to be simulated, intrinsic facts of the water body as its detailed bathymetry, contours, and boundary conditions as wind forcing, tides, flow discharges to the water body, and so forth in order to accurately determine the transport of toxic substances. In this sense, the required field work to accomplish the study with this model is enormous, but it provides excellent and more accurate results than most of models.
The procedure adopted to validate the water quality module coupled to the hydrodynamic module is based on a trial-and-error procedure with the aim of adjusting the coefficients of the reaction equation terms for each metal. Concentration field measurements were used to validate the model by adjusting its parameters until acceptable simulation was achieved. Although the validation procedure was designed specifically for the present case of study, it can be straightforwardly extended to other cases. Although this constitutes a robust method to validate the model that yields accurate results, it requires high computational burden and execution times.
In this paper, a hydrodynamics-based WQM for the specific evaluation of heavy metals is developed and tested. The model was set for a specific ecosystem located at the east of Tabasco State, Mexico.
A heavy metal water quality module, based on a laterally averaged two-dimensional hydrodynamics and sediment transport model, was developed and applied to the tidal
In this way, this model constitutes an excellent option when a distribution of the solutes with a high accuracy is required. Nevertheless, the most challenging fact on carrying out metal transport numerical simulations is the lack of data for validation as well as the lack of information about the values of the reaction equation terms coefficients.
Finally, it ought to be remarked that the necessity of developing this model arose from the fact that it was more convenient to solve and program the differential equations and be able to access and adjust all the model parametrisation to simulate in a better way the hydrodynamics and metals transport. Thus, beside the important assessment of metals transport in the considered estuary, the main contribution of this work is to provide a highly accurate water quality model able to deal with the dynamics of these toxicants in the water body.
The data measured to support the findings of this study are available from the corresponding author upon request.
The authors declare that they have no conflicts of interest.