2.1. Study Area
The Yucatan Peninsula is located in the southeast of Mexico and is one of the biggest trans-boundary aquifers in the world—around 165,000 km2
. It is shared by Mexico, Guatemala and Belize [19
]. The Mexican part includes the states of Yucatan, Campeche and Quintana Roo (Figure 1
a). The Peninsula is composed mainly of limestone, with dolomite and anhydrite from the Mesozoic and Cenozoic periods reaching thicknesses > 1500 m [20
]. The Peninsula aquifer contains a well-developed conduit system at variable scale ranges with primary and secondary porosity in the rock matrix [19
]. Around 7.5 Mm3
of groundwater per year is extracted for human consumption [21
]; however, fresh water extraction does not jeopardize the water availability since aquifer recovery is constant and fast [22
]. Water balance in the region is positive, with a high availability per capita of about 7600 m3
]; this value is high compared to the Mexican national average.
Yucatan is a developing area, which places groundwater resources under special pollution stress and therefore, calls for strong protection policies. Yucatan is characterized by a tropical weather with a marked precipitation regime with variations in time and space. Mean precipitation ranges between 200–400 mm/year along the coastal area and 1000–1200 mm/year in the southeast [24
]. Two distinctive periods are characterized: dry, from November to April, and wet, from May to October. The present study focuses on Yucatan, specifically on the Merida Metropolitan Area (MMA). With around 1.1 million inhabitants, out of the total Yucatan population of 2.1 million, the MMA is a densely populated area composed of six municipalities where urbanization is continuously increasing (Figure 1
b). The MMA is located inside the hydrogeological region known as the Inner Cenote Ring (ICR), one of four hydrogeological regions in Yucatan [25
]. The ICR, also known as the Chixchulub sedimentary basin, is delimited by a semi-circular belt of approximately 180 km in diameter [26
]; this belt, also named the Cenote Ring, has a high sinkhole density. This ring is considered to be a surface expression of an asteroid impact at the end of the cretaceous period [27
]. The ICR is a relatively new sedimentary basin with a low level of karstification, although it is fractured, which explains the low number of sinkholes inside the ring compared with the crater rim. Some of the main characteristics of the area are the flatness of the terrain and lack of surface flow. The ICR has a mean slope of 1.5% and an average altitude of 28 m above sea level, except for a small area in the southeast of the inner ring. The flat topography and fracturing do not allow generation of surface streams, infiltrating precipitation at fast rates [28
]. Additionally, flatness and high hydraulic conductivity originate in low hydraulic gradients ranging from 7 to 10 mm/km with groundwater flow in a north-west direction [29
The Yucatan aquifer faces constant pollution since sanitary sewer systems are almost non-existent [4
]. Only around 10% of the generated grey and black water is treated in Yucatan. Groundwater pollution risk increases in the MMA due to the increasing population density and the disposal of household and industrial wastewater, which is mainly disposed into artisanal septic tanks. Wastewater undergoes short residence times, a couple of hours, in such tanks because they are not sealed; therefore, untreated wastewater percolates and reaches groundwater almost immediately [14
]. This continuous infiltration from permeable septic tanks has created a plume, contaminating the upper 15 m of the aquifer below Merida city [31
]. However, in recent years the extension of this pollution plume has been measured, reaching up 20 m of depth (L. Marín, personal communication, July 2016) but its extension and hydraulic behavior is still unknown (Figure 1
c). Additionally, in urban areas, rainwater infiltrates directly into groundwater through boreholes located along the streets; this is a common practice for rainwater disposal in this region. Conceptualization of the general Yucatan aquifer shows an unconfined fresh water lens floating above saline water which intrudes more than 40 km inland [32
]; the exception is an area along the coast that is classified as an aquitard [34
]. For simplification purposes, this aquitard is not included in the model presented in this work.
2.2.1. Modeling Approach and Conceptual Model
To estimate pollutant residence time, groundwater modeling was carried out using MODFLOW code 2005 run in Model Muse version 220.127.116.11 (released in March 2018). The working space was built by dividing the MMA into 50 columns and 70 rows with square grids of 1 km2
. For output analysis purposes, an additional discretization was made between columns 21 to 58 and rows 30 to 70 with a grid size of 0.0025 km2
). Model discretization was performed by importing a Digital Elevation Model (DEM) into an ASCII file using ArcGIS version 10.5. To get model top elevation and to define the thickness of sub-surface layers, the fitted surface interpolation included in MODFLOW was utilized. The bottom of the aquifer was defined at 80 m below the surface. Studies have estimated the saline interface as around 58 m of depth below Merida city. Since the area of interest in this work is the MMA, this depth is representative enough. Hydraulic conductivities (K) are the same as those estimated from a groundwater flow model in the area assuming EPM behavior presented in the work of González [22
To describe turbulent flow in the karstic aquifer, the Conduit Flow Process (CFP) package is used [35
]. However, the CFP package has a drawback when modeling target pollution studies due to its incompatibility with the groundwater solute transport simulator of MODFLOW (MT3DMS). Therefore, two modeling steps were applied to solve this problem:
The CFP was applied for particle tracking to obtain a general idea of the residence time of any particle in the aquifer, not considering transport processes.
An equivalent porous media (EPM) model was adjusted with the CFP parameters to enable the MT3DMS to run with nitrate data to analyze the pollution plume behavior within the study area.
The void diameter percentage, required for the CFP, was set at 0.9 given the existence of preferential flows paths at different depths of the aquifer. However, as a pre-test, the void value was evaluated between 0.9 and 0.5, without significant effects. Reynolds’s numbers were maintained at 2000 and 4000 as the default settings in the program.
Since the study area is part of a major trans-boundary coastal aquifer, some simplifications to define the system were taken for the numerical model; these are as follows:
Temperature and density remain constant through the whole system, which implies that the saline interface does not play an important role even though it is a coastal aquifer.
The saline intrusion occurring inland, 110 km from the coast towards the Cenote Ring, does not have a great impact in the fresh water lens behavior. Therefore, the saline interactions were not taken into consideration. This is supported by reports and studies performed by water authorities in the area [37
]. Currently, there is no model derived from CFP flow solutions that can be coupled with the sea water intrusion process [42
]. Since the CFP has at least two different ways to solve the conduit problems, it was decided to use the simplest one: layers of turbulent flow imbedded with laminar flow zones. This decision is based on previous studies which suggest at least three different preferential flow paths located between 11 to 12 m, 15 to 16 m, and 29 to 32 m of depth [43
The aquifer was simulated using an EPM approach for transport since the study area is located inside a young sedimentary basin with low development of karstic features such sinkholes and caves; also, the fracture density is quite low in comparison with areas outside the ICR.
Steady state was assumed given the low variability in the water table time series. This also means that the current status of the aquifer is labeled as underexploited.
Recharge was assumed to be instantaneous, thus no process occurring within the vadose zone was included. In order to model what happens in the unsaturated zone, information regarding depth, conductance and some other parameters, which are not available for the region, are necessary to run the unsaturated zone flow (UZF) package in Model Muse. This is a major simplification that neglects the possible simulation of the Epikarst part of the aquifer and its buffer role in pollutant adsorption.
Available public data was gathered and managed to create the necessary input files for the model (Table 1
). Recharge was computed using the multi-parameter GIS-based methodology APLIS, (altitude, slope, lithology, infiltration and soils respectively) to take into consideration in situ characteristics of karst areas [44
The MODFLOW packages used for CFP and EPM simulations are described as follows:
Time-Variant Specified-Head Package (CHD): for the north boundary of the study area, a constant head of 0 m (sea level at the coastline) was established. The discharge area towards the ocean has variable thickness along the coast with depths ranging between 5 and 18 m [19
]. The CHD was also established at the south limit towards the cenote ring. Hydraulic heads in this boundary were computed interpolating point measurements provided by the water authority (CONAGUA) time series from 2002 to 2015 with recordings, on average, every 4 months.
Recharge (RCH): Since the aquifer recovers in the range of hours, according to local studies and time series of water table levels, the storage does not change on average for a hydrological year. Monthly recharge rates were estimated to run the model with 12 stress periods; each period of 8,4600 s, or one day, represented each month in a steady state condition. For the transport model, a whole stress period of 60 years was run in transient mode using a computed average recharge out of the 12 individual stress periods; recharge was further discretized according the APLIS methodology values (Figure 3
Head-Observation (HOB): This package was used to define real observed head values. These values were used to calibrate the model. MODFLOW compares observed values with calculated ones from the program solutions and give useful statistics to calibrate the model once it has been solved. In the model, each HOB element (an observation well) is defined within a grid, assigning a head value from available time series of head observations. Then, the model computes the residuals between modeled and observed heads, giving in return a RMSE value that helps to define how accurate the model is.
For analysis purposes two places were defined as the origin of the particles: the constant head at the south of the MMA and Merida city. The former was selected to investigate the time it would take for particles to reach the coast to assess the effects of the pumping well fields distributed in the Merida city periphery and to evaluate if a preferential flow path (layer 3) exerts influence on particle movement. The later was defined to evaluate the pollution plume behavior in the Merida sub-surface.
Default values for transport were used and the activated packages for MT3MS were the basic transport (BTN), the advective-transport (ADV), dispersion (DSP), sink and source mixing (SSM) and the generalized conjugate gradient solver (GCG) pane. The species particle was NO3
and the finite differences solver was used, code 0. At the beginning of the transport simulation, plumes are constrained near to the areas where the pollutant infiltration takes place. Simulations in this work do not consider the probable increment of NO3
due to economic and population growth. A 3D representation of the model is displayed in Figure 4
To calibrate the model, two parameters were adjusted along the process: hydraulic conductivity for the X and Z axis (first Kx and then Kz, if the vertical infiltration is higher) and recharge rates. The time series for monitoring wells from 2002–2015, provided digitally by CONAGUA, served to analyze the values adjusted during the calibration process.
After several trials it was evident that the modifications in the Kz
were not significant. Therefore, the only parameter left for trial was Kx
. It was decided not to go above the suggested values of Kx
found in the literature since they are already quite high even for karst standards according to Marín [29
]. Calibration was ended at the best RMS value (0.2221) without going beyond the suggested Kx
values of 1.115 m/s. There are no uniform criteria to define what constitutes a good RMSE, so we defined a threshold of 0.2500 to stop the calibration. Table 2
displays best fit for CFP parameters achieved by manual calibration. Values for Kz
were all fixed as 1.115 m/s.
Recharge plays a fundamental role in the water budget of the study area with at least 30% of the contribution to the final discharge. Although the main input is the groundwater flow coming from the south, recharge is expected to be a driven hydraulic process when it comes to pollutant behavior. Recharge values, officially reported by the water authority, are part of a study of the whole aquifer. The average recharge for the MMA is approximately 0.18 Mm3
according to the study mentioned above; the recharge rate obtained after calibration is approximately 0.23 Mm3
, which indicates that the model tends to overestimate recharge. However, modeled discharge values are close with those reported by CONAGUA [21
]. Appendix A Table A1
displays the general settings utilized for the model before calibration.