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Article

Assessment of Nitrate in Groundwater from Diffuse Sources Considering Spatiotemporal Patterns of Hydrological Systems Using a Coupled SWAT/MODFLOW/MT3DMS Model

by
Alejandra Correa-González
1,*,
Joel Hernández-Bedolla
1,
Marco Antonio Martínez-Cinco
2,
Sonia Tatiana Sánchez-Quispe
1 and
Mario Alberto Hernández-Hernández
3
1
Facultad de Ingeniería Civil, Universidad Michoacana de San Nicolas de Hidalgo, Morelia 58030, Mexico
2
Facultad de Ingeniería Química, Universidad Michoacana de San Nicolas de Hidalgo, Morelia 58030, Mexico
3
Investigador por México CONAHCYT-Instituto de Geofísica, Universidad Nacional Autónoma de México, Circuito de la Investigación Científica SN, Ciudad Universitaria, Coyoacán 04510, Mexico
*
Author to whom correspondence should be addressed.
Hydrology 2023, 10(11), 209; https://doi.org/10.3390/hydrology10110209
Submission received: 13 September 2023 / Revised: 17 October 2023 / Accepted: 29 October 2023 / Published: 9 November 2023
(This article belongs to the Special Issue Groundwater Pollution: Sources, Mechanisms, and Prevention)
Browse Figures
Figure 1
<p>Agricultural land distribution in the basin.</p> "> Figure 2
<p>Percentage of crops of total agriculture in LCB—main crops.</p> "> Figure 3
<p>Geology of the Morelia–Querendaro aquifer, obtained from National Institute of Statistics and Geography (INEGI; <a href="https://www.inegi.org.mx/temas/" target="_blank">https://www.inegi.org.mx/temas/</a>; accessed on 28 October 2023).</p> "> Figure 4
<p>Coupling of mathematical models. Quantitative and qualitative inputs and outputs of each model.</p> "> Figure 5
<p>Monthly average recharge of the Morelia–Querendaro aquifer; 1 hm<sup>3</sup> = 1,000,000 m<sup>3</sup>.</p> "> Figure 6
<p>Annual and monthly average nitrate load entering the Morelia–Querendaro aquifer. Amounts are shown in 10<sup>3</sup> tons of nitrogen.</p> "> Figure 7
<p>Quantitative and qualitative inputs and outputs of each model.</p> "> Figure 8
<p>Historical and modeled flow series, calibrated. (<b>A</b>) Point S1, period 1960–1989. (<b>B</b>) Point S2, period 1960–2002. (<b>C</b>) Point S3. Validation, period 2000–2002. 1 hm<sup>3</sup> = 1,000,000 m<sup>3</sup>.</p> "> Figure 9
<p>Point S3, calibrated. Historical and modeled nitrate concentrations, period 2008–2009.</p> "> Figure 10
<p>Historical and simulated groundwater level. (<b>A</b>) Point G4, period 1970–2010. (<b>B</b>) Point G5, period 1970–2010.</p> "> Figure 11
<p>Nitrate concentrations in groundwater. (<b>A</b>) Point NG1. (<b>B</b>) Point NG3. (<b>C</b>) Point NG4. (<b>D</b>) Point NG5. Period simulated: 1970–2010.</p> ">
Versions Notes

Abstract

:
In recent years, due to various anthropogenic activities, such as agriculture and livestock, the presence of nitrogen-associated contaminants has been increasing in surface- and groundwater resources. Among these, the main compounds present in groundwater are ammonia, nitrite, and nitrate. However, it is sometimes difficult to assess such effects given the scarcity or lack of information and the complexity of the system. In the current study, a methodology is proposed to assess nitrate in groundwater from diffuse sources considering spatiotemporal patterns of hydrological systems using a coupled SWAT/MODFLOW/MT3DMS model. The application of the model is carried out using a simplified simulation scheme of hydrological and agricultural systems because of the limited spatial and temporal data. The study area includes the Cuitzeo Lake basin in superficial flow form and the Morelia–Querendaro aquifer in groundwater flow form. The results within the methodology are surface runoff, groundwater levels, and nitrate concentrations present in surface- and groundwater systems. The results indicate that the historical and simulated nitrate concentrations were obtained within acceptable values of the statistical parameters and, therefore, are considered adequate.

1. Introduction

The world’s population requires large food resources. Food demand is expected to double by the middle of the century [1]. The growing demand for food has increased pressure on agricultural areas [2,3]. Irrigated and rainfed crops depend on fertilizers for greater efficiency [4]. Moreover, nitrogen fertilizer is a component of food security [5,6]. In agricultural areas, the main contaminants in groundwater are ammonia, nitrite, and nitrate due to the use of nitrogen fertilizers and extensive livestock farming [7]. The presence of nitrate in groundwater is higher than that of nitrite since nitrite is converted to nitrate in the presence of oxygen [8]. In addition, nitrate, being a mobile compound, drains through the subsurface with minimal uptake [9].
Nitrite and nitrate in drinking water can cause hemoglobinemia in infants younger than six months and affect children up to six years of age [10]. In addition, water consumption with high concentrations of nitrite and nitrate has been associated with other types of diseases, such as cancer, thyroid diseases, and congenital disabilities [11,12]. In 2006, the International Agency for Research Cancer (IARC) placed nitrite and nitrate in group 2A as “probably carcinogenic to humans” after several studies [13]. According to several authors, the primary sources of nitrate entering groundwater are agriculture and wastewater discharges, with agriculture being the key factor for the presence of nitrate in water [14,15,16]. However, the evaluation of nitrogen compounds in subsoil is a complex system with a large number of factors. These include parameters associated with the nitrogen cycle and spatiotemporal hydrological variables such as soil characteristics and water movement through the subsoil and porous media [15,16].
Mathematical modeling in hydrology is a widely used tool for the evaluation of various problems associated with water resources [17,18,19,20] and groundwater management [21,22]. Some authors developed surface runoff models to quantify the surface runoff of a basin [23], highlighting the importance of basin-level studies like a fundamental unit for the study of water resources in surface systems [24,25]. Examples of mathematical rainfall runoff models are Témez [26], Sacramento [27], and the Soil Conservation Service Curve Number (SCS-CN) method [28].
The hydrological model of Témez is commonly used in Spain [29,30] for estimating runoff and recharge in the surface system. It is an aggregated continuous simulation model of a few parameters and monthly time scale. It simulates the main water transfer processes in the hydrological cycle considering two storages: soil and aquifer [31]. The Sacramento model is a conceptual daily passage rainfall runoff model developed by the U.S. River Weather Service. This method has been applied to various watersheds worldwide [32,33]. The SCS-CN method is another popular method for obtaining surface runoff [34,35,36]. It is empirically developed to estimate the amount of runoff according to land type and land use. The SCS-CN method was incorporated in a semi-distributed Soil and Water Assessment Tool (SWAT) [37] and the Hydrologic Modeling System (HEC-HMS) [38]. Other surface runoff models are based on kinematic wave approximation, for example, the KINEmatic Runoff and EROSion Model (KINEROS) [39,40,41,42,43], fully distributed Gridded Surface Subsurface Hydrologic Analysis (GSSHA) [44,45,46], and fully distributed European Hydrological System Model (MIKE-SHE) [47,48,49,50].
For groundwater flow simulation, the finite difference method and the method of eigenvalues and eigenvectors [51] are used to solve the equations that govern groundwater flow. The modular three-dimensional finite difference groundwater flow model, MODFLOW [52], incorporates the finite difference method, while the Aquival model [53] solves the equations of water flow in porous media through the eigenvalue method and eigenvector matrix [54]. Both methods are commonly applied worldwide [55,56,57].
Furthermore, several water quality models have been formulated and incorporated into surface runoff or groundwater flow models to evaluate various pollutants [37,53,58], as well as the evaluation of nitrate in surface runoff [59,60] and groundwater [61,62,63]. Over the last decades, several models of nutrient transport have been developed, for example, the export coefficient modelling adopted by the Environmental Protection Agency (EPA) [64,65,66,67,68,69], Bayesian hierarchical approach [70,71,72], inverse Bayesian modeling approach [73], GIS mass balance method [74], mass balance coupled modeling approach [75], and lysimeter-based approach [76].
Different methodologies have been developed to obtain the transport of nitrogenous compounds in surface runoff and groundwater. For example, the SWAT model developed by the U.S. Agricultural Research Service, ARS [37], is internationally used [77,78]. The PATRICAL model, a Spanish acronym for precipitation input in integrated network sections with water quality [79], has been used in numerous studies carried out in Spain [80]. The modular three-dimensional transport model, MT3D [81], offers several advanced versions such as the modular three-dimensional multispecies transport model, MT3DMS [82], and the reactive transport in a three-dimensional model, RT3D [83], which are models that have been widely used in combination with MODFLOW to simulate the transport of contaminants in groundwater [62,84,85].
The MT3D, MT3DMS, and RT3D groundwater transport models determine solute transport through the porous media using the sequential iteration approach (SIA). The SIA consists of separately solving the transport and chemical reaction terms [86]. The SIA has been applied to develop several models, such as PHREEQC [87] and PHT3D [88], due to its simplicity compared to the direct solution method. PHREEQC is a one-dimensional transport model designed to perform a wide variety of aqueous geochemical (homogeneous or heterogeneous kinetic reactions, heterogeneous equilibria, and transport of solute) assessments [89] and PHT3D is a computer code for general reactive transport calculations, coupling MODFLOW/MT3DMS for transport and PHREEQC for chemical reactions [58].
Nitrate transport in groundwater is influenced by surface factors associated with hydrologic cycle inputs and subsurface flow; in recent years, several models have been coupled to evaluate the previous factors [90,91]. The conjunctive use of the SWAT and MODFLOW models has been one of the most common [92,93]. This model coupling has also been used with the MT3DMS or RT3D models to assess nitrate transport in groundwater [94,95,96]. The present study proposes nitrate assessment in groundwater using a coupled SWAT/MODFLOW/MT3DMS model in the Morelia–Querendaro aquifer (central Mexico) with limited information. The objective of multiple coupling is to implement a robust model to calculate nitrate in groundwater, which involves surface factors and reflects its spatial and temporal variability. In developing countries, there is no information on the use of nitrogen fertilizers in agricultural areas. Therefore, it is necessary to develop a reliable methodology capable of generating results for the study area.

2. Materials and Methods

2.1. Study Area

The study area is located in west-central Mexico (Figure 1). The study area includes the Cuitzeo Lake basin (CLB) on the surface and the Morelia–Querendaro aquifer (MQA). The CLB is endorheic and has an area of 4000 km2 [97]. According to CONAGUA [98], the MQA has an extension of 3507 km2. The study area defines geomorphological features resulting from very intense tectonic forces and volcanic activity. To the southwest, there are mountains and ridges made up predominantly of extrusive igneous rocks of Tertiary age, and in the southern portion of the area, andesites and basalts of the Paleogene Neogene, which reach elevations above 3000 m above sea level and have a very steep relief, with steep fronts and steep slopes. In the northeast, there are valleys of tectonic and fluvial origin. The plains located in the central portion of the zone are formed by the floodplains of the rivers and streams that flow into Lake Cuitzeo [69]. The average annual temperature, precipitation, and potential evaporation are 17.4 °C, 797 mm, and 1810 mm, respectively, with a rainfall regime mostly from June to September [99].
Agriculture is an activity that is carried out in 39.65% of the basin, which accounts for 53.69% of the extraction destined for the aquifer. Most of the agricultural area is concentrated in the lowland areas of the basin (Figure 1) and its production is presented in summer with activities beginning in February–March and ending in September–October. The primary agricultural products in the region are corn, grain, alfalfa, vegetable and fodder sorghum, oats, and wheat (Figure 2). In addition, depending on the crop and municipality, the type and amount of mineral fertilizer may vary. The main fertilizers are ammonium sulfate and nitrates with an applied amount of 200 to 600 kg/ha [100].
The predominant soil types in CLB are Andosols, Luvisols, Acrisols, Vertisols, and Planosols. To the southwest are Andosols and Acrisols. The Andosols occur at altitudes of 2300 to 3100 masl, with a medium texture and hydraulic conductivity of 10 to 12 mm/h. Luvisols occur at altitudes of 2000 to 2350 masl, with a medium texture and hydraulic conductivity of 1.5 to 12 mm/h. In the plains, there are Vertisols and Planosols, with fine and medium texture, respectively. The Vertisol and Planosol soils have hydraulic conductivities ranging from 0.05 to 2.5 mm/h and from 1.5 to 12 mm/h, respectively.
MQA is heterogeneous and anisotropic, generally unconfined, with local semi-confinement conditions. The aquifer is located in a tectonic depression and is made up, in its upper portion, of clastic sediments of varied granulometry as well as clayey sediments that were deposited in the lower part of the basin where Lake Cuitzeo is located; the lower portion is made up of volcanic rocks. The granular and fractured environments form a single hydrogeological unit that typically has medium to high permeability and an average thickness of 300 to 400 m, and depth to the groundwater levels varies from 10 to 200 m. The different units that make up the aquifer show variations: to the west, it is mainly hosted by pumiceous tuffs with lithic and clayey horizons and welded tuffs; towards the plain, it is mainly made up of clastic sediments of the size of gravels and sands; and towards the area adjacent to Lake Cuitzeo by clayey sediments, andesitic breccias, basalts, as well as basaltic breccias and ashes (Figure 3). The groundwater balance in the MQA shows a yearly deficit of 20.95 cubic hectometers (hm3) [101].

2.2. Coupled SWAT/MODFLOW/MT3DMS Model

An integrated modeling framework was used to assess the concentration of nitrate in groundwater by quantifying the spatiotemporal patterns of groundwater–surface water interaction with limited information. The first stage is related to the hydrological surface modeling, used to calculate the spatial and temporal aquifer recharge. The second stage consists of using the same model to estimate the nitrate concentration that enters through subsurface percolation and later reaches the saturated zone as recharge. The third stage evaluates the groundwater levels of the aquifer. The last stage assesses nitrate transport within the aquifer. The coupling of the models was carried out manually. The information obtained in the hydrological modeling was used for the implementation of the modeling in MODFLOW/MT3DMS. Figure 4 shows the stages of model coupling, as well as the quantitative and qualitative inputs and outputs of each model.
SWAT (the Soil and Water Assessment Tool) [20], developed by the U.S. Agricultural Research Service (ARS), is a sub-aggregated, physically based, daily time-lagged model. It incorporates watershed equations of the hydrological balance and nitrogen cycle. Although SWAT simulates two aquifers in each subbasin (shallow and deep aquifer), it does not currently print groundwater height in the output files [102]. SWAT considers five different forms of nitrogen in the soil: two are inorganic forms of nitrogen (NH4 and NO3), while the other three forms are organic (fresh, stable, and active organic nitrogen). The model contemplates immobilization, mineralization, nitrification, denitrification, fixation, and leaching reactions.
MODFLOW [52] simulates three-dimensional, multilayer-type groundwater flow through a porous medium using a finite difference method. The three-dimensional movement of constant density groundwater through the porous earth material is calculated using the partial differential equation governed by the law of Darcy.
The coupling of these models allows us to evaluate the spatiotemporal patterns according to integrated water and balance, which influence the presence of nitrate in groundwater. Therefore, the transport of nitrate in the aquifer system is evaluated using inputs and transformations of different nitrogen compounds from the surface system that, when coupled in MODFLOW, recharge to the aquifer (Equation (1)).
N O 3 r c h a r g , i = 1 − e x p − 1 δ g w N O 3 p e r c + e x p − 1 δ g w N O 3 r c h a r g , i − 1
where NO3rchrg,i is the amount of nitrate in the recharge entering the aquifer at day i (kg N/ha), δgw is the lag time or drainage time of the overlying geological formations (days), NO3perc is the total amount of nitrate leaving the bottom of the soil profile on day i (kg N/ha), NO3rchrg,i−1 is the amount of nitrate in the recharge entering the aquifer at day i − 1 (kg N/ha).
The linkage between the models is performed by means of hydrologic response units (HRU) defined in SWAT and the numerical grid made in the aquifer in MODFLOW. Once the concentrations of nitrate enter the aquifer with the recharge, its transport is simulated with the MT3DMS model. Advection and hydrodynamic dispersion were simulated (Equation (2)) considering nitrate as a conservative compound, once it enters the aquifer.
∂ ( θ C k ) ∂ t = ∂ ∂ x i θ D i j ∂ C K ∂ x j − ∂ ∂ x i θ v i C K + q s C s k + ∑ R n    
where θ is the porosity of the geological media (dimensionless), Ck is the dissolved concentration of species k (ML−3), t is time (t), x (i,j) is the distance along the respective coordinate axis (L), Dij is the tensor of the hydrodynamic dispersion coefficient (L/t), vi is the infiltration velocity or linear pore water velocity (Lt−1), qs is the volumetric flow rate per volume unit of the aquifer representing fluid sources and sinks (t−1), C s k is the concentration of source or sink flow for species k (ML−3), and ∑Rn is the chemical reaction term (ML−3 t−1).

2.3. Watershed Model

The hydrological modeling was performed by means of ten climatological stations. The precipitation and temperature series cover the years between 1960 and 2010. This information was obtained from the CLICOM database [103].
Observed surface runoff point information was collected from hydrometric stations permanently established within the drainage network. There are three hydrometric stations in the study area, with a variable period according to each station (1960–1989, 1960–2002, and 2000–2002, respectively). This information was obtained from the BANDAS database [104].
The thematic georeferenced geographic Information was obtained from INEGI (https://www.inegi.org.mx/temas/; accessed on 28 October 2023), including the digital elevation model (DEM), land use, and soil type. The DEM was entered with a resolution of 500 by 500 m. The information about soil type was provided by thematic georeferenced geographic information. This information includes basic soil characteristics, such as dominant surface texture and chemical (salt, sodium) or physical (rock, tepetate, stoniness). The reclassification of the type of use map was carried out according to the SWAT database. The modeling period was from 1960 to 2010 (50 years). The basin was delimited into 73 subbasins with a threshold of 300 ha. Potential evapotranspiration was calculated using the Penman–Monteith method. A global agricultural scheme was proposed for the entire study area, in which it was considered seasonal, starting in February–March and ending in September–October. The planted crop was corn, given that it is the predominant crop in the region (Table 1). The modeled actions were planting, fertilizing, and cultivating without leaving residues in the fields. The proposed fertilizer application is 200 to 600 kg/ha, with a mineral nitrogen content of 0 to 46% or an organic nitrogen content of 0.5 to 3.7%.
To simulate the nitrate passing to the subsoil, the amount of nitrate runoff and infiltration was considered equal in the model. This is the simple model used by Perez [79]. Since around 1970 in LCB, agricultural activities started intensively due to the enlargement of the hydraulic structure, the initial reserve of ammonia in the soil, and the initial concentrations of the aquifer being considered zero. Nitrogen consumption by plants is according to soil use.
The model parameters that were calibrated cover mainly watershed and soil characteristics, the relationship with groundwater, and agricultural practices; these were hydraulic conductivity, hydrogeological group, thickness depth, and base flow factor; in the case of nitrate, it is the porosity fraction from which anions are excluded and the organic carbon content. The values obtained are shown in Table 1.

2.4. Groundwater Flow Model

The groundwater flow modeling was carried out in a single unconfined layer, considering anisotropy in the hydraulic properties, according to geological materials present in the area. The configuration of initial groundwater levels for the year 1970 proposed are according to the study carried out by CONAGUA [105]. Since no additional information on this aquifer is available, the vertical limits of the aquifer are proposed based on the topographic limits depicted using the DEM, with an average thickness of 400 m. The lateral boundary conditions of the aquifer consist of cells of constant heights and constant flow. The lower boundary in the domain was assumed as the impermeable boundary. On the margin of the lake, limits of imposed potential were established. For the model, the discretization of the study area was carried out in 26 columns by 30 rows in cells of 3000 by 3000 m. The 3507 km2 area of the aquifer was represented by 407 active cells with 343 inactive cells. There are 40 cells defining the Cuitzeo Lake, assigning them a constant level of 1835 masl. Inflows to the aquifer are composed of lateral groundwater channels, vertical and induced recharge, and outflows are represented by well extraction, groundwater channels, spring discharge, and evapotranspiration. The modeling was performed in transient states for the period 1970 to 2010. The calibration period was divided into 480 stress periods where each stress period corresponds to one month.
Inflows and outflows from groundwater side channels, induced recharge, well extraction, groundwater channels, spring discharge, and evapotranspiration were used as annual values with constant values. The induced recharge and lateral groundwater were 38.5 and 88 hm3, respectively [101]. Extraction by wells were 162.2 hm3, groundwater channels were 3.3 hm3, springs were 60.267 hm3, and evapotranspiration was 81.8 hm3 [71]. Recharge from precipitation was 182 hm3, which has a spatial and temporal distribution according to the results obtained in the SWAT modeling (Figure 5).

2.5. Nitrate Transport Model

The groundwater levels obtained from MODFLOW were used for the nitrate transport model. Porosity and longitudinal dispersivity were assigned depending on the soil material. The calibration of the transport model was carried out manually by trial and error. Only advection and longitudinal dispersion phenomena were considered in the modeling. We obtained a longitudinal dispersion value of 0.3–1.2 m. The daily average nitrate concentrations are calculated from the nitrate recharge and nitrate load, both monthly averages.
The monthly nitrate load entering the aquifer is considered with a spatial and temporal distribution according to the results of the SWAT model (Figure 6). April and May demonstrate a greater load of nitrates entering the aquifer, which coincides with the fertilizer placement in the soil.
The calibration was performed at thirteen calibration points. Three surface points to compare runoff and nitrate concentrations; ten points in the aquifer; five points with elevation information; and five nitrate concentration points (Figure 7). The surface points are located permanently. The stream network runs from southwest to northeast, stations S1 and S3 are located within the main network and S2 is located in a minor tributary. The surface nitrate calibration points are the only ones for which information is available. The groundwater level measurement points were selected because they have a greater amount of information.

3. Model Calibration and Validation

Calibration and validation are performed using six statistical parameters to quantify the best fit of the models, distinguishing between the surface system and the aquifer system. These parameters are the mean absolute error (MAE; Equation (3)), the root mean square error (RMSE; Equation (4)), the correlation coefficient (R; Equation (5)), the Nash–Sutcliffe efficiency index (NSE; Equation (6)), standard deviation of measured data (RSR; Equation (7)), and the percentage bias (PBIAS; Equation (8)).
M A E =   ∑ i = 1 n H i − M i n  
R M S E = ∑ i = 1 n H i − M i 2 n
R = ∑ i = 1 n ( H i − H m ) ( P i − M m ) ∑ i = 1 n ( H i − H m ) 2 ( M i − M m ) 2
N S E = 1 − ∑ i = 1 n ( H i − M i ) 2 ∑ i = 1 n ( H i − H m ) 2
R S R = ∑ i = 1 n ( H i − M i ) 2 ∑ i = 1 n ( H i − M m ) 2
P B I A S =   ∑ i = 1 n H i − M i ∑ i = 1 n H i × 100
where H i is the historical value for event i, M i is the modeled value for event i, H m   is the mean of historical values, M m is the mean of modeled values, n is the number of events.
For the surface system, the parameters R, RSR, NSE, and PBIAS are used to evaluate according to four levels of adjustment [106,107] for the quantification of the flow and transport of nitrogen compounds. In the case of R and NSE, values of one represent a perfect fit and values of zero for RSR and PBIAS obtain the best results [59].
In the case of the aquifer system, MAE, R, and RMSE parameters are used, which are widely used to evaluate the groundwater level fit [7,108,109]. For MAE and RMSE, values close to zero provide the best fit [110]. R has been used because it is recommended by several guidelines in hydrological and groundwater modeling [106,107,111,112]. RMSE is one of the most widely used statistical parameters in groundwater SWAT/MODFLOW coupling [94,108,113,114,115].

3.1. Watershed Model

The calibration was carried out based on the surface runoff’s monthly values. Two points, S1 and S2, were used to calibrate and point S3 was used to validate the series.
Calibration of nitrate concentrations was performed based on daily values for 2008 and 2009.
According to the statistical parameters, values ranging from “poor” to “very good” were obtained. It is observed that the values of the historical mean and the modeled mean are similar. The statistical parameter with the best fit is R, and the one with the poorest fit is RSR (Table 2).
At S1, where R = 0.60 and PBIAS = 16.17, a “good” level was reached. NSE = 0.33 had an “acceptable” level, while RSR = 0.82 was a “poor” level. In S2, R = 0.80 obtained a “very good” level. Both PBIAS = −15.18 and NSE = 0.51 showed a “good” classification, while RSR = 0.74 reached a “poor” level. At point S3, a “very good” level was presented, with R = 0.84. PBIAS = 8.31 had an “excellent” level, while NSE = 0.42 and RSR = 0.76 were a “poor” level. At S3 for nitrate. The PBIAS of −16.29 was reached, which is considered “good”, while the R with a value of 0.45 is “acceptable”. The parameters NSE and RSR are a “poor” fit.

3.2. Groundwater Flow Model

Results of the groundwater level estimations results were calibrated with five wells, which are located in the central part of the aquifer, where most observed data are available. In both cases, similar values were observed in the monthly mean and correlation coefficient, R > 0.61. These values are considered “acceptable” (Table 3).
In G1, there is a difference between the modeled and historical mean groundwater level of 3.08 m, where MAE = 0.35, RMSE = 4.64, and R = 1. G2 has the largest difference between the modeled and historical mean groundwater level of 5.73 m, where MAE = 0.64, RMSE = 6, and R = 0.98. In G3, elevations of 1909.23 and 1914.87 were obtained, where MAE = 0.93, RMSE = 8.46, and R = 0.85. Overall, the best modeling results were acquired in G4, although there is a difference between the mean modeled and historical groundwater level of 3.24 m, with an R = 0.96, MAE = 0.08, and RMSE = 1.2. In G5, similar results were obtained for modeled and historical mean groundwater level of 1877.31 and 1877.60 masl, respectively. The results R = 0.16, MAE = 0.01, and RMSE = 0.89 were obtained.

3.3. Nitrate Transport Model

Calibration of nitrate concentrations in groundwater was performed over a 4-month period (March, April, October 2013 and February 2014). The comparison of historical and modeled means, as well as the results of the statistical parameters, are presented in Table 4. The value of the correlation coefficient according to the calibration data could not be calculated. In NG1, the modeled and historical mean values are almost equal, with MAE = 0.004, RMSE = 0.0004. In NG2, the simulated and historical mean values are 0.0079 and 0.0074, respectively, MAE = 0.0007, RMSE = 0.008. In NG3, the modeled and historical means are 0.0044 and 0.0046, respectively, while MAE = 0.0098, RMSE = 0.0107. In NG4, the simulated and historical mean values are 0.003 and 0.0061, respectively, with MAE = 0.0031, RMSE = 0.0034. Finally, in NG5, the modeled and historical means are 0.00288 and 0.0041, respectively, while MAE = 0.0012, RMSE = 0.001.

4. Results

4.1. Watershed Model

The results presented in the SWAT hydrologic modeling show an underestimation of peak flows. At the S1, modeling was performed for the period from 1960 to 1989; the historical and modeled mean obtained were 0.34 and 0.40 m3/s, respectively (Figure 8A). At the S2, modeling was performed for the period from 1960 to 2002. The historical and modeled mean obtained were 2.36 and 2.14 m3/s, respectively (Figure 8B). At the S3, the modeling was validated over a period from 2000 to 2002; the historical and modeled mean obtained were 0.37 and 0.33 m3/s, respectively (Figure 8C).
The calibration of nitrate concentrations was performed based on daily values for 2008 and 2009. The historical and modeled means obtained were 0.29 and 0.335 mg N/L, respectively (Figure 9).
The monthly series of nitrate concentration in the river was obtained. Therefore, the values of nitrate concentrations range from 0 to 3.42 mg N/L, with a monthly average of 0.43 mg N/L.

4.2. Groundwater Flow Model

The modeling results of nitrate transport in the aquifer were calibrated at six points, all located on the southern margin of Lake Cuitzeo, which is considered the discharge area for the aquifer system. The historical and modeled means obtained were 1876.328 masl and 1876.236 masl, respectively. At point G4, there is a significant drop in water table levels due to the fact that it is located in an urban area (Figure 10A). At point G5, on the other hand, being on the shore of Lake Cuitzeo, the groundwater level remains practically constant over time (Figure 10B).

4.3. Nitrate Transport Model

Results from the estimation of nitrate concentrations in groundwater show that observed and historical information indicates low concentrations according to the recommended limits for human use and consumption [116]. Since the results obtained with SWAT were calibrated using points in the southwest and the calibration of MT3DMS was performed using points near the lake, the calibration performed in MT3DMS shows a difference between modeled and historical values.
It is observed in Figure 11B–D that at points NG3, NG4, NG5, respectively, there is a graphical difference. At points NG4 and NG5, it is observed that the modeled mean (0.0030 and 0.0028, respectively) remains below the historical mean (0.0061 and 0.0041, respectively), and there is a difference of 0.0031 and 0.0013, respectively. These two points are observed to be close; therefore, it is considered that this underestimation of concentrations occurs in this area, in particular. In addition, at point NG3, there is an underestimation of the historical and modeled mean (0.0144 and 0.0046, respectively).

5. Discussion

The following proposed method was used to assess nitrate concentration in groundwater by quantifying the spatiotemporal patterns of groundwater–surface water interaction with limited information. It is presented as a methodology, since according to studies [93,94,117,118,119,120,121], the coupling of SWAT/MODFLOW/MT3DMS and SWAT/MODFLOW models is performed by calibrating parameters associated with recharge and the passage of water through the subsurface (plant available soil water capacity, curve number, surface runoff lag coefficient, deep aquifer percolation fraction, and others). However, in the present study, in addition to these parameters associated with recharge, it is calibrated using the characteristics of a single soil type.
In recent years, the importance of quantifying the influence of multiple variables associated with the presence of nitrogen in groundwater has become evident [122,123,124]. One of the most relevant is the diffuse sources associated with agricultural areas [125,126,127]. However, this is not a variable that can be directly quantified, since it depends on soil characteristics, agricultural practices, hydrological factors, as well as factors inherent to the nitrogen cycle [128,129].
Over the years, several methodologies have been developed for the assessment of nitrogen compounds in groundwater. They mainly focus on the modeling of the groundwater system (aquifer nitrate) [130,131,132], leaving aside the interrelation of surface variables of great influence on the presence of nitrogen compounds. Furthermore, the spatial and temporal variation in these variables is not considered.
In recent years, studies at the basin level have been proposed for the management of water resources and their adequate management in the conjunctive surface–groundwater system [133,134]. Therefore, the coupling of the basin–aquifer system by means of mathematical models has been used more frequently in recent years, highlighting the importance of basin-level studies and their interrelationship with the subsurface system [59,96], as it allows for the assessment of climatic variables and soil characteristics that influence surface runoff and important spatiotemporal patterns that influence groundwater, as well as conceptualizing and quantifying their interrelationships [135,136].
However, the application of a mathematical model as a tool to assess the presence of nitrogenous compounds in groundwater requires information that is not equally available in all regions. Therefore, this methodology aims to take advantage of spatiotemporal patterns within the interaction of the hydrological system, surface–subsurface. The implementation of the SWAT model, as a tool to evaluate this interrelation of the hydrological system, presents a great advantage in water resources management. In addition, as observed in previous works [115,136], the calibrated parameters are related to the interrelationship that occurs in the subsoil [117,118,137], towards the recharge in order to make the coupling with MODFLOW. However, in this study, in addition to calibrating these parameters, soil characteristics were calibrated, as shown in Table 1.
The use of various statistical parameters reinforces the calibration of each stage with the comparison of the historical and modeled data, unlike other articles that present a smaller number of parameters used in the calibration or the absence of these in some stages of the calibration [118,137,138]. The values obtained in the statistical parameters performed using SWAT, with the SWAT/MODFLOW coupling, are presented with values similar to those of several authors [94,115,139] and the mean values for hydrological modeling and water quality in the calibration [59,106,107,140] are acceptable.
The lack of a better fit is due to the limited information and the uncertainty associated with the use of the model as a third stage, which did not allow for better results. The calibration performed in MODFLOW and MT3DMS presented a lower error than the present study [117,131,137,138], with acceptable results [132].
In addition, this methodology evaluates diffuse sources through a global scheme of agriculture in the study area to quantify the presence of nitrate in groundwater considering variables of the water system in a spatiotemporal way and presenting a first approximation of the interrelation of the surface water–groundwater system. This can be used in regions with limited information and prone to the presence of nitrogen compounds in groundwater, whose main source is agriculture, to be used as a tool to evaluate diverse schemes of practices within the water system and its interrelationships. One of the main challenges in the evaluation of nitrogen compounds in the study area is the variables associated with soil characteristics. Therefore, as a first step, the present study takes the equal partitioning of nitrate to runoff and infiltration, as is performed in some models [79], in addition to considering nitrate in the subsoil as a conservative being a possible limiting factor. Therefore, for future studies, there may be an area of opportunity to evaluate the transformations that nitrate may present in subsoil, as well as studies associated with the factors that govern the dynamics of infiltration–runoff.

6. Conclusions

This paper presented an assessment of nitrate in groundwater from diffuse sources considering spatiotemporal patterns of hydrological systems using a coupled SWAT/MODFLOW/MT3DMS model involving the variability of different factors that directly or indirectly influence nitrate transport to groundwater.
Groundwater recharge was calculated based on climatological variables, such as temperature and precipitation, topography, geology, hydraulic parameters, and soil information. Subsequently, a nitrogen balance in the subsoil was performed to obtain the amount of nitrogen that can drain or run off from the unsaturated zone to the aquifer. The implementation of a surface hydrological model such as SWAT, for this stage, can present a challenge in sites with limited information, but the present study was adapted to work with the available information within a simplified conceptual scheme.
In order to strengthen the methodology and validate the results quantitatively, statistical parameters were used to compare the results obtained against historical data. According to the results of the runoff simulation in SWAT, it was observed that the R and PBIAS present acceptable values in mathematical terms. Since they presented values close to one in R and small values of PBIAS, there was a coherent trend with the measured and modeled values. For the NSE parameter, intermediate values were obtained, considering an intermediate consistency. The RSR parameter resulted in the lowest level because the coincidence between historical and modeled maximum expenditures was reduced. The statistical results for the groundwater levels of the aquifer simulated in MODFLOW and compared with the observed values were considered with a good approximation, presenting high values in the correlation coefficients. The mean absolute error and mean square error values were regarded as acceptable values. Regarding nitrate transport, despite the scarce information on its presence in groundwater, the results are acceptable and valid since they comply with the restrictions of the statistical parameters. It was observed that, in the historical and modeled means, the values are similar, with high R values and low MAE and RMSE values close to zero.
The results obtained show that the concentrations present in the groundwater are small compared to those recommended by the WHO (50 mg/L as nitrate ion) [116]. In addition, it was observed that, according to the results obtained in the conjunctive simulation, agriculture and diffuse sources of nitrate concentration largely explain the concentrations observed in the groundwater of the study area.
One of the most important limitations of the methodology is the lack of data for groundwater management in time and space, which is a limitation to reducing the uncertainty of the estimated distributed values of groundwater elevation and nitrate concentrations, which we believe can be achieved by incorporating local stakeholders and water users in order to promote continuous monitoring of hydrological and chemical variables. In addition, this study does not quantify nitrogen transformations in the surface and groundwater system, considering physical and nonchemical factors in its transport.
It is worth mentioning that the methodology is recommended for hydrological basins in which there is great affectation by surface factors due to industrial and urban discharges or by diffuse contamination from agriculture. An adequate conceptualization of the study area is necessary, for example, identifying the main inputs and their associated processes, since the present methodology does not consider other sources of nitrogen compounds, such as wastewater discharges and livestock areas, among others.

Author Contributions

Conceptualization, J.H.-B. and A.C.-G.; methodology, J.H.-B. and M.A.H.-H.; software, M.A.M.-C. and J.H.-B.; validation, S.T.S.-Q., A.C.-G. and J.H.-B.; formal analysis, M.A.H.-H. and A.C.-G.; investigation, J.H.-B. and S.T.S.-Q.; resources, M.A.H.-H.; data curation, M.A.H.-H.; writing—original draft preparation, S.T.S.-Q. and J.H.-B.; writing—review and editing, M.A.H.-H. and S.T.S.-Q.; visualization, M.A.M.-C.; supervision, S.T.S.-Q.; project administration, S.T.S.-Q.; funding acquisition, M.A.M.-C.; and S.T.S.-Q. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Data Availability Statement

Not applicable.

Acknowledgments

We thank the Catedras CONAHCYT program, the anonymous reviewers, and the editor for their constructive comments on the manuscript.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Agricultural land distribution in the basin.
Figure 1. Agricultural land distribution in the basin.
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Figure 2. Percentage of crops of total agriculture in LCB—main crops.
Figure 2. Percentage of crops of total agriculture in LCB—main crops.
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Figure 3. Geology of the Morelia–Querendaro aquifer, obtained from National Institute of Statistics and Geography (INEGI; https://www.inegi.org.mx/temas/; accessed on 28 October 2023).
Figure 3. Geology of the Morelia–Querendaro aquifer, obtained from National Institute of Statistics and Geography (INEGI; https://www.inegi.org.mx/temas/; accessed on 28 October 2023).
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Figure 4. Coupling of mathematical models. Quantitative and qualitative inputs and outputs of each model.
Figure 4. Coupling of mathematical models. Quantitative and qualitative inputs and outputs of each model.
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Figure 5. Monthly average recharge of the Morelia–Querendaro aquifer; 1 hm3 = 1,000,000 m3.
Figure 5. Monthly average recharge of the Morelia–Querendaro aquifer; 1 hm3 = 1,000,000 m3.
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Figure 6. Annual and monthly average nitrate load entering the Morelia–Querendaro aquifer. Amounts are shown in 103 tons of nitrogen.
Figure 6. Annual and monthly average nitrate load entering the Morelia–Querendaro aquifer. Amounts are shown in 103 tons of nitrogen.
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Figure 7. Quantitative and qualitative inputs and outputs of each model.
Figure 7. Quantitative and qualitative inputs and outputs of each model.
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Figure 8. Historical and modeled flow series, calibrated. (A) Point S1, period 1960–1989. (B) Point S2, period 1960–2002. (C) Point S3. Validation, period 2000–2002. 1 hm3 = 1,000,000 m3.
Figure 8. Historical and modeled flow series, calibrated. (A) Point S1, period 1960–1989. (B) Point S2, period 1960–2002. (C) Point S3. Validation, period 2000–2002. 1 hm3 = 1,000,000 m3.
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Figure 9. Point S3, calibrated. Historical and modeled nitrate concentrations, period 2008–2009.
Figure 9. Point S3, calibrated. Historical and modeled nitrate concentrations, period 2008–2009.
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Figure 10. Historical and simulated groundwater level. (A) Point G4, period 1970–2010. (B) Point G5, period 1970–2010.
Figure 10. Historical and simulated groundwater level. (A) Point G4, period 1970–2010. (B) Point G5, period 1970–2010.
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Figure 11. Nitrate concentrations in groundwater. (A) Point NG1. (B) Point NG3. (C) Point NG4. (D) Point NG5. Period simulated: 1970–2010.
Figure 11. Nitrate concentrations in groundwater. (A) Point NG1. (B) Point NG3. (C) Point NG4. (D) Point NG5. Period simulated: 1970–2010.
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Table 1. Soil characteristics calibrated in the study area.
Table 1. Soil characteristics calibrated in the study area.
Soil TypeHydraulic
Conductivity
(mm/h)		Hydrogeological
Group		Soil
Thickness (mm)		Base
Flow
Factor (1/d)		Porosity FractionOrganic
Carbon
Content
(%)
Vertic luvisol15A35000.010.0050.05
Dystric andosol5B14000.0610.7
Fine leptic skeletal2D3000.010.0050
Eutric regosol2D10000.060.70.05
Leptic planosol dístric10A10000.0480.80
Phaeozem skeletal10A15000.0111
Lytic dystric leptosol10A10000.0110
Table 2. SWAT model fit of flow rate and nitrate concentrations according to statistical parameters.
Table 2. SWAT model fit of flow rate and nitrate concentrations according to statistical parameters.
TypePointM.M.M.H.RNSERSRPBIAS
S10.400.340.580.330.8216.17
FlowS22.142.360.800.510.74−15.18
S30.330.370.840.420.76−8.31
NitrateS30.290.3350.450.180.89−16.29
M.M. = modeled mean; M.H. = historical mean.
Table 3. MODFLOW and MT3DMS model fits according to statistical parameters.
Table 3. MODFLOW and MT3DMS model fits according to statistical parameters.
TypePointM.M. 1M.H. 1MAERMSER
G11888.541885.460.354.641
GroundwaterG21875.711869.980.646.90.98
G31909.231914.870.938.460.85
G41887.451890.690.081.20.96
G51820.711820.180.020.990.61
M.M. = modeled mean; M.H. = historical mean. 1 The units of M.M and M.H. are m for groundwater level.
Table 4. MT3DMS models fit according to statistical parameters.
Table 4. MT3DMS models fit according to statistical parameters.
TypePointM.M. 1M.H. 1MAERMSE
NG10.01150.01130.00040.0004
NitrateNG20.00790.00740.00070.0008
NG30.01440.00460.00980.0107
NG40.00300.00610.00310.0034
NG50.00280.00410.00120.001
M.M. = modeled mean; M.H. = historical mean. 1 The units of M.M and M.H. are mg/L for nitrate concentrations.
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Correa-González, A.; Hernández-Bedolla, J.; Martínez-Cinco, M.A.; Sánchez-Quispe, S.T.; Hernández-Hernández, M.A. Assessment of Nitrate in Groundwater from Diffuse Sources Considering Spatiotemporal Patterns of Hydrological Systems Using a Coupled SWAT/MODFLOW/MT3DMS Model. Hydrology 2023, 10, 209. https://doi.org/10.3390/hydrology10110209

AMA Style

Correa-González A, Hernández-Bedolla J, Martínez-Cinco MA, Sánchez-Quispe ST, Hernández-Hernández MA. Assessment of Nitrate in Groundwater from Diffuse Sources Considering Spatiotemporal Patterns of Hydrological Systems Using a Coupled SWAT/MODFLOW/MT3DMS Model. Hydrology. 2023; 10(11):209. https://doi.org/10.3390/hydrology10110209

Chicago/Turabian Style

Correa-González, Alejandra, Joel Hernández-Bedolla, Marco Antonio Martínez-Cinco, Sonia Tatiana Sánchez-Quispe, and Mario Alberto Hernández-Hernández. 2023. "Assessment of Nitrate in Groundwater from Diffuse Sources Considering Spatiotemporal Patterns of Hydrological Systems Using a Coupled SWAT/MODFLOW/MT3DMS Model" Hydrology 10, no. 11: 209. https://doi.org/10.3390/hydrology10110209

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