# Probability of Non-Exceedance of Arsenic Concentration in Groundwater Estimated Using Stochastic Multicomponent Reactive Transport Modeling

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

^{−1}decreased on average from ~43% to ~39% and the average As concentration from ~32 μgL

^{−1}to ~27 μgL

^{−1}. Meanwhile, PNE increased from 55% to 60% when 10 μgL

^{−1}was set as target threshold, and from 71% to 78% for 50 μgL

^{−1}. The time dependence of As attenuation can be ascribed to the increase of oxidizing conditions during rainfall-dependent aquifer recharge, which causes As sorption on precipitating iron hydroxides. When computing the same statistics for the shallowest 6 m, As attenuation was even more evident. The volume fraction of aquifer with As > 10μgL

^{−1}dropped from 40% to 28% and the average As concentration from 31 μgL

^{−1}to 20 μgL

^{−1}, whereas PNE increased from 58% to 70% for As < 10 μgL

^{−1}and from 71% to 86% for As < 50 μgL

^{−1}. Thus, the wells screen depth in the aquifer can be a critical aspect when estimating As risk, owing to the depth-dependent relative change in redox conditions during rainfall events.

## 1. Introduction

^{−1}(i.e., 10 ppb) [4]. However, up to 220 million people may be potentially exposed to As > 10 μgL

^{−1}[3], the vast majority being in Asia, where groundwater in contact with shallow (<50 m), commonly Holocene sediments can exceed the WHO threshold by a factor of 100 [5]. In many countries, the As concentration threshold for drinking is set to 50 μgL

^{−1}[6]. Yet, a lifetime exposure to just 50 μgL

^{−1}of As in drinking water may kill one in a hundred people prematurely [7].

^{−1}and 50 μgL

^{−1}critical thresholds.

## 2. Materials and Methods

#### 2.1. Background

^{2}and with a population close to 1 million inhabitants (Italian National Institute of Statistics, 2001). Arsenic concentrations in the VAP shallow groundwater can exceed the Italian maximum concentration limit and the WHO-recommended threshold of 10 μgL

^{−1}[26,27,28,29]. Following the EU Water and Groundwater Directive, implemented in Italy mainly through the National Decree D.Lgs 152/2006, an excess of As concentration in groundwater implies that local administration should properly monitor and characterize the extension of the contamination, the natural background levels and thresholds values that can potentially entail a risk for the groundwater consumers. Although the water distribution is supplied to virtually all households in the Drainage Basin of Venice Lagoon, groundwater is mainly used for irrigation purposes and there could be a potential for direct human consumption through private wells.

^{−1}, are variably distributed in the shallow VAP aquifer, without an apparent relationship with high concentrations of As-bearing minerals [26]. Moreover, concentrations measured at a few piezometers were found to fluctuate with time above or below the 10 μgL

^{−1}concentration thresholds. This observation was described during different surveys [26], including the 2009 and 2017 surveys reported in Supplementary Information (Section SI-1) and later analyzed in this work. The erratic occurrence of As excess in groundwater urged environmental regulators to perform systematic analyses and establish collaborations with universities and other research centers to unravel the factors controlling As mobility in the VAP. A target of these activities was to quantify the probability of non-exceedance (PNE) of As concentrations above 10 μgL

^{−1}, to be later used for measuring the risk to which the population could be exposed if As-contaminated groundwater is consumed unwarily.

^{−1}threshold as well as another relevant thresholds for As risk, the 50 μgL

^{−1}, at the scale of the WAA, bypassing the limitations of DL2020 model. Leveraging the knowledge gained by DL2020, the new model aims at mechanistically predicting As mobility in the multidimensional heterogeneous WAA, testing the capability of DL2020 conceptual model to quantify the PNE of As concentrations at a wider, regional scale.

#### 2.2. Model Setup

- A 3-D flow model embedding a heterogeneous distribution of lithological materials was setup to simulate groundwater flow in the WAA.
- The flow model was used for the advective and dispersive transport of a multidimensional MRTM model. This model inherited the geochemical reactions proposed by DL2020 to describe As mobility in the WAA.
- Within a Monte-Carlo framework, indicator-based geostatistical modeling was used to build spatially correlated random realizations of GICs. Such GICs were employed to run independent MRTM simulations.
- The ensemble of results was then collected and examined to estimate the PNE and useful statistics that allow gaining insight into the expected variation of As and related key variables in the WAA.

#### 2.2.1. Flow Model

_{s}) and specific yield (S

_{y}) to each of the four materials. The resulting K, S

_{s}and S

_{y}maps were then used to populate the PHAST model. The porosity (ϕ) was assumed as homogeneously distributed, varying less than the other relevant hydraulic parameters such as K. The flow model was adequately calibrated, using the continuous logs of hydraulic heads collected at PZP36, PZP40 and PZP41 as calibration targets. More information regarding the calibration process is reported in the Supplementary Information (SI-3).

#### 2.2.2. Deterministic Transport Model

_{3}). The SCM considers the influence of competing ions such as phosphate or bicarbonate as well as the density of adsorption sites on the host minerals. The thermodynamic database WATEQ4F [38] provided the reference stability constants for HFOs equilibrium based on Dzombak and Morel [39].

_{3}by altering the Fe

^{2+}/Fe

^{3+}redox couple. When the aquifer becomes more oxidized (i.e., the ORP increases), Fe is more prone to pass to a higher oxidation status (Fe

^{2+}→ Fe

^{3+}) and precipitate as amorphous Fe(OH)

_{3}. Since HFOs are directly linked to the amount of Fe(OH)

_{3}, a change in ORP intrinsically leads to a change in the concentration of surfaces on which As can sorb. Fe(OH)

_{3}was introduced to the reaction network as an equilibrium phase.

_{2(aq)}in equilibrium with the atmosphere. It was concluded that infiltrating water could be enriched in other dissolved oxidizing species (e.g., nitrates or sulfates generated by agriculture practices and leached through the topsoil). Alternatively, gas-phase oxygen could be pushed through the vadose zone, reaching the aquifer. We lack specific information regarding the dominant mechanism controlling the excess of oxidants in the infiltrating water. Since the goal of this work is to present a general tool to compute the excess of As at the regional scale using a probabilistic approach, we adopted a simplified approach and equilibrated the infiltrating water with a much higher O

_{2}concentration than the atmospheric gas. Hence, the infiltrating boundary brings a much higher amount of O

_{2}molecules than in real life, while not adding other species to the aquifer. Note that this assumption is not a limitation of the study, since we still preserve the very essence of the study, i.e., evaluating the probability of As non-exceedance as a function of the uncertain input factors (the geochemical initial conditions), as carefully explained in the next section.

_{x}) to 100 m, the horizontal transverse dispersivity (α

_{y}) to 10 m and the vertical transverse dispersivity to 1 m, The chosen dispersivities satisfy the stability condition by which the Peclet number (Pe), such that Pe = Δx

_{i}/α

_{i}≤ 2, where Δx defines the cell size and i the direction (i = x, y, z). The effective diffusion coefficient (D) was set to D = 10

^{−9}m

^{2}/s.

#### 2.2.3. Stochastic Transport Model

- The spatial structure (i.e., the variogram) of As was initially computed from the 34 boreholes sampled in 2009. The As variogram was used to generate N
_{mc}= 100 sequential indicator simulations (SISs) [43,44] of As. The simulations were created on a 2D grid having the same size as the PHAST models (43 × 46 cells). - These simulations (or “realizations”) were conditioned to the 2017 measurements of As and obtained from the eight sampled piezometers. Examples of maps generated using the SIS algorithm are shown in the Supplementary Information SI-4.
- The procedure at steps 1 and 2 was repeated for Fe, to obtain N
_{mc}= 100 Fe realizations. - We treated the eight hydrogeochemical surveys performed in 2017 as eight PHREEQC “solutions”. We then created N
_{mc}= 100 empty grids of the same size of the stochastic realizations (43 × 46 cells) and populated them with a unique solution in each grid cell. Such solution was chosen by minimizing, for each cell of each j-th pair of As and Fe realizations ($j=1,\dots ,{N}_{mc}$), the pairwise Euclidean distance between the simulated As and Fe concentrations and the observed concentrations from the 8 PHREEQC solutions.

_{mc}= 100 random maps of solutions (i.e., the geochemical initial conditions, GICs), which were used to populate the PHAST models. The mapping algorithm was coded through an in-house MATLAB script, which included the native pdist function to calculate pairwise Euclidean distance. The variograms and SIS computation was performed using SGEMS [45]. The resulting variograms are reported in the Supplementary Information SI-4.

^{−1}and of Fe = 2.214 mgL

^{−1}, shown respectively in the map on the left and on the right. The closest pairwise distance between measured and computed As and Fe concentrations in this specific cell correspond to the concentrations represented by the “Solution 4”. In the cell marked by the magenta square, the concentrations of As = 0.012 mgL

^{−1}and Fe = 1.354 mgL

^{−1}are instead closer to the “Solution 6”. For each cell (i.e., x-y position), we assigned the same solution in all layers, since the composition of the groundwater which is sampled by fully penetrating observation wells is an average aquifer composition of the entire borehole.

- A “full depth” analysis, where the statistics of As concentrations and other variables were calculated considering the entire model extension in the vertical direction.
- A “shallow depth” analysis, where the same statistics were calculated for the top half of the model (i.e., up to 6 m), as a representative value for partially-penetrating pumping wells.

## 3. Results

#### 3.1. Flow and Deterministic Transport Model

#### 3.2. Stochastic Transport Model

#### 3.2.1. Whole Aquifer Depth

^{−1}), which are directly correlated to the rainfall events.

^{−1}decrease with time. Initially, ~43% of the entire aquifer is characterized by As concentrations above 10 μgL

^{−1}. As time elapses, the fraction drops toward a final value of ~39%. This behavior is linked to a decrease in average As concentration which tends to drop from ~32 μgL

^{−1}to ~27 μgL

^{−1}. Although the model was not calibrated using geochemical information, the decreasing trend in As concentration simulated by the stochastic model is consistent with the previous results by DL2020. Since As and Fe are strongly correlated, dissolved Fe concentrations also drop with time, following a similar pattern as As concentrations. The drop in dissolved Fe is opposed to an increase in reactive surfaces (HFOs), whose amount depends directly on the amount of amorphous iron Fe(OH)

_{3}existing in the system. The concentration of amorphous iron is inversely correlated to the amount of dissolved Fe. This is explained considering that, as the time proceeds, the ensemble mean of saturation index of Fe(OH)

_{3}tends towards higher values, i.e., SI → 0. In other words, as time elapses the system tends towards equilibrium conditions for Fe(OH)

_{3}.

^{−1}(blue dotted vertical line). The shape of the ecdfs is alike among the different realizations. It is characterized by a stepwise increase in the cumulative probability, as a result of the SIS-based stochastic realizations used as GICs in the reactive transport models Figure 4. The SIS realizations include eight categories (i.e., the “solutions”), resulting in an equivalent number of steps, since each solution occupies a different proportion of the aquifer volume.

^{−1}.

^{−1}. The ecfds spreading is explained considering that the relative proportion of As in the GICs is random outcome of the SIS algorithm. While on average all realizations embed the same statistics, each individual realization can produce a slightly different proportion of a specific solution. As such, we calculated the ensemble mean of the ecdfs to obtain a unique reference PNEs for the two analyzed times reported in Figure 8a,b.

^{−1}was 55% at t = 0, and increased to 60% at t = 115 d. This means that, on average, the fraction of aquifer that can be considered contaminated by arsenic at the end of the simulation was lower by 5% compared to the beginning of the simulation. For 50 μgL

^{−1}, another common threshold which is sometimes a maximum concentration in drinking water in countries such as Bangladesh, the probability of non-exceedance has increased from 71% at t = 0 to 78% at t = 115 d.

#### 3.2.2. Shallower Aquifer Portion

^{−1}dropped from 40% to 28%, which is linked to a decrease in average As concentrations from 31 μgL

^{−1}at t = 0 to 20 μgL

^{−1}at t = 115 d. A higher relative change was also observed for the other key parameters controlling As mobility.

^{−1}, the probability increased from 58% at t = 0 to 70% at t = 115 d, while for As < 50 μgL

^{−1}, the PNE increased from 71%% at t = 0 to 86% at t = 115 d. Thus, the relative risk due to As excess in drinking water is more reduced if groundwater is withdrawn at shallower depths, owing to the better attenuating effects of rainfall-driven recharge on As.

## 4. Discussion

## 5. Conclusions

^{−1}. The complex spatial and temporal variations of As concentrations complicate the decisions regarding control and mitigation of As risk in the area.

^{−1}as target threshold, and from 71% to 78% when the target was 50 μgL

^{−1}. The result corroborates the conclusions of a previous study [29] who proposed that rainfall could add oxidants to the shallow aquifer and promote the formation of sorption surfaces, on which As can be temporarily removed from the aqueous environment.

^{−1}dropped from 40% to 28% during the 115 simulated days, while the average As concentration dropped from 31 μgL

^{−1}to 20 μgL

^{−1}. The PNE computed for different thresholds also changed when shallower parts of the aquifer were sampled compared to the full-aquifer sampling. For As < 10 μgL

^{−1}, the PNE increased from 58% to 70%, while for As < 50 μgL

^{−1}the probability increased from 71% to 86%. Thus, the PNE was higher if groundwater was withdrawn at shallower depths. This is explained considering that the impact of rainfall on As attenuation is exacerbated in the shallower parts of the aquifer, since rainfall-controlled recharge has a more effective redox control in the shallower portions of the aquifer compared to the deeper parts.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) Geographical location of the Drainage Basin of Venice Lagoon (DBVL), which includes the studied area (WAA). Acronyms refer to the major cities of the Veneto regions. The arrow represents the regional-scale groundwater flow direction. (

**b**) Conceptual not-to-scale vertical sketch of the stratified distribution of the main hydrofacies in the VAP. The trace of this section is parallel to the groundwater flow direction depicted in frame (

**a**). Note that the amount of fine-grained sediments increases towards the Adriatic sea, forming the multilevel aquifer around the WAA. The figure has been modified after [26].

**Figure 2.**(

**a**) The model extension on top of the technical topographic map of the studied area, showing the position of the eight piezometers (“PZP”) monitored in the December 2017 campaign. The figure also shows the lateral flow boundary conditions (BCs), implemented as General Head Boundaries (“GHB”), and the drain (“DRN”). On the DRN, the numbers represent the nodes used to build the drain’s feature in the model. (

**b**) The discretized mesh of the PHAST model, illustrating the position of the GHBs and DRN BCs as well as the zonation of the recharge (“RCH”) BCs.

**Figure 3.**Subsurface lithological model of WAA created using spMC [36]. (

**a**) Volume material distribution. (

**b**) cross-sections, illustrating the position of the boreholes used to compute the transiograms and to condition the stochastic maps.

**Figure 4.**(

**a**) The example shows how pairs of As and Fe values are extracted from two specific cells on As (

**left**) and Fe (

**right**) random maps and associated to the closest PHREEQC solution (

**b**) Two maps showing the distribution of PHREEQC solutions after completing the mapping in the whole domain. These maps represent the geochemical initial conditions (GICs) used to populate the stochastic PHAST models.

**Figure 5.**(

**a**) Relative volumetric proportion of the four “materials” in the modelled WAA. (

**b**–

**d**) Box plots of the mean length of the four materials (in meters), respectively along the x, y and z direction.

**Figure 6.**Simulated hydraulic head distribution within the WAA. The shown result refers to the end of the transient simulation after 115 days. The central zone is characterized by a depressed hydraulic head level as effect of the mechanical drainage system (green dotted line).

**Figure 7.**Key results of the stochastic transport analysis. This figure refers to the “full depth” analysis. For each variable, the blue lines reproduce the ensemble mean obtained from averaging over the 100 stochastic simulations, while the red dotted lines represent the 95% (±2σ) uncertainty envelop. The gray bars represent the recharge rates (ms

^{−1}).

**Figure 8.**Ensembles of ecdfs of As concentration calculated for the entire aquifer (

**a**) at the beginning of the simulations (t = 0) and (

**b**) at the end of the simulations (t = 115 d). In (

**c**), the ensemble-mean ecdfs are reported, suggesting a time-dependent change in the probability that As does not exceed a specific threshold.

**Figure 9.**Key results of the stochastic transport analysis. This figure refers to the “shallow depth” analysis. For each variable, the blue lines reproduce the ensemble mean obtained from averaging over the 100 stochastic simulations, while the red dotted lines represent the 95% (±2σ) uncertainty envelop. The gray bars represent the recharge rates (ms

^{−1}).

**Figure 10.**Ensembles of ecdfs of As concentration calculated for the shallow (top six meters) of the aquifer (

**a**) at the beginning of the simulations (t = 0) and (

**b**) at the end of the simulations (t = 115 d). In (

**c**), the ensemble-mean ecdfs are reported, suggesting a time-dependent change in the probability that As does not exceed a specific threshold.

Material | K (ms^{−1}) | S_{s} (m^{−1}) | S_{y} (-) |
---|---|---|---|

Sand | 1.25 × 10^{−4} | 1.00 × 10^{−7} | 2.00 × 10^{−1} |

Silt | 5.00 × 10^{−6} | 1.00 × 10^{−4} | 1.00 × 10^{−2} |

Clay | 1.00 × 10^{−8} | 5.00 × 10^{−4} | 5.00 × 10^{−3} |

Peat | 1.00 × 10^{−8} | 5.00 × 10^{−4} | 5.00 × 10^{−3} |

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**MDPI and ACS Style**

Dalla Libera, N.; Pedretti, D.; Casiraghi, G.; Markó, Á.; Piccinini, L.; Fabbri, P.
Probability of Non-Exceedance of Arsenic Concentration in Groundwater Estimated Using Stochastic Multicomponent Reactive Transport Modeling. *Water* **2021**, *13*, 3086.
https://doi.org/10.3390/w13213086

**AMA Style**

Dalla Libera N, Pedretti D, Casiraghi G, Markó Á, Piccinini L, Fabbri P.
Probability of Non-Exceedance of Arsenic Concentration in Groundwater Estimated Using Stochastic Multicomponent Reactive Transport Modeling. *Water*. 2021; 13(21):3086.
https://doi.org/10.3390/w13213086

**Chicago/Turabian Style**

Dalla Libera, Nico, Daniele Pedretti, Giulia Casiraghi, Ábel Markó, Leonardo Piccinini, and Paolo Fabbri.
2021. "Probability of Non-Exceedance of Arsenic Concentration in Groundwater Estimated Using Stochastic Multicomponent Reactive Transport Modeling" *Water* 13, no. 21: 3086.
https://doi.org/10.3390/w13213086