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Environmentally sensitive areas along coastlines may be adversely affected by saltwater intrusion (SI), a condition which can be worsened by extensive groundwater extraction. Given the uncertainty of problem parameters, the risk of contamination of the vegetation capture zone needs to be cast in a probabilistic framework. In order to exemplify real situations existing along the Adriatic coast of Emilia-Romagna, a case study involving a pinewood strip and a well field drawing freshwater from an unconfined coastal aquifer was examined. On the basis of a widely adopted sharp interface formulation, key hydrogeological problem parameters were modeled as random variables, and a global sensitivity analysis was carried out to determine their influence on the position of the interface. This analysis utilized an efficient model reduction technique based on Polynomial Chaos Expansion. The risk that saltwater intrusion affects coastal vegetation was then evaluated via a two-step procedure by computing the probability that (i) the leading edge of the saltwater wedge reaches the sensitive area in the horizontal plane, and (ii) the freshwater/saltwater interface reaches the capture zone. The influence of the design parameters of the well field on the overall probability of contamination was investigated, revealing the primary role of the pumping discharge in the examined configuration.

Contamination of freshwater bodies caused by saltwater intrusion (SI) is a global issue, affecting water quality, vegetation, and soil conditions along coastal lines. Deterioration of this freshwater resource threatens the sustainability of the water supply of coastal communities and their economic development [

Over the last several decades SI has become a crucial issue in Italy as denoted by many studies conducted on different coastal areas [

In recent years, numerical approaches have been increasingly adopted to represent the detailed and complex processes involved in SI [

A rigorous application of RA in environmental problems has been promoted by several environmental agencies and institutions [

In this work we expand upon this approach by providing a general methodology applicable to different contexts and model complexities. In particular, using examples and characteristics of the coastal aquifers found in the area of Ravenna in Emilia-Romagna, we propose a basic scheme representing the key features of steady-state SI in a probabilistic framework. First, an analytical model based on the theory of Strack [

Map of the Adriatic coast around Ravenna [

The Adriatic Sea is a shallow basin whose depth rises southwards and is characterized by a modest tidal excursion. The Adriatic coastline south of the Po River was originally part of its delta and alluvial plain. The province of Ravenna, bounded to the north by the Comacchio Valleys and to the south by the city of Cervia, is characterized by a high population, about 350,000 inhabitants whose density more than triples during the summer. In this area, many unpermitted and poorly-constructed wells have been drilled by bathing establishments and farms, resulting in environmental damage [

The coastal phreatic aquifer of Ravenna, the focus of this study, is primarily located within the littoral sands, and locally in the shallow marine wedge deposits. The groundwater basin is unconfined in the east, but 3–4 km from the coast it becomes overlain and confined by the most recent alluvial fine-grained continental deposits. The basin thickness varies from a maximum of 30 m in the area of San Vitale Forest to a minimum of about 15 m in the vicinity of Cervia [

Along the coast of Ravenna, pine forests are situated mostly on sandy dunes and were planted in the last century by farmers to protect their land from sea-salt spray. Plant ecologists have reported that the distribution of plant species in the coastal area varies depending on elevation, soil salinity, water salinity, and the duration of various stress periods by which the vegetation is affected [

In this study, the theory developed by Strack [_{f}_{f}_{f}^{2}T^{−1}] the uniform discharge to the sea per unit width of aquifer [_{f}_{s}_{f}_{f}

Following the approach of Strack for an unconfined aquifer [^{2}] is defined as:
_{f}_{s}_{f}

Now consider then the presence of a pumping/recharging well with discharge _{w}^{3}T^{−1}], located at a distance _{w}^{−1}] represents the hydraulic conductivity of the aquifer. The location of the leading edge, or “toe”, of the saltwater wedge can be computed from Equations (5) and (6) as:

Finally, combining expressions (3) and (4) with (6) allows for the determination of the elevation of the hydraulic head above the MSL:
_{f}/_{s} − γ_{f}_{f}

For multiple pumping wells, Equation (6) can be extended to:
_{i}_{i}_{i}

(

In order to evaluate the effects of SI on coastal vegetation due to both natural and anthropogenic causes, a simplified conceptualization representing specific areas of the Emilia-Romagna coast was configured (_{lim}

Following a probabilistic approach, we model the hydrogeological parameters

Once the uncertain parameters are defined, the extension _{toe}_{toe}_{toe}_{crit}_{crit}_{i}_{toe}_{1}_{crit}

In this selected case study, as _{1}_{i}_{2}, was considered.

The proposed methodology is suitable to predict the risk to which coastal vegetation is subjected, considering the uncertainty of the parameters involved. For this purpose, the evaluation of the mean position of the toe (considering the schematic scenario described above) and its variance, applying global sensitivity analysis [

Design parameters of the well field represented in

Parameters | Values |
---|---|

_{(m)} |
650 |

_{(m)} |
300 |

_{(m)} |
100 |

_{(m)} |
300 |

_{1} _{(m)} |
800 |

_{1} _{(m)} |
950 |

_{2} _{(m)} |
800 |

_{2} _{(m)} |
550 |

_{3} _{(m)} |
800 |

_{3} _{(m)} |
150 |

_{1}, _{2} _{3} _{(m}^{3}_{/day)} |
200 |

_{(m}^{3}_{/day)} |
600 |

Well field and location of pine forest in

Main characteristic parameters of the model.

Parameters | Distribution |
---|---|

_{(m/day)} |
_{(}_{K}_{ = 40;} _{K}_{= 0.1)} |

_{(m2/day)} |
_{(}_{q}_{ = 0.9;} _{q}_{= 0.1)} |

_{(m)} |
_{(}_{d}_{ = 20;} _{d}_{= 0.001)} |

Simplified conceptualization of the problem, in _{crit}

In order to perform the stochastic analysis described above, time intensive simulation methods based on the Monte Carlo (MC) approach are typically applied. For this analysis, a different, more efficient strategy was implemented that relied on model reduction via Polynomial Chaos Expansion (PCE) [

Let the model response of interest,

The resulting formulation constitutes a metamodel, _{j}_{j} denote the suitable multivariate polynomial basis in the Hilbert space containing the response.

A non-intrusive regression-based approach can be employed to calculate the coefficients _{j}

Once the PCE is available, simple analytical post-processing allows derivation of (i) the first two moments of the approximated response, and (ii) the global sensitivity indices of Sobol, that represent dimensionless ratios among the partial variance of the response, due to a generic subset of uncertain model parameters, and the total variance of the response [_{0} in the Equation (15), and the total variance of the response and the generic Sobol index are given, respectively, by:

Furthermore, the PCE metamodel represents a suitable basis to perform Monte Carlo simulations, allowing for a more efficient means to perform risk analysis or to solve inverse problems with reduced computational time/cost. This methodology has demonstrated excellent promise for use in many other applications related to flow and transport processes in porous media (e.g., [

Applying the methodology outlined in _{toe}

The mean value of _{toe}_{toe}_{crit}_{toe}

The standard deviation _{toe}

(_{toe}_{toe}_{q}_{K}_{d}

This study also evaluated he influence on SI on the risk for vegetation health due to variations of the deterministic parameters

The mean and the standard deviation of _{toe}_{toe}_{crit}_{i}_{i}^{3}/day) (_{toe}

A similar analysis is illustrated in _{toe}_{toe}

Finally, the influence of _{toe}_{toe}_{crit}_{crit}_{toe}_{crit}_{toe}

For this analysis the design parameters of the well field demonstrated that SI was extremely sensitive to the pumping discharge

(_{toe}_{toe}_{i}_{i}

(

(

In order to complete the analysis, the effects of the variability in the parameters characterizing the well field on the risk of contamination were evaluated. The results obtained increasing _{i}_{i}_{i}^{3}/day. In

Overall, when comparing all of the different simulation results obtained for the risk of SI (_{lim} = 12 m, the results show that risk ranged between 0.2 and 0.7 when varying parameter

It should be noted that the parameters of the well field can also be modeled as random variables and investigated via a global sensitivity analysis to appropriately understand their influence on the risk of contamination. This could be particularly useful for problems that require optimization solutions [e.g., 20]. Although the analyses herein primarily focused on a risk assessment for vegetation in coastal areas influenced by SI, this study also revealed that both the pumping rate and domain heterogeneity (

This study presents a computationally efficient technique to evaluate risk to ecosystems (

A simplified analytical formulation was adopted to allow for the evaluation of the probability that the vegetation capture zone overlaps with the intruding saltwater wedge. Anthropogenic influence on the risk to vegetation due to saltwater intrusion was modeled through the presence of a well field, specifically accounted for through adjustment of (i) the pumping discharge; (ii) the wells distance from the coast; and (iii) the mutual distance between wells. For the simplified scenario representative of the Ravenna coast, the comprehensive results of the modeling analyses revealed the parameters most responsible for influencing the extent of saltwater intrusion. For example, increases in the overall pumping discharge of the well field produced the most significant increase in the probability that saltwater intrusion reaches the vegetation capture zone.

The computational methodology used herein can be applied to more complex systems whereby a closed-form solution is not available and would require more time-consuming numerical approaches (

Marco Marcaccio and Andrea Chahoud of ARPA Emilia-Romagna are gratefully acknowledged for helpful discussions.

The authors declare no conflict of interest.

_{2}O fluxes and N leaching from corn crops