# Uncertainty Estimation and Evaluation of Shallow Aquifers’ Exploitability: The Case Study of the Adige Valley Aquifer (Italy)

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Site Description

^{2}at Trento), is mainly controlled by snow and glacier melting (e.g., [47,48,49]), although it is also significantly influenced by anthropogenic activities such as hydropower production [50] and agriculture [48]. The catchment is characterized by a sub-alpine climate with a long-term mean annual precipitation of 1022 mm.

^{2}with a mean head gradient of 0.08%–0.09% (Figure 1A). Land use is distributed as follows: 47% rural zones, 33% forest and 20% urban areas.

**Figure 1.**(

**A**) The Adige valley is highlighted in yellow, the aquifer considered in this study is delimited by a dashed black line, the red line indicates the Adige River and the three main tributaries, Noce, Avisio and Fersina, are indicated with the light blue, orange and green lines, respectively; (

**B**) Conceptual model of the aquifer in the Adige Valley in proximity of Trento.

^{3}/s [51]). Land reclamation was performed constructing a network of ditches, which drains the agricultural land and discharges the collected water into the Adige River and its main tributaries (i.e., Noce, Avisio and Fersina) in proximity of the confluences. When the water level in the rivers is higher than the ground level, dewatering pumps are activated to empty the ditches. The area considered in this study is interested by 23 dewatering systems, which can extract up to 68 m

^{3}/s. The presence of the ditches and their management are fundamental for agricultural activities and to regulate water uses. The ditches, in fact, are also used to distribute water used for irrigation during the dry periods. Only the two most spatially extended networks of ditches in the northern part of the area were considered in this study: Roverè della Luna and Nave San Rocco (Figure 1B).

^{3}/s. Three important tributaries join the Adige River within the study area (Figure 1A). The Noce River has a mean water discharge of 46 m

^{3}/s and a timing strongly modified by four hydropower plants located within its catchment [50]. From entrance in the Adige valley, it flows for 11 km before joining the Adige River. The Avisio River has a mean water discharge of 23.5 m

^{3}/s, which is significantly smaller than the natural mean streamflow due to the diversion of water toward three hydropower systems with powerhouse outside the catchment. It flows for 3.2 km along the Adige valley before joining the Adige River. Finally, the Fersina River has a mean water discharge of 2.0 m

^{3}/s and flows in the Adige valley for 2.7 km before joining the Adige River.

#### 2.2. Assessment Criteria

_{i,j}(Digital Terrain Model) is the elevation of the ground surface at the cell i,j of a horizontal grid sharing in the horizontal plane the same nodes of the computational grid and h

_{i,j}is the aquifer water level at the same position. Shallow aquifers are often endangered by surface contamination, hence the DTW is an important index of their vulnerability. In addition, DTW is also indicative of the costs of exploiting the aquifer, since the pumping cost depends on the hydraulic head, which in an unconfined aquifer is equal to the water level.

_{i,j}is the flow exchanged [L

^{3}/T] across the four columns (a parallelepiped with a rectangular base and height equals to the aquifer thickness) surrounding the central column i,j, and R

_{i,j}is the groundwater recharge/discharge index [56,57,58]. The subscripts (i − 1,j), (i + 1,j), (i,j − 1) and (i,j + 1) identify the columns located to the South North and West, East of the cell (i,j), respectively (Figure 2A). Imbalances between inflows and outflows in a vertical column can occur only if ${R}_{i,j}$ differs from zero. Lin and Anderson [57], Lin et al. [58] and Stoertz and Bradbury [59] proposed a methodology for estimating the recharge/discharge rates based on water balance, which can be applied in conjunction with parameters estimation. In this study ${R}_{i,j}$ is known (when it represents the water pumped from the extraction wells and the infiltration water rate from the unsaturated soil) and is estimated thorough the inversion of the hydraulic head data available when it represents the exchange flux with surface water and with the lateral external aquifers.

_{out}for the central cell is given by the sum of Q

_{2}, Q

_{3}and Q

_{4}. If the water extraction activity increases in the central cell (Figure 2C) while the recharge rate remains the same in the eastern cell, the flow is redistributed among the other cells according to their recharge capacity (from the neighbor cells). Let us assume that only the northern cell is able to increase its Q

_{out}in order to provide more water to the center cell (Q

_{2}' > Q

_{2}) whereas the southern and the western cells are less productive (Q

_{4}' < Q

_{4}and Q

_{3}' < Q

_{3}), we observe a decrease in the Q

_{out}values for the central, southern and western cells. This leads to positive values of ${S}_{i,j}$ (green in Figure 2C) for the north cell and to negative values of ${S}_{i,j}$ for the southern, western and central cells (red in Figure 2C). Therefore, ${S}_{i,j}\left(\u2206W\right)$ compares the initial condition of the aquifer, i.e., considering the actual wells distribution and extraction rates, against a new water management strategy. It is desirable that areas with ${S}_{i,j}\left(\u2206W\right)>0$ occur away from zones vulnerable to contamination, because their increased ${Q}_{i,j}^{out}$ to the neighboring cells may intensify the transport of contaminants, whereas areas with ${S}_{i,j}\left(\u2206W\right)<0$ can be considered less productive and not suitable for further water exploitation.

**Figure 2.**(

**A**) Flow scheme utilized for computing the recharge/discharge index; (

**B**) example of flow scheme with a recharge R in the eastern cell and a discharge R in the center cell; (

**C**) example of flow scheme with a recharge R in the eastern cell and a discharge 2R in the center cell under the hypothesis that only the northern cell is able to increase its Q

_{out}flux for sustaining the increase in the discharge rate in the center cell.

#### 2.3. Physical Model for the Aquifer

#### 2.3.1. River–Aquifer Exchange Model

_{riv}) was modeled using the river package implemented in MODFLOW-2005 [63]:

_{riv}is the hydraulic conductance of the riverbed, H

_{riv}is the hydraulic stage of the river and R

_{bot}is the river bed elevation. Reproducing the effects of the surface water/groundwater exchange on aquifers dynamics is challenging because the hydraulic conductance C

_{riv}is hardly identifiable from piezometric head measurements, while they are crucial to the evaluation of the exchange fluxes [64] and depend also on the computational grid size [65]. Furthermore, Lackey et al. [66] showed that the hydraulic conductance of the riverbed is spatially variable. In the present study, we adopt a block type heterogeneous distribution of the hydraulic conductance of the riverbed. To this purpose, the Adige course was split into four segments (0 to 3 km/3 to 13 km/13 to 26 km/26 to 30 km) characterized by four different values of C

_{riv}, while a single value of C

_{riv}was considered sufficient to characterize each of the tributaries. The Adige riverbed bottom elevation (Figure 3) was obtained by the longitudinal profile of the river with a discretization of 200 m, updated in 1996 [65]; the riverbed of the Noce, Avisio and Fersina Rivers have been extrapolated from the DTM of the Trento Province (Lidar 2007, Provincia Autonoma di Trento). The River stage along the course of the Adige River (Figure 3) was computed by solving the one dimensional shallow water equation with a numerical model implemented in the flood protection and warning system of the Adige River in use at the Office of Risk Prevention of the Trento Province, by using a grid spacing of 200 m.

**Figure 3.**Riverbed bottom elevation for the Adige River and the river stage computed with variable water discharge along the course equal to the mean recorded during the period 23 to 25 June 2008.

^{3}/s and 425 m

^{3}/s, respectively. In CASE 2 (13 to 15 October 2008) the flow rates are reduced to 100 m

^{3}/s and 147 m

^{3}/s, respectively. For the Noce, Avisio and Fersina Rivers, the river flows were considered constant along their course and the river stages were computed with the Chezy formulation for uniform flow [67], using the roughness coefficient computed at the gauge station by using the rating curve.

#### 2.3.2. Ditches–Aquifer Exchange Model

_{riv}= R

_{bot}. The ditches bottom elevation was obtained from the 2 m resolution DTM of the Province of Trento. In the second case, the ditches are simulated through the river package of MODFLOW-2005 [63] which computes the flux from the ditches to the aquifer by using Equation (4) under the assumption that the water stage is constant in all the ditches forming the network and equal to 0.5 m (H

_{riv}− R

_{bot}= 0.5 m) [68]. The riverbed conductance was considered constant for the two networks of ditches

#### 2.3.3. Leakage Model

_{r}is soil thickness of the unsaturated zone, θ∈(0,1) is the degree of saturation, P is the rainfall, Irr is the irrigation flux and ET is the evapotranspiration. It is assumed that runoff takes place when the rainfall overcomes the available storage into the soil. The degree of saturation θ(t) is computed explicitly with a time step of one day from the 1 January 2007 to 25 October 2008:

_{0}(t) = [θ(t)−1] × n × Z

_{r}is available for runoff and θ(t) is set to 1, before moving to the next step. The external forcing P(t) and Irr(t) were assigned to each cell by interpolation with the Thiessen polygons. Finally, ET was represented through the following model [71]:

_{max}is the potential evapotranspiration, which depends only on meteorological variables and is independent from θ, θ

_{w}is the wilting point and E

_{w}is the correspondent evapotranspiration loss, θ* represents the soil moisture content below which the plant starts to reduce transpiration to protect stomata and θ

_{h}is the hygroscopic point. In the present study, we used for E

_{max}, which depends on the cultivated crop and the type of spontaneous vegetation, the estimates proposed by [70].

_{s}is the saturated hydraulic conductivity, θ

_{fc}is the saturation at the field capacity, and β = 2b + 4 where b is an empirical parameter used in the soil-water retention curve: Ψ

_{s}= Ψ*

_{s}θ

^{−b}, where Ψ

_{s}is the water potential and Ψ*

_{s}is another empirical parameter, which depends on the type of soil. It varies from 12 for sand to 26 for clay. The characteristic soil in the Adige Valley can be categorized as loamy sand, therefore the parameters utilized are listed in Table 1, reproduced from Laio et al. [69]. Figure 4 shows as illustrative example the recharge L simulated in a cell located in the northern part of the study area (x

_{utm}= 667,798; y

_{utm}= 5,124,101).

$\beta $ | ${K}_{s}(\frac{m}{d})$ | ${E}_{w}(\frac{m}{d})$ | ${s}_{fc}$ | ${s}_{h}$ | ${s}_{w}$ | ${s}^{*}$ | $n$ | ${Z}_{r}(m)$ |
---|---|---|---|---|---|---|---|---|

12.7 | 1.0 | 0.0001 | 0.52 | 0.08 | 0.11 | 0.31 | 0.42 | 1.0 |

**Figure 4.**Simulated time series of soil water content (blue line) and leakage (red line) at the position (x

_{utm}= 667,798; y

_{utm}= 5,124,101) of the Adige valley. Precipitation is also shown (black bars).

#### 2.3.4. Heterogeneous Hydraulic Conductivity Fields

_{2}at x + d provided that the material m

_{1}has been observed at x. Since the inspection of stratigraphy identified four materials, the transition probabilities assume the form of a 4 × 4 matrix T(d

_{φ}):

_{φ}is the transition rate matrix:

_{x}, d

_{y}, d

_{z}) of the two-point separation distance. The diagonal terms of R

_{φ}are related to the mean length (L) of the facies along the direction φ:

**Table 2.**Proportions of materials and the corresponding mean lengths utilized for the T-PROGS simulations.

Mean Length (m) | ||||
---|---|---|---|---|

Material | Volume Fraction (%) | X (strike) | Y (dip) | Z (vertical) |

1 | 30.0 | 100.0 | 510.0 | 6.02 |

2 | 39.0 | 41.3 | 55.0 | 3.4 |

3 | 20.0 | 63.2 | 63.0 | 3.11 |

4 | 11.0 | 58.0 | 58.0 | 3.87 |

**Figure 5.**Example of the generated hydraulic conductivity fields (

**A**to

**B**); zonation for the hydraulic conductivity values (

**C**).

#### 2.4. Parameter Estimation and Uncertainty of the Assessment Criteria

_{a}= 31 unknown parameters A (listed in the Supplementary Material in Tables S1–S3) were calibrated for CASE 1 by minimizing the absolute difference between the measured and simulated heads at 102 observation points (piezometers or wells). In the CASE 2, referring to the piezometric heads measured in October 2008, the parameters were kept fixed to the values obtained in the CASE 1 with exception of the 11 lateral flows, which show seasonal variability and hence were calibrated anew by using the new head measurements. In doing that, CASE 2 constitutes the validation of the 20 structural parameters ideally independent from the hydrodynamic conditions of the aquifer as dictated by the boundary conditions. They are 12 hydraulic conductivities and eight river conductances.

_{p}= 15 particles and N

_{s}= 220 iterations, for a maximum of 3300 forward runs for each Monte Carlo realization.

_{i}is the number of elements in the sample contained within the interval $\text{\Delta}{V}_{i}$ centered at V

_{i}and MC is the sample dimension (i.e., the number MC of Monte Carlo realizations). The Equation (14) approximates the a-posteriori probability density function (PDF) ${f}_{V|Z}\left(V\right)$, which characterizes the uncertainty of the assessment criterion.

## 3. Results and Discussion

#### 3.1. Calibration and Validation of the Numerical Model

**Figure 6.**Simulated versus observed hydraulic heads for the CASE 1 and CASE 2 considering all Monte Carlo realizations ((

**A**) and (

**B**), respectively) and considering only the realization with the best fitness (i.e., the smallest L (Equation (13))) ((

**C**) and (

**D**), respectively).

#### 3.2. Assessment Criteria Evaluation

Name | Description |
---|---|

Base | CASE 1 (Calibrated shallow aquifer model for June 2008) |

RS05 | CASE 1 with the rivers stage halved |

PW2 | CASE 1 with the rate of each pumping well doubled and assuming that the ditches quickly drain the water from the aquifer |

PW5A | CASE 1 with the rate of each pumping well quintupled and assuming that the ditches quickly drain the water from the aquifer |

PW5B | CASE 1 with the rate of each pumping well quintupled and assuming that the ditches are able to store water and are refilled by surface water. |

#### 3.2.1. Depth to Water

**Figure 7.**Maps of the mean DTWs for the base case (

**A**); and scenarios RS05, PW2, PW5A and PW5B (panels (

**B**) to (

**E**) in the first row). In addition, probability of DTW not exceeding the threshold of 2 m is shown for the base case (

**F**) and the four scenarios RS05, PW2, PW5A, PW5B (panels (

**G**) to (

**L**) in the second row).

^{−2}. This result depends on the fact that the simulations considered here are obtained with the parameters that minimize the deviation between observed and simulated hydraulic heads. By increasing the extraction rate (Figure 7H,I,L), the zones with a lower probability of a DTW smaller than 2 m, are more extended than in Figure 7A. However, uncertainty in this case does not impact the general interpretation of the result, since most of the domain is characterized by a probability to exceed the given threshold either close to zero (blue) or one (red). This assessment criterion is therefore robust and it is not particularly prone to large variations caused by uncertainty in the distribution of hydro-geological facies.

#### 3.2.2. Recharge/Discharge Analysis

_{i,j}of all the cells interacting with the same source/sink (i.e., the Adige River, the Avisio River, the Noce River, the Fersina River, the Roverè Ditches, the Nave San Rocco Ditches and the lateral exchange flows highlighted in red in Figure 1B). Figure 8A,B show the boxplots of the positive and negative exchange fluxes of the aquifer with the surface water and the lateral aquifers, respectively, computed with reference to the 25 Monte Carlo simulations of CASE 1.

**Figure 8.**(

**A**) Boxplots of the recharge of the aquifer; (

**B**) Boxplots of the discharge from of the aquifer.

**Figure 9.**Boxplots of the exchange fluxes between Adige River and shallow aquifer along the river path resulting from 25 Monte Carlo simulations.

**Figure 10.**Box plots of the exchange fluxes between surface water bodies and the aquifer for the Base Scenario (

**A**); the Scenario RS05 (

**B**); the Scenario PW5A (

**C**) and the Scenario PW5B (

**D**), computed by using 25 Monte Carlos simulations.

#### 3.2.3. Sustainability of the Aquifer

**Figure 11.**Maps with the mean (

**A**to

**D**) of the coefficient s (m

^{2}/d) computed for the Scenarios RS05, PW2, PW5A and PW5B, and the probability of exceeding the threshold s = 0 (

**E**to

**H**) for the same scenarios.

## 4. Conclusions

- •
- The Adige River plays a fundamental role in aquifer behavior, and globally, in June 2008, the aquifer recharged the river. The actual equilibrium between surface and groundwater would be broken by increasing extractions from the wells.
- •
- DTW is generally affected by the river stage and by well extractions and locally also by the ditch management. In particular, the Adige River stage rules the aquifer DTW with a clear effect on the vulnerability of the aquifer, on the pumping costs and potentially on the ecological status of the aquifer. In the ditch areas, the increase in the DTW due to well extraction can be balanced by the recharge flow from the ditches under the hypothesis that they are refilled with external surface water.
- •
- The recharge/discharge pattern is chiefly affected by the Adige River stage and by the amount of water extracted from the wells. Increasing the recharge from the Adige River to aquifer may affect the vulnerability of the aquifer.
- •
- The S index shows heterogeneous patterns, highlighting areas with different recharge capacity, which should be evaluated in order to minimize the adverse effect of aquifer exploitation.

## Supplementary Materials

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

Q_{riv} (L^{3}/T) | Exchange flux between aquifer and river |

C_{riv} (L^{2}/T) | Riverbed conductance of the river bed |

H_{riv} (L) | River stage |

R_{bot} (L) | Riverbed bottom elevation |

i | Row position index of each numerical grid cell |

j | Column position index of each numerical grid cell |

k | Layer number of each numerical grid cell |

h_{ijk} (L) | Hydraulic head computed at the numerical grid cell i,j,k |

n | Soil porosity |

Z_{r} (L) | Soil thickness of the unsaturated zone |

θ | Degree of saturation of the unsaturated zone |

P (L/T) | Rainfall rate |

Irr (L/T) | Irrigation rate |

ET (L/T) | Evapotranspiration rate |

L (L/T) | Aquifer recharge due to the leakage from the unsaturated soil |

θ_{h} | Degree of saturation of the hygroscopic point |

Θ_{w} | Degree of saturation of the wilting point |

E_{w} (L/T) | Evapotranspiration loss at the wilting point |

E_{max} (L/T) | Potential evapotranspiration |

θ* | Soil moisture content under which the plants start to reduce transpiration to protect stomata |

K_{s} (L/T) | Saturated hydraulic conductivity of the superficial soil |

Θ_{fc} | Degree of saturation at the field capacity |

β | Empirical parameters of the water-retention curve |

t_{m1},_{m2} | Transition probability of the Markov chain method between material m1 and material m2 with reciprocal distance equal to d |

T (d_{φ}) | Transition probability matrix |

R_{φ} | Transition rate matrix for each direction φ = x,y,z |

L_{l,φ} (L) | Mean facies length along φ composed by the material l |

DTW (L) | Depth to water index |

Q_{i±1,j±1} (L^{3}/T) | Volume exchange between the numerical grid cell i,j and the surrounding cells |

R_{i,j} (L^{3}/T) | Recharge/Discharge Index for the numerical grid cell identified by i,j |

W (L^{3}/T) | Total amount of water extracted from the aquifer in the Base scenario |

ΔW (L^{3}/T) | Total amount of extracted water in the over-exploited scenarios for the aquifer minus the total amount of water extracted from the aquifer in the Base scenario |

S_{i,j} (L^{3}/T) | Sustainability Index for the numerical grid cell identified by i,j |

s (L^{2}/T) | Specific Sustainability Index for the numerical grid cell identified by i,j, computed as
$s=S/\text{\Delta}x$, where $\text{\Delta}x$
is the cell’s size |

Q_{ij}°^{ut} (L^{3}/T) | Global flow exiting the vertical column i,j (from the position i,j to the surrounding vertical columns) |

Z (L) | Head measurements collected in field in correspondence to the observing points |

V | Assessment criteria |

N_{V} | Total number of assessment criteria |

Z* (L) | Hydraulic heads simulated by the numerical model in correspondence to the observing points |

N_{obs} | Number of observing points of the hydraulic heads |

A | Unknown parameters of the numerical model utilized for reproducing the aquifer behavior and which are calibrated with the PSO |

N_{a} | Number of unknown parameters of the numerical model |

N_{p} | Number of particles utilized in the PSO algorithm |

N_{s} | Number of iterations of the PSO algorithm |

MC | Number of Monte Carlo simulations |

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**MDPI and ACS Style**

Castagna, M.; Bellin, A.; Chiogna, G.
Uncertainty Estimation and Evaluation of Shallow Aquifers’ Exploitability: The Case Study of the Adige Valley Aquifer (Italy). *Water* **2015**, *7*, 3367-3395.
https://doi.org/10.3390/w7073367

**AMA Style**

Castagna M, Bellin A, Chiogna G.
Uncertainty Estimation and Evaluation of Shallow Aquifers’ Exploitability: The Case Study of the Adige Valley Aquifer (Italy). *Water*. 2015; 7(7):3367-3395.
https://doi.org/10.3390/w7073367

**Chicago/Turabian Style**

Castagna, Marta, Alberto Bellin, and Gabriele Chiogna.
2015. "Uncertainty Estimation and Evaluation of Shallow Aquifers’ Exploitability: The Case Study of the Adige Valley Aquifer (Italy)" *Water* 7, no. 7: 3367-3395.
https://doi.org/10.3390/w7073367