# Modelling of the Complex Groundwater Level Dynamics during Episodic Rainfall Events of a Surficial Aquifer in Southern Italy

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

- Improving the understanding of the hydrogeological behavior of the Ionian coastal plain aquifer, highlighting how the geological and lithological features are interrelated with hydrogeologic processes.
- Demonstrating the presence of unconfined–confined flow conditions in the study area.
- Testing whether the kinematic dispersion wave model can adequately represent the infiltration processes due to episodic recharge events in the study area.

## 2. Materials

#### 2.1. Geological, Lithological and Hydrogeological Setting

- (a)
- A substratum of middle-late Pleistocene and silty clays of the sub-Apenine type (Argille Subappennine); a formation with an irregular upper boundary at a depth of about 15–30 m, deepening locally in correspondence of the paleovalley.
- (b)
- Upper unit (late Pleistocene and Holocene) of fluvial and/or deltaic sandy-gravelly deposits with clayey intercalations with a thickness of 15–30 m, deepening locally in accordance with the paleovalley. The plain is covered by a thin layer (4–5 m) of alluvial silty clayey deposits.

^{–6}–5.69 × 10

^{−3}ms

^{−1}[3]. Specifically, in the interfluvial area between Cavone and Basento rivers corresponding to the Terra Montonata monitoring station, the hydraulic conductivity has the average value of 2.28 × 10

^{−4}ms

^{−1}.

#### 2.2. General Hydrodynamic Observations

**P**(mm) and averaged groundwater level

**Z**(m AMSL) have been investigated (Figure 3).

_{w}**P**presents Mediterranean characteristics with a peak in December and the minimum in August with the average annual precipitation (in 2002–2012 period) equal to 530 mm.

**Z**shows a seasonal behavior characterized by a constant increase in the water level during the autumn and winter period with a peak at the beginning of the spring and a recession period during the spring/summer period.

_{w}#### 2.2.1. Lateral/Upward Groundwater Supply

^{−2}) is the transmissivity of aquifer, x is the horizontal direction and S (-) is the storage coefficient. The terraced deposits present a minimum distance from the monitoring station equal to x

_{0}= 1200 m. The surficial aquifer is characterized by an average hydraulic conductivity value of K = 2.2 × 10

^{−4}ms

^{−1}with an average thickness of 20 m (Figure 2). Then the transmissivity will be equal to T = 4.4 × 10

^{−3}m

^{2}s

^{−1}. Assuming that the surficial aquifer is subject to an instantaneous unit rise pulse in correspondence with the terraced deposits (x = 0), groundwater level wave will be propagated according to the following analytical solution for the one-dimensional diffusion equation along semi-infinite boundary [36]:

^{−2}) is the hydraulic diffusivity. Equation (2) reaches its peak at time t

_{p}equal to:

_{0}where the monitoring station of Terra Montonata is located. t

_{p}assumes a value of 121.83 d for S = 0.2, which is a value of S in good agreement with the sandy lithology of the aquifer. This time is coherent with the time lag from the comparison between the average monthly rainfall regime

**P**and the average monthly groundwater level

**Z**which shows 3–4 months as the lag.

_{w},#### 2.2.2. Evidence of Direct Groundwater Supply

## 3. Methods

#### 3.1. Rainfall Infiltration Dynamics

^{−1}) exceeds the infiltration capacity of the topsoil q

_{c}(LT

^{−1}), runoff surficial flow is generated, increasing the infiltration rate in the top soil q(0, t) (LT

^{−1}) along the preferential flow paths. Moreover, the infiltration rate of topsoil is limited according to the following expression:

_{crit}(LT

^{−1}) represents the critical value of the infiltration rate. The precipitation in excess does not feed the preferential flow paths [40]. The infiltration travels along the vadose zone, reaching the water table, giving rise to the infiltration rate hydrograph at water table q(L, t) (LT

^{−1}). L (L) is the water table depth from topsoil.

#### 3.2. Groundwater-Level Variation Analysis

^{−1}) is the total change rate of the groundwater level, q(L, t)/S(L) is the accretion rate and $H\left(t\right)/\tau $ is the recession rate. Due to the expected groundwater flow conversion mechanism, S is represented as function of the water table depth L.

_{c}and q

_{crit}. According to the permeability of the surficial thin clayey matrix of the topsoil, q

_{c}has been assumed to be equal to 0.5 mmh

^{−1}.

_{crit}governs the susceptibility of the preferential flow in the study area. It represents the maximum infiltration rate which can travel along the preferential flow paths in the vadose zone. According to Equations (5) and (8) the average storage coefficient $\overline{S}$ increases as q

_{crit}increases. Besides, the values of $\overline{S}$ must be consistent with the value of the storage coefficient equal to 0.2, which is coherent with a time lag of 3–4 months between the average monthly rainfall regime and the average monthly groundwater level, as discussed in the previous section. Then, q

_{crit}has been estimated to be equal to 6 mmh

^{−1}, which allows one to have the value for the average storage coefficients $\overline{S}$ (determined for each rainfall event) closest to 0.2.

#### 3.3. Kinematic Dispersion Wave Model

^{3}L

^{−3}) is the mobile volumetric water content within a volume V (L

^{3}) of soil profile flowing along preferential pathways, b (LT

^{−1}) is the conductance term, a is the preferential flow distribution index, α

_{w}(L) is the water dispersivity coefficient. Starting from the conservation laws, [25] derived a non-linear kinematic dispersion wave equation to describe infiltration processes with the infiltration rate q as the state variable:

^{2}T

^{−1}) is the hydraulic dispersion and ${c}_{w}$ (LT

^{−1}) is the celerity.

_{w}. The following initial and boundary conditions have been imposed:

#### 3.4. Numerical Model

_{w}is replaced by:

_{i}of each i-th particle at time t + Δt is updated as:

_{w,i}’ and D

_{w,i}represent the celerity and the hydraulic dispersion associated with the i-th particle. They are functions of the infiltration rate which changes throughout the depth.

_{j}is the number of particles within the j-th cell and Δz (L) is the cell size. Once one knows θ

_{j}

^{t+}

^{Δt}, the value of the infiltration rate for each cell is determined as:

_{i}.

_{out}outside the domain (z

_{i}(t + Δt) > L(t)):

_{0}= 5 m), two depths have been defined: L

_{1}= L

_{0}+ d

_{1}and L

_{2}= L

_{0}− d

_{2}. Then S will be equal to: S

_{1}if the water table depth is higher than L

_{1}; S

_{2}if the water table depth is lower than L

_{2}; S

_{0}if the water table depth is between L

_{1}and L

_{2}.

## 4. Results

#### 4.1. Simulation Results

^{0}

_{w}. Note that due to the presence of a long-term lateral groundwater recharge mechanism Z

^{0}

_{w}varies over time, as shown in Figure 4, whereas the recession time τ is constant and equal to 18 day. Simulations began after summer. Thus, the initial mobile water content and the infiltration rate were set to zero.

_{o}< 0.1. For each time step, a number of particles equal to 10

^{5}× [q(0, t + Δt)/b]

^{1/a}were released in the top soil. The time of the simulation was equal to 212 d, corresponding to a period between October 1st and April 30th. According to kinematic theory [21] the parameter a assumes a value equal to either 2 or 3. α

_{w}and b have been estimated by means of the comparison between the observed groundwater levels and the simulated ones.

^{4}mmh

^{−1}for a = 3 and 3.6 × 10

^{3}mmh

^{−1}for a = 2 and α

_{w}= 200 mm.

_{w}, while imposing a constant value of the storage coefficient instead of the step function shown in Figure 8.

#### 4.2. Analysis of Infiltration Processes

^{−1}. The maximum values reached by the average celerity are strictly dependent on rainfall intensity. For all periods, average celerity is more or less equal to 500 mmd

^{−1}for lower intensity rainfall events and equal to 1800 md

^{−1}for higher intensity rainfall events.

_{s}(LT

^{−1}), saturated volumetric water content θ

_{s}(L

^{3}L

^{−3}), residual water content θ

_{r}(L

^{3}L

^{−3}) and Brooks and Corey parameters such as the air entry pressure head h

_{d}(L

^{−1}) and the coefficient n (-) represent the hydraulic soil parameters of the implemented numerical model [42]. Steady state initial pressure head has been assumed to represent the most favorable condition for the infiltration dynamics. Groundwater level has been considered a constant overlapping the bed of the silty clay unit (5 m AMSL). The flux boundary condition has been applied at the topsoil equal to the hourly precipitation hydrograph. The silty clay unit has been assumed homogeneous and isotropic. Different configurations of the hydraulic parameters have been set. Figure 11 shows the relative cumulative infiltration at the water table obtained though the (1) kinematic dispersion wave model and the Brooks and Corey-based Richards’ model with the hydraulic parameters corresponding to (2) silty clay soil, (3) silty soil and (4) sandy soil.

^{−3}ms

^{−1}—incoherent with the detected units. This supports the fact that the observed quick response of the aquifer was due to preferential flow mechanisms occurring in the vadose zone. A more complex heterogeneous and multi-porosity model based on Richards’ equation can improve the simulated response depicting the preferential flow paths mechanisms. However, the additional complexity required significantly greater data collection to estimate the model parameters.

## 5. Discussion

^{3}and 3.6 × 10

^{4}mmh

^{−1}.

_{w}equal to 200 mm was found. This parameter attenuates the infiltration wave, leading both to an infiltration rate hydrograph at the water table and the rising limb of groundwater level being more distributed in time.

^{−1}—lower than those used by the authors presenting a minimum value of 30.35 mmh

^{−1}. As a result, the conductance term is lower in this study according to the expected theoretic value. Anyway, the water dispersivity is higher. This is due to several factors linked to the scale dependence of dispersion phenomena. In an analogous manner to solute dispersion theory, water dispersion results are scale dependent. As the depth of the vadose zone increases, the probability that the wetting front moving downwards breaks up into more and more fingers increases. On the other hand, the capillary contribution to the wetting front movement can further attenuate the infiltration rate propagation. Moreover, as the depth increases, the conductance of the preferential flow pathways can be reduced. As a result, the infiltration rate hydrograph at water table is more attenuated.

_{crit}indicates how much rain, occurring at high intensity, becomes recharged. The critical rate is 6 mmh

^{−1}—mainly, the significant rainfall events occurred between 2003–2004 and 2004–2005. According to the source responsive theory [40], q

_{crit}is equal to the product between a constant parameter that assumes a value of 2.1 × 10

^{−6}m

^{2}h

^{−1}at temperature of water equal to 20 °C, and the smallest value of the facial area density M

_{min}(L

^{−1}) which characterizes the preferential flow path. Then in the present study a value of M

_{min}equal to 2857 m

^{−1}was found. It represents the minimum fraction of the total specific surface area of the vadose zone on which preferential flow takes place. This parameter measures the susceptibility of a field site to preferential flow. Cuthbert et al. 2013 found a value of M

_{min}between 250 and 750 m

^{−1}at field site in Shropshire (UK) [44]. Nimmo 2010 found a value of M

_{min}equal to 4000 m

^{−1}for Masser site in Pennsylvania [40].

^{−1}, which is consistent with the value reported for preferential flow in [38]. The comparison between the observed groundwater levels and simulated ones highlighted a delay in the rising period of the simulated groundwater level with respect to the observed one that systematically occurred at the first rainfall event of each investigated time series. This can be ascribed to the fact that the value of mobile water content is assumed equal to zero at the beginning of simulation, underestimating the speed of the infiltration wave. Anyway, since the time series begin just after the dry season, the imposed initial condition should not be very different from the real case. Another explanation can be attributed to the fact that the velocity of the wetting front is greater when the soil is dry, in contrast with the theory that higher antecedent soil moisture condition hydraulically activates the preferential pathways [45,46]. However, several authors support the theory that when the soil is dry, preferential flow is more evident [47]. With less antecedent soil moisture, shrinkage cracks play an important role in rapid and deep water movement through dry soil. Water backfills the shrinkage cracks, increasing the opportunity for preferential flow via preferential pathways caused by wetting instability due to the compression of air below the accumulated water into the shrinkage cracks. With more antecedent soil moisture, preferential flow is more dominated by the stable preferential pathways. Lateral flow from macropores to the soil matrix reduces, and as a consequence the amount of preferential flow and number of channels increase.

## 6. Summary and Conclusions

_{crit}of 6 mmh

^{−1}.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Location of study area with the indication of Terra Montonata monitoring station used in this study and the trace of cross section A–A illustrated in Figure 2.

**Figure 2.**(

**a**) Geological cross-section in interfluve area. (1) Coastal plain deposits; (2) terrace deposits; (3) sub-Apennines clays; (

**b**) detail of stratigraphy detected close to Terra Montonata monitoring station (not to scale).

**Figure 3.**Monthly trends in the period 2002–2012 of rainfall

**P**(mm) and groundwater level

**Z**(m AMSL) determined on the basis of the time series with time resolution of 20 min derived from the monitoring station of Terra Montonata.

_{W}**Figure 4.**Comparison between daily precipitation (mm), daily average groundwater level (m AMSL), and monthly average groundwater level (m AMSL). Red lines represent the recession curve determined in correspondence with the significant rainfall event. For each recession curve, the recession time τ (d) is indicated, as is the respective value the groundwater level will attain if no episodic recharge occurs ${Z}_{w}^{0}$ (m). The grey bar indicates the depth of the bed of the silty and clay unit.

**Figure 5.**Summary of conceptual model to represent the infiltration processes. L(t) is the water table depth, H(t) is the height of groundwater level above the base level Z

^{0}

_{w}, q(0, t) is the infiltration rate for the topsoil, q(L, t) is the infiltration rate for the water table, q

_{c}is the infiltration capacity of the topsoil, q

_{crit}is the critical value of the infiltration rate.

**Figure 6.**Cumulative precipitation (mm) and cumulative accretion (m) determined with Equation (7): (

**a**) event #1 (

**b**) event #2.

**Figure 7.**Relationship between the average groundwater level AMSL (m) (water table depth (m) BGL) and the average storage coefficient, as reported in Table 1. The storage coefficient decreases systematically when the average groundwater level is higher than ≈5 m AMSL.

**Figure 8.**Estimated step function of the storage coefficient as a function of the water table depth determined by means of the minimization between the observed and simulated groundwater level.

**Figure 9.**Comparison between the observed daily groundwater level and simulated groundwater level with the optimized values of the kinematic dispersion wave model parameters of a = 3, b = 3.6 × 10

^{4}mmh

^{−1}and α

_{w}= 200 mm. A red curve indicates the simulated groundwater level obtained using the step function shown in Figure 8 to represent the variation of storage coefficient as a function of the groundwater level. Dashed curves indicate the simulated groundwater level obtained by imposing constant storage coefficients equal to 0.1, 0.2 and 0.3 instead of the step function shown in Figure 8.

**Figure 10.**(

**a**) Daily precipitation (mm), cumulative infiltration at topsoil Q(0, t) (mm) and cumulative infiltration at water table Q(L, t) (mm); (

**b**) time lag (d) and average celerity (mmd

^{−1}) as functions of the cumulative infiltration. The two graphs permit us to highlight the relationship between each episodic rainfall event and the infiltration processes characterized by the time lag and the average celerity.

**Figure 11.**Relative infiltration at water table Q(L,t)/Q

_{max}(L,t). (1) Kinematic dispersion wave model solution with a = 3, b = 3.6 × 104 mmh

^{−1}and α

_{w}= 200 mm. Brooks and Corey-based Richards’ solution for: (2) silty clay soil with K

_{s}= 2.500 × 10

^{−7}ms

^{−1}, θ

_{s}= 0.479 m

^{3}/m

^{3}, θ

_{r}= 0.056 m

^{3}/m

^{3}, h

_{d}= 0.342 m, n = 0.127; (3) silty soil with K

_{s}= 1.889 × 10

^{−6}ms

^{−1}, θ

_{s}= 0.501 m

^{3}/m

^{3}, θ

_{r}= 0.015 m

^{3}/m

^{3}, h

_{d}= 0.207 m, n = 0.211; (4) sandy soil with K

_{s}= 1.157 × 10

^{−3}ms

^{−1}, θ

_{s}= 0.437 m

^{3}/m

^{3}, θ

_{r}= 0.020 m

^{3}/m

^{3}, h

_{d}= 0.146 m, n = 0.520.

N | Date Interval (month/day/year) | Total Precipitation (mm) | Total Infiltration (mm) | Total Accretion (m) | Average GWL (m) | Average Storage (-) | Time Lag (day) |
---|---|---|---|---|---|---|---|

1 | 11/01/02–01/04/03 | 277.80 | 222.60 | 1.43 | 5.48 | 0.16 | 9.11 |

2 | 01/04/03–02/28/03 | 127.60 | 91.00 | 1.33 | 5.28 | 0.07 | 2.97 |

3 | 12/01/03–12/20/03 | 163.60 | 97.20 | 0.68 | 4.97 | 0.14 | 2.19 |

4 | 12/20/03–01/18/04 | 52.20 | 38.30 | 0.50 | 5.24 | 0.08 | 3.84 |

5 | 11/01/04–11/25/04 | 216.80 | 114.40 | 0.83 | 4.88 | 0.14 | 2.79 |

6 | 11/26/04–01/12/05 | 87.60 | 68.60 | 1.06 | 5.17 | 0.06 | 2.69 |

7 | 12/01/05–12/26/05 | 102.40 | 76.80 | 0.51 | 4.65 | 0.15 | 2.83 |

8 | 02/15/06–03/06/06 | 83.20 | 63.10 | 0.58 | 4.69 | 0.11 | 2.56 |

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**MDPI and ACS Style**

Pastore, N.; Cherubini, C.; Doglioni, A.; Giasi, C.I.; Simeone, V.
Modelling of the Complex Groundwater Level Dynamics during Episodic Rainfall Events of a Surficial Aquifer in Southern Italy. *Water* **2020**, *12*, 2916.
https://doi.org/10.3390/w12102916

**AMA Style**

Pastore N, Cherubini C, Doglioni A, Giasi CI, Simeone V.
Modelling of the Complex Groundwater Level Dynamics during Episodic Rainfall Events of a Surficial Aquifer in Southern Italy. *Water*. 2020; 12(10):2916.
https://doi.org/10.3390/w12102916

**Chicago/Turabian Style**

Pastore, Nicola, Claudia Cherubini, Angelo Doglioni, Concetta Immacolata Giasi, and Vincenzo Simeone.
2020. "Modelling of the Complex Groundwater Level Dynamics during Episodic Rainfall Events of a Surficial Aquifer in Southern Italy" *Water* 12, no. 10: 2916.
https://doi.org/10.3390/w12102916