# Groundwater Circulation in Fractured and Karstic Aquifers of the Umbria-Marche Apennine

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{2}, includes the following main reliefs: Mt. Cucco (1566 m a.s.l.), Mt. Maggio (1362 m a.s.l.), Mt. Serrasanta (1423 m a.s.l.), Mt. Penna (1432 m a.s.l.), Mt. Burella (1095 m a.s.l.), and Mt. Pennino (1572 m a.s.l.). Each relief represents a distinct hydrostructure with internal aquifer systems connected to one or more springs in their recharge areas (Table 1).

#### 2.2. Data Acquisition

#### 2.3. Recession Analysis

_{t}is the discharge at time t and Q

_{0}is the discharge at time t = 0. Specifically, the modified Maillet equation was used, which can be expressed by a sum of several exponential components that represent the presence of possible sub-regimes [13,18,50,51,52]:

_{0i}represents the discharge of media i at t = 0, and n represents the number of sub-regimes or flow components. A karst aquifer can always be divided into different sub-regimes based on the different hydraulic conductivities of the media that comprise it [52,53,54]. Therefore, the modified Maillet equation can be written as:

_{q}and Q

_{b}are the initial discharges, and α

_{q}and α

_{b}are the recession coefficients of the quickflow and baseflow, respectively.

#### 2.4. Time-Series Analysis

_{t}is the value of the studied variable at time t, and m is the cutting point [56]. The cutting point determines the interval within which the analysis is conducted. The correlogram reflects the “memory effect” of a system [26,50,57,58], i.e., the time needed for the system to “forget” its initial conditions, and corresponds to the lag time required for the ACF to reach 0.2 [54,55,59]. The CCF is used to examine the dependence of output series y (discharge) on the input series x (precipitation) and can be calculated using the following equation [27]:

_{t}and y

_{t}are input and output time series, respectively, r

_{xy}(k) is the cross-correlation function, σ

_{x}and σ

_{y}are the standard deviations of the time series, and C

_{xy}(k) is the cross-correlogram [56].

## 3. Results

#### 3.1. Discharge Time Series Description

^{2}and its discharge averages 214.9 l/s [44]. The time-series of the Scirca spring is rather continuous and the hydrograph passes from quick- to baseflow conditions, with the corresponding rapid decrease in water level, generally in early summer.

^{2}and a mean discharge of about 119 l/s. The time-series is rather incomplete (24% of data is missing). The gaps in data are due to instrumental errors. The spring’s hydrograph shows a very fast response to recharge events and rather clear passages from quick- to baseflow during dry periods.

^{2}).

^{2}.

^{2}and the karst system shows the same behavior as the Capo d’Acqua spring. Differences between quick- and baseflow regimes are not observable and the decrease in water level is very slight and delayed. The high average discharge of the San Giovenale spring cannot be explained by the size of the recharge area. Most likely, this carbonate system is supplied by non-negligible groundwater flows from the Colfiorito plain [43].

#### 3.2. MRCs Analysis

_{q}) are rather high, ranging from 0.015 d

^{−1}(Bagnara spring) to 0.1 d

^{−1}(Boschetto spring). This may be caused by the change of hydraulic or geometric characteristics of the aquifer during the depletion process [65]. According to Amit et al. [11], the exponential term with the largest slope represents a rapid depletion of flow channels with the highest hydraulic conductivity.

^{−1}, a value with the same order of magnitude as baseflow recession coefficients of the previously described springs with bimodal behavior. An exponential term with a small slope corresponds to slow depletion of a flow network with low hydraulic conductivity [11]. The recession coefficient of San Giovenale spring (0.0115 d

^{−1}), on the other hand, is very similar to quickflow components of aquifer springs with bimodal behavior.

#### 3.3. Time-Series Analysis: Autocorrelation and Cross-Correlation

#### 3.3.1. Autocorrelation Function (ACF)

_{k}= 0.2 after 80 days. The shape of the autocorrelation functions and the high memory effect implies a significant storage capacity, probably linked to a well-developed fracture network.

_{k}= 0.2 at a much slower rate after 90 days, a response characteristic of a baseflow sub-regime. In the case of the Boschetto spring, the decrease in the autocorrelation function is uneven and marked by two discrete components. The first drops quickly, within about 20 days, while the second decreases more slowly and reaches r

_{k}= 0.2 at 89 days, indicating a strong duality of these karst systems. The Bagnara spring shows a very slight decrease in ACF with no steps. The estimated memory effect is high, with a value of about 121 days, indicating a higher storage capacity and high filtration potential of this aquifer systems. The correlogram of Capo d’Acqua spring discharge displays a regular decrease in the slope of the ACF, reaching r

_{k}= 0.2 with the same time lag as the other systems seen thus far (90 days). This suggests the prevalence of the baseflow component, probably due to a fractured matrix. The ACF for the flow rates at San Giovenale spring diminishes very slowly when the time lag increases. This karst system shows a memory effect of 150 days, presenting great inertia and indicating that the aquifer has a large storage capacity, which is drained very slowly.

#### 3.3.2. Cross-Correlation Function (CCF)

_{xy}(k) values (between 0.18 to 0.27). This indicates that the precipitation signal is significantly reduced between its entry into the system and the time when it reaches the water table via the unsaturated zone [29].

## 4. Discussion

_{b}) and systems with a bimodal behavior (characterized by two flow components, α

_{q}and α

_{b}). The number of flow phases depends mainly on the degree of karstification [70].

^{−3}(α

_{b}of Vaccara spring) and 0.1 day

^{−1}(α

_{q}of Boschetto spring). This is in agreement with Mangin [10] and Amit et al. [11] and confirms the presence of two types of flow (fast and slow), as verified by the two main slopes exhibited by the recession curves. The exponential term with the largest slope, αq, represents a fast depletion (quickflow sub-regime) of flow channels with high transfer capacity, while the largest α-value likely reflects extensive fracturing and intrakarst connectivity [11].

^{−3}day

^{−1}(analogous to bimodal aquifers during baseflow conditions), whereas the San Giovenale spring showed a depletion coefficient of 1.15 × 10

^{−2}day

^{−1}, which is the lowest value, but bears the same magnitude as bimodal aquifers under a quickflow sub-regime. Therefore, the drainage of the Capo d’Acqua spring occurs as a diffusive flow in low hydraulic conductivity conditions, most likely controlled by a dense fracture network in the rock matrix. In contrast, the discharge of the San Giovenale spring occurs in intermediate flow conditions (diffusive-turbulent) through a well-developed fracture network with the possible presence of karst conduits of a limited extent.

_{k}= 0.2 after about 150 days. This great inertia indicates a low karstification degree and, consequently, the large storage capacity of the system. From a hydrogeological point of view, the aquifer is characterized by a large recharge area (10.5 km

^{2}) and a rather limited thickness (Figure 7d), due to drainage that occurs only into the Maiolica complex.

## 5. Conclusions

^{−3}, and the conduit networks controlled the fast drainage (quickflow sub-regime) with an αq of one order of magnitude lower than that of the matrix. This reflects the karstification degree (3.7–4, according to the classification of Malík and Vojtková [23]), where conduit networks of limited extent were characterized by rare interconnected systems and surrounded by a fractured rock mass with irregularly developed and moderately opened fissures. These carbonate aquifers were defined by the hydrostratigraphic contact between the Maiolica Complex and the Massiccio Complex. The Capo d’Acqua and San Giovenale springs, on the other hand, presented unimodal behavior, showing a single exponential flow component with values of recession coefficients lower than other, previously seen aquifer systems. This is explained by groundwater circulation that happens only within the Maiolica complex, where the karst is scarcely developed, and water moves through fracture networks [77].

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Simplified hydrogeological map of the study area at a regional scale (Northern Apennines), illustrating different geological and hydrogeological elements: a partial stratigraphic column of the Umbria-Marche stratigraphic succession spanning the Upper Triassic to the Upper Miocene; the locations of the studied aquifer springs: (1) Scirca spring, (2) Vaccara spring, (3) Boschetto spring, (4) Capo d’acqua spring, (5) San Giovenale spring, and (6) Bagnara spring; the hydrogeological recharge area boundaries; the locations of the rain gauge stations used: (a) Mt Cucco station, (b) Gualdo Tadino station, and (c) Nocera Umbra station.

**Figure 2.**Daily rainfall data provided by of the Hydrographic Service of Umbria Region for three rain gauge stations: MC (Monte Cucco), GT (Gualdo Tadino), and NU (Nocera Umbra).

**Figure 4.**Master Recession Curves of springs with bimodal behavior. (

**a**) Scirca spring; (

**b**) Vaccara spring; (

**c**) Boschetto spring and (

**d**) Bagnara spring.

**Figure 5.**Master Recession Curves of springs with unimodal behavior. (

**a**) Capo d’Acqua spring and (

**b**) San Giovenale spring.

**Figure 6.**Auto-correlation functions of the analyzed aquifer springs; (

**a**) Scirca spring, (

**b**) Vaccara spring, (

**c**) Boschetto spring, (

**d**) Capo d’Acqua spring, (

**e**) San Giovenale spring, and (

**f**) Bagnara spring.

**Figure 7.**Cross-correlation functions of the analyzed aquifer springs; (

**a**) Scirca spring, (

**b**) Vaccara spring, (

**c**) Boschetto spring, (

**d**) Capo d’Acqua spring, (

**e**) San Giovenale spring, and (

**f**) Bagnara spring.

**Figure 8.**Geological sketch of flow dynamics in the carbonate hydrostructures: geological cross-section, graphics of recession curves (MRC analysis), and their relative equations describing karst spring discharge.

**Table 1.**General characteristics of the carbonate complexes and their related catchment areas (geographic coordinates are expressed in WGS84 UTM Zone 33N).

Hydro- Structures | Spring | Latitude | Longitude | Spring Altitude (m a.s.l.) | Recharge Area (km ^{2}) |
---|---|---|---|---|---|

Mt Cucco | Scirca | 323,040.1821 | 4,774,571.7434 | 575 | 8.0 |

Mt Maggio | Vaccara | 325,711.2678 | 4,774,969.1254 | 468 | 6.2 |

Mt Penna | Boschetto | 324,530.5164 | 4,782,340.2809 | 538 | 11.5 |

Mt Penna | Capo d’Acqua | 316,236.3956 | 4,802,705.2176 | 570 | 7.4 |

Mt Burella | San Giovenale | 301,037.8923 | 4,823,140.7066 | 480 | 10.5 |

Mt Pennino | Bagnara | 321,608.1134 | 4,783,863.2012 | 630 | 4.9 |

**Table 2.**Location and characteristics of rain gauge station (geographic coordinate system is expressed in WGS84 UTM Zone 33).

Rain Gauge Station | Gauge Station Code | Latitude | Longitude | Monitored Period | Station Altitude (m a.s.l.) |
---|---|---|---|---|---|

Mt Cucco | MT-13015 | 316,280.8388 | 4,805,532.5274 | 2007–2015 | 1116 |

Gualdo Tadino | GT-27422 | 321,232.2980 | 4,789,176.7740 | 2007–2015 | 563 |

Nocera Umbra | NU-12907 | 320,698.8825 | 4,775,721.4408 | 2007–2015 | 542 |

Spring | Monitored Period | No. of All Data | No. Miss Data | Time-Series Lag (%) |
---|---|---|---|---|

Scirca | 2007–2015 | 3186 | 107 | 3.4 |

Vaccara | 2007–2015 | 3097 | 754 | 24.3 |

Boschetto | 2007–2015 | 3194 | 246 | 7.7 |

Capo d’Acqua | 2007–2015 | 3232 | 55 | 1.7 |

San Giovenale | 2007–2015 | 2107 | 180 | 5.8 |

Bagnara | 2007–2015 | 3240 | 47 | 1.5 |

**Table 4.**Characteristics of recession curves of springs with bimodal behavior and their related sub-regimes (baseflow or quickflow).

Spring | No. of Recession Segments | Q_{b}^{1}(l/s) | α_{b}(d ^{−1}) | t_{b}(day) | Q_{q}^{2}(l/s) | α_{q}(d ^{−1}) | t_{q}(day) |
---|---|---|---|---|---|---|---|

Scirca | 8 | 180 | 0.0060 | 225 | 220 | 0.025 | 150 |

Vaccara | 7 | 90 | 0.0053 | 200 | 220 | 0.080 | 60 |

Boschetto | 7 | 180 | 0.0065 | 200 | 650 | 0.100 | 50 |

Bagnara | 6 | 120 | 0.0085 | 300 | 180 | 0.015 | 200 |

^{1}b = baseflow;

^{2}q = quickflow.

Spring | No. of Recession Segments | Q (l/s) | α (d ^{−1}) | t_{r}(day) |
---|---|---|---|---|

Capo d’acqua | 4 | 145 | 0.0074 | 200 |

San Giovenale | 6 | 380 | 0.0115 | 200 |

**Table 6.**Time series analysis parameters: system memory effect, maximum discharge/rainfall cross-correlation coefficient, and time lag for maximum cross-correlation coefficient (Q discharge).

Aquifer Spring | Memory Effect (days) | Cross-Correlation Coef. | Time LagSS (days) |
---|---|---|---|

Scirca | 80 | 0.24 | 13 |

Vaccara | 90 | 0.18 | 2 |

Boschetto | 89 | 0.27 | 2 |

Capo d’Acqua | 90 | 0.18 | 74 |

San Giovenale | 150 | 0.18 | 119 |

Bagnara | 121 | 0.20 | 39 |

Spring | Characteristics of Recession Curve Parameters | Karstification Degree |
---|---|---|

Scirca | αb > 0.0043 αc < 0.060 | 3.7 |

Vaccara | αb = 0.0041 to 0.018 αc = 0.055 to 0.16 | 4.0 |

Boschetto | αb = 0.0041 to 0.018 αc = 0.055 to 0.16 | 4.0 |

Bagnara | αb > 0.0043 αc < 0.060 | 3.7 |

Capo d’Acqua | α > 0.007 | 2.3 |

San Giovenale | α > 0.007 | 2.3 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Tamburini, A.; Menichetti, M.
Groundwater Circulation in Fractured and Karstic Aquifers of the Umbria-Marche Apennine. *Water* **2020**, *12*, 1039.
https://doi.org/10.3390/w12041039

**AMA Style**

Tamburini A, Menichetti M.
Groundwater Circulation in Fractured and Karstic Aquifers of the Umbria-Marche Apennine. *Water*. 2020; 12(4):1039.
https://doi.org/10.3390/w12041039

**Chicago/Turabian Style**

Tamburini, Andrea, and Marco Menichetti.
2020. "Groundwater Circulation in Fractured and Karstic Aquifers of the Umbria-Marche Apennine" *Water* 12, no. 4: 1039.
https://doi.org/10.3390/w12041039