# Assessing the Effect of Conduit Pattern and Type of Recharge on the Karst Spring Hydrograph: A Synthetic Modeling Approach

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## Abstract

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## Highlights:

- The network maze conduit pattern is generated based on a newly developed code.
- A synthetic modeling approach is applied to characterize the shape of the spring hydrograph.
- The interaction of conduit patterns and recharge types mainly affects the spring hydrograph.
- Peak discharge and time are controlled by conduit patterns and recharge events, respectively.
- The recession coefficient is mainly affected by the density of conduits.

## 1. Introduction

## 2. Methods

#### 2.1. Generation of Conduit Networks

#### 2.2. Conceptual Model and Model Description

**Figure 5.**Schematic presentation of the synthetic karst aquifer (modified from Hubinger and Birk [46]).

#### 2.3. Simulation Scenarios

## 3. Results and Discussion

**Figure 11.**Schematic representation of karst spring hydrograph [49] and recession curve [47].${Q}_{P}$ is the peak discharge of spring, ${q}_{0}^{b}$ is the base discharge, ${t}_{P}$ is the time duration to reach the peak discharge, and ${t}_{b}$ represents the return time from the peak discharge to the baseflow. In the recession curve, $Q$ or $q$ is the flow rate, $V$ is the discharge volume, $\alpha $ is the recession coefficient, and $t$ is time. Index $0$ indicative beginning points, and indices of $f$, $i$ and $b$ are the abbreviation of fast, intermediate, and baseflow, respectively.

#### 3.1. The Effect of the Conduit Pattern

#### 3.2. The Effect of the Conduit Density

#### 3.3. The Effect of Recharge Type

## 4. Field Examples to Verify the Results

^{3}/d, is much lower than the Oje de Agua spring (5000–10,000 m

^{3}/d). The recession limb of this spring has a much steeper slope compared to Oje de Agua spring, denoting a relatively short residence time in the conduit network [3,63]. Although Rodriguez-Martinez [63] classified Oje de Agua spring and Oje de Guillo spring as diffuse-type and conduit-type springs, respectively, Ghasemizadeh et al. [3] believe that conduits feed both springs. The discrepancies in their responses are mostly due to the recharge differential, with the Ojo de Guillo spring having a greater share of concentrated recharge at sinkholes and dolines. These conclusions are based on the results of scenario C.

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**A graphical representation of spring hydrograph components. The first inflection point shows the maximum infiltration state, and the second inflection point represents the end of the infiltration event [13].

**Figure 2.**Common patterns of dissolution conduits in carbonate rocks. The size of the black circles shows the relative abundance of cave types in each of the listed categories [25].

**Figure 3.**The branchwork pattern assuming different orders for conduits generated based on the invasion theory [38]. The blue star displays the location of the spring that initiates conduit formation.

**Figure 4.**(

**a**) The assumed random joint system and (

**b**) the generated conduit network pattern with the order of conduits. The blue star is the seed cell (spring).

**Figure 8.**Three types of conduit patterns used in scenario A. (

**a**) Curvilinear branchwork. (

**b**) Rectilinear branchwork. (

**c**) Network maze.

**Figure 9.**Curvilinear branchwork patterns with different conduit densities in scenario B. (

**a**–

**d**) represent the base curvilinear branchwork model, with 25%, 50%, and 75% reduction in the length of conduits, respectively. Rectilinear branchwork and network maze patterns with different conduit densities in scenario B can be found in the Supplementary Materials (Figures S1 and S2, respectively).

**Figure 10.**The conduit pattern (curvilinear branchwork) used in scenario C. (

**a**) Model runs only under diffuse recharge. (

**b**) In addition to the diffuse recharge, two different point recharge modes are also applied to the model. The purple squares represent the location of point recharge as sinkholes. Other conduit patterns (rectilinear branchwork and network maze) in scenario C can be found in the Supplementary Materials (Figure S3).

**Figure 12.**(

**a**) The spring hydrographs were obtained from the different conduit network patterns in diffuse recharge (scenario A). (

**b**) Recession curves (${\alpha}_{f},{\alpha}_{i}$, and ${\alpha}_{b}$ are the fast flow, intermediate flow, and baseflow recession coefficients, respectively). The blue lines at top of graph (

**a**) indicate recharge.

**Figure 14.**(

**a**,

**c**,

**e**) The spring hydrographs were obtained from curvilinear branchwork patterns, rectilinear branchwork patterns, and network maze patterns with different conduit network density (scenario B). (

**b**,

**d**,

**f**) Recession curves (${\alpha}_{f},{\alpha}_{i}$, and ${\alpha}_{b}$ are the fast flow, intermediate flow, and baseflow recession coefficients, respectively). The blue lines at top of graphs indicate recharge.

**Figure 16.**(

**a**,

**c**,

**e**) The spring hydrographs were obtained from curvilinear branchwork, rectilinear branchwork, and network maze patterns under different recharge types (scenario C). (

**b**,

**d**,

**f**) Recession curves (${\alpha}_{f},{\alpha}_{i}$, and ${\alpha}_{b}$ are the fast flow, intermediate flow, and baseflow recession coefficients, respectively). The blue lines at top of graphs indicate recharge.

**Figure 18.**Short-term spring response in the stationary model: recharge and discharge time series for different evolution times. Yrs is the abbreviation of years. For example, 005000 yrs shows the evolution of channels after this time. Run21 × 21 × 21_5a shows the model domain that is discretized into 21 × 21 × 21 nodal points. 5a indicates the fifth uplift of the basin [58].

**Figure 19.**A comparison of the daily rainfall hydrograph with the daily mean discharge hydrograph, both simulated and observed, for the Oje de Agua spring in Vega Baja and the Oje de Guillo spring in Manati between June 1993 and February 1996 [3].

Conduit Pattern Characteristics | Diameter of Conduit (m) | |||
---|---|---|---|---|

Order | Conduit Node | Curvilinear Branchwork | Rectilinear Branchwork | Network Maze |

1 | 371 | 0.5 | 0.7 | 0.8 |

2 | 246 | 1 | 0.9 | 0.88 |

3 | 147 | 1.5 | 1.2 | 1 |

4 | 10 | 2 | 1.5 | 1.25 |

Scenario | Constant Parameters | Variable Parameters | Assumed Conduit Network | Recharge Type | The Number of Models Run | |
---|---|---|---|---|---|---|

Scenario A | Hydrogeological characteristics of the aquifer (K, T, and S), K-exchange, Volume of conduit network, Boundary conditions (No flow boundary, Fixed head boundary, Karst spring), and Type of recharge | Conduit pattern | A1: Curvilinear branchwork | Diffuse Recharge (100%) | Point Recharge (0%) | 3 |

A2: Rectilinear branchwork | ||||||

A3: Network maze | ||||||

Scenario B | Hydrogeological characteristics of the aquifer (K, T, and S), K-exchange, Conduit pattern, Boundary conditions (No flow boundary, Fixed head boundary, Karst spring), and Type of recharge | Conduit density | B1: the base model, including A1, A2, and A3 | Diffuse Recharge (100%) | Point Recharge (0%) | 9 |

B2: 25% reduction in the length of the base model, including A1, A2, and A3 | ||||||

B3: 50% reduction in the length of the base model including A1, A2, and A3 | ||||||

B4: 75% reduction in the length of the base model, including A1, A2, and A3 | ||||||

Scenario C | Hydrogeological characteristics of the aquifer (K, T, and S), K-exchange, Volume of conduit network, Boundary conditions (No flow boundary, Fixed head boundary, Karst spring), and Conduit pattern | Recharge type and amount | C1 (same as A1 or A2 or A3) | Diffuse Recharge (100%) | Point Recharge (0%) | 6 |

C2 (A1 or A2 or A3) | Diffuse Recharge (75%) | Point Recharge (25%) | ||||

C3 (A1 or A2 or A3) | Point Recharge (50%) | Diffuse Recharge (50%) |

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**MDPI and ACS Style**

Ostad, H.; Mohammadi, Z.; Fiorillo, F.
Assessing the Effect of Conduit Pattern and Type of Recharge on the Karst Spring Hydrograph: A Synthetic Modeling Approach. *Water* **2023**, *15*, 1594.
https://doi.org/10.3390/w15081594

**AMA Style**

Ostad H, Mohammadi Z, Fiorillo F.
Assessing the Effect of Conduit Pattern and Type of Recharge on the Karst Spring Hydrograph: A Synthetic Modeling Approach. *Water*. 2023; 15(8):1594.
https://doi.org/10.3390/w15081594

**Chicago/Turabian Style**

Ostad, Hadi, Zargham Mohammadi, and Francesco Fiorillo.
2023. "Assessing the Effect of Conduit Pattern and Type of Recharge on the Karst Spring Hydrograph: A Synthetic Modeling Approach" *Water* 15, no. 8: 1594.
https://doi.org/10.3390/w15081594