# A New Index to Assess the Effect of Climate Change on Karst Spring Flow Rate

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## Abstract

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## 1. Introduction

^{3}/year groundwater are estimated to be extracted or discharged from 920 wells and 37,490 springs (75% of which from carbonate formations), respectively [27]. In addition, hydrochemistry samples from some karst regions in Iran show good quality in terms of low electrical conductivity, often less than 1000 μS/cm [28], which makes them a valuable resource for drinking water supply. So far and to the knowledge of the authors, the impact of climate change on hydrogeological conditions in karstic regions in Iran is rarely reported. An investigation by [29,30] on Bibitarkhon Spring in the Lali region revealed no considerable change in the spring flowrate using an artificial neural network (ANN) with hopeful durability. But in a drier region in south-central Iran (Firouzabad), an evaluation the effect of climate change showed that the quantity and quality of the Firouzabad river and some saline and karstic springs decrease using the coupled global climate model (CGCM) [31].

## 2. Study Area

## 3. Methodology

_{xy}(k) of two time series x and y is calculated as follows:

_{x}and σ

_{y}are the standard deviation of x or rainfall and y or spring flow rate, respectively. When n is the length of the time series and μ

_{x}and μ

_{y}are the average of x and y, respectively, C

_{xy}(k) is calculated from the following equation:

_{xy}(k)) explains how much two random variables with different spatial or temporal separation change and describe the second-order dependence of random processes. The popularity of covariance functions in spatial and space-time statistics is due to the fact that the properties of Gaussian random fields are fully described by first- and second-order moments. Therefore, covariance functions are very important for the estimation and prediction of Gaussian random fields. This assumes that the value of the time delay calculated in the historical period will be the same in the future, which is a correct assumption considering that the karst system in terms of conduit characteristics will not change during the next 60 years. Therefore, ${C}_{xy}\left(k\right)$ or ${C}_{PQ}\left(k\right)$, which is obtained based on the measured data and is a function of the covariance between rainfall and the springs flow rate, does not change in the future. Hence, the standard deviation of the spring flow rate (${\sigma}_{Q}$) in the future can be calculated from the following formula:

_{t}is the spring flow rate at any time and Q

_{mean}is the average flow rate of the springs:

_{f}) and the historical period (P

_{b}).

## 4. Results and Discussion

#### 4.1. Precipitation under Climate Change

_{b}of about 0.55 under the SSP1-1.9 scenario (Figure 4). The amount of precipitation multiplies by about 0.50 in Tangsiab in the first time period and Farsan in the second time period. The worst possible scenario in terms of precipitation reduction for the Zagros region in this study is SSP2-4.5. At stations Gaemieh and Kuhrang, dP is in the range of −80 to −120 mm/year and −240 to −280 mm/year with dP/P

_{b}of −0.15 to −0.22, respectively. Tangsiab, Polechehr, and Brojerd experienced almost the same rainfall reduction (dP = 40 mm/year) (Figure 4). Likewise, Farsan and Lordgan do not tolerate much precipitation reduction in the near future (almost 18 to 27 mm/year) but in the far future, dP is about 55–67 mm/year with dP/P

_{b}of −0.09 to −0.12. In the first 30-year period, future precipitation decreases to a maximum of 22 mm and the ratio of dP/P

_{b}is about −0.04 at Sarpolezahab and Polechehr stations under the SSP5-8.5 scenario. However, dP/P

_{b}decreases more to about −0.08 for some places such as Kuhrang and Lordgan in the second 30-year period of the future under this scenario. Brojerd and Tangsiab experience more precipitation of up to 69 and 50 mm/year than P

_{b}in the near and far periods, respectively.

#### 4.2. Time Series Analysis

#### 4.3. Flow Rate under Climate Change

#### 4.4. Limitations and Uncertainties

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

ACF | autocorrelation analysis function |

ANN | artificial neural network |

CCF | cross correlation function |

CGCM | coupled global climate model |

CMIP6 | coupled model intercomparison project 6 |

DEM | digital elevation model |

GCM | general circulation models |

GHGs | greenhouse gases |

IPCC | intergovernmental panel on climate change |

LARS-WG | Long Ashton Research Station weather generator |

masl | meters above sea level |

PCCF | partial cross correlation function |

SDF | spectral density function |

SSP | shared socio-economic pathway |

SWAT | soil and water assessment tool |

Notations | |

${C}_{PQ}\left(k\right)$ | the covariance function between rainfall and the springs flow rate |

C_{xy} (k) | the covariance function |

d | square root of ${\sum}_{t=1}^{N}{\left({Q}_{t}-{Q}_{mean}\right)}^{2}$ |

dP | is the difference between the precipitation in the future climate change scenario (P_{f}) and the historical period (P_{b}) |

$d{Q}_{d}$ | variability of spring discharge from past to future |

${I}_{{Q}_{d}}$ | variability index of spring discharge from past to future |

${I}_{{dQ}_{d}}$ | spring discharge variability over the historical data |

${I}_{cc}$ | effect of precipitation and spring discharge change together |

${r}_{PQ}\left(k\right)$ | the correlation coefficient between rainfall and the springs flow rate |

${r}_{yy}\left(k\right)$ | correlation between the elements of a series with other elements of the same series |

k | time lag |

n | the length of a time series |

N | the number of measurements |

P | rainfall |

P_{b} | precipitation in the historical period |

P_{f} | precipitation in the future climate change scenario |

Q | spring flow rate |

Q_{mean} | the average flow rate of the springs |

Q_{t} | the spring flow rate at any time |

μ_{x} | the average of x |

μ_{y} | the average of y |

σ_{x} | the standard deviation of x |

σ_{y} | the standard deviation of y |

${\sigma}_{P}$ | the standard deviation of the rainfall |

${\sigma}_{Q}$ | the standard deviation of the springs flow rate |

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**Figure 3.**Conceptual model of climate change impacts of hydrological functioning of a karst system: (

**a**) dry condition of conduit and spring, (

**b**) conduit with free water surface, (

**c**) flooded conduit, and (

**d**) flood condition. New Age sediments (Q), Gachsaran formation (Gs), Asmari (As), Pabdeh (Pb) and Gurpi (Gp).

**Figure 4.**Precipitation change (dP) with respect to the historical period precipitation (P

_{b}) under three scenarios in the two 30-year periods from 2021 to 2080.

**Figure 5.**Chart of ACF values in springs based on monthly temporal resolution: (

**a**) Sasan; (

**b**) Pirghar, Barm, and Dimeh; (

**c**) Tangsiab, Todehzan, and Cureh; and (

**d**) Biston, Bernaj, and Sarabgarm.

**Figure 6.**Chart of CCF values in springs. (

**a**) Sasan Spring and Gaemieh station. (

**b**) Pirghar Spring and Farsan station, Barm Spring and Lordegan station, and Dimeh Spring and Kohrang station. (

**c**) Tangsiab Spring and Tangsiab station, Tudehzan and Cureh Springs and Borujerd station. (

**d**) Biston and Bernaj Springs and Sararoud station and Sarabgarm Spring and Sarpolezahab station.

**Figure 7.**Changes in d in springs in the historical period and under three climate change scenarios SSP1-1.9, SSP2-4.5 and SSP5-8.5 in two time periods of the near future (2050–2021) and far future (2051–2080).

**Figure 8.**$d{Q}_{d}$ value changes in terms of L/s in springs based on climate change scenarios SSP1-1.9, SSP2-4.5 and SSP5-8.5 in two time periods of the near future (2050–2021) and distant (2080–2051).

**Figure 9.**${I}_{{dQ}_{d}}$ in the springs under SSP1-1.9, SSP2-4.5, and SSP5-8.5 in two time periods of the near future (2050–2021) and far future (2080–2051). See Figure 3 for the concept of different terms of flow regime.

**Figure 10.**${I}_{cc}$ in springs under SSP1-1.9, SSP2-4.5, and SSP5-8.5 in two time periods of the near future (2050–2021) and far future (2080–2051). See Figure 3 for the concept of different terms of flow regime.

Spring | Mean Discharge Q (L/s) | Catchment Area (km ^{2}) | Q Trend | Meteorological Station | Elevation (m) | Rainfall P (mm/year) | P Trend |
---|---|---|---|---|---|---|---|

Todehzan | 158 | 171 | −0.01 | Brojerd | 1629 | 473 | 0.0003 |

Cureh | 218 | 99.2 | −0.02 | Brojerd | 1629 | 473 | 0.0003 |

Biston | 674 | 34.4 | −0.02 | Polechehr | 1270 | 372 | −0.00004 |

Tangsiab | 1344 | 130 | −0.04 | Tangsiab | 900 | 394 | −0.0004 |

Sasan | 1686 | 351 | −0.05 | Ghaemieh | 922 | 548 | −0.0007 |

Pirgahr | 1818 | 72.1 | −0.12 | Farsan | 2062 | 414 | −0.0037 |

Sarabgarm | 1824 | 62.9 | −0.06 | Sarpolezahab | 545 | 422 | −0.0011 |

Bernaj | 1869 | 193 | −0.03 | Polechehr | 1270 | 372 | −0.00004 |

Barm | 2183 | 556 | −0.05 | Lordgan | 1611 | 535 | −0.0009 |

Dimeh | 2960 | 310 | −0.09 | Kuhrang | 2365 | 1309 | −0.0033 |

**Table 2.**The range of ${I}_{{Q}_{d}}$, ${I}_{{dQ}_{d}}$, and ${I}_{cc}$ and the concept of possible groundwater flow conditions in idealized karst aquifers are illustrated in Figure 3.

${\mathit{I}}_{{\mathit{Q}}_{\mathit{d}}}$ | ${\mathit{I}}_{{\mathit{d}\mathit{Q}}_{\mathit{d}}}$ | I_{cc} | Possible Corresponding Flow Conditions in Karst | Description |
---|---|---|---|---|

<0.50 | <(−0.50) | >0.25 | Overflow/Flooding | Groundwater flow is beyond conduit capacity; it recharges the matrix and the excess amount flows as runoff (back-flooding). |

0.50–0.80 | (−0.50)–(−0.20) | 0.10–0.25 | Pressurized flow | Groundwater flows in the whole cross section of conduits and it recharges the matrix. |

0.80–0.90 | (−0.20)–(−0.10) | 0.05–0.10 | Mild flow increase | The growth of groundwater flow is mild. |

0.90–1 | (−0.10)–0.00 | 0.00–0.05 | Little flow increase | There is no much difference with the previous flow conditions apart from a trivial flow rise. |

1–1.10 | 0.00–0.10 | (−0.05)–0.00 | Little flow decline | There is no much difference with the previous flow conditions apart from a trivial flow reduction. |

1.10–1.20 | 0.10–0.20 | (−0.05)–(−0.10) | Mild flow decline | The reduction in groundwater flow is mild |

1.20–1.50 | 0.20–0.50 | (−0.10)–(−0.25) | Free surface flow | Groundwater flows in some part of conduits and it discharges the matrix. |

>1.50 | >0.50 | <(−0.25) | Spring dryness | The possibility of spring going dry is highly likely, especially in the event of low average rainfall and dominancy of conduit flow; soil-matrix flow may become dominant in case of soil layer existence. |

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## Share and Cite

**MDPI and ACS Style**

Behrouj Peely, A.; Mohammadi, Z.; Sivelle, V.; Labat, D.; Naderi, M.
A New Index to Assess the Effect of Climate Change on Karst Spring Flow Rate. *Sustainability* **2024**, *16*, 1326.
https://doi.org/10.3390/su16031326

**AMA Style**

Behrouj Peely A, Mohammadi Z, Sivelle V, Labat D, Naderi M.
A New Index to Assess the Effect of Climate Change on Karst Spring Flow Rate. *Sustainability*. 2024; 16(3):1326.
https://doi.org/10.3390/su16031326

**Chicago/Turabian Style**

Behrouj Peely, Ahmad, Zargham Mohammadi, Vianney Sivelle, David Labat, and Mostafa Naderi.
2024. "A New Index to Assess the Effect of Climate Change on Karst Spring Flow Rate" *Sustainability* 16, no. 3: 1326.
https://doi.org/10.3390/su16031326