# Improvement of the KarstMod modeling platform for a better assessment of karst groundwater resources

Vianney Sivelle, Guillaume Cinkus, Naomi Mazzilli, David Labat, Bruno Arfib, Nicolas Massei, Yohann Cousquer, Dominique Bertin, Hervé Jourde

► To cite this version:

Vianney Sivelle, Guillaume Cinkus, Naomi Mazzilli, David Labat, Bruno Arfib, et al. Improvement of the KarstMod modeling platform for a better assessment of karst groundwater resources. Hydrology and Earth System Sciences Discussions, In press, 10.5194/hess-2023-17. [https://doi.org/10.5194/hess-2023-17](https://doi.org/10.5194/hess-2023-17)

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Submitted on 3 Jun 2024

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# Improvement of the KarstMod modeling platform for a better assessment of karst groundwater resources

Vianney Sivelle, Guillaume Cinkus, Naomi Mazzilli, David Labat, Bruno Arfib, Nicolas Massei, Yohann Cousquer, Dominique Bertin, Hervé Jourde

► To cite this version:

Vianney Sivelle, Guillaume Cinkus, Naomi Mazzilli, David Labat, Bruno Arfib, et al. Improvement of the KarstMod modeling platform for a better assessment of karst groundwater resources. 2024. [hal-04527880](https://hal.science/hal-04527880v1)

HAL Id: hal-04527880

https://hal.science/hal-04527880v1

Preprint submitted on 3 Jun 2024

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
<figure><img src="image_2.png" /></figure>

# Improvement of the KarstMod modeling platform for a better assessment of karst groundwater resources

Vianney Sivelle<fnref n="1" />, Guillaume Cinkus<fnref n="1" />, Naomi Mazzilli<fnref n="2" />, David Labat<fnref n="3" />, Bruno Arfib<fnref n="4" />, Nicolas Massei<fnref n="5" />,
Yohann Cousquer<fnref n="1" />, Dominique Bertin<fnref n="6" />, and Hervé Jourde<fnref n="1" />

**Correspondence:** vianney.sivelle@umontpellier.fr

**Abstract.** We propose an updated version of KarstMod, an adjustable platform dedicated to lumped parameter rainfall-discharge modeling of karst aquifers. KarstMod provides a modular, user-friendly modeling environment for educational, research and operational purposes. It also includes numerical tools for time series analysis, model evaluation and sensitivity analysis. The modularity of the platform facilitates common operations related to lumped parameter rainfall-discharge modeling, such as (i) set up and parameter estimation of a relevant model structure, and (ii) evaluation of internal consistency, parameter sensitivity and hydrograph characteristics. The updated version now includes (i) external routines to better consider the input data and their related uncertainties, i.e. evapotranspiration and solid precipitation, (ii) enlargement of multi-objective calibration possibilities, allowing more flexibility in terms of objective functions as well as observation type and (iii) additional tools for model performance evaluation including further performance criteria and tools for model errors representation.

## 1 Introduction

Karst systems consist of heterogeneous aquifers characterized with the co-existence of three types of porosity: (i) inter-granular porosity, (ii) fracture porosity and (iii) large voids and conduits (Palmer, 1991) characterized by contrasted hydrodynamic properties. The existence of surface karst features such as shaft or swallow hole often leads to concentrated point-source recharge towards karst conduits in addition to the more common homogeneous diffuse recharge over the catchment. It also implies that flow regimes can be either laminar or turbulent. Karst aquifers constitute an essential source of drinking water for about 9.2% of the world population (Stevanović, 2019) and it is estimated that one-quarter of the world population depends on freshwater from karst aquifers (Ford and Williams, 2013). Karst aquifers contain an important volume of freshwater while only 1% of its annually renewable water is used for drinking water supply (Stevanović, 2019). Karst groundwater thus represents an unique opportunity to limit the increasing imbalance between growing demand and limited freshwater resource (Wada et al., 2016; Bierkens and Wada, 2019) in the present context of global change. However, karst aquifers are also particularly

15

20

<footnote n="1">¹HSM, Univ Montpellier, CNRS, IRD, Montpellier, France</footnote>

<footnote n="2">²EMMAH, INRAe, Avignon Université, 84000 Avignon, France</footnote>

<footnote n="3">³Geosciences Environment Toulouse UMR CNRS IRD Université Paul Sabatier CNES, 14 Avenue Edouard Belin 31400 TOULOUSE</footnote>

<footnote n="4">⁴Aix-Marseille Univ, CNRS, IRD, INRAE, Coll de France, CEREGE, Aix-en-Provence, France</footnote>

<footnote n="5">⁵Univ Rouen Normandie, Univ Caen Normandie, CNRS, M2C, UMR 6143, F-76000 Rouen, France</footnote>

<footnote n="6">⁶GEONOSIS, France</footnote>
<figure><img src="image_2.png" /></figure>

# Improvement of the KarstMod modeling platform for a better assessment of karst groundwater resources

Vianney Sivelle<fnref n="1" />, Guillaume Cinkus<fnref n="1" />, Naomi Mazzilli<fnref n="2" />, David Labat<fnref n="3" />, Bruno Arfib<fnref n="4" />, Nicolas Massei<fnref n="5" />,
Yohann Cousquer<fnref n="1" />, Dominique Bertin<fnref n="6" />, and Hervé Jourde<fnref n="1" />

**Correspondence:** vianney.sivelle@umontpellier.fr

**Abstract.** We propose an updated version of KarstMod, an adjustable platform dedicated to lumped parameter rainfall-discharge modeling of karst aquifers. KarstMod provides a modular, user-friendly modeling environment for educational, research and operational purposes. It also includes numerical tools for time series analysis, model evaluation and sensitivity analysis. The modularity of the platform facilitates common operations related to lumped parameter rainfall-discharge modeling, such as (i) set up and parameter estimation of a relevant model structure, and (ii) evaluation of internal consistency, parameter sensitivity and hydrograph characteristics. The updated version now includes (i) external routines to better consider the input data and their related uncertainties, i.e. evapotranspiration and solid precipitation, (ii) enlargement of multi-objective calibration possibilities, allowing more flexibility in terms of objective functions as well as observation type and (iii) additional tools for model performance evaluation including further performance criteria and tools for model errors representation.

## 1 Introduction

Karst systems consist of heterogeneous aquifers characterized with the co-existence of three types of porosity: (i) inter-granular porosity, (ii) fracture porosity and (iii) large voids and conduits (Palmer, 1991) characterized by contrasted hydrodynamic properties. The existence of surface karst features such as shaft or swallow hole often leads to concentrated point-source recharge towards karst conduits in addition to the more common homogeneous diffuse recharge over the catchment. It also implies that flow regimes can be either laminar or turbulent. Karst aquifers constitute an essential source of drinking water for about 9.2% of the world population (Stevanović, 2019) and it is estimated that one-quarter of the world population depends on freshwater from karst aquifers (Ford and Williams, 2013). Karst aquifers contain an important volume of freshwater while only 1% of its annually renewable water is used for drinking water supply (Stevanović, 2019). Karst groundwater thus represents an unique opportunity to limit the increasing imbalance between growing demand and limited freshwater resource (Wada et al., 2016; Bierkens and Wada, 2019) in the present context of global change. However, karst aquifers are also particularly

15

20

<footnote n="1">¹HSM, Univ Montpellier, CNRS, IRD, Montpellier, France</footnote>

<footnote n="2">²EMMAH, INRAe, Avignon Université, 84000 Avignon, France</footnote>

<footnote n="3">³Geosciences Environment Toulouse UMR CNRS IRD Université Paul Sabatier CNES, 14 Avenue Edouard Belin 31400 TOULOUSE</footnote>

<footnote n="4">⁴Aix-Marseille Univ, CNRS, IRD, INRAE, Coll de France, CEREGE, Aix-en-Provence, France</footnote>

<footnote n="5">⁵Univ Rouen Normandie, Univ Caen Normandie, CNRS, M2C, UMR 6143, F-76000 Rouen, France</footnote>

<footnote n="6">⁶GEONOSIS, France</footnote>
<figure><img src="image_3.png" /></figure>

vulnerable to potential source of contamination, including emergent contaminants (Lukač Reberski et al., 2022), residues of phyto-sanitary products (Lorette et al., 2022) and wastewater (Doummar et al., 2021). Understanding the functioning of karst aquifers and developing operational tools to predict the evolution of freshwater resources is therefore a major challenge for the hydrological science community (Blöschl et al., 2019). Such tools are also required for a better assessment of groundwater vulnerability as well as sustainable management of the groundwater resources (Elshall et al., 2020).

KarstMod is an adjustable modeling platform (Mazzilli et al., 2019) dedicated to lumped parameter rainfall-discharge modeling allowing for (i) simulation of spring discharge, piezometric head and surface discharge, (ii) hydrodynamic analysis of the internal fluxes considered in the model, (iii) model performance evaluation and parametric sensitivity analysis. In this paper, we present the new features incorporated in KarstMod: (i) external routines to better consider the input data and their related uncertainties, i.e. evapotranspiration and solid precipitation, (ii) enlargement of multi-objective calibration possibilities, allowing more flexibility in terms of objective functions as well as observation type with the possibility to include surface water discharge in the calibration procedure and (iii) model performance evaluation, including additional performance criteria as well as additional tools for model errors representation such as the diagnostic efficiency plot (Schwemmle et al., 2021). Also, we present two cases studies to illustrate how KarstMod is useful in the framework of the assessment of karst groundwater resources and its sensitivity to groundwater abstraction. Section 2 is devoted to the presentation of the background and motivations to improve the functionalities of the platform while section 3 presents the main features of KarstMod. Section 4 illustrates the application of rainfall-discharge modeling using KarstMod within the Touvre (western France) and the Lez (southern France) karst systems, which both constitute strategic fresh water resources and ensure drinking water supply.

# 2 Background and motivations

## 2.1 Challenges in karst groundwater resources

Karst aquifers are affected by the combination of different components of global change such as (i) effects of climate change which are particularly pronounced in the Mediterranean area (Dubois et al., 2020; Nerantzaki and Nikolaidis, 2020), (ii) increasing groundwater abstraction (Labat et al., 2022), as well as (iii) changes in land cover land use (Bittner et al., 2018; Sarrazin et al., 2018). Therefore, the assessment of karst groundwater resources vulnerability in the present context requires operational tools for estimating the sustainable yield of karst aquifers but also to predict the impacts of climatic or anthropogenic forcing on groundwater resources in the long term (Sivelle et al., 2021). In order to address these issues, different modeling approaches have been developed (Jeannin et al., 2021) such as, among others, fully-distributed models (Chen and Goldscheider, 2014), semi-distributed models (Doummar et al., 2012; Dubois et al., 2020; Ollivier et al., 2020), and lumped parameter models (Mazzilli et al., 2019) including semi-distributed recharge (Bittner et al., 2018; Sivelle et al., 2022a). Among these, lumped parameter models are recognized as major tools to explore the ability of conceptual representations to explain observations in karst systems (Poulain et al., 2018; Sivelle et al., 2019; Duran et al., 2020; Frank et al., 2021) and for managing karst groundwater resources (Sivelle and Jourde, 2020; Sivelle et al., 2021; Labat et al., 2022; Cousquer and Jourde, 2022).
<figure><img src="image_3.png" /></figure>

vulnerable to potential source of contamination, including emergent contaminants (Lukač Reberski et al., 2022), residues of phyto-sanitary products (Lorette et al., 2022) and wastewater (Doummar et al., 2021). Understanding the functioning of karst aquifers and developing operational tools to predict the evolution of freshwater resources is therefore a major challenge for the hydrological science community (Blöschl et al., 2019). Such tools are also required for a better assessment of groundwater vulnerability as well as sustainable management of the groundwater resources (Elshall et al., 2020).

KarstMod is an adjustable modeling platform (Mazzilli et al., 2019) dedicated to lumped parameter rainfall-discharge modeling allowing for (i) simulation of spring discharge, piezometric head and surface discharge, (ii) hydrodynamic analysis of the internal fluxes considered in the model, (iii) model performance evaluation and parametric sensitivity analysis. In this paper, we present the new features incorporated in KarstMod: (i) external routines to better consider the input data and their related uncertainties, i.e. evapotranspiration and solid precipitation, (ii) enlargement of multi-objective calibration possibilities, allowing more flexibility in terms of objective functions as well as observation type with the possibility to include surface water discharge in the calibration procedure and (iii) model performance evaluation, including additional performance criteria as well as additional tools for model errors representation such as the diagnostic efficiency plot (Schwemmle et al., 2021). Also, we present two cases studies to illustrate how KarstMod is useful in the framework of the assessment of karst groundwater resources and its sensitivity to groundwater abstraction. Section 2 is devoted to the presentation of the background and motivations to improve the functionalities of the platform while section 3 presents the main features of KarstMod. Section 4 illustrates the application of rainfall-discharge modeling using KarstMod within the Touvre (western France) and the Lez (southern France) karst systems, which both constitute strategic fresh water resources and ensure drinking water supply.

# 2 Background and motivations

## 2.1 Challenges in karst groundwater resources

Karst aquifers are affected by the combination of different components of global change such as (i) effects of climate change which are particularly pronounced in the Mediterranean area (Dubois et al., 2020; Nerantzaki and Nikolaidis, 2020), (ii) increasing groundwater abstraction (Labat et al., 2022), as well as (iii) changes in land cover land use (Bittner et al., 2018; Sarrazin et al., 2018). Therefore, the assessment of karst groundwater resources vulnerability in the present context requires operational tools for estimating the sustainable yield of karst aquifers but also to predict the impacts of climatic or anthropogenic forcing on groundwater resources in the long term (Sivelle et al., 2021). In order to address these issues, different modeling approaches have been developed (Jeannin et al., 2021) such as, among others, fully-distributed models (Chen and Goldscheider, 2014), semi-distributed models (Doummar et al., 2012; Dubois et al., 2020; Ollivier et al., 2020), and lumped parameter models (Mazzilli et al., 2019) including semi-distributed recharge (Bittner et al., 2018; Sivelle et al., 2022a). Among these, lumped parameter models are recognized as major tools to explore the ability of conceptual representations to explain observations in karst systems (Poulain et al., 2018; Sivelle et al., 2019; Duran et al., 2020; Frank et al., 2021) and for managing karst groundwater resources (Sivelle and Jourde, 2020; Sivelle et al., 2021; Labat et al., 2022; Cousquer and Jourde, 2022).
<figure><img src="image_4.png" /></figure>

## 2.2 Challenges in lumped parameters modeling in karst hydrology

Lumped parameter models consist of a functional approach that analyzes an hydrogeological system at the catchment scale and describes the transformation from rainfall into discharge using empirical or conceptual relationships. Therefore, parameter values or distributions cannot be determined directly from catchment physical characteristics or *in-situ* measurements, excepted the discharge coefficient to the spring that can be estimated on the basis of recession curve analysis. Instead, model parameters values must be estimated by history-matching. In a general way, rainfall-discharge models in karst hydrology are calibrated considering spring discharge measurements.

Former studies have shown the interest of considering various type of observations such as natural hydro-chemical tracers: NO₃ and SO₄ concentrations (Hartmann et al., 2013), electrical conductivity (Chang et al., 2021) or excess air (Sivelle et al., 2022b). Indeed, the consideration of complementary observation data in groundwater model calibration appears relevant in many applications (Schilling et al., 2019) but requires additional investigations before a suitable implementation in Karst-Mod. Therefore, in this paper, we will focus on the use of hydrodynamics observations only. Indeed, considering piezometric head variations in lumped parameters rainfall-discharge models may lead to better model performance (Mazzilli et al., 2011; Cousquer and Jourde, 2022). Nonetheless, the information content of the piezometric head time series (directly measured, or derived from ground-based gravity measurements) for lumped parameters rainfall-discharge models calibration purpose can be disputable when the available data is not adequate to characterize the whole catchment due to the important heterogeneity in karst aquifers (Sivelle and Jourde, 2020; Mazzilli et al., 2013). Also, Cousquer and Jourde (2022) account for the surface runoff in a lumped parameters rainfall-discharge model calibration procedure allowing to reduce the parametric uncertainties.

Another key point in lumped parameter rainfall-discharge modeling concerns the evaluation of the meteorological forcing, i.e. precipitation (*P*) and evapotranspiration (*ET*). The transformation of precipitation into recharge and finally into discharge includes several processes with characteristic time covering several orders of magnitude (Blöschl and Sivapalan, 1995). Thus, the temporal resolution of the hydrological model must be suitable in the range of time and space scale where the physical phenomenons take place. Coupling hydrological models at multiple temporal resolutions can provide a better model consistency (Sivelle et al., 2019) since the transfer function in karst aquifers may present short response time. Also, errors in rainfall time series can significantly affect model parameters and structure (Oudin et al., 2006). Finally, the response of karst spring discharge is sensitive to energy and water fluxes within the soil-vegetation-atmosphere (SVA) continuum as well as changes in climatic conditions (Hartmann et al., 2017). Bittner et al. (2021) computed several models to evaluate the fluxes related to interception, evapotranspiration and snow process. The results show significant uncertainties related to input data as well as potential compensation between the various uncertain processes. In some cases, snow melt is a controlling factor in the water balance (Doummar et al., 2018a; Liu et al., 2021), thus a suitable snow melt estimation is required to improve hydrological model performance (Çallı et al., 2022). Therefore, two meteorological modules have been added to KarstMod: (i) a "Snow routine" and (ii) a "PET routine" allowing to better account for snow and evapotranspiration processes.
<figure><img src="image_4.png" /></figure>

## 2.2 Challenges in lumped parameters modeling in karst hydrology

Lumped parameter models consist of a functional approach that analyzes an hydrogeological system at the catchment scale and describes the transformation from rainfall into discharge using empirical or conceptual relationships. Therefore, parameter values or distributions cannot be determined directly from catchment physical characteristics or *in-situ* measurements, excepted the discharge coefficient to the spring that can be estimated on the basis of recession curve analysis. Instead, model parameters values must be estimated by history-matching. In a general way, rainfall-discharge models in karst hydrology are calibrated considering spring discharge measurements.

Former studies have shown the interest of considering various type of observations such as natural hydro-chemical tracers: NO₃ and SO₄ concentrations (Hartmann et al., 2013), electrical conductivity (Chang et al., 2021) or excess air (Sivelle et al., 2022b). Indeed, the consideration of complementary observation data in groundwater model calibration appears relevant in many applications (Schilling et al., 2019) but requires additional investigations before a suitable implementation in Karst-Mod. Therefore, in this paper, we will focus on the use of hydrodynamics observations only. Indeed, considering piezometric head variations in lumped parameters rainfall-discharge models may lead to better model performance (Mazzilli et al., 2011; Cousquer and Jourde, 2022). Nonetheless, the information content of the piezometric head time series (directly measured, or derived from ground-based gravity measurements) for lumped parameters rainfall-discharge models calibration purpose can be disputable when the available data is not adequate to characterize the whole catchment due to the important heterogeneity in karst aquifers (Sivelle and Jourde, 2020; Mazzilli et al., 2013). Also, Cousquer and Jourde (2022) account for the surface runoff in a lumped parameters rainfall-discharge model calibration procedure allowing to reduce the parametric uncertainties.

Another key point in lumped parameter rainfall-discharge modeling concerns the evaluation of the meteorological forcing, i.e. precipitation (*P*) and evapotranspiration (*ET*). The transformation of precipitation into recharge and finally into discharge includes several processes with characteristic time covering several orders of magnitude (Blöschl and Sivapalan, 1995). Thus, the temporal resolution of the hydrological model must be suitable in the range of time and space scale where the physical phenomenons take place. Coupling hydrological models at multiple temporal resolutions can provide a better model consistency (Sivelle et al., 2019) since the transfer function in karst aquifers may present short response time. Also, errors in rainfall time series can significantly affect model parameters and structure (Oudin et al., 2006). Finally, the response of karst spring discharge is sensitive to energy and water fluxes within the soil-vegetation-atmosphere (SVA) continuum as well as changes in climatic conditions (Hartmann et al., 2017). Bittner et al. (2021) computed several models to evaluate the fluxes related to interception, evapotranspiration and snow process. The results show significant uncertainties related to input data as well as potential compensation between the various uncertain processes. In some cases, snow melt is a controlling factor in the water balance (Doummar et al., 2018a; Liu et al., 2021), thus a suitable snow melt estimation is required to improve hydrological model performance (Çallı et al., 2022). Therefore, two meteorological modules have been added to KarstMod: (i) a "Snow routine" and (ii) a "PET routine" allowing to better account for snow and evapotranspiration processes.
<figure><img src="image_5.png" /></figure>

## 3 Implementation

The updated version of KarstMod implements additional features to enhance the rainfall-discharge modeling practices. First, we describe the additional modules (snow and PET routines) for a better meteorological forcing estimation. Then, we introduce the additional tools proposed for (i) set up and calibration of the model structure, (ii) model performance evaluation as well as (iii) uncertainties consideration.

### 3.1 Meteorological modules

#### 3.1.1 Snow routine

KarstMod allows using either observation-based precipitation time series $P$ [L.T$^{-1}$] or estimated precipitation time series $P_{sr}$ [L.T$^{-1}$] using a snow routine. The latter is similar to the one used by Chen et al. (2018) – without the radiation components – which has been successfully used for improving the simulation of karst spring discharge in snow-covered karst systems (Chen et al., 2018; Cinkus et al., 2022b). It consists of a modified HBV-snow routine (Bergström, 1992) for simulating snow accumulation and melt over different sub-catchments based on altitude ranges (appendix A). The estimated precipitation $P_{sr}$ gives the water leaving the snow routine, equivalent to the recharge into the first compartment of the model (compartment E in KarstMod). $P_{sr}^*$ for each sub-catchment is proportional to its surface regarding the complete catchment area. The snow routine workflow requires both air temperature $T$ [°C] and precipitation $P$ [L.T$^{-1}$] time series. $P$ is considered as snow when $T$ in the sub-catchment is lower than the temperature threshold $T_s$. Snow melt starts when the temperature overpasses the threshold according to a degree-day expression. The snow melt is a function of the melt coefficient $MF$ and the degrees above the temperature threshold $T_s$. Runoff starts when the liquid water holding capacity of snow $CWH$ is exceeded. The refreezing coefficient ($CFR$) stands for refreezing liquid water in the snow when snow melt is interrupted (Bergström, 1992). The output of the snow routine consists of a redistributed precipitation time series $P_{sr}$. The four parameters of the snow routine (i.e. $T_s$, $MF$, $CWH$ and $CFR$) can be considered in the parameter estimation procedure as well as sensitivity analysis.

#### 3.1.2 PET routine

Evapotranspiration in KarstMod can be tackle in four different ways :

(a) Effective precipitation time series ($Peff$) can be pre-processed by user (Eq. 1) and the evapotranspiration flux is not activated in the model structure selection window in KarstMod. Therefore, $Peff$ is given through the $P$ time series in the input data file.

$$Peff = P - ETa \quad (1)$$

where $Peff$ is effective precipitation [L.T$^{-1}$], $P$ is precipitation [L.T$^{-1}$] and $ETa$ is user-defined actual evapotranspiration [L.T$^{-1}$] computed by observation-based data or external model.
<figure><img src="image_5.png" /></figure>

## 3 Implementation

The updated version of KarstMod implements additional features to enhance the rainfall-discharge modeling practices. First, we describe the additional modules (snow and PET routines) for a better meteorological forcing estimation. Then, we introduce the additional tools proposed for (i) set up and calibration of the model structure, (ii) model performance evaluation as well as (iii) uncertainties consideration.

### 3.1 Meteorological modules

#### 3.1.1 Snow routine

KarstMod allows using either observation-based precipitation time series $P$ [L.T⁻¹] or estimated precipitation time series $P_{sr}$ [L.T⁻¹] using a snow routine. The latter is similar to the one used by Chen et al. (2018) – without the radiation components – which has been successfully used for improving the simulation of karst spring discharge in snow-covered karst systems (Chen et al., 2018; Cinkus et al., 2022b). It consists of a modified HBV-snow routine (Bergström, 1992) for simulating snow accumulation and melt over different sub-catchments based on altitude ranges (appendix A). The estimated precipitation $P_{sr}$ gives the water leaving the snow routine, equivalent to the recharge into the first compartment of the model (compartment E in KarstMod). $P_{sr}$* for each sub-catchment is proportional to its surface regarding the complete catchment area. The snow routine workflow requires both air temperature $T$ [°C] and precipitation $P$ [L.T⁻¹] time series. $P$ is considered as snow when $T$ in the sub-catchment is lower than the temperature threshold $T_s$. Snow melt starts when the temperature overpasses the threshold according to a degree-day expression. The snow melt is a function of the melt coefficient $MF$ and the degrees above the temperature threshold $T_s$. Runoff starts when the liquid water holding capacity of snow $CWH$ is exceeded. The refreezing coefficient ($CFR$) stands for refreezing liquid water in the snow when snow melt is interrupted (Bergström, 1992). The output of the snow routine consists of a redistributed precipitation time series $P_{sr}$. The four parameters of the snow routine (i.e. $T_s$, $MF$, $CWH$ and $CFR$) can be considered in the parameter estimation procedure as well as sensitivity analysis.

#### 3.1.2 PET routine

Evapotranspiration in KarstMod can be tackle in four different ways :

(a) Effective precipitation time series ($Peff$) can be pre-processed by user (Eq. 1) and the evapotranspiration flux is not activated in the model structure selection window in KarstMod. Therefore, $Peff$ is given through the $P$ time series in the input data file.

$$Peff = P - ETa \quad (1)$$

where $Peff$ is effective precipitation [L.T⁻¹], $P$ is precipitation [L.T⁻¹] and $ETa$ is user-defined actual evapotranspiration [L.T⁻¹] computed by observation-based data or external model.
<figure><img src="image_6.png" /></figure>

(b) User defined potential evapotranspiration($PET$) can be given as input in KarstMod for the evapotranspiration time series. Compartment E stands for a soil and epikarst storage zone, where water is available for actual evapotranspiration ($ETa$), flows to lower level of the model structure or outflow as surface discharge losses. Using $E_{min}$, user can simulate water holding capacity and non-linear behavior of karst recharge.

(c) User-defined actual evapotranspiration ($ETa$) can be given as input data in KarstMod for evapotranspiration time series instead of potential evapotranspiration. KarstMod computes effective precipitation by limiting the evapotranspiration to water content available in compartment E; calculated actual evapotranspiration can then be lower than user's input $ETa$.

(d) The new feature in KarstMod is the PET routine which estimates the potential evapotranspiration based on the Oudin's formula (Oudin et al., 2005) (Eq. 2). It needs a temperature time series and two parameters to be estimated, which can be considered in the parameter estimation procedure as well as sensitivity analysis.

$$PET = \frac{R_e}{\lambda \cdot \rho} \times \frac{T + K2}{K1} \quad \text{if } T + K2 > 0 \quad \text{else } PET = 0 \quad (2)$$

where $R_e$ is the extraterrestrial radiation [MJ.L⁻²T⁻¹] depending only on latitude $Lat$ and Julian day, $\lambda$ is the latent heat flux (taken equal to 2.45 MJ M⁻¹), $\rho$ is the density of water [M.L⁻³] and $T$ is the mean daily air temperature [°C], which is therefore a single function of the Julian day for a given location. $K1$ [°C] and $K2$ [°C] are constants to adjust over the catchment for rainfall-discharge model, which both can be considered in the parameter estimation procedure as well as sensitivity analysis.

<figure><img src="image_7.png" /><figcaption>**Figure 1.** The four ways to account for evapotranspiration in KarstMod ($P$ is precipitation, $ETa$ is actual evapotranspiration, $PET$ is potential evapotranspiration, $PET_{Oudin}$ is KarstMod's computed potential evapotranspiration with Oudin's formula)</figcaption></figure>

## 3.2 Set up and calibration of the model structure

The modular structure proposed in KarstMod is based on a widely used conceptual model which separates karst aquifers into an infiltration zone and a saturated zone. Based on this conceptual representation, the platform offers four compartments organized as a two-level structure: (i) compartment E (higher level) and (ii) compartments L, M and C (lower level). The
<figure><img src="image_6.png" /></figure>

(b) User defined potential evapotranspiration($PET$) can be given as input in KarstMod for the evapotranspiration time series. Compartment E stands for a soil and epikarst storage zone, where water is available for actual evapotranspiration ($ETa$), flows to lower level of the model structure or outflow as surface discharge losses. Using $E_{min}$, user can simulate water holding capacity and non-linear behavior of karst recharge.

(c) User-defined actual evapotranspiration ($ETa$) can be given as input data in KarstMod for evapotranspiration time series instead of potential evapotranspiration. KarstMod computes effective precipitation by limiting the evapotranspiration to water content available in compartment E; calculated actual evapotranspiration can then be lower than user's input $ETa$.

(d) The new feature in KarstMod is the PET routine which estimates the potential evapotranspiration based on the Oudin's formula (Oudin et al., 2005) (Eq. 2). It needs a temperature time series and two parameters to be estimated, which can be considered in the parameter estimation procedure as well as sensitivity analysis.

$$PET = \frac{R_e}{\lambda \cdot \rho} \times \frac{T + K2}{K1} \quad \text{if } T + K2 > 0 \quad \text{else } PET = 0 \quad (2)$$

where $R_e$ is the extraterrestrial radiation [MJ.L$^{-2}$T$^{-1}$] depending only on latitude $Lat$ and Julian day, $\lambda$ is the latent heat flux (taken equal to 2.45 MJ M$^{-1}$), $\rho$ is the density of water [M.L$^{-3}$] and $T$ is the mean daily air temperature [°C], which is therefore a single function of the Julian day for a given location. $K1$ [°C] and $K2$ [°C] are constants to adjust over the catchment for rainfall-discharge model, which both can be considered in the parameter estimation procedure as well as sensitivity analysis.

<figure><img src="image_7.png" /><figcaption>**Figure 1.** The four ways to account for evapotranspiration in KarstMod ($P$ is precipitation, $ETa$ is actual evapotranspiration, $PET$ is potential evapotranspiration, $PET_{Oudin}$ is KarstMod's computed potential evapotranspiration with Oudin's formula)</figcaption></figure>

## 3.2 Set up and calibration of the model structure

The modular structure proposed in KarstMod is based on a widely used conceptual model which separates karst aquifers into an infiltration zone and a saturated zone. Based on this conceptual representation, the platform offers four compartments organized as a two-level structure: (i) compartment E (higher level) and (ii) compartments L, M and C (lower level). The
<figure><img src="image_8.png" /></figure>

modular structure proposed in KarstMod is based on a widely used conceptual model which separates karst aquifers into an infiltration zone and a saturated zone, or low and quick flows through the unsaturated and saturated zones. Based on this conceptual representations, the platform offers four compartments organized as a two-level structure: (i) compartment E (higher level) and (ii) compartments L, M and C (lower level). A priori, the higher-level stands for the infiltration zone or the soil and epikarst. At the lower level, compartments L, M, and C stand for the different sub-systems of the saturated zone, or for low and quick flows of the whole hydrosystem. The various model structures and their governing equations are presented in Mazzilli et al. (2019, 2022).

The user can activate (or deactivate) the various compartments (E, L, M and C), the fluxes and their activation threshold as well as the exponent of the discharge law $\alpha$ (in case of non-linear discharge law such $\alpha \neq 1$). The figure 2 gives an example of model structure in KarstMod where the solid and faded colors represent the activated and the inactivated features respectively. The user must provide the warm-up, calibration and validation periods. The warm-up period must be set in order to be independent from initial conditions to avoid bias in the parameter estimation procedure (Mazzilli et al., 2012). Then, a calibration period (i.e. the period in which the parameter are estimated to reduce the predictive errors) and a validation period (i.e. period separated from the calibration period) can be defined to run the split sample test procedure (Klemeš, 1986). For calibration purpose, KarstMod proposes several widely used performance criteria $\phi$: the Pearson's correlation coefficient $r_p$ (Freedman et al., 2007), the Spearman rank correlation coefficient $r_s$ (Freedman et al., 2007), the Nash-Sutcliffe Efficiency $NSE$ (Nash and Sutcliffe, 1970), the volumetric error $VE$ (Criss and Winston, 2008), the modified balance error $BE$ (Perrin et al., 2001), the Kling-Gupta Efficiency $KGE$ (Gupta et al., 2009) and a non-parametric variant of the Kling-Gupta Efficiency $KGENP$ (Pool et al., 2018). To compute a multi-objective calibration procedure the user can create his own objective function $\Phi$ as a weighted sum of several objective functions:

$$ \Phi = \sum_{i=1}^{N} \omega_{i} \times \phi_{i}(U) \qquad (3) $$

where $\omega$ is the weight affected to the objective function $\phi(U)$ with $\sum w_i = 1$ and $U$ a general notation for the observations used for parameter estimation purpose. In the KarstMod modeling platform $U$ corresponds to either spring discharge $Q_s$, piezometric head measurements $Z$ (available for compartments E, L, M and C) or surface water discharge $Q_{loss}$ from compartment E. Also, the objective function $\phi$ can be computed on transformed $U$ to avoid high water level bias on quadratic error. The following transformation are available in KarstMod: $1/U$, $\sqrt{U}$, $1/\sqrt{U}$. Therefore, the user can use any combination of the objective function $\phi$, observations $U$ and variable transformations. Depending on the modelling purpose, the user must refer to the literature to define the suitable objective function (Bennett et al., 2013; Ferreira et al., 2020; Hauduc et al., 2015; Jackson et al., 2019).

The model is calibrated using a quasi Monte-Carlo sampling procedure with a Sobol sequence sampling of the parameter space (Sobol, 1976). The procedure consists in finding an ensemble of parameter set providing an objective function $\phi$ greater than the user defined value. The calibration procedure is stopped when either the user-defined maximum duration $t_{max}$ is reached or the user-defined number of parameter set $n_{max}$ are collected. KarstMod offers a "run" option allowing to run the
<figure><img src="image_8.png" /></figure>

modular structure proposed in KarstMod is based on a widely used conceptual model which separates karst aquifers into an infiltration zone and a saturated zone, or low and quick flows through the unsaturated and saturated zones. Based on this conceptual representations, the platform offers four compartments organized as a two-level structure: (i) compartment E (higher level) and (ii) compartments L, M and C (lower level). A priori, the higher-level stands for the infiltration zone or the soil and epikarst. At the lower level, compartments L, M, and C stand for the different sub-systems of the saturated zone, or for low and quick flows of the whole hydrosystem. The various model structures and their governing equations are presented in Mazzilli et al. (2019, 2022).

The user can activate (or deactivate) the various compartments (E, L, M and C), the fluxes and their activation threshold as well as the exponent of the discharge law $\alpha$ (in case of non-linear discharge law such $\alpha \neq 1$). The figure 2 gives an example of model structure in KarstMod where the solid and faded colors represent the activated and the inactivated features respectively. The user must provide the warm-up, calibration and validation periods. The warm-up period must be set in order to be independent from initial conditions to avoid bias in the parameter estimation procedure (Mazzilli et al., 2012). Then, a calibration period (i.e. the period in which the parameter are estimated to reduce the predictive errors) and a validation period (i.e. period separated from the calibration period) can be defined to run the split sample test procedure (Klemeš, 1986). For calibration purpose, KarstMod proposes several widely used performance criteria $\phi$: the Pearson's correlation coefficient $r_p$ (Freedman et al., 2007), the Spearman rank correlation coefficient $r_s$ (Freedman et al., 2007), the Nash-Sutcliffe Efficiency $NSE$ (Nash and Sutcliffe, 1970), the volumetric error $VE$ (Criss and Winston, 2008), the modified balance error $BE$ (Perrin et al., 2001), the Kling-Gupta Efficiency $KGE$ (Gupta et al., 2009) and a non-parametric variant of the Kling-Gupta Efficiency $KGENP$ (Pool et al., 2018). To compute a multi-objective calibration procedure the user can create his own objective function $\Phi$ as a weighted sum of several objective functions:

$$ \Phi = \sum_{i=1}^{N} \omega_{i} \times \phi_{i}(U) \qquad (3) $$

where $\omega$ is the weight affected to the objective function $\phi(U)$ with $\sum w_i = 1$ and $U$ a general notation for the observations used for parameter estimation purpose. In the KarstMod modeling platform $U$ corresponds to either spring discharge $Q_s$, piezometric head measurements $Z$ (available for compartments E, L, M and C) or surface water discharge $Q_{loss}$ from compartment E. Also, the objective function $\phi$ can be computed on transformed $U$ to avoid high water level bias on quadratic error. The following transformation are available in KarstMod: $1/U$, $\sqrt{U}$, $1/\sqrt{U}$. Therefore, the user can use any combination of the objective function $\phi$, observations $U$ and variable transformations. Depending on the modelling purpose, the user must refer to the literature to define the suitable objective function (Bennett et al., 2013; Ferreira et al., 2020; Hauduc et al., 2015; Jackson et al., 2019).

The model is calibrated using a quasi Monte-Carlo sampling procedure with a Sobol sequence sampling of the parameter space (Sobol, 1976). The procedure consists in finding an ensemble of parameter set providing an objective function $\phi$ greater than the user defined value. The calibration procedure is stopped when either the user-defined maximum duration $t_{max}$ is reached or the user-defined number of parameter set $n_{max}$ are collected. KarstMod offers a "run" option allowing to run the
<figure><img src="image_9.png" /></figure>

model for user-defined parameter set, without calibration procedure, and so allowing to investigate "by-hand" the parameter space and the sensitivity of the model to specific parameters.

## 3.3 Model evaluation

The model performance can be evaluated for both the calibration and validation periods. It allows (i) to ensure the robustness of model predictions, even under changing conditions (which is a key point for the assessment of climate change impact) and (ii) to avoid model over-fitting within a specific range of hydro-climatic conditions observed during the calibration period. KarstMod allows the computation of the above mentioned performance criteria for both calibration and validation periods. Even though the notation "validation" is disputable such procedure is required to evaluate both explanatory and predictive dimensions of the model structure (Andréassian, 2023). Then, KarstMod offers an ensemble of numerical tools devoted to (i) check the model consistency, i.e. explanatory dimension of the model (Beven, 2001; Shmueli, 2010), (ii) evaluate the model performance, i.e. predictive dimension of the model structure.

To check the model consistency, the simulation based on the parameter set that provides the highest objective function value can be analyzed through an ensemble of graphs such as (i) internal and external fluxes as a function of time, (ii) cumulative volumes for both observed and simulated time series for spring discharge $Q_s$ and surface water discharge $Q_{loss}$, (iii) simulated mass-balance as function of time, (iv) comparison of observations and simulations for either $Q_s$ or $Q_{loss}$ with probability function plots, auto-correlogram of the spring discharge time series, cross-correlogram of precipitation-discharge time series.

To evaluate the model performance, KarstMod offers a "Model evaluation" panel that includes several sub-panels, from the left to the right (see the KarstMod Graphical User Interface screenshot figure 4):

- The diagnostic efficiency *DE* (Schwemmle et al., 2021) which consists of a diagnostic polar plot that facilitates the model evaluation process as well as the comparison of multiple simulations. The *DE* accounts for constant, dynamics and timing errors, and their relative contribution to the model errors. Also, the decomposition of the errors between the periods of high flows and low flows allows to better investigate the model bias, as well as to provide critical evaluation for impact studies, particularly for the assessment of climate change impacts. Indeed, the accurate evaluation of low flow periods (in terms of frequency, intensity and duration) becomes more and more crucial for groundwater resource variability assessment.

- The available objective functions $\phi$ are presented as a radar chart which consists of a polygon where the position of each point from the center gives the value of the performance criteria. The closer the point is to the outside of the radar chart, the better the model performs. The radar chart is made for both calibration and validation periods and for each of the calibration variables considered in the modelling ($Q_s$, $Z_{obs}^A$ with A for either E, M, C or L compartments and $Q_{loss}$).

- The *KGE* (Gupta et al., 2009) consists of a diagonal decomposition of the *NSE* (Nash and Sutcliffe, 1970) to separate Pearson's correlation coefficient $r_p$, representation of bias $\beta_{KGE}$, and variability $\alpha_{KGE}$. Thus, the *KGE* is comparable to multi-objective criteria for calibration purpose (Pechlivanidis et al., 2013). The sub-panel offers (i) a bi-plot of the three *KGE*'s components and (ii) a radar plot visualization of the *KGE*'s components, allowing to identify potential
<figure><img src="image_9.png" /></figure>

model for user-defined parameter set, without calibration procedure, and so allowing to investigate "by-hand" the parameter
space and the sensitivity of the model to specific parameters.

3.3 Model evaluation

The model performance can be evaluated for both the calibration and validation periods. It allows (i) to ensure the robustness of model predictions, even under changing conditions (which is a key point for the assessment of climate change impact) and (ii) to avoid model over-fitting within a specific range of hydro-climatic conditions observed during the calibration period. KarstMod allows the computation of the above mentioned performance criteria for both calibration and validation periods. Even though the notation "validation" is disputable such procedure is required to evaluate both explanatory and predictive dimensions of the model structure (Andréassian, 2023). Then, KarstMod offers an ensemble of numerical tools devoted to (i) check the model consistency, i.e. explanatory dimension of the model (Beven, 2001; Shmueli, 2010), (ii) evaluate the model performance, i.e. predictive dimension of the model structure.

To check the model consistency, the simulation based on the parameter set that provides the highest objective function value
can be analyzed through an ensemble of graphs such as (i) internal and external fluxes as a function of time, (ii) cumulative
volumes for both observed and simulated time series for spring discharge Qs and surface water discharge Qloss, (iii) simulated
mass-balance as function of time, (iv) comparison of observations and simulations for either Qs or Qloss with probability
function plots, auto-correlogram of the spring discharge time series, cross-correlogram of precipitation-discharge time series.

To evaluate the model performance, KarstMod offers a "Model evaluation" panel that includes several sub-panels, from the
left to the right (see the KarstMod Graphical User Interface screenshot figure 4):

- The diagnostic efficiency *DE* (Schwemmle et al., 2021) which consists of a diagnostic polar plot that facilitates the model evaluation process as well as the comparison of multiple simulations. The *DE* accounts for constant, dynamics and timing errors, and their relative contribution to the model errors. Also, the decomposition of the errors between the periods of high flows and low flows allows to better investigate the model bias, as well as to provide critical evaluation for impact studies, particularly for the assessment of climate change impacts. Indeed, the accurate evaluation of low flow periods (in terms of frequency, intensity and duration) becomes more and more crucial for groundwater resource variability assessment.

- The available objective functions $\phi$ are presented as a radar chart which consists of a polygon where the position of each point from the center gives the value of the performance criteria. The closer the point is to the outside of the radar chart, the better the model performs. The radar chart is made for both calibration and validation periods and for each of the calibration variables considered in the modelling ($Q_s, Z_{obs}^A$ with A for either E, M, C or L compartments and $Q_{loss}$).

- The KGE (Gupta et al., 2009) consists of a diagonal decomposition of the NSE (Nash and Sutcliffe, 1970) to separate Pearson's correlation coefficient $r_p$, representation of bias $\beta_{KGE}$, and variability $\alpha_{KGE}$. Thus, the KGE is comparable to multi-objective criteria for calibration purpose (Pechlivanidis et al., 2013). The sub-panel offers (i) a bi-plot of the three KGE's components and (ii) a radar plot visualization of the KGE's components, allowing to identify potential
<figure><img src="image_10.png" /></figure>

counterbalancing errors according to these different components (Cinkus et al., 2022a). The two above mentioned plots also include the decomposition of the *KGENP* (Pool et al., 2018) in terms of Spearman's rank correlation coefficient *r*<sub>s</sub>, representation of bias *β*<sub>KGENP</sub> and non-parametric variability *α*<sub>KGENP</sub>.

## 3.4 Dealing with uncertainties

Moges et al. (2021) summarize the various source of uncertainties in hydrological models including structural and parametric uncertainties as well as uncertainties related to input data and observations. The latter concern both the input (i.e. precipitation and evapotranspiration) and the output (i.e. discharge) of the modeled systems. Many references are devoted to the uncertainties related to input data and observations. As an example, Westerberg et al. (2020) include information about the discharge uncertainty distribution in the objective function and perform better discharge simulation. Also, the precipitation error can be dependent on the data time step (McMillan et al., 2011) and could impact the hydrological model performance (Ficchì et al., 2016). KarstMod allows to perform hydrological modeling on both daily and hourly temporal resolutions, allowing to account for uncertainty related to the data time step. Lumped parameter hydrological models generally consider meteorological time series representative of a whole catchment, which may require some pre-processing, particularly for snow processes since it can have a strong influence on flow dynamics. Thus, KarstMod includes variables related to both the snow routine (i.e. the redistributed precipitation time series *P*<sub>sr</sub>) and the PET routine (i.e. estimated potential evapotranspiration *PET*) in the parameter estimation procedure. This allows to investigate the sensitivity of the flow simulation to these input data, when using snow and PET routines. Nonetheless, KarstMod does not include features to investigate the impact of observation uncertainties on the parameter estimation.

As many environmental problems, parameter estimation in rainfall-discharge modeling consists generally in ill-posed problems, i.e. the modeling encounters issues about the unicity, identifiability and stability of the problem solution (Ebel and Loague, 2006). As a consequence, several representations of the modeled catchment may be considered as equally acceptable (Beven, 2006). Knoben et al. (2020) evaluate the performance of 36 daily lumped parameter models over 559 catchments and show that between 1 and up to 28 models can show performance close to the model structure with the highest performance criteria. Such results are widely covered in catchment hydrology (Zhou et al., 2021; Pandi et al., 2021; Dakhlaoui and Djebbi, 2021; Darbandsari and Coulibaly, 2020; Gupta and Govindaraju, 2019) but still poorly investigated in karst hydrology. Indeed, the structural uncertainty impacts on rainfall-discharge modeling in karst hydrology is not properly evaluated whereas many studies consider several hydrological model structure to include structural uncertainty in flow simulation (Hartmann et al., 2012; Jiang et al., 2007; Jones et al., 2006; Sivelle et al., 2021). KarstMod includes more than 50 combinations of the various compartments as well as various compartments model (i.e. compartment with linear or non-linear discharge law and compartment with infinite characteristic time) and allows a quick implementation of the various model structures. The user can easily manage to start the modeling with one single compartment and gradually move to more complex model structure with up to 4 compartments, 5 fluxes connected to the spring, 4 internal fluxes and 1 flux running out of the system.

Considering each model structure, parametric equifinality can be investigated using (i) dotty plots of the values of the objective function against the parameter values, (ii) dotty plot of the values of the performance criteria used to define the aggregated
<figure><img src="image_10.png" /></figure>

counterbalancing errors according to these different components (Cinkus et al., 2022a). The two above mentioned plots also include the decomposition of the *KGENP* (Pool et al., 2018) in terms of Spearman's rank correlation coefficient *r*<sub>s</sub>, representation of bias *β*<sub>KGENP</sub> and non-parametric variability *α*<sub>KGENP</sub>.

## 3.4 Dealing with uncertainties

Moges et al. (2021) summarize the various source of uncertainties in hydrological models including structural and parametric uncertainties as well as uncertainties related to input data and observations. The latter concern both the input (i.e. precipitation and evapotranspiration) and the output (i.e. discharge) of the modeled systems. Many references are devoted to the uncertainties related to input data and observations. As an example, Westerberg et al. (2020) include information about the discharge uncertainty distribution in the objective function and perform better discharge simulation. Also, the precipitation error can be dependent on the data time step (McMillan et al., 2011) and could impact the hydrological model performance (Ficchì et al., 2016). KarstMod allows to perform hydrological modeling on both daily and hourly temporal resolutions, allowing to account for uncertainty related to the data time step. Lumped parameter hydrological models generally consider meteorological time series representative of a whole catchment, which may require some pre-processing, particularly for snow processes since it can have a strong influence on flow dynamics. Thus, KarstMod includes variables related to both the snow routine (i.e. the redistributed precipitation time series *P*<sub>sr</sub>) and the PET routine (i.e. estimated potential evapotranspiration *PET*) in the parameter estimation procedure. This allows to investigate the sensitivity of the flow simulation to these input data, when using snow and PET routines. Nonetheless, KarstMod does not include features to investigate the impact of observation uncertainties on the parameter estimation.

As many environmental problems, parameter estimation in rainfall-discharge modeling consists generally in ill-posed problems, i.e. the modeling encounters issues about the unicity, identifiability and stability of the problem solution (Ebel and Loague, 2006). As a consequence, several representations of the modeled catchment may be considered as equally acceptable (Beven, 2006). Knoben et al. (2020) evaluate the performance of 36 daily lumped parameter models over 559 catchments and show that between 1 and up to 28 models can show performance close to the model structure with the highest performance criteria. Such results are widely covered in catchment hydrology (Zhou et al., 2021; Pandi et al., 2021; Dakhlaoui and Djebbi, 2021; Darbandsari and Coulibaly, 2020; Gupta and Govindaraju, 2019) but still poorly investigated in karst hydrology. Indeed, the structural uncertainty impacts on rainfall-discharge modeling in karst hydrology is not properly evaluated whereas many studies consider several hydrological model structure to include structural uncertainty in flow simulation (Hartmann et al., 2012; Jiang et al., 2007; Jones et al., 2006; Sivelle et al., 2021). KarstMod includes more than 50 combinations of the various compartments as well as various compartments model (i.e. compartment with linear or non-linear discharge law and compartment with infinite characteristic time) and allows a quick implementation of the various model structures. The user can easily manage to start the modeling with one single compartment and gradually move to more complex model structure with up to 4 compartments, 5 fluxes connected to the spring, 4 internal fluxes and 1 flux running out of the system.

Considering each model structure, parametric equifinality can be investigated using (i) dotty plots of the values of the objective function against the parameter values, (ii) dotty plot of the values of the performance criteria used to define the aggregated
<figure><img src="image_11.png" /></figure>

objective function, and (iii) the variance-based, first-order $S_i$ and total $S_{Ti}$ sensitivity indexes for the model parameters. Details concerning the computation of sensitivity indexes within KarstMod are given in Mazzilli et al. (2019, 2022).

# 4 Case studies

To illustrate KarstMod application and the use of the above presented functionalities for the assessment of karst groundwater resources, we propose two case studies: (i) the Touvre karst system and (ii) the Lez karst system. Both karst systems consist of strategic freshwater resources for drinking water supply (DWS), for the city of Angoulême (western France) and Montpellier (southern France) respectively.

## 4.1 The Touvre karst system (La Rochefoucauld)

The Touvre karst system is a binary karst system where the infiltration consists of (i) a delayed infiltration of effective rainfall on karstic recharge area and (ii) a direct infiltration of surface water from the Tardoire, Bandiat, and Bonnieure rivers. These lasts are surface stream flow within metamorphic rocks that partly infiltrate to subterranean at the contact with sedimentary formations, mainly composed of Middle to Upper Jurrasic limestones. The springs of the Touvre, located 7 km east of Angoulême (western France), have three main outlets (the Bouillant, the Dormant and the Font de Lussac) and a secondary outlet (the Lèche) (Labat et al., 2022). In the following, the discharge of the four outlets are accumulated and named Touvre spring.

The Touvre karst system constitutes a strategic freshwater resource for drinking water supply (DWS) of Angoulême, with around 110,000 inhabitants, but also contributes to water supply for industry and agriculture. In 2015, there were 84 pumping wells over the karstic impluvium of the Touvre karst system, and around 100 more in the Tardoire, Bandiat, and Bonnieure rivers catchment. Based on the data provided by the Adour-Garonne Water Agency, the annual groundwater abstraction for agriculture represents 4.6 Mm³ whereas annual groundwater abstraction for DWS represents 1.1 Mm³ over the karstic impluvium of the Touvre karst system. On the three rivers catchment (out of the karstic impluvium), the annual groundwater abstraction represents 2.5 Mm³ for agriculture and 3.3 Mm³ for DWS, mainly through river intakes or alluvial groundwater abstraction. The total annual volume of abstracted groundwater in the area represents around 5% of the annual volume of transit at the Touvre spring. This is quite low compared with karst aquifers in France exploited for their groundwater resource, such as the Lez spring (Jourde et al., 2014) and the Oeillal's spring karst catchment (Sivelle et al., 2021), where the annual groundwater abstraction volume represents respectively 50% and 15% of annual volume of transit at the spring. Therefore, the Touvre catchment seems not to be over exploited at the moment but the impact of groundwater abstraction should be addressed in the actual context of global change to ensure a sustainable management of this strategic fresh water resource.

The area is characterized by an ocean influenced climate with a mean annual precipitation around 800 mm/year distributed over 255 rainy days. The estimation is performed with Thiessen polygon methods based on eleven meteorological stations over the area (Labat et al., 2022). The mean annual potential evapotranspiration is around 770 mm/year according to the Penman-Monteith estimation provided by the french meteorological survey (Météo-France). The Touvre spring discharge shows a significant variability ranging from 3 m³/s to 49 m³/s with a coefficient of variation around 0.46 (Figure 3, b). The surface
<figure><img src="image_11.png" /></figure>

objective function, and (iii) the variance-based, first-order $S_i$ and total $S_{Ti}$ sensitivity indexes for the model parameters. Details concerning the computation of sensitivity indexes within KarstMod are given in Mazzilli et al. (2019, 2022).

# 4 Case studies

To illustrate KarstMod application and the use of the above presented functionalities for the assessment of karst groundwater resources, we propose two case studies: (i) the Touvre karst system and (ii) the Lez karst system. Both karst systems consist of strategic freshwater resources for drinking water supply (DWS), for the city of Angoulême (western France) and Montpellier (southern France) respectively.

## 4.1 The Touvre karst system (La Rochefoucauld)

The Touvre karst system is a binary karst system where the infiltration consists of (i) a delayed infiltration of effective rainfall on karstic recharge area and (ii) a direct infiltration of surface water from the Tardoire, Bandiat, and Bonnieure rivers. These lasts are surface stream flow within metamorphic rocks that partly infiltrate to subterranean at the contact with sedimentary formations, mainly composed of Middle to Upper Jurrasic limestones. The springs of the Touvre, located 7 km east of Angoulême (western France), have three main outlets (the Bouillant, the Dormant and the Font de Lussac) and a secondary outlet (the Lèche) (Labat et al., 2022). In the following, the discharge of the four outlets are accumulated and named Touvre spring.

The Touvre karst system constitutes a strategic freshwater resource for drinking water supply (DWS) of Angoulême, with around 110,000 inhabitants, but also contributes to water supply for industry and agriculture. In 2015, there were 84 pumping wells over the karstic impluvium of the Touvre karst system, and around 100 more in the Tardoire, Bandiat, and Bonnieure rivers catchment. Based on the data provided by the Adour-Garonne Water Agency, the annual groundwater abstraction for agriculture represents 4.6 Mm³ whereas annual groundwater abstraction for DWS represents 1.1 Mm³ over the karstic impluvium of the Touvre karst system. On the three rivers catchment (out of the karstic impluvium), the annual groundwater abstraction represents 2.5 Mm³ for agriculture and 3.3 Mm³ for DWS, mainly through river intakes or alluvial groundwater abstraction. The total annual volume of abstracted groundwater in the area represents around 5% of the annual volume of transit at the Touvre spring. This is quite low compared with karst aquifers in France exploited for their groundwater resource, such as the Lez spring (Jourde et al., 2014) and the Oeillal's spring karst catchment (Sivelle et al., 2021), where the annual groundwater abstraction volume represents respectively 50% and 15% of annual volume of transit at the spring. Therefore, the Touvre catchment seems not to be over exploited at the moment but the impact of groundwater abstraction should be addressed in the actual context of global change to ensure a sustainable management of this strategic fresh water resource.

The area is characterized by an ocean influenced climate with a mean annual precipitation around 800 mm/year distributed over 255 rainy days. The estimation is performed with Thiessen polygon methods based on eleven meteorological stations over the area (Labat et al., 2022). The mean annual potential evapotranspiration is around 770 mm/year according to the Penman-Monteith estimation provided by the french meteorological survey (Météo-France). The Touvre spring discharge shows a significant variability ranging from 3 m³/s to 49 m³/s with a coefficient of variation around 0.46 (Figure 3, b). The surface
<figure><img src="image_12.png" /></figure>

stream flow rates for the Bonnieure, Bandiat and Tardoire rivers are concentrated within the autumn and winter periods. During the summer period, the discharge in the three rivers are very low (Figure 3, c). The more significant groundwater abstraction is performed during the summer period, while the Touvre spring discharge reaches its lowest values within the late summer and early autumn periods (Figure 3, c and d).

Figure 2 shows the model structure for the Touvre karst system that consists of three compartments organized in two levels (Labat et al., 2022). The upper level corresponds to reservoir E and represents both the unsaturated part of the system and a temporary aquifer. This reservoir is connected with the two reservoirs of the lower level: C (Conduit) and M (Matrix). The upper level of the model structure is affected by precipitation *P* and potential evapotranspiration *PET* while the lower level of the model structure is affected by (i) groundwater abstraction and (ii) sinking river stream-flow from the surface to underground.
Figure 3 shows the various time series required for the hydrological modeling of the Touvre karst system. The methodology for daily time series preparation given in Labat et al. (2022) allows to account for the influence of groundwater abstraction on transmissive or capacitive part of the karst aquifer as well as the influence of concentrated and diffuse infiltration of the surface river stream-flow.

<figure><img src="image_13.png" /><figcaption>**Figure 2.** Screenshot of KarstMod with a focus on the panel "Model structure" for the Touvre karst system. The solid lines correspond to the activated fluxes whereas the faded color lines are not activated. $Q_p^M$ and $Q_p^C$ stand for groundwater abstraction that affects compartments M and C respectively while $Q_s^M$ and $Q_s^C$ stand for sinking flow that affects compartments M and C respectively.</figcaption></figure>
<figure><img src="image_12.png" /></figure>

stream flow rates for the Bonnieure, Bandiat and Tardoire rivers are concentrated within the autumn and winter periods. During the summer period, the discharge in the three rivers are very low (Figure 3, c). The more significant groundwater abstraction is performed during the summer period, while the Touvre spring discharge reaches its lowest values within the late summer and early autumn periods (Figure 3, c and d).

Figure 2 shows the model structure for the Touvre karst system that consists of three compartments organized in two levels (Labat et al., 2022). The upper level corresponds to reservoir E and represents both the unsaturated part of the system and a temporary aquifer. This reservoir is connected with the two reservoirs of the lower level: C (Conduit) and M (Matrix). The upper level of the model structure is affected by precipitation *P* and potential evapotranspiration *PET* while the lower level of the model structure is affected by (i) groundwater abstraction and (ii) sinking river stream-flow from the surface to underground.
Figure 3 shows the various time series required for the hydrological modeling of the Touvre karst system. The methodology for daily time series preparation given in Labat et al. (2022) allows to account for the influence of groundwater abstraction on transmissive or capacitive part of the karst aquifer as well as the influence of concentrated and diffuse infiltration of the surface river stream-flow.

<figure><img src="image_13.png" /><figcaption>**Figure 2.** Screenshot of KarstMod with a focus on the panel "Model structure" for the Touvre karst system. The solid lines correspond to the activated fluxes whereas the faded color lines are not activated. $Q_p^M$ and $Q_p^C$ stand for groundwater abstraction that affects compartments M and C respectively while $Q_s^M$ and $Q_s^C$ stand for sinking flow that affects compartments M and C respectively.</figcaption></figure>
<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /><figcaption>**Figure 3.** Daily time series for the Touvre system: a) precipitation (P) and potential evapotranspiration (PET), b) observed and simulated karst spring discharge ($Q_{Touvre}$ obs and $Q_{Touvre}$ sim), c) river streamflow discharge ($Q_{Bonnieure}$, $Q_{Bandiat}$, $Q_{Tardoire}$), d) and e) groundwater abstraction discharge ($Q_p^{agriculture}$, $Q_p^{domestic}$)</figcaption></figure>

The objective of the hydrological modeling is to assess the impact of groundwater abstraction on spring discharge, and more particularly during low flow periods (Labat et al., 2022). So, the calibration is performed according to the *KGENP* that improve the simulations during mean and low-flow conditions using the Spearman rank correlation due to its insensitivity to extreme values (Pool et al., 2018). The sampling procedure is set up to find $n_{obj} = 5000$ simulations with *KGENP* greater than 0.9. Afterwards the model is evaluated using the various features proposed in KarstMod (Figure 4). The diagnostic efficiency plot (Figure 4 a) testifies of several elements: (i) the model seems to slightly overestimate high flow and underestimate low flow, (ii) the timing error is about 0.9, testifying of suitable flow dynamics in the model, (iii) low flow periods contribute more to the model errors, and (iv) there is no offset in the simulated spring hydrograph. The radar chart (Figure 4 b) shows a good equilibrium between the various objective functions which values are greater than 0.8, excepted for the *NSE* criteria (*NSE*
<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /><figcaption>**Figure 3.** Daily time series for the Touvre system: a) precipitation (P) and potential evapotranspiration (PET), b) observed and simulated karst spring discharge ($Q_{Touvre}$ obs and $Q_{Touvre}$ sim), c) river streamflow discharge ($Q_{Bonnieure}$, $Q_{Bandiat}$, $Q_{Tardoire}$), d) and e) groundwater abstraction discharge ($Q_p^{agriculture}$, $Q_p^{domestic}$)</figcaption></figure>

The objective of the hydrological modeling is to assess the impact of groundwater abstraction on spring discharge, and more particularly during low flow periods (Labat et al., 2022). So, the calibration is performed according to the *KGENP* that improve the simulations during mean and low-flow conditions using the Spearman rank correlation due to its insensitivity to extreme values (Pool et al., 2018). The sampling procedure is set up to find $n_{obj} = 5000$ simulations with *KGENP* greater than 0.9. Afterwards the model is evaluated using the various features proposed in KarstMod (Figure 4). The diagnostic efficiency plot (Figure 4 a) testifies of several elements: (i) the model seems to slightly overestimate high flow and underestimate low flow, (ii) the timing error is about 0.9, testifying of suitable flow dynamics in the model, (iii) low flow periods contribute more to the model errors, and (iv) there is no offset in the simulated spring hydrograph. The radar chart (Figure 4 b) shows a good equilibrium between the various objective functions which values are greater than 0.8, excepted for the *NSE* criteria (*NSE*
<figure><img src="image_16.png" /></figure>

= 0.75). It is the consequence of the design of this criteria that tends to overweight the errors during floods. Here the NSE value still greater than 0.7 and testifies of a "very good" fit according to Moriasi et al. (2007). Finally, the decomposition of the KGE (Figure 4 c and d) shows r<sub>p</sub> = 0.91, α = 1.15 and β = 1.02 testifying of accurate dynamics and low bias, but slightly too high variability.

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<figure><img src="image_17.png" /><figcaption>**Figure 4.** Screenshot of KarstMod with a focus on the sub-panel "Model evaluation". Application for the model evaluation on the Touvre system: (a) diagnostic efficiency plot (Schwemmle et al., 2021), (b) radar chart of the objective functions, (c) bi-plot of the *KGE*'s (square) and *KGENP*'s (triangle) components, and (d) radar chart of the *KGE*'s components.</figcaption></figure>

## 4.2 The Lez spring

The Lez spring (southern France) consists of the main outlet of a karst system encompassed in the North Montpellierian Garrigue hydrogeological unit delimited to the west by the Herault river, and to the north and east by the Vidourle river. The geology in the area corresponds to the Upper Jurassic layers separated by the Corconne-Matelle fault (oriented N30°), leading to two main compartments in the aquifer (Bérard, 1983; Clauzon et al., 2020). The karst aquifer is unconfined in the western compartment and is locally confined in the eastern compartment. The Lez spring is located about 15 km north of Montpellier. It is of Vauclusian-type with an overflow level at 65 m a.s.l, and a maximum discharge of approximately 15 m³/s. The area is characterized by a typical Mediterranean climate with dry summers and rainy autumns. Over the 2009-2019 period, the mean annual precipitation is around 900 mm/year distributed over 133 rainy days (estimation with Thiessen polygon methods based on four meteorological stations over the area: Prades le Lez, Saint Martin de Londres, Sauteyrargues and Valflaunes), a mean annual potential evapotranspiration is around 900 mm/year according to the estimation based on Oudin's formula with the temperature measured at Prades le Lez station while the mean annual evapotranspiration is around 450 mm/year (eddy covariance flux-station of Puéchabon).

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Since 1854, the Lez spring supplies the drinking water to Montpellier city and the surroundings. It currently constitutes the main fresh water resource for around 350,000 people in the area. The present water management scheme allows pumping at higher rates than the natural spring discharge during low flow periods, while supplying a minimum discharge rate (~ 230 l/s) into the Lez river to ensure ecological flow downstream, and reducing flood hazards via rainfall storage in autumn (Avias, 1995;

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<figure><img src="image_16.png" /></figure>

= 0.75). It is the consequence of the design of this criteria that tends to overweight the errors during floods. Here the NSE value still greater than 0.7 and testifies of a "very good" fit according to Moriasi et al. (2007). Finally, the decomposition of the KGE (Figure 4 c and d) shows r<sub>p</sub> = 0.91, α = 1.15 and β = 1.02 testifying of accurate dynamics and low bias, but slightly too high variability.

290

<figure><img src="image_17.png" /><figcaption>**Figure 4.** Screenshot of KarstMod with a focus on the sub-panel "Model evaluation". Application for the model evaluation on the Touvre system: (a) diagnostic efficiency plot (Schwemmle et al., 2021), (b) radar chart of the objective functions, (c) bi-plot of the *KGE*'s (square) and *KGENP*'s (triangle) components, and (d) radar chart of the *KGE*'s components.</figcaption></figure>

## 4.2 The Lez spring

The Lez spring (southern France) consists of the main outlet of a karst system encompassed in the North Montpellierian Garrigue hydrogeological unit delimited to the west by the Herault river, and to the north and east by the Vidourle river. The geology in the area corresponds to the Upper Jurassic layers separated by the Corconne-Matelle fault (oriented N30°), leading to two main compartments in the aquifer (Bérard, 1983; Clauzon et al., 2020). The karst aquifer is unconfined in the western compartment and is locally confined in the eastern compartment. The Lez spring is located about 15 km north of Montpellier. It is of Vauclusian-type with an overflow level at 65 m a.s.l, and a maximum discharge of approximately 15 m³/s. The area is characterized by a typical Mediterranean climate with dry summers and rainy autumns. Over the 2009-2019 period, the mean annual precipitation is around 900 mm/year distributed over 133 rainy days (estimation with Thiessen polygon methods based on four meteorological stations over the area: Prades le Lez, Saint Martin de Londres, Sauteyrargues and Valflaunes), a mean annual potential evapotranspiration is around 900 mm/year according to the estimation based on Oudin's formula with the temperature measured at Prades le Lez station while the mean annual evapotranspiration is around 450 mm/year (eddy covariance flux-station of Puéchabon).

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Since 1854, the Lez spring supplies the drinking water to Montpellier city and the surroundings. It currently constitutes the main fresh water resource for around 350,000 people in the area. The present water management scheme allows pumping at higher rates than the natural spring discharge during low flow periods, while supplying a minimum discharge rate (~ 230 l/s) into the Lez river to ensure ecological flow downstream, and reducing flood hazards via rainfall storage in autumn (Avias, 1995;

305
<figure><img src="image_18.png" /></figure>

Jourde et al., 2014). The pumping plant was built in 1982 with four deep wells drilled to intercept the karst conduit feeding the spring, 48 m below the overflow level of the spring. Pumping in these wells allows up to 1800 l/s to be withdrawn under low flow periods (with an authorized maximum drawdown of 30 m), while the average annual pumping flow rate is about 1010 l/s (over the 2008-2019 period). Due to the pumping management of the aquifer, which supplies about 30 to 35 Mm³ of water per year to the metropolitan area of Montpellier, the discharge at the Lez spring is often low or nil.

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In the present context of global change, Mediterranean karst systems already show significant decrease in spring discharge (Hartmann et al., 2012; Fiorillo et al., 2012; Smiatek et al., 2013; Doummar et al., 2018b; Nerantzaki and Nikolaidis, 2020; Dubois et al., 2020) which could be aggravated with groundwater abstraction (Sivelle et al., 2021). The Lez spring is strongly exposed to global change impact: (i) the Mediterranean area is identified as a climate change hot-spot (Diffenbaugh and Giorgi, 2012) where the projected warming spans 1.83–8.49°C according to CMIP6 and 1.22–6.63°C according to CMIP5 during the summer period (Cos et al., 2022), and (ii) the water management scheme will have to adapt to the future need in drinking water for the growing population in the area as well as changes in the fresh water consumption practice (e.g. water use restriction order). Therefore, a sustainable water management plan for the Lez spring requires a good appreciation of the hydrological functioning as well as operational hydrological model to properly address impacts studies. In this framework, KarstMod allows choosing and calibrating a suitable model structure. This constitutes a first step for global change impact study that requires prediction tools to simulate the aquifer response to various external forcing.

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Figure 5 shows the model structure for the Lez karst catchment (Mazzilli et al., 2011) that consists of three compartments organized in two levels. The upper level corresponds to compartment E and represents the unsaturated part of the system, including a soil water holding capacity $E_{min}$ and a discharge lost from the compartment $Q_{loss}$. The compartment E is exposed to precipitation P and evapotranspiration ET and discharge towards the lower level of the model structure starts when the water level exceeds the water holding $E_{min}$. The lower level consists of two inter-connected compartments M and C allowing to reproduce the lateral exchanges, denoted $Q_{MC}$, between transmissive function (compartment C) and capacitive function (compartment M) of the karst aquifer. Both M and C compartments are considered bottomless, allowing to reproduce period of non-overflow at the Lez spring when the mean water level in the aquifer stands below 65 m a.s.l., mainly during summer periods due to pumping in the karst conduit. Figures 6a and 6b show the various daily time series required for the hydrological modeling of the Lez karst system (i.e. P, ET and $Q_{pump}$).

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<figure><img src="image_18.png" /></figure>

Jourde et al., 2014). The pumping plant was built in 1982 with four deep wells drilled to intercept the karst conduit feeding the spring, 48 m below the overflow level of the spring. Pumping in these wells allows up to 1800 l/s to be withdrawn under low flow periods (with an authorized maximum drawdown of 30 m), while the average annual pumping flow rate is about 1010 l/s (over the 2008-2019 period). Due to the pumping management of the aquifer, which supplies about 30 to 35 Mm³ of water per year to the metropolitan area of Montpellier, the discharge at the Lez spring is often low or nil.

310

In the present context of global change, Mediterranean karst systems already show significant decrease in spring discharge (Hartmann et al., 2012; Fiorillo et al., 2012; Smiatek et al., 2013; Doummar et al., 2018b; Nerantzaki and Nikolaidis, 2020; Dubois et al., 2020) which could be aggravated with groundwater abstraction (Sivelle et al., 2021). The Lez spring is strongly exposed to global change impact: (i) the Mediterranean area is identified as a climate change hot-spot (Diffenbaugh and Giorgi, 2012) where the projected warming spans 1.83–8.49°C according to CMIP6 and 1.22–6.63°C according to CMIP5 during the summer period (Cos et al., 2022), and (ii) the water management scheme will have to adapt to the future need in drinking water for the growing population in the area as well as changes in the fresh water consumption practice (e.g. water use restriction order). Therefore, a sustainable water management plan for the Lez spring requires a good appreciation of the hydrological functioning as well as operational hydrological model to properly address impacts studies. In this framework, KarstMod allows choosing and calibrating a suitable model structure. This constitutes a first step for global change impact study that requires prediction tools to simulate the aquifer response to various external forcing.

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Figure 5 shows the model structure for the Lez karst catchment (Mazzilli et al., 2011) that consists of three compartments organized in two levels. The upper level corresponds to compartment E and represents the unsaturated part of the system, including a soil water holding capacity $E_{min}$ and a discharge lost from the compartment $Q_{loss}$. The compartment E is exposed to precipitation P and evapotranspiration ET and discharge towards the lower level of the model structure starts when the water level exceeds the water holding $E_{min}$. The lower level consists of two inter-connected compartments M and C allowing to reproduce the lateral exchanges, denoted $Q_{MC}$, between transmissive function (compartment C) and capacitive function (compartment M) of the karst aquifer. Both M and C compartments are considered bottomless, allowing to reproduce period of non-overflow at the Lez spring when the mean water level in the aquifer stands below 65 m a.s.l., mainly during summer periods due to pumping in the karst conduit. Figures 6a and 6b show the various daily time series required for the hydrological modeling of the Lez karst system (i.e. P, ET and $Q_{pump}$).

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<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /><figcaption>**Figure 5.** Screenshot of KarstMod with a focus on the panel "Model structure" for the Lez karst system. The solid lines correspond to the activated fluxes whereas the faded color lines are not activated. $Q_{loss}$ stands for the surface discharge from the epikarst compartment, $Q_p^C$ stands for groundwater abstraction that affects compartments C while $Z_C$ stands for piezometric head measurements considered as representative of the compartment C.</figcaption></figure>
<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /><figcaption>**Figure 5.** Screenshot of KarstMod with a focus on the panel "Model structure" for the Lez karst system. The solid lines correspond to the activated fluxes whereas the faded color lines are not activated. $Q_{loss}$ stands for the surface discharge from the epikarst compartment, $Q_p^C$ stands for groundwater abstraction that affects compartments C while $Z_C$ stands for piezometric head measurements considered as representative of the compartment C.</figcaption></figure>
<figure><img src="image_21.png" /></figure>

<figure><img src="image_22.png" /><figcaption>**Figure 6.** Daily time series for the Lez system: a) precipitations (P) and evapotranspiration (ET), b) groundwater abstraction ($Q_{pump}$), c) observed and simulated karst spring discharge ($Q_{Lez \text{ obs}}$ and $Q_{Lez \text{ sim}}$), d) observed and simulated piezometric head ($Z_{Lez \text{ obs}}$ and $Z_{Lez \text{ sim}}$), e) surface water discharge ($Q_{loss}$) and f) simulated exchanges fluxes between compartment M and C ($Q_{MC}$).</figcaption></figure>

The available hydrological observations for model calibration consist of spring discharge $Q_S$, piezometric head measurement $Z_C$ at the Lez spring and surface water discharge from secondary outlets and intermittent springs $Q_{loss}$ (Figure 6, c, d and e). The surface water discharge is estimated as the difference in discharge measured at the Lavalette station (15 km downstream the Lez spring) and the discharge measured at the Lez spring, as performed in Cousquer and Jourde Cousquer and Jourde (2022). Therefore, $Q_{loss}$ includes all the water loss from the epikarst within several seasonal overflowing springs (i.e. Lirou spring, Restinclière spring and Fleurette spring). KarstMod allows to easily handle with the various parameter estimation depending on the considered hydrological observations (i.e. spring discharge, piezometric head measurement, and surface discharge from the epikarst). The sampling procedure is set up to find $n_{obj} = 5000$ simulations with an aggregated objective function $\Phi$ greater than 0.6. As suggested by Cousquer and Jourde (2022), using complementary hydrological observations in addition to the

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<figure><img src="image_21.png" /></figure>

<figure><img src="image_22.png" /><figcaption>**Figure 6.** Daily time series for the Lez system: a) precipitations (P) and evapotranspiration (ET), b) groundwater abstraction ($Q_{pump}$), c) observed and simulated karst spring discharge ($Q_{Lez \text{ obs}}$ and $Q_{Lez \text{ sim}}$), d) observed and simulated piezometric head ($Z_{Lez \text{ obs}}$ and $Z_{Lez \text{ sim}}$), e) surface water discharge ($Q_{loss}$) and f) simulated exchanges fluxes between compartment M and C ($Q_{MC}$).</figcaption></figure>

The available hydrological observations for model calibration consist of spring discharge $Q_S$, piezometric head measurement $Z_C$ at the Lez spring and surface water discharge from secondary outlets and intermittent springs $Q_{loss}$ (Figure 6, c, d and e). The surface water discharge is estimated as the difference in discharge measured at the Lavalette station (15 km downstream the Lez spring) and the discharge measured at the Lez spring, as performed in Cousquer and Jourde Cousquer and Jourde (2022). Therefore, $Q_{loss}$ includes all the water loss from the epikarst within several seasonal overflowing springs (i.e. Lirou spring, Restinclière spring and Fleurette spring). KarstMod allows to easily handle with the various parameter estimation depending on the considered hydrological observations (i.e. spring discharge, piezometric head measurement, and surface discharge from the epikarst). The sampling procedure is set up to find $n_{obj} = 5000$ simulations with an aggregated objective function $\Phi$ greater than 0.6. As suggested by Cousquer and Jourde (2022), using complementary hydrological observations in addition to the

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<figure><img src="image_23.png" /></figure>

spring discharge allows to reduce the parametric uncertainties in the modeling of the Lez spring discharge. Therefore, using a multi-objective calibration procedure implemented in KarstMod, the objective function is build such as:

$$ \Phi = \frac{1}{3} \times NSE(Q_s) + \frac{1}{3} \times NSE(Z_C) + \frac{1}{3} \times NSE(Q_{loss}) \quad (4) $$

The calibration procedure leads to an optimal $\Phi = 0.65$ decomposed such as $\phi Q_s = 0.70$, $\phi Z_C = 0.57$ and $\phi Q_{loss} = 0.70$ within the calibration period. Model performance evaluation on the validation period shows suitable model performance for both spring discharge and piezometric with $\phi Q_s = 0.54$ and $\phi Z_C = 0.79$, but poor model performance according to the surface water discharge with $\phi Q_{loss} = 0.36$. Afterwards the results can be evaluated using the various features proposed in KarstMod (Figure 7). The results show higher model performances for $Q_s$ and $Z_C$ than for $Q_{loss}$. The model performance appears quite satisfactorily concerning the variable of interest to assess the impact of water management scheme on the groundwater resources within the Lez aquifer.

The simulated exchanges fluxes between compartment M and C (Figure 6f) show consistent dynamics with the observations. Indeed, during periods of high flow the exchange fluxes are oriented from the compartment C to compartment M (i.e. $Q_{MC} < 0$). Significant precipitation events lead to rapid rises in piezometric head, saturation of the transmissive part of the aquifer and finally the establishment of overflow at the Lez spring (i.e. $Q_s > 0$) as well as the overflowing springs (i.e. $Q_{loss} > 0$). Conversely, during the periods of low piezometric head (i.e. both $Q_s$ and $Q_{loss}$ are nil), the simulated exchange fluxes are oriented from compartment M to compartment C (i.e. $Q_{MC} < 0$). Such flow exchanges between capacitive and transmissive part of karst aquifers has been evidenced using KarstMod on other karst environment (Sivelle et al., 2019; Duran et al., 2020; Frank et al., 2021; Labat et al., 2022).
<figure><img src="image_23.png" /></figure>

spring discharge allows to reduce the parametric uncertainties in the modeling of the Lez spring discharge. Therefore, using a multi-objective calibration procedure implemented in KarstMod, the objective function is build such as:

$$ \Phi = \frac{1}{3} \times NSE(Q_s) + \frac{1}{3} \times NSE(Z_C) + \frac{1}{3} \times NSE(Q_{loss}) \quad (4) $$

The calibration procedure leads to an optimal $\Phi = 0.65$ decomposed such as $\phi Q_s = 0.70$, $\phi Z_C = 0.57$ and $\phi Q_{loss} = 0.70$ within the calibration period. Model performance evaluation on the validation period shows suitable model performance for both spring discharge and piezometric with $\phi Q_s = 0.54$ and $\phi Z_C = 0.79$, but poor model performance according to the surface water discharge with $\phi Q_{loss} = 0.36$. Afterwards the results can be evaluated using the various features proposed in KarstMod (Figure 7). The results show higher model performances for $Q_s$ and $Z_C$ than for $Q_{loss}$. The model performance appears quite satisfactorily concerning the variable of interest to assess the impact of water management scheme on the groundwater resources within the Lez aquifer.

The simulated exchanges fluxes between compartment M and C (Figure 6f) show consistent dynamics with the observations. Indeed, during periods of high flow the exchange fluxes are oriented from the compartment C to compartment M (i.e. $Q_{MC} < 0$). Significant precipitation events lead to rapid rises in piezometric head, saturation of the transmissive part of the aquifer and finally the establishment of overflow at the Lez spring (i.e. $Q_s > 0$) as well as the overflowing springs (i.e. $Q_{loss} > 0$). Conversely, during the periods of low piezometric head (i.e. both $Q_s$ and $Q_{loss}$ are nil), the simulated exchange fluxes are oriented from compartment M to compartment C (i.e. $Q_{MC} < 0$). Such flow exchanges between capacitive and transmissive part of karst aquifers has been evidenced using KarstMod on other karst environment (Sivelle et al., 2019; Duran et al., 2020; Frank et al., 2021; Labat et al., 2022).
<figure><img src="image_24.png" /></figure>

<figure><img src="image_25.png" /><figcaption>**Figure 7.** Screenshot of KarstMod with a focus on the sub-panel "Model evaluation". Application for the model evaluation on the Lez system. The panel is composed such as (i) each row correspond to the variable for calibration ($Q_S$, $Q_{loss}$ and $Z_C$) and (ii) each columns corresponds to (a) diagnostic efficiency plot, (b) radar plots, one should note that VE and BE are not computed according to the piezometric time series, (c) decomposition of KGE (square) and KGENP (triangle) and (d) radar plot of the KGE decomposition.</figcaption></figure>

# 5 Conclusions

KarstMod consists in a useful tool for the assessment of karst groundwater variability and sensitivity to anthropogenic pressures (e.g. groundwater abstraction). This tool is devoted to promote good practices in hydrological modeling for learning and occasional users. KarstMod requires no programming skills and offers a user friendly interface allowing any user to easily handle hydrological modeling. As a first step, KarstMod can be used to explore the ability of conceptual representations to explain observations such as discharge or piezometric heads in karst systems. A more advanced use of KarstMod is also possible as it provides a complete framework for (i) primary analysis of the data, (ii) comparison of various model structures, (iii) evaluation of the hydrological model performance as well as (iv) first assessment of parametric uncertainties. The research community increasingly uses KarstMod to address various challenges in karst hydrology, from understanding hydrological processes to practical applications such as evaluation of groundwater management plan, or even assessment of the impact of groundwater abstraction and climate changes on karst groundwater resources.

Future developments of KarstMod might include: (i) the consideration of land cover land use (LCLU) to consider the spatial heterogeneity in recharge processes (Sivelle et al., 2022a), (ii) the simulation of electrical conductivity (Chang et al., 2021), major ions concentration (Hartmann et al., 2013) or natural tracer such as air excess (Sivelle et al., 2022b), and (iii) the assessment of structural uncertainty (Cousquer et al., 2022). KarstMod should tend toward an open-source research software to avoid duplication of efforts in karst hydrological modeling. Also, a Python version is required for a better connection with additional framework for sensitivity analysis such as SAFE toolbox (Pianosi et al., 2015) and for model calibration
<figure><img src="image_24.png" /></figure>

<figure><img src="image_25.png" /><figcaption>**Figure 7.** Screenshot of KarstMod with a focus on the sub-panel "Model evaluation". Application for the model evaluation on the Lez system. The panel is composed such as (i) each row correspond to the variable for calibration ($Q_S$, $Q_{loss}$ and $Z_C$) and (ii) each columns corresponds to (a) diagnostic efficiency plot, (b) radar plots, one should note that VE and BE are not computed according to the piezometric time series, (c) decomposition of KGE (square) and KGENP (triangle) and (d) radar plot of the KGE decomposition.</figcaption></figure>

# 5 Conclusions

KarstMod consists in a useful tool for the assessment of karst groundwater variability and sensitivity to anthropogenic pressures (e.g. groundwater abstraction). This tool is devoted to promote good practices in hydrological modeling for learning and occasional users. KarstMod requires no programming skills and offers a user friendly interface allowing any user to easily handle hydrological modeling. As a first step, KarstMod can be used to explore the ability of conceptual representations to explain observations such as discharge or piezometric heads in karst systems. A more advanced use of KarstMod is also possible as it provides a complete framework for (i) primary analysis of the data, (ii) comparison of various model structures, (iii) evaluation of the hydrological model performance as well as (iv) first assessment of parametric uncertainties. The research community increasingly uses KarstMod to address various challenges in karst hydrology, from understanding hydrological processes to practical applications such as evaluation of groundwater management plan, or even assessment of the impact of groundwater abstraction and climate changes on karst groundwater resources.

Future developments of KarstMod might include: (i) the consideration of land cover land use (LCLU) to consider the spatial heterogeneity in recharge processes (Sivelle et al., 2022a), (ii) the simulation of electrical conductivity (Chang et al., 2021), major ions concentration (Hartmann et al., 2013) or natural tracer such as air excess (Sivelle et al., 2022b), and (iii) the assessment of structural uncertainty (Cousquer et al., 2022). KarstMod should tend toward an open-source research software to avoid duplication of efforts in karst hydrological modeling. Also, a Python version is required for a better connection with additional framework for sensitivity analysis such as SAFE toolbox (Pianosi et al., 2015) and for model calibration
<figure><img src="image_26.png" /></figure>

procedure such as particle swarm optimization (Eberhart and Kennedy, 1995; Lee, 2014). Finally, the development of the KarstMod modeling platform will benefit better transparency and repeatability with an open-source approach, as observed on other numerical tools (Pianosi et al., 2020).

## Appendix A: Snow routine

Figure A1 shows the general workflow implemented in the snow routine. $Psr^*$ (liquid water leaving the routine) is estimated for each time step $t$ based on the precipitation $P$ and air temperature $T$ time series for each sub-catchment. The total snow routine output $Psr$ is calculated as a weighted sum of $Psr^*$ time series:

$$Psr = \sum_{i}^{N} Psr_{i}^{*} \times p_{i} \qquad (A1)$$

where $p_i$ is the proportion of the sub-catchment $i$ regarding the complete catchment area such as $\sum p_i = 1$, and $N$ is total number of sub-catchments.

The snow routine requires four parameters, whose values are the same for all subcatchments: the snowmelt temperature threshold $Ts$ [°C], the melt factor $MF$ [L.T$^{-1}$.°C$^{-1}$], the refreezing factor $CFR$ [-], and the water holding capacity of snow $CWH$ [-]. The snow routine allows estimating $Psr^*$ according to the algorithm A1.

<figure><img src="image_27.png" /><figcaption>Figure A1. Snow routine workflow.</figcaption></figure>
<figure><img src="image_26.png" /></figure>

procedure such as particle swarm optimization (Eberhart and Kennedy, 1995; Lee, 2014). Finally, the development of the KarstMod modeling platform will benefit better transparency and repeatability with an open-source approach, as observed on other numerical tools (Pianosi et al., 2020).

## Appendix A: Snow routine

Figure A1 shows the general workflow implemented in the snow routine. $Psr^*$ (liquid water leaving the routine) is estimated for each time step $t$ based on the precipitation $P$ and air temperature $T$ time series for each sub-catchment. The total snow routine output $Psr$ is calculated as a weighted sum of $Psr^*$ time series:

$$Psr = \sum_{i}^{N} Psr_{i}^{*} \times p_{i} \qquad (A1)$$

where $p_i$ is the proportion of the sub-catchment $i$ regarding the complete catchment area such as $\sum p_i = 1$, and $N$ is total number of sub-catchments.

The snow routine requires four parameters, whose values are the same for all subcatchments: the snowmelt temperature threshold $Ts$ [°C], the melt factor $MF$ [L.T$^{-1}$.°C$^{-1}$], the refreezing factor $CFR$ [-], and the water holding capacity of snow $CWH$ [-]. The snow routine allows estimating $Psr^*$ according to the algorithm A1.

<figure><img src="image_27.png" /><figcaption>Figure A1. Snow routine workflow.</figcaption></figure>
<figure><img src="image_28.png" /></figure>

**Algorithm A1 Estimating Psr\* in sub-catchment**

With $Psr\* = $ water leaving the routine/recharge to the soil (mm/dt), $T_a = $ active temperature for snowmelt (°C), $T_n = $ active temperature for refreezing (°C), $m = $ snow melt (mm/dt), $rfz = $ refreezing (mm/dt), $v = $ solid component of snowpack depth (mm), $vl = $ liquid component of snowpack depth (mm), and $dt = $ temporal resolution.

for $t=1$ to $t_{max}$ do

$$m[t] = \min((MF \times T_a[t]), v[t])$$

$$rfz[t] = \min(CFR \times MF \times T_n[t], vl[t])$$

$$v[t + dt] = v[t] - m[t] + snow[t] + rfz[t]$$

if $vl[t + dt] > CWH \times v[t + dt]$ then

$$Psr\*[t] = vl[t + dt] - CWH \times v[t + dt]$$

$$vl[t + dt] = CWH \times v[t + dt]$$

else

$$Psr\*[t] = 0$$

end

end

*Code availability.* The KarstMod modeling platform is developed and made freely accessible within the framework of the KARST observatory network (SNO KARST) initiative from the INSU/CNRS. The platform can be downloaded here: https://sokarst.org/en/softwares-en/karstmod-en/

*Author contributions.* V. Sivelle: methodology, software, writing—original draft. G. Cinkus: methodology, software, writing—review and editing. N. Mazzilli: methodology, software, project administration, writing—review and editing. H. Jourde: methodology, software, project administration, funding acquisition, writing—review and editing. D. Labat: methodology, software, writing—review and editing. B. Arfib: methodology, software, writing—review and editing. N. Massei: methodology, software, writing—review and editing. Y. Cousquer: writing—review and editing. D. Bertin: methodology, software, writing—review and editing.

*Competing interests.* The authors declare no competing interest.

*Acknowledgements.* This platform is developed within the framework of the KARST observatory network (SNO KARST) initiative from the INSU/CNRS (France), which aims to strengthen knowledge-sharing and promote crossdisciplinary research on karst systems at the national scale. This work, as well as V. Sivelle post-doctoral position, was supported by the European Commission through the Partnership for Research and Innovation in the Mediterranean Area (PRIMA) program under Horizon 2020 (KARMA project, grant agreement number 01DH19022A).
<figure><img src="image_28.png" /></figure>

**Algorithm A1 Estimating $Psr^*$ in sub-catchment**

With $Psr^* = $ water leaving the routine/recharge to the soil (mm/dt), $T_a = $ active temperature for snowmelt (°C), $T_n = $ active temperature for refreezing (°C), $m = $ snow melt (mm/dt), $rfz = $ refreezing (mm/dt), $v = $ solid component of snowpack depth (mm), $vl = $ liquid component of snowpack depth (mm), and $dt = $ temporal resolution.

for $t=1$ to $t_{max}$ do

$$m[t] = \min((MF \times T_a[t]), v[t])$$

$$rfz[t] = \min(CFR \times MF \times T_n[t], vl[t])$$

$$v[t + dt] = v[t] - m[t] + snow[t] + rfz[t]$$

if $vl[t + dt] > CWH \times v[t + dt]$ then

$$Psr^*[t] = vl[t + dt] - CWH \times v[t + dt]$$

$$vl[t + dt] = CWH \times v[t + dt]$$

else

$$Psr^*[t] = 0$$

end

end

*Code availability.* The KarstMod modeling platform is developed and made freely accessible within the framework of the KARST observatory network (SNO KARST) initiative from the INSU/CNRS. The platform can be downloaded here: https://sokarst.org/en/softwares-en/karstmod-en/

**Author contributions.** V. Sivelle: methodology, software, writing—original draft. G. Cinkus: methodology, software, writing—review and editing. N. Mazzilli: methodology, software, project administration, writing—review and editing. H. Jourde: methodology, software, project administration, funding acquisition, writing—review and editing. D. Labat: methodology, software, writing—review and editing. B. Arfib: methodology, software, writing—review and editing. N. Massei: methodology, software, writing—review and editing. Y. Cousquer: writing—review and editing. D. Bertin: methodology, software, writing—review and editing.

**Competing interests.** The authors declare no competing interest.

*Acknowledgements.* This platform is developed within the framework of the KARST observatory network (SNO KARST) initiative from the INSU/CNRS (France), which aims to strengthen knowledge-sharing and promote crossdisciplinary research on karst systems at the national scale. This work, as well as V. Sivelle post-doctoral position, was supported by the European Commission through the Partnership for Research and Innovation in the Mediterranean Area (PRIMA) program under Horizon 2020 (KARMA project, grant agreement number 01DH19022A).
<figure><img src="image_29.png" /></figure>

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Beven, K.: On explanatory depth and predictive power, Hydrological Processes, 15, 3069–3072, https://doi.org/10.1002/hyp.500, _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/hyp.500, 2001.

Beven, K.: A manifesto for the equifinality thesis, Journal of Hydrology, 320, 18–36, https://doi.org/10.1016/j.jhydrol.2005.07.007, 2006.

Bierkens, M. F. P. and Wada, Y.: Non-renewable groundwater use and groundwater depletion: a review, Environmental Research Letters, 14, 063 002, https://doi.org/10.1088/1748-9326/ab1a5f, publisher: IOP Publishing, 2019.

Bittner, D., Narany, T. S., Kohl, B., Disse, M., and Chiogna, G.: Modeling the hydrological impact of land use change in a dolomite-dominated karst system, Journal of Hydrology, 567, 267–279, https://doi.org/10.1016/j.jhydrol.2018.10.017, 2018.

Bittner, D., Richieri, B., and Chiogna, G.: Unraveling the time-dependent relevance of input model uncertainties for a lumped hydrologic model of a pre-alpine karst system, Hydrogeology Journal, https://doi.org/10.1007/s10040-021-02377-1, 2021.

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<figure><img src="image_29.png" /></figure>

## References

Andréassian, V.: On the (im)possible validation of hydrogeological models, Comptes Rendus. Géoscience, 355, 1–9, https://doi.org/10.5802/crgeos.142, 2023.

Avias, J. V.: Gestion active de l'exsurgence karstique de la Source du Lez (Hérault, France) 1957-1994, Hydrogéologie (Orléans), pp. 113-127, http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=6307091, 1995.

Bennett, N. D., Croke, B. F., Guariso, G., Guillaume, J. H., Hamilton, S. H., Jakeman, A. J., Marsili-Libelli, S., Newham, L. T., Norton, J. P., Perrin, C., Pierce, S. A., Robson, B., Seppelt, R., Voinov, A. A., Fath, B. D., and Andreassian, V.: Characterising performance of environmental models, Environmental Modelling & Software, 40, 1–20, https://doi.org/10.1016/j.envsoft.2012.09.011, 2013.

Bergström, S.: The HBV model – its structure and applications, SMHI, https://www.smhi.se/polopoly_fs/1.83592!/Menu/general/extGroup/attachmentColHold/mainCol1/file/RH_4.pdf, 1992.

Beven, K.: On explanatory depth and predictive power, Hydrological Processes, 15, 3069–3072, https://doi.org/10.1002/hyp.500, _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/hyp.500, 2001.

Beven, K.: A manifesto for the equifinality thesis, Journal of Hydrology, 320, 18–36, https://doi.org/10.1016/j.jhydrol.2005.07.007, 2006.

Bierkens, M. F. P. and Wada, Y.: Non-renewable groundwater use and groundwater depletion: a review, Environmental Research Letters, 14, 063 002, https://doi.org/10.1088/1748-9326/ab1a5f, publisher: IOP Publishing, 2019.

Bittner, D., Narany, T. S., Kohl, B., Disse, M., and Chiogna, G.: Modeling the hydrological impact of land use change in a dolomite-dominated karst system, Journal of Hydrology, 567, 267–279, https://doi.org/10.1016/j.jhydrol.2018.10.017, 2018.

Bittner, D., Richieri, B., and Chiogna, G.: Unraveling the time-dependent relevance of input model uncertainties for a lumped hydrologic model of a pre-alpine karst system, Hydrogeology Journal, https://doi.org/10.1007/s10040-021-02377-1, 2021.

Blöschl, G. and Sivapalan, M.: Scale issues in hydrological modelling: A review, Hydrological Processes, 9, 251–290, https://doi.org/10.1002/hyp.3360090305, 1995.

Blöschl, G., Bierkens, M. F., Chambel, A., Cudennec, C., Destouni, G., Fiori, A., Kirchner, J. W., McDonnell, J. J., Savenije, H. H., Sivapalan, M., Stumpp, C., Toth, E., Volpi, E., Carr, G., Lupton, C., Salinas, J., Széles, B., Viglione, A., Aksoy, H., Allen, S. T., Amin, A., Andréassian, V., Arheimer, B., Aryal, S. K., Baker, V., Bardsley, E., Barendrecht, M. H., Bartosova, A., Batelaan, O., Berghuijs, W. R., Beven, K., Blume, T., Bogaard, T., Borges de Amorim, P., Böttcher, M. E., Boulet, G., Breinl, K., Brilly, M., Brocca, L., Buytaert, W., Castellarin, A., Castelletti, A., Chen, X., Chen, Y., Chen, Y., Chifflard, P., Claps, P., Clark, M. P., Collins, A. L., Croke, B., Dathe, A., David, P. C., de Barros, F. P. J., de Rooij, G., Di Baldassarre, G., Driscoll, J. M., Duethmann, D., Dwivedi, R., Eris, E., Farmer, W. H., Feiccabrino, J., Ferguson, G., Ferrari, E., Ferraris, S., Fersch, B., Finger, D., Foglia, L., Fowler, K., Gartsman, B., Gascoin, S., Gaume, E., Gelfan, A., Geris, J., Gharari, S., Gleeson, T., Glendell, M., Gonzalez Bevacqua, A., González-Dugo, M. P., Grimaldi, S., Gupta, A. B., Guse, B., Han, D., Hannah, D., Harpold, A., Haun, S., Heal, K., Helfricht, K., Herrnegger, M., Hipsey, M., Hlaváčiková, H., Hohmann, C., Holko, L., Hopkinson, C., Hrachowitz, M., Illangasekare, T. H., Inam, A., Innocente, C., Istanbulluoglu, E., Jarihani, B., Kalantari, Z., Kalvans, A., Khanal, S., Khatami, S., Kiesel, J., Kirkby, M., Knoben, W., Kochanek, K., Kohnová, S., Kolechkina, A., Krause, S., Kreamer, D., Kreibich, H., Kunstmann, H., Lange, H., Liberato, M. L. R., Lindquist, E., Link, T., Liu, J., Loucks, D. P., Luce, C., Mahé, G., Makarieva, O., Malard, J., Mashtayeva, S., Maskey, S., Mas-Pla, J., Mavrova-Guirguinova, M., Mazzoleni, M., Mernild, S., Misstear, B. D., Montanari, A., Müller-Thomy, H., Nabizadeh, A., Nardi, F., Neale, C., Nesterova, N., Nurtaev, B., Odongo, V. O., Panda, S., Pande, S., Pang, Z., Papacharalampous, G., Perrin, C., Pfister, L., Pimentel, R., Polo, M. J., Post, D., Prieto Sierra, C., Ramos, M.-H., Renner, M., Reynolds, J. E., Ridolfi, E., Rigon, R., Riva, M., Robertson, D. E., Rosso, R., Roy, T., Sá, J. H., Salvadori, G., Sandells, M., Schaeфli,
<figure><img src="image_30.png" /></figure>

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455

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460

Chen, Z., Hartmann, A., Wagener, T., and Goldscheider, N.: Dynamics of water fluxes and storages in an Alpine karst catchment under current and potential future climate conditions, Hydrology and Earth System Sciences, 22, 3807–3823, https://doi.org/10.5194/hess-22-3807-2018, publisher: Copernicus GmbH, 2018.

Cinkus, G., Mazzilli, N., Jourde, H., Wunsch, A., Liesch, T., Ravbar, N., Chen, Z., and Goldscheider, N.: When best is the enemy of good; critical evaluation of performance criteria in hydrological models, Hydrology and Earth System Sciences Discussions, pp. 1–25, https://doi.org/10.5194/hess-2022-380, publisher: Copernicus GmbH, 2022a.

465

Cinkus, G., Wunsch, A., Mazzilli, N., Liesch, T., Chen, Z., Ravbar, N., Doummar, J., Fernández-Ortega, J., Barberá, J. A., Andreo, B., Goldscheider, N., and Jourde, H.: Comparison of artificial neural networks and reservoir models for simulating karst spring discharge on five test sites in the Alpine and Mediterranean regions, Hydrology and Earth System Sciences Discussions, pp. 1–41, https://doi.org/10.5194/hess-2022-365, publisher: Copernicus GmbH, 2022b.

Clauzon, V., Mayolle, S., Leonardi, V., Brunet, P., Soliva, R., Marchand, P., Massonnat, G., Rolando, J.-P., and Pistre, S.: Fault zones in limestones: impact on karstogenesis and groundwater flow (Lez aquifer, southern France), Hydrogeology Journal, https://doi.org/10.1007/s10040-020-02189-9, 2020.

470

Cos, J., Doblas-Reyes, F., Jury, M., Marcos, R., Bretonnière, P.-A., and Samsó, M.: The Mediterranean climate change hotspot in the CMIP5 and CMIP6 projections, Earth System Dynamics, 13, 321–340, https://doi.org/10.5194/esd-13-321-2022, publisher: Copernicus GmbH, 2022.

Cousquer, Y. and Jourde, H.: Reducing Uncertainty of Karst Aquifer Modeling with Complementary Hydrological Observations for the Sustainable Management of Groundwater Resources, Journal of Hydrology, p. 128130, https://doi.org/10.1016/j.jhydrol.2022.128130, 2022.

475

Cousquer, Y., Sivelle, V., and Jourde, H.: Estimating the Structural Uncertainty of Lumped Parameter Models in Karst Hydrology: a Bayesian Model Averaging (BMA), Tech. Rep. IAHS2022-522, Copernicus Meetings, https://meetingorganizer.copernicus.org/IAHS2022/IAHS2022-522.html, conference Name: IAHS2022, 2022.
<figure><img src="image_30.png" /></figure>

B., Schumann, A., Scolobig, A., Seibert, J., Servat, E., Shafiei, M., Sharma, A., Sidibe, M., Sidle, R. C., Skaugen, T., Smith, H., Spiessl, S. M., Stein, L., Steinsland, I., Strasser, U., Su, B., Szolgay, J., Tarboton, D., Tauro, F., Thirel, G., Tian, F., Tong, R., Tussupova, K., Tyralis, H., Uijlenhoet, R., van Beek, R., van der Ent, R. J., van der Ploeg, M., Van Loon, A. F., van Meerveld, I., van Nooijen, R., van Oel, P. R., Vidal, J.-P., von Freyberg, J., Vorogushyn, S., Wachniew, P., Wade, A. J., Ward, P., Westerberg, I. K., White, C., Wood, E. F., Woods, R., Xu, Z., Yilmaz, K. K., and Zhang, Y.: Twenty-three unsolved problems in hydrology (UPH) – a community perspective, Hydrological Sciences Journal, 64, 1141–1158, https://doi.org/10.1080/02626667.2019.1620507, 2019.

445

Bérard, P.: Alimentation en eau de la ville de Montpellier: captage de la source du Lez—etude des relations entre la source et son réservoir aquifère [Water supply of Montpellier: Lez Spring catchment—study of the relationship between the spring and its aquifer], Tech. rep., BRGM, Montpellier, France, http://infoterre.brgm.fr/rapports/84-AGI-171-LRO-EAU.pdf, 1983.

450

Chang, Y., Hartmann, A., Liu, L., Jiang, G., and Wu, J.: Identifying More Realistic Model Structures by Electrical Conductivity Observations of the Karst Spring, Water Resources Research, 57, e2020WR028587, https://doi.org/10.1029/2020WR028587, _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1029/2020WR028587, 2021.

455

Chen, Z. and Goldscheider, N.: Modeling spatially and temporally varied hydraulic behavior of a folded karst system with dominant conduit drainage at catchment scale, Hochifen-Gottesacker, Alps, Journal of Hydrology, 514, 41–52, https://doi.org/10.1016/j.jhydrol.2014.04.005, 2014.

460

Chen, Z., Hartmann, A., Wagener, T., and Goldscheider, N.: Dynamics of water fluxes and storages in an Alpine karst catchment under current and potential future climate conditions, Hydrology and Earth System Sciences, 22, 3807–3823, https://doi.org/10.5194/hess-22-3807-2018, publisher: Copernicus GmbH, 2018.

Cinkus, G., Mazzilli, N., Jourde, H., Wunsch, A., Liesch, T., Ravbar, N., Chen, Z., and Goldscheider, N.: When best is the enemy of good; critical evaluation of performance criteria in hydrological models, Hydrology and Earth System Sciences Discussions, pp. 1–25, https://doi.org/10.5194/hess-2022-380, publisher: Copernicus GmbH, 2022a.

465

Cinkus, G., Wunsch, A., Mazzilli, N., Liesch, T., Chen, Z., Ravbar, N., Doummar, J., Fernández-Ortega, J., Barberá, J. A., Andreo, B., Goldscheider, N., and Jourde, H.: Comparison of artificial neural networks and reservoir models for simulating karst spring discharge on five test sites in the Alpine and Mediterranean regions, Hydrology and Earth System Sciences Discussions, pp. 1–41, https://doi.org/10.5194/hess-2022-365, publisher: Copernicus GmbH, 2022b.

Clauzon, V., Mayolle, S., Leonardi, V., Brunet, P., Soliva, R., Marchand, P., Massonnat, G., Rolando, J.-P., and Pistre, S.: Fault zones in limestones: impact on karstogenesis and groundwater flow (Lez aquifer, southern France), Hydrogeology Journal, https://doi.org/10.1007/s10040-020-02189-9, 2020.

470

Cos, J., Doblas-Reyes, F., Jury, M., Marcos, R., Bretonnière, P.-A., and Samsó, M.: The Mediterranean climate change hotspot in the CMIP5 and CMIP6 projections, Earth System Dynamics, 13, 321–340, https://doi.org/10.5194/esd-13-321-2022, publisher: Copernicus GmbH, 2022.

Cousquer, Y. and Jourde, H.: Reducing Uncertainty of Karst Aquifer Modeling with Complementary Hydrological Observations for the Sustainable Management of Groundwater Resources, Journal of Hydrology, p. 128130, https://doi.org/10.1016/j.jhydrol.2022.128130, 2022.

475

Cousquer, Y., Sivelle, V., and Jourde, H.: Estimating the Structural Uncertainty of Lumped Parameter Models in Karst Hydrology: a Bayesian Model Averaging (BMA), Tech. Rep. IAHS2022-522, Copernicus Meetings, https://meetingorganizer.copernicus.org/IAHS2022/IAHS2022-522.html, conference Name: IAHS2022, 2022.
<figure><img src="image_31.png" /></figure>

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Dakhlaoui, H. and Djebbi, K.: Evaluating the impact of rainfall–runoff model structural uncertainty on the hydrological rating of regional climate model simulations, Journal of Water and Climate Change, 12, 3820–3838, https://doi.org/10.2166/wcc.2021.004, 2021.

485
Darbandsari, P. and Coulibaly, P.: Inter-comparison of lumped hydrological models in data-scarce watersheds using different precipitation forcing data sets: Case study of Northern Ontario, Canada, Journal of Hydrology: Regional Studies, 31, 1007–1023, https://doi.org/10.1016/j.ejrh.2020.100730, 2020.

Differbaugh, N. S. and Giorgi, F.: Climate change hotspots in the CMIP5 global climate model ensemble, Climatic Change, 114, 813–822, https://doi.org/10.1007/s10584-012-0570-x, 2012.

490
Doummar, J., Sauter, M., and Geyer, T.: Simulation of flow processes in a large scale karst system with an integrated catchment model (Mike She) – Identification of relevant parameters influencing spring discharge, Journal of Hydrology, 426–427, 112–123, https://doi.org/10.1016/j.jhydrol.2012.01.021, 2012.

Doummar, J., Hassan Kassem, A., and Gurdak, J. J.: Impact of historic and future climate on spring recharge and discharge based on an integrated numerical modelling approach: Application on a snow-governed semi-arid karst catchment area, Journal of Hydrology, 565, 636–649, https://doi.org/10.1016/j.jhydrol.2018.08.062, 2018a.

495
Doummar, J., Margane, A., Geyer, T., and Sauter, M.: Assessment of key transport parameters in a karst system under different dynamic conditions based on tracer experiments: the Jeita karst system, Lebanon, Hydrogeology Journal, 26, 2283–2295, https://doi.org/10.1007/s10040-018-1754-x, 2018b.

500
Doummar, J., Fahs, M., Aoun, M., Elghawi, R., Othman, J., Alali, M., and Kassem, A. H.: Assessment of water quality and quantity of springs at a pilot-scale: Applications in semi-arid Mediterranean areas in Lebanon, preprint, Hydrology, https://doi.org/10.1002/essoar.10508719.1, 2021.

Dubois, E., Doummar, J., Pistre, S., and Larocque, M.: Calibration of a lumped karst system model and application to the Qachqouch karst spring (Lebanon) under climate change conditions, Hydrology and Earth System Sciences, 24, 4275–4290, https://doi.org/10.5194/hess-24-4275-2020, publisher: Copernicus GmbH, 2020.

505
Duran, L., Massei, N., Lecoq, N., Fournier, M., and Labat, D.: Analyzing multi-scale hydrodynamic processes in karst with a coupled conceptual modeling and signal decomposition approach, Journal of Hydrology, 583, 124–140, https://doi.org/10.1016/j.jhydrol.2020.124625, 2020.

Ebel, B. A. and Loague, K.: Physics-based hydrologic-response simulation: Seeing through the fog of equifinality, Hydrological Processes, 20, 2887–2900, https://doi.org/10.1002/hyp.6388, _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/hyp.6388, 2006.

510
Eberhart, R. and Kennedy, J.: Particle swarm optimization, in: Proceedings of the IEEE international conference on neural networks, vol. 4, pp. 1942–1948, Citeseer, 1995.

Elshall, A. S., Arik, A. D., El-Kadi, A. I., Pierce, S., Ye, M., Burnett, K. M., Wada, C. A., Bremer, L. L., and Chun, G.: Groundwater sustainability: a review of the interactions between science and policy, Environmental Research Letters, 15, 093004, https://doi.org/10.1088/1748-9326/ab8e8c, publisher: IOP Publishing, 2020.

515
Ferreira, P. M. d. L., Paz, A. R. d., and Bravo, J. M.: Objective functions used as performance metrics for hydrological models: state-of-the-art and critical analysis, RBRH, 25, e42, https://doi.org/10.1590/2318-0331.252020190155, 2020.

Ficchì, A., Perrin, C., and Andréassian, V.: Impact of temporal resolution of inputs on hydrological model performance: An analysis based on 2400 flood events, Journal of Hydrology, 538, 454–470, https://doi.org/10.1016/j.jhydrol.2016.04.016, 2016.
<figure><img src="image_31.png" /></figure>

480
Criss, R. E. and Winston, W. E.: Do Nash values have value? Discussion and alternate proposals, Hydrological Processes, 22, 2723–2725, https://doi.org/10.1002/hyp.7072, _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/hyp.7072, 2008.

Dakhlaoui, H. and Djebbi, K.: Evaluating the impact of rainfall–runoff model structural uncertainty on the hydrological rating of regional climate model simulations, Journal of Water and Climate Change, 12, 3820–3838, https://doi.org/10.2166/wcc.2021.004, 2021.

485
Darbandsari, P. and Coulibaly, P.: Inter-comparison of lumped hydrological models in data-scarce watersheds using different precipitation forcing data sets: Case study of Northern Ontario, Canada, Journal of Hydrology: Regional Studies, 31, 1007–1023, https://doi.org/10.1016/j.ejrh.2020.100730, 2020.

Differbaugh, N. S. and Giorgi, F.: Climate change hotspots in the CMIP5 global climate model ensemble, Climatic Change, 114, 813–822, https://doi.org/10.1007/s10584-012-0570-x, 2012.

490
Doummar, J., Sauter, M., and Geyer, T.: Simulation of flow processes in a large scale karst system with an integrated catchment model (Mike She) – Identification of relevant parameters influencing spring discharge, Journal of Hydrology, 426–427, 112–123, https://doi.org/10.1016/j.jhydrol.2012.01.021, 2012.

Doummar, J., Hassan Kassem, A., and Gurdak, J. J.: Impact of historic and future climate on spring recharge and discharge based on an integrated numerical modelling approach: Application on a snow-governed semi-arid karst catchment area, Journal of Hydrology, 565, 636–649, https://doi.org/10.1016/j.jhydrol.2018.08.062, 2018a.

495
Doummar, J., Margane, A., Geyer, T., and Sauter, M.: Assessment of key transport parameters in a karst system under different dynamic conditions based on tracer experiments: the Jeita karst system, Lebanon, Hydrogeology Journal, 26, 2283–2295, https://doi.org/10.1007/s10040-018-1754-x, 2018b.

Doummar, J., Fahs, M., Aoun, M., Elghawi, R., Othman, J., Alali, M., and Kassem, A. H.: Assessment of water quality and quantity of springs at a pilot-scale: Applications in semi-arid Mediterranean areas in Lebanon, preprint, Hydrology, https://doi.org/10.1002/essoar.10508719.1, 2021.

500
Dubois, E., Doummar, J., Pistre, S., and Larocque, M.: Calibration of a lumped karst system model and application to the Qachqouch karst spring (Lebanon) under climate change conditions, Hydrology and Earth System Sciences, 24, 4275–4290, https://doi.org/10.5194/hess-24-4275-2020, publisher: Copernicus GmbH, 2020.

Duran, L., Massei, N., Lecoq, N., Fournier, M., and Labat, D.: Analyzing multi-scale hydrodynamic processes in karst with a coupled conceptual modeling and signal decomposition approach, Journal of Hydrology, 583, 124–140, https://doi.org/10.1016/j.jhydrol.2020.124625, 2020.

Ebel, B. A. and Loague, K.: Physics-based hydrologic-response simulation: Seeing through the fog of equifinality, Hydrological Processes, 20, 2887–2900, https://doi.org/10.1002/hyp.6388, _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/hyp.6388, 2006.

Eberhart, R. and Kennedy, J.: Particle swarm optimization, in: Proceedings of the IEEE international conference on neural networks, vol. 4, pp. 1942–1948, Citeseer, 1995.

Elshall, A. S., Arik, A. D., El-Kadi, A. I., Pierce, S., Ye, M., Burnett, K. M., Wada, C. A., Bremer, L. L., and Chun, G.: Groundwater sustainability: a review of the interactions between science and policy, Environmental Research Letters, 15, 093004, https://doi.org/10.1088/1748-9326/ab8e8c, publisher: IOP Publishing, 2020.

Ferreira, P. M. d. L., Paz, A. R. d., and Bravo, J. M.: Objective functions used as performance metrics for hydrological models: state-of-the-art and critical analysis, RBRH, 25, e42, https://doi.org/10.1590/2318-0331.252020190155, 2020.

Ficchì, A., Perrin, C., and Andréassian, V.: Impact of temporal resolution of inputs on hydrological model performance: An analysis based on 2400 flood events, Journal of Hydrology, 538, 454–470, https://doi.org/10.1016/j.jhydrol.2016.04.016, 2016.
<figure><img src="image_32.png" /></figure>

Fiorillo, F., Revellino, P., and Ventafridda, G.: Karst aquifer draining during dry periods, Journal of Cave and Karst Studies, 74, 148–156, https://doi.org/10.4311/2011JCKS0207, 2012.

520 Ford, D. and Williams, P.: Karst hydrogeology and geomorphology, John Wiley & Sons, Hoboken, NJ, USA, 2013.

Frank, S., Goeppert, N., and Goldscheider, N.: Improved understanding of dynamic water and mass budgets of high-alpine karst systems obtained from studying a well-defined catchment area, Hydrological Processes, 35, e14033, https://doi.org/10.1002/hyp.14033, _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/hyp.14033, 2021.

Freedman, D., Pisani, R., Purves, R., and Adhikari, A.: Statistics, WW Norton & Company New York, 2007.

525 Gupta, A. and Govindaraju, R. S.: Propagation of structural uncertainty in watershed hydrologic models, Journal of Hydrology, 575, 66–81, https://doi.org/10.1016/j.jhydrol.2019.05.026, 2019.

Gupta, H. V., Kling, H., Yilmaz, K. K., and Martinez, G. F.: Decomposition of the mean squared error and NSE performance criteria: Implementations for improving hydrological modelling, Journal of Hydrology, 377, 80–91, https://doi.org/10.1016/j.jhydrol.2009.08.003, 2009.

530 Hartmann, A., Lange, J., Vivó Aguado, M., Mizyed, N., Smiatek, G., and Kunstmann, H.: A multi-model approach for improved simulations of future water availability at a large Eastern Mediterranean karst spring, Journal of Hydrology, 468-469, 130–138, https://doi.org/10.1016/j.jhydrol.2012.08.024, 2012.

Hartmann, A., Wagener, T., Rimmer, A., Lange, J., Brielmann, H., and Weiler, M.: Testing the realism of model structures to identify karst system processes using water quality and quantity signatures, Water Resources Research, 49, 3345–3358, https://doi.org/10.1002/wrcr.20229, 2013.

535 Hartmann, A., Gleeson, T., Wada, Y., and Wagener, T.: Enhanced groundwater recharge rates and altered recharge sensitivity to climate variability through subsurface heterogeneity, Proceedings of the National Academy of Sciences, 114, 2842–2847, https://doi.org/10.1073/pnas.1614941114, 2017.

Hauduc, H., Neumann, M. B., Muschalla, D., Gamerith, V., Gillot, S., and Vanrolleghem, P. A.: Efficiency criteria for environmental model quality assessment: A review and its application to wastewater treatment, Environmental Modelling & Software, 68, 196–204, https://doi.org/10.1016/j.envsoft.2015.02.004, 2015.

Jackson, E. K., Roberts, W., Nelsen, B., Williams, G. P., Nelson, E. J., and Ames, D. P.: Introductory overview: Error metrics for hydrologic modelling – A review of common practices and an open source library to facilitate use and adoption, Environmental Modelling & Software, 119, 32–48, https://doi.org/10.1016/j.envsoft.2019.05.001, 2019.

Jeannin, P.-Y., Artigue, G., Butscher, C., Chang, Y., Charlier, J.-B., Duran, L., Gill, L., Hartmann, A., Johannet, A., Jourde, H., Kavousi, A., Liesch, T., Liu, Y., Lüthi, M., Malard, A., Mazzilli, N., Pardo-Igúzquiza, E., Thiéry, D., Reimann, T., Schuler, P., Wöhling, T., and Wunsch, A.: Karst modelling challenge 1: Results of hydrological modelling, Journal of Hydrology, p. 126508, https://doi.org/10.1016/j.jhydrol.2021.126508, 2021.

Jiang, T., Chen, Y. D., Xu, C.-y., Chen, X., Chen, X., and Singh, V. P.: Comparison of hydrological impacts of climate change simulated by six hydrological models in the Dongjiang Basin, South China, Journal of Hydrology, 336, 316–333, https://doi.org/10.1016/j.jhydrol.2007.01.010, 2007.

Jones, R. N., Chiew, F. H. S., Boughton, W. C., and Zhang, L.: Estimating the sensitivity of mean annual runoff to climate change using selected hydrological models, Advances in Water Resources, 29, 1419–1429, https://doi.org/10.1016/j.advwatres.2005.11.001, 2006.

Jourde, H., Lafare, A., Mazzilli, N., Belaud, G., Neppel, L., Dörfliger, N., and Cernesson, F.: Flash flood mitigation as a positive consequence of anthropogenic forcing on the groundwater resource in a karst catchment, Environmental Earth Sciences, 71, 573–583, https://doi.org/10.1007/s12665-013-2678-3, 2014.
<figure><img src="image_32.png" /></figure>

Fiorillo, F., Revellino, P., and Ventafridda, G.: Karst aquifer draining during dry periods, Journal of Cave and Karst Studies, 74, 148–156, https://doi.org/10.4311/2011JCKS0207, 2012.

520 Ford, D. and Williams, P.: Karst hydrogeology and geomorphology, John Wiley & Sons, Hoboken, NJ, USA, 2013.

Frank, S., Goeppert, N., and Goldscheider, N.: Improved understanding of dynamic water and mass budgets of high-alpine karst systems obtained from studying a well-defined catchment area, Hydrological Processes, 35, e14033, https://doi.org/10.1002/hyp.14033, _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/hyp.14033, 2021.

Freedman, D., Pisani, R., Purves, R., and Adhikari, A.: Statistics, WW Norton & Company New York, 2007.

525 Gupta, A. and Govindaraju, R. S.: Propagation of structural uncertainty in watershed hydrologic models, Journal of Hydrology, 575, 66–81, https://doi.org/10.1016/j.jhydrol.2019.05.026, 2019.

Gupta, H. V., Kling, H., Yilmaz, K. K., and Martinez, G. F.: Decomposition of the mean squared error and NSE performance criteria: Implementations for improving hydrological modelling, Journal of Hydrology, 377, 80–91, https://doi.org/10.1016/j.jhydrol.2009.08.003, 2009.

530 Hartmann, A., Lange, J., Vivó Aguado, M., Mizyed, N., Smiatek, G., and Kunstmann, H.: A multi-model approach for improved simulations of future water availability at a large Eastern Mediterranean karst spring, Journal of Hydrology, 468-469, 130–138, https://doi.org/10.1016/j.jhydrol.2012.08.024, 2012.

Hartmann, A., Wagener, T., Rimmer, A., Lange, J., Brielmann, H., and Weiler, M.: Testing the realism of model structures to identify karst system processes using water quality and quantity signatures, Water Resources Research, 49, 3345–3358, https://doi.org/10.1002/wrcr.20229, 2013.

535 Hartmann, A., Gleeson, T., Wada, Y., and Wagener, T.: Enhanced groundwater recharge rates and altered recharge sensitivity to climate variability through subsurface heterogeneity, Proceedings of the National Academy of Sciences, 114, 2842–2847, https://doi.org/10.1073/pnas.1614941114, 2017.

540 Hauduc, H., Neumann, M. B., Muschalla, D., Gamerith, V., Gillot, S., and Vanrolleghem, P. A.: Efficiency criteria for environmental model quality assessment: A review and its application to wastewater treatment, Environmental Modelling & Software, 68, 196–204, https://doi.org/10.1016/j.envsoft.2015.02.004, 2015.

Jackson, E. K., Roberts, W., Nelsen, B., Williams, G. P., Nelson, E. J., and Ames, D. P.: Introductory overview: Error metrics for hydrologic modelling – A review of common practices and an open source library to facilitate use and adoption, Environmental Modelling & Software, 119, 32–48, https://doi.org/10.1016/j.envsoft.2019.05.001, 2019.

545 Jeannin, P.-Y., Artigue, G., Butscher, C., Chang, Y., Charlier, J.-B., Duran, L., Gill, L., Hartmann, A., Johannet, A., Jourde, H., Kavousi, A., Liesch, T., Liu, Y., Lüthi, M., Malard, A., Mazzilli, N., Pardo-Igúzquiza, E., Thiéry, D., Reimann, T., Schuler, P., Wöhling, T., and Wunsch, A.: Karst modelling challenge 1: Results of hydrological modelling, Journal of Hydrology, p. 126508, https://doi.org/10.1016/j.jhydrol.2021.126508, 2021.

Jiang, T., Chen, Y. D., Xu, C.-y., Chen, X., Chen, X., and Singh, V. P.: Comparison of hydrological impacts of climate change simulated by six hydrological models in the Dongjiang Basin, South China, Journal of Hydrology, 336, 316–333, https://doi.org/10.1016/j.jhydrol.2007.01.010, 2007.

Jones, R. N., Chiew, F. H. S., Boughton, W. C., and Zhang, L.: Estimating the sensitivity of mean annual runoff to climate change using selected hydrological models, Advances in Water Resources, 29, 1419–1429, https://doi.org/10.1016/j.advwatres.2005.11.001, 2006.

Jourde, H., Lafare, A., Mazzilli, N., Belaud, G., Neppel, L., Dörfliger, N., and Cernesson, F.: Flash flood mitigation as a positive consequence of anthropogenic forcing on the groundwater resource in a karst catchment, Environmental Earth Sciences, 71, 573–583, https://doi.org/10.1007/s12665-013-2678-3, 2014.
<figure><img src="image_33.png" /></figure>

Klemeš, V.: Operational testing of hydrological simulation models, Hydrological Sciences Journal, 31, 13–24, https://doi.org/10.1080/02626668609491024, 1986.

Knoben, W. J. M., Freer, J. E., Peel, M. C., Fowler, K. J. A., and Woods, R. A.: A Brief Analysis of Conceptual Model Structure Uncertainty Using 36 Models and 559 Catchments, Water Resources Research, 56, e2019WR025975, https://doi.org/10.1029/2019WR025975, _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1029/2019WR025975, 2020.

Labat, D., Argouze, R., Mazzilli, N., Ollivier, C., and Sivelle, V.: Impact of Withdrawals on Karst Watershed Water Supply, Water, 14, 1339, https://doi.org/10.3390/w14091339, number: 9 Publisher: Multidisciplinary Digital Publishing Institute, 2022.

Lee, A.: pyswarm: Particle swarm optimization (PSO) with constraint support, https://github.com/tisimst/pyswarm, 2014.

Liu, Y., Wagener, T., and Hartmann, A.: Assessing Streamflow Sensitivity to Precipitation Variability in Karst-Influenced Catchments With Unclosed Water Balances, Water Resources Research, 57, e2020WR028598, https://doi.org/10.1029/2020WR028598, _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1029/2020WR028598, 2021.

Lorette, G., Sebilo, M., Buquet, D., Lastennet, R., Denis, A., Peyraube, N., Charriere, V., and Studer, J.-C.: Tracing sources and fate of nitrate in multilayered karstic hydrogeological catchments using natural stable isotopic composition (δ15N-NO3- and δ18O-NO3-). Application to the Toulon karst system (Dordogne, France), Journal of Hydrology, p. 127972, https://doi.org/10.1016/j.jhydrol.2022.127972, 2022.

Lukač Reberski, J., Terzić, J., Maurice, L. D., and Lapworth, D. J.: Emerging organic contaminants in karst groundwater: A global level assessment, Journal of Hydrology, 604, 127–242, https://doi.org/10.1016/j.jhydrol.2021.127242, 2022.

Mazzilli, N., Jourde, H., Guinot, V., Bailly-Comte, V., and Fleury, P.: Hydrological modelling of a karst aquifer under active groundwater management using a parsimonious conceptual model, H2Karst - 9th Conference on Limestone Hydrogeology, p. 4, 2011.

Mazzilli, N., Guinot, V., and Jourde, H.: Sensitivity analysis of conceptual model calibration to initialisation bias. Application to karst spring discharge models, Advances in Water Resources, 42, 1–16, https://doi.org/10.1016/j.advwatres.2012.03.020, 2012.

Mazzilli, N., Jourde, H., Jacob, T., Guinot, V., Le Moigne, N., Boucher, M., Chalikakis, K., Guyard, H., and Legtchenko, A.: On the inclusion of ground-based gravity measurements to the calibration process of a global rainfall-discharge reservoir model: case of the Durzon karst system (Larzac, southern France), Environmental Earth Sciences, 68, 1631–1646, https://doi.org/10.1007/s12665-012-1856-z, 2013.

Mazzilli, N., Guinot, V., Jourde, H., Lecoq, N., Labat, D., Arfib, B., Baudement, C., Danquigny, C., Dal Soglio, L., and Bertin, D.: KarstMod: A modelling platform for rainfall - discharge analysis and modelling dedicated to karst systems, Environmental Modelling & Software, 122, 103–927, https://doi.org/10.1016/j.envsoft.2017.03.015, 2019.

Mazzilli, N., Sivelle, V., Cinkus, G., Jourde, H., and Bertin, D.: KarstMod User Guide - version 3.0, 2022.

McMillan, H., Jackson, B., Clark, M., Kavetski, D., and Woods, R.: Rainfall uncertainty in hydrological modelling: An evaluation of multiplicative error models, Journal of Hydrology, 400, 83–94, https://doi.org/10.1016/j.jhydrol.2011.01.026, 2011.

Moges, E., Demissie, Y., Larsen, L., and Yassin, F.: Review: Sources of Hydrological Model Uncertainties and Advances in Their Analysis, Water, 13, 28, https://doi.org/10.3390/w13010028, number: 1 Publisher: Multidisciplinary Digital Publishing Institute, 2021.

Moriasi, D. N., Arnold, J. G., Liew, M. W. V., Bingner, R. L., Harmel, R. D., and Veith, T. L.: Model Evaluation Guidelines for Systematic Quantification of Accuracy in Watershed Simulations, Transactions of the ASABE, 50, 885–900, https://doi.org/10.13031/2013.23153, 2007.

Nash, J. E. and Sutcliffe, J. V.: River flow forecasting through conceptual models part I — A discussion of principles, Journal of Hydrology, 10, 282–290, https://doi.org/10.1016/0022-1694(70)90255-6, 1970.

Nerantzaki, S. D. and Nikolaidis, N. P.: The response of three Mediterranean karst springs to drought and the impact of climate change, Journal of Hydrology, 591, 125–296, https://doi.org/10.1016/j.jhydrol.2020.125296, 2020.
<figure><img src="image_33.png" /></figure>

Klemeš, V.: Operational testing of hydrological simulation models, Hydrological Sciences Journal, 31, 13–24, https://doi.org/10.1080/02626668609491024, 1986.

Knoben, W. J. M., Freer, J. E., Peel, M. C., Fowler, K. J. A., and Woods, R. A.: A Brief Analysis of Conceptual Model Structure Uncertainty Using 36 Models and 559 Catchments, Water Resources Research, 56, e2019WR025975, https://doi.org/10.1029/2019WR025975, _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1029/2019WR025975, 2020.

Labat, D., Argouze, R., Mazzilli, N., Ollivier, C., and Sivelle, V.: Impact of Withdrawals on Karst Watershed Water Supply, Water, 14, 1339, https://doi.org/10.3390/w14091339, number: 9 Publisher: Multidisciplinary Digital Publishing Institute, 2022.

Lee, A.: pyswarm: Particle swarm optimization (PSO) with constraint support, https://github.com/tisimst/pyswarm, 2014.

Liu, Y., Wagener, T., and Hartmann, A.: Assessing Streamflow Sensitivity to Precipitation Variability in Karst-Influenced Catchments With Unclosed Water Balances, Water Resources Research, 57, e2020WR028598, https://doi.org/10.1029/2020WR028598, _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1029/2020WR028598, 2021.

Lorette, G., Sebilo, M., Buquet, D., Lastennet, R., Denis, A., Peyraube, N., Charriere, V., and Studer, J.-C.: Tracing sources and fate of nitrate in multilayered karstic hydrogeological catchments using natural stable isotopic composition (δ15N-NO3- and δ18O-NO3-). Application to the Toulon karst system (Dordogne, France), Journal of Hydrology, p. 127972, https://doi.org/10.1016/j.jhydrol.2022.127972, 2022.

Lukač Reberski, J., Terzić, J., Maurice, L. D., and Lapworth, D. J.: Emerging organic contaminants in karst groundwater: A global level assessment, Journal of Hydrology, 604, 127–242, https://doi.org/10.1016/j.jhydrol.2021.127242, 2022.

Mazzilli, N., Jourde, H., Guinot, V., Bailly-Comte, V., and Fleury, P.: Hydrological modelling of a karst aquifer under active groundwater management using a parsimonious conceptual model, H2Karst - 9th Conference on Limestone Hydrogeology, p. 4, 2011.

Mazzilli, N., Guinot, V., and Jourde, H.: Sensitivity analysis of conceptual model calibration to initialisation bias. Application to karst spring discharge models, Advances in Water Resources, 42, 1–16, https://doi.org/10.1016/j.advwatres.2012.03.020, 2012.

Mazzilli, N., Jourde, H., Jacob, T., Guinot, V., Le Moigne, N., Boucher, M., Chalikakis, K., Guyard, H., and Legtchenko, A.: On the inclusion of ground-based gravity measurements to the calibration process of a global rainfall-discharge reservoir model: case of the Durzon karst system (Larzac, southern France), Environmental Earth Sciences, 68, 1631–1646, https://doi.org/10.1007/s12665-012-1856-z, 2013.

Mazzilli, N., Guinot, V., Jourde, H., Lecoq, N., Labat, D., Arfib, B., Baudement, C., Danquigny, C., Dal Soglio, L., and Bertin, D.: KarstMod: A modelling platform for rainfall - discharge analysis and modelling dedicated to karst systems, Environmental Modelling & Software, 122, 103–927, https://doi.org/10.1016/j.envsoft.2017.03.015, 2019.

Mazzilli, N., Sivelle, V., Cinkus, G., Jourde, H., and Bertin, D.: KarstMod User Guide - version 3.0, 2022.

McMillan, H., Jackson, B., Clark, M., Kavetski, D., and Woods, R.: Rainfall uncertainty in hydrological modelling: An evaluation of multiplicative error models, Journal of Hydrology, 400, 83–94, https://doi.org/10.1016/j.jhydrol.2011.01.026, 2011.

Moges, E., Demissie, Y., Larsen, L., and Yassin, F.: Review: Sources of Hydrological Model Uncertainties and Advances in Their Analysis, Water, 13, 28, https://doi.org/10.3390/w13010028, number: 1 Publisher: Multidisciplinary Digital Publishing Institute, 2021.

Moriasi, D. N., Arnold, J. G., Liew, M. W. V., Bingner, R. L., Harmel, R. D., and Veith, T. L.: Model Evaluation Guidelines for Systematic Quantification of Accuracy in Watershed Simulations, Transactions of the ASABE, 50, 885–900, https://doi.org/10.13031/2013.23153, 2007.

Nash, J. E. and Sutcliffe, J. V.: River flow forecasting through conceptual models part I — A discussion of principles, Journal of Hydrology, 10, 282–290, https://doi.org/10.1016/0022-1694(70)90255-6, 1970.

Nerantzaki, S. D. and Nikolaidis, N. P.: The response of three Mediterranean karst springs to drought and the impact of climate change, Journal of Hydrology, 591, 125–296, https://doi.org/10.1016/j.jhydrol.2020.125296, 2020.
<figure><img src="image_34.png" /></figure>

Ollivier, C., Mazzilli, N., Olioso, A., Chalikakis, K., Carrière, S. D., Danquigny, C., and Emblanch, C.: Karst recharge-discharge semi distributed model to assess spatial variability of flows, Science of The Total Environment, 703, 134368, https://doi.org/10.1016/j.scitotenv.2019.134368, 2020.

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Oudin, L., Hervieu, F., Michel, C., Perrin, C., Andréassian, V., Anctil, F., and Loumagne, C.: Which potential evapotranspiration input for a lumped rainfall–runoff model? Part 2—Towards a simple and efficient potential evapotranspiration model for rainfall–runoff modelling, Journal of Hydrology, 303, 290–306, https://doi.org/10.1016/j.jhydrol.2004.08.026, 2005.

600

Oudin, L., Perrin, C., Mathevet, T., Andréassian, V., and Michel, C.: Impact of biased and randomly corrupted inputs on the efficiency and the parameters of watershed models, Journal of Hydrology, 320, 62–83, https://doi.org/10.1016/j.jhydrol.2005.07.016, 2006.

Palmer, A. N.: Origin and morphology of limestone caves, Geological Society of America Bulletin, 103, 1–21, 1991.

Pandi, D., Kothandaraman, S., and Kuppusamy, M.: Hydrological models: a review, International Journal of Hydrology Science and Technology, 12, 223–242, https://doi.org/10.1504/IJHST.2021.117540, publisher: Inderscience Publishers, 2021.

605

Pechlivanidis, I., Jackson, B., McMillan, H., and Gupta, H. V.: Using an informational entropy-based metric as a diagnostic of flow duration to drive model parameter identification, Global NEST Journal, 14, 325–334, https://doi.org/10.30955/gnj.000879, 2013.

Perrin, C., Michel, C., and Andréassian, V.: Does a large number of parameters enhance model performance? Comparative assessment of common catchment model structures on 429 catchments, Journal of Hydrology, 242, 275–301, https://doi.org/10.1016/S0022-1694(00)00393-0, 2001.

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Pianosi, F., Sarrazin, F., and Wagener, T.: How successfully is open-source research software adopted? Results and implications of surveying the users of a sensitivity analysis toolbox, Environmental Modelling & Software, 124, 104579, https://doi.org/10.1016/j.envsoft.2019.104579, 2020.

615

Pool, S., Vis, M., and Seibert, J.: Evaluating model performance: towards a non-parametric variant of the Kling-Gupta efficiency, Hydrological Sciences Journal, 63, 1941–1953, https://doi.org/10.1080/02626667.2018.1552002, 2018.

Poulain, A., Watlet, A., Kaufmann, O., Van Camp, M., Jourde, H., Mazzilli, N., Rochez, G., Deleu, R., Quinif, Y., and Hallet, V.: Assessment of groundwater recharge processes through karst vadose zone by cave percolation monitoring, Hydrological Processes, 32, 2069–2083, https://doi.org/10.1002/hyp.13138, 2018.

620

Sarrazin, F., Hartmann, A., Pianosi, F., Rosolem, R., and Wagener, T.: V2Karst V1.1: a parsimonious large-scale integrated vegetation–recharge model to simulate the impact of climate and land cover change in karst regions, Geoscientific Model Development, 11, 4933–4964, https://doi.org/10.5194/gmd-11-4933-2018, 2018.

Schilling, O. S., Cook, P. G., and Brunner, P.: Beyond Classical Observations in Hydrogeology: The Advantages of Including Exchange Flux, Temperature, Tracer Concentration, Residence Time, and Soil Moisture Observations in Groundwater Model Calibration, Reviews of Geophysics, 57, 146–182, https://doi.org/10.1029/2018RG000619, _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1029/2018RG000619, 2019.

625

Schwemmle, R., Demand, D., and Weiler, M.: Technical note: Diagnostic efficiency – specific evaluation of model performance, Hydrology and Earth System Sciences, 25, 2187–2198, https://doi.org/10.5194/hess-25-2187-2021, publisher: Copernicus GmbH, 2021.

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630
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595

Ollivier, C., Mazzilli, N., Olioso, A., Chalikakis, K., Carrière, S. D., Danquigny, C., and Emblanch, C.: Karst recharge-discharge semi distributed model to assess spatial variability of flows, Science of The Total Environment, 703, 134368, https://doi.org/10.1016/j.scitotenv.2019.134368, 2020.

Oudin, L., Hervieu, F., Michel, C., Perrin, C., Andréassian, V., Anctil, F., and Loumagne, C.: Which potential evapotranspiration input for a lumped rainfall-runoff model? Part 2—Towards a simple and efficient potential evapotranspiration model for rainfall-runoff modelling, Journal of Hydrology, 303, 290–306, https://doi.org/10.1016/j.jhydrol.2004.08.026, 2005.

600

Oudin, L., Perrin, C., Mathevet, T., Andréassian, V., and Michel, C.: Impact of biased and randomly corrupted inputs on the efficiency and the parameters of watershed models, Journal of Hydrology, 320, 62–83, https://doi.org/10.1016/j.jhydrol.2005.07.016, 2006.

Palmer, A. N.: Origin and morphology of limestone caves, Geological Society of America Bulletin, 103, 1–21, 1991.

Pandi, D., Kothandaraman, S., and Kuppusamy, M.: Hydrological models: a review, International Journal of Hydrology Science and Technology, 12, 223–242, https://doi.org/10.1504/IJHST.2021.117540, publisher: Inderscience Publishers, 2021.

605

Pechlivanidis, I., Jackson, B., McMillan, H., and Gupta, H. V.: Using an informational entropy-based metric as a diagnostic of flow duration to drive model parameter identification, Global NEST Journal, 14, 325–334, https://doi.org/10.30955/gnj.000879, 2013.

Perrin, C., Michel, C., and Andréassian, V.: Does a large number of parameters enhance model performance? Comparative assessment of common catchment model structures on 429 catchments, Journal of Hydrology, 242, 275–301, https://doi.org/10.1016/S0022-1694(00)00393-0, 2001.

610

Pianosi, F., Sarrazin, F., and Wagener, T.: A Matlab toolbox for Global Sensitivity Analysis, Environmental Modelling & Software, 70, 80–85, https://doi.org/10.1016/j.envsoft.2015.04.009, 2015.

Pianosi, F., Sarrazin, F., and Wagener, T.: How successfully is open-source research software adopted? Results and implications of surveying the users of a sensitivity analysis toolbox, Environmental Modelling & Software, 124, 104579, https://doi.org/10.1016/j.envsoft.2019.104579, 2020.

615

Pool, S., Vis, M., and Seibert, J.: Evaluating model performance: towards a non-parametric variant of the Kling-Gupta efficiency, Hydrological Sciences Journal, 63, 1941–1953, https://doi.org/10.1080/02626667.2018.1552002, 2018.

Poulain, A., Watlet, A., Kaufmann, O., Van Camp, M., Jourde, H., Mazzilli, N., Rochez, G., Deleu, R., Quinif, Y., and Hallet, V.: Assessment of groundwater recharge processes through karst vadose zone by cave percolation monitoring, Hydrological Processes, 32, 2069–2083, https://doi.org/10.1002/hyp.13138, 2018.

620

Sarrazin, F., Hartmann, A., Pianosi, F., Rosolem, R., and Wagener, T.: V2Karst V1.1: a parsimonious large-scale integrated vegetation–recharge model to simulate the impact of climate and land cover change in karst regions, Geoscientific Model Development, 11, 4933–4964, https://doi.org/10.5194/gmd-11-4933-2018, 2018.

Schilling, O. S., Cook, P. G., and Brunner, P.: Beyond Classical Observations in Hydrogeology: The Advantages of Including Exchange Flux, Temperature, Tracer Concentration, Residence Time, and Soil Moisture Observations in Groundwater Model Calibration, Reviews of Geophysics, 57, 146–182, https://doi.org/10.1029/2018RG000619, _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1029/2018RG000619, 2019.

625

Schwemmle, R., Demand, D., and Weiler, M.: Technical note: Diagnostic efficiency – specific evaluation of model performance, Hydrology and Earth System Sciences, 25, 2187–2198, https://doi.org/10.5194/hess-25-2187-2021, publisher: Copernicus GmbH, 2021.

Shmueli, G.: To Explain or to Predict?, Statistical Science, 25, 289–310, https://doi.org/10.1214/10-STS330, publisher: Institute of Mathematical Statistics, 2010.

630
<figure><img src="image_35.png" /></figure>

Sivelle, V. and Jourde, H.: A methodology for the assessment of groundwater resource variability in karst catchments with sparse temporal measurements, Hydrogeology Journal, 29, 137–157, https://doi.org/10.1007/s10040-020-02239-2, 2020.

Sivelle, V., Labat, D., Mazzilli, N., Massei, N., and Jourde, H.: Dynamics of the Flow Exchanges between Matrix and Conduits in Karstified Watersheds at Multiple Temporal Scales, Water, 11, 569, https://doi.org/10.3390/w11030569, 2019.

Sivelle, V., Jourde, H., Bittner, D., Mazzilli, N., and Tramblay, Y.: Assessment of the relative impacts of climate changes and anthropogenic forcing on spring discharge of a Mediterranean karst system, Journal of Hydrology, 598, 126–396, https://doi.org/10.1016/j.jhydrol.2021.126396, 2021.

Sivelle, V., Jourde, H., Bittner, D., Richieri, B., Labat, D., Hartmann, A., and Chiogna, G.: Considering land cover and land use (LCLU) in lumped parameter modeling in forest dominated karst catchments, Journal of Hydrology, 612, 128–264, https://doi.org/10.1016/j.jhydrol.2022.128264, 2022a.

Sivelle, V., Pérotin, L., Ladouche, B., de Montety, V., Bailly-Comte, V., Champollion, C., and Jourde, H.: A lumped parameter model to evaluate the relevance of excess air as a tracer of exchanged flows between transmissive and capacitive compartments of karst systems, Frontiers in Water, 4, https://www.frontiersin.org/articles/10.3389/frwa.2022.930115, 2022b.

Smiatek, G., Kaspar, S., and Kunstmann, H.: Hydrological Climate Change Impact Analysis for the Figeoh Spring near Damascus, Syria, Journal of Hydrometeorology, 14, 577–593, https://doi.org/10.1175/JHM-D-12-065.1, publisher: American Meteorological Society Section: Journal of Hydrometeorology, 2013.

Sobol, I. M.: Uniformly distributed sequences with an additional uniform property, USSR Computational Mathematics and Mathematical Physics, 16, 236–242, https://doi.org/10.1016/0041-5553(76)90154-3, 1976.

Stevanović, Z.: Karst waters in potable water supply: a global scale overview, Environmental Earth Sciences, 78, 662, https://doi.org/10.1007/s12665-019-8670-9, 2019.

Wada, Y., Flörke, M., Hanasaki, N., Eisner, S., Fischer, G., Tramberend, S., Satoh, Y., van Vliet, M. T. H., Yillia, P., Ringler, C., Burek, P., and Wiberg, D.: Modeling global water use for the 21st century: the Water Futures and Solutions (WFaS) initiative and its approaches, Geoscientific Model Development, 9, 175–222, https://doi.org/10.5194/gmd-9-175-2016, 2016.

Westerberg, I. K., Sikorska-Senoner, A. E., Viviroli, D., Vis, M., and Seibert, J.: Hydrological model calibration with uncertain discharge data, Hydrological Sciences Journal, 0, null, https://doi.org/10.1080/02626667.2020.1735638, publisher: Taylor & Francis_eprint: https://doi.org/10.1080/02626667.2020.1735638, 2020.

Zhou, S., Wang, Y., Li, Z., Chang, J., and Guo, A.: Quantifying the Uncertainty Interaction Between the Model Input and Structure on Hydrological Processes, Water Resources Management, 35, 3915–3935, https://doi.org/10.1007/s11269-021-02883-7, 2021.

Çallı, S. S., Çallı, K., Tuğrul Yılmaz, M., and Çelik, M.: Contribution of the satellite-data driven snow routine to a karst hydrological model, Journal of Hydrology, 607, 127–511, https://doi.org/10.1016/j.jhydrol.2022.127511, 2022.
<figure><img src="image_35.png" /></figure>

Sivelle, V. and Jourde, H.: A methodology for the assessment of groundwater resource variability in karst catchments with sparse temporal measurements, Hydrogeology Journal, 29, 137–157, https://doi.org/10.1007/s10040-020-02239-2, 2020.

Sivelle, V., Labat, D., Mazzilli, N., Massei, N., and Jourde, H.: Dynamics of the Flow Exchanges between Matrix and Conduits in Karstified Watersheds at Multiple Temporal Scales, Water, 11, 569, https://doi.org/10.3390/w11030569, 2019.

Sivelle, V., Jourde, H., Bittner, D., Mazzilli, N., and Tramblay, Y.: Assessment of the relative impacts of climate changes and anthropogenic forcing on spring discharge of a Mediterranean karst system, Journal of Hydrology, 598, 126–396, https://doi.org/10.1016/j.jhydrol.2021.126396, 2021.

Sivelle, V., Jourde, H., Bittner, D., Richieri, B., Labat, D., Hartmann, A., and Chiogna, G.: Considering land cover and land use (LCLU) in lumped parameter modeling in forest dominated karst catchments, Journal of Hydrology, 612, 128–264, https://doi.org/10.1016/j.jhydrol.2022.128264, 2022a.

Sivelle, V., Pérotin, L., Ladouche, B., de Montety, V., Bailly-Comte, V., Champollion, C., and Jourde, H.: A lumped parameter model to evaluate the relevance of excess air as a tracer of exchanged flows between transmissive and capacitive compartments of karst systems, Frontiers in Water, 4, https://www.frontiersin.org/articles/10.3389/frwa.2022.930115, 2022b.

Smiatek, G., Kaspar, S., and Kunstmann, H.: Hydrological Climate Change Impact Analysis for the Figeoh Spring near Damascus, Syria, Journal of Hydrometeorology, 14, 577–593, https://doi.org/10.1175/JHM-D-12-065.1, publisher: American Meteorological Society Section: Journal of Hydrometeorology, 2013.

Sobol, I. M.: Uniformly distributed sequences with an additional uniform property, USSR Computational Mathematics and Mathematical Physics, 16, 236–242, https://doi.org/10.1016/0041-5553(76)90154-3, 1976.

Stevanović, Z.: Karst waters in potable water supply: a global scale overview, Environmental Earth Sciences, 78, 662, https://doi.org/10.1007/s12665-019-8670-9, 2019.

Wada, Y., Flörke, M., Hanasaki, N., Eisner, S., Fischer, G., Tramberend, S., Satoh, Y., van Vliet, M. T. H., Yillia, P., Ringler, C., Burek, P., and Wiberg, D.: Modeling global water use for the 21st century: the Water Futures and Solutions (WFaS) initiative and its approaches, Geoscientific Model Development, 9, 175–222, https://doi.org/10.5194/gmd-9-175-2016, 2016.

Westerberg, I. K., Sikorska-Senoner, A. E., Viviroli, D., Vis, M., and Seibert, J.: Hydrological model calibration with uncertain discharge data, Hydrological Sciences Journal, 0, null, https://doi.org/10.1080/02626667.2020.1735638, publisher: Taylor & Francis_eprint: https://doi.org/10.1080/02626667.2020.1735638, 2020.

Zhou, S., Wang, Y., Li, Z., Chang, J., and Guo, A.: Quantifying the Uncertainty Interaction Between the Model Input and Structure on Hydrological Processes, Water Resources Management, 35, 3915–3935, https://doi.org/10.1007/s11269-021-02883-7, 2021.

Çallı, S. S., Çallı, K., Tuğrul Yılmaz, M., and Çelik, M.: Contribution of the satellite-data driven snow routine to a karst hydrological model, Journal of Hydrology, 607, 127–511, https://doi.org/10.1016/j.jhydrol.2022.127511, 2022.