# Calibration of groundwater seepage against the spatial distribution of the stream network to assess catchment-scale hydraulic properties

Ronan Abhervé, Clément Roques, Alexandre Gauvain, Laurent Longuevergne, Stéphane Louaisil, Luc Aquilina, Jean-Raynald de Dreuzy

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Ronan Abhervé, Clément Roques, Alexandre Gauvain, Laurent Longuevergne, Stéphane Louaisil, et al. Calibration of groundwater seepage against the spatial distribution of the stream network to assess catchment-scale hydraulic properties. Hydrology and Earth System Sciences, 2023, 27 (17), pp.3221-3239. 10.5194/hess-27-3221-2023 . insu-04204313

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# Calibration of groundwater seepage against the spatial distribution of the stream network to assess catchment-scale hydraulic properties

Ronan Abhervé¹,², Clément Roques¹,², Alexandre Gauvain¹,⁴, Laurent Longuevergne¹, Stéphane Louaisil³, Luc Aquilina¹, and Jean-Raynald de Dreuzy¹

¹Geosciences Rennes – UMR 6118, Univ. Rennes, CNRS, 35000 Rennes, France

²Centre for Hydrogeology and Geothermics (CHYN), Université de Neuchâtel, 2000 Neuchâtel, Switzerland

³Eau du Bassin Rennais, 35000 Rennes, France

⁴Laboratoire de Météorologie Dynamique – IPSL, CNRS, Sorbonne Université, 75005 Paris, France

**Correspondence:** Ronan Abhervé (ronan.abherve@univ-rennes.fr, ronan.abherve@unine.ch, ronan.abherve@gmail.com)

Received: 2 May 2022 – Discussion started: 16 May 2022

Revised: 17 February 2023 – Accepted: 24 July 2023 – Published: 8 September 2023

**Abstract.** The assessment of effective hydraulic properties at the catchment scale, i.e., hydraulic conductivity (K) and transmissivity (T), is particularly challenging due to the sparse availability of hydrological monitoring systems through stream gauges and boreholes. To overcome this challenge, we propose a calibration methodology which only considers information from a digital elevation model (DEM) and the spatial distribution of the stream network. The methodology is built on the assumption that the groundwater system is the main driver controlling the stream density and extension, where the perennial stream network reflects the intersection of the groundwater table with the topography. Indeed, the groundwater seepage at the surface is primarily controlled by the topography, the aquifer thickness and the dimensionless parameter K/R, where R is the average recharge rate. Here, we use a process-based and parsimonious 3D groundwater flow model to calibrate K/R by minimizing the relative distances between the observed and the simulated stream network generated from groundwater seepage zones. By deploying the methodology in 24 selected headwater catchments located in northwestern France, we demonstrate that the method successfully predicts the stream network extent for 80% of the cases. Results show a high sensitivity of K/R to the extension of the low-order streams and limited impacts of the DEM resolution as long the DEM remains consistent with the stream network observations. By assuming an average recharge rate, we found that effective K values vary between 1.0 × 10⁻⁵ and 1.1 × 10⁻⁴ m s⁻¹, in agreement with local estimates derived from hydraulic

tests and independent calibrated groundwater model. With the emergence of global remote-sensing databases compiling information on high-resolution DEM and stream networks, this approach provides new opportunities to assess hydraulic properties of unconfined aquifers in ungauged basins.

## 1 Introduction

Evaluating the availability of water resources and its evolution under global changes requires a quantitative assessment of water fluxes at the catchment scale (Fan et al., 2019). Such an evaluation involves the development of advanced hydrological models resolving relevant hillslope- to catchment-scale processes (Refsgaard et al., 2010; Holman et al., 2012; Wada et al., 2010) in a wide variety of high-stake areas (Elshall et al., 2020; Vergnes et al., 2020). Within the local hydrological cycle, aquifers ensure the storage of water during and after recharge periods, increasing the availability of the resources (Fan, 2015; Fan et al., 2015), and transfer this water to surface systems during rain-free periods (Winter, 1999; Sophocleous, 2002; Alley et al., 2002; Anderson et al., 2015). Quantifying groundwater fluxes remains a challenge, as the hydraulic properties of aquifers, i.e., hydraulic conductivity (K) and transmissivity (T), have classically been constrained through sparse borehole-scale characterization (Anderson et al., 2015; Carrera et al., 2005). They are classically estimated using hydraulic tests at centimeter scales for laboratory experiments up to decimeter scales for well
tests (Renard, 2005; Freeze and Cherry, 1979; Domenico and
Schwartz, 1990). Other methods have been proposed at larger
scales based on the analysis of streamflow dynamics (Troch
et al., 2013; Mendoza et al., 2003; Vannier et al., 2014; Brut-
saert and Nieber, 1977), earth tides (Hsieh et al., 1987; Rot-
zoll and El-Kadi, 2008) and borehole head dynamics (Zlot-
nik and Zurbuchen, 2003; Jiménez-Martínez et al., 2013) as
well as from the calibration of large-scale hydrological mod-
els (Eckhardt and Ulbrich, 2003; Etter et al., 2020; Chow
et al., 2016). Multi-objective calibration has been proposed
to reduce uncertainties, considering complementary data like
temperature (Bravo et al., 2002), groundwater ages derived
from environmental tracers (Kolbe et al., 2016) or continu-
ous geochemical monitoring (Schilling et al., 2019). In ad-
dition, recent advances in machine learning technics show
promising results to evaluate hydraulic properties at the re-
gional scale (Cromwell et al., 2021; Marçais and de Dreuzy,
2017; Reichstein et al., 2019).

To tackle the numerous challenges related to the upscal-
ing of hydraulic properties from the local to the regional or
global scales, several databases provide exhaustive compila-
tions of measurements performed all around the world (Co-
munian and Renard, 2009; Achtziger-Zupančič et al., 2017;
Ranjram et al., 2015; Kuang and Jiao, 2014). By compil-
ing values obtained from calibrated groundwater models,
Gleeson et al. (2014) proposed a global-scale hydraulic con-
ductivity map (GLobal HYdrogeology MaPS, GLHYMPS),
with an update by Huscroft et al. (2018), where values have
been interpolated based on a high-resolution Global Li-tho-
logical Map (GliM; Hartmann and Moosdorf, 2012). Be-
sides inconsistencies and methodological biases supported
in Gleeson et al. (2014), the compiled permeabilities above
the regional scale (> 5 km) are not suitable at the catchment
scale. Therefore, estimating subsurface hydraulic properties
that correctly represent observed catchment-scale processes
remains a major challenge for the hydrological community
(Blöschl et al., 2019). New opportunities have been identified
through the increasing availabilities of surface observations
(Beven et al., 2020; Gleeson et al., 2021), specifically with
an application for ungauged basins.

Information on the spatial distribution of groundwater
seepage appears to be a critical observation to use for the
calibration of subsurface hydraulic properties in hydrologic
models (Grayson and Blöschl, 2000). This approach can be
applied on the assumption that the density and extent of
the stream network is primarily controlled by groundwa-
ter flow. This assumption is valid in temperate and wet cli-
mates for unconfined aquifers, where surface and subsur-
face hydrological systems are well connected (Cuthbert et
al., 2019; Fan et al., 2013) with important discharge of the
aquifer directly into the streams (Haitjema and Mitchell-
Bruker, 2005). Indeed, a groundwater seepage network domi-
nantly controls the structure of a continuous-stream network,
its spatial extent and its ramification (De Vries, 1994; De-
vauchelle et al., 2012; Strahler, 1964; Leibowitz et al., 2018;

Pederson, 2001). Under steady-state conditions, the distribu-
tion of groundwater seepage is then controlled by the char-
acteristic hillslope geometry, the recharge rate (R) and the
aquifer transmissivity (T), i.e., the product of the hydraulic
conductivity (K) and the saturated aquifer thickness (d sat)
(Litwin et al., 2022; Luijendijk, 2021; Bresciani et al., 2014;
Haitjema and Mitchell-Bruker, 2005; Gleeson and Manning,
2008). At a given recharge rate, low transmissive aquifers
display high groundwater table elevations and, consequently,
dense stream networks in the upper part of the catchments.
Conversely, highly transmissive aquifers will display lower
groundwater tables, higher discharge rates in fewer seepage
areas and, consequently, sparser stream networks confined in
the lower-elevation valleys (Day, 1980; Lovill et al., 2018;
Dunne, 1975; Luo et al., 2016; Dietrich and Dunne, 1993;
Godsey and Kirchner, 2014; Prancevic and Kirchner, 2019).

Previous studies have focused on the comparison of an ob-
served hydrographic network with a simulated hydrographic
network computed from different methods. The organization
of stream networks has been predicted directly from a digital
elevation model (DEM) based on a predefined accumulation
threshold value determining whether an upstream surface is
capable of producing significant flow (Mardhel et al., 2021;
Le Moine, 2008; Schneider et al., 2017; Luo and Stepinski,
2008; Lehner et al., 2013). Lumped parameter models, such
as TOPMODEL (Beven and Kirkby, 1979), have also been
extensively used to predict the spatial patterns of seepage ar-
eas (Merot et al., 2003) allowing us to constrain the subsur-
face hydraulic properties (Blazkova et al., 2002; Güntner et
al., 2004; Franks et al., 1998). Luo et al. (2010) proposed
a method leading to a spatial distribution of hydraulic con-
ductivities by constraining a 1D groundwater model based
on the Dupuit–Forcheimer (DF) assumption on drainage dis-
section patterns. However, these approaches are limited to
considering a subsurface flow path equal and parallel to the
downslope topography (Luo and Stepinski, 2008). Relying
on explicit simulations of the spatial stream network with
a process-based hillslope model following the DF assump-
tion (Weiler and McDonnell, 2004), Stoll and Weiler (2010)
proposed to overcome this limitation by routing the down-
slope subsurface flow from the groundwater table with a grid
cell by grid cell approach (Wigmosta and Lettenmaier, 1999).
The assessed subsurface hydraulic properties are intended
to guide the calibration of hydrological models in ungauged
basins, using only a DEM and a hydrographic network map.
These approaches are especially relevant as rapid advances in
remote sensing are improving the description of global river
networks (Schneider et al., 2017; Lehner and Grill, 2013),
wetlands (Tootchi et al., 2019; Rapinel et al., 2023) and soil
moisture (Vergopolan et al., 2021). Lidar and high-resolution
satellite imagery offer new opportunities to determine the
surface characteristics of landscapes (Levizzani and Cattani,
2019; Blöschl et al., 2019) and, by extension, the hydrolog-
ical parameters of local to continental ungauged catchments
(Barclay et al., 2020; Dembélé et al., 2020).
<figure><img src="image_4.png" /><figcaption>**Figure 1.** Model workflow for the calibration of subsurface hydraulic properties from the observed stream network.</figcaption></figure>

In this work, we propose a new methodology to quantify effective hydraulic properties of unconfined aquifers from topographical and stream network observations now available at high resolution. From a parsimonious 3D groundwater flow model, we aim at estimating the catchment-scale *K*, based on surface information only, which is the spatial distribution of the stream network. We propose a novel performance criterion to assess the similarity between the simulated seepage areas and the observed stream network, coupled with a stand-alone calibration procedure. We present the full methodology and its sensitivity to different hydrographic network observation products in 24 catchments covering various geological contexts in northwestern France. We finally discuss opportunities and perspectives to systematically characterize aquifers in ungauged catchments from surface observations.

## 2 Materials and methods

An overview of the method workflow is illustrated in Fig. 1. Each block refers to a specific subsection detailed below (from Sect. 2.1 to 2.5).

1. A digital elevation method (DEM) is used as the top boundary of the groundwater flow model (Sect. 2.1).

2. Three-dimensional groundwater flow is solved in the model domain, and simulated seepage areas are extracted (Sect. 2.2).

3. A selected stream network independent of the DEM is taken as the observed reference (Sect. 2.3).

4. The dimensionless ratio $K/R$ [–] is calibrated to reach the best match between the simulated seepage areas and the extent of the observed stream network (Sect. 2.4).

5. From the optimized $K/R$, the optimal hydraulic conductivity $K_{\text{optim}}$ [L T⁻¹] is deduced by considering the recharge $R$. The optimal transmissivity $T_{\text{optim}}$ [L² T⁻¹] is obtained considering the average thickness of the saturated aquifer $d_{\text{sat}}$ [L] computed by the model (Sect. 2.5).

### 2.1 Definition of the model domain based on the analysis of the topography

We first select the digital elevation model (DEM) that will be defined as the upper boundary of the groundwater model. In this study, we use the 75 m grid resolution DEM available at the scale of France. It is generated from photogrammetric restitution and provided by BD ALTI (IGN, 2021). We also explore the impact of different DEM resolutions on the final estimations of $K/R$. We consider two higher-resolution DEMs of 5 and 25 m also provided by BD ALTI. For coarser resolutions, the 25 m DEM was downsampled with the nearest-neighbor option to larger cell sizes, i.e., 100, 200 and 300 m.

Geospatial processing is performed using the software WhiteboxTools available in Python (Lindsay, 2016), labeled WBT with the respective functions quoted in brackets in the
following. First, the raw DEM is corrected by filling all de-
pressions and by removing flat areas (WBT FillDepressions)
to ensure continuous flow between grid cells. The vec-
tor point shapefile of the outlet is moved to the loca-
tion coincident with the highest flow accumulation value
(WBT.D8FlowAccumulation) within a specified maximum
distance taken as twice the DEM resolution (e.g., 150 m for a
75 m resolution DEM) (WBT.SnapPourPoints). A flow direc-
tion raster (WBT.D8Pointer) is used to extract the drainage
basin (WBT.Watershed).

## 2.2 Groundwater flow model parameterization

The MODFLOW software suite (Harbaugh, 2005) is used to
solve the groundwater flow equation under steady-state con-
ditions for an unconfined aquifer using a three-dimensional
finite-difference approach (Harbaugh, 2005; Niswonger et
al., 2011). The hydraulic head, *h* [L], is calculated as a
function of the hydraulic conductivity, *K* [L T⁻¹], and the
recharge rate, *R* [L T⁻¹], applied on top of the water col-
umn. At the surface of the model domain, the drain package
(DRN) of MODFLOW accounts for the intersection of the
groundwater table with the surface and for the induced seep-
age. Overland flows and surface water re-infiltration are not
integrated as they remain marginal in the conditions of tem-
perate climate and low topographical gradients of the studied
sites.

We use the FloPy Python package (Bakker et al., 2016) to
set and handle simulations. To reduce uncertainties linked to
potential flow across topographic boundaries, a buffer zone is
added to the topographical catchment boundaries, increasing
the modeled domain area by 10%. The 3D model domain
is discretized laterally using the regular mesh of the DEM
and vertically into six layers of equal thickness. Convergence
tests are performed to ensure the stability of the result in-
dependently of numerical discretization. In agreement with
field observations undertaken in the region, a homogeneous
thickness of the aquifer, *d* [L], is set to a constant value of
30 m. This thickness represents the typical depth of the in-
terface between the shallow weathered and/or fractured zone
with the underlying fresh bedrock (Dewandel et al., 2006;
Roques et al., 2016; Mougin et al., 2008; Kolbe et al., 2016).
The model assumes a uniform and isotropic hydraulic con-
ductivity.

The recharge is estimated by the land EXternalized SUR-
Face model (SURFEX version 8.1; Le Moigne et al., 2020).
For more detailed information, the reader is referred to https:
//www.umr-cnrm.fr/surfex/ (last access: 1 September 2023).
Supplied by meteorological variables, SURFEX computes
the energy and water fluxes at the interfaces between soil,
vegetation and the atmosphere (Noilhan and Mahfouf, 1996).
The groundwater recharge of SURFEX is computed as the
proportion of the water mobilized down to the aquifer after
infiltrating through the soil column (Vergnes et al., 2020).
SURFEX was supplied by the SAFRAN meteorological re-

analysis (Vidal et al., 2010; Quintana-Seguí et al., 2008),
available over the French metropolitan area at a 64 km²
(8 × 8 km) resolution. Here, we took the steady-state recharge
as the long-term average recharge rates computed over the
period 1960–2019 and applied them uniformly over the sur-
face of the 3D domain.

## 2.3 Spatial distribution of the observed stream network

The observed stream network is extracted from the French
hydrographic network database BD TOPAGE as a vector
format at the scale of 1 : 10 000 (IGN and OFB, 2019).
The main vector file labeled “Cours d'eau” (rivers) of BD
TOPAGE represents the majority of perennial sections of the
stream network, i.e., filled and/or continuous-flow segments
throughout the year. Note that the information classifying
perennial or intermittent streams collected in the database is
still under development to increase accuracy (Schneider et
al., 2017). It has been rasterized at a grid resolution simi-
lar to the groundwater flow model in order to facilitate the
comparison of the results (WBT VectorLinesToRaster). Due
to the uncertainty in the positioning of the stream network
vector with respect to the DEM, an error of the order of
1 pixel is considered (plus or minus 75 m in this case). The
influence of this error is analyzed in the results presented
in Sect. 3.1 (Fig. 4). We also quantify the impacts of other
DEM product resolutions by considering five other hydro-
graphic network products from three different sources: the
global-scale database HydroRIVERS (labeled case A), the
French database BD TOPAGE (cases B, C and D) and local-
scale inventories (cases E and F) performed within the frame-
work of SAGE (Schéma d'Aménagement et de Gestion des
Eaux). The HydroRivers product is derived from the process-
ing of the DEM at lower resolution (approximately 500 m at
the Equator), while the local inventories are completed by
more detailed field observations. More information on these
products can be found in Appendix A.

## 2.4 Calibration criteria between observed and simulated spatial patterns

For each pixel where seepage is simulated by the ground-
water flow model, we trace the nearest downslope flow path
to the observed stream and compute its distance D<sub>so</sub> [L]
(WBT.TraceDownslopeFlowpaths) (Fig. 2a). This function
of WhiteboxTools uses the topographic structure to compute
the path from cells on the surface to the catchment outlet.
This procedure converts the initial discontinuous spatial pat-
tern of seepage zones simulated by the groundwater flow
model into a continuous-stream network (Fig. 2b).

The distances of the simulated stream network to the ob-
served D<sub>so</sub> are calculated and averaged into the criterion la-
beled D&#773;<sub>so</sub> (WBT.DownslopeDistanceToStream). High D&#773;<sub>so</sub>
values are characteristic of stream networks extending far
away from the observed steams. We also compute the mean
<figure><img src="image_5.png" /><figcaption>(b) Distance map for each stream cell</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Figure 2. (a) Definition of the main metrics used for calibration, with $\overline{D}_{so}$, the average distances computed from simulated stream pixels (in orange) to the nearest (downslope flow path) observed stream pixels (in blue) and $\overline{D}_{os}$ the average distances obtained conversely. (b) Three-dimensional conceptual diagram of the groundwater flow model and of a cross section through the catchment. Continuous streams are generated from pixels where the simulated groundwater table intercepts the topography. By comparison with the observed stream network, some of the simulated streams are correctly estimated (valid, in green), overestimated (excess, in red) or underestimated (missing, in blue).</figcaption></figure>

distance of the observed to the simulated stream networks following a similar procedure. The distance $D_{os}$ [L] from each observed stream network pixel to the simulated stream is computed along the steepest downslope path. In the following, we consider its average $\overline{D}_{os}$ obtained over all pixels of the observed streams. High $\overline{D}_{os}$ values are characteristic of an underdeveloped stream network. The minimum absolute difference between $\overline{D}_{so}$ and $\overline{D}_{os}$ (Eq. 1), labeled $J$, is used as the calibration criterion expressing the closest match of the observed and simulated streams or, in other words, the most relevant combination of missing and excess streams (Fig. 2):

$$J = |\overline{D}_{so} - \overline{D}_{os}|. \qquad (1)$$

$\overline{D}_{so}$ and $\overline{D}_{os}$ intersect when the calibration criterion $J$ is met. This criterion based on both $\overline{D}_{so}$ and $\overline{D}_{os}$ achieves the best equilibrium between over- and underestimations.

At this point, we define the distance $D_{optim}$ [L] as the average of $\overline{D}_{so}$ and $\overline{D}_{os}$ (Eq. 2):

$$D_{optim} = \frac{\overline{D}_{so} + \overline{D}_{os}}{2}. \qquad (2)$$

The smaller the value of $D_{optim}$, the better the match of the simulated seepage pattern and the observed stream network. $D_{optim}$ will thus be used as an indicator of the calibration performance. In order to compare cases with different DEM resolution DEMres [L], $D_{optim}$ is normalized by the DEM resolution:

$$r_{optim} = \frac{D_{optim}}{DEM_{res}}. \qquad (3)$$

$r_{optim}$ [-] should remain small to ensure the consistency of the observed and simulated stream networks. It will practically be limited to 2 considering that the mismatch cannot exceed the resolution of 2 pixels:

$$r_{optim} \leq 2. \qquad (4)$$

## 2.5 Estimating the optimal hydraulic conductivities

The model parameter $K/R$ ratio is calibrated by minimizing the objective function defined by Eq. (1), for a given aquifer thickness ($d$). Optimization is performed by a dichotomy approach (Burden and Faires, 1985). The convergence criterion is reached when $K/R$ varies by less than 1 %. In order to ensure that $K$ estimates are representative of catchment-scale processes driving the spatial distribution of the stream network, independently of the aquifer thickness set in the model, we computed the equivalent normalized transmissivity, $T/R$, by multiplying $K/R$ by the average saturated aquifer thickness ($d_{sat}$) computed by the model at the catchment scale (Fig. 2b). In our modeling approach, $K$ and $d$ are input parameters of the model, while $T$ is an output including the computed $d_{sat}$. Finally, optimal transmissivity $T_{optim}$ and hydraulic conductivity $K_{optim}$ are evaluated assuming the applied average groundwater recharge rate, $R$, and with known aquifer thickness.

## 2.6 Testing the methodology on selected pilot catchments

The approach is deployed in 24 selected catchments located in Brittany and Normandy (France) (Fig. 3), where an oceanic and temperate climate prevails. The average catchment area ranges from 12 to 141 km² with an average of 58 km² (Table 1), which corresponds to an average of 61 800 elements for the domain model discretization. These catchments were selected because of the diversity of their geological and geomorphological settings. Most of them are also subject to extensive research activities for their importance in providing freshwater to the nearby cities (sites 1, 2, 3, 4, 5, 6, 15, 16, 18, 19) or flooding dynamics (sites 20, 21, 22, 23, 24). Some of these sites are also studied in col-
<figure><img src="image_7.png" /><figcaption>**Figure 3.** (a) Location of the pilot catchments (Armorican Massif in Brittany and Normandy, northwestern part of France). (b) Zoom on sites along with a simplified map of the main lithological units (1 : 1000 000 scale) in sub-panels A, B, C and D.</figcaption></figure>

<table><caption>**Table 1.** Main landscape characteristics, model input parameters and modeling results, including hydraulic conductivities and transmissivities for the 24 catchments studied.</caption><thead><tr><th>Catchment</th><th>Site ID</th><th>Main lithology</th><th>Area [km²]</th><th>Slope [%]</th><th>Drainage density [km⁻¹]</th><th>R [mm yr⁻¹]</th><th>K<sub>optim</sub>/R [-]</th><th>D<sub>optim</sub> [m]</th><th>K<sub>optim</sub> [m s⁻¹]</th><th>d<sub>sat</sub> [m]</th><th>T<sub>optim</sub> [m² s⁻¹]</th></tr></thead><tbody><tr><td>Basance</td><td>15</td><td>Plutonic</td><td>26</td><td>4.0</td><td>1.8</td><td>237</td><td>1783</td><td>40</td><td>1.3 × 10⁻⁵</td><td>27.9</td><td>3.7 × 10⁻⁴</td></tr><tr><td>Nançon</td><td>16</td><td>rocks</td><td>65</td><td>3.3</td><td>1.5</td><td>237</td><td>1397</td><td>73</td><td>1.1 × 10⁻⁵</td><td>28.0</td><td>2.9 × 10⁻⁴</td></tr><tr><td>Serein</td><td>4</td><td>Paleozoic</td><td>13</td><td>3.7</td><td>0.8</td><td>226</td><td>1514</td><td>87</td><td>1.1 × 10⁻⁵</td><td>27.7</td><td>3.0 × 10⁻⁴</td></tr><tr><td>Chèze</td><td>5</td><td>sandstone/</td><td>12</td><td>2.5</td><td>0.8</td><td>226</td><td>3125</td><td>106</td><td>2.3 × 10⁻⁵</td><td>27.5</td><td>6.2 × 10⁻⁴</td></tr><tr><td>Canut</td><td>6</td><td>schist</td><td>30</td><td>2.2</td><td>0.7</td><td>215</td><td>2677</td><td>147</td><td>1.8 × 10⁻⁵</td><td>28.1</td><td>5.1 × 10⁻⁴</td></tr><tr><td>Gaël</td><td>1</td><td></td><td>132</td><td>2.5</td><td>0.7</td><td>201</td><td>7344</td><td>149</td><td>4.7 × 10⁻⁵</td><td>28.0</td><td>1.3 × 10⁻³</td></tr><tr><td>Garun</td><td>2</td><td></td><td>96</td><td>2.4</td><td>0.7</td><td>175</td><td>5938</td><td>144</td><td>3.3 × 10⁻⁵</td><td>27.9</td><td>9.2 × 10⁻⁴</td></tr><tr><td>Vaunoise</td><td>3</td><td></td><td>62</td><td>2.7</td><td>0.8</td><td>168</td><td>5469</td><td>106</td><td>2.9 × 10⁻⁵</td><td>28.0</td><td>8.2 × 10⁻⁴</td></tr><tr><td>Estret</td><td>9</td><td></td><td>14</td><td>2.0</td><td>1.0</td><td>161</td><td>3985</td><td>106</td><td>2.0 × 10⁻⁵</td><td>27.6</td><td>5.6 × 10⁻⁴</td></tr><tr><td>Linonlac</td><td>10</td><td>Brioverian</td><td>16</td><td>2.9</td><td>0.8</td><td>164</td><td>5860</td><td>97</td><td>3.1 × 10⁻⁵</td><td>28.1</td><td>8.6 × 10⁻⁴</td></tr><tr><td>Bouteille</td><td>11</td><td>schist</td><td>24</td><td>2.9</td><td>0.8</td><td>161</td><td>8281</td><td>80</td><td>4.2 × 10⁻⁵</td><td>28.0</td><td>1.2 × 10⁻³</td></tr><tr><td>Flume</td><td>12</td><td></td><td>134</td><td>2.9</td><td>0.9</td><td>161</td><td>3243</td><td>105</td><td>1.6 × 10⁻⁵</td><td>28.0</td><td>4.6 × 10⁻⁴</td></tr><tr><td>Vignoc</td><td>13</td><td></td><td>41</td><td>3.0</td><td>0.9</td><td>172</td><td>3243</td><td>82</td><td>1.8 × 10⁻⁵</td><td>27.8</td><td>4.9 × 10⁻⁴</td></tr><tr><td>Néal</td><td>14</td><td></td><td>95</td><td>2.7</td><td>0.9</td><td>175</td><td>2774</td><td>107</td><td>1.5 × 10⁻⁵</td><td>27.9</td><td>4.3 × 10⁻⁴</td></tr><tr><td>Seulles</td><td>23</td><td></td><td>134</td><td>4.7</td><td>1.1</td><td>274</td><td>4688</td><td>342</td><td>4.0 × 10⁻⁵</td><td>28.2</td><td>1.1 × 10⁻³</td></tr><tr><td>Le Home</td><td>7</td><td></td><td>19</td><td>2.4</td><td>1.0</td><td>190</td><td>1739</td><td>135</td><td>1.0 × 10⁻⁵</td><td>27.8</td><td>2.9 × 10⁻⁴</td></tr><tr><td>Arguenon</td><td>8</td><td>Schist/</td><td>103</td><td>4.7</td><td>0.8</td><td>234</td><td>7891</td><td>190</td><td>5.8 × 10⁻⁵</td><td>28.2</td><td>1.7 × 10⁻³</td></tr><tr><td>Guidel</td><td>17</td><td>plutonic</td><td>24</td><td>3.8</td><td>1.0</td><td>307</td><td>10 312</td><td>112</td><td>1.0 × 10⁻⁴</td><td>28.1</td><td>2.8 × 10⁻³</td></tr><tr><td>Lannénec</td><td>18</td><td>rocks</td><td>13</td><td>3.1</td><td>0.9</td><td>234</td><td>10 078</td><td>243</td><td>7.5 × 10⁻⁵</td><td>28.2</td><td>2.1 × 10⁻³</td></tr><tr><td>Ploemeur</td><td>19</td><td></td><td>15</td><td>2.9</td><td>0.9</td><td>307</td><td>4063</td><td>81</td><td>3.9 × 10⁻⁵</td><td>27.8</td><td>1.1 × 10⁻³</td></tr><tr><td>Mue</td><td>20</td><td></td><td>99</td><td>1.5</td><td>0.4</td><td>179</td><td>19 687</td><td>114</td><td>1.1 × 10⁻⁴</td><td>27.7</td><td>3.1 × 10⁻³</td></tr><tr><td>Laizon</td><td>21</td><td>Limestone</td><td>141</td><td>2.2</td><td>0.5</td><td>182</td><td>19 375</td><td>581</td><td>1.1 × 10⁻⁴</td><td>28.0</td><td>3.2 × 10⁻³</td></tr><tr><td>Thue</td><td>22</td><td></td><td>52</td><td>1.9</td><td>0.5</td><td>172</td><td>12 031</td><td>222</td><td>6.5 × 10⁻⁵</td><td>27.8</td><td>1.8 × 10⁻³</td></tr><tr><td>Gronde</td><td>24</td><td></td><td>25</td><td>1.7</td><td>0.4</td><td>179</td><td>19 87</td><td>146</td><td>1.1 × 10⁻⁴</td><td>27.6</td><td>3.1 × 10⁻³</td></tr></tbody></table>

laboration with local stakeholders in issues related to water quality and river restoration (sites 8, 9, 10, 11, 12, 13, 14, 17, 18 19) or within observatories and research infrastructures (site 7: long-term socio-ecological research (LTSER) “Zone Atelier Armorique (ZAAr)”; sites 17, 18, 19: French network

of Critical Zone Observatories (OZCAR) “Ploemeur-Guidel CZO”). None of these catchments present any reservoir or stream obstacle that would significantly alter the stream network. The study sites cover five major lithologies including Brioverian schist (sedimentary rock), Paleozoic sandstone
and schist (sedimentary rock), plutonic rocks (mainly gran-
ite), mica schist (metamorphic sedimentary rock), and lime-
stone (sedimentary rock). Sites have a homogeneous lithol-
ogy (1 : 1000 000 scale) throughout the catchment except for
five sites (sites 7, 8, 17, 18, 19) that present two lithologies.

3 Results

**3.1 Detailed analysis of model results at a single site**

Before presenting the results obtained for the ensemble of
pilot sites, we first illustrate the results of the methodology
at one specific site, the Canut catchment (Fig. 3, site 6). We
provide details on the different steps of the numerical method
and assess their performance. The main results of the cali-
bration method are presented in Fig. 4. The dimensionless
ratio K/R strongly controls the spatial distribution of the
hydraulic head, i.e., the saturated aquifer thickness d<sub>sat</sub>, the
shape of the groundwater table and its intersection with the
surface (Fig. 4a). As K/R increases, the head gradient de-
creases and progressively disconnects from the surface. This
implies that the seepage areas become sparser, mostly orga-
nized downstream close to the catchment outlet. Inversely,
lower values of K/R tend to expand the seepage patterns
along the valleys and depressions towards the head of the
catchment. Figure 4a shows the sensitivity of D&#773;<sub>so</sub> and D&#773;<sub>os</sub>,
considering three values of K/R. It confirms that the dis-
tance from the observed to the simulated stream network
D&#773;<sub>os</sub> increases with K/R and inversely that the distance from
the simulated to the observed stream network D&#773;<sub>so</sub> decreases
with K/R.

High-order streams are accurately predicted in all three
simulations as shown by the green pixels (Fig. 4a). Low-
order streams are more sensitive and drive most of the vari-
ations in D<sub>so</sub> and D<sub>os</sub> as shown by the evolving red to green
pixels when changing K/R. In other words, the calibration
is controlled by the spatial extent of the streams from the
valleys to the headwaters following the topographic depres-
sions. D<sub>optim</sub> is equal to 147 m and remains smaller than
twice the resolution of the DEM indicating a close match
of the observed streams (Fig. 4b). Using the DEM resolu-
tion of 75 m as an indicator of uncertainty, K/R ranges be-
tween 1458 and 7082 (shaded area in Fig. 4b), correspond-
ing to a hydraulic conductivity ranging between 1.1 × 10<sup>-5</sup>
and 4.8 × 10<sup>-5</sup> m s<sup>-1</sup> for an estimated average recharge of
215 mm yr<sup>-1</sup>. In this case, the optimal hydraulic conductiv-
ity K<sub>optim</sub> is estimated at 1.8 × 10<sup>-5</sup> m s<sup>-1</sup>. We deduce the
optimal transmissivity T<sub>optim</sub> of 5.1 × 10<sup>-4</sup> m<sup>2</sup> s<sup>-1</sup> consider-
ing an average saturated thickness of 28.1 m simulated by the
model (Fig. 4b).

We evaluate the impact of the maximum aquifer thickness on $T_{\text{optim}}$ by running the calibration procedure considering five different values of $d$: 5, 10, 50, 100 and 300 m. We found that the simulated stream network matches the observed one for all thicknesses ($d$) (Fig. 5a1, A to F). However, we found differences in the estimated $T_{\text{optim}}$ (Fig. 5a2). For cases C, D, E and F, where the maximum aquifer thicknesses are greater than 30 m, the optimal transmissivity $T_{\text{optim}}$ remains constant at around $4.0 \times 10^{-4} \text{ m}^2 \text{ s}^{-1}$. For cases A and B with smaller thicknesses (< 30 m), $T_{\text{optim}}$ reaches much larger values of $4.1 \times 10^{-3}$ and $1.8 \times 10^{-3} \text{ m}^2 \text{ s}^{-1}$, respectively. Such divergences come from the breakdown of the Dupuit-Forchheimer assumption. Small thicknesses bring the flow lines closer to the surface and widen the seepage areas (Bresciani et al., 2014), effects that must be offset by substantially higher hydraulic conductivities and transmissivities to lower the water table.

We also investigate the sensitivity of the resolutions of both the DEM (Fig. 5b) and the observed stream network (Fig. 5c) to the estimations of $T_{\text{optim}}$. The resolution of the DEM has only a minor influence on the estimation of optimal transmissivity, while the resolution of the stream network has a major impact. Figure 5b1 shows that the simulated stream network corresponds well to the observed network for the different DEM resolutions. However, the estimated optimal transmissivities vary significantly across the different cases (Fig. 5b2). For cases C, D and E, the estimated $T_{\text{optim}}$ values remain close to each other, ranging from $5.0 \times 10^{-5}$ to $5.6 \times 10^{-5} \text{ m}^2 \text{ s}^{-1}$. For case F, $T_{\text{optim}}$ reaches a value of $2.9 \times 10^{-4} \text{ m}^2 \text{ s}^{-1}$, while for A and B, it takes values of $1.9 \times 10^{-3}$ and $9.7 \times 10^{-4} \text{ m}^2 \text{ s}^{-1}$, respectively. For cases C to F, the $r_{\text{optim}}$ criterion (Eq. 3) remains close to 1 (from 0.5 to 1.8), smaller than the threshold of 2 (Eq. 4). However, for the 5 and 25 m resolutions tested (cases A and B), the distances $D_{\text{so}}$ and $D_{\text{os}}$ are highly sensitive to the mismatch between an increasingly accurate DEM and a coarsely defined stream network. The main factor driving $D_{\text{so}}$ and $D_{\text{os}}$ is no longer the hydraulic conductivity but the mismatch between the DEM and the observed stream network, with $r_{\text{optim}}$ values becoming larger (respectively, 46.5 and 7.7 for the 5 and 25 m resolutions tested). These results emphasize that DEMs with resolutions that are too fine, here 5 and 25 m, cannot be used with the observed stream network selected in this study, at least at the current stage of the methodological development. Resolutions of 75 m and coarser, however, lead to consistent estimations of the hydraulic conductivity confirming the validity of the modeling approach.

We have systematically tested the method using six dif-
ferent stream network products issued by global, national
and local databases (Fig. 5c1). These products display im-
portant differences in the extent and densities of the stream
network coming from their origin and scale of observations
(Appendix A). For case A, the global-scale product HydroR-
IVERS (Lehner et al., 2013) locates rivers away from the
topographic valleys of the DEM, with consequently a $D_{\text{optim}}$
<figure><img src="image_8.png" /><figcaption>**Figure 4.** (a) Two-dimensional map views of distances computed along the steepest slope from simulated stream pixels to the nearest observed ones ($D_{so}$) and from the observed stream pixels to the nearest simulated ones ($D_{os}$) for the Canut catchment. Results are presented for the lowest, optimal and highest $K/R$ values explored. (b) Average distances $\bar{D}_{so}$ and $\bar{D}_{os}$ as functions of $K/R$. The shaded areas in gray around the curves correspond to the 75 m uncertainty range equal to the resolution the DEM. The optimal simulation is obtained for $K_{optim}/R$ at the intersection between the two curves. At this point $\bar{D}_{so}$ and $\bar{D}_{os}$ are both equal to $D_{optim}$, and, in this case, $r_{optim}$ is close to 2. The estimated optimal hydraulic conductivity $K_{optim}$ is derived by using the recharge rate provided by SURFEX, and $T_{optim}$ is obtained considering the mean saturated aquifer thickness ($d_{sat}$). To further illustrate the methodology, an animated figure representing 2D map views of the simulated seepage areas as a function of $K/R$ is available in the Supplement with the associated objective minimization function results in Appendix B.</figcaption></figure>

value more than 10 times larger than DEM<sub>res</sub>. For cases B to F, the criterion $r_{optim}$ (Eq. 3) remains smaller than 2, the hydrographic network is well captured and the method estimates $T_{optim}$ consistently (Fig. 5c2). $T_{optim}$ varies over 1 order of magnitude from $2.0 \times 10^{-4}$ to $3.8 \times 10^{-3} \text{ m}^2 \text{ s}^{-1}$ and logically tends to decrease when the density and extent of the mapped stream network increases. Indeed, for a fixed recharge rate, lower transmissivities raise the groundwater table and broaden the headwater streams (Fig. 5c, E and F). Conversely, higher values of $T$ contract the hydrographic networks with streams located mainly at lower elevations (Fig. 5c1, A and B). The extent of the stream system and the first-order stream locations appear to be highly sensitive to the estimated transmissivity confirming its capacity to inform the hydraulic conductivity.

## 3.2 Application to the ensemble of catchments

The method has been applied to the 23 other catchments (Fig. 3) with the same DEM resolution of 75 m, the product for the observed reference stream network and an aquifer thickness of 30 m. Both $\bar{D}_{so}$ and $\bar{D}_{os}$ were found to systematically intersect defining optimal $D_{optim}$ (Fig. 6) and $K_{optim}/R$ values (Table 1). For 19 sites, the value of $D_{optim}$ is less than 2 pixels (Fig. 6), showing good consistency between the simulated and the observed stream network, and $K_{optim}/R$ varies between 1397 to 19687. Considering $d_{sat}$ computed by the model, $T_{optim}$ values range over 1 order of magnitude from $2.9 \times 10^{-4}$ to $3.2 \times 10^{-3} \text{ m}^2 \text{ s}^{-1}$ (Fig. 6), resulting in $K_{optim}$ values between $1.0 \times 10^{-5}$ and $1.1 \times 10^{-4} \text{ m s}^{-1}$ (Table 1).

The model captures correctly the features of the observed stream network even in the presence of singular topographical features such as extended depressions or sharp changes in slope (Gauvain et al., 2021; Schumm et al., 1995). This is especially the case at site 7 where the seepage along the foot slope issued by a steep slope transition (6% on 1000 m of length) located along a lithological contact is well represented both by the model and in the observations as a significant and perennial groundwater spring and/or wetland (Vautier et al., 2019; Kolbe et al., 2016).

# 4 Discussion

## 4.1 A new calibration method for the assessment of effective catchment-scale hydraulic properties

We have presented a process-based groundwater modeling approach to assess effective catchment-scale hydraulic properties ($K$ and $T$) from the sole information on the density and spatial extent of the stream network. The proposed method (1) simulates the stream network by physically representing the 3D groundwater flows, (2) quantifies the mismatch between observed and simulated stream networks through distance-based spatial indicators and (3) calibrates the subsurface hydraulic properties by minimizing a performance criterion. We compare it with existing approaches and indicators.

Previous modeling approaches were mostly based on TOPMODEL applications (Blazkova et al., 2002; Güntner et
<figure><img src="image_9.png" /><figcaption>**Figure 5.** Sensitivity analysis of the method for the Canut catchment (site 6) to (a) the DEM resolution, (b) the density and extent of the stream network displayed by different stream network products, and (c) the aquifer thickness. Panels (a1, b1, c1) show the downslope flow path distances of the simulated stream pixels projected onto the observed reference stream network for $K_{\text{optim}}/R$. Panels (a2, b2, c2) show $r_{\text{optim}}$ as a function of $T_{\text{optim}}$.</figcaption></figure>

al., 2004; Franks et al., 1998) or hillslope-scale flows (Luo et al., 2010). They had the advantage of simplicity but were limited in simple cases where flows are topography-driven. Like the 1D hillslope-scale approach of Stoll and Weiler (2010), our 3D distributed- and process-based groundwater approach remains valid in conditions where the groundwater table is not a strict replicate of the topography becoming “recharge controlled” (Haitjema and Mitchell-Bruker, 2005). It also accounts for the discontinuities of the seepage structure coming from the irregular connections of the subsurface flows with the surface (Godsey and Kirchner, 2014; Whiting and

Godsey, 2016; Warix et al., 2021). It follows numerous field observations and synthetic experiments showing the strong influence of 3D groundwater flow organizations on the location of seepage zones (Goderniaux et al., 2013; Fleckenstein et al., 2006; Gauvain et al., 2021; Dohman et al., 2021).

Several indicators have been proposed to compare the spatial patterns of the modeled and observed saturated areas mostly based on cell-by-cell and cell-neighborhood approaches. This includes the likelihood measure (Franks et al., 1998; Blazkova et al., 2002), the Kappa goodness-of-fit statistic (Stoll and Weiler, 2010) and the Euclidean distance
<figure><img src="image_10.png" /></figure>

**Figure 6.** *D*<sub>optim</sub> and *r*<sub>optim</sub> criteria as functions of *T*<sub>optim</sub> estimated for the 24 sites. The optimal transmissivity *T*<sub>optim</sub> is obtained by considering *K*<sub>optim</sub>, and the mean saturated aquifer thickness *d*<sub>sat</sub> is computed. The shaded area corresponds to sites with *r*<sub>optim</sub> > 2. The DEM resolution is 75 m and the aquifer thickness is 30 m. The error bars correspond to the estimated *T*<sub>optim</sub> considering the DEM resolution as an uncertainty indicator.

between cells (Güntner et al., 2004). These indicators are es-
sentially local and readily accessible from information on to-
pography and stream networks. We propose more integra-
tive indicators based on the distance between the observed
and simulated stream networks computed along the steepest
slope between them, as does the IDPR (Network Develop-
ment and Persistence Index), to identify zones predominantly
favorable to infiltration or runoff (Mardhel et al., 2021). The
advantages of this procedure are to account for the topo-
graphical structure within the definition of the distances and
to constrain the comparison to the best compromise between
the over- and undersaturation, mainly driven by D̅<sub>so</sub> and D̅<sub>os</sub>,
respectively.

## 4.2 Comparison of estimated hydraulic conductivities with previously published values

As shown in Fig. 6, the method predicts a distribution of *T*
values that stands within 1 order of magnitude despite the
broad range of lithological units investigated. Overall, our
estimates of hydraulic properties are consistent with values
found in previous studies conducted for similar sites and
lithologic settings (Roques et al., 2016; Mougin et al., 2008;
Dewandel et al., 2021; Cornette et al., 2022; Leray et al.,
2012). We compared the estimated hydraulic conductivity, *K*<sub>optim</sub>, with local to regional values found in the literature *K*<sub>literature</sub> (Fig. 7). We focused on the comparison with local estimates from hydraulic tests or numerical groundwater models for two of the studied sites (Le Borgne et al., 2006; Kolbe et al., 2016; Jiménez-Martínez et al., 2013) or on

<figure><img src="image_11.png" /></figure>

**Figure 7.** Comparison of *K*<sub>optim</sub> obtained for the 24 catchments with values found in the literature *K*<sub>literature</sub> grouped into two categories according to the scale of investigation (local vs. regional). Diamonds: values from hydraulic tests and/or groundwater modeling compiled in regional syntheses according to lithologies (BRGM, 2018; Laurent et al., 2017). Circles: *K* obtained from local hydraulic tests for site 19 (Le Borgne et al., 2006; Jiménez-Martínez et al., 2013) and groundwater modeling for site 7 (Kolbe et al., 2016). The values provided in transmissivity by the literature are translated into hydraulic conductivities by applying the same aquifer thickness of 30 m.

those compiled in regional syntheses according to the lithol-
ogy (Laurent et al., 2017; BRGM, 2018). Figure 7 shows a
good agreement between our results and the other values.
More specifically, the local values extracted for catchments 7
and 19 slightly underestimate the one from the literature by
about 33% (Fig. 7, diamonds). The hydraulic conductivities
derived from regional synthesis remain within the same or-
der of magnitude with a limited overestimation of a factor
of 2 (Fig. 7, circles). This slight overestimation might result
from testing methods as well as the fact that local hydraulic
tests are often carried out close to transmissive geological
features of major interest for water supply. Our results were
also compared to those compiled in the global-scale database
GLHYMPS (Huscroft et al., 2018). From the database, we
derived equivalent hydraulic conductivities for each of the
catchments. They range over 4 orders of magnitude, sys-
tematically lower by 1 to several orders of magnitude than
our estimates (Appendix C). As shown in previous studies
(de Graaf et al., 2020; Tashie et al., 2021), we find that the
hydraulic conductivity dataset compiled in GLHYMPS may
be locally underestimated.

The results also show a range of values consistent with
those given by classical textbooks for the investigated litholo-
<figure><img src="image_12.png" /><figcaption>**Figure 8.** For the five sites corresponding to $r_{\text{optim}} > 2$, representation of the observed stream network on top of the simplified geological map (1 : 1000 000 scale), with the downslope flow path distances of the simulated seepage areas projected to the observed streams. For site 8, differences are larger on the plutonic rocks. For the other sites, the white square identifies the area where differences are the largest.</figcaption></figure>

gies (Freeze and Cherry, 1979; Domenico and Schwartz, 1990). Crystalline rocks characterized by weathering and fractures (Roques et al., 2014; Dewandel et al., 2006) have a lower hydraulic conductivity than sedimentary rocks, here represented by limestones with a karstic systems (IGN and OFB, 2019) that, as expected, display higher conductivities. Lower conductivities suggest a high water table inducing a larger spatial extent of the stream network, confirmed by local knowledge, with a much higher observed drainage density for crystalline sites compared to limestone sites (Table 1). Although our results show evidence that effective conductivities are related to variations in dominant lithologies, it is also clear that other reported factors like erosion, bedrock weathering and fracturing may tend to homogenize the hydraulic properties in similar erosion and/or weathering settings (Luo et al., 2016; Yoshida and Troch, 2016; Jefferson et al., 2010; Litwin et al., 2022).

## 4.3 Sensitivity to input and/or model parameters: related improvements for broader applicability

The $D_{\text{optim}}$ indicator (Eq. 2) provides information on the level of uncertainty. It depends on the quality of the data (observed reference stream network and the DEM) and on the model assumptions. Five sites (8, 18, 21, 22 and 23) over the 23 sites studied display a low match between the simulated and observed stream networks ($r_{\text{optim}} > 2$), with $D_{\text{optim}}$ values ranging from 190 to 581 m (Fig. 6). Figure 8 maps the simulation results for these five sites. For site 18, the model predicts a seepage zone induced by a topographic depression representing potential ponds, lakes and wetlands, which are not in the observations. For sites 21 and 22, the main differences are located at a non-reported subsurface flow in the

observed stream network within a karstic system (IGN and OFB, 2019); however, this is represented well by the model due to a topographic depression along this area. For site 23, the simulated flow at the bottom of the DEM valley appears to be parallel to the observed flow. In this case, it seems to be a registration error in the alignment of the stream location data within the DEM. For site 8, differences come principally from the model and, more specifically, from the assumption of a uniform hydraulic conductivity. For this site with lateral lithologic heterogeneity, we found that the model underestimates the extent and density of the stream network in the part with dominant plutonic rocks and overestimates them in the schists. At site 8, the IDPR (Mardhel et al., 2021) indicates that the granitic area is less permeable than the schist area and generally displays the limestone sites 21 and 22 primarily dominated by infiltration, consistent with our results.

The high sensitivity of applied $K/R$ to both the density and spatial extent of the observed stream network highlights the requirement of using high-quality stream products. Several issues may arise. First, river maps available in national to global databases are often incomplete compared to local databases compiled by stakeholders in direct field observations, leading to an overestimation of the effective hydraulic properties. Second, artificial channels, drainage ditches and any other departure from the geomorphic equilibrium may alter the stream network system and lead to an overestimation of the hydraulic properties in highly impacted zones. Third, the resolution of the DEM and reference stream network must be close. Nevertheless, the observed stream network layer could be adjusted to better match the DEM resolution.

Major limitations and improvements may also arise from the assumptions of the hydrogeological model. The proposed
methodology can be used with other parameterizations and model conceptualizations. The model domain can be extended and the boundary conditions modified to better represent potentially longer and deeper regional groundwater circulations. If the information is available, the method could be tested with heterogeneous recharge at the catchment scale. The geometry of the aquifer could be adapted, applying flat- or irregular-bottom aquifers based on geophysical measurements (Pasquet et al., 2022) or depth to bedrock databases (Shangguan et al., 2017; Hengl et al., 2017; Pelletier et al., 2016). Exponentially decreasing conductivity with depth can be applied to the model in order to estimate the initial value of *K* at the surface or its characteristic decay depth. At the current stage of the method, catchment-scale lithological heterogeneities can be considered by applying the methodology independently on sub-areas characterized by a homogeneous lithology. For example, at the studied site 8, the application of the methodology on granite-dominated sub-catchments should result in lower *K* estimates than in the schist areas. Localized heterogeneities including weathering, fractures, faults and other discontinuities cannot be identified. They should be explicitly introduced into the model and characterized by other methods.

## 5 Conclusions

Global syntheses compiling accurate predictions of hydraulic properties of the subsurface are critically needed to predict water resource availabilities (Fan et al., 2019) in ungauged catchments (Sivapalan et al., 2003; Hrachowitz et al., 2013) and to assess the impact of hillslope- and catchment-scale hydrology on global change predictions (Taylor et al., 2013). Besides the climatic forcing data, requiring only a stream network map to calibrate a groundwater flow model built from a DEM, the approach presented in this article addresses this challenge, specifically for ungauged basins. Under the assumption that the transmissivity (hydraulic conductivity integrated over the saturated aquifer thickness) controls the extension and density of the hydrographic network, the approach calibrates the effective hydraulic properties against the stream network. The resolution of the stream network and DEM should be consistent. We showed that the spatialized performance criterion based on the distances between the simulated and observed stream network achieves an equilibrium between over- and undersaturation of the underlying groundwater system, as well as an equilibrium between over- and underestimation of the stream network extent. The resulting estimated *K* values are consistent with local values found in the literature.

A major advantage is the ease of deployment and transferability of the methodology to other catchments. Although the proposed methodology is limited to unconfined aquifers and particularly suited to contexts with significant subsurface-surface interactions, where groundwater primarily feeds streams, it aims to be deployed at multiple spatial scales by taking advantage of databases compiling topographic, hydrologic and climate information. Such deployment improving subsurface characterization from surface information would leverage the current development in crowdsourcing (Etter et al., 2020) and innovations in remote sensing (Biancamaria et al., 2016) that now provide high-resolution surface DEM products (Hawker et al., 2022; Yamazaki et al., 2017) and mapping of hydrographic networks (Grill et al., 2019; Yamazaki et al., 2019) distinguishing the perennial and intermittent streams (Fovet et al., 2021; Messager et al., 2021).

## Appendix A: Hydrographic network product information

### A1 Global database

HydroRIVERS (available on this website: https://www.hydrosheds.org/page/hydrorivers, last access: 1 September 2023) (Linke et al., 2019) is derived from HydroSHEDS (Lehner et al., 2013), a mapping product that provides stream information for regional- and global-scale applications, based on a grid resolution of 15 arcsec (approximately 500 m at the Equator).

### A2 National database

The BD TOPAGE (available on this website: https://bdtopage.eaufrance.fr, last access: 1 September 2023) database classifies streams as perennial or intermittent based on historical photogrammetric reconstructions.

### A3 Local database

The local stream and wetland inventory maps are based on observations and field surveys validated by the “Schéma d’Aménagement et de Gestion des Eaux” (SAGE) (available on this website: https://sdage-sage.eau-loire-bretagne.fr/home.html, last access: 1 September 2023).
## Appendix B: Objective function of the calibration criteria

<figure><img src="image_13.png" /><figcaption>(b)</figcaption></figure>

<figure><img src="image_14.png" /></figure>

**Figure B1.** For the Canut catchment (site 6), (a) 2D map views of simulated seepage areas and nearest downslope flow path distances (simulated to observed and observed to simulated) for the two *K*/*R* values at the bounds of the uncertainty (lower and higher) and (b) the objective function based on the developed performance criteria obtained.

## Appendix C: Comparison with the Global Hydrogeology MaPS (GLHYMPS 2.0) permeability

<figure><img src="image_15.png" /></figure>

**Figure C1.** Comparison of *K*<sub>optim</sub> obtained for the 24 catchments with values from the literature, *K*<sub>GLHYMPS</sub>, provided by the GL-HYMPS 2.0 global permeability map (Huscroft et al., 2018) and averaged over each catchment.

*Code and data availability.* A Python code to test the method is available online in a shared repository: https://doi.org/10.5281/zenodo.8311547 (Abhervé, 2023).

*Supplement.* The supplement related to this article is available online at: https://doi.org/10.5194/hess-27-3221-2023-supplement.

*Author contributions.* All co-authors were involved in the conceptualization of the original methods, identification of the research questions and the interpretation of the results. RA and AG developed the model, performed the simulations and analyzed the results. RA created the figures and prepared the first draft of the manuscript. All co-authors reviewed and edited the paper.

*Competing interests.* The contact author has declared that none of the authors has any competing interests.

*Disclaimer.* Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

*Acknowledgements.* Clément Roques acknowledges financial supports from the Rennes Métropole research chair "Ressource en Eau du Futur" and the European project WATERLINE (project
ID CHIST-ERA-19-CES-006). Alexandre Gauvain acknowledges funding from the RIVAGES Normands 2100 project. The investigations also benefited from the support of the Network of hydrogeological research sites (H+) observatory and the French research observatory network of Critical Zone Observatories: Research and Applications (OZCAR-RI).

*Financial support.* This work was funded by Eau du Bassin Rennais and Rennes Métropole, through the "Eaux et Territoires" ("Water and Territories") research chairs of the Foundation of the University of Rennes (Fondation Rennes 1).

*Review statement.* This paper was edited by Markus Weiler and reviewed by Ciaran Harman and one anonymous referee.

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