# Using natural tracers and calibrated analytical filter to highlight baseflow contribution to mountainous Mediterranean rivers in a context of climate change

P.A. Guisiano, Sébastien Santoni, Frédéric Huneau, Emilie Garel, Alexandra Mattei

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P.A. Guisiano, Sébastien Santoni, Frédéric Huneau, Emilie Garel, Alexandra Mattei. Using natural tracers and calibrated analytical filter to highlight baseflow contribution to mountainous Mediterranean rivers in a context of climate change. Journal of Hydrology, 2024, 641, pp.131842. 10.1016/j.jhydrol.2024.131842. hal-04802605

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# Using natural tracers and calibrated analytical filter to highlight baseflow contribution to mountainous Mediterranean rivers in a context of climate change

P.A. Guisiano<sup>a, b, *</sup>, S. Santoni<sup>a, b</sup>, F. Huneau<sup>a, b</sup>, A. Mattei<sup>a, b</sup>, E. Garel<sup>a, b</sup>

## ARTICLE INFO

Handling Editor: S. Sally Elizabeth Thompson

### Keywords:

- Baseflow analysis

- Tracer-based methods

- Calibrated filter

- Mediterranean rivers

- Groundwater contribution

- Corsica

## ABSTRACT

Baseflow defined as the contribution of groundwater and delayed subsurface flow, is generally described by indices such as the baseflow index (BFI), the long-term ratio of baseflow to streamflow. Characterizing baseflow is challenging because it is not directly accessible, particularly in sensitive areas to climate change like the mountainous Mediterranean regions with hard-rock aquifers. In these areas, little is known about the temporal and spatial contribution of baseflow to streamflow. This study aimed to address this scientific gap by using the first calibrated and validated recursive digital filter with natural tracers for such regions. Two watersheds of Corsica (France), the Tavignanu and the Fiumaltu, were chosen as application models for calibration and validation, respectively, due to their representative characteristics of these regions. Various methods exist for baseflow analysis, including empirical, analytical and physical methods. Empirical and analytical methods, such as digital filters, are easy to use but lack physical significance. Conversely, physical methods using natural tracers, such as isotopes and ions, are more physically representative but are difficult to implement. By calibrating and validating analytical methods with tracers in this specific context, we were able to leverage the strengths of both approaches for effective long-term baseflow analysis. This innovative approach confirmed that baseflow was the main contributor to river flow during dry months, with a contribution of 88–90 % for both watersheds. Notably, baseflow remained a significant contributor during periods of high flow, averaging 54 % for the Tavignanu and 60 % for the Fiumaltu. Over a 25-year period, the mean annual contribution was substantial, at 73 % for the Tavignanu and 77 % for the Fiumaltu. In a particularly dry year, which are expected to become more common with climate change, baseflow contribution was even higher, confirming its origin from deep groundwater and delayed subsurface components. Our results demonstrate that, in the context of climate change, groundwater and delayed subsurface flow will play an increasingly important role in sustaining rivers, connected ecosystems, as well as many human activities in the mountainous Mediterranean regions.

## 1. Introduction

The Mediterranean region is prone to marked precipitation and climate seasonality (Lulla, 1987; Vicente-Serrano, 2006; Quintana Seguí et al., 2010). In these regions, the majority of humid areas are located in the mountains, while lowlands and coastal regions are dominated by human activities and urban areas. Therefore, coastal socio-economic activities and ecosystems heavily rely on water from these mountainous headwaters, which are increasingly under threat from agricultural development, population growth, and climate change. These factors are already impacting the water cycle and are expected to intensify (Leduc

et al., 2017). In the Mediterranean domain, these shifts affect continental water sources, where global warming has caused a decrease in streamflow (–0.13 to –0.25 l/s.km².year) for the Ebro and Sava watersheds (Lutz et al., 2016). Annual rainfall generally remains steady, but some areas experience notable decreases, with distinctively long-term distribution (e.g., a 4 % reduction in rainfall per 1 °C global temperature increase) (Intergovernmental Panel on Climate Change (IPCC), 2023). Future projections indicate more frequent and severe droughts, reduced streamflow, and precipitation in central and southern Mediterranean regions (Moutahir et al., 2017; Cramer et al., 2018). Considering this mountainous context, marked variability in rainfall and climate

<footnote><sup>a</sup> Université de Corse Pascal Paoli, Département d'Hydrogéologie, Campus Grimaldi, BP52, 20250 Corte, France</footnote>

<footnote><sup>b</sup> CNRS, UMR 6134 SPE, BP52, 20250 Corte, France</footnote>

<footnote>* Corresponding author at: Université de Corse Pasquale Paoli, Département d'Hydrogéologie, Campus Grimaldi, UMR CNRS SPE 6134, BP52 20250 Corte, France.
E-mail address: guisiano_p@univ-corse.fr (P.A. Guisiano).</footnote>
and future projections, baseflow plays, and will play, a growing impor-
tant role in water management, withdrawals, river flow, and ecological
continuity, particularly during dry periods and droughts (Singh et al.,
2019). It is therefore an important component of hydrographs and
streamflow that needs to be better characterized over time and space, as
its definition may vary depending on the applied framework. It can be
viewed as a reflection of watershed processes, representing the com-
bined contribution, along with other components, to streamflow (typi-
cally surface runoff and baseflow). Baseflow is often considered to orig-
inate from deep groundwater and delayed subsurface sources, such as
shallow underground storage (Hall, 1968; Smakhtin, 2001; Tallaksen,
1995). Baseflow has been studied in various hydroclimatic contexts
worldwide, including the Mediterranean region. Notably, research has
covered lowlands (Lu et al., 2022), agricultural areas (Kronholm and
Capel, 2015), continental mountains (Miller et al., 2015), arid and
semi-arid regions (Rimmer and Hartmann, 2014; Shao et al., 2020), and
watersheds of various sizes (Lott and Stewart, 2016; Zhang et al.,
2017). Its relative contribution to streamflow varies widely, influenced
by the studied area and context. For instance, in arid to semi-arid wa-
tersheds in China's Yellow River basin (2,799 to 10,653 km2, 2.58 to
19.4 % average slope, mostly loess hilly landform landscape), mean an-
nual baseflow contributions range from 35.4 to 50.2 % (Hu et al.,
2021). In the state of Michigan (warm summer humid continental cli-
mate - USA), covering the period from 1967 to 2011, 17 watersheds
exhibited a mean annual baseflow contribution of 71 % (Zhang et al.,
2013b). In temperate and Mediterranean environments, higher base-
flow contributions have been observed. For example, Lu et al. (2022)
found that over 30 years, three temperate lowland watersheds (ranging
from 95 to 893 km², mainly sandy and loamy) displayed baseflow rela-
tive contributions ranging between 70 % and 84 %. A small wet
Mediterranean watershed in Italy (3 km², made of sandstone) displayed
seasonal variability, with values ranging from 90 % in dry conditions to
40 % in wet, rainy conditions (Longobardi et al., 2016). Finally, water-
sheds in the upper Manavgat River in the Taurus Mountains (karstic
Mediterranean environment) showed a mean annual baseflow contribu-
tion of 73 % to 88 % (Eris and Wittenberg, 2015). Nevertheless, a scien-
tific gap persists as no studies have yet explored the baseflow compo-
nent in a mountainous Mediterranean environment with hard-rock
aquifers and mostly perennial streams. Further evidence is required in
this region, taking into account the specific context and resulting water
management issues. However characterizing baseflow on a watershed
scale across space and time is a challenge due to the difficulties of direct
measurement (Cheng et al., 2022). To address this requirement, several
methods classified into two main branches have been developed (Hu et
al., 2021). The first category, known as tracer-based methods, utilizes
natural environmental tracers, including geochemical and isotopic
tools. The End-Member Mixing Analysis 'EMMA' (Christophersen et al.,
1990) is a widely employed approach, assuming that the tracers defin-
ing end-members remain conservative and stable over time (Barthold et
al., 2011; Delsman et al., 2013). The second category encompasses
more empirical and analytical techniques, namely the non tracer-based
methods, such as digital filters, and are intended for different purposes.
Some may focus on the scale of rainy events, while others aim to com-
pute baseflow responses from long continuous streamflow time series
(Mei and Anagnostou, 2015). Tracer-based tools are more effective be-
cause they take into account chemical and physical processes and com-
ponents such as baseflow at the watershed scale, but they can be cost-
lier, challenging, and time-consuming to implement (Stewart et al.,
2007; Mei and Anagnostou, 2015; Zhang et al., 2017). Non tracer-based
methods, relying on empirical information, are more dependent on pa-
rameterization and user assumptions, but their outputs can be easily au-
tomated and reproduced using only streamflow data as input to derive
baseflow contribution (Gonzales et al., 2009; Mei and Anagnostou,
2015). Eckhardt (2005) suggested combining the two approaches to
overcome the limitations of the two methods by calibrating non tracer-

based methods with isotopic and geochemical data for long-term base-
flow analysis. The present article therefore aims to characterize the
baseflow component in a mountainous Mediterranean context with
hard-rock aquifers under climate change conditions, by enhancing the
understanding of baseflow mechanisms and patterns using innovative
methodology. The innovation in the methodology comes from the tools
employed to do this, i.e. the use of the first calibrated and validated non
tracer-based methods in a Mediterranean area presenting hard-rock
aquifers. The calibration and validation processes and the investigation
focuses on two Corsican watersheds, the Tavignanu and Fiumaltu, as
application models. These watersheds share common hydroclimatic,
hydrogeological, and morphometric characteristics with other hard-
rock aquifers in the Mediterranean mountains, making Corsica an ideal
location for this research and allowing for the study of baseflow in this
specific context (Erostate et al., 2019; Juhlke et al., 2021; Nlend et al.,
2023; Santoni et al., 2016). The innovative method involving the first
calibration of non tracer-based methods (empirical filtering and analyt-
ical digital filtering methods) was performed with natural tracer data
(end-member mixing models) from prior work (Mattei et al., 2021;
2024), undertaken for the specific mountainous Mediterranean context.
This calibration procedure of non tracer-based methods was conducted
on the Tavignanu watershed. A protocol to assess then the performance
and uncertainty of these calibrated non tracer-based methods is em-
ployed on the Fiumaltu watershed to validate and select the most suit-
able method for this specific context. To address the scientific gap re-
garding baseflow in such regions, functional analysis and temporal
(seasonal, and interannual) characterization of baseflow is achieved us-
ing the selected and validated non tracer-based method, the two-
parameter analytical recursive digital filter (TPDF) by Eckhardt (2005).
The seasonal and interannual distribution of the baseflow index (BFI),
which is the ratio of baseflow to total streamflow, is examined as an in-
dicator of deep groundwater and delayed subsurface flow contributions
sustaining streamflow. The study also explores baseflow behaviour,
mechanisms, and patterns, its origin, its relation with rainfall, and BFI
distribution during a specific drought year, a phenomenon that is ex-
pected to become more frequent in the region, based on climate projec-
tions (Calvache et al., 2020; Intergovernmental Panel on Climate
Change (IPCC), 2022; Tramblay et al., 2020).

2. Materials and methods

2.1. Study sites

2.1.1. Location of study sites and morphometric characteristics

This study was conducted on the Tavignanu and Fiumaltu water-
sheds on the island of Corsica, France, situated in the western part of
the Mediterranean basin (Fig. 1 – a). The Tavignanu watershed covers a
total area of 795.74 km², with a rounded shape (Gravelius index of
1.28), and a well-developed hydrographic network. The main stream is
88.7 km long, with 76 listed tributaries and a Strahler number of 5. The
slope distribution follows the shift of the main geological features, de-
creasing from the steep mountain tops towards the watershed outlet
with an average gradient of 23.7°. The Fiumaltu watershed has a total
area of 126.67 km² and exhibits a more tapered shape, indicated by a
Gravelius index of 1.52. Although the Fiumaltu River is smaller than
the Tavignanu (30.9 km), it collects 34 tributaries along its flow path,
also having a Strahler number of 5. The average slope index (24.8°) and
slope distribution are relatively similar. Refer to Fig. 1 – b for water-
shed locations and elevations, and Fig. 1 – c for a representation of the
hydrographic network.

2.1.2. Hydroclimatic, hydrological context and land use

The coastal regions of both watersheds exhibit a hot summer csa cli-
mate, mid-mountain areas a hot summer csb climate, and higher alti-
tudes a subarctic dfc climate (Köppen and Geiger, 1930). This Mediter-
<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Location of Corsica in the Western Mediterranean basin (a). Elevation map and location of study sites (b). Simplified geological maps and hydrographic networks of study sites (c).</figcaption></figure>

ranean hydroclimatic context implies significant interseasonal and in-
terannual temperature and precipitation variations (B bonaccorso et al.,
2003; V icente-Serrano, 2006). Precipitation distribution follows the
northern Mediterranean climate pattern, with the lowest amounts in
hot, dry summers and the highest in wet, mild months. Notably, higher
altitude mountains are wetter, while coastal plains are drier and
warmer. The mountainous landscape, particularly in the Tavignanu wa-
tershed where snowfall occurs, contributes to a torrential river regime
due to seasonality, intense rainfall, and steep topography. Both streams
exhibit perennial characteristics and follow a northern Mediterranean
pattern where low flows align with hot, dry summers, and high flows
occur during cold, mild winters. For the future, models predict that
global change will further impact hydroclimatic conditions in the west-
ern Mediterranean with more extreme weather. Reduced precipitation
(10–30 % during the dry season) and temperature increases (1 to
3.1 °C) are expected by the end of the 21st century (Cramer et al., 2018;
Seker and Gumus, 2022). This could result in further impacts on water
resources, affecting their sustainability, quantity, quality, and use and
management (Cao et al., 2022). River flow is expected to decrease by
10 % to 50 % by the end of the 21st century as well. Furthermore,
longer droughts and shorter aquifer recharge periods are also antici-
pated (Intergovernmental Panel on Climate Change IPCC, 2022). Both
watersheds have been monitored daily at stations since April 1960,
with a data gap in the 90 s, for continuous water levels and computed
discharge data. Mean daily discharge data are directly accessible from
the French Hydroportail database (https://hydro.eaufrance.fr/) and
have been used from 1997 to 2019 for the Fiumaltu at the Acitaja
Bridge, and until 2021 for the Tavignanu watershed at the Faiu Bridge.
The average monthly discharges for this period (1997–2019/2021) are
11.1 m³/s for the Tavignanu and 1.37 m³/s for the Fiumaltu (see Fig. 1
c for location of monitoring stations). The mean annual precipitation
amount in the Tavignanu (1997–2021) is approximately 974 mm,
while in the Fiumaltu (1997–2019) it is about 1116 mm. The average

monthly temperature recorded during the period of 1997–2019 is
13.1 °C for the Fiumaltu and 11.9 °C during the period of 1997–2021
for the Tavignanu. The average monthly potential evapotranspiration is
45.4 mm for the Fiumaltu during the period of 1997–2019 and
43.1 mm for Tavignanu during the period of 1997–2021. Please refer to
Table 1 for a summary of the hydroclimatic settings of the study sites
over the period 1997–2021. The averages were computed aggregating
data of weather stations (located upstream of each monitoring station)
from the French national weather service, Meteo France (https://
meteofrance.com/) (two stations each in Corti and Vivariu, and one in
Venacu for the Tavignanu, and La Porta, Quercitellu, and Scata for Fiu-
maltu, see Fig. 1 – b,c). See Fig. 2 for discharge and precipitation data
patterns over 1997–2019/2021 for both watersheds (a) and the study
period for the Tavignanu at the Faiu Bridge (b) and the Fiumaltu at the
Acitaja Bridge (c). The Tavignanu watershed features diverse land uses,
with forests covering most of the area (87.85 %), agriculture (11.3 %)
near the river mouth and coastal plain, and limited urban areas
(0.85 %). Corti is the largest town in the watershed with 7549 inhabi-
tants. In the Fiumaltu watershed, higher-altitude areas are predomi-
nantly forested (93.1 %). Urban areas (0.8 %) consist of small villages
near agricultural fields (6.1 %), primarily located in the lower-altitude
areas close to the coastal plain. Folelli, with 3355 inhabitants, is the
largest town in the watershed.

### 2.1.3. Geological and hydrogeological background

The Fiumaltu watershed, ranging from 50 to 800 m.a.s.l, exhibits
dominant metamorphic geological features, including serpentinites,
black quartz schists, marmoreal limestones, and quartzites in the head-
watershed, followed by alternating carbonate-silicate schists (Guieu
and Mathely, 1994; Rossi and Rouire, 1994; Genevier et al., 2013a). To-
ward the river mouth, recent Tertiary sedimentary rocks (succession of
marsls, sands, sandy marsls, conglomerates with rhyolite pebbles) and
Quaternary formations (post-glacial alluvium), are present (Guieu and
<table><caption>**Table 1**
Summary of the hydroclimatic settings for the two study sites for the period 1997–2019/2021.</caption><thead><tr><th>Study sites</th><th>Hydroclimatic settings</th><th>Mean annual precipitation amount (mm)</th><th>Mean monthly temperature (°C)</th><th>Mean monthly evapotranspiration (mm)</th></tr></thead><tbody><tr><td rowspan="3">Tavignanu (1997–2021)</td><td>Min</td><td>657</td><td>6.5</td><td>34.9</td></tr><tr><td>Max</td><td>1630</td><td>16.5</td><td>47.1</td></tr><tr><td>Mean</td><td>974</td><td>11.9</td><td>43.1</td></tr><tr><td rowspan="3">Fium'Altu (1997–2019)</td><td>Min</td><td>704</td><td>11.3</td><td>44.2</td></tr><tr><td>Max</td><td>2135</td><td>15.8</td><td>46</td></tr><tr><td>Mean</td><td>1116</td><td>13.1</td><td>45.4</td></tr></tbody></table>

Mathely, 1994). The capacity of hard-rock aquifers in metamorphic units is heterogeneous but remains significant. Groundwater can circulate in the deep (50 to 100 m below the surface) weathered surface layer and the network of faults and fractures (the permeable stratiform layer, the 'SFL'). Shallower groundwater, percolating towards the deeper SFL, may also come from the unconsolidated subsurface (0 to 50 m below the surface) part of the hard-rock aquifers, the saprolites or alterites layer, which is less transmissive but more capacitive (Wyns et al., 1999; Lachassagne et al., 2021). In addition, numerous ferruginous springs with high mineralization are found near the river (Genevier et al., 2013b; Dupuy et al., 2021). Upstream to downstream, the Tavignanu watershed presents three main geological features: high mountains (over 800 m.a.s.l) of igneous origin composed mainly of monzogranites and granodiorites, mid-mountain areas (50 to 800 m.a.s.l) resting on a metamorphic ophiolitic base of carbonate-silicate schists, and a coastal plain with Tertiary sedimentary rocks (marls, sands, sandy marls and conglomerates) covered by Quaternary post-glacial alluvial deposits (Rossi and Rouire, 1994). The whole watershed has heterogeneous but significant aquifer hydrodynamic properties as well. In the same way, groundwater in igneous features can flow through the most superficial alteration profiles (the subsurface component or end-member, represented by the alterites) or much deeper into the weathered bedrock through the network of pre-existing well-connected fractures and joints (the deep groundwater component or end-member – the SFL) (Frissant et al., 2010; Lachassagne et al., 2021). Refer to Fig. 1 – c for simplified geological maps.

## 2.2. Data collection and analysis

Field surveys and stream water samples were collected monthly at both monitoring stations (Acitaja Bridge and Faiu Bridge for Fiumaltu and Tavignanu rivers, respectively) from September 2017 to September 2019 for in situ measurements, stable isotopes, and major ion analyses. On-site measurements, including electrical conductivity 'EC', dissolved oxygen, pH, and temperature, were taken using a WTW 3310 multi-parameter and a WTW 3310 IDS oximeter (WTW GmbH, Weilheim, Germany). Bicarbonate ($HCO_3^-$) concentrations were determined through on-site volumetric titration (HACH Company, Loveland, USA). Samples for stable water isotope analysis ($\delta^{18}\text{O}$ and $\delta^{2}\text{H}$) were collected in 20 ml amber glass bottles to eliminate the presence of air space. Analyses were conducted using a DLT-100 liquid-water stable isotope analyzer (Los Gatos Research, San Jose, USA) following the International Atomic Energy Agency analytical procedure (IAEA, 2007). Water samples for the analysis of major dissolved ions ($Na^+$, $K^+$, $Mg^{2+}$, $Cl^-$, $NO_3^-$ and $SO_4^{2-}$) were filtered through 0.45 µm nitrocellulose membranes and collected in two 50 mL polyethylene bottles, one of which was acidified for cation analysis using ultrapure $HNO_3$. Major ion concentrations were determined using a Dionex ICS 1100 ion chromatograph (Thermo Dionex, Sunnyvale, CA, USA). The analysis of major dissolved ions and stable isotopes in water was conducted at the Hydrogeology Department (CNRS UMR 6134 SPE, University of Corsica,

France). The field surveys, specific monthly rainfall data during the study period on the Tavignanu from September 2017 to September 2019, and all the tracer datasets detailed above come from (Mattei et al., 2021; 2024).

## 2.3. Baseflow separation tools

### 2.3.1. Non tracer-based methods, recession analysis, and BFI<sub>max</sub> estimation

Non tracer-based methods, including empirical to analytical filtering and digital filter methods, are easy to use for baseflow analysis because requiring only streamflow data as input. The results can also be easily replicated and involve few hypotheses (Mei and Anagnostou, 2015). The filter methods include local minimum, sliding, and fixed interval (Pettyjohn and Henning, 1979). These filter methods automatically compute baseflow by connecting low points within specific intervals on the streamflow hydrograph. The width of the interval is empirically determined following:

$$N = A^{0.2} \qquad (1)$$

Where N is the number of days after runoff cessation, the interval width can be calibrated to the nearest number between 3 and 11, equal to 2 N, and A is the watershed area in km$^2$. Digital filters derived from signal analysis (Nathan and McMahon, 1990) improve previous filtering methods by introducing the linear relation between storage and discharge (Yang et al., 2021). One-parameter filters usually used comprise but are not limited to (Lyne and Hollick, 1979), (Chapman, 1991), (Chapman and Maxwell, 1996). Eckhardt, (2005), proposed a new digital filter with an additional parameter, to better constrain geological and hydrogeological features of watersheds (Raffensperger et al., 2017; Eckhardt, 2023). Eckhardt (2005) also notes that all one-parameter filters are special cases of the Two-Parameter digital filter 'TPDF'. Baseflow using the TPDF is computed as follows:

$$b_t = \frac{(1 - BFI_{max}) \times \alpha \times b_{(t-1)} + (1 - \alpha) \times BFI_{max} \times Q_t}{1 - \alpha \times BFI_{max}} \qquad (2)$$

Where $b_t$ is the baseflow discharge in m$^3$/s at any time t, $\alpha$ is the first filter parameter, ranging from 0 to 1, and $BFI_{max}$ is the second parameter, ranging from 0 to 1 and representing the maximum baseflow index that can be computed ($BFI_{max}$ value of 1 would indicate 100% baseflow contribution so that the storage and infiltration capacity of aquifers is high e.i.). Both digital filter parameters can be estimated through a recession analysis for $\alpha$ and various approaches for $BFI_{max}$. The filter parameter $\alpha$ is usually associated with the recession constant K, found as the slope of an individual recession curve in a semi-logarithmic hydrograph representation (Kissel and Schmalz, 2020). The TPDF also needs the $BFI_{max}$ parameter, which is not directly measurable (Eckhardt, 2005; Longobardi et al., 2016). To address this, a backward filter for BFI<sub>max</sub> estimation was proposed (Collischonn and Fan, 2013). Gonzales et al. (2009) used tracer data, and Rimmer and Hartmann (2014) proposed an algorithm minimizing the root-mean-square value of $BFI_{max}$. The backward filter also assumes a linear relationship between groundwater discharge and storage over long recession periods:

$$b_{(t-1)} = \frac{b_t}{\alpha} \qquad (3)$$

Where $b_t$ is the baseflow discharge (m$^3$/s) at any time t. Equation (5) acts as a backward filter, stopping when baseflow is greater than streamflow. As the BFI represents the long-term baseflow to streamflow ratio, $BFI_{max}$ can be estimated as:

$$BFI_{max} = \frac{\sum_{t=1}^{n} b_t}{\sum_{t=1}^{n} Q_t} \qquad (4)$$
<figure><img src="image_5.png" /><figcaption>Fig. 2. Overview of the patterns of change in streamflow (m³/s), rainfall (mm), and EC (µS/cm) at the two study sites during the study period. Average monthly streamflow discharge and rainfall amount patterns for the two study sites during 1997/2019–2021 period (a). Changes in mean daily streamflow discharge at sampling day, the three reference-tracer baseflow and EC for the Tavignanu watershed during study period (b). Changes in mean daily streamflow discharge at sampling day, mean monthly rainfall amount and EC for the Fiumaltu watershed during study period (c).</figcaption></figure>

In this study, the Sephydro online application (Danielescu et al., 2018) was used for daily baseflow separation applying several non tracer-based methods. The application includes the aforementioned filtering methods (Pettyjohn and Henning, 1979) and one to multi-parameter recursive digital filters (Lyne and Hollick, 1979; Chapman, 1991; Chapman and Maxwell, 1996; Eckhardt, 2005) using time series of daily streamflow data as the only input. The N parameter for the filtering methods was calibrated to the nearest number between 3 and 11 by trial and error. K for the digital filters was estimated through recession analysis, following the linear reservoir hypothesis (Boussinesq,

1877; Maillet, 1905; Horton, 1933; Thomas et al., 2015), implying that streamflow in dry conditions and recession periods is composed solely of baseflow and decreases exponentially:

$$Q_t = Q_0 \times e^{(at)} \qquad (5)$$

where $Q_t$ is the streamflow discharge in m³/s at any time t, $Q_0$ is the initial discharge when the recession begins, $a$ is a negative constant and the expression $e^{(a)}$ is generally replaced by the recession constant K or the first filter parameter $\alpha$:
protocol described in section 2.4 involving a visual inspection of computed baseflow hydrographs, performance assessment using statistical indices, and examination of baseflow statistics from calibrated non tracer-based methods. This fulfils the requirement for at least two years of complete tracer data for mass balance and mixing model procedures (Hooper, 2003), with two hydrological years used for calibration and validation. Furthermore, performance improves with higher time steps and discrete monthly tracer data are adequate for the calibration and validation of non-tracer-based methods (Moria si et al., 2007; Saraiva Okello et al., 2018). The final validation and approval of the model also considers the uncertainties encountered at the different stages of the method. These include the uncertainty linked to the definition of the reference tracer baseflow, which is used to calibrate and validate the non tracer-based method, and the uncertainties associated with the output of calibrated and validated non tracer-based methods, notably, the computed baseflow and BFI over long periods. In tracer-based methods, uncertainties in mixing fractions are linked to analytical precision and to the tracers themselves (identification of end-members, variations in their concentration, and non-conservative tracers) (Beven and Binley, 1992; Barthold et al., 2011). In non tracer-based methods, uncertainties in computed baseflow and BFI are related to the input streamflow data such as inaccuracies in flood stage, discharge measurement, and rating curve extrapolation, (Lang et al., 2006) and to the selection of parameters (N, α and BFImax) (Eckhardt, 2012). In this study, both uncertainties have been taken into account by the general uncertainty propagation technique following (Genereux, 1998):

$$W_y = \sqrt{\left(\frac{\partial y}{\partial x_1} \times W_{x1}\right)^2 + \left(\frac{\partial y}{\partial x_2} \times W_{x2}\right)^2 + \dots + \left(\frac{\partial y}{\partial x_n} \times W_{xn}\right)^2} \quad (9)$$

Subscript y is a measured parameter which is a function of several measurands (subscripts x_n), $\frac{\partial y}{\partial x_n}$ are the partial derivatives of y with respect to each measurand x_n and W represents the absolute uncertainty related to y and x_n. It was used by (Mattei et al., 2021; 2024) to constrain the propagation of uncertainty in each mixing fraction (contributing end-members) in the three-component EMMA model, and in the present study to define the propagated uncertainty in computed BFI by calibrated and validated non tracer-based methods. Subsequent general propagated uncertainties are given for the t statistics for the 70 % confidence interval. A workflow diagram is presented in Fig. 3 to summarize the materials, methods, and steps utilized for calibrating and validating non-tracer-based methods with tracer-based methods in a mountainous Mediterranean context.

## 3. Results & discussion

### 3.1. Selection of the reference tracer baseflow

Before calibration, it was important to first assess non tracer-based methods performance in a Mediterranean mountainous context and then, to select the best reference tracer baseflow, as they behave differently based on the method used (Fig. 2 – b). Twenty-five tests of non tracer-based methods were conducted by randomly adjusting parame-

<figure><img src="image_6.png" /><figcaption>Fig. 3. Workflow diagram summarizing the materials, methods and steps used for calibration and validation of non tracer-based with tracer-based tools for mountainous Mediterranean area use. The various non tracer-based methods are represented by purple circles, while the tracer-based methods are represented by blue circles. Input and output data are represented by white circles. Calibration/validation processes are represented by a green circle. The actions steps are numbered from 1 to 4 and represented by rectangles referring to the different chapters. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>
ters (N, α, BFImax), with due consideration of the values recommended
in the literature in light of the characteristics of the study sites
(Pettyjohn and Henning, 1979; Lyne and Hollick, 1979; Chapman,
1991; Chapman and Maxwell, 1996; Eckhardt, 2005). The performance
overview of these tests, following the procedure in section 2.4, revealed
consistently poor results, emphasizing the necessity for calibration in a
Mediterranean mountainous context. As described in section 2.3, a
three-component EMMA derived contributions from the SFL (deep
groundwater component), the alterites layer (subsurface flow), and sur-
face runoff in the Tavignanu and Fiumaltu watersheds (Mattei et al.,
2021; 2024). A two-component CMB was also performed based on the
assumptions mentioned earlier. To select the most efficient reference
tracer baseflow for calibration and validation, a performance compari-
son of all tracer-based with non tracer-based methods was carried out.
Although all non tracer-based methods performed poorly (except for
Chapman and Chapman and Maxwell digital filters), the best perfor-
mance was obtained when defining baseflow as contributions from
deep groundwater combined with delayed subsurface flow in the three-
component EMMA. The results of these tests demonstrated the neces-
sity to calibrate and validate the non tracer-based methods for this
Mediterranean context with hard-rock aquifers. Furthermore, the three-
component EMMA was selected as the reference tracer baseflow for cal-
ibration and validation as it demonstrated the best performance with all
non-tracer-based methods in the initial testing. In addition, the afore-
mentioned tests permitted the preliminary selection of value intervals
for the parameters N, α and BFImax of the non tracer-based methods for
subsequent calibration and validation processes. This was defined
based on the most optimal performance observed during the twenty-
five random tests. The table in Supplementary Material S1 provides a

test example with N=3, α = 0.4, BFImax = 0.25, and the best perfor-
mance is observed between the Lyne and Hollick filter and the three
component EMMA. This model was then selected as the reference tracer
baseflow.

## 3.2. Calibration of non tracer-based methods for mountainous Mediterranean use

3.2.1. Estimation of α parameter – recession analysis

The R.C. software and RECESS tool automatically select recession
curves by specifying the analysis period and minimum flow duration.
For this study (period June to September 1996–2021 on the Tavignanu
watershed), continuous streamflow decrease during dry conditions in
the Mediterranean context (Neira, 2021) was assumed. Manual inspec-
tion of the recession curves on a semi-logarithmic graph has led to the
selection of 24 linear-shaped curves following the linear reservoir as-
sumption for all recession analyses and MRC construction. The α values
obtained are 0.9425 (Excel spreadsheets) and 0.979 (RECESS tool) for
the correlation method, 0.981 for the matching strip method (R.C. soft-
ware) and 0.989 for the MRC constructed using the RECESS tool. An
overall average α of 0.973 and a high mean α (considering only the
highest values) of 0.983 were calculated. Fig. 4 a, b and c illustrates K
and α values obtained depending on the method. The resulting MRC
from the RECESS tool appears curved, but linear portions can be identi-
fied, consistent with findings by Kissel and Schmalz (2020). Typical K
values for surface runoff (0.2–0.8), interflow (0.7–0.94) and baseflow
(0.93–0.995) agree with the α values obtained (Tallaksen, 1995) and
the preselected values intervals for this parameter that were identified
previously. Calibration tests can now be carried out to optimize perfor-

<figure><img src="image_7.png" /><figcaption>Fig. 4. Estimation of α and BFImax parameters for the Tavignanu watershed. MRC construction in orange using matching strip method with selected recession curves in blue (a). MRC construction in blue using RECESS tool in GWtoolbox, orange part is the linear section (b). α estimation using the correlation method in Excel spreadsheets (c). BFImax parameter estimation using the backward filter method with a α value of 0.9423 from September 2017 to September 2019 (d). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>
mance with different α values for one-parameter digital filters (Chapman, Chapman and Maxwell, Lyne and Hollick). The TPDF also requires prior estimation of the BFImax parameter before calibration tests.

### 3.2.2. Estimation of BFImax parameter

A range of BFImax values on the Tavignanu watershed were estimated using the previous α values. The Excel spreadsheet and the RECESS tool correlation method estimated BFImax at 0.76 and 0.42, respectively. The matching strip method provided an estimated BFImax of 0.39, while the MRC constructed using the RECESS tool yielded 0.28. The overall mean α resulted in a BFImax value of 0.53, and the high mean α was 0.37 for BFImax. Fig. 4-d) illustrates the estimated BFImax value using the backward filter with α derived from the correlation method (0.9423). Despite initial assumptions (Neira, 2021) of higher BFImax values during dry conditions in Mediterranean regions (see Fig. 4-a), the obtained BFImax values appear lower, potentially influenced by estimating its value over the entire year and not just during dry conditions. Consequently, and following the recommendations of Eckhardt (2005), a BFImax parameter was also estimated using tracer data. It was set at the highest tracer BFI observed during the study period in the Tavignanu (0.91 for October 2017) and Fiumaltu (0.81 for October 2017). Calibration tests can now be conducted using different combinations of previously estimated α for the one-parameter digital filters and BFImax for the TPDF. The N parameter can be calibrated manually by trial and error for the filtering methods.

### 3.2.3. Calibration of non tracer-based methods with natural tracers

The calibration process for filtering methods (local minimum, fixed, and sliding interval) involves manual adjustments to the N parameter (number of days after which runoff has ceased), by trial and error and taking into account the pre-selected value intervals of the N parameter. Optimal N values were found as 5 for the sliding interval and 7 for both the local minimum and fixed interval methods. Notably, the local minimum method gave the best performance with a superior RSR of 0.39, a PBIAS of 7.08, and an NSE of 0.84. These results suggest the calibrated local minimum is the most suitable filtering method for the mountainous Mediterranean conditions. The performance before and after calibration is comparable, with all indicators ranking very well, except absolute PBIAS, which improved from good (12.05) to very good (7.08) after calibration. Values during periods of high-flows are less constrained due to imperfect matching with tracer data during peak flows. However, the calibrated local minimum method exhibited improved fit during the low-flow conditions. See Table in Supplementary Material S2 for before-after calibration comparison. Among digital filters, the TPDF was chosen because of its better performance and broader physical basis, with the addition of the BFImax parameter (Raffensperger et al., 2017; Eckhardt, 2023). Several tests were conducted to determine the optimal performance using different combinations of calibrated α and BFImax. The results consistently showed improved good to excellent performance for the TPDF for most combinations, except for R². It has been observed here that the BFImax parameter had a greater impact on the computed baseflow data compared to the α parameter. The optimal combination of calibrated α and BFImax parameters for the TPDF was determined to be α = 0.979 and BFImax = 0.81. While this choice slightly reduces the overall performance of the Tavignanu watershed, it remains highly acceptable (RSR = 0.54, absolute PBIAS = 3.38, NSE = 0.71, R² = 0.71). See Table in Supplementary Material S2 for before-after TPDF performance comparison. In addition, the b > Q index, below 30 % for a dataset of 886 points, indicates a good performance as well. Table 3 shows the performance evaluation using the statistical indices for both calibration and validation. Visual inspection of computed baseflow after calibration showed improved congruence during both high and low-flow periods (Fig. 5-a). Consequently, the chosen parameter set (α = 0.979, BFImax = 0.81) appears well-suited for the hydroclimatic context of the study. However, to validate their applicability,

<table><caption>**Table 3**
TPDF performance for calibration and validation processes.</caption><thead><tr><th>Watersheds</th><th>Process</th><th>RMSE</th><th>RSR</th><th>Absolute PBIAS</th><th>NSE</th><th>R<sup>2</sup></th><th>α</th><th>BFImax</th></tr></thead><tbody><tr><td>Tavignanu</td><td>Calibration</td><td>3.64</td><td>0.54</td><td>3.38</td><td>0.71</td><td>0.71</td><td>0.979</td><td>0.81</td></tr><tr><td>Fiumaltu</td><td>Validation</td><td>0.74</td><td>0.6</td><td>46.56</td><td>0.62</td><td>0.8</td><td></td><td></td></tr></tbody></table>

further testing is recommended in another Mediterranean mountainous watershed (Fiumaltu River). While the two calibrated methods, local minimum and TPDF, exhibit comparable overall performance (see Table in Supplementary Material S2), the baseflow curves of the TPDF display better congruence during both low and high-flow conditions. As the local minimum method may present non-significant behaviour, such as plateaus (Raffensperger et al., 2017), the calibrated TPDF was then selected among all non-tracer-based methods for the validation phase in the Fiumaltu watershed.

### 3.2.4. Validation of calibrated TPDF and frameworks for mountainous Mediterranean area use

The calibrated α parameters (0.979) and BFImax (0.81) for TPDF were applied in the Fiumaltu watershed for validation. Visual inspection reveals proximity of computed baseflow data with tracers during low-flows. Computed data are slightly underestimated in recession periods but match tracers closely in peak flows (Fig. 5-b). Performance is excellent for R², good for RSR and NSE, but poor for PBIAS. The b > Q index is very good with a value of 18.48 % for 947 data points. PBIAS is the only indicator whose performance is poor. Moriasi et al. (2007) suggest that lower performance during validation may occur due to previously fixed input parameters (N, α, BFImax). In addition, the calibration conditions and assumptions may differ from validation. Despite both watersheds being mountainous and Mediterranean with hard-rock aquifers, environmental variations may contribute to performance differences. Overall, validation suggests good model performance. The validated TPDF can directly compute baseflow discharge values from streamflow data alone, but caution is warranted due to its underlying assumptions. Specifically, it assumes a linear relationship between discharge and storage, which may not be true in scenarios involving significant groundwater storage variations, such as seasonal or interannual fluctuations, and aquifer properties regarding storage levels (Hall, 1968; Aksoy et al., 2009). Moreover, uncertainties associated with the TPDF are carefully considered. This acknowledges the propagated uncertainties within each mixing fraction of the three-component EMMA model, which serves as a reference tracer for baseflow and is considered acceptable (Mattei et al., 2021; 2024). The propagated uncertainties in computed baseflow and BFI in the validated TPDF are handled similarly. Refer to Supplementary Materials S3 and S4 for a comprehensive overview of general uncertainties related to mixing fractions, computed baseflow and BFI, associated partial derivatives, and detailed results tables for both the Tavignanu and Fiumaltu watersheds. The now approved TPDF can be applied over extended streamflow recording periods to conduct functional analysis and characterize baseflow patterns in mountainous Mediterranean watersheds where geochemical or isotopic data is lacking. The Mediterranean context exhibits a pronounced seasonality in rainfall and streamflow, influenced by high altitude gradients and a subarctic subclimate (Köppen and Geiger, 1930). The approved TPDF is applicable to Mediterranean watersheds with diverse geological features but similar hydrogeological properties such as hard-rock aquifers, morphometric characteristics with a well-developed hydrographic network, and size.

### 3.2.5. Long seasonal and interannual behaviour of baseflow in mountainous Mediterranean watersheds highlighted by the distribution of the BFI

Baseflow separation using the previously approved TPDF was conducted for both watersheds from 1997 to 2019 for Fiumaltu and from
<figure><img src="image_8.png" /><figcaption>Fig. 5. Calibration on the Tavignanu watershed (a) and validation on the Fiumaltu watershed (b) of the TPDF.</figcaption></figure>

1997 to 2021 for Tavignanu. A more detailed examination focused on the BFI, specifically its long seasonal and interannual distribution at both sites and its correlation with recorded rainfall amounts. Additionally, consideration of extreme rainfall deficit periods between 2017 and 2019 aimed to observe the potential impact of droughts on the very short-term (monthly time step) distribution of BFI, as these conditions are predicted to recur. The geochemical composition of streamflow during the 2017–2019 period in the Fiumaltu watershed was considered to identify and confirm the terrigenous origin of BFI and baseflow, providing a basis for correlation of discussions.

### 3.2.6. Relationship between the BFI and rainfall in a climate change context

The potential impact of climate change on baseflow responses over time was examined throughout the study sites. With the predicted reduction of streamflow and precipitation, an increase in the relative proportion of baseflow is expected for rivers under gaining conditions. However, the Mann-Kendal test (Yue and Wang, 2004) used here revealed no significant interannual trend in BFI distribution for the study watersheds from 1997 to 2019/2021. While the limited number of study years might contribute to this result, similar research has demonstrated the resilience of groundwater in northern Mediterranean regions to short-to-medium-term climate variability. Indeed, groundwater that may have a long residence time in aquifers, appears less sensitive to hydroclimatic hazards like rainfall variation and severe drought in Mediterranean regions. This resilience suggests that groundwater can function as a buffer against short-to-medium-term climate variability and change (Cramer et al., 2018; Fader et al., 2020). This highlights the importance of groundwater in sustaining streamflow, fluvial ecological continuity, and ensuring a reliable water supply, particularly during low-flow periods (Gao et al., 2015; Hu et al., 2021). While the short-to-medium-term BFI displays no visible trend, hydroclimatic conditions, and precipitation distribution significantly influence the BFI at a smaller monthly scale. Monthly BFI and rainfall amounts (January

1997 to December 2020) were plotted for the Fiumaltu and the Tavignanu watersheds. Fig. 6 (a-b) shows a decreasing linear correlation between BFI and precipitation in the Tavignanu and Fiumaltu watersheds with satisfactory and good correlation coefficients ($R^2$ values at 0.5242 and 0.6787, respectively). The highest $R^2$ values were observed with a 0-month lag between precipitation and BFI, aligning with geological and morphometric settings (steep slopes) of the watersheds where the majority of runoff reaches rivers during rainfall and flood events. Consequently, lower precipitation corresponds to higher BFI values, and vice versa, as confirmed by Contingency Tables 4 and 5. The tables highlight the correlation between the lowest precipitation classes in both watersheds and the highest BFI classes, and conversely. In situations where precipitation minimally affects streamflow, rivers continue to flow, indicating a larger relative contribution from deep groundwater and delayed subsurface reservoirs (high BFI). Conversely, heavy rainfall tends to reduce the proportion of deep groundwater and delayed subsurface flow by mixing, consequently impacting baseflow and BFI.

### 3.2.7. Interannual distribution of the BFI

Close attention was devoted to the analysis of the interannual distribution of the BFI. Deep groundwater and delayed subsurface flow significantly contributed to both watersheds over the nearly 25-year study, resulting in an average BFI of 73 % (0.73 ± 0.04) for the Tavignanu and 77 % (0.77 ± 0.01) for the Fiumaltu, indicating that both watersheds are dependent on these resources (see Fig. 7-a). Despite differences in morphometric and geological features, findings align with those of temperate lowland watersheds (with 70–84 % baseflow contribution over 30 years) (Lu et al., 2022) and Mediterranean watersheds (73 to 88 % mean baseflow contribution). This indicates a higher significance of groundwater and delayed subsurface flow in sustaining river flow in these temperate and Mediterranean environments. Differences are found in studies in semi-arid and humid climates, reporting notably
<figure><img src="image_9.png" /><figcaption>Fig. 6. Relationship between monthly rainfall amounts (mm) and BFI values over 1997–2021 for the Tavignanu (a) and the Fiumaltu (b) watersheds.</figcaption></figure>

Table 4

Contingency table of rainfall and BFI classes for the Tavignanu watershed. The rainfall classes have exclusive intervals of 50 mm, ranging from 0 to 450 mm. The BFI classes are also exclusive, ranging from 0 to 1 with an interval of 0.1.

<table><thead><tr><th colspan="13">BFI classes</th></tr><tr><th>Rainfall classes (mm)</th><th>[0;0.10[</th><th>[0.10;0.20[</th><th>[0.20;0.30[</th><th>[0.30;0.40[</th><th>[0.40;0.50[</th><th>[0.50;0.60[</th><th>[0.60;0.70[</th><th>[0.70;0.80[</th><th>[0.80;0.90[</th><th>[0.90;1[</th><th>Sum</th></tr></thead><tbody><tr><td>[0;50[</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>15</td><td>27</td><td>54</td><td>38</td><td>135</td></tr><tr><td>[50;100[</td><td>0</td><td>0</td><td>0</td><td>0</td><td>2</td><td>10</td><td>24</td><td>26</td><td>14</td><td>4</td><td>80</td></tr><tr><td>[100;150[</td><td>0</td><td>0</td><td>0</td><td>2</td><td>6</td><td>11</td><td>10</td><td>9</td><td>2</td><td>0</td><td>40</td></tr><tr><td>[150;200[</td><td>0</td><td>0</td><td>1</td><td>2</td><td>4</td><td>5</td><td>7</td><td>3</td><td>0</td><td>0</td><td>22</td></tr><tr><td>[200;250[</td><td>0</td><td>0</td><td>0</td><td>0</td><td>4</td><td>5</td><td>1</td><td>0</td><td>0</td><td>0</td><td>10</td></tr><tr><td>[250;300[</td><td>0</td><td>0</td><td>0</td><td>1</td><td>2</td><td>4</td><td>0</td><td>0</td><td>0</td><td>0</td><td>7</td></tr><tr><td>[300;350[</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>3</td></tr><tr><td>[350;400[</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>2</td><td>0</td><td>0</td><td>0</td><td>0</td><td>2</td></tr><tr><td>[400;450[</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td></tr><tr><td>Sum</td><td>0</td><td>0</td><td>1</td><td>6</td><td>20</td><td>38</td><td>58</td><td>65</td><td>70</td><td>42</td><td>300</td></tr><tr><td colspan="13">Tavignanu watershed</td></tr></tbody></table>

Table 5

Contingency table of rainfall and BFI for the Fiumaltu watershed. The rainfall classes range from 0 to 650 mm, with exclusive intervals of 50 mm. The BFI classes are indexed from 0 to 1 and are also exclusive.

<table><thead><tr><th colspan="13">BFI classes</th></tr><tr><th>Rainfall classes (mm)</th><th>[0;0.10[</th><th>[0.10;0.20[</th><th>[0.20;0.30[</th><th>[0.30;0.40[</th><th>[0.40;0.50[</th><th>[0.50;0.60[</th><th>[0.60;0.70[</th><th>[0.70;0.80[</th><th>[0.80;0.90[</th><th>[0.90;1[</th><th>Sum</th></tr></thead><tbody><tr><td>[0;50[</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>14</td><td>55</td><td>56</td><td>125</td></tr><tr><td>[50;100[</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>0</td><td>8</td><td>35</td><td>22</td><td>11</td><td>78</td></tr><tr><td>[100;150[</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>4</td><td>6</td><td>8</td><td>4</td><td>1</td><td>23</td></tr><tr><td>[150;200[</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>7</td><td>8</td><td>2</td><td>0</td><td>0</td><td>18</td></tr><tr><td>[200;250[</td><td>0</td><td>0</td><td>0</td><td>2</td><td>1</td><td>3</td><td>4</td><td>2</td><td>0</td><td>0</td><td>12</td></tr><tr><td>[250;300[</td><td>0</td><td>0</td><td>0</td><td>1</td><td>1</td><td>2</td><td>2</td><td>0</td><td>0</td><td>0</td><td>6</td></tr><tr><td>[300;350[</td><td>0</td><td>1</td><td>0</td><td>2</td><td>5</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>9</td></tr><tr><td>[350;400[</td><td>0</td><td>0</td><td>0</td><td>0</td><td>2</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>3</td></tr><tr><td>[400;450[</td><td>1</td><td>0</td><td>0</td><td>0</td><td>2</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>3</td></tr><tr><td>[450;500[</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr><tr><td>[500;550[</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td></tr><tr><td>[550;600[</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td></tr><tr><td>[600;650[</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>1</td></tr><tr><td>Sum</td><td>1</td><td>1</td><td>0</td><td>8</td><td>14</td><td>17</td><td>29</td><td>61</td><td>81</td><td>68</td><td>280</td></tr><tr><td colspan="13">Fiumaltu watershed</td></tr></tbody></table>

lower BFI values (Hu et al., 2021; Zhang et al., 2013b), thus suggesting a higher relative contribution of groundwater in subsurface flow in the Mediterranean context compared to humid and arid to semi-arid regions. Segura et al. (2019) provide detailed insights into the factors impacting baseflow contribution and the BFI in a mountainous watershed during both a typical hydrological year and a drought year, including hydroclimatic conditions, precipitation distribution, geological features, morphometrics, and land use. At the watershed scale, hydroclimatic conditions, encompassing temperature, rainfall patterns, and spatial distribution, play an important role in controlling baseflow (Qin et al., 2017; Segura et al., 2019). Geomorphological and geological features such as aquifer permeability and porosity significantly influence baseflow dynamics, particularly in drought years, as they control groundwater infiltration, storage, discharge, and transit times (Longobardi and Villani, 2023; Pfister et al., 2017). Additionally, morphometric characteristics, including watershed area, topography, and
<figure><img src="image_10.png" /><figcaption>**Fig. 7.** Seasonal, interannual, and specific dry-year patterns of change of the BFI. Interannual variation in the annual mean BFI for both watersheds from 1997 to 2021 (a). Monthly average changes in the BFI for both watersheds from 1997 to 2021 (b). Patterns of change in BFI during the specific dry year of 2017 (bold line), compared to the minimum, maximum, and mean BFI observed during the study period (grey area) for the Tavignanu (left part) and the Fiumaltu (right part) watersheds (c).</figcaption></figure>

slope distribution, contribute to the behaviour of baseflow (Zimmer and Gannon, 2018). In this study, the observed differences or similarities between present results and those of other studies can be explained by these factors influencing the higher or lower relative contribution of baseflow (refer to Fig. 7-a and Table in the Supplementary Materials S5 and S6 for detailed BFI values).

### 3.2.8. Seasonal distribution of BFI

The BFI distribution from 1997–2019/2021 displays a strong seasonality, aligning with local hydroclimatic patterns in rainfall and streamflow. Peak baseflow contributions in the Tavignanu occur between May and August, while those in Fiumaltu are between April and August (Fig. 7-b). Sustaining river flow in dry conditions relies on deep groundwater and delayed subsurface flow, contributing up to 89 % for Tavignanu and 90 % for Fiumaltu. The lowest contributions are observed from September to December for Tavignanu and October to November for Fiumaltu. Even in the wettest months, baseflow remains significant, representing 54 % (0.54 ± 0.01) for Tavignanu and 60 % (0.60 ± 0.04) for Fiumaltu (Fig. 7-b). These results align with findings in Mediterranean dry conditions but exceed expectations in wet periods. Longobardi et al. (2016) similarly observed strong seasonality in a small sandstone watershed in Italy with up to 90 % groundwater contribution in dry conditions and 40 % during wet months. It is important to recall the initial assumptions of this paper, defining baseflow by two components: deep groundwater from the SFL and delayed subsurface flow from the alterites layer. This definition helps to understand high values during wet conditions compared to Longobardi et al. (2016). Seasonal BFI distribution slightly varies between the Tavignanu and Fiumaltu watersheds, particularly in spring and autumn. While the two watersheds share some hydroclimatic similarities, their geological and morphometric characteristics differ. As hard-rock aquifers share similar hydrogeological properties, the BFI distribution contrast is primarily due to morphometric differences (variations in shape, area, and draining surface). Assumptions about the baseflow definition, including groundwater and delayed subsurface contribution, also contribute to these differences. Depending on the season and precipitation history, one component (deep SFL or subsurface alterites layer) can dominate over the other.

### 3.2.9. Influence of droughts on the BFI distribution and correlation with its origin

Furthermore, mirroring the findings in the relationship between the BFI and rainfall section, severe droughts linked to precipitation significantly impact monthly BFI. Analysing the BFI distribution in 2017, a notably dry year, revealed a considerable rainfall deficit reported by local authorities across most of the island from March to November (DREAL Corse, 2018). The average rainfall during this period was 21.9 mm for Tavignanu and 24.4 mm for Fiumaltu, clearly lower than the average monthly rainfall from 1997 to 2019/2021 (80.9 mm for Tavignanu and 90.9 mm for Fiumaltu). A decline in both Tavignanu and Fiumaltu discharge was observed, averaging 4.15 m³/s and 0.64 m³/s, respectively, during the drought period. This is lower than the respective average monthly discharge of 11.1 m³/s for Tavignanu (1997–2021) and 1.37 m³/s for Fiumaltu (1997–2019), yet rivers continue to flow. Notably, baseflow exhibited a direct response during severe drought at the monthly time-step, particularly from March to November, where both watersheds displayed a higher BFI, approaching the average maximum BFI values (refer to Fig. 7-c). Additionally, in the 2017–2019 study period, the geochemical composition of streamflow was examined to establish a correlation with the assumed deep and subsurface origin of baseflow and BFI. Monthly chemical data points from the previously described dataset were used to investigate the relationship between ions in streamflow, resulting from precipitation or long-term water-rock interactions. To prevent any interpretational bias, the natural tracers previously employed in the mixing models were removed. For this purpose, the local rainfall line ratio was employed to compare various cations to chloride (Cl⁻) in the Fiumaltu watershed. Cl⁻ serves as a conservative tracer for marine and precipitation components (Appelo and Postma, 2005) and has not been used as a natural tracer in mixing models previously. The Cl⁻ vs Na⁺ binary diagram for the Fiumaltu watershed reveals a very good R² of 0.9075, indicating the best and most significant linear correlation. Therefore, only this combination is illustrated in Fig. 8. Much of the chemical streamflow data, situated below the local ratio line, exhibits Na⁺ enrichment, suggesting a terrigenous origin. Conversely, a small portion aligns near the rainfall ratio line, indicating that Na⁺ in this group originates from precipitation, similarly to Cl⁻. Monthly BFI values computed for the Fiumaltu over 2017–2019 were added to the diagram as a third dimension to
<figure><img src="image_11.png" /><figcaption>**Fig. 8.** Relationship between Cl- and Na+ ions concentrations in the Fiumaltu river with respect to classes of BFI values and their origin.</figcaption></figure>

identify their origin, whether from precipitation or water-rock interactions. BFI was classified into three categories: low (BFI < 0.5), medium (0.5 to 0.75), and high (BFI > 0.75). Data points with small and medium BFI contributions gather around the local rainfall line, aligning with the earlier findings in this section and the relationship between the BFI and rainfall section. Low BFI values are expected when rainfall proportion in streamflow is higher, leading to increased mixing between groundwater and surface runoff. The area showing Na⁺ ion enrichment, indicating a distinct origin from precipitation, predominantly exhibits high BFI values. This enrichment reflects a terrigenous origin, signifying the influence of long water-rock interactions within the deeper SFL and unconsolidated alterites layers in the hard-rock aquifers, consistent with the geochemical background of hard-rock aquifers in the Fiumaltu. As seen in section 2.1, the geological features of the Fiumaltu watershed are primarily composed of alternating carbonate-silicate schists. While sodium is not the dominant element in schists, it can be present in specific minerals like feldspars and micas. Feldspars, as sodium plagioclases, may contain sodium, and the structure of mica (e.g., muscovite) may also have Na⁺ cations (Marshall, 1962; Helmke and Sparks, 2018). This suggests that during high BFI values, baseflow originates almost exclusively from deep groundwater in the SFL and delayed subsurface flow in the alterites layer. This confirms that high BFI in streamflow is predominantly influenced by groundwater and delayed subsurface flow. This is of great importance, especially considering climatic models projecting more pronounced droughts, reduced precipitation, and lower future streamflow in the Mediterranean basin (Noto et al., 2022). Groundwater and subsurface flow will increasingly play a fundamental role in sustaining river flow, ecological continuity of the ecosystem, and related socio-economic activities. This highlights the need for improved characterization of the baseflow component across various watersheds and climate classes, emphasizing the importance of constraining parameters influencing baseflow for sustainable resource management.

## 4. Conclusion

This paper introduces the first calibrated and validated digital filter with natural tracers for baseflow separation in two mountainous

Mediterranean watersheds with hard-rock aquifers. Calibrating and validating the TPDF with monthly tracer data for the specific context has enabled the analysis of baseflow over an extended period, filling a significant knowledge gap in this region. Further examinations of the seasonal, interannual, and dry-year distributions of Baseflow Index (BFI), which indicates the contribution of deep groundwater and delayed subsurface flow to streamflow, were carried out. This was correlated with precipitation and the terrigenous origin of the BFI and baseflow. The findings show that BFI in mountainous Mediterranean areas follows a seasonal pattern, with the highest contributions (88–90 %) during dry conditions, confirming initial assumption. Even during the wettest months, baseflow significantly contributes to streamflow, with a high contribution of 54 % in the Tavignanu and 60 % in the Fiumaltu. Precipitation exerts a short-term influence on BFI, with the highest BFIs observed during the lowest precipitation amounts over 25 years. However, no specific trend was observed in the BFI distribution over the short-to-medium term (1997–2021 for the Tavignanu and 1997–2019 for the Fiumaltu). The average interannual contribution was also notably high, at 73 % for the Tavignanu and 77 % for the Fiumaltu, indicating reliance of river on baseflow and groundwater in the short-to-medium term. This demonstrate that groundwater can buffer hydroclimatic hazards, thereby improving its resilience. During severe droughts, BFI values well above the 25-year averages, confirming the terrigenous origin of BFI from prolonged water-rock interactions in hard-rock aquifers. Meaning, the deep groundwater component from the SFL, and the delayed subsurface flow component from the more superficial unconsolidated layer (alterites). In the context of climate change, with prediction of increased drought, reduced rainfall, and lower runoff in the Mediterranean basin, the utilisation of the calibrated digital filter is significant to provide valuable insights into behavior of mountainous Mediterranean watersheds. This made possible to show the increasingly important role of groundwater and delayed subsurface flow in sustaining rivers, ecosystems, and the human activities in this context. In response, this is of significant importance for stakeholders to better adapt and differentiated their water resource plans for this specific and sensitive region.

## CRediT authorship contribution statement

P.A. Guisiano: Writing – original draft, Methodology, Investigation, Data curation, Conceptualization. S. Santoni: Writing – review & editing, Investigation, Data curation, Conceptualization. F. Huneau: Writing – review & editing, Resources, Investigation, Funding acquisition, Data curation, Conceptualization. A. Mattei: Writing – review & editing, Investigation, Data curation, Conceptualization. E. Garel: Writing – review & editing, Investigation, Data curation, Conceptualization.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgements

This research was supported by the Cullevitittà di Corsica through the GERHYCO interdisciplinary project dedicated to water management, ecology and hydro-ecosystem services in island context.

## Data availability

Data will be made available on request.
# Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.jhydrol.2024.131842.

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