# Impact of vegetation cover on hydro-sedimentary fluxes in the marly badlands of the Southern Alps
(Draix-Bleone Critical Zone Observatory, SE France)

Raphael Bunel, Yoann Copard, Caroline Le Bouteiller, Nicolas Massei, Nicolas Lecoq

Lecoq

► To cite this version:

Raphael Bunel, Yoann Copard, Caroline Le Bouteiller, Nicolas Massei, Nicolas Lecoq. Impact of vegetation cover on hydro-sedimentary fluxes in the marly badlands of the Southern Alps (Draix-Bleone Critical Zone Observatory, SE France). Geomorphology, 2025, 478, pp.109726. 10.1016/j geomorph.2025.109726. hal-05060949

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# Impact of vegetation cover on hydro-sedimentary fluxes in the marly badlands of the Southern Alps (Draix-Bléone Critical Zone Observatory, SE France)

Raphaël Bunel<sup>a,*</sup>, Yoann Copard<sup>a</sup>, Le Bouteiller Caroline<sup>b</sup>, Nicolas Massei<sup>a</sup>, Nicolas Lecoq<sup>a</sup>

## ARTICLE INFO

**Keywords:**

Southern Alps

Badlands

Vegetation cover

Hydro-sedimentary fluxes

Field data

CAESAR-Lisflood model

## ABSTRACT

Located in the Southern Alps, the Terres Noires region is characterized by highly erodible and poorly permeable soils. This, combined with the steep slopes and short, intense rains of the Mediterranean climate results in the formation of highly rilled/gullied surfaces known as badlands. Anthropogenic activities such as deforestation have exacerbated runoff and erosion on these surfaces. The aim of this study is to characterize the influence of vegetation cover on the multiscale temporal hydro-sedimentary functioning (and its controlling factors) of badlands. For this purpose, an approach combining the analysis of field data and the use of the physics-based model CAESAR-Lisflood was developed. The results indicate that the forested surfaces exhibit greater dampening of the fluxes than the bare surfaces, especially in the short term. The lower hydrological reactivity of the forested areas compared to the bare areas can be attributed to the higher retention and percolation capacity of the forested soils. Additionally, vegetation impedes the formation of regolith and the physical disaggregation of particles by regulating humidity and temperature fluctuations. With regard to predictive capacity, the model provides reliable estimates of the hydrologic balance of the catchments. However, there is potential for improvement in the calibration process to better represent the temporal dynamics of water flows and the amplitude and variability of sediment fluxes. The results of this study can serve as a basis for the development of water and soil management strategies in the badlands of the Southern Alps.

## 1. Introduction

The Southern Alps are subject to intense episodes of flooding and erosion that can cause significant human and economic damage. For example, the catastrophic Rhône floods of May–June 1856 (Phillips et al., 2013), November 1993, January and November 1994 and September and November 2002 (Antonelli et al., 2004; Maillet et al., 2006) caused billions of euros of damage and dozens of victims.

In the Mediterranean Alps, intense runoff and erosion are related to a combination of climatic, topographic, lithological and anthropogenic factors. The very intense rainfall of the Mediterranean mountain climate, coupled with the steep and locally impervious and erodible surfaces of the mountain areas, leads to runoff, mass movements and rill/gully erosion (Poesen and Hooke, 1997). These phenomena have been exacerbated by human activities such as deforestation for

agricultural purposes, tillage and homogenization of soils, and overgrazing.

In the Southern Alps, the Terres Noires region is characterized by highly erodible and poorly permeable soils on marl parent materials (composed of 35 % calcium carbonate and 65 % clay), that are poorly developed and mainly consist out of fragmented regolith resulting from marl weathering. This, combined with the steep slopes and short, intense rains of the Mediterranean climate, results in significant surface runoff and erosion (Antoine et al., 1995). These processes lead to the formation of highly rilled/gullied surfaces known as badlands. Despite representing only 0.2 % of the surface area of the Rhône catchment, they produce 14 % of the total suspended solids exported to the Mediterranean Sea (Copard et al., 2018). This significant transfer of sediment also results in the rapid siltation of reservoirs behind hydroelectric dams, disrupting their operation. To maintain the functionality of reservoirs, it is

<footnote><sup>a</sup> Univ Rouen Normandie, Université Caen Normandie, CNRS, Normandie Univ, M2C UMR 6143, F-76000 Rouen, France</footnote>

<footnote><sup>b</sup> Université Grenoble Alpes, INRAE, CNRS, IRD, Grenoble INP, IGE, Grenoble, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail addresses: raphaël.bunel1@univ-rouen.fr (R. Bunel), yoann.copard@univ-rouen.fr (Y. Copard), caroline.le-bouteiller@inrae.fr (L.B. Caroline), nicolas.massei@univ-rouen.fr (N. Massei), nicolas.lecoq@univ-rouen.fr (N. Lecoq).</footnote>
necessary to undertake regular cleaning, which is a costly operation (Lièbault et al., 2005). An alternative, sustainable solution is to reduce runoff and erosion through reforestation, or the installation of facilities (e.g. check dams, enclosures, terracing or stone bunds) thereby retaining sediment in the catchments upstream of the reservoirs (Valentin et al., 2005).

However, despite their initial importance in stabilizing soils and promoting revegetation, engineered structures inevitably degrade or collapse without maintenance, ceasing to function as sediment traps (Bartley et al., 2020; Bombino et al., 2024). Additionally, these structures, which are more challenging to install on steep mountain slopes, require maintenance and removal of accumulated sediment to continue fulfilling their role. Therefore, it is essential to prioritize reforestation efforts to ensure the long-term success of soil erosion reduction programs in hard-to-reach areas. There is a large body of literature documenting the effect of revegetation on reducing erosion rates and trapping sediment. For example, Rey (2004) and Rey and Burylo (2014) demonstrated that a vegetation barrier covering the lower part of a 500 m² plot (20 % of the area) captured all the sediments eroded from upstream. Molina et al. (2009) demonstrated that substantial plant cover in gully beds drastically reduces sediment transfer: eroded volumes can be deposited in the gully bed for >25 % of the total volume of sediment eroded in the catchment.

As early as the end of the 19th century, numerous reforestation programs were initiated in the region and elsewhere in the world (Phillips et al., 2013). Since then, the role of vegetation in flood and erosion control has been a topic of considerable debate (Warmerdam and Stricker, 2009). To ascertain the impact of forest cover on runoff and soil erosion, studies have been conducted on small experimental catchments (Mathys et al., 2003; Li et al., 2009; Warmerdam and Stricker, 2009). These studies have shown that forests, more than any other vegetation, reduce annual runoff and peak flows and support low flows (Robinson and Whitehead, 1993; Ice and Stednick, 2004). Similarly, several studies have demonstrated the critical role of land use and forest cover in reducing soil erosion (e.g., García-Ruiz et al., 2015).

However, in these studies, the characterization of the hydro-sedimentary response of catchments is very often done only by a few simple statistical descriptors, such as mean, maximum, etc. There is no quantitative indication of how the relationship between vegetation and runoff, erosion, and sediment fluxes varies across time scales. These studies provide only a partial picture of how vegetation cover modulates the hydro-sedimentary response of catchments to precipitation. However, this modulation may prove to be complex and vary according to the time scales of climate variability (e.g., event, seasonal, or multi-year scales).

In addition, vegetation influences a variety of hydrological and erosive processes, such as evapotranspiration, runoff, infiltration, sediment erosion, transport or deposition, mechanical disaggregation of particles, alteration of parent material, etc. (Marston, 2010). However, it is difficult to accurately and exhaustively identify the separate effect of vegetation on each of these different processes based on field measurements. Furthermore, some of these processes and their related features are challenging to measure or translate into relevant quantitative information (e.g. mechanical disaggregation of particles; Carrillo et al., 2011).

Another approach, physics-based numerical modeling, can partially mitigate the aforementioned observability problem by allowing one to interrogate, in a perfectly controlled environment, how vegetation cover acts to generate the observed hydro-sedimentary response (Carrillo et al., 2011; Bunel et al., 2021). Few studies have been carried out to model the hydrological and sedimentary response of badlands in the Mediterranean Alps (Lukey et al., 2000; Mathys et al., 2003; Carrière et al., 2020). Mathys et al. (2003) used the conceptual model ETC (Erosion des Torrents en Crue) to simulate runoff and sediment transport in a small catchment. Although the model simulates erosion, deposition, and channel bed armoring processes, the results showed that there was a

need to improve the representation of slope and sediment storage processes in the channels and to include the effects of vegetation on erosion. The SHETRAN physical model used by Lukey et al. (2000) and applied to the same site provides a better description of these processes. However, the errors and uncertainties resulting from the over-parameterization of this type of model probably explain the model's poor prediction of sediment fluxes for certain flood events. This is probably one of the reasons why Carriere et al. (2020) preferred to use the reduced complexity Landlab model to simulate sediment dynamics at this site. However, this study only attempted to simulate annual sediment fluxes, with a rather modest prediction performance (prediction bias of up to 200 %).

The objective of this study is to better characterize the influence of vegetation cover on the temporal variability of the hydro-sedimentary response of badlands catchments and to explicitly characterize the effects of vegetation on the controlling factors of this response. The objectives are to answer the following research questions: 1) Does the influence of vegetation cover on the hydro-sedimentary dynamics of these surfaces vary with the time scale considered? 2) Which factors controlling hydro-sedimentary fluxes are most sensitive to changes in vegetation cover?

These scientific questions will be addressed by combining two approaches. (i) The analysis of field data from two small experimental catchments, located in the badlands of the Southern Alps, which did not receive the same reforestation effort: a completely reforested catchment and a non-reforested catchment. ii) The modeling of the hydro-sedimentary functioning of these two catchments in order to specify, through a model calibration phase, the parameters, aspects and hydro-sedimentary processes that characterize the vegetated and denuded surfaces. The ability of the model used in this work to reproduce the hydro-sedimentary dynamics of the studied catchments will be evaluated.

## 2. Study site

The study site is part of the Draix-Bléone Observatory (Klotz et al., 2023). The Draix-Bléone Observatory is located in the Alpes de Haute Provence and is part of the French research infrastructure dedicated to the observation and study of the critical zone (OZCAR; Gaillardet et al., 2018). Two catchments that did not receive the same reforestation efforts are examined (Fig. 1 A). The Brusquet catchment has been completely reforested, while the Laval catchment, with a current vegetation cover of only 32 %, has not been reforested (Fig. 1B).

The parent materials of the Laval and Brusquet catchments are composed of Jurassic black marls dipping ~30–45° towards 120°N (Lofi et al., 2012). Elevations range from 852.7 to 1259.6 m in the Laval catchment and from 797.7 to 1259.9 m in the Brusquet catchment (Fig. 1 A). Local slopes are steep, often exceeding 35°.

The Laval and Brusquet catchments show a Mediterranean mountain climate (Csa according to the Köppen classification), with frequent freeze-thaw cycles in winter. Differences in annual precipitation are small, with a percentage difference of barely 10 % on the interannual module (respectively 818 mm and 909 mm for the Brusquet and Laval catchments). Summers are dry, with short, intense thunderstorms, and most precipitation and runoff occurs in spring (between April and May) and fall (between September and October; Mathys et al., 2003; Fig. S1). Freeze-thaw and wet-dry cycles are important weathering processes in black marl (Antoine et al., 1995). Their amplitude depends on temperature and humidity conditions. They control the seasonal sediment dynamics of the catchments in all its components (i.e. production, detachment and transport). From December to March, cryoclastic disaggregation of the marl bedrock leads to the development of regolith on the slopes, which is transported to the drainage network by gelifluction (Bechet et al., 2016). Intense and short rainfall events on dry soils in summer and moderate rainfall events on wet soils in spring and fall trigger runoff events that allow all the sediment stored in the
A

<figure><img src="image_3.png" /></figure>

B

<figure><img src="image_4.png" /><figcaption>Fig. 1. (A) Location, topography, hydrography, measuring stations and (B) land use in the Laval and Brusquet catchments.</figcaption></figure>

drainage network to be removed (Descroix and Mathys, 2003).

Runoff and erosion also vary spatially, and are influenced by slope
exposition, vegetation cover, slope gradient and the angle formed by the
slope and dip of the marl layers. Runoff and soil erosion are minimal on
vegetated soils and maximal on bare soils. In areas with no vegetation,
erosion rates are four times higher on north-facing slopes perpendicular
to the dip (~12 mm/yr) than on south-facing slopes parallel to the dip

(~3 mm/yr; Descroix and Mathys, 2003), even though runoff is lower in
these areas due to the structural configuration of the marls.

The information presented in this section will be further developed
and applied in the process of parameterizing and adjusting the func-
tionalities of the CAESAR-Lisflood model (cf. 3.2).
## 3. Materials and methods

An approach combining field data analysis and the application of the physics-based CAESAR-Lisflood model (Coulthard et al., 2013) was employed to quantify and simulate the influence of vegetation cover on the hydro-sedimentary dynamics of the Laval and Brusquet catchments.

The analysis of the field data consisted in directly quantifying the effect of forest cover on the hydro-sedimentary response of the Laval and Brusquet catchments to precipitation. High-frequency time series of water discharge and sediment fluxes at the outlet were analyzed using a tool never used before for this site, the Fourier spectrum. This tool sheds new light on how land use affects the variability and multi-scale correlation structure (event to decadal) of the hydrological and sedimentary signals from the Laval and Brusquet catchments. At the same time, a hydro-sedimentary modeling of the two catchments was carried out using the CAESAR-Lisflood model, and its results were used to interpret the results derived from the analysis of the observed data.

### 3.1. Field data

An extensive set of hydro-sedimentary data is available for the Laval and Brusquet catchments (https://dx.doi.org/10.17180/obs.draix). The reader is referred to Klotz et al. (2023) for a detailed description of the measurement setup. The dataset includes (i) precipitation measured by 4 rain gauges since 1983 at irregular time steps ranging from seconds to minutes, (ii) daily mean air temperature data measured since 1983 by 2 meteorological stations, (iii) water discharge and suspended sediment concentrations measured at the outlets of the Laval and Brusquet catchments since 1984 and 1987, respectively, at irregular time steps ranging from 1 to 10 min, and (iv) event bedload volumes at the outlets, available since 1985 for the Laval catchment and 1988 for the Brusquet catchment (fig. 1 A; fig. S5).

### 3.2. Description, developments and parameterization of the CAESAR-Lisflood model

The CAESAR-Lisflood model (Coulthard et al., 2013) belongs to the category of landscape evolution models (LEM), which allow efficient and deterministic simulation of the flow and sediment transport in a catchment. A detailed description of LEMs can be found in the extensive literature on the subject (e.g. Tucker and Hancock, 2010; Baartman et al., 2013; Coulthard et al., 2012; Coulthard and Van De Wiel, 2017; Bunel et al., 2023). CAESAR-Lisflood offers several advantages over other LEMs such as SIBERIA (Willgoose et al., 1991), CHILD (Tucker et al., 2001) or LAPSUS (Schoorl et al., 2002). It provides a more detailed representation of hydrology (including short rainfall events), flow hydraulics (hydrodynamic component), erosion and deposition phenomena, and sediment transport (e.g. diversity of transport modes according to sediment particle size; Bunel et al., 2021). This LEM couples a hydrological model (based on TOPMODEL; Beven and Kirkby, 1979) and a quasi-2D hydrodynamic model (LISFLOOD-FP; Bates et al., 2010) to generate surface runoff in a continuous and spatialized modeling framework (cf. Sup. Mat Text S1; eqs. S1 to S5). Flow heights and velocities are then used to calculate fluvial erosion and deposition for up to nine particle size classes (cf. Sup. Mat Text S1; eqs. S8 to S21). The latter are embedded in a system of superimposed layers overlying a non-erodable layer (bedrock). Slope processes (landslide, creep, rill and gully erosion), physical disaggregation of sediment particles and weathering of the bedrock are also simulated by the model (cf. Sup. Mat Text S1; eqs. S22 to S25). For each component of the model, the space is discretized into a regular 2D set of square cells whose size is defined by the user (see Sup. Mat Text S1 for a detailed description of the model functionalities).

The functionalities of the CAESAR-Lisflood model were extended in this study to take into account the specificities of the catchments treated. The model now considers the evolution of creep, bedrock weathering,

rill and gully erosion as a function of soil water saturation, temperature, terrain slope, vegetation, slope exposition and the angle formed by the terrain slope and the dip of the marl layers (cf. Sup. Mat Text S2).

The input data required by the model for its application to the Laval and Brusquet catchments are presented in Table S4 (cf. Sup. Mat).

### 3.3. Model calibration

In view of the specificities of the study site (lithology prone to weathering processes, intense solifluction and rilling/gullyling, etc.) and model sensitivity analyses (Ziliani et al., 2013; Skinner et al., 2018), we considered the adjustment of 13 parameters necessary (Table 1). These include two hydrological parameters ($m$, $M[q_{tot}]$), two hydraulic parameters ($n$, $Q_{min}$), five sediment parameters ($C$, $g_{si}$, $prop$, $g_{si}$, $\Delta Z_{max}$ and $D_{min}$), two slope parameters ($C_{rate}$ and $E_r$) and two pedogenesis parameters ($p_1$ and $k_1$) (Table 1; cf. Supplementary Material Text S3 for further details on parameter selection). To facilitate the adjustment of parameters varying in space and time or having multiple modalities ($p_1$, $C_{rate}$, $E_r$, $m$, $n$ and $g_{si}$), multiplying terms that allow an ensemble adjustment of the values were preferred for calibration ($M[p_1]$, $M[C_{rate}]$, $M[E_r]$, $M[m]$, $M[n]$ and $M[g_{si}]$).

The data on runoff depth (RD), suspended and bedload sediment yield (SSY and BSY, respectively) presented in section 3.1 were used to calibrate and evaluate the CAESAR-Lisflood outputs.

The parameters selected for calibration were sampled using a quasi Monte-Carlo procedure with uniform sampling of the parameter space (Sobol, 1977; Bunel et al., 2023; Table 1).

Three performance criteria, grouped under a multi-objective function, were used to assess the performance of the model for each calibration variable (RD, SSY and BSY). (i) The Nash-Sutcliffe criterion $[-\infty; 1]$ (NSE; Nash and Sutcliffe, 1970), (ii) the percentage bias (PBIAS; Gupta et al., 1999) and (iii) the ratio of the root mean square error (RMSE) to the standard deviation of the observed values (RSR $[0; +\infty]$; Moriasi et al., 2007). The best parameter set was defined as the one that minimizes the following multiobjective function (eq. 1; Pareto optimum; Ochoa-Tocachi et al., 2019, Bunel et al., 2023):

$$MultiObj_i = \sqrt{NSE_i^{norm2} + RSR_i^{norm2} + PBIAS_i^{norm2}} \quad (1)$$

where $MultiObj_i$ is the multiobjective function for the parameter set i.

A geomorphological performance criterion, which consists in verifying the absence of sediment storage in the catchment over the long term (i.e. over the calibration period) was also considered. We used the export ratio (ER) developed by Carriere et al. (2020), which corresponds to the ratio between the total volume of sediment passing through the catchment outlet and the volume of sediment produced on the hillslopes.

In order to simultaneously optimize the calibration of RD (MultiObj RD), SSY (MultiObj SSY), BSY (MultiObj BSY) and geomorphology ($ER_{norm}$), the parameter set producing the lowest MultiObj-W value was selected for model validation (eq. 2):

$$MultiObj\_W_i = \frac{MultiObj\_RD_i + MultiObj\_SSY_i + MultiObj\_BSY_i + ER_i^{norm}}{4} \quad (2)$$

The calibration (2000–2009) and validation (1994–1999 and 2010–2013) periods were defined to cover the maximum amount of data and hydrological conditions for all stations and calibration variables (fig. S5). The simulation starts with a bedrock that outcrops over the entire catchment, i.e. with no sediment stored in the system. This choice is justified by the seasonal hydrosedimentary dynamics of the catchments considered, which suggest that most of the regolith produced on the slopes each year is exported at the end of the year (cf. 2. Study site). Therefore, we assume that vegetation, where present, is established directly in the bedrock. The associated biochemical and pedogenetic weathering processes leading to soil formation are not considered. The
<table><caption>**Table 1**

Description of the parameters used to calibrate the CAESAR-Lisflood model and justification of the value ranges selected for the Laval and Brusquet catchments.</caption><thead><tr><th rowspan="2">Parameter (unit)</th><th rowspan="2">Description</th><th colspan="2">Selected value range</th><th rowspan="2">Justification</th></tr><tr><th>Laval</th><th>Brusquet</th></tr></thead><tbody><tr><td>Hydrology</td><td></td><td></td><td></td><td></td></tr><tr><td>M[m] (-)</td><td>Multiplier for the overall (spatial) adjustment of the m parameter that affects soil water holding capacity.</td><td>[0.2;1.0]</td><td>[0.25;2]</td><td>Range of variation determined as part of a preliminary exploration phase.</td></tr><tr><td>M[q<sub>tot</sub>] (-)</td><td>Multiplier for the overall (spatial) adjustment of q<sub>tot</sub>, corresponding to the water flux added to the surface by TOPMODEL.</td><td>[0.33; 1]</td><td>[0.2;1]</td><td>Range of variation determined as part of a preliminary exploration phase.</td></tr><tr><td>Flow Routing</td><td></td><td></td><td></td><td></td></tr><tr><td>Q<sub>min</sub> (m<sup>3</sup>/s)</td><td>The water flux added to the surface by TOPMODEL is only distributed over cells with a flow rate greater than Q<sub>min</sub>.</td><td>[0.025;0.075]</td><td>[0.025; 0.075]</td><td>Recommended value (one hundredth of DEM resolution - here 5 m) changed by ±50 %.</td></tr><tr><td>M[n] (-)</td><td>Multiplier for overall (spatial) adjustment of Manning's n coefficient, which represents the roughness of the soil surface.</td><td>[0.5; 2]</td><td>[0.25; 2]</td><td>Range defined to keep the n coefficient within a range of realistic values.</td></tr><tr><td>Fluvial erosion</td><td></td><td></td><td></td><td></td></tr><tr><td>M[gs] (-)</td><td>Multiplier that allows for an overall adjustment of the size of the two particulate fractions considered in this study.</td><td>[0.1; 1.5]</td><td>[0.1; 1.5]</td><td>Range defined to keep grain sizes within a realistic range.</td></tr><tr><td>prop.gs<sub>1</sub> (-)</td><td>Proportion of fine particle fraction.</td><td>[0.1; 0.9]</td><td>[0.1; 0.9]</td><td>The range is defined in such a way that a wide range of scenarios can be considered and therefore the sensitivity of the outputs to this parameter can be clearly identified.</td></tr><tr><td>C (-)</td><td>Factor added to the sediment transport formula to adjust the magnitude of erosion rates.</td><td>[0.25; 50]</td><td>[0.000001; 0.0001]</td><td>Range of variation determined as part of a preliminary exploration phase.</td></tr><tr><td>ΔZ<sub>max</sub> (m)</td><td>Maximum permitted erosion rate. Used to control the time step and the stability of the model.</td><td>[0.001; 0.025]</td><td>[0.001; 0.025]</td><td>Range of variation based on Skinner et al. (2018)</td></tr><tr><td>D<sub>min</sub> (m)</td><td>Minimum water depth required to calculate erosion in a cell.</td><td>[0.001; 0.01]</td><td>[0.001; 0.01]</td><td>Commonly accepted value range for this parameter.</td></tr><tr><td>Hillslope erosion</td><td></td><td></td><td></td><td></td></tr><tr><td>M[C<sub>rate</sub>] (-)</td><td>Multiplier for the overall (spatial) adjustment of C<sub>rate</sub> parameter used in solifluction calculation</td><td>[0.2; 12]</td><td>[0.001; 1]</td><td>Range of variation determined as part of a preliminary exploration phase.</td></tr><tr><td>M[E<sub>r</sub>] (-)</td><td>Multiplier for the overall (spatial) adjustment of the E<sub>r</sub> parameter used to calculate gully erosion.</td><td>[0.2; 12]</td><td>[0.2;12]</td><td>Range of variation determined as part of a preliminary exploration phase.</td></tr><tr><td>Soil development</td><td></td><td></td><td></td><td></td></tr><tr><td>M[p<sub>1</sub>] (-)</td><td>Multiplier for the overall (spatial) adjustment of parameter p<sub>1</sub>, which corresponds to the potential weathering rate of the bedrock.</td><td>[0.1;10]</td><td>[0.001;1]</td><td>Range of variation determined as part of a preliminary exploration phase.</td></tr><tr><td>k<sub>1</sub> (1/yr)</td><td>Rate of physical weathering of particles on the surface.</td><td>[0.000001; 0.001]</td><td>[0.000001; 0.001]</td><td>Range of variation based on Temme and Vanwalleghem (2016)</td></tr></tbody></table>

current model configuration therefore only provides information on the weathering rates that control regolith availability.

### 3.4. Results analysis steps

In a first step (section 4.1), the influence of the CAESAR-Lisflood parameters on the simulation quality of the RD (MultiObj_RD), SSY (MultiObj_SSY) and BSY (MultiObj_BSY) was analyzed by calculating the first-order ($S_i$) and total ($S_T$) Sobol indices for each parameter $i$. This analysis was carried out separately for the Laval and Brusquet catchments, in order to study how the influence of the calibrated parameters varied between the two catchments. Sobol indices were calculated using two meta-models to assess the robustness of the estimates: Gaussian process regression (or Kriging) which is a Bayesian probabilistic non-linear regression algorithm (Marrel et al., 2009) and multivariate adaptive spline regression (MARS) which is a non-parametric method based on a linear combination of functions called splines (Friedman, 1991). Additionally, one-dimensional scatterplots were used to analyze how optimal parameter values, which are associated with specific hydro-sedimentary processes, evolve from one catchment to another.

Secondly (section 4.2), the observed hydro-sedimentary fluxes of the Laval and Brusquet catchments were analyzed and compared, primarily based on the Fourier spectra of the time series (Lima et al., 2003;

Morales and Poveda, 2009; Fig. 2). The Fourier spectrum is a tool used to measure the distribution of signal energy (variance) across frequencies (or scales; Morales and Poveda, 2009). Fourier spectra were also used to individualize scalar regimes (or scale invariance regimes), i.e. frequency ranges for which the scaling law is the same (Morales and Poveda, 2009; eq. 3):

$$E_n(\omega) = \omega^B \qquad (3)$$

$E_n(\omega)$ is the power spectral density (unit of the signal squared and divided by frequency), and B is the spectral exponent or spectral slope, which can be estimated on a bi-logarithmic representation of the spectrum (Fig. 2). The spectral slope, B, is a measure of the intermittency of the signal, which quantifies the temporal coherence of the signal. While a spectral slope B equal to 0 characterizes a purely random signal (un-correlated signal in time, e.g. white noise), a high spectral slope B corresponds to a highly coherent and correlated signal in time (Morales and Poveda, 2009). Fourier spectra typically exhibit one, two or three different scalar regimes (Fig. 2). A change in scalar regime at a characteristic frequency Tx implies a different temporal correlation of the signal above and below Tx. This thus reveals the existence of multiple temporal structures in the signal, each of which is the signature of a distinct physical process. The Tx break frequencies and B scalar regime slopes were estimated using segmented regression models (or piecewise
<figure><img src="image_5.png" /><figcaption>Fig. 2. Fourier spectra of the Laval catchment rainfall. Break frequencies Tx and spectral slopes B are plotted on the spectrum.</figcaption></figure>

linear regression models built using the statistical approach of Muggeo, 2003; Fig. 2).

Finally (section 4.3), the performance of the modified version of the model was fully investigated. An unconventional approach involving the aforementioned Fourier analysis was also used to assess the model's ability to reproduce the frequency content and correlation structure of the observed time series. This complementary approach can provide insights into the behavior and shortcomings of the model, as well as the influence of its parameters (Weedon et al., 2015).

# 4. Results

## 4.1. Sensitivity analysis

The similarity of the indices obtained through Kriging on the one hand and through MARS on the other confirms a stable estimation of each sensitivity measure (Fig. 3). Nevertheless, we note the existence of several estimation discrepancies regarding the MultiObj_BSY fit criterion, especially in the estimation of interaction effects. It is also noteworthy that the three fit criteria differ in their parameter sensitivities. As might be expected, runoff depth (MultiObj_RD) is mainly sensitive to soil retention capacity ($M[m]$; Table 1) and percolation ($M[q_{tot}]$; table 1) for both catchments. SSY and BSY are also controlled by $M[m]$ and $M[q_{tot}]$, as well as by the potential weathering rate of the bedrock ($M[p_1]$; Table 1), sediment particle diameter ($M[gs_i]$; Table 1) and Manning's coefficient ($M[n]$; see Table 1).

<figure><img src="image_6.png" /><figcaption>Fig. 3. Estimation, for the Laval and Brusquet catchments, of the first-order $S_i$ and total $S_{Ti}$ Sobol indices for the multi-objective functions MultiObj_RD (runoff), MultiObj_SSY (suspended sediment yield), MultiObj_BSY (bedload sediment yield) and ER (export ratio).</figcaption></figure>
### 4.1.1. Runoff depth

The $S_i$ indices of the parameters $M[m]$ and $M[q_{tot}]$ are, respectively, 0.15 (average of the estimates obtained by Kriging and MARS) and 0.47 for the Laval catchment and 0.08 and 0.67 for the Brusquet catchment (Fig. 3). The remaining variance comes from weak to moderate effects, involving $M[q_{tot}]$, $M[m]$ and $Q_{min}$ (see Table 1) for the Laval catchment and $M[q_{tot}]$, $M[m]$ and $D_{min}$ (see Table 1) for the Brusquet catchment.

A better reproduction of RD is obtained for higher values of $M[q_{tot}]$ (0.6–0.7) and lower values of $m$ (0.004–0.006 m) for the Laval catchment and for lower values of $M[q_{tot}]$ (0.2–0.4) and higher values of $m$ (0.02–0.04 m) for the Brusquet catchment (fig. 4).

### 4.1.2. Sediment yields

The parameters $M[m]$ and $M[q_{tot}]$ also contribute strongly to the variability of the SSY (Fig. 3). SSY are also sensitive to the parameters $M[p_1]$, $propYG_1$ (cf. Table 1), $M[gs_1]$, $M[n]$ and $M[Crate]$ (cf. Table 1) except for the Laval catchment where only the effects of $M[p_1]$ and $propYG_1$ seem to be significant. Regarding BSY, the effects of $M[q_{tot}]$, $M[p_1]$ and $propYG_1$ remain predominant for the Laval catchment, while those of $M[gs_1]$, $M[q_{tot}]$ et $M[n]$ prevail for the Brusquet catchment.

As for the RD, a better reproduction of the sediment yields is obtained for high values of $M[q_{tot}]$ and low values of $m$ for the Laval catchment and for low values of $M[q_{tot}]$ and high values of $m$ for the Brusquet catchment (Figs. 5 et 6). The values of $p_1$, $prop_YG_1$, $gs_1$ and $gs_2$ that allow the best simulation of SSY and BSY are higher for the Laval catchment than for the Brusquet catchment (figs. 5 and 6).

## 4.2. Analysis of field data

### 4.2.1. Runoff depth

The flood peaks measured at the outlet of the non-forested catchment (Laval) are notably high, reaching values exceeding 10 mm, while they consistently remain below 3 mm for the Brusquet catchment (Fig. 7A and B). The rise and fall of the RD during a rainy episode are more rapid for the Laval catchment than for the Brusquet catchment (Fig. 7C). The observed monthly and annual RD is lower for the Brusquet catchment than for the Laval catchment, ranging from 20 to 295 mm (expressed in annual equivalent) for the former and from 110 to 640 mm for the latter (Fig. 7D and E). Furthermore, Fig. 7D and E show strong (intra)seasonal and interannual variability in runoff, more pronounced for the Laval catchment than for the Brusquet catchment, as corroborated by the Fourier spectra (Fig. 8A). The peaks at 6 months (6 m), 1 year (1y), and 1.5–15 years (1.5–15 yrs), which are markers of intraseasonal, seasonal and interannual variability respectively, are of greater amplitude in the Laval catchment spectrum than in the Brusquet catchment spectrum.

The runoff spectra can be divided into three distinct invariance regimes (Fig. 8A). The spectral slopes B1, B2 and B3 are –0.18, –0.48, and –0.88 for the Laval catchment and –0.47, –1.65, and –3.11 for the Brusquet catchment, respectively. Consequently, the persistence of runoff is mainly observed at small scales. The larger decay of the Brusquet catchment RD spectrum over all scale ranges indicates a greater degree of dissipation of the high and even low frequency energy of the rainfall signal.

### 4.2.2. Sediment yield

The maximum sediment yields measured at the Brusquet catchment

<figure><img src="image_7.png" /><figcaption>**Fig. 4.** Sensitivity of the MultiObj RD objective function (runoff depth) to the first-order effect of model parameters for the Laval (L) and the Brusquet (B) catchments. Only plots of parameters for which $S_i$ is strongest are shown. On each plot, the black dots represent the best and worst fit (for the MultiObj RD objective function), the dotted line corresponds to a loess smoothing of the scatterplot and $r$ corresponds to Pearson's correlation coefficient.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>Fig. 5. Sensitivity of the MultiObj_SSY (suspended sediment yield) objective function to the first-order effect of model parameters for the Laval (L) and the Brusquet (B) catchments. Only plots of parameters for which $S_i$ is strongest are shown. On each plot, the black dots represent the best and worst fit (for the MultiObj_SSY objective function), the dotted line corresponds to a less smoothing of the scatterplot and $r$ corresponds to Pearson's correlation coefficient.</figcaption></figure>

outlet is 100 to 250 times lower than that measured at the Laval catchment outlet (Figs. 9A, B, C, 10A and B). The mean annual SSY for the Laval and Brusquet catchments is 79.44 and 0.21 t/ha, respectively, and the mean annual BSY is 72.58 and 0.13 t/ha, respectively. The seasonal pattern of SSY (Fig. 9D) and BSY (Fig. 10C) differs between the two catchments. The maximum SSY occurs in summer for the Laval catchment, despite a low total runoff during this period (Fig. 7D). In contrast, for the Brusquet catchment, the highest values are obtained in spring (May) and fall (November), which are the periods with the highest runoff. These variabilities at 1 year and 180 days appear as peaks on the Fourier spectra of the Laval and the Brusquet catchments respectively (Fig. 11A). The annual dynamics we describe for the SSY are slightly different for BSY, especially for the Laval catchment, where the highest BSY values occur during the high total runoff in November (Fig. 10C).

There is also a strong interannual variability in SSY (Fig. 9E) and BSY (Fig. 10D), which is greater for the Laval catchment than for the Brusquet catchment (Fig. 11A). Sediment export dynamics vary not only across catchments, but also by particle diameter (bedload vs. suspended

load; Figs. 9E and 10D).

As with RD, the Fourier spectra of SSY decrease with increasing frequency (Figs. 8A and 11A). However, the slope of the Fourier spectra across frequencies is weaker, indicating that sediment dynamics are therefore much more intermittent than hydrological dynamics. Similar to RD spectra, SSY spectra can be divided into three invariance regimes. For the Laval catchment, the seasonal cycle separates the low-frequency invariance regime from the mid-frequency invariance regime, with spectral coefficients of 0.73 and – 0.11, respectively. The positive value of B1 indicates that SSY exhibits relatively low variability on time scales >1 year. This reflects the negative autocorrelation of SSY (blue noise) induced by the seasonal cycle of exports: high values in the summer months are followed by low values in the winter months. The spectral coefficients of the Brusquet catchment spectrum are all greater than those of the Laval catchment spectrum. This indicates a greater persistence of sediment transport for the Brusquet catchment, especially in the short term ($T < 9.8$ h).
<figure><img src="image_9.png" /><figcaption>**Fig. 6.** Sensitivity of the MultiObj_BSY objective function (bedload sediment yield) to the first-order effect of model parameters for the Laval (L) and the Brusquet (B) catchments. Only plots of parameters for which $S_i$ is strongest are shown. On each plot, the black dots represent the best and worst fit (for the MultiObj_BSY objective function), the dotted line corresponds to a loess smoothing of the scatterplot and $r$ corresponds to Pearson's correlation coefficient.</figcaption></figure>

### 4.3. Predictive ability

#### 4.3.1. Runoff depth

The calibration and validation results demonstrate that the CAESAR-Lisflood model simulates the RD at the Laval and Brusquet catchments outlets with reasonable accuracy (Table 2), despite a notable estimation bias for the Brusquet catchment (calibration PBIAS = +21.3 %).

Nevertheless, on a semi-hourly scale, for both Laval and Brusquet catchments, CAESAR-Lisfood tends to overestimate RD when RD is low and to underestimate it when RD is high (Fig. 7A and B).

There is a satisfactory reproduction of annual and monthly RD for both catchments (Fig. 7D and E). The largest discrepancies occur during the wettest and driest months and years. For the Laval catchment, the model over-reacts during months and years with low runoff and conversely minimizes runoff during the wettest months and years. Similarly, at the Brusquet catchment, CAESAR-Lisflood overestimates runoff in low-flow months and years. A comparison of the power spectra of the observed and simulated RD confirms these observations (i.e. underestimation of the amplitude of the spectra for these time scales; Fig. 8). For periods exceeding 3–5 days, the slopes of the observed and simulated spectra are almost identical (underestimation of the spectral coefficient B1 by only 17–32 %). The underestimation of the amplitude of the interannual and seasonal flow cycles explains this slight imbalance in the energy distribution. On the other hand, the spectra begin to diverge for periods of <3–5 days, due to the insufficient variability of flows at the flood scale (Fig. 7C). Therefore, the B2 and B3 coefficients are strongly overestimated, especially for the Laval catchment.

#### 4.3.2. Sediment yield

For the Laval catchment, the model overestimates SSY and BSY by an average of 138 % and 55 % respectively, over the calibration period (Table 2). The NSE and RSR criteria are 0.19 and 0.9 respectively for SSY and – 7.40 and 2.89 for BSY, reflecting the poor predictive ability of the model for sediment flux. The model's performance in predicting sediment yields from the Brusquet catchment is also very poor.

A direct comparison of observed and simulated SSY (Fig. 9A and B) and BSY (Fig. 10A and B), using a scatter plot, shows little relationship for the two catchments. The model underestimates the variability of SSY

and BSY for both catchments. The decline in the fluxes following the flood peaks is consistently too slow and regular, whereas it should manifest as sudden shifts, especially for the Laval catchment (Fig. 9C). This is corroborated by comparing the Fourier spectra of the observed and simulated series (Fig. 11). For periods less than few days, the persistence of the SSY for the Laval and the Brusquet catchments is clearly exaggerated.

The aggregation of values at monthly and annual time steps does not result in improved agreement between observed and simulated sediment yields (Figs. 9D, E, 10C and D). In both the Laval and Brusquet catchments, the simulated SSY and BSY are higher than the observed values, especially during winter, with deviations exceeding +500 %. These discrepancies are large enough to shift the export peak to the winter months. With regard to the Laval catchment, the overestimation of the annual SSY and BSY is mainly evident from 2005 onwards, and remains so until the end of the calibration period (Fig. 9E).

Therefore, the regolith production by frost at the end of the simulation period, which is a function of the potential weathering rate of the bedrock $p_1$, is overestimated. Indeed, the Laval catchment SSY and BSY for the years 2006, 2009, 2010 and 2011, which are not exceptionally strong (Figs. 9E and 10D), are characterized by high cumulative $p_1$ values (Figs. S6A and S7A). Similarly, for the Brusquet catchment, an overestimation (underestimation) of fluxes (suspension or bedload) tends to occur when the calculated $p_1$ coefficient is high (low) (Figs. S6B and S7B). The absolute differences between the measured and simulated annual fluxes do not appear to be related to the quality of the simulation of annual RD (Figs. S6 and S7). The figures demonstrate that years with high regolith production can have a long-term effect by increasing the simulated sediment yields in subsequent years. The low variability of SSY revealed by Fourier analysis over periods longer than 1 year is therefore not reproduced by the model (Fig. 11).

## 5. Discussion

### 5.1. Influence of vegetation on runoff depth and sediment yields

#### 5.1.1. Runoff depth

The greater autocorrelation and persistence of flows for the Brusquet
<figure><img src="image_10.png" /><figcaption>**Fig. 7.** Comparison of observed and simulated runoff depth (RD) values over the period January 1, 1994 to March 31, 2013 at semi-hourly (A: Laval catchment, B: Brusquet catchment), event (C), monthly (D) and annual (E) scales for the Laval and Brusquet catchments.</figcaption></figure>

catchment indicate that the vegetation cover of this catchment strongly accentuates its hydrological memory. The capacity of the vegetation cover to store and retain runoff (m) enables it to regulate floods, as evidenced by a low peak flow and a slow rise and fall (Fig. 12A). According to the Fourier analysis, vegetation exerts a more limited influence on long-term hydrological variability (e.g. seasonal and interannual; Piégay et al., 2004). This influence of vegetation cover on the correlative and spectral properties of runoff was already observed by Julian and Gardner (2014) for 87 catchments on the east coast of the USA. They showed, via the Fourier spectrum, that the rainfall signal for predominantly forested catchments is more strongly attenuated than for other catchments, particularly in its high-frequency part (< ~6 days).

Furthermore, the results permit the conclusion that the vegetation

cover of the Brusquet catchment generates an annual and monthly hydrological response whose amplitude is radically weaker than that of the Laval catchment. The high root biomass of the forests favors evapotranspiration, resulting in a higher soil water deficit. The forested areas of the Brusquet catchment, which also have soils with high porosity and water storage capacity (M[q<sub>tot</sub>] and m), therefore significantly reduce the saturation-excess runoff in spring and autumn (Collins et al., 2004; Marston, 2010; Mallet et al., 2020). Moreover, in addition to their role in soil retention capacity, forests increase the roughness and infiltration capacity of surface soils, thus attenuating Hortonian runoff in summer (Cosandey et al., 2005; Istanbulluoglu and Bras, 2005; Marston, 2010; Fig. 12A). It is important to note that uncertainties associated with water discharge measurements are inevitable, particularly when water flows
<figure><img src="image_11.png" /><figcaption>**Fig. 8.** Fourier spectra of observed (a) and simulated (b) runoff depth (RD) series for the Laval (red) and Brusquet (green) catchments. Break frequencies Tx1 and Tx2 and spectral slopes B1, B2 and B3 are indicated on each spectrum. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

are low, due to the inadequacy of measuring equipment under these conditions (see 5.2.1). This could limit the reliability of calculated monthly and annual water balances (Klotz et al., 2023).

### 5.1.2. Sediment yields

For the Brusquet catchment, the presence of a protective vegetation cover alters the sensitivity of the surfaces to runoff, frost weathering and erosion, resulting in the observed differences in the amplitude and (seasonal and inter-annual) periodicity/variability of the fluxes. Indeed, in the Laval catchment, suspended sediment flow appears to occur primarily during the Hortonian runoff events of summer. For the forested Brusquet catchment, it seems to occur when soil water saturation is reached in spring and fall (Mathys et al., 2003). The high sediment transport in the Laval catchment during the summer could potentially limit sediment availability and, as a consequence, SSY during the winter (negative autocorrelation of SSY highlighted by Fourier analysis; Rainato et al., 2017). This interpretation assumes that all the fine sediments stored in this catchment are evacuated during the year, which supports the hypothesis of Bechet et al. (2016) regarding a rapid export (a few months) of suspended solids.

The effect of vegetation in reducing runoff and erosion is supported by the results of the sensitivity analysis which show that the deep infiltration (M[q<sub>tot</sub>]) and retention capacity (m) of soils increase with the presence of vegetation, thereby limiting soil water erosion (Collins et al., 2004). Vegetation also impedes the production of regolith (p<sub>1</sub>) and the physical disaggregation of particles (prop_gs<sub>i</sub> and gs<sub>i</sub>) through wet-drying and freeze-thawing. It does this by regulating variations in humidity (Welsh et al., 2009; Niu et al., 2019) and temperature and by limiting the anisotropy of the marls through pedogenesis, which could potentially prevent deep penetration of frost and wetting fronts (Fig. 12B; Esteves et al., 2005; Mathys et al., 2005). From a temperature perspective, vegetation limits the decrease in soil temperature at night by re-emitting part of the nighttime radiation back to the soil, and reduces the increase in soil temperature during the day by intercepting part of the solar

radiation (20 % in the study by Chen et al., 2020; D'Odorico et al., 2013; Guo et al., 2018 and Xu et al., 2021) The root system of vegetation ensures better material cohesion, which limits the sediment entrainment in and around the drainage network (increasing the critical shear stress – gs; Prosser et al., 1995; Gyssels et al., 2002).

On the other hand, the results of the sensitivity analysis indicate that the vegetation exerts little influence on the erosive power of the runoff, both in channelized sections (parameter C) and in the first rills/gullies of the catchment (parameter E<sub>r</sub>). It also has a minimal effect on the physical disaggregation rate of surface particles (k<sub>1</sub>). It is possible that the effect of k<sub>1</sub> may be obscured by the influence of other parameters acting on the soil particle size distribution (gs<sub>i</sub> and prop_gs<sub>i</sub>) and more globally on sediment transport. Grain size field data recently collected by Ariagno et al. (2023) at different times at the study site could help to better constrain the values of k<sub>1</sub>. Carriere et al. (2020), applying the Landlab model to the Laval and Brusquet catchments, also found that vegetation acts on erosion primarily by reducing sediment availability and surface erodibility on the hillslopes rather than by reducing the erosivity of runoff in the stream network. In an environment as energetic as this one (steep slopes), it is reasonable to conclude that vegetation can have a greater effect on substrate alteration and physical disaggregation of particles, and therefore on sediment availability, than on water flow transport capacity. Given the steep slopes of the catchment, the transport capacity of the runoff may be sufficient to allow most of the hydrological memory to be transferred into sediment fluxes. As a result, the anticipated greater intermittency of SSY in vegetated catchments, due to the dissipation of RD energy and raising of the sediment entrainment threshold, does not occur (the spectrum of SSY mirrors that of RD).

## 5.2. Predictive ability

### 5.2.1. Runoff depth

According to the criteria of Moriasi et al. (2007, 2015, NSE > 0.5 and PBIAS < ±15%), the present study shows satisfactory performance of
<figure><img src="image_12.png" /><figcaption>**Fig. 9.** Comparison of observed and simulated suspended sediment yield (SSY) values over the period January 1, 1994 to March 31, 2013 at semi-hourly (A: Laval catchment, B: Brusquet catchment), event (C), monthly (D) and annual (E) scales for the Laval and Brusquet catchments.</figcaption></figure>

the CAESAR-Lisflood model in simulating the hydrological dynamics of the Laval and Brusquet catchments. The simulation quality of the Laval catchment RD is superior to that of previous studies (Table 5). The model is able to reproduce the increase in water flow dampening with the presence of vegetation.

The model tends to underestimate the amplitude of semi-hourly, seasonal and interannual RD variations. Setting the *m* parameter too low could explain the insufficient catchment response to a rainfall event (Fig. 13A). Insufficient temporal resolution of rainfall (semi-hourly) may also result in low, persistent runoff, as it fails to capture short, intense rainfall events (Coulthard and Skinner, 2016).

The underestimation of the amplitude of seasonal and interannual runoff variations is explained by the minimization of catchment drying

during the driest months and years. This is probably due to the fact that the hydrological module of the model does not represent all surface hydrological processes, in particular the evolution of soil water saturation under the effect of evapotranspiration. Furthermore, a compensation effect could explain the underestimation of runoff during wet periods, since an exaggeration of percolation ($M[q_{tot}]$ too low), leading to an underestimation of runoff during the wettest months and years, could have been generated to limit the overestimation of runoff during dry periods (Fig. 13A).

However, the comparison of simulated and observed RD at low and very high-water flows is challenging due to the high uncertainty associated with water discharge measurements. In fact, the measurement uncertainties would be 10 % for water flows between 40 and 1890 l/s,
<figure><img src="image_13.png" /><figcaption>**Fig. 10.** Comparison of observed and simulated values of bedload sediment yield (BSY) over the period January 1, 1994 to March 31, 2013 at semi-hourly (A: Laval catchment, B: Brusquet catchment), monthly (C) and annual (D) scales for the Laval and Brusquet catchments.</figcaption></figure>

while they would be close to 30 % for water flows outside this range (Klotz et al., 2023; Mathys, 2006). Therefore, for half-hours with RD between 8.37·10⁻² and 3.96 mm, the aforementioned analyses and comparisons are relatively reliable, while for the remaining values they should be treated with more caution, especially when the deviations are small.

### 5.2.2. Sediment yields

Although the uncertainties in measured SSY (10 % for heavily loaded floods to 60 % for lightly loaded floods; Klotz et al., 2023) and BSY (6–10 % for high deposition values to 30 % for low deposition values; Mathys, 2006) are high, the measurement uncertainty is not sufficient to mask the frequently considerable discrepancies between observed and

simulated values (Moriasi et al., 2007, 2015). Nevertheless, in some cases, the quality of the sediment yield simulations is comparable to or even better than that of previous studies (cf. PBIAS TSY Laval and PBIAS SSY Brusquet; Table 5).

For both the Laval and Brusquet catchments, the contribution of suspended solids is excessive. This is probably attributable to an over-estimation of the proportion of fine particles (72.5 % for the Laval catchment and 61.1 % for the Brusquet catchment) identified during the model calibration (Table 4).

The results suggest an excessive persistence of SSY in the short term, which may be associated with the simulation of excessively flat hydrographs. Similarly, it could be linked to an excessive mobility of sedimentary particles associated with an underestimation of their size ($gs_1$
<figure><img src="image_14.png" /><figcaption>Fig. 11. Fourier spectra of observed (a) and simulated (b) suspended sediment yield (SSY) series for the Laval (red) and Brusquet (green) catchments. Break frequencies Tx1 and Tx2 and spectral slopes B1, B2 and B3 are indicated on each spectrum. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

Table 2

Goodness-of-fit criteria (NSE, PBIAS and RSR) produced by the best parameter set (see Table 3) for each catchment (Laval and Brusquet) and each variable (RD, SSY, BSY and ER) on non-aggregated (semi-hourly) data for the calibration and validation periods. Values in brackets indicate the performance of the best parameter set in each situation (for the particular variable and criterion) during model calibration.

<table><thead><tr><th rowspan="2"></th><th rowspan="2"></th><th colspan="3">Calibration</th><th colspan="3">Validation</th></tr><tr><th>NSE</th><th>PBIAS (%)</th><th>RSR</th><th>NSE</th><th>PBIAS (%)</th><th>RSR</th></tr></thead><tbody><tr><td rowspan="4">Laval</td><td>RD</td><td>0.65 (0.67)</td><td>-11 (1.50)</td><td>0.59 (0.58)</td><td>0.57</td><td>-1.3</td><td>0.66</td></tr><tr><td>SSY</td><td>0.19 (0.29)</td><td>138.4 (-3.30)</td><td>0.9 (0.84)</td><td>0.15</td><td>179.6</td><td>0.92</td></tr><tr><td>BSY</td><td>-7.40 (0.51)</td><td>55.5 (4.10)</td><td>2.89 (0.70)</td><td>-7.03</td><td>58.7</td><td>2.82</td></tr><tr><td>ER</td><td>0.68 (0.68)</td><td></td><td></td><td>0.88</td><td></td><td></td></tr><tr><td rowspan="4">Brusquet</td><td>RD</td><td>0.65 (0.66)</td><td>21.3 (-0.5)</td><td>0.59 (0.58)</td><td>0.63</td><td>10</td><td>0.61</td></tr><tr><td>SSY</td><td>-0.04 (0.17)</td><td>71.4 (-6.8)</td><td>1.02 (0.91)</td><td>0</td><td>-25.3</td><td>1</td></tr><tr><td>BSY</td><td>-0.34 (0.44)</td><td>-27.3 (0)</td><td>1.12 (0.72)</td><td>-0.95</td><td>-90.5</td><td>1.36</td></tr><tr><td>ER</td><td>0.89 (0.89)</td><td></td><td></td><td>1</td><td></td><td></td></tr></tbody></table>

Table 3

Best parameter set identified by the automatic calibration procedure for the Laval and Brusquet catchments. The best parameter set is the best-performing parameter set for all metrics (NSE, RSR, PBIAS) and variables (RD, SSY, BSY and ER).

<table><thead><tr><th>Parameter (unit)</th><th>Laval optimal value</th><th>Brusquet optimal value</th></tr></thead><tbody><tr><td>M[m] (-)</td><td>2.07 × 10<sup>-1</sup></td><td>4.77 × 10<sup>-1</sup></td></tr><tr><td>M[q<sub>tot</sub>] (-)</td><td>4.03 × 10<sup>-1</sup></td><td>2.53 × 10<sup>-1</sup></td></tr><tr><td>Q<sub>min</sub> (m<sup>3</sup>/s)</td><td>2.57 × 10<sup>-2</sup></td><td>5.32 × 10<sup>-2</sup></td></tr><tr><td>M[n] (-)</td><td>8.06 × 10<sup>-1</sup></td><td>7.92 × 10<sup>-1</sup></td></tr><tr><td>M[gs] (-)</td><td>1.03 × 10<sup>-1</sup></td><td>1.43 × 10<sup>-1</sup></td></tr><tr><td>prop.gs<sub>1</sub> (-)</td><td>7.25 × 10<sup>-1</sup></td><td>6.11 × 10<sup>-1</sup></td></tr><tr><td>C (-)</td><td>40.33</td><td>8.62 × 10<sup>-5</sup></td></tr><tr><td>ΔZ<sub>max</sub> (m)</td><td>1.10 × 10<sup>-2</sup></td><td>1.91 × 10<sup>-2</sup></td></tr><tr><td>D<sub>min</sub> (m)</td><td>1.13 × 10<sup>-3</sup></td><td>1.25 × 10<sup>-3</sup></td></tr><tr><td>M[C<sub>rate</sub>] (-)</td><td>4.08</td><td>0.68</td></tr><tr><td>M[E<sub>r</sub>] (-)</td><td>11.66</td><td>8.67</td></tr><tr><td>M[p<sub>1</sub>] (-)</td><td>2.98 × 10<sup>-1</sup></td><td>1.51 × 10<sup>-3</sup></td></tr><tr><td>k<sub>1</sub> (1/yr)</td><td>8.39 × 10<sup>-4</sup></td><td>4.21 × 10<sup>-6</sup></td></tr></tbody></table>

equal to 8.23 µm for the Laval catchment and 11.4 µm for the Brusquet catchment - Table 4). However, these diameters are comparable to the median diameter of suspended particles measured by Le Bouteiller et al. (2011) in the waters of the Laval catchment (10 µm). The excessive persistence of SSY over the long term (> 2.8 days) simulated for the Laval catchment could be due to excessive sediment production on the slopes, associated with an overestimation of the potential weathering rate of the substratum $p_1$ (table 4). In fact, in this case, the discontinuity of the flux, which occurs annually in the fall due to the depletion of the available sediment, is not replicated.

The results also indicate an overestimation of the sediment yield during winter. Sediments produced on the slopes during winter could enter the drainage network too quickly (overestimation of the creep coefficient $C_{rate}$) and in too large quantities (overestimation of $p_1$), resulting in premature resumption of fluvial transport. Moreover, an underestimation of sediment particle diameters could ensure an efficient transport of suspended and bedload sediments, even during low intensity winter floods. This dynamic could limit the sediment volumes available for the following months, since we observe for the Brusquet
<figure><img src="image_15.png" /></figure>

## B

<figure><img src="image_16.png" /><figcaption>Fig. 12. Summary of the study results concerning the influence of vegetation cover on runoff (A) and erosion (B) in the marly badlands of the Southern Alps.</figcaption></figure>
## A. Model error sources

<figure><img src="image_17.png" /></figure>

* Missing physical processes (changes in soil water saturation due to evapotranspiration, rainfall interception)

* Need for better representation of certain processes in the model (percolation, gelifraction, rill erosion)

## B. Erosion (<0) / Deposition (>0) [mm/yr]

<figure><img src="image_18.png" /><figcaption>Fig. 13. (A) Summary of the various sources of error in modeling the hydro-sedimentary dynamics of the Laval and Brusquet catchments; (B) Simulated erosion and deposition rate maps for the period 1995–2012 for the Laval (left) and Brusquet (right) catchments.</figcaption></figure>

catchment, and to a lesser extent for the Laval catchment, an underestimation of the simulated fluxes (suspension and bedload) during summer and autumn. For the Laval catchment, the underestimation of SSY during the summer can also be attributed to the model's inability to accurately capture the hydrological reactivity of the catchment to intense rainfall (see section 5.2.1). The intense runoff that occurs in the rills/gullies during summer storms may be insufficient to allow sediment transport and evacuation (ER too low, between 0.68 and 0.88 for the Laval catchment; Table 2). Indeed, as shown by the erosion and deposition rate maps for the period December 1, 1995 to November 30, 2012, not all the material produced on the Laval slopes is removed from the catchment (Fig. 13B). Some of it is permanently stored in the drainage network and remains beyond the annual cycle. In some gullies, deposition rates can exceed 200 mm/year.

The model does not adequately capture the interannual dynamics of bedrock weathering, and the daily mean air temperature, from which the number and intensity of freeze-thaw cycles were inferred, is not a good proxy for gelifraction. In the present study, a freeze-thaw cycle occurs whenever the mean air temperature changes from negative to positive the following day, and the intensity of the cycle is proportional to the temperature difference between these two days (cf. Sup. Mat. Text S2). An alternative temperature criterion, based exclusively on freezing/frost-cracking phenomena (instead of the freeze-thaw used here), could be considered, such as the number of hours with negative ground surface temperature or the criterion of Hales and Roering (2007), which according to Ariagno et al. (2022) are good predictors of the amount of sediment produced during each winter at the Laval catchment. On the other hand, we assume that the extent of gelifraction is linearly
<caption>**Table 4**</caption>

Spatio-temporal averages of *m*, *M[q<sub>tot</sub>]*, *Q*<sub>min</sub>, *n*, *gs*<sub>1</sub>, *gs*<sub>2</sub>, *prop. gs*<sub>1</sub>, *C*, *ΔZ*<sub>max</sub>, *D*<sub>min</sub>, *C*<sub>rate</sub>, *E*<sub>r</sub>, *p*<sub>1</sub> and *k*<sub>1</sub> deduced from the optimal CAESAR-Lisflood configuration (cf. Table 3) for the Laval and Brusquet catchments.

<table><caption>**Table 5**</caption><thead><tr><th>Parameter (unit)</th><th>Laval optimal value</th><th>Brusquet optimal value</th></tr></thead><tbody><tr><td><i>m</i> (m)</td><td>2.45 × 10<sup>-3</sup></td><td>9.54 × 10<sup>-3</sup></td></tr><tr><td><i>q</i><sub>tot</sub><i>M</i> (–)</td><td>4.03 × 10<sup>-1</sup></td><td>2.53 × 10<sup>-1</sup></td></tr><tr><td><i>Q</i><sub>min</sub> (m<sup>3</sup>/s)</td><td>2.57 × 10<sup>-2</sup></td><td>5.32 × 10<sup>-2</sup></td></tr><tr><td><i>n</i> (s/m<sup>1/3</sup>)</td><td>7.87 × 10<sup>-2</sup></td><td>1.58 × 10<sup>-2</sup></td></tr><tr><td>gs<sub>1</sub>/gs<sub>2</sub> (m)</td><td>8.23 × 10<sup>-6</sup> / 2.06 × 10<sup>-4</sup></td><td>1.14 × 10<sup>-5</sup> / 2.86 × 10<sup>-4</sup></td></tr><tr><td><i>prop. gs</i><sub>1</sub> (–)</td><td>7.25 × 10<sup>-1</sup></td><td>6.11 × 10<sup>-1</sup></td></tr><tr><td><i>C</i> (–)</td><td>40.33</td><td>8.62 × 10<sup>-5</sup></td></tr><tr><td>Δ<i>Z</i><sub>max</sub> (m)</td><td>1.10 × 10<sup>-2</sup></td><td>1.91 × 10<sup>-2</sup></td></tr><tr><td><i>D</i><sub>min</sub> (m)</td><td>1.13 × 10<sup>-3</sup></td><td>1.25 × 10<sup>-3</sup></td></tr><tr><td><i>C</i><sub>rate</sub> (m<sup>2</sup>/yr)</td><td>7.07</td><td>7.88 × 10<sup>-1</sup></td></tr><tr><td><i>E</i><sub>r</sub> (m/yr)</td><td>6.78 × 10<sup>-2</sup></td><td>2.77 × 10<sup>-2</sup></td></tr><tr><td><i>p</i><sub>1</sub> (m/yr)</td><td>1.03</td><td>4.99 × 10<sup>-4</sup></td></tr><tr><td><i>k</i><sub>1</sub> (1/yr)</td><td>8.39 × 10<sup>-4</sup></td><td>4.21 × 10<sup>-6</sup></td></tr></tbody></table>

Comparison of the predictive quality of the water flows and sediment fluxes in the Laval and Brusquet catchments obtained by the present study with that of previous studies.

<table><thead><tr><th></th><th>Lukey et al. (2000)</th><th>Mathys et al. (2003)</th><th>Carriere et al. (2020)</th><th>This study</th></tr></thead><tbody><tr><td>PBIAS RD Laval (calibration; %)</td><td>24.31</td><td>11</td><td>–</td><td>–11</td></tr><tr><td>PBIAS RD Laval (validation; %)</td><td>17.02</td><td>22</td><td>–</td><td>–1.3</td></tr><tr><td>NSE RD Laval (calibration)</td><td>0.36</td><td>–</td><td>–</td><td>0.65</td></tr><tr><td>NSE RD Laval (validation)</td><td>0.27</td><td>–</td><td>–</td><td>0.57</td></tr><tr><td>PBIAS TSY Laval (calibration &amp; validation; %)</td><td>–66.93; 131.03</td><td>–</td><td>–</td><td>108.63</td></tr><tr><td>PBIAS BSY Laval (calibration &amp; validation; %)</td><td>–</td><td>–4.76</td><td>–</td><td>57.11</td></tr><tr><td>PBIAS SSY Laval (validation; %)</td><td>–</td><td>–</td><td>28.6</td><td>179.6</td></tr><tr><td>PBIAS SSY Brusquet (validation; %)</td><td>–</td><td>–</td><td>211</td><td>–25.3</td></tr><tr><td>ER Laval (calibration)</td><td>–</td><td>–</td><td>~0.9</td><td>0.68</td></tr><tr><td>ER Brusquet (calibration)</td><td>–</td><td>–</td><td>~0.9</td><td>0.89</td></tr></tbody></table>

correlated with the degree of rock saturation, while Fagerlund (2004) suggests that this relationship is only valid above a saturation threshold.

## 6. Conclusion

High-frequency measurements of RD, SSY and BSY over a period of almost 40 years for two catchments distinguished by their land use have enabled a precise analysis of the influence of vegetation on runoff and erosion in the Southern Alps badlands.

The analysis of the internal temporal structure of these series using a signal processing method, the Fourier spectrum, made it possible to characterize the influence of vegetation on the variability of flows and sediment transport in the short and long term. At the same time, the hydrosedimentary functioning of these catchments was modelled in order to specify the hydrosedimentary mechanisms through which vegetated surfaces act.

Compared to the bare Laval catchment, the forested Brusquet catchment is characterized by soils with high retention and infiltration capacity. These hydrodynamic properties of vegetated soils enable a notable regulation of the hydrological response of vegetated catchments to rainfall, stronger in the short term than in the long term. There is also

a significant influence of vegetation on the weathering rate of bedrock and soil granulometry. The vegetation of the Brusquet catchment slows down the production of regolith and the physical disaggregation of particles. The greater intermittency of SSY that might be expected for vegetated catchments does not occur.

Regarding the predictive capacity of CAESAR-Lisflood, the model produces comparable results for both catchments, with satisfactory water flow reproduction. The model provides a good prediction of runoff, with an error of less than ±15 % for both catchments during the validation period. However, the average estimation biases for SSY and BSY are high, exceeding ±100 % for the Laval catchment and ±25 % for the Brusquet catchment. Moreover, the model fails to adequately capture the interannual dynamics of bedrock weathering, and the daily mean air temperature, from which the number and intensity of freeze-thaw cycles were derived, is not a reliable proxy for gelifraction. Consequently, it is imperative to enhance the manner in which the gelifraction process is considered within the model. Nonetheless, CAESAR-Lisflood was able to reproduce the two orders of magnitude difference observed in sediment yield in the Laval and Brusquet catchments. It produces results of equal or better quality than previous studies. Finally, this study provides a better understanding of the influence of vegetation on the temporal variability of hydro-sedimentary fluxes. It can provide a basis for water and soil management and conservation strategies in the Badlands of the Southern Alps. The model developed here can be used to test land use scenarios under climate change in this area in order to better guide reforestation programs.

## Abbreviations

<table><tr><td>S<sub>f</sub></td><td>1st-order Sobol index</td></tr><tr><td>S<sub>f1</sub></td><td>Total Sobol index</td></tr><tr><td>RD</td><td>Runoff Depth</td></tr><tr><td>SSY</td><td>Suspended Sediment Yield</td></tr><tr><td>BSY</td><td>Bedload Sediment Yield</td></tr><tr><td>TSY</td><td>Total Sediment Yield</td></tr><tr><td>MultiObj RD</td><td>Multi-objective function associated to RD</td></tr><tr><td>MultiObj SSY</td><td>Multi-objective function associated to SSY</td></tr><tr><td>MultiObj BSY</td><td>Multi-objective function associated to BSY</td></tr><tr><td>ER</td><td>Export Ratio</td></tr></table>

## CRediT authorship contribution statement

**Raphaël Bunel:** Writing – review & editing, Writing – original draft, Visualization, Software, Methodology, Investigation, Formal analysis, Conceptualization. **Yoann Copard:** Writing – review & editing, Validation, Supervision, Project administration, Conceptualization. **Le Bouteiller Caroline:** Writing – review & editing, Data curation. **Nicolas Massei:** Writing – review & editing, Validation, Project administration, Methodology, Funding acquisition, Conceptualization. **Nicolas Lecoq:** Writing – review & editing, Validation, Supervision, Software, Project administration, Methodology, 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.

## Acknowledgments

This work was carried out as part of the CLIMAPHROS research project, funded by the Agence de l'Eau Seine Normandie (AESN) and the OZCAR (French Critical Zone Observatories, Research and Applications) research infrastructure through the Réseau de Bassins Versants (RBV). We would like to thank all those involved in collecting data for the Draix Bléone Observatory - as well as Tom Coulthard for free access to the CAESAR-Lisflood model (https://sourceforge.net/projects/caesar-
lifsflood/). We thank the reviewers for their useful comments, which improved the manuscript.

## Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j geomorph 2025.109726.

## Data availability

The data set used during the current study is available on BDOH portal (https://bdoh.irstea.fr/DRAIX/) and has the DOI identifier 10.17180/OBS.DRAIX.

## References

Antoine, P., Giraud, D., Meunier, M., Van Ash, T., 1995. Geological and geotechnical properties of the "Terres Noires" in southeastern France: weathering, erosion, solid transport and instability. Eng. Geol. 40, 223-234.

Antonelli, C., Provansal, M., Vella, C., 2004. Recent morphological channel changes in a deltaic environment. The case of the Rhône River. France. Geomorphology 57, 385-402.

Ariagno, C., Le Bouteiller, C., van der Beek, P., Klotz, S., 2022. Sediment export in marly badland catchments modulated by frost-cracking intensity, Draix-Bléone critical Zone Observatory, SE France. Earth Surf. Dyn. 10, 81-96.

Ariagno, C., Pasquet, S., Le Bouteiller, C., van der Beek, P., Klotz, S., 2023. Seasonal dynamics of marly badlands illustrated by field records of hillslope regolith properties, Draix-Bléone Critical Zone Observatory, South-East France. Earth Surf. Process. Landf. 48, 1526-1539.

Baartman, J.E.M., Masselink, R., Keesstra, S.D., Temme, A.J.A.M., 2013. Linking Landscape Morphological Complexity and Sediment Connectivity. Earth Surf. Process. Landf. 38, 1457-1471.

Bartley, R., Poesen, J., Wilkinson, S., Vanmaercke, M., 2020. A review of the magnitude and response times for sediment yield reductions following the rehabilitation of gullied landscapes. Earth Surf. Process. Landf. 45, 3250-3279.

Bates, P.D., Horritt, M.S., Fewtrell, T.J., 2010. A simple inertial formulation of the shallow water equations for efficient two-dimensional flood inundation modelling. J. Hydrol. 387, 33-45.

Bechet, J., Duc, J., Loye, A., Jaboyedoff, M., Mathys, N., Malet, J., Travelletti, J., 2016. Detection of seasonal cycles of erosion processes in a black marl gully from a time series of high-resolution digital elevation models (DEMs). Earth Surf. Dyn. 4, 781-798.

Beven, K.J., Kirkby, M.J., 1979. A physically based variable contributing-area model of catchment hydrology. Hydrol. Sci. Bull. 24, 43-69.

Bombino, G., Barbaro, G., Agostino, D.D., Denisi, P., Foti, G., Zimbone, S.M., 2024. Relationships between torrent check dam systems and shoreline dynamics in semi-arid Mediterranean area: a sub-regional focus in Calabria. Italy. Geomorphology 458, 109259.

Bunel, R., Lecog, N., Copard, Y., Guérin, E., Van De Wiel, M., Massei, N., 2021. Generation of realistic synthetic catchments to explore fine continental surface processes. Earth Surf. Process. Landf. 46, 593-610.

Bunel, R., Lecog, N., Copard, Y., Massei, N., 2023. Effects of climate variability changes on runoff and erosion in the Western European Loess Belt region (NW, France). Sci. Total Environ. 903, 166536.

Carriere, A., Le Bouteiller, C., Tucker, G.E., Klotz, S., Naaim, M., 2020. Impact of vegetation on erosion: Insights from the calibration and test of a landscape evolution model in alpine badland catchments. Earth Surf. Process. Landf. 45, 1085-1099.

Carrillo, G., Troch, P.A., Sivapalan, M., Wagener, T., Harman, C., Sawicz, K., 2011. Catchment classification: hydrological analysis of catchment behavior through process-based modeling along a climate gradient. Hydrol. Earth Syst. Sci. 15, 3411-3430.

Chen, L., Yu, W.B., Han, F.L., Lu, Y., Zhang, T.Q., 2020. Effects of desertification on permafrost environment in Qinghai-Tibetan Plateau. J. Environ. Manag. 262, 110302.

Collins, D.B.G., Bras, R.L., Tucker, G.E., 2004. Modelling the effects of vegetation erosion coupling on landscape evolution. J. Geophys. Res. Earth Surf. 109, 1-11.

Copard, Y., Eyrolle, F., Radakovitch, O., Poirel, A., Raimbault, P., Gairoard, S., Di-Giovanni, C., 2018. Badlands as a hot spot of petrogenic contribution to riverine particulate organic carbon to the Gulf of lion (NW Mediterranean Sea). Earth Surf. Process. Landf. 43, 2495-2509.

Cosandey, C., Andréassian, V., Martin, C., Didon-Lescot, J.F., Lavabre, J., Folton, N., Mathys, N., Richard, D., 2005. The hydrological impact of the Mediterranean forest: a review of French research. J. Hydrol. 301, 235-249.

Coulthard, T.J., Neal, J.C., Bates, P.D., Ramirez, J., de Almeida, G.A.M., Hancock, G.R., 2013. Integrating the LISFLOOD-FP 2D hydrodynamic model with the CAESAR model: implications for modelling landscape evolution. Earth Surf. Process. Landf. 38, 1897-1906.

Coulthard, T.J., Ramirez, J., Fowler, H.J., Glenis, V., 2012. Using the UKCP09 probabilistic scenarios to model the amplified impact of climate change on drainage basin sediment yield. Hydrol. Earth Syst. Sci. 16, 4401-4416.

Coulthard, T.J., Skinner, C.J., 2016. The sensitivity of landscape evolution models to spatial and temporal rainfall resolution, Earth Surf. Dynam. 4, 757-771.

Coulthard, T.J., Van De Wiel, M.J., 2017. Modelling Long Term Basin Scale Sediment Connectivity, Driven by Spatial Land Use changes. Geomorphology 277, 265-281.

Descroix, L., Mathys, N., 2003. Processes, spatio-temporal factors and measurements of current erosion in the French southern Alps: a review. Earth Surf. Process. Landf. 28, 993-1011.

D'Odorico, P., He, Y., Collins, S., De Wekker, S.F.J., Engel, V., Fuentes, J.D., 2013. Vegetation- microclimate feedbacks in woodland-grassland ecotones. Gob. Ecol. Biogeogr. 22, 364-379.

Esteves, M., Descroix, L., Mathys, N., Lapetite, J.M., 2005. Soil hydraulic properties in a marly gully catchment (Draix, France). Catena 63, 282-298.

Fagerlund, G., 2004. A Service Life Model for Internal Frost damage in Concrete. In: Division of Building Materials. LTH, Lund University.

Friedman, J.H., 1991. Multivariate Adaptive Regression Splines. Ann. Stat. 19, 1-67.

Gaillardet, J., Braud, I., Hankard, F., Anquetin, S., Bour, O., Dorfliger, N., de Dreuzy, J.R., Galle, S., Galy, C., Gogo, S., Gourcy, L., Habets, F., Laggoun, F., Longuevergne, L., le Borgne, T., Naaim-Bouvet, F., Nord, G., Simonneaux, V., Six, D., Zitouna, R., 2018. OZCAR: the French network of critical zone observatories. Vadose Zone J. 17, 180067.

García-Ruiz, J.M., Beguería, S., Nadal-Romero, E., González-Hidalgo, J.C., Lana-Renault, N., Sanjuan, Y., 2015. A meta-analysis of soil erosion rates across the world. Geomorphology 239, 160-173.

Guo, W., Liu, H., Anenkhonov, O.A., Shangguan, H., Sandanov, D.V., Korolyuk, A.Y., Hu, G., Wu, X., 2018. Vegetation can strongly regulate permafrost degradation at its southern edge through changing surface freeze-thaw processes. Agric. For. Meteorol. 252, 10-17.

Gupta, H.V., Sorooshian, S., Yapo, P.O., 1999. Status of automatic calibration for hydrologic models: Comparison with multilevel expert calibration. J. Hydrol. Eng. 4, 135-143.

Gyssels, G., Poesen, J., Nachtergale, J., Govers, G., 2002. The impact of sowing density of small grains on rill and ephemeral gully erosion in concentrated flow zones. Soil Tillage Res. 64, 189-201.

Males, T.C., Roering, J.J., 2007. Climatic controls on frost cracking and implications for the evolution of bedrock landscapes. J. Geophys. Res. 112, F02033.

Ice, G.G., Stednick, J.D., 2004. Forest Watershed Research in the United States. Forest History Today 17, 16-26.

Istanbulluoglu, E., Bras, R.L., 2005. Vegetation-modulated landscape evolution: Effects of vegetation on landscape processes, drainage density, and topography. J. Geophys. Res. Earth 110, F02012.

Julian, J.P., Gardner, R.H., 2014. Land cover effects on runoff patterns in eastern Piedmont (USA) watersheds. Hydrol. Process. 28, 1525-1538.

Klotz, S., Le Bouteiller, C., Mathys, N., Fontaine, F., Ravanat, X., Olivier, J.-E., Lièbault, F., Jantzi, H., Coulmeau, P., Richard, D., Cambon, J.-P., Meunier, M., 2023. A high-frequency, long-term data set of hydrology and sediment yield: the alpine badland catchments of Draix-Bléone Observatory. Earth Syst. Sci. Data 15, 4371-4388.

Le Bouteiller, C., Naaim-Bouvet, F., Mathys, N., Lavé, J., 2011. A new framework for modeling sediment fining during transport with fragmentation and abrasion. J. Geophys. Res. Earth 116, F03002.

Li, Z., Liu, W.Z., Zhang, X.C., Zheng, F.L., 2009. Impacts of land-use change and climate volatility on hydrology in an agricultural catchment on the Loess Plateau of China. J. Hydrol. 377, 35-42.

Lièbault, F., Gomez, B., Page, M., Marden, M., Peacock, D., Richard, D., Trotter, C.M., 2005. Land-use change, sediment production and channel response in upland regions. River Res. Appl. 21, 739-756.

Lima, M.I.L.P. de, Lima, J.L.M.P. de, Coelho, M.F.E.S., 2003. Spectral analysis of scale invariance in the temporal structure of precipitation in mainland Portugal Eng. Civil 16, 73-82.

Lofi, J., Pezard, P., Loggia, D., Garel, E., Gautier, S., Merry, C., Bondabou, K., 2012. Geological discontinuities, main flow path and chemical alteration in a marly hill prone to slope instability: assessment from petrophysical measurements and borehole image analysis. Hydrol. Process. 26, 2071-2084.

Lukey, B.T., Sheffield, J., Bathurst, J.C., Hiley, R.A., Mathys, N., 2000. Test of the SHETRAN technology for modelling the impact of reforestation on badlands runoff and sediment yield at Draix, France. J. Hydrol. 235, 44-62.

Maillet, G., Vella, C., Berne, S., Friend, P.L., Amos, C.L., Fleury, T.J., Normand, A., 2006. Morphological changes and sedimentary processes induced by the December 2003 flood event at the present mouth of the Grand Rhône River (southern France). Mar. Geol. 234, 159-177.

Mallet, F., Marc, V., Douvinet, J., Rossello, P., Joly, D., Ruy, S., 2020. Assessing soil water content variation in a small mountainous catchment over different time scales and land covers using geographical variables. J. Hydrol. 591, 125593.

Marrel, A., Jooss, B., Laurent, B., Roustant, O., 2009. Calculations of sobol indices for the gaussian process metamodel. Reliab. Eng. Syst. Saf. 94, 742-751.

Marston, R.A., 2010. Geomorphology and vegetation on hillslopes: interactions, dependencies, and feedback loops. Geomorphology 116, 206-217.

Mathys, N., 2006. Analyse et modélisation à différentes échelles des mécanismes d'érosion et de transport de matériaux solides: cas des petits bassins versants de montagne sur marne (Draix, Alpesde-Haute-Provence). PhD thesis, University of Grenoble.

Mathys, N., Brochot, S., Meunier, Richard, M.D., 2003. Erosion quantification in the small marly experimental catchments of Draix (Alpes-de-Haute-Provence, France). Calibration of the ETC rainfall runoff-erosion model. Catena 50, 527-548.

Mathys, N., Klotz, S., Esteves, M., 2005. Runoff and erosion in the Black Marls of the French Alps: observations and measurements at the plot scale. Catena 63, 261-281.
Molina, A., Govers, G., Van den Putte, A., Poesen, J., Vanacker, V., 2009. Assessing the reduction of the hydrological connectivity of gully systems through vegetation restoration: field experiments and numerical modelling. Hydrol. Earth Syst. Sci. 13, 1823–1836.

Morales, J., Poveda, G., 2009. Diurnally driven scaling properties of Amazonian rainfall fields: Fourier spectra and order-q statistical moments. J. Geophys. Res. 2009 (114), D11104.

Moriasi, D., Arnold, J., Van Liew, M., Bingner, R., Harmel, R., Veith, T., 2007. Model evaluation guidelines for systematic quantification of accuracy in watershed simulations. Transactions of the American Society of Agricultural and Biological Engineers 50, 885–900.

Moriasi, D.N., Gitau, M.W., Pai, N., Daggupati, P., 2015. Hydrologic and water quality models: performance measures and evaluation criteria. Trans. ASABE 58, 1763–1785.

Muggeo, V., 2003. Estimating regression models with unknown break-points. Stat. Med. 22, 3055–3071.

Nash, J.E., Sutcliffe, J.V., 1970. River flow forecasting through conceptual models: part 1. A discussion of principles. J. Hydrol. 10, 282–290.

Niu, F.J., Gao, Z.Y., Lin, Z.J., Luo, J., Fan, X.W., 2019. Vegetation influence on the soil hydrological regime in permafrost regions of the Qinghai-Tibet Plateau. China. Geoderma 354, 113892.

Ochoa-Tocachi, B.F., Alemie, T.C., Guzman, C.D., Tilahun, S.A., Zimale, F.A., Buytaert, W., Steenhuis, T.S., 2019. Sensitivity analysis of the parameter efficient distributed (PED) model for discharge and sediment concentration estimation in degraded humid landscapes. Land Degrad. Dev. 30, 1–15.

Phillips, C.J., Rey, F., Marden, M., Liebault, F., 2013. Revegetation of steeplands in France and New Zealand: geomorphic and policy responses. N. Z. J. For. Sci. 43, 14.

Piégay, H., Walling, D.E., Landon, N., He, Q., Liébault, F., Petiot, R., 2004. Contemporary changes in sediment yield in an alpine mountain basin due to afforestation (the upper Drôme in France). Catena 55, 183–212.

Poesen, J.W.A., Hooke, J.M., 1997. Erosion, flooding and channel management in Mediterranean environments of southern Europe. Prog. Phys. Geogr. 21, 157–199.

Prosser, I.P., Dietrich, W.E., Stevenson, J., 1995. Flow resistance and sediment transport by concentrated overland flow in a grassland valley. Geomorphology 13, 73–86.

Rainato, R., Mao, L., Garcia-Rama, A., Picco, L., Cesca, M., Vianello, A., Lenzi, M.A., 2017. Three decades of monitoring in the Rio Cordon instrumented basin: Sediment budget and temporal trend of sediment yield. Geomorphology 291, 45–56.

Rey, F., 2004. Effectiveness of vegetation barriers for marly sediment trapping. Earth Surf. Process. Landf. 29, 1161–1169.

Rey, F., Burylo, M., 2014. Can bioengineering structures made of willow cuttings trap sediment in eroded marly gullies in a Mediterranean mountainous climate? Geomorphology 204, 564–572.

Robinson, M., Whitehead, P.G., 1993. A review of experimental and representative basin studies. Methods of Hydrological Basin Comparison (ed. by M. Robinson), 1–12 (Fourth Conf. Of the European Network of Experimental and Representative Basins). Report 120, Inst. of Hydrology, Wallingford, UK.

Schoorl, J., Veldkamp, A., Bouma, J., 2002. Modeling water and soil redistribution in a dynamic landscape context. Soil Sci. Soc. Am. J. 66, 1610.

Skinner, C.J., Coulthard, T.J., Schwanghart, W., Van De Wiel, M.J., Hancock, G., 2018. Global sensitivity analysis of parameter uncertainty in landscape evolution models. Geosci. Model Dev. 11, 4873–4888.

Sobol, I., 1977. Uniformly distributed sequences with an additional uniform property. USSR Comput. Math. Math. Phys. 16, 236–242.

Temme, A.J.A.M., Vanwalleghem, T., 2016. LORICA – a new model for linking landscape and soil profile evolution: development and sensitivity analysis. Comput. Geosci. 90, 131–143.

Tucker, G., Hancock, G., 2010. Modelling Landscape Evolution. Earth Surf. Process. Landf. 35, 28–50.

Tucker, G.E., Lancaster, S.T., Gasparini, N.M., Bras, R.L., Rybarczyk, S.M., 2001. An object-oriented framework for hydrologic and geomorphic modeling using triangular irregular networks. Comput. Geosci. 27, 959–973.

Valentin, C., Poesen, J., Li, Y., 2005. Gully erosion: impacts, factors and control. Catena 63, 132–153.

Warmerdam, P. and Stricker, H., 2009. Fundamental hydrological research results drawn from studies in small catchments. Status and Perspectives of Hydrology in Small Basins, IAHS Publ., Proceedings of the Workshop, 30 March–2 April 2009, GoslarHahnenklee, Germany, 47–53.

Weedon, G.P., Prudhomme, C., Crooks, S., Ellis, R.J., Folwell, S.S., Best, M.J., 2015. Evaluating the Performance of Hydrological Models via Cross-Spectral Analysis: Case Study of the Thames Basin, United Kingdom. J. Hydrometeorol. 16, 214–231.

Welsh, K.E., Dearing, J.A., Chiverrell, R.C., Coulthard, T.J., 2009. Testing a cellular modelling approach to simulating late-Holocene sediment and water transfer from catchment to lake in the French Alps since 1826. The Holocene 19, 785–798.

Willgoose, G., Bras, R.L., Rodriguez-Iturbe, I., 1991. A coupled channel network growth and hillslope evolution model, 1, theory. Water Resour. Res. 27, 1671–1684.

Xu, G., Huang, M., Li, P., Li, Z., Wang, Y., 2021. Effects of land use on spatial and temporal distribution of soil moisture within profiles. Environ. Earth Sci. 80, 128.

Ziliani, L., Surian, N., Coulthard, T.J., Tarantola, S., 2013. Reduced-complexity modeling of braided rivers: Assessing model performance by sensitivity analysis, calibration, and validation. J. Geophys. Res. Earth 118, 2243–2262.