A crucial issue in soil C dynamics modelling is to develop models suitable for regional **scale**, but based on local and short-time **scale** observations. Recent research has illustrated the strong linkage
between SOC dynamics and landscape processes. There is increasing evidence that lateral fluxes of SOC, sediment and water will further enhance the variability of SOC dynamics, especially on agricultural land. Hence, in this study, we aim to improve our understanding of soil C dynamics by quantifying the soil respiration response of carbon pools at different positions along a slope catena, characterized by different soil moisture and temperature conditions and by different SOC stock and C pool distributions. The study was performed on a **hillslope** in the belgian loamy belt. Time series of soil moisture, temperature and surface CO2 fluxes were monitored on a regular basis (at least once a week, during spring and autumn 2011) along the hillsope, at the soil surface. At the same positions, soil cores (1 to 1.5 m depth) were collected and analyzed for SOC, C distribution (using a chemical fractionation), mineral oxides (oxalate extractions), pH, and texture. Our results show that substantial lateral transport of soil materials takes place along this **hillslope**, with a continuous burying of surface C and minerals at the bottom of the slope. This results in the development of a colluvial soil with an increasing SOC stock. This colluvial C stock mainly consists of labile C (66%), and this labile C stock in the colluvium is 3.5 higher than the labile C stock at the other slope positions. This stock is thus poorly stabilized and has a higher potential for mineralization. The other part of this C stock is stabilized by organo-mineral associations (19%) or is recalcitrant C (15%). Compared to the other slope positions, this colluvial stable C stock is significant, as it is 1.5 to 2 times higher. The spatial gradient of the measured soil respiration is consistent with the previous C pool distribution observations along the **hillslope**, since there is a significant higher respiration at the bottom of the slope (colluvial area) than at the other slope positions. The measured temporal dynamics of the soil respiration is explained by moisture and temperature variations. This measured space-time

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topographic, geomorphologic, and soil characteristics that exert an important control on the dynamics of subsur- face water storage and groundwater flow and on the timing and magnitude of surface runoff generation [e.g., Loague, 1988; Woods and Sivapalan, 1999; Grayson and Blo¨schl, 2000]. Many existing **hillslope** drainage models based on Dupuit-Forchheimer, Boussinesq, or kinematic wave theory provide useful and efficient solutions for idealized config- urations (one-dimensional flow, unit-width **hillslope**, homo- geneous soil, saturated conditions under a free surface boundary, simple endpoint boundary conditions, etc), but clearly these models cannot be considered realistic beyond their restricted base of assumptions. Simplicity is desirable because even at the **hillslope** **scale** practical application of, for example, a three-dimensional numerical Richards equa- tion (RE) model is not always feasible. The difficulties here are both structural and computational: parameter identifi- ability problems that engender a mismatch between model complexity and the amount and accuracy of data which is normally available to parameterize, initialize, and calibrate such a model; and the fine spatiotemporal grids (and consequent high computer memory and CPU costs) needed to avoid numerical convergence problems and to accurately capture the dynamics of subsurface water drainage, infiltra- tion, and redistribution during storm and interstorm periods. [ 3 ] An equally urgent need is for a basis or framework

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Correspondence: Mariano Moreno-de-las-Heras (mariano.moreno@idaea.csic.es) Received: 24 October 2019 – Discussion started: 2 January 2020
Revised: 12 April 2020 – Accepted: 24 April 2020 – Published: 29 May 2020
Abstract. Connectivity has emerged as a useful concept for exploring the movement of water and sediments between landscape locations and across spatial scales. In this study, we examine the structural and functional controls of surface- patch to **hillslope** runoff and sediment connectivity in three Mediterranean dry reclaimed mining slope systems that have different long-term development levels of vegetation and rill networks. Structural connectivity was assessed using flow path analysis of coupled vegetation distribution and surface topography, providing field indicators of the extent to which surface patches that facilitate runoff and sediment produc- tion are physically linked to one another in the studied hill- slopes. Functional connectivity was calculated using the ra- tio of patch-**scale** to **hillslope**-**scale** observations of runoff and sediment yield for 21 monitored hydrologically active rainfall events. The impact of the dynamic interactions be- tween rainfall conditions and structural connectivity on func- tional connectivity were further analysed using general lin- ear models with a backward model structure selection ap- proach. Functional runoff connectivity during precipitation events was found to be dynamically controlled by antecedent

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[ 2 ] Hillslopes are the basic landscape elements of many
catchments. Understanding the interaction and feedbacks between **hillslope** forms and the processes responsible for transportation of water, sediments, and pollutants is of crucial importance for catchment **scale** water and land management. Since the 1950s many **hillslope** hydrological studies have been conducted. Of particular interest are two landmark books edited by Kirkby [1978] and Anderson and Brooks [1996]. The mathematical models of **hillslope** flow processes presented in these works are either complex numerical integrations of the 3-D subsurface flow equa- tions, or simplified hydraulic groundwater equations based on the Dupuit-Forchheimer assumptions applied to unit- width hillslopes. Neither of these references presents models to account for the three-dimensional **hillslope** form while still using simple flow equations. The geometry of the **hillslope** exerts a major control on hydrologic response because it defines the domain and the boundary conditions of moisture storage. Models that most fully describe three- dimensional flow processes, based on the 3-D Richards equation, are highly nonlinear and require the solution of large systems of equations even for small-**scale** problems. Moreover, the parameterization of these models requires detailed information about soil hydraulic properties, infor- mation which is generally not at hand at the catchment **scale**. In order to improve our understanding of the response of hillslopes to atmospheric forcing (precipita- tion, evapotranspiration), simplified dynamic descriptions of the hydrologic system are needed. The central question of this problem was formulated by Duffy [1996]: ‘‘Can low dimensional dynamic models of **hillslope**-**scale** and catchment-**scale** flow processes be formulated such that the essential physical behavior of the natural system is preserved?’’

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While many hydrologic model assessment studies have reported good agreement between simulated and observed data when performance is measured against a single re- sponse variable, there are comparatively few studies that have made use of observation data from multiple response variables. Brunner et al. (2012), for instance, examined the performance of a one-dimensional (1-D) unsaturated zone flow model when water table measurements were supple- mented by evapotranspiration and soil moisture observations. Sprenger et al. (2015) assessed the performance of three in- verse modeling strategies based on the use of soil moisture and porewater isotope concentration data for a 1-D unsatu- rated flow and transport model. Kampf and Burges (2007) obtained encouraging results for a 2-D Richards equation flow model using integrated (subsurface outflow) and in- ternal (piezometric water level and volumetric water con- tent) measurements from a **hillslope**-**scale** experiment. Ku- mar et al. (2013) used multiple discharge measurements to calibrate and apply a distributed hydrologic model to 45 sub- catchments of a river basin in Germany. Investigations based on hypothetical experiments are more common. Mishra and Parker (1989), for example, obtained smaller errors for si- multaneous estimation of flow and transport parameters than for sequential estimation based on synthetically generated observations of water content, pressure head, and concentra- tion.

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and subsurface fluxes and exchanges at the catchment **scale** (e.g., CATchment HYdrology (CATHY) [ 6 ], HydroGeoSphere [ 7 , 8 ], and ParFlow [ 9 ]. Few models as yet allow simulation of detailed reactive transfer processes in a 3D coupled (surface/subsurface) context.
Pesticide transfer modeling at the **hillslope** **scale** raises several challenges. Solute flux coupling between the surface and subsurface can be managed with various methods, amongst them, the conceptual exchange layer [ 10 ] and the diffusion coefficient [ 11 – 13 ] are largely used. They both require a calibration to give efficient results [ 10 , 14 ]. Parameter setting is also a critical issue. At the **hillslope** **scale**, the representation of heterogeneity [ 15 , 16 ] or pore connectivity [ 17 ] can have non negligible effects on the output results. These variables often have nonlinear effects with strong interactions, sometimes resulting in unexpected outputs [ 18 ]. Whatever numerical coupling and parametrization strategies are adopted, model evaluation is crucial to assess the relevance of the results.

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- Simulations are consistant with observed data at the **hillslope** **scale**
- The CATHY model allows a better understanding of pesticide fate in 3D at the **hillslope** **scale**, in particular in complex surface / subsurface interaction cases - The model parametrisation is complex, and a sensitivity analysis is necessary to prioritize influential parameters.

The field is ideal to study complex processes and thus represents a major challenge for CATHY with reactive transfers. Additionally, some existing processes are not explicitly represented (macroporosity, diffusion and dispersion) and we will verify CATHY's ability to globally report major processes at the **hillslope** **scale**. The aim is not to reproduce exact observations, but more to analyse model's results on chosen synthetic cases.

Abstract Integrated surface-subsurface hydrological models (ISSHMs) are well established numerical tools to investigate water flow and contaminant transport processes over a wide range of spatial and temporal scales. However, their ability to correctly reproduce the response of hydrological systems to natural and anthropogenic forcing depends largely on the accuracy of model parameterization, including the level of detail in the representation of the bedrock. This latter is typically incorporated in some way via the bottom boundary of the model domain. Issues of bedrock topography, variable soil depth, and the resulting **hillslope** storage distribution representation in ISSHMs are vitally important but to date have received little attention. A standard treatment of the bottom boundary, especially in large catchment and continental **scale** applications, is to model it as a flat or inclined (e.g., parallel to the surface) impermeable base (sometimes with some simple leakage term). This approach does not allow the model to correctly reproduce bedrock-controlled threshold responses such as the fill and spill process, as observed across many **hillslope** and catchment **scale** field studies. It is still unclear whether Richards equation-based numerical models are actually able to generate such responses. Here we use a Richards equation-based model (CATHY) to simulate internal transient subsurface stormflow dynamics observed at the well-characterized Panola experimental **hillslope** in Georgia (USA). Soil and bedrock properties were calibrated starting from values reported in previous studies at the site. Our simulation results show that the model was able to reproduce threshold mechanisms, which in turn affected both the integrated and distributed hydrologic responses of the Panola **hillslope**. We then developed a set of virtual experiments with modified boundary conditions and base topography at the soil-bedrock interface to explore the bedrock boundary control on transient groundwater flow patterns. Our results show that accurate representation of the lower boundary is crucial for ISSHM simulations of **hillslope**-**scale** storm runoff and for connectivity of transient groundwater. We summarize our findings with the development of a new bedrock topographic wetness index that takes into account the unsaturated infiltration dynamics. The index is able to help represent the spatial variability of water table response over the bedrock surface compared to standard surface topography-based indices. This new index may be useful in larger-**scale** ISSHM applications where an exact bedrock topography representation is not feasible or possible.

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decades there have been many attempts to model **hillslope** and catchment hydrological processes. Most of these attempts have been aimed at predicting outflow rates, but recently several model studies have also investigated the water table dynamics (or saturated storage dynamics) that are of crucial importance in determining the location and size of variable source areas, and thereby also to assess the risk for flood peaks in the channel network draining a **hillslope** or catchment. Examples include work by Wigmosta et al. [1994] and Ivanov et al. [2004], who present high- dimensional catchment-**scale** models, and Seibert and McDonnell [2002], Weiler and McDonnell [2004], and Brooks et al. [2007] who present the results of a conceptual modeling study applied to the **hillslope** **scale**. Even though these models have been applied successfully in the studies presented, they are all partly or fully conceptual instead of physically based, which makes the investigation of the exact interactions between the saturated and unsaturated zones cumbersome. In this work we have presented a physically based low-dimensional **hillslope** model. In the test cases we assumed that the conductivity, soil depth and other soil properties are constant in depth and in the direction along the **hillslope**, but the saturated module of the coupled model and the original HSB model are capable of handling spatial variability along these axes. On the other hand, since all variables and properties are assumed to be constant over the width of the **hillslope**, we cannot account for spatial variability along this axis. In the current version of the coupled formulation we also cannot account for spatial variability in rainfall rate or soil hydraulic properties of the unsaturated zone, because a single soil moisture profile

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− +
+ .
In this section, biodegradation kinetics and transport parameters have been set. Reactive terms come also from an averaging process, because we measure the reactivity in a porous medium composed of several REV. Those represent a macroscale behaviour which have been coupled with the macro **scale** model presented. Determining the parameters missing by measurements, we are now able to use this numerical tool and try to check if it matches with experimental data.

almost isotropic, as U rms varies with F r. The forcing **scale**
is defined as L = π/k f . All the simulations are performed at
Schmidt number Sc = ν/κ = 1.
this expression represents the rate of contraction of the phase space (here the configuration space) under the dy- namics. When it is negative we expect that trajectories of floaters will collapse on a (dynamical) fractal attrac- tor in the phase space. An example of the attractor is displayed in Fig. which shows that the large **scale** con- finement in the vertical direction coexists with a small **scale** clustering with fractal distribution on the isopycnal surface.

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Stumpf, Wiuf & May ( 2005 ) : sub-network of **scale**-free larger networks are not strictly **scale**-free, but extended **scale**-free.
1 From Strict **Scale**-Free to **Scale**-Free Types
**scale**-free network is a network whose degree distribution follows a power law, at least asymptotically. When studying internet networks, Barabási & Albert ( 1999 ) observed that some nodes, that they called hubs, had much more connections than others, and that the distribution of the number of links connecting to a node was a power-law. They coined the term **scale**-free network to describe that class of networks, when degrees have a power-law distribution. Clauset, Cosma & Newman ( 2007 ) studied real networks, and found some exhibiting that property. Nevertheless, recently, Broido & Clauset ( 2019 ) claimed that (strict) **scale**-free network are actually rare. More specifically, inspired by Alderson et al. ( 2009 ), they define various notions of weak or strong **scale**-free networks. If their taxonomy of **scale**-free network, in interesting we will consider here only the concept of strict **scale**-free if the degree distribution above a given cutoff k min is a power law (as in Barabási & Albert ( 1999 )).

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Fig. 2. Example of peaks detections on a sinusoid signal contaminated with strong additive white Gaussian noise. ρ = 0.1.
peaks in a global fashion, because it promotes the detection of peaks that are present in the data at multiple scales. Furthermore, it provides an ordering of the importance of the picks through the computation of a pick presence criterion. The resulting **Scale**-Space Peak Picking algorithm (SSPP) is easily implemented and features only one free parameter for the user to tune, which is either the number of desired peaks or a threshold related to the desired peak density.

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Unite´ de recherche INRIA Lorraine, Technopoˆle de Nancy-Brabois, Campus scientifique, 615 rue du Jardin Botanique, BP 101, 54600 VILLERS LE` S NANCY Unite´ de recherche INRIA Rennes, Ir[r]

of the variable ζ = z − θ computed along particle trajectories. The dynamics of ζ is given by the time evolution of the field θ along the trajectory of a floater and gives (neglecting the diffusive term) d(z − θ)/dt = −(z − θ)(1 − ∂θ/∂z)/τ . In the absence of fluctuations (θ = 0) this equation would simply represent the linear relaxation of particles towards the isopycnal layer z = 0 [22]. This is not achieved since the term ∂θ/∂z is fluctuating without a definite sign. Figure 4 shows the normalized PDF of the variable ζ for three different values of τ at F r = 1.0. It is evident that the statistics is neither Gaussian nor **scale** invariant and the PDF develops large tails for small relaxation times [31]. These large fluctuations are due to the folding of the isopycnal surface. In correspondence of a fold the stratification is inverted, (1 − ∂θ/∂z) changes sign and (z − θ) grows exponentially (assuming that the field θ is quenched) until the particle reaches the nearest branch, above or below, of the isopycnal. This mechanism, which is enhanced at large F r, produces large fluctuations of the distance between the particles and the isopycnal surface, and causes the development of large tails in the PDF of ζ.

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Nevertheless, this choice model, as all ranking-based choice models (Farias et al., 2013), is based on products with historical sales data and therefore cannot intrinsically learn how to[r]

This includes: the cone calorimeter [I], which can be used to determine the ignitability, heat release rate, mass loss rate, effective heat of combustion and visible smoke development[r]

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Heat Flux Sensor
The total heat exposure to the test specimen was measured by two Gardon Gauge heat flux sensors (see Figure 5), 2.5 mm diameter and 2.5 mm long copper cylinder, with an accuracy of 6 3%. These sensors were water cooled and mounted flush with the specimen surface at the locations shown in Figure 3 (full-**scale**) and Figure 4 (intermediate-**scale**). The source of water flow was maintained at 40 ° C during the entire test as specified by the manufacturer of the sensors.

Aurore Degré 1
1 Soil Water Plant Exchanges, BIOSE, Gembloux Agro-Bio Tech, University of Liège, Gembloux, Belgium, 2 Chemical Engineering, University of Liège, Liège, Belgium
For decades, the development of new visualization techniques has brought incredible insights into our understanding of how soil structure affects soil function. X-ray microtomography is a technique often used by soil scientists but challenges remain with the implementation of the procedure, including how well the samples represent the uniqueness of the pore network and structure and the systemic compromise between sample size and resolution. We, therefore, chose to study soil samples from two perspectives: a macroscopic **scale** with hydrodynamic characterization and a microscopic **scale** with structural characterization through the use of X-ray microtomography (X-ray µCT) at a voxel size of 21.5 3 µm 3 (resampled at 43 3 µm 3 ). The

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