D Trévisan

P Taillandier

B Sarrazin

D Etienne

N Ayari

C Petiqueux

P Quétin

C Janin

OPALE: OPerational Assessment of Landscape water Eco-functionalities

Keywords: farming systems, decision rules, agricultural landscapes, crop management, hydrological processes, agroecology

Highlights

-We develop OPALE, a suite of programs for the representation and analysis of landscapes in arable crops and grasslands conditions ; -OPALE allows for efficient evaluation of water and matter outflows (nutrient, suspended matter and fecal bacteria) and leads to usable computed indicators for the assessment of landscape functioning and water-related eco-functionality in various geographical situations.

Introduction

Agroecology is aimed at developing several approaches to solve current agricultural production challenges [START_REF] Wezel | Agroecology as a science, a movement and a practice[END_REF][START_REF] Hatt | Spatial diversification of agroecosystems to enhance biological control and other regulating services: an agroecological perspective[END_REF]. It develops field-and territory-level innovations to increase interactions among plant, animal and microorganism communities. As mentioned by [START_REF] Gascuel-Odoux | Gérer les paysages et les territoires pour la transition agroécologique[END_REF], a major challenge is not only to promote designs of production systems and crop management methods on an ecological basis, but also to consider innovations at the territorial level. A main challenge is to find ways of defining new farmland organizations to enhance ecological landscape functionalities while considering economic activities, bio-geochemical cycles and biological processes [START_REF] Poggi | How can models foster the transition towards future agricultural landscapes[END_REF]. Stakeholders are increasingly concerned by soil management and natural resource protection, as well as by the closure of the water and nutrient cycles, the control of contaminants, etc., as all of them are highly dependent on land use and land cover at the catchment scale.

Agricultural landscapes can be considered as macro-ecosystems resulting from interactions between the human society and biophysical processes. Landscapes constitute 'the mirror of past and present relationships between human beings and their surrounding nature [START_REF] Vanier | The manufacturing process of territories in the Rhône-Alpes region actors, myths and practices[END_REF]. We considered landscapes as spatial arrangements of features (agricultural fields, urban / forested / semi natural elements like hedges, grass strips, ditches) and flows operating at different time and spatial scales. Some of them are controlled by human activities (flows of energy, fertilizers, farm effluents, flows caused by herd displacements, etc.), others are inherent in the functioning of the eco-biophysical context. Considering the importance of water issues in the context of global change, the ambitions of the agroecological transition [START_REF] Gascuel-Odoux | Gérer les paysages et les territoires pour la transition agroécologique[END_REF], and landscapes-water quality relationships [START_REF] Chaplin-Kramer | Landscape configuration is the primary driver of impacts on water quality associated with agricultural expansion[END_REF], the present article is focused on landscape eco-functionalities related to water flows (water displacement within landscapes and associated movements of solutes and living or inert suspended matter).

The operational assessment of landscape eco-functionalities is aimed at evaluating the links between landscape composition (land uses), structure (spatial arrangement of different land uses), and water flows and nutrient/pollutant flows associated with water movements. It requires the implementation of interdisciplinary approaches. Modeling can offer an adapted framework to analyze and interpret the complexity of landscape macro-ecosystems [START_REF] Poggi | How can models foster the transition towards future agricultural landscapes[END_REF], especially when considering numerous links between decisions, climate, soils and organisms within the critical zone. Landscapes have been the object of several modeling developments, focusing on the design of agricultural territories -see for example MAELIA [START_REF] Rizzo | A rapid, spatially explicit approach to describe cropping systems dynamics at the regional scale[END_REF]-or the interpretation of landscape organizations in terms of water budget and flows -MYDHAS [START_REF] Moussa | Effects of the spatial organization of agricultural management on the hydrological behaviour of a farmed catchment during flood events[END_REF]-. To the best of our knowledge, links between these two approaches are sparse. As mentioned by [START_REF] Langhammer | Agricultural landscape generators for simulation models: a review of existing solutions and an outline of future directions[END_REF] and [START_REF] Zellner | Exploring reciprocal interactions between groundwater and land cover decisions in flat agricultural areas and variable climate[END_REF], developing generic modeling of the links between human decisions, water needs and water ecosystem functions is central to achieve evaluations of landscapes and elaborate territory prospects in a context of global change.

The present article describes OPALE, a tool developed to address the issue of the agroecological transition at the landscape level. The model considers a large set of agricultural production systems and hydrological conditions. It is focused on (i) landscape design resulting from farming system parameters and decisions; (ii) surface hydrology and biophysical processes.

More precisely, the tool includes a set of libraries about the following items:

• the design of the landscape occupied by farmland, providing the distribution of crops across farmed fields based on from farming practices and schedules (land use and land cover change model (LULCC));

• the modeling of water movements within previous simulated landscapes, considering surface, hypodermical and deep trajectories (water movements within landscapes model (WMWL));

• the evaluation of -inert and living-solute and suspended matter transfers associated with water displacements, including N, P, Escherischia Coli (EC) and suspended matter (solute and suspended matter transfer (SSMT));

• the construction of normalized indicators of landscape functions in order to assess their regulation services.

A theoretical frame will be first presented to introduce our working hypotheses and our methods. Then, OPALE software architecture will be presented with three different application cases differing in terms of agricultural and hydrological context. They were implemented to assess several issues related to soil conservation, nutrient cycling and surface water eutrophication or the degradation of the bacteriological quality of water resources.

Method and Theory

Land use and land cover change (LULCC)

The unutilised agricultural area (NUAA) of landscapes (non productive infrastructures, urban areas, forests) is documented by geographical databases (Corine Land Cover, shapes of forested areas)

Simulating LULCC in utilised agricultural areas a is somewhat complex because of the diversity of farming systems and associated practices [START_REF] Thenail | The contribution of crop-rotation organization in farms to crop-mosaic patterning at local landscape scales[END_REF]Benoit et al., 2012).

Several models working at the plot level (a plot corresponds here to an agricultural parcel: a continuous area of land declared by a farmer, on which a single group of crops is cultivated) concern the organization of annual crop rotations [START_REF] Dury | Models to support cropping plan and crop rotation decisions. A review[END_REF], but those that enable dealing with livestock or both livestock and crop farms are scarce. One of the difficulties lies in their ability to manage the distribution of technical rules among plots, and their respective contribution to the overall fodder balance for livestock and to commercial benefits for annual crop production.

For annual crops, landscapes change every year in relation with crop successions and rotation rules. [START_REF] Taillandier | A new BDI agent architecture based on the belief theory[END_REF] formulated the choice of crop rotation as a multi-criteria decision problem: for each plot, the farmer chooses a crop rotation, following evaluations at the farm level based on several criteria (financial risk, expected income, workload, farmer's habits).

Other works only focus on the crop allocation problem. For example, [START_REF] Martel | Impact of farming systems on agricultural landscapes and biodiversity: from plot to farm and landscape scales[END_REF] formalized it as a constraint satisfaction problem integrating agronomic and crop distribution constraints. Another work using optimization proposes to solve the crop allocation problem by computing the maximum flow of a transition graph of all possible multi-year crop successions (itineraries) permitted by rotation rules [START_REF] Houet | Improving the simulation of fine-resolution landscape changes by coupling top-down and bottom-up land use and cover changes rules[END_REF]. Then, an optimization process is applied to select the itineraries allowing for the objectives of annual cropping plans (expected surfaces of crop production) to be achieved at the farm level.

For livestock and mixed crop-livestock farms, constraints are determined by livestock feed demands. Landscapes are quite stable from one year to the next, as they are not subject to rotation and succession rules. However, the distribution of biomasses varies intra-annually in relation to the grazing and hay-cutting schedule. Landscapes show spatial structures with blocks (assemblages of several plots) of specific uses. We considered three blocks (fig. 1): block 1 grouped priority plots for pastures of productive animals (practices P1, HP1, cf. supplementary material S1), permanent or temporary meadows for hay production and late pasture (H3CP1 and H2CP1 and HP2), as well as distant pastures for non-productive animals (P2). The area of these blocks depends on the farming system (for example the first block had to provide around 50% of unit forage needs/ha in a milk-round bale system, versus 90% for traditionnal systems, cf. supplementary material S1). Several constraints determine the extension and location of these blocks, such as plant growth rates and palatability, distance between livestock sheds and fields, accessibility, slope and soil conditions [START_REF] Marie | Le rôle de la distance dans l'organisation des pratiques et des paysages agricoles : l'exemple du fonctionnement des exploitations laitières dans l'arc atlantique[END_REF]. For example, in case of dairy production, a permanent meadow, according to its slope, its agronomic potential and its distance from the milking parlor, may not be equally assigned to the grazing of dairy cows, hay crops or the grazing of young cattle. Giving that livestock headcount cannot be easily changed in livestock systems, landscape construction was modeled with reference to cascade rules and supplydemand constraints, where pasture for productive animal are the priority, followed by crops and hay crops productions and finally pasture for heifers or lots of non productive animals for the remaining surfaces [START_REF] Josselin | Proposition d'une lecture territoriale des flux agricoles[END_REF]. As the drivers of the distribution of activities of a crop farm and a livestock farm differ greatly, we did not use the same approach to represent the landscape design.

For crops farms (including vegetable production), we chose an algorithm similar to the one proposed by [START_REF] Houet | Improving the simulation of fine-resolution landscape changes by coupling top-down and bottom-up land use and cover changes rules[END_REF] where the spatial distribution of crops depends on an optimization process based on maximal flow computations. In this representation, activities are constraint by cropping plans and rules related to permitted of forbidden crop rotations (Figure 1), with the following hypothesis: (i) in the case of vegetable production with crops requiring regular/daily intervention (seeding/planting, harvesting/packaging), priority blocks nearby working sheds must be first allocated before implementing maximum flow computations; (ii) crop system landscapes do not change according to seasonal climate changes as farmers can adjust irrigation schedules or change the final commercialization of the harvested products depending on the way meteorological conditions evolve; (iii) all the plots concerned by the maximum flow computation are considered to be unconstrained by edaphic (humidity, stoniness, etc.), topographical (slope) or cadastral conditions. In the event that one or several plots cannot be used for annual crops, their dominant use must be indicated in the geographical database describing the NUAA. Arrows between Set1-Set2 and Set2-Set3 represent graph edges with a capacity equal to field surfaces; between set3-Set4, edges with a capacity equal to the total surface of a given farm. An optimization process selected an itinerary between Set1 and Set4 across a total area similar to the farm's cropping objectives.

The maximum flow was computed using the classic Edmonds-Karp max flow algorithm [START_REF] Edmonds | Theoretical improvements in algorithmic efficiency for network flow problems[END_REF]. As this algorithm is stochastic, different solutions of spatial crop allocation can be obtained between two executions depending on random choices for the construction of graph-edges. Unlike [START_REF] Taillandier | A new BDI agent architecture based on the belief theory[END_REF], labor tasks were not explicitly evaluated, but plowing, sowing and hoeing dates were stochastically distributed in the computed crop successions to generate "noise" in calendars.

For livestock farms (Figure 2), we implemented stepwise computations controlling the adequacy between plot supply and the priorities for pasture and forage demands, as proposed by [START_REF] Marie | Le rôle de la distance dans l'organisation des pratiques et des paysages agricoles : l'exemple du fonctionnement des exploitations laitières dans l'arc atlantique[END_REF]. Considering farming systems and livestock heads, we determined the forage needs and allocated them to farmlands, following priorities and surface ratios of forage practices (intensive or extensive meadows and pastures), cf. supplementary material S1. We considered that the extent of spatial blocks could change under unfavorable climatic situations because livestock feeding is priority over the constitution of forage stocks. Landscapes and the dynamics of grass biomass were therefore modified following seasonal climatic evolution in accordance with priority rules for livestock needs. P1-first-priority pastures for productive animals; pM-permanent meadows; tM-temporary meadows; P2-second-priority meadows for non productive animals. Three blocks of fields composed the farm landscape, in relation with distance to livestock sheds and environmental constraints (slope and soil moisture). A step computation scheme selected the available fields for the crop requirements of the farm systems and several climatic conditions. Pasture requirements for productive animals were computed iteratively by adding P1 surfaces and late pastures following hay cuts.

The time step for the simulations of livestock or crop systems is one day, and the time span of the simulation is fixed by the user (one year is the minimum required to buid a landscape over the seasons, much longer in crop sytems to evaluate landscape evolution according to successions).

Water movements within landscapes (WMWL)

Modeling water movements requires implementing distributed approaches in which a computational domain is defined by the watershed boundaries (a watershed is a land area that channels rainfall and snowmelt to rivers and to an outflow point), generally represented by square grid meshes where each individual cell (defined as a sqare area of a dimension fixed by the pixel dimension of the digital elevation model) is the object of water balance. Computations may use simultaneous or sequential approaches.

In the simultaneous approach, implicit digital schemes can be performed to solve partial differential matrix equations, considering all flows and local processes of the computational domain, as in MODFLOW [START_REF] Harbaugh | Modflow, the U.S. Geological survey modular ground-water model. The groundwater flow process[END_REF]. Such an implementation is no straightforward task.

As an example, boundary conditions must be defined for domains where the deepest geological structures and their links with the hydrological network are generally unknown or poorly known. Also, the stability of the solution of the matrix equations is unsure because it depends on the configuration of the digital schemes.

To overcome these difficulties, the sequential approach considers cell balance solved explicitly by cascade schemes, from up-slopes to the watershed outlet, [START_REF] Kiesel | Application of a hydrological-hydraulic modelling cascade in lowlands for investigating water and sediment fluxes in catchment, channel and reach[END_REF]. In addition, all the processes that control soil moisture (e.g., evapotranspiration, percolation) are evaluated successively, in the same way as in the distributed SMDR model [START_REF] Gérard-Marchant | Distributed hydrological modelling of total dissolved phosphorus transport in an agri-cultural landscape, part I: distributed runoff generation[END_REF], or in the semi distributed SWAT model (Arnold and Fohrer, 2005). We chose this approach although it does not represent hydrodynamic processes simultaneously. First, errors are restrained when time-step computations are shortened (Trevisan and Periáňez, 2016); second, there are several operational gains: (i) the deepest domain can be represented by black-box representations, (ii) equations are formal, giving an eprouved ability to provide evaluations of time-varying land management practices [START_REF] Me | Modelling hydrology and water quality in a mixed land use catchment and eutrophic lake : effect of nutrient load reductions and climate change[END_REF] ; (iii) no solver configuration is required. (1) [START_REF] Gérard-Marchant | Distributed hydrological modelling of total dissolved phosphorus transport in an agri-cultural landscape, part I: distributed runoff generation[END_REF]; (2) [START_REF] Obled | TOPMODEL : principes de fonctionnement et application[END_REF]; (3) [START_REF] Cerdan | Modelling interrill erosion in small cultivated catchments[END_REF]; (4) Arnold and Fohrer(2005) ; ( 5) [START_REF] Lellay | Modélisation hydrologique dans un contexte de variabilité hydro-climatique[END_REF]; ( 6) [START_REF] Gurnell | The dynamics of a drainage network[END_REF]; ( 7) [START_REF] Tarboton | A new method for the determination of flow directions and contributing areas in grid digital elevation models[END_REF]. Refer to the text for comments.

Two soil volumes were considered in the WMWL model: (i) the vadose zone in the topsoil, delimited by root depth, overlying (ii) the saturated zone (figure 3). The general water balance for extended hydrodynamic situations was: 3.

= -+ + + + -, (1)
We accounted for a large diversity of hydrodynamic processes to extend the applicability of the WMWL model to generic situations.

• Biomass dynamics, root depth and evapotranspiration flows were computed for vegetables, crops and pastures by the generalized plant growth model [START_REF] Gérard-Marchant | Distributed hydrological modelling of total dissolved phosphorus transport in an agri-cultural landscape, part I: distributed runoff generation[END_REF], detailed in Appendix A, §7.1. The model is based on a computation of cumulative degreedays. Several thresholds were considered, accounting for plant growth rates, practices and farming schedules (seeding, cuts, etc.), all of them tabulated from the LULCC model outputs;

• We introduced first-order kinetics to describe water table behavior (Arnold and Fohrer, 2005 ;[START_REF] Lellay | Modélisation hydrologique dans un contexte de variabilité hydro-climatique[END_REF]. The seepage of the water table into the river network was evaluated from a transfer function applied during a restitution period [START_REF] Hingray | Hydrologie, 2. Une science pour l'ingénieur[END_REF]. In this representation, one of the major issues [START_REF] Sarrazin | MNT et observations multi-locales du réseau de drainage d'un petit bassin versant rural dans une perspective d'aide à la modélisation spatialisée[END_REF] is the capacity of the model to reproduce the hydrologically active areas of watersheds (zones where groundwater tables can effectively seep into the river network). Following [START_REF] Gurnell | The dynamics of a drainage network[END_REF], we considered that the representation of a river network dynamics accounted for temporary drying out of the river network, and calculated the number of river segments where seepage was effective;

• Hypodermic water movement along slopes where topsoils are bounded by restricting layers or low-permeability layers can favor the rising of sub-surface water tables over the soil surface in thalweg and down-slope conditions [START_REF] Obled | TOPMODEL : principes de fonctionnement et application[END_REF][START_REF] Gérard-Marchant | Distributed hydrological modelling of total dissolved phosphorus transport in an agri-cultural landscape, part I: distributed runoff generation[END_REF]. For this reason, the Variable Source Area hydrology concept [START_REF] Dunne | Recognition and prediction of runoff-producing zones in humid regions[END_REF] was integrated in the WMWL computing scheme;

• Soil surface crusting is a main determinant of hortonian runoff. Process-based models -e.g., see [START_REF] Jetten | Sensitivity of the model LISEM to variables related to agriculture[END_REF] -were developed to estimate hortonian runoff flows from hydrodynamic properties of soil surface crusts. Their applicability to agricultural contexts where the crusting dynamics is driven by farming practices and plant biomass development is challenging [START_REF] Takken | Spatial evaluation of a physically based distributed erosion model (LISEM)[END_REF]. To avoid over-parameterization, we implemented expert-based rules from the STREAM model [START_REF] Cerdan | Modelling interrill erosion in small cultivated catchments[END_REF] to focus on the dominant drivers of crusting;

• Following [START_REF] Kiesel | Application of a hydrological-hydraulic modelling cascade in lowlands for investigating water and sediment fluxes in catchment, channel and reach[END_REF], we implemented a cascading computational scheme to evaluate water flows along slopes, in which water balance was calculated for successive cells sorted by decreasing elevation and increasing index of topographic accumulation [START_REF] Schwanghart | TopoToolbox: a set of Matlab functions tor topographical analysis[END_REF].

WMWL equations are fully described in Appendix A.

Solute and suspended matter transfers (SSMTs).

The SSMT model calculates transfer functions to provide standardized evaluations of landscape functioning and help end-users in the comparison of landscape configurations and structures. Transfer functions correspond to a density of mass-transfer rate of compounds originating from transient stores, often described by exponential or power-law distributions [START_REF] Haggerty | Power-law residence time distribution in the hyporheic zone of a 2nd-order mountain stream[END_REF]. We calculated surface and subsurface transfer functions (SSTFs) for surface and subsurface flows by applying particle-tracking methods, considered as a key technology for assessing the diversity of displaced matters [START_REF] Chenouard | Objective comparison of particle tracking methods[END_REF]. Here, particles represent a solute mass of nutrients in solution, SM or EC numbers.

To assess landscape functioning during critical periods and save computational time, SSTF calculations were restricted to ''transfer periods'' ( -, . . . , ), where is the transfer duration (days), following a daily meteorological event of interest (DMEI) starting at date -.

DMEIs are events representative of typical soil moisture conditions and biomass development, e.g., low-water periods or fall high-flow recovery. During the transfer period, the SSMT module counts the number of particles that reach the watershed outlet as a function of water trajectories computed by the WMWL model and sink-source determinism. Water trajectories and particle displacements can be interrupted on cells where the soil moisture balance does not exceed saturation thresholds. During the transfer period, we restricted water exchanges with the atmosphere to evapotranspiration flows (rainfall was set to 0) to only account for particle displacements resulting from the landscape draining and water redistribution dynamics produced by DMEIs.

Particle tracking was based on previous schemes accounting for pollutant build-up, wash-off and transport processes [START_REF] Jiang | A Physical-Based Particle-Tracking Scheme for Non-Point Source Particulate Pollutants Wash-off and Transport Processes in Urban Impervious Surfaces[END_REF]. During the transfer period, for each days of the interval (0, … , ), we considered the $ % ( -) build-up stocks located on the & cells of the computational domain, each of them affected by wash-off rates ' % ( -) transferred to the outlet with associated ( % ( ) transfer probabilities. Based on [START_REF] Trévisan | Coupling indicators and lumpedparameter modeling to assess suspended matter and soluble phosphorus losses[END_REF], the amount of particles produced by a DMEI was given by:

∑ * + , -( ) = ∑ * + , ∑ % . $ % ( -)' % ( -)( % ( ). (2)
For surface and subsurface flows, transfer delays are generally short, in the range of several days or one/two weeks [START_REF] Dorioz | Dynamique du phosphore dans les bassins versants: importance des phénomènes de rétention dans les sédiments[END_REF]. Consequently, the following build-up stocks $ % ( -, . . . , ) and wash-off 3D matrices ' % ( -, . . . , ) were computed for = 15 days.

Two indicators of underlying processes driving exchanges and sink-source effects operating at the landscape scale were evaluated by SSMT outputs. First, the DMEI-SSTF distribution obtained by particle counting at the catchment outlet:

/(1), . . . , /( ) = 1(*) ∑ 2 + 3 1(*)
.

(3)

Second, 4( -), the landscape delivery ratio associated to the DMEI started at ( -) :

4( -) = ∑ 2 + 3 1(*) ∑ 5
6 5 ( 7* + )8 5 ( 7* + ) , (4) varying from 0 for systems in which no matter flows out of the landscape to 1 in opposite conditions. SSTF and 4( -) provided by particle counting were catchment-scaled and DMEIs single-event-dependent representations of landscape functioning. The SSMT equations of particle behavior driving $ % ( -), ' % ( -) and -( ) values are given in Appendix B.

Deeper transfer delays were greater than previously, in the range of several months [START_REF] Hingray | Hydrologie, 2. Une science pour l'ingénieur[END_REF]. As the groundwater table was represented by a black-box analysis, particle counting was not fitted. The corresponding groundwater transfer function (GTF) was given by /(1), . . . , /( ) = 79:; , with < a WMWL power-law parameter for deep water transfer (Appendix A), the duration of the seepage period, and a retardation factor accounting for sink effects [START_REF] Holzbecher | Environmental Modeling using MATLAB[END_REF] equal to 0 in case of N transfer (no sinks outside the vadose zone).

GTF were catchment-scaled and generic-event scaled representations of landscape functioning.

Model validation

LULCC and WMWL modeling

We evaluated the deviation between the farmers' cropping plans and the simulated plans through the absolute deviation = = ∑ > ?@6 |B C ? 7B ? | ∑ > ?@6 B C ?

, where 1. . . D is the set of possible land uses, E C the sum of areas of land use F expected by the cropping plan, and E the corresponding simulated sum. River outflows summing all water components computed by the WMWL model were confronted to observed values trough the Nash Sutcliffe coefficient [START_REF] Wallach | Working with Dynamic Crop Models: Methods, Tools and Examples for Agriculture andEnvironment[END_REF].

Particle tracking and SSMT modeling

The amount -( ) of particles reaching the outlet depends on delayed flows that affect the number of particles G % ( -) produced in each cell of the computational domain and available for water transfer:

G % ( -) = $ % ( -)' % ( -). (5)
We can write:

-( ) = ∑ % . H * + , G % ( -)( % ( ) = ∑ % . G % ( ) * ( % ( ), (6)
where the asterisk represents the convolution product and ( % ( ) the transfer probabilities generated by DEMIs representative of hydro-agrosystem conditions over the transfer period.

The individual particle behaviors and trajectories of surface and subsurface transfers cannot be measured directly. To compare SSMT results with observed values, we introduced delivery ratios (eq. 4), produced stocks G % (eq.5) and SSFT /( ) (eq. 3) values into a lumped formulation of particle flows -I ( ) equivalent to ∑ * +

. -( ), the SSMT outflows (Appendix C):

-I ( ) = 4( -) ∑ % . G % ( ) * /( ). (7)
In case of finite built-up stocks, the production function is lowered by previous outflows, with minimum values fixed to 0:

∑ % . G % ( ) = ∑ % . $ % ( )' % ( ) --I ( -1) (8)
For nutrient and EC stocks, $ % ( ) were obtained by updating the balance $ % ( ) = $ % ( -1) -J$ % ( -1) , where J accounts for plant assimilation/mineralization/denitrification/mortality. At the beginning of the simulation ( , ) or for each period of fertilizer supply or manure disposal, initial $ % ( , ) values were defined considering fertilization supplies or residual stocks of land uses (supplementary material S2). For SM, $ % ( ) depended on the crusting dynamics (Appendix B).

Solute matter outflows from deep water table seepage were calculated by eq. 7, where the distribution /( ) is given by the GTF (cf. paragraph 2.3) and 4K -L = 1.

Lumped-computed N, total P and soluble P, EC and SM outflows were confronted in separate worksheets to observed values, following [START_REF] Trévisan | Coupling indicators and lumpedparameter modeling to assess suspended matter and soluble phosphorus losses[END_REF]. A unit conversion factor M was evaluated by minimizing the objective function [-O ( ) -M-I ( )] Q between observed -O and calculated -I values of matter outflows.

Software architecture

WMWL and OPALE GUIs (figure 4) were implemented in the MATLAB environment, while the LULCC and SSMT programs (figure 5) were implemented with the GAMA platform [START_REF] Taillandier | Building, composing and experimenting complex spatial models with the gama platform[END_REF]. The OPALE GUI allows users to select libraries, implement IOF writing/reading and parameterize commands in the two environments and SAGA geographical treatment (http://www.saga-gis.org). OPALE executable for the Windows-64 bit environment, source codes and documentation are available at github1 . All programs were run on a computer with a CPU IntelCore(R) i7 and 32 Go RAM. At the center of the OPALE GUI a workflow scheme organizes the workflow steps for landscape assessment. The workflow scheme differs depending on the selected production systems (from the listbox items -Livestocks / Crops & Livestock or Crop / vegetables-).

At step 1, the 'New project' button and a subsequent 'Exec'-clic allows reading input files.

Then, it opens the GAMA GUI where users can launch an initialization program, linking together geographical information (soils, hydrological network, fields, farm systems, etc., as described in supplementary material S3). The computational mesh is also defined here, with the sizes of the square grids based on the resolution of the digital elevation model.

Then, the LULCC program is opened, and performs maximum flow or step computation schemes depending on the selected production systems. Configuring decision rules for crop successions and distance priorities between farms and practices is allowed. LULCC outputs are agricultural landscape structures (i.e. an assemblage of different agricultural plots) and landscape infrastructures (e.g. hedges, filter strips, non-productive areas), as referenced by grids where their proportion area in the cells of the computational mesh are calculated to limit topological representation biases for the following WMWL calculations.

The 'G=> M' button (Step 2) builds matrices for the Matlab environment and performs Step 4 allows opening an M=>G library to configure the $ % build-up matrices for Gama SSMT modeling.

On Geographical inputs are detailed in supplementary materials S3. Miribel catchment was mainly concerned by hortonian overland flows from annual crops, including fine silt texture conditions and a high sensitivity to soil surface crusting [START_REF] Lepilleur | L'imperméabilisation de la surface du sol[END_REF]. Due to the low permeability of lacustrine deposits preventing deep water percolation, Autran catchment was subject to soil moisture saturation of variable source areas causing frequent surface runoff [START_REF] Petitqueux | Organisation agropaysagère du Val du Méaudret : rôles des acteurs territoriaux et état des structures paysagères[END_REF]. On the contrary, Aiguebelette tertiary sandstone was favorable to high soil permeability, and water percolation was predominant [START_REF] Pezet | Bilans et transferts de phosphore dans le bassin versant du lac du Bourget : caractérisation, interprétation et modélisation des flux[END_REF]. [START_REF] Poulenard | Infrared spectroscopy tracing of sediment sources in a smallrural watershed (French Alps)[END_REF] studied a catchment nearby Aiguebelette sharing the same geographical context and showed that matter from riverbank erosion was predominant in suspended matter flows and that livestock played a role too. These authors observed that the relative contributions of topsoils and river bank sediments were seasonal, with an increase of the topsoil contribution during spring and summer pastures and a decrease in late fall and winter, in relation with the access of livestock to the river network.

Examples of applications

Stakeholders are concerned by erosion, soil protection and mud flows in Miribel, nutrient losses and eutrophication of surface waters in Aiguebelette, and bacteriological water quality in Autrans.

Stream flows were monitored using weirs placed at the catchment outlets. Water samples were collected in 2016 and 2017 by automatic samplers programmed for weekly flow-weighted composite sampling. In Miribel, the Nephelometric Turbidity Unit (NTU) was monitored with an OBS300 Campbell Scientific probe for SM flow evaluation. In Aiguebelette, SM, soluble reactive phosphorus (SRP), total phosphorus (TP) and nitrates were analyzed by standard colorimetric methods (AFNOR, 1990). In Autrans, instantaneous water samples were collected manually and sent within 24h to the laboratory for EC enumeration, following standard protocols ISO 9308-2

for water bacteriological quality assessment. In addition, to differentiate between the proportions of human and bovine contamination, water sub-samples were treated to quantify HF183 and Rum2Bac bacteroidales markers, following [START_REF] Mauffret | Relevance of bacteroidales and f-specific RNA bacteriophages for efficient fecal contamination tracking at the level of a catchment in france[END_REF]. Doing so and considering the respective soil conditions, the bottom permeability ratio & was high in Miribel and Aiguebelette but low in Autrans. Horton store emptying was considered rapid, and a maximum T Q value was thus retained. The saturation overflow emptying value T U was lower, considering potential retardation effects due to variable extension of source areas. All SSMT parameters were predefined (`, k % , % , & , e % , l % ), referenced from available data given in table 2, as well as those proposed in the LULCC model (supplementary material S1 parameters), although a few decision variables can be redefined from the GAMA GUI to account for local organization and decision rules (fig. 5).

Model parameterization

Landscape reconfiguration prospects

Farming system evolutions and grassland landscape reshaping to control vole overgrowths and bacteriological water quality degradation

Specialized livestock breeding territories can be associated with faecal contamination of water but also with grassland vole overgrowths, in relation with low landscape heterogeneities, the increasing number of permanent meadows, the lack of disturbing activities (plowing) or natural barriers (paths, banks) for rodent populations, as well as the regression of natural refuges (hedges, forested patches) for terrestrial and aerial predators [START_REF] Halliez | Historical agricultural changes and the expansion of a water vole population in an Alpine valley[END_REF]. The following changes were tested on E. coli flows in the Autrans area: (i) modification of farming systems to increase the area of plowed parcels (two cases were evaluated with introductions of 10ha and 25ha of spring barley in cereals-milk round-bale systems, corresponding to 1.5 and 3.8 % of additionnal plowed surface in the watershed area, respectively); (ii) implementation of hedges (5m wide, considered equivalent to a caduceous forested area) following 5 modalities: 10 km long along a preferential east-west direction; 10 km along a north-south direction; 10 km EW and 10 km NS; 20 km NS; 20 km NS and 10 km EW).

Changes in farming systems and agricultural practices, and implementation of grass filter strips to control soil erosion and suspended matter flows

Industrial vegetable production is often associated with soil compaction and severe runoff and erosion events [START_REF] Lepilleur | L'imperméabilisation de la surface du sol[END_REF]. We evaluated the effects of changes in the distribution of farming systems on SM with a 10% increase of annual crop systems in the Miribel area. In addition, we tested the generalization of hoeing on row crops and the implementation of 0.2, 0.4, 3.4, 3.8, 22, 42 and 96 ha of grass filter strips (these latter filters were first positionned on critical source aeras selected by vizualizing displacements of SM particle clouds -cf. fig. 11 -and thereafter generalized to the catchment along the drainage network).

Water management

As a consequence of periurbanization in the Aiguebelette area, stakeholders are confronted with the extension of the artificial hydrological network aimed at draining humid areas. We tested the effect of river network reshaping on SRP loads by adding 1296m of open drain length to the 4262 m of the present hydrological network in a sub-catchment (137 ha) of the studied area (2700 ha).

Discussed results

LULCC modeling

For crop/vegetable landscapes, the AD ratio between expected crop surfaces and calculated crop surfaces differed depending on the farming systems (fig. 6). Mean values were centered on 1, showing the ability of the LULCC model to construct reliable landscapes according to the farm production objectives. For annual crops and mixed systems, the deviation from the mean was low. However, it was greater for specialized vegetable systems, as a great number of vegetable species can be introduced in crop successions depending on the evolution of the market demand.

Figure 6: Distribution of ratios between expected and calculated surfaces in Miribel catchment.

For grassland landscapes, expected/calculated ratios were also centered on the mean value 1 (fig. 7), giving quite realistic landscapes regarding farms needs. Moreover, a few differences were visible, noticeably in the area of first priority for productive animal pastures, where fields were not subdivided like farmers can do to adjust seasonal livestock needs to vegetation production. Deviations from true landscapes mainly resulted from uniform patterns of decision rules, not always adapted to account for local/seasonnal adaptations to farm plot configurations. In some instances, this reflected our choices for the implementations of the landscape models, mainly driven by the need to provide a sufficiently exhaustive but also simplified representation of agricultural landscapes allowing us to infer accessible input data.

Figure 7: Distribution of ratios between expected and calculated surfaces in Autrans catchment.

P1 : first priority pasture ; H : hay one cut ; H2C : hay two cuts ; H3 : hay three cuts ; P2 : second priority pasture.

WMWL modeling

The following figures confront calculated and observed data. For Miribel (fig. 8), the Nash-Sutcliffe efficiency (NSE) coefficient was 0.81. Model biases were not detected, as observedcalculated couples were regularly placed around the bisector line. For Autrans, similar patterns were observed, although NSE was lower (NSE=0.56, fig. 9), yet above the 0.5 threshold agreed upon for model accuracy [START_REF] Moriasi | Model evaluation guidelines for systematic quantification of accuracy in watershed simulations[END_REF]. Calculated water flows for Aiguebelette also fitted rather well with observed data (NSE=0.72, fig. 10). The main difference between the three catchments came from their sensitivity to loose deep water (as expected, the T . value corresponded to high impermeable territory at Autrans, tab. 2). We also noted a higher drainage dynamics at Miribel (high groundwater table delay λ value), according to the high drainage density in this annual cropland zone. Global responses were also specific to the geographical contexts, and fitted well with the hydrological patterns of the areas. Thus, hortonian runoff represented 12.5% of total outflows in Miribel, and around 1% in the other two catchments. It was quite the same with saturation runoff (9.6 % in Autrans, negligible elsewhere). In Autrans, peak flows came first from water table drainage (89%) and secondly from urban runoff from impermeable surfaces (9%). In Aiguebelette, rural overland flows were reduced ( < 1% ). Considering the low number of WWML model parameters, the various soils and agricultural conditions in which it was applied, the diversity of hydrological processes taken into account, the efficiency of acceptable flow representations, as well as the good agreements with the characteristics of the hydrosystems, we considered that the underlying hypotheses about water balance and movement were founded. During spring and early summer = 44, . . . ,151, SSTFs were rather similar, with delivery ratios 4( ) around 0.075. Considering the similarity of the spring SSTF responses, we considered that the SSTF( = 44) was a good representative of the spring transfer dynamics and used it for the whole spring season to predict Miribel SM flows from hortonian runoff. Following [START_REF] Boiffin | Influence des systèmes de culture sur les risques d'érosion par ruissellement concentré. I. -Analyse des conditions de déclenchement de l'érosion[END_REF], hortonian runoff was modeled considering the extension of low-permeability surface crusts (structures named F2) and the rearrangement of high-permeability soil surfaces (structures named F3), cf Appendix A, §7.5. In summer, no particle was generated because the soil surface permeability remained high (the mean extension area of F3 exceeded that of F2). The lowering of the water table and drying out of the drainage network led to a strong decrease of water flows (in wet conditions, the river length was nearly 40 Km; in summer, based on eq. 23, it was 500 m), so that the turbidity probe at the catchment outlet was not permanently covered by water flows. In early fall ( = 311), the drying out of the drainage network persisted but was lower than in summer (the drainage network length was around 10 % of its initial length). Due to the disconnection of active overland flow areas, the SSTF sharply decreased with reduced 4( )

SSMT modeling

(=0.02).
For Autrans catchment, several DMEIs were evaluated (fig. 13). Two main SSTF response patterns were described, with a first type in which distributions showed sharp decreases when /( . ) > 0.5, and a second type with lower decrease. They corresponded to rapid losses when active areas were close to the river network, or differed transfer rates from more distant sources, respectively. The first sharp type was generated when the variable source area (VSA) flows was greater than 1.5 G U . $ 7. . The delivery ratios also differed throughout the season according to hydrological conditions, with a general trend given by the statistical relationship 4( ) = 0.099 ( ) + 0.051 ( e Q = 0.6 * * ). Consequently , two SSTF types and the relationships between the delivery ratio and the variable source flow were introduced in -I ( ), the lumped evaluation of EC flows. 31, 64, 113, 167, 212 ,315) were rather equivalent, with a sharp decrease similar to the one described in Miribel at = 311 (fig. 12), due to the fact that the water movements were essentially vertical and limited volumes moved laterally in this filtering context.

Modeling of matter outflows

At Miribel, turbidity probes operated until late spring, and data were collected to evaluate SSMT outputs (figure 14, NSE=0.73). One event (obs=2.51 ntu. 7. ; cal=1.40 ntu. 7. ) situated at the end of the modeled sequence reduced the NSE ratio. It corresponded to stochastic conjunctions of the plowing, sowing or hoeing dates that probably led to lower F2-F3 differences. The solute transport in Aiguebelette was analyzed considering eq. 7 and 8 and the GTF transfer distribution /( ) associated to the < parameter describing water table seepage. For SM and particulate matter, we developed the lumped modeling schemes described in previous studies for similar bank erosion situations [START_REF] Trévisan | Coupling indicators and lumpedparameter modeling to assess suspended matter and soluble phosphorus losses[END_REF], considering that the production function G( ) was obtained from stores $( ) related to the active river length and livestock pressure, and wash-off '( ) was associated with drainage flow and urban runoff. Fig. 16 gives results obtained at Aiguebelette for solutes or suspended compounds recorded at the outlet.

NSEs were equal to 0.91, 0.92 and 0.90 for nitrogen, total phosphorus and SM, respectively.

Efficiencies were high, and residuals were regularly dispersed around bisectors.

Despite the variety of transferred compounds and modes of matter displacement, outflows were quite well reproduced by SSMT modeling, and provided evidence of the efficiency of OPALE outputs (4( ), $( ), '( ), SSFT and GTF) in assessing the links between practices and water-related functions in agricultural landscapes.

Landscape reconfigurations

The values of efficiency coefficients v w are given in table 3. For the Miribel catchment, hoeing of all row crops slightly reduced SM flows, insofar as the benefits are expected to be limited to the few weeks following hoeing in this context of high soil crusting sensitivity. Efficiency is greater when the numbers of farming systems with annual crops increase (in such sytems soil surfaces are much more protected from erosivity because intercropping reduces the length of the periods when soils are non covered by aerial biomass, whereas unprotected, compacted and emissive harvesting sites can be prolonged in vegetable production depending on the market demand). The efficiency of landscape reconfiguration by GFS increased with the GFS area, and increased sharply when GFS implementations were located on areas where SM particles converged, in accordance with the need for better recognition and monitoring of critical source areas [START_REF] Heathwaite | Modelling and managing critical sources areas of diffuse pollution from agricultural land using flow connectivity simulation[END_REF].

Miribel

In Autrans, the extension of plowed surfaces increased the landscape efficiency against E.

Coli loads. This was probably explained by the reduced pressure of manure spreads, as these are buried by plowing and thereby not sources of bacterial emissions from overland runoff [START_REF] Sistani | Broiler Litter Application Method and Runoff Timing Effects on Nutrient and Losses from Tall Fescue Pasture[END_REF][START_REF] Meals | Demonstration of methods to reduce E-coli runoff from dairy manure application sites[END_REF]. However, efficiency was lower for R+25ha than for R+10ha of spring cereals. This can be attributed to the fact that the closer proximmity of pastures to the river network when cereal production was enlarged increased the pressure and transfer dynamics of E. coli. It is also conceivable that the extension of the cereal production area went together with an increased risk of hortonian runoff. High-stemmed hedges increase landscape efficiency, especially when hedges are planted in a NS direction (the direction perpendicular to the main slope and the water flow direction). This suggests that the effects of hedges are mainly attributable to the interception of surface runoff trajectories, firstly by increasing the reinfiltration of runoff due to the greater evapotranspiration potential of hedges compared to grasslands [START_REF] Granier | Rôle des prairies dans le cycle de l'eau. Comparaison avec la forêt[END_REF][START_REF] Merot | Influence du réseau de haies des paysages bocagers sur le cheminement de l'eau de surface[END_REF], and secondly by a trapping effect, which is debated for bacteria [START_REF] Vansteelant | Évaluation des risques de contaminations microbiologiques liés aux épandages de matières organiques sur prairies de montagne[END_REF]. These examples show how several landscape ecofunctionnalities can be associated in order to rationally fight against water contamination, the proliferation of grassland vole overgrowths, as well as better conditions for pasture, thanks to shading effects associated with hedge networks.

Drainage of humid areas in Aiguebelette is concomitant with decreasing efficiency of landscapes against the control of SRP flows from hypodermical transfers. The decrease is much sharper during the growing season (April and June), when plant root systems are fully active, compared to winter or autumn when evapotranspiration and nutrient uptake are low [START_REF] Granier | Rôle des prairies dans le cycle de l'eau. Comparaison avec la forêt[END_REF] and efficiency less deprecated.

Conclusion

Landscape eco-functionalities are related to agricultural uses and schedules [START_REF] Wezel | Agroecology as a science, a movement and a practice[END_REF][START_REF] Gascuel-Odoux | Gérer les paysages et les territoires pour la transition agroécologique[END_REF], and stakeholders use operational tools to assess the incidence of global change (climatic perturbations, urbanization) and evaluate the adaptations of farming systems or new land-use practices. A number of ecological infrastructures can be implemented to control and protect water resources, such as filter strips [START_REF] Dorioz | The effect of grass buffer strips on phosphorus dynamics. A critical review and synthesis as a basis for application in agricultural landscapes in France[END_REF], interstitial hedgerows [START_REF] Merot | Influence du réseau de haies des paysages bocagers sur le cheminement de l'eau de surface[END_REF], riparian hedgerows [START_REF] Zaimes | Total phosphorus concentrations and compaction in riparian areas under different riparian land-uses of Iowa[END_REF], and ecological infrastructures including meanders, marshes, etc. [START_REF] Wang | Using a landscape approach to interpret diffuse phosphorus pollution and assist with water quality management in the basins of lake Champlain (Vermont) and lake Léman (France)[END_REF][START_REF] Trévisan | Coupling catchment hydrology and transient storage to model the fate of solutes during low-flow conditions of an upland river[END_REF]. In practice, the efficiency of mitigation practices or landscape infrastructures strongly depends on their position in the landscape, as well on cumulative effects [START_REF] Wang | Using a landscape approach to interpret diffuse phosphorus pollution and assist with water quality management in the basins of lake Champlain (Vermont) and lake Léman (France)[END_REF]. OPALE -the tool presented in this article -was developed as an assessment tool of landscape organization to meet such demands by addressing several scientific and operational issues.

Landscapes are built from production objectives of farming systems and related decision rules; as such, they are the seat of water displacements commonly analyzed through the common concept of transfer functions, representing the distribution over time of elementary water volumes exported at catchment outlets [START_REF] Haggerty | On the late-time behavior of tracer test breakthrough curves[END_REF][START_REF] Hingray | Hydrologie, 2. Une science pour l'ingénieur[END_REF]. This representation is well developed in catchment hydrology to predict water flows and associated signals (natural or artificial tracers) at the outlet of catchments, e.g., Nilo de Oliveira Nascimento et al. (1999), but also in river hydrology to evaluate channel organization and responses [START_REF] Gooseff | Comparing transient storage modeling and residence time distribution (RTD) analysis in geomorphically varied reaches in the Lookout Creek basin, Oregon, USA[END_REF][START_REF] Trévisan | Coupling catchment hydrology and transient storage to model the fate of solutes during low-flow conditions of an upland river[END_REF]. Despite available knowledge on the relationship between topographic patterns of catchments and the variability of their residence times OPALE allowed for efficient evaluations of water and matter outflows and led to transfer functions and delivery ratios usable as synthetic indicators of the assessment of landscape functioning and eco-functionality.We demonstrated the effectiveness of OPALE procedures regarding such criteria through three diverse true-life cases in terms of agriculture, soil and hydrology conditions.

Aknowledgments

This research was funded by the TIPTOP-PSDR4 program, with the contribution of INRA, Région Auvergne-Rhône Alpes, IRSTEA and the FEADER and PEI-AGRI European Union funds.

Appendix A: WMWL model formulations

Hydraulic properties (field moisture capacity, saturated hydraulic conductivity) were computed using pedotransfer functions [START_REF] Bruand | Estimation des propriétés de rétention en eau des sols : utilisation de classes de pédotransfert après stratifications texturale et texturo-structurale[END_REF].

Plant development model

The depth of the root zone was updated daily, applying the plant growth model developed by [START_REF] Gérard-Marchant | Distributed hydrological modelling of total dissolved phosphorus transport in an agri-cultural landscape, part I: distributed runoff generation[END_REF] and in SMDR (2013). The first step of the computation was the evaluation of degree-day units :

= x X -X O = i yz{ 7i | Q + i y?> 7i | Q for X >= X O 0 for X < X O , (9)
where X , X W , X € are the mean daily, maximum and minimum temperatures

• . = . '' ƒ ; (10)
• Q = . '' ƒ '' ƒ 7'' 6 '' … 7'' 6 ; (11)
• U = -0.6

.

'' yz{ 7'' ƒ (12)
The plant development factor was obtained from:

Z ' = • . if < . (slow development); Z ' = 1 + • Q ( - Q ) if Q > > . (rapid development); Z ' = 1 if U > > Q (maturity); Z ' = 1 + • U ( - U ) if W > > U (senescence) and; Z ' = 0 if > W (dormancy).
Root depth † was then computed between † € and † W , the minimum and maximum values, from:

† = † € + Z ' ( † W - † € ). (13)
The ratio Y ‡ between potential and real evapotranspiration ( = Y ‡ ) was calculated from minimum to maximum values following

Y ‡ = Y ‡ € + Z (Y ‡ W -Y ‡ € ). †
and Y ‡ values are crop dependent and tabulated in SMDR (2013). A biomass indicator ^O was computed as follows:

x ^ˆ‰( ) = ^ˆ‰( -1) + Z ' * f if ( ) < U = 0 if ( ) > U = 0 if ≥ t(harvest) (14)
where f -varying from 0 to 1 and depending on soil moisture (Arnold and Forhrer, 2005)reduces plant development in case of water stress. Water stress was considered as soon as the vadose zone moisture j dropped below j '" , the easily usable water reserve ( j '" = 0.25(j ‡ ‡ -j 8 ) + j 8 , where j ‡ ‡ and j 8 are the field capacity and the wilting point, respectively). The water stress predictor was obtained from f = l"((5(j /j '" -1)).

Drainage D

Excess water available for vertical or lateral movements ' was obtained from ] at the bottom of the vadose zone, given by:

Y O = & Y , ( 15
)
where & is a coefficient that accounts for the reduction of the vadose zone hydraulic al., 1998):

-= › š š (£ " + ℎ , + ¥ ‡ ), (16)
where Y ‡ is crust conductivity, ¥ ‡ crust thickness, ℎ , surface runoff depth and £ " root zone suction. £ " depends on soil moisture and was modeled by the Van Genuchten's equation: The degradation of the soil structure owing to the impact of raindrops at the soil surface produces a typical deposit structure named «2 . Particles are rearranged by splash and sedimentation at the soil surface, a very-low-permeability crust is formed, and surface roughness and water retention decrease [START_REF] Boiffin | Influence des systèmes de culture sur les risques d'érosion par ruissellement concentré. I. -Analyse des conditions de déclenchement de l'érosion[END_REF]. However, as the plant cover increases along the crop season, «2 structures are reshaped and progressively rearranged by alternating moistening/desiccation phases or by biological activity, making way for high-permeability «3 structures. In addition, rainfall is redirected by leaves and stems to the collars of plants, where soil surface permeability is elevated. We therefore considered that soil crusting and plant development had opposite effects and we calculated the extension of crust deposits e (the computational time, particle build-up is evaluated under the Matlab environment during the period preceding a DMEI. We did not consider lateral exchanges between cells, as this is commonly done in the field of environemental studies for the evaluation of agricultural pressures [START_REF] Massa | Territ'eau, une méthode et des outils pour améliorer la gestion des paysages agricoles en vue de préserver la qualité de l'eau. Ingénieries EAT[END_REF]. In the contrary, during the transfer period following a DMEI, wash-off and sink-source effects were evaluated in the Gama environement, considering cascade effects between upslope and downslope cells.

Particle build-up

Build-up stocks $ % ( ) are generated on computational cells & by agricultural pressure and depend on crop requirements and practices. We defined several proxies as substitute variables for the different kinds of build-up stocks.

We evaluated nutrient build-up $ % ( ), considering the net stock of nutrients from a rough balance between fertilizer supply, mineralization, and assimilation, all of them documented by tables provided by technical institutes for crop production and protection [START_REF] Comifer | Calcul de la fertilisation azotée. Guide méthodologique pour l'établissement des prescriptions locales[END_REF]. N leaching was evaluated from Burn's model [START_REF] Burns | A model for predicting the redistribution of salts applied to fallow soils after excess rainfall orevaporation[END_REF]. EC stocks were evaluated for grasslands, taking proportional links between fecal populations and N inputs from farm effluent spreading into account. EC inputs from deciduous and perennial forest wildlife were not excluded. Total nutrient needs, daily rates of net assimilation and EC particle patterns are given in supplementary material S2. We hypothesized that SM stocks $ % ( ) were produced by impermeable soil surface structures. They were evaluated by calculating $ % ( ) = Gk"(0, «2 % ( ) -«3 % ( )) , where «2 % ( ) and «3 % ( ) are the extents of continuous and discontinuous crusts, respectively (see kinetic to calculate the value of the retention function: e % ( ) = G % gh ( -)l 7ÁI , where is the width of the crossed infrastructure and f a length parameter. Additional SM particles can come from runoff concentrations [START_REF] Cerdan | Modelling interrill erosion in small cultivated catchments[END_REF]. As linear relationships often occur between erosion rates and runoff amounts [START_REF] Mamedov | Soil erosion-runoff relationships: insights from laboratory studies[END_REF][START_REF] Pardini | Rainfall/runoff/erosion relationships and soil properties survey in abandoned shallow soils of NE Spain[END_REF], we considered the source effects with additional production l % ( ) = jℎ C % ( -), where j is a proportionality factor and ℎ C % ( -) the surface runoff volume accumulated up-slope of cell &.

Appendix C: SSMT validation

To simplify formulations, we considered outflows provided by a transfer period of duration = 1. Based on eq. 3, 4 and 7, we calculated: We retained that the lumped modeling of particle outflows equaled the SSMT particle count. AFNOR, 1990. Eaux, méhodes d'essais. Technical Report. ISBN 2121790411. Arnold, J., Fohrer, N., 2005. Swat2000 : Current capabilities and research opportunities in applied watershed modelling. Hydrological Processes 19, 563-572.

Â Ã Ã Ã Ä Ã Ã Ã Å -I ( ) =

Figure 1 :

 1 Figure 1: Diagram of the LULCC model for crop systems. For non-priority crops possibly remote

Figure 2 :

 2 Figure 2: Diagram of the LULCC model for livestock systems. nF-non forage crops; F-forage crops;

Figure 3 :

 3 Figure 3: Computation algorithm and parameterization of the water flow model. Rectangles

Figure 4 :

 4 Figure 4: OPALE GUI.

  plant development and topography calculations to build the cascade scheme for sequential water flow balances along slopes. The Step 3 top buttons open the WMWL model for optimization. WMWL optimization can be done contextually based on soil and hydro-system properties, or automatically with the lsqcurvefit tool in Matlab. All calculations up to this stage provide a baseline on the current landscape. The Step 3 bottom buttons open simulation purposes, and build new matrices that can be compared to the current landscape. If the user needs to analyze production system changes, the workflow differs depending on farming conditions. For crop/vegetable systems (crop distribution determined by random selections in the LULCC model), forward planning of farming systems is implemented by modifying the crop areas of the first year of the crop succession in order to follow the initial patterns of crop distributions. The aim is to avoid repeated simulations to obtain converging agent-based model simulations outputs that are commonly done to compare present and future territories[START_REF] Grillot | Multi-level analysis of nutrient cycling within agro-sylvo-pastoral landscapes in West Africa using an agent-based model[END_REF]. The price to pay is that only the first year of the crop succession of current and future landscapes can be compared. We implemented such modifications within the Matlab environment, where the first year of the current landscape matrices of crop allocation are modified according to the expected proportions of crop groups indicated by the user in the agricultural-system-landscape panel. To do this, we applied an algorithm in which parcels are progressively assigned to new expected productions until the user's constraints are met. As breeding landscapes are not constrained by random choices of potential crop successions but by priority schemes, modifications of farming systems and climatic conditions have to be calculated by re-launching the LULCC model on an annual or pluriannual basis in which each new farming objective indicated in the agricultural system-landscape panel is evaluated in terms of priority practices and field availability.

  the right side of the OPALE GUI, three panels are enabled/disabled depending on the workflow selection step. The 'Landscape => Water' panel contains several dialog boxes for WMWL parameters (& , T . , T Q , T U , <, V, F W , see Appendix A) and check-box options to configure WMWL output plots (when the 'obs, cal' check-box is selected, the Nash Sutcliffe coefficient[START_REF] Wallach | Working with Dynamic Crop Models: Methods, Tools and Examples for Agriculture andEnvironment[END_REF] is computed to compare observed or calculated river flow outputs) or to select parameters to be optimized by the lsqcurvefit program. Optimization processes can be paused for plot-zooming and inspection (from the upper tool bar) or to analyze the contributions of water components to river outflows or select DMEI dates. The 'Agricultural system => Landscape panel' allows configuring the proportions of the farming systems, as well as climatic conditions, farming practices or infrastructure distribution (several choices are possible, with filter strips or hedgerows of deciduous of perennial tree species). With the 'Interface' button, the program interacts with SAGA libraries to re-calculate the proportions of the infrastructures in the computational meshes. Finally, with step 4, the 'Landscapes => Ecofunctionality' panel allows evaluating the transfer functions SSTF and the nature of the particle matter to be treated in SSMT.

Figure 5 :

 5 Figure 5: GAMA GUI. A button and list-box panel allows the user to define parameter values and

  schemes aimed at valorizing landscape ecofunctionnalities and controlling water cycle and

Figure 8 :

 8 Figure 8: Observed and calculated water flow outputs in Miribel catchment.

Figure 9 :

 9 Figure 9: Observed and calculated water flow outputs in Autrans catchment.

Figure 10 :

 10 Figure 10: Observed and calculated water flow outputs in Aiguebelette catchment.

Figure 11

 11 Figure 11 gives an example of SSMT outputs. These are maps of Miribel catchment

Figure 11 :

 11 Figure 11: Spatial particle distribution following a winter DMEI

Figure 12 :

 12 Figure 12: Transfer functions of hortonian surface runoff for several DMEIs and corresponding

Figure 13 :

 13 Figure 13: Transfer functions for saturation excess runoff in Autrans catchment. Red lines: type 1;

Figure 14 :

 14 Figure 14: Observed and calculated SM flow outputs in Miribel catchment.

Figure 15 :

 15 Figure 15: Observed and calculated EC flow outputs of Autrans catchment.

Figure 16 :

 16 Figure 16: Observed and calculated N, P and SM flows of Aiguebelette catchment.

(

  [START_REF] Mcguire | The role of topography on catchment-scale water residence time[END_REF], eco-hydrology developments are expected to evaluate the relationships between landscape composition-structure and transfer patterns[START_REF] Mcguire | A review and evaluation of catchment transit time modeling[END_REF].Our work is a contribution to such issues. It proposes several libraries aimed at (i) analyzing the dynamics of the restitution of water and associated matter to the catchment outlet from the explicit resolution of distributed water balances and particle tracking methods, and (ii) evaluating the efficiency of developed methods by using lumped modeling techniques and confronting them to a variety of real-world observations. Operational issues mainly concern (i) the need for generic models adapted to a large geographical diversity of production systems, biophysical environments and landscape features, (ii) data accessibility, (iii) robustness of algorithms to avoid over-parameterization and over-fitting problems, and (iv) workable interfaces limiting I/O data manipulation as much as possible and allowing fast workflows from data configuration to diagnosis.

  with the soil moisture and ‡ ‡ the moisture at field capacity [m]. Drainage was obtained from (Arnold and Fohrer, 2005) by = ' (1 -l 7 6 -), where the time delay coefficientis deduced from -= ˜z™ 7 šš › |oe™ , with the moisture at saturation [m], Y O the saturated hydraulic conductivity [m.day 7.

  j ' , j are the vadose zone soil moisture, the residual water content and the corresponding moisture at saturation, respectively. D and Z were parameters depending on texture conditions, and G = 1 -.€. With ^ rainfall intensity, e the proportion of crusted soil [m 2 .m -2 ] and rainfall depth, if -< ^, the overland hortonian runoff was given by:

Table 1 :

 1 Study sites. Summary of agricultural and geographical conditions. The main soil types are referenced from the World Reference Base for Soil Resources (2014).

	Site	Area (ha) Localization	Agricultural	Geography
			wgs84	systems
	Miribel	1132	lat.: 45°.853	Annual crops	altitude: 300 m
			lon.: 4°.943	Vegetables	geology: loess
					main soils: haplic lixisols
					main use: agriculture
	Autrans	1965	lat.: 45°.107	Livestock	altitude: 1,000 m
			lon.: 5°.532	Annual crops	geology: lacustrine
					deposits
					main soil: cambisols
					main use: agriculture-
					tourism

4.1. Catchment description and monitoring

OPALE was tested in three different territories in terms of farming systems and geographical conditions. Site properties are given in table 1.

Table 2

 2

	Parameter	Definition	Value	Source
	X O ,	...	7.1) W temperature thresholds ( §	reference values	SMDR (2013)
	&		bottom Y	[-] ratio (eq. 15)	M.: 1.0; Au.: 0.8; Ai.: 1.0	C. op.
	T .	deep aquifer losses (eq.20) M.: 0.88; Au.: 10; Ai.: 1.3	A. op.

gives parameter values for the WMWL and SSMT models. We evaluated the parameters of the WMWL model ( & , T . , T Q , T U , < , V , F W ), following the lsqcurvefit automatic optimization module or by referencing contextual values from expert estimation.

Table 2 :

 2 Parameter values (M.: Miribel; Au.: Autrans; Ai.: Aiguebelette; C. op.: Contextual

	optimization; A. op.: automatic optimization). S2 : supplementary material 2 ; S4 : supplementary
	material 4.

  [°C], respectively, and X O a plant development threshold. Tables for X O are given in the SMDR

	manual. Every day, the new computed	value was added to the previous day value, following
	rules for stopping	accumulation in case of negative temperatures or after harvest. Several
	formulas were applied to compute Z , a plant development factor (varying from 0 to 1 for
	maximum plant development), between different	-accumulation thresholds (slow
	development	. ; rapid development	Q , maturity	U and senescence	W ):

https://github.com/TipTop-PSDR/OPALE.git

conductivity Y . At the end of each day iteration, the daily groundwater production ( ) was added to • ' , the deep water store: • ' ( ) = • ' ( -1) + ( ).

Lateral flow L

Lateral flow ( ) was given by ( ) =

, where j , j ‡ ‡ are the soil moisture at saturation [m.m 7. ], and the distance between two adjacent cells, respectively.

was equal to , the cell size of the computational square mesh in case of orthonormal flow directions, and to √2 when flow directions were north east, south east, south west or north west. Lateral flows were routed to down-slope cells occupied by a river segment, following the ∞ algorithm [START_REF] Tarboton | A new method for the determination of flow directions and contributing areas in grid digital elevation models[END_REF] and cascade schemes [START_REF] Kiesel | Application of a hydrological-hydraulic modelling cascade in lowlands for investigating water and sediment fluxes in catchment, channel and reach[END_REF].

Variable source area surface flows

Following [START_REF] Obled | TOPMODEL : principes de fonctionnement et application[END_REF], effective rainfall was added daily to the vadose zone.

When the resulting moisture exceeded ˜z™ (the saturated soil moisture), the overland flow was computed by = -˜z™ . At the end of each day iteration, the daily production ( ) was added to • , the VSA surface store: • ( ) = • ( -1) + ( ).

Hortonian surface flows

We considered that hortonian runoff mainly came from the crusted, low-permeability area [START_REF] Cerdan | Modelling interrill erosion in small cultivated catchments[END_REF]. The flow q infiltrated into crusted soils was obtained from (Jetten et proportion of cell surface covered by crust deposits) with e = Gk"(0, «2 -«3).

We considered the extension of crust «2 by calculating:

where ‡" is cumulative rainfall, daily updated from the seeding date of annual crops, and T _Q an agricultural parameter. T _Q values were calculated from experimental surveys of crusting dynamics [START_REF] Vansteelant | Conditions d'apparition du ruissellement dans les cultures annuelles de la région lémanique. Relations avec le fonctionnement des exploitations agricoles[END_REF][START_REF] Lepilleur | L'imperméabilisation de la surface du sol[END_REF], given in supplementary material S4. F3

(varying from 0 to 1) was obtained from

, where ^O ® (eq.14) was the maximum value of the biomass indicator at the time of annual crop harvest. At the end of each day iteration, the daily production ( ) was added to • , the hortonian surface store:

River outflow

• ' ( ) and • ( ) and • ( ) stores are subject to losses or transfer delays described by first-order kinetics (Arnold and Fohrer,2005). Daily drainage losses ' ( ) directed to the external aquifer not included in the catchment balance were given by ' ( ) = • ' ( -1)(1l 7 ‡ 6 ¯ ), leading to:

Outputs from hortonian • ( ) or saturation • ( ) overflows directed to river segments were obtained from :

respectively. Transfer delays linked to the internal aquifer seeping into river segments were modeled considering long restitution periods . Following [START_REF] Hingray | Hydrologie, 2. Une science pour l'ingénieur[END_REF], seepage • ' " was given by calculating:

Following [START_REF] Gurnell | The dynamics of a drainage network[END_REF], the number of river segments (cells connected to the outlet) G was given by the rounded value:

where °; was the maximum number of river cells, V a shape parameter, =/^ the previous pluviometric index

and =/^ W the maximum pluviometric index (F = F W ).

The river outflow ³ [m 3 .s -1 ] transferred to the catchment outlet was obtained by calculating:

where was the dimension of a cell [m], ½ the number of impervious cells in urban areas, and ( ) rainfall.

Appendix B: SSMT model formulation

We will successively consider particle build-up, wash-off and sink-source effects, i.e., biophysical processes contributing to particle mobilization, extinction or withdrawal. To save Appendix A). Depending on their nature, particle stocks are not equally available for all water components. Except for surface flows where N, P, EC and SM can potentially be displaced from upstream to downstream cells, particle displacement by subsurface flows was restricted to N and soluble P, and only to N particles in the deepest water tables. The aim was to account for trapping and filtering effects acting on EC and SM [START_REF] Muirhead | Numbers and transported state of Escherichia coli in runoff direct from fresh cowpats under simulated rainfall[END_REF][START_REF] Dorioz | The effect of grass buffer strips on phosphorus dynamics. A critical review and synthesis as a basis for application in agricultural landscapes in France[END_REF] and for lower soluble P adsorption onto organic matter-enriched environments such as topsoils [START_REF] Jarvie | Role of river bed sediments as sources and sinks of phosphorus across two major eutrophic UK river basins: the Hampshire Avon and Herefordshire Wye[END_REF]. The stock distributions of the different hortonian runoff ℎ % ( ), VSA runoff ℎ % ( ), subsurface % ( ) and drainage % ( ) flows were calculated considering their respective proportions. For example:

gave the amount of particles available for hortonian runoff $ % ( ).

Particle wash-off

During the transfer period = (0, … , ) and referring to salt redistribution [START_REF] Burns | A model for predicting the redistribution of salts applied to fallow soils after excess rainfall orevaporation[END_REF] or soil-water relationships [START_REF] Holzbecher | Environmental Modeling using MATLAB[END_REF], we considered a generalized formulation of the ' % ( -) wash-off:

where ` was a mobility coefficient for particulate or solute matters, ℎ % ( -) a water flow component, e the half of soil depth in case of solutes (equals to one otherwise).

Sinks-sources

The store of particles was updated throughout the transfer period. Sink effects were considered:

where, if suited to particle nature, k % ( ) was the net assimilation rate (the balance between daily mineralization and daily assimilation), % ( ) denitrification and & ( ) mortality.

The production function G % ( -) of particles available to down-slope transfer was obtained by calculating:

giving the amount of particles originating from cell & and transferred during steps to downslope cells & + 1 , where if suited to particle nature, e % ( ) was retention and l % ( ) an additional wash-off source.

Daily assimilation rates k % ( ) of N and P were estimated considering the length of plant development phases. De-nitrification losses % ( ) were accounted for when soil moisture exceeded the field-capacity threshold [START_REF] Nicolardot | La dynamique de l'azote dans les sols cultivés. in Maîtrise de l'azote dans les agrosystèmes[END_REF]. Following COMIFER (2013), they were evaluated by calculating % ( ) = T $ % À ( -) where T is a de-nitrification constant and $ % À ( -) the initial N store, respectively. EC decay & ( ) was accounted for during the growth and maturity phases of plant development from experimental counts of EC populations on meadow canopies following manure application (Trevisan et al., 2002). Particles from SM production G % gh ( -) were retained when overland flows crossed filtering infrastructures.

Based on experimental data obtained by [START_REF] Trévisan | Bandes herbeuses et lutte contre la pollution diffuse agricole. critère d'efficacité et conditions d'implantation[END_REF], we applied a first-order