domain: phys sde

text:
ENGEES Cécile Choley
email: cecile.choley@inria.fr

Pascal Finaud-Guyot
email: pascal.finaud-guyot@umontpellier.fr

Pierre-André Garambois
email: pierre-andre.garambois@inrae.fr

Robert Mose
email: mose@unistra.fr

An effective urban flood model accounting for street-building exchanges AN EFFECTIVE URBAN FLOOD MODEL ACCOUNTING FOR STREET-BUILDING EXCHANGES

Keywords: Flooding management, Numerical model, Shallow water equations, Street-building exchanges model

Floods in cities are a worrying phenomenon as cities concentrate a growing population and activity and are expected to increase in both intensity and frequency in the context of climate change. Flood management provided by public services relies especially on 2D models that do not consider the potential street-building exchanges, considering buildings to be waterproof. A new model is proposed to represent each building as a mass conservation law and an additional source term in the classical 2D shallow water equations. A synthetic test case, with a channel and 200 buildings, shows that the buildings lead to a reduction of both the discharge (30%) and the water depth (18%) peaks in the street and generate a lag time in their time evolution. The interest of the proposed model is highlighted on the modeling of the Richelieu district (Nîmes, France): street-building exchanges impact significantly (up to 0.6 m and 1 m/s) the street hydrodynamics. The water level modifications are generalized in the synthetic case whereas they are more localized in the real-world simulation. Moreover, the model simulates the building water depth allowing for the determination of the maximal level and the submersion duration. These new results pave the way to new information for flood damage analysis and operational management.

INTRODUCTION

Floods are among the most frequent and serious natural disasters and are expected to increase in both intensity and frequency due to climate change. According to the World Bank, 29% of the world population is at risk of a 100 years return period flood. By 2050, cities could concentrate 68% of the global population [START_REF]World Urbanization Prospects: The 2018 Revision (ST/ESA/SER.A/420)[END_REF] and floods in urban areas are thus of major interest.

Public services are facing an increasing necessity for numerical models to simulate urban floods with accuracy. With the aim of developing and validating innovative numerical approaches, many experimental studies of urban flood processes have been performed over the last 15 years. These works cover urban flooding processes at various scales: from a single crossroad [START_REF] Mignot | Impact of topographic obstacles on the discharge distribution in open-channel bifurcations[END_REF] or manhole [START_REF] Beg | Effect of surcharge on gully-manhole flow[END_REF], to a whole street with several inlet and overflow exchange structures [START_REF] Bazin | Modeling Flow Exchanges between a Street and an Underground Drainage Pipe during Urban Floods[END_REF] and finally to more global urban districts 1 Corresponding author SimHydro 2021: Models for complex and global water issues -Practices and expectations [START_REF] Paquier | Estimation des niveaux d'inondation pour une crue éclair en milieu urbain : comparaison de deux modèles hydrodynamiques sur la crue de Nîmes d'octobre 1988[END_REF][START_REF] Park | Tsunami inundation modeling in constructed environments: A physical and numerical comparison of free-surface elevation, velocity, and momentum flux[END_REF][START_REF] Schubert | Building treatments for urban flood inundation models and implications for predictive skill and modeling efficiency[END_REF] June 2021, Sophia Antipolis -Choley, C., Finaud-Guyot, P., Garambois, P.A., & Mose, R. -An effective urban flood model accounting for street-building exchanges [START_REF] Smith | A comprehensive urban flood-plain dataset for model benchmarking[END_REF][START_REF] Testa | Flashflood flow experiment in a simplified urban district[END_REF]. Experiments of urban districts are all based on a flooded street level where the flow invades the streets around the buildings and the building blocks [START_REF] Finaud-Guyot | Experimental insight for flood flow repartition in urban areas[END_REF]. Nevertheless, some advanced experiments consider additional flow paths such as the invasion of underground volumes (malls, metro, parking...) [START_REF] Ishigaki | Hydraulic model tests of inundation in urban area with underground space[END_REF], the river flow over-topping towards an urban area [START_REF] Larocque | Experiments on Urban Flooding Caused by a Levee Breach[END_REF], the rain falling directly on the roofs [START_REF] Cea | Experimental validation of two-dimensional depthaveraged models for forecasting rainfall-runoff from precipitation data in urban areas[END_REF] or tsunami waves invading a coastal city [START_REF] Park | Tsunami inundation modeling in constructed environments: A physical and numerical comparison of free-surface elevation, velocity, and momentum flux[END_REF].

To our best knowledge, few experiments consider water intrusion within buildings: [START_REF] Zhou | Experimental Assessment of Building Blockage Effects in a Simplified Urban District[END_REF] studies the intrusion effect of the hydrodynamic characteristic within the streets, [START_REF] Sturm | Experimental measurements of flood-induced impact forces on exposed elements[END_REF] investigates the effect of the building opening on the resultant forces due to flooding. [START_REF] Mignot | Measuring the flow intrusion towards building areas during urban floods: Impact of the obstacles located in the streets and on the façade[END_REF] provides lab experiments for a single building along a synthetic channel and a theoretical laws comparison for the discharge entering the building through one opening only similar to a door or a window. None of these works could however measure or even describe the discharge entering the buildings.

Classical practices for urban flood modeling consider the buildings as full or partial obstruction to the flow [START_REF] Schubert | Building treatments for urban flood inundation models and implications for predictive skill and modeling efficiency[END_REF] but neglect in any case the street-building flow exchanges [START_REF] Syme | Flooding in Urban Areas -2d Modelling Approaches for Buildings and Fences[END_REF] although these exchanges can (i) create a flood retention within blocks and potential reduction of the peak discharge [START_REF] Gems | 3-D hydrodynamic modelling of flood impacts on a building and indoor flooding processes[END_REF], (ii) produce secondary connection between streets through blocks and (iii) explain most part of the damage at the building scale [START_REF] Sturm | Experimental measurements of flood-induced impact forces on exposed elements[END_REF][START_REF] Cepri | Guide Le bâtiment face à l'inondation[END_REF]. The lack of models to represent such phenomenon, coherent with an operational application, obliges, for classical approaches on risk management and characterization, to assume that the water level inside the building is the same as in the outside immediate neighboring area. This paper presents a new modeling approach accounting for the street-building exchanges during a flood event and investigates the potentiality of such model for operational purposes. The model is presented in the first section while the second focuses on model evaluation in both synthetic and real like test cases. The last section proposes concluding remarks and perspectives.

MODEL PRESENTATION

The proposed model is based on a 2D representation of the flow within the streets coupled to a reservoir model to represent buildings (inspired form models with lockers); the coupling between the street and the building is represented by different openings. Each building can be connected to several openings pointing to different cells (representing the street). Conversely, a computational cell can be connected to several openings and buildings. The buildings are defined by their area 𝑆 𝑏𝑢𝑖𝑙𝑑𝑖𝑛𝑔 and their bottom elevation 𝑧 𝑏,𝑏𝑢𝑖𝑙𝑑𝑖𝑛𝑔 ; the geometry of each opening is rectangular (width: 𝑤 𝑜𝑝𝑒𝑛𝑖𝑛𝑔 ). The evolution of the water depth within a building ℎ 𝑏𝑢𝑖𝑙𝑑𝑖𝑛𝑔 is represented with a storage law:

𝑑ℎ 𝑏𝑢𝑖𝑙𝑑𝑖𝑛𝑔 𝑑𝑡 = ∑ 𝑄 𝑖 𝑖∈𝑁 𝑆 𝑏𝑢𝑖𝑙𝑑𝑖𝑛𝑔 (1)
where 𝑡 is the time, 𝑄 𝑖 is the discharge through the opening 𝑖 and 𝑁 is the set of openings connected to the building.

Using a mass and momentum balance over a control volume within the street, the flows are modeled with the classical 2D shallow water equations:

𝜕𝑼 𝜕𝑡 + 𝜕𝑭 𝜕𝑥 + 𝜕𝑮 𝜕𝑦 = 𝑺 -𝑩 (2a) 𝑼 = [ ℎ 𝑞 𝑟 ] ; 𝑭 = [ 𝑞 𝑞 2 ℎ + 1 2 𝑔ℎ 2 𝑞𝑟 ℎ ] ; 𝑮 = [ 𝑟 𝑞𝑟 ℎ 𝑟 2 ℎ + 1 2 𝑔ℎ 2 ] ; 𝑺 = [ 0 𝑔ℎ(𝑆 0,𝑥 -𝑆 𝑓,𝑥 ) 𝑔ℎ(𝑆 0,𝑦 -𝑆 𝑓,𝑦 ) ] ; 𝑩 = [ 𝑞 𝑏 𝛼 𝑥 𝑞 𝑏 𝛼 𝑦 𝑞 𝑏 ] (2b)
where 𝑥 and 𝑦 stand for the space coordinates, ℎ is the water depth, 𝑔 represents the gravitational acceleration, 𝑞 (resp. 𝑟) is the unit-discharge component in the 𝑥 (resp. 𝑦) direction. 𝑆 0,𝑋 = 𝜕𝑧 𝑏 /𝜕𝑋 (resp. 𝑆 𝑓,𝑋 ) is the bottom (resp. energy line) slope in the 𝑋-direction (𝑋 = {𝑥, 𝑦}); 𝑧 𝑏 is the bottom elevation (also denoted as 𝑧 𝑏,𝑠𝑡𝑟𝑒𝑒𝑡 to avoid confusion with the building bottom elevation). 𝑆 𝑓,𝑋 is classically estimated using the Strickler formulae:

where 𝐾 𝑋 and u X are respectively the Strickler coefficient and the flow velocity in the 𝑋-direction.

In the shallow water equations, the additional source term 𝐁 is developed to account for local mass (first line of (2b)) and momentum balance (second and third lines of (2b)) modification in the street due to street-building exchanges. The unit-discharge 𝑞 𝐵 is defined as:

𝑞 𝑏 = ∑ 𝑄 𝑖 𝑆 ( 4
)
where S is the area of the volume of control. 𝛼 𝑥 and 𝛼 𝑦 account for the effect of the street-building exchanges on the momentum balance in the street:

𝛼 𝑥 = 𝑞 ℎ ; 𝛼 𝑦 = 𝑟 ℎ if 𝑞 𝑏 > 0 (5a)
𝛼 𝑥 = 𝛼 𝑦 = 0 if 𝑞 𝑏 ≤ 0 (5b) When 𝑞 𝑏 > 0, the momentum in the volume of water leaving the street is taken out accordingly. Conversely, when 𝑞 𝑏 < 0, immobile water (with thus no momentum) is added to the street. This leads to an unmodified momentum while reducing the flow velocity.

The opening discharge is estimated using a classical weir law based on the geometry and both hydrodynamics in the street and in the building (Figure 1) depending on the regime [START_REF] Cunge | Practical aspects of computational river hydraulics[END_REF][START_REF] Mahmood | Unsteady Q (m3/s) in open channels[END_REF]. 𝑧 𝑠𝑡𝑟𝑒𝑒𝑡 and 𝑧 𝑏𝑢𝑖𝑙𝑑𝑖𝑛𝑔 define the upstream and the downstream sides of the weir: the upstream being the side for which the free surface elevation is the higher at the beginning of the timestep.

𝑄 𝑖 = 𝐶 𝑑 𝑤 𝑜𝑝𝑒𝑛𝑖𝑛𝑔 √2𝑔ℎ 1 3 2 if ℎ 2 ≤ 2 3 ℎ 1 (6a) 𝑄 𝑖 = 3√3 2 𝐶 𝑑 𝑤 𝑜𝑝𝑒𝑛𝑖𝑛𝑔 √2𝑔ℎ 2 (ℎ 1 -ℎ 2 ) 1 2 if ℎ 2 > 2 3 ℎ 1 (6b)
where ℎ 1 = max(ℎ 𝑤,𝑠𝑡𝑟𝑒𝑒𝑡 ; ℎ 𝑤,𝑏𝑢𝑖𝑙𝑑𝑖𝑛𝑔 ) and ℎ 2 = min(ℎ 𝑤,𝑠𝑡𝑟𝑒𝑒𝑡 ; ℎ 𝑤,𝑏𝑢𝑖𝑙𝑑𝑖𝑛𝑔 ) are respectively the water depth above the weir crest on the upstream and downstream side and 𝐶 𝑑 is a discharge coefficient.

The first (resp. second) line of (6) corresponds to the unsubmerged (resp. submerged) case. By convention, 𝑄 𝑖 is positive when the street is filling up the building (𝑧 𝑠𝑡𝑟𝑒𝑒𝑡 > 𝑧 𝑏𝑢𝑖𝑙𝑑𝑖𝑛𝑔 ) and negative when the building is emptying (𝑧 𝑠𝑡𝑟𝑒𝑒𝑡 < 𝑧 𝑏𝑢𝑖𝑙𝑑𝑖𝑛𝑔 ). For the sake of clarity, the grey lines represent the building walls and roof but are currently not accounted in the street-building model.

The street-building exchanges model is implemented in the sw2d model 2 . Equations ( 1) and ( 2) are discretized using an explicit finite volume scheme. The source terms are solved using a classical time splitting method: the hyperbolic part of equation ( 2) and the bottom source terms are solved in a first time; the friction and building source terms are then calculated separately. The ability of the proposed model to represent the flood dynamics in both the street and the buildings is assessed against two test cases. The first case presents a synthetic configuration to evaluate the potential effect of accounting the street-building exchanges. The comparison is then performed on a real-like test case based on the 1988 flood in Nîmes (France). A validation against several analytical test cases has been realized in simple configurations but is not presented here for the sake of simplicity.

TEST CASES

Idealized street-building exchanges test case

Presentation of the synthetic test case

The synthetic test case evaluates the effect of the street-building exchanges on the flood propagation in a simple 15 𝑚 width channel. An imposed hydrograph is injected at the upstream end (Figure 2). The channel is 5000 𝑚 long and the duration is long enough (30000 𝑠) to ensure that the flow reaches the end of the channel. The downstream boundary condition imposes a Froude number equal to 1. The channel (i.e. the street) is meshed using a 1D-like approach: the cell width is equal to the channel width and the longitudinal discretization is 𝑑𝑥 = 5 𝑚. Dry initial conditions and uniform Strickler coefficient are set (K = 40 𝑚 1/3 . s -1 ).

For the simulation with buildings, 200 identical idealized buildings are equally distributed along the channel (1 building every 10 𝑚 i.e. 1 building every 2 cells). Each building has a 100 𝑚² area. The first building is linked to the first cell (from 𝑥 = 0 to 5 𝑚) and the last one is connected to the cell number 399 th located between 𝑥 = 1990 to 1995 𝑚. For the sake of simplicity, the same opening is used to connect each building to the corresponding cell. Classical dimensions for a door are used for the width 𝑤 𝑜𝑝𝑒𝑛𝑖𝑛𝑔 = 0.9 𝑚. The bottom elevation is identical in the building and in the street (𝑧 𝑏,𝑠𝑡𝑟𝑒𝑒𝑡 = 𝑧 𝑏,𝑏𝑢𝑖𝑙𝑑𝑖𝑛𝑔 ) and no step separate the building from the street (𝑧 𝑤𝑒𝑖𝑟 = 𝑧 𝑏,𝑠𝑡𝑟𝑒𝑒𝑡 ). An arbitrary but classical discharge coefficient 𝐶 𝑑 = 0.42 is used.

Buildings effect in the street

Figure 2a compares, at different locations, the discharge and the water level evolution in time with and without buildings. For both simulations, the maximal simulated variable (either street discharge or water depth) decreases along the street direction due to the natural flood spreading. For every location, accounting for the street-building exchanges lead to a reduction of both the maximal discharge and water level compared to the reference simulation without buildings. At 𝑥 = 2000 𝑚 (corresponding to the end of the buildings area), the reduction reaches 30% of the discharge and 18% for the water depth. Furthermore, the peaks of discharge and water depth are delayed for the simulation with buildings; the delay increases with the distance. At 𝑥 = 2000 m, the peak appears around 1000 𝑠 later for the discharge and 2500 𝑠 later for the water depth. Accounting for the buildings effect in a flood propagation model thus leads to a significant modification of the street hydrodynamics. Interestingly, after 16000 𝑠 (end of the discharge injection at the inlet) the water levels and discharge curves converge and decrease slowly together, which can be related to the time for which the upstream discharge becomes nil.

Figure 2b

presents the water depth along the street. The black and purple dotted lines correspond to the maximal water depth over the whole simulation with and without buildings. The water depths gap between the two simulations increases from the inlet to 𝑥 = 2000 𝑚 (corresponding to the end of the buildings area) and then decreases while going downstream. This highlights the cumulative effect of the buildings on the flood propagation. Figure 2b also shows the flowlines for the configuration with building at different times. For 𝑡 > 16000 𝑠 (end of the discharge injection at the inlet), the water levels are barely homogeneous for 𝑥 < 2000 𝑚. Indeed, the difference between the maximal and minimal water depths represents 8 𝑐𝑚 for 𝑡 = 16000 𝑠 and is reduced around 4 𝑐𝑚 for 𝑡 = 19000 𝑠. In the meantime, the velocity does not exceed 0.2 𝑚/𝑠. This phenomenon is due to the nil discharge at the upstream end that acts an impervious boundary for 𝑡 > 16000 𝑠. Moreover, at 19000 𝑠, the flow reaches the downstream end of the channel and thus the flow is influenced by the downstream boundary condition. The following analysis concerning the buildings are thus carried out for 𝑡 < 16000 𝑠, ensuring that the analysis is not influenced by the downstream boundary condition.

Buildings water depth

Figure 3a compares for several building the water depth evolution for 𝑡 < 16000 𝑠. The maximal water depth within the building reaches 1.2 𝑚 for the 1 st building (close to the inlet) and is reduced to 0.8 𝑚 for the last building. This reduction of the maximal water depth along the street axis is similar in the building and in the street (Figure 2b). The position of the building thus plays a significant role on the maximal water level reached during a flood event. Interestingly, the last building (building 200, x = 1995 𝑚) has the steepest slope during its filling, which suggests the fastest filling speed. Each building is linked to a single computational cell. Thus, it is possible to calculate the ratio 𝑟(𝑡) of the water depth in the building and the street for the buildings for each (stored) computational time:

𝑟(𝑡) = ℎ 𝑏𝑢𝑖𝑙𝑑𝑖𝑛𝑔 (𝑡)/ℎ 𝑠𝑡𝑟𝑒𝑒𝑡 (𝑡) (7) When ℎ 𝑠𝑡𝑟𝑒𝑒𝑡 = 0 or ℎ 𝑏𝑢𝑖𝑑𝑙𝑖𝑛𝑔 = 0, 𝑟 is not computed. 𝑟̃𝑖 represents the 𝑖 𝑡ℎ value of 𝑟, the sorted chronicle of r. Since the storing time is constant, 𝑖/𝑁 (N the number of values in the chronicle) corresponds to the percentage of simulation time the ratio is smaller than 𝑟̃𝑖. Figure 3b presents 𝑟̃ for some single openings for 𝑡 < 16000 𝑠. Considering the most left blue curve (building 1, 𝑥 = 5 𝑚), 𝑟̃ = 0.8 for 𝑡 = 0.02; this indicates that the difference ℎ 𝑠𝑡𝑟𝑒𝑒𝑡 -ℎ 𝑏𝑢𝑖𝑙𝑑𝑖𝑛𝑔 is bigger than (1 -0.8) * ℎ 𝑠𝑡𝑟𝑒𝑒𝑡 = 0.2 * ℎ 𝑠𝑡𝑟𝑒𝑒𝑡 only 2% of the plotted time (here 16000 𝑠). This difference appears to be SimHydro 2021: Models for complex and global water issues -Practices and expectations [START_REF] Paquier | Estimation des niveaux d'inondation pour une crue éclair en milieu urbain : comparaison de deux modèles hydrodynamiques sur la crue de Nîmes d'octobre 1988[END_REF][START_REF] Park | Tsunami inundation modeling in constructed environments: A physical and numerical comparison of free-surface elevation, velocity, and momentum flux[END_REF][START_REF] Schubert | Building treatments for urban flood inundation models and implications for predictive skill and modeling efficiency[END_REF] June 2021, Sophia Antipolis -Choley, C., Finaud-Guyot, P., Garambois, P.A., & Mose, R. -An effective urban flood model accounting for street-building exchanges significant only 7% of the time which indicates that the street and buildings have mostly the same water depth: ℎ 𝑏𝑢𝑖𝑙𝑑𝑖𝑛𝑔 = ℎ 𝑠𝑡𝑟𝑒𝑒𝑡 93% of the time. The difference is significative only during the beginning of the simulation that corresponds to the filling of the buildings. This very low dephasing between the street and the building water depth highlights the high conveyance of the openings; smaller conveyance should lead to more significative differences between the street and the building. The global curve on Figure 3b represents 𝑟̃ based on the values of 𝑟(𝑡) for all the openings together. The spreading around the global curve indicates the variety of the building hydrodynamics around the district average hydrodynamics.

Real configuration: Richelieu district in Nîmes, France

Richelieu description

The city of Nîmes (France) has suffered from a significant flooding on the 3 rd of October 1988 with a return-period estimated between 150 and 250 years [START_REF] Desbordes | Inondations sur Nîmes et sa région[END_REF]. The Richelieu district was particularly impacted with water depths of up to 3 𝑚 in the streets. The present study aims to assess the interest of the proposed street-building model; the comparison will focus on the street hydrodynamics and the characterization of the building flooding.

For the sake of simplicity and to reduce the simulation time, the computational domain is limited to a subpart of the Richelieu district limited by the streets Faïta, Sully and Semard (Figure 4a). In this zone, the streets network is rather simple with intersections with an angle of barely 90°. The average slope is oriented from North to South and reaches 1%. The simulation domain is included in the whole Nîmes modeling constructed by INRAE 3 [START_REF] Paquier | Estimation des niveaux d'inondation pour une crue éclair en milieu urbain : comparaison de deux modèles hydrodynamiques sur la crue de Nîmes d'octobre 1988[END_REF] that is thus used to provide the boundary conditions.

Modeling of the street networks

The streets network is extracted from the BD TOPO® (2020-12-15) and the 5 𝑚 DEM of the Gard department from the RGE ALTI® (2020-02-13) both from the French National Geographical Institute. The mesh is built such as having one to three cells of the street width (Figure 4).

The hydraulics conditions modeled by INRAE at the limits of the considered domain are set as boundary conditions. Upstream, the discharge is injected either at the upstream end of streets Sully and Vincent Faïta or at the connection between the Vincent Faïta street and those coming from the North. At the peak of the flood, the total injected discharge is 176 𝑚 3 . 𝑠 -1 with up to 92 𝑚 3 . 𝑠 -1 in the Sully street and 47 𝑚 3 . 𝑠 -1 in the Faïta street. At the downstream end, the free surface elevations computed by the INRAE modeling are imposed at the limits corresponding to an outlet street. They vary in the range of [0.46 𝑚 1.77 𝑚]. The simulation lasts 55000 𝑠. For the friction, as in the INRAE model, a uniform Strickler coefficient 𝐾 = 40 m 1/3 . s -1 is applied [START_REF] Mignot | Etude expérimentale et numérique de l'inondation d'une zone urbanisée : cas des écoulements dans les carrefours en croix[END_REF].

Building data

The building limits are defined from the BD TOPO® thus allowing to compute their area 𝑆 𝑏𝑢𝑖𝑙𝑑𝑖𝑛𝑔 . For the sake of simplicity and due to the lack of data regarding the connections between buildings, only the ones directly along the street network are considered. Each building bottom elevation 𝑧 𝑏,𝑏𝑢𝑖𝑙𝑑𝑖𝑛𝑔 is computed as the mean elevation of the 5 𝑚 DEM from the RGE ALTI® within the building limits plus 0.19 𝑚 to account for the door elevation (see next paragraph). With this approximation, 50% of the buildings are 0.19 𝑚 above the street bottom elevation. Over the range of the modeled buildings, the bottom elevation 𝑧 𝑏,𝑏𝑢𝑖𝑙𝑑𝑖𝑛𝑔 -𝑧 𝑏,𝑠𝑡𝑟𝑒𝑒𝑡 lies in the range [-42 𝑐𝑚; 64 𝑐𝑚]. This suggests that for some buildings, the different rooms should have been modeled for a better representation of the storage capacity.

The INRAE field survey on doors and windows of the Catinat Street is used to characterize the modeled building openings. Based on 58 buildings (including 46 buildings in the simulated domain), the average dimensions have been determined (Table 1). The variability of the openings' height, width and elevation above the street ground is quite important. For the sake of simplicity, the same opening 3 'Institut national de recherche pour l'agriculture, l'alimentation et l'environnement SimHydro 2021: Models for complex and global water issues -Practices and expectations [START_REF] Paquier | Estimation des niveaux d'inondation pour une crue éclair en milieu urbain : comparaison de deux modèles hydrodynamiques sur la crue de Nîmes d'octobre 1988[END_REF][START_REF] Park | Tsunami inundation modeling in constructed environments: A physical and numerical comparison of free-surface elevation, velocity, and momentum flux[END_REF][START_REF] Schubert | Building treatments for urban flood inundation models and implications for predictive skill and modeling efficiency[END_REF] June 2021, Sophia Antipolis -Choley, C., Finaud-Guyot, P., Garambois, P.A., & Mose, R. -An effective urban flood model accounting for street-building exchanges elevation is considered corresponding to the average field height and elevation above the street ground (𝑧 𝑤𝑒𝑖𝑟 -𝑧 𝑏,𝑠𝑡𝑟𝑒𝑒𝑡 ).

Due to the lack of information on the precise location of the real openings, the assumption is used that each building wall (adjacent to the street) includes one single door and one single window. Each opening has the same weir height corresponding to the average dimension determined from the field survey. To account for the wall lengths variability, each opening width 𝑤 ′ is computed as: 𝑤′ = 𝐿 𝑤𝑎𝑙𝑙 × 𝑛 𝑜𝑝𝑒𝑛𝑖𝑛𝑔 × 𝑤 𝑜𝑝𝑒𝑛𝑖𝑛𝑔 (8) where 𝐿 𝑤𝑎𝑙𝑙 is the length of the wall of the building adjacent to the street; 𝑛 𝑜𝑝𝑒𝑛𝑖𝑛𝑔 and 𝑤 𝑜𝑝𝑒𝑛𝑖𝑛𝑔 are the mean number of openings per building façade length and the mean opening width that has been estimated thanks to the field survey as defined in Table 1.

Effects of buildings on the streets water depth

Simulations without and with buildings are run; variables with subscript ℎ 𝑏𝑢𝑖𝑙𝑑𝑖𝑛𝑔 (resp. ℎ 𝑟𝑒𝑓 ) correspond to the simulation with (resp. without) buildings. Figure 4a compares the maximal water depths in the two simulations: max(ℎ 𝑏𝑢𝑖𝑙𝑑𝑖𝑛𝑔 ) -max(ℎ 𝑟𝑒𝑓 ). The difference of the maximal computed water depths is in the range [-0.4 𝑚; 0.6 𝑚] highlighting that the street-building exchanges can be important to characterize the flood risk within the streets. The buildings lead to a reduction (right cells on Figure 4a) of the maximal water depth in the upstream (V. Faïta and Sully) streets and an increase (blue cells on Figure 4a) in the North-South streets and around the crossroad between the streets Richelieu and Catinat. This might suggest that the buildings modify the discharge partition between the inside of the district and the surrounding streets.

Figure 4b

compares the maximum difference of the water depth at each time: max(ℎ 𝑏𝑢𝑖𝑙𝑑𝑖𝑛𝑔ℎ 𝑟𝑒𝑓 ). Over the flood duration, the difference between the simulated water depth is in the range [-0.6 𝑚; 0.8 𝑚] which is bigger than the difference on the maximal water depth. This indicates that the maximal differences are not reached at the flood peak but rather during the rising or the falling limb. The distribution of the differences between the maximal value and the maximal difference along the simulation are globally coherent even if some inversions can be identified (see for instance the western part of the Richelieu street). Moreover, during the simulation, some significant differences occur while the maximal value are identical in both simulations (see for instance the P. Semard street). Similar analysis on the norm of the velocity vector (not presented here for the sake of concision) highlight that the modelled velocity differs up to 1.3 𝑚/𝑠; either positively or negatively. The comparison of both simulations highlights that the hydrodynamics can be significantly modified while accounting for the street-building exchanges.

Maximal water depth distribution

The maximal water depths simulated in the buildings and in the streets are presented in Figure 5. The maximal water depth is up to 3.5 𝑚 which is coherent with what is known from the 1988 event. The North area is the most impacted. 9 over 438 simulated buildings are not flooded over the whole event (water depth = 0 𝑚). The maximal water depth pattern in the buildings is globally coherent with the street distribution. However, significant differences can be highlighted for some buildings which might be explained by the gap between the bottom elevation of the building and the corresponding street (see section 3.2.3). The classical approach assuming the maximal water level in the building corresponds to the maximal free surface elevation [START_REF] Eleuterio | Flood risk analysis: impact of uncertainty in hazard modelling and vulnerability assessments on damage estimations[END_REF] appears here to be valid.

Buildings water depths evolution

Each opening is associated to a surface elevation in the street and in the building. d(t) represents the surface elevation difference between both: 𝑑(𝑡) = 𝑧 𝑠𝑡𝑟𝑒𝑒𝑡 (𝑡) -𝑧 𝑏𝑢𝑖𝑙𝑑𝑖𝑛𝑔 (𝑡) (9) Figure 6a shows the surface elevation difference for two openings in red and blue that reach the extremum values: the blue line achieves the maximum difference during the simulation and the red one the minimum. For the red line, 50% of the time the surface elevation in the building is greater than 0.5 𝑚 above the one in the street. The blue line shows that the surface elevations are equals 15% of the time and for the rest, the surface elevation in the street is higher than the one in the building. These variable tendencies are possible because a building can have several openings connected to different mesh of the street, each mesh having its own bottom elevations. Thus, the results depend on the opening through which the surface elevations are observed (a building can be filled more quickly than it is drained and conversely) and on the bottom elevation difference of the building and the associated mesh. The bold black curve represents d for all the 1302 openings together. 60% of the time, the difference is nil, which means that the surface elevation of the building and the street are equals. The rest of the time is equally divided between the two possible cases: either the surface elevation in the street is above the one in the building and conversely. The maximum value is up to 1.16 𝑚 and the minimum reaches -0.76 𝑚.

Figure 6b presents the cumulative curve of the submersion duration over the modelled buildings.

A building is considered as flooded when the simulated water depth is positive. Interestingly, only a few buildings (26 over the 438 simulated buildings) are flooded for less than 6 ℎ and 50% of the buildings are flooded for more than 10 ℎ. The spatial distribution of the duration should be characterized and related to the street geometry and building parameters and especially the location within the district (i.e. the vicinity to the inlet) and the number and conveyance of the openings. Moreover, except for the gap from 10 to 12 ℎ, the trend appears to be quite similar. Further study should be investigated and try to confirm this particular feature.

CONCLUSION

Numerical models are frequently used to characterize and forecast flood impact especially in urban areas. In classical 2D approaches, the street-building exchanges remains neglected despite evidences from flood event feedbacks. The present paper proposes a new 2D modelling approach allowing to consider the exchanges between street and building during urban flood. Building water depth is modeled using a classical mass conservation law while opening discharge is represented with a weir law. This new model enables to compute both the street hydrodynamics using the 2D shallow water equations and the water depth evolution in buildings.

This model is validated against both an idealized urban test case and a real-world configuration representing the Richelieu district (Nîmes, France). Comparing the results with and without buildings allow to highlight their effect on the street flow. Accounting for the street-building exchanges lead to a significant modification of the street hydrodynamics. Over the range of the tested configurations, the street water is either increase or decrease of up to 60 𝑐𝑚. Subsequently, the flow velocity norm is modified of 1 𝑚/𝑠. Interestingly, the street depth modification is generalized in the idealized test case and more localized in the real-world simulation. These configuration-dependent effects pave the way to a wider study to be able to predict in which configuration the street-building exchanges play a significant role.

In the buildings, the modelling of the water depth evolution provides a new valuable information. Over the range of the tested configurations, several building patterns have been identified. In the idealized test case, the building water depth followed closely the street evolution highlighting the importance of the opening conveyance. In the Richelieu district simulation, the variability of the building flooding duration shows the interest of the proposed model to better characterize the flood impacts on the buildings and thus the potential damages. Moreover, the comparison of the free surface elevation in both the building and the linked street highlights significant differences (either positive or negative) occurring up to 60% of the flood duration. This information on the building dynamics might be of prime interest for flood damages and safety study.

The present work provides a relevant tool to better study the influence of the street-building exchange during an urban flood event. This preliminary work should be deepened by a sensitivity analysis on the discharge computation. Indeed, the present analysis is based on a simple weir law that might not be representative for some configurations highlighted in the real-world test case for which the free surface elevation reaches the top of the opening. The sensitivity analysis should also focus on the parameters of the opening laws. The Richelieu test case also pointed out the problematic of the representation of the buildings. The available data concerning the topography within the building (bottom elevation, room organization and connectivity) is currently not available at a large scale. The sensitivity of the results to this information should also be investigated, either to state in which measure they can be roughly described or to identify a requirement of new types of data. Finally, an interdisciplinary study on flood damages and safety estimation can be based on the proposed model.

Figure 1 :

 1 Figure 1: Schematic representation of the street-building exchanges in the transverse direction to the street axis.For the sake of clarity, the grey lines represent the building walls and roof but are currently not accounted in the street-building model.

Figure 2 :

 2 Figure 2: Comparison of the street hydrodynamics with and without buildings. a: Discharge and water depth at different locations; b: Water depth along the channel at different time t (reference: simulation without any building, max: maximum water depth).

Figure 3 :

 3 Figure 3: Characterization of the hydrodynamics inside buildings (legend: building number and position). a: Water level evolution in time; b: Building and street water depth ratio.

  width (m) 𝑤 𝑜𝑝𝑒𝑛𝑖𝑛𝑔 weir height (m) 𝑧 𝑤𝑒𝑖𝑟 -𝑧 𝑏,𝑠𝑡𝑟𝑒𝑒𝑡 Number of openings per unit length (m -1 )

SimHydro 2021 :Figure 4 :

 20214 Figure 4: Comparison of the water depth computed in the streets with and without buildings. a: Difference of the maximal water depth (max(ℎ 𝑏𝑢𝑖𝑙𝑑𝑖𝑛𝑔 ) -max(ℎ 𝑟𝑒𝑓 )); b: Maximal difference (max(ℎ 𝑏𝑢𝑖𝑙𝑑𝑖𝑛𝑔 -ℎ 𝑟𝑒𝑓 ).

SimHydro 2021 :Figure 5 :

 20215 Figure 5: Maximal water depth in the streets and in the buildings.

SimHydro 2021 :Figure 6 :

 20216 Figure 6: Contributions of the model for economic perspectives. a: Building and street water surface elevation difference (m); b: Submersion duration (h).

SimHydro 2021 :

 2021 Models for complex and global water issues -Practices and expectations 16-18 June 2021, Sophia Antipolis -Choley, C., Finaud-Guyot, P., Garambois, P.A., & Mose, R. -An effective urban flood model accounting for street-building exchanges

  SimHydro 2021: Models for complex and global water issues -Practices and expectations 16-18 June 2021, Sophia Antipolis -Choley, C., Finaud-Guyot, P., Garambois, P.A., & Mose, R. -An effective urban flood model accounting for street-building exchanges

2 https://sw2d.inria.fr/

Table 1 :

 1 Mean dimensions (+-standard deviation) for openings from the field survey (Nîmes, France)

ACKNOWLEDGMENTS

This work has been supported by the French National Research Agency (ANR) under the grant ANR-18-CE01-0020.


Amélie Saumonneau

Nathan Lagneau

Lydia Awuor Ogonda

Catherine Dupré

Dr Franck Daligault
email: franck.daligault@univ-nantes.fr

Stéphanie Dutertre

Dominique Grizeau

Charles Tellier

Cyrille Grandjean

Disruption of Botryococcus braunii colonies by glycoside hydrolases

Keywords: Botryococcus braunii, microalga, glycosidase, flow cytometry, extracellular matrix, hydrocarbons

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Microalgae and cyanobacteria were originally produced for food and animal feed, and have been cultivated in large scale for some decades, notably in Asia. They contain valuable compounds such as proteins, sugar, vitamins, pigments and fatty acids among other metabolites [START_REF] Spolaore | Commercial applications of microalgae[END_REF][START_REF] Borowitzka | High-value products from microalgae-their development and commercialisation[END_REF][START_REF] Pulz | Valuable products from biotechnology of microalgae[END_REF]. The interest in green microalgae comes from their ability to convert carbon dioxide and sunlight to biomass and valuable products. If many microalgae produce useful proteins, carbohydrates and lipids, a few produce specific long-chain hydrocarbons such as botryococcens [START_REF] Kumar | Bioengineering of microalgae: recent advances, perspectives, and regulatory challenges for industrial application[END_REF]. Some of these excreted molecules appear to have promising biological activities. [START_REF] Oliva | Elucidation of the potential hair growthpromoting effect of Botryococcus terribilis, its novel compound methylated-Meijicoccene, and C32 Botryococcene on cultured hair follicle dermal papilla cells using DNA microarray gene expression analysis[END_REF][START_REF] Sasaki | Modulation of neurogenesis through the promotion of energy production activity is behind the antidepressant-like effect of colonial green alga, Botryococcus braunii[END_REF] ACCEPTED MANUSCRIPT / CLEAN COPY Botryococcus braunii is a fresh water colonial oleaginous green microalga and is classified in four different races A, B, L and S, according to the chemical structure of the hydrocarbons it produces [START_REF] Metzger | Botryococcus braunii: a rich source for hydrocarbons ACCEPTED MANUSCRIPT / CLEAN COPY and related ether lipids[END_REF]Jin et al., 2016b).

Although this microalga is known to deliver large amount of exopolysaccharides and carotenoids [START_REF] Cheng | High-value chemicals from Botryococcus braunii and their current applications-A review[END_REF], the interest in B. braunii rests mainly on hydrocarbons. The production of such energetically demanding hydrocarbons is supposed to be responsible to the low growth of B. braunii in comparison to other microalgae [START_REF] Banerjee | Botryococcus braunii: a renewable source of hydrocarbons and other chemicals[END_REF]. Nevertheless, this microalga is considered as a great candidate for the production of liquid hydrocarbons that can represent up to 61% of dry biomass e.g. in race A (Jin et al., 2016b). In contrast to other oleaginous microalgae, hydrocarbons synthesized in B. braunii are mostly secreted in the extracellular space and not accumulated as lipid bodies in the cytoplasm [START_REF] Hirose | Active hydrocarbon biosynthesis and accumulation in a green alga, Botryococcus braunii (race A)[END_REF]. However, these hydrocarbons of interest are retained in an extracellular matrix (ECM) consisting in three different components: the liquid hydrocarbon containing extracellular space, a colony retaining wall and a polysaccharide colony sheath [START_REF] Weiss | Colony organization in the green alga Botryococcus braunii (Race B) is specified by a complex extracellular matrix[END_REF].

Because of this structural specificity and its slow growth, the exploitation of B. braunii is therefore not very profitable by conventional methods of hydrocarbon extraction [START_REF] Banerjee | Botryococcus braunii: a renewable source of hydrocarbons and other chemicals[END_REF]. The colony sheath and retaining wall have to be deconstructed in order to release the liquid hydrocarbons from the extracellular matrix of B. braunii. These components are mainly composed of carbohydrates (97%) where arabinose (42%) and galactose (39%) are predominant. The polysaccharide consists in a backbone made of galactose with mainly 1,2 linked side chains and ends composed of arabinofuranose. However the galactose in the backbone shows an unusual substitution pattern where linkages in position 2 and 3 ACCEPTED MANUSCRIPT / CLEAN COPY are the most abundant, in comparison to the more common 1,4 or 1,6 linkages [START_REF] Weiss | Colony organization in the green alga Botryococcus braunii (Race B) is specified by a complex extracellular matrix[END_REF]. One can also assume the B. braunii cells interact with the ECM through their cell wall, which prevent their efficient release from the ECM. Thus targeting the cell wall polysaccharide consisting in β-1,4 and/or β-1,3 linked glucans in addition to the polysaccharide sheath is an appealing strategy to favor hydrocarbon release [START_REF] Weiss | Colony organization in the green alga Botryococcus braunii (Race B) is specified by a complex extracellular matrix[END_REF].

The aim of this work was therefore to use glycosidases to hydrolyze the polysaccharides involved in the different components of a colony in a targeted and gentle manner in order to make accessible the hydrocarbons from the extracellular space. We demonstrate that specific endoglycanases (cellulases, arabinanases and galactanases) promote a significant disruption of the size of B. Braunii colonies. The most efficient disruption was observed with endocellulases that have been fused with carbohydrate binding module (CBM3a), which allowed the cellulases to target the crystalline cellulose of the cell walls.

Material and methods

Enzymes

Cellulase (C-0901) EC 232.734.4 from Penicillium funicolosum, (5 units/mg solid) and Hemicellulase (H7649) EC 232.799.9 from Aspergillus niger, (1.5 units/mg solid) were purchased from Sigma-Aldrich® (France). Endo-1,5arabinanase (BtABN43A) , endo-1,4-galactanase (BsGan53A) and exo-1,3galactanase (CtGan43A) were acquired from Nzytech (Portugal).

Botryococcus braunii suspension cell culture

B. braunii Kützing SAG 30.81 race A was provided by the Culture Collection of Algae at Gottingen University (Sammlung von Algenkulturen, SAG). This race A strain was previously purified and studied (Jin et al., 2016a). The colonies were grown in the ACCEPTED MANUSCRIPT / CLEAN COPY buffered AF6 culture medium [START_REF] Provasoli | The ecology of algae[END_REF] within Erlenmeyer flasks on a rotating shaker (100 rpm). Some assays were conducted with colonies from a continuous culture within a labscale photobioreactor (0.35 L) at 20°C and under continuous illumination corresponding to a Photon Flux Density of 150 µmol m -2 s -1 .

To prevent the interaction of possible exopolysaccharides with enzymatic activities, cell-colonies were previously rinsed and transferred to new buffered culture medium.

Gene cloning and YFP fusion

The BpGH9 and CBM3a-BpGH9 constructs containing an in frame C-terminal polyhistidine tag for purification by immobilized ion metal affinity chromatography (IMAC)

were obtained as described previously [START_REF] Ogonda | Characterization and engineering of two new GH9 and GH48 cellulases from a Bacillus pumilus isolated from Lake Bogoria[END_REF]. For in vitro studies and imaging, the YFP gene was inserted at the 5' extremity of the constructs in the original pECa plasmid used in the previous study. These constructs were assembled using Gibson Assembly® protocol (New England BioLabs ® Inc) with recombinant primers to amplify by PCR (Polymerase Chain Reaction) the YFP gene and to insert it in the pECa already containing the BpGH9 and CBM3a-BpGH9 genes. The successful constructs were then confirmed by colony PCR and sequencing. for 1 h at 4°C, then loaded onto a manual column. The column was washed using 25 mL of washing buffer (20mM Tris-HCl pH 8.0, 25 mM imidazole), then elution buffer

Production and purification of YFP-

(5-fold 500 µl = 2,5 ml) was added (20mM Tris-HCl pH 8.0, 250 mM imidazole). The purity of the final product was checked by sodium dodecyl sulfate-polyacrylamide 12% gel electrophoresis (SDS-PAGE). Enzyme concentration was determined by UV absorbance at 280 nm using a NanoDrop 1000 (ThermoScientific) with the protein extinction coefficient () calculated using http://atchimiebiologie.free.fr/proteinecalc/proteinecalc.html.

Enzymatic activity characterization

To assess the enzymatic activities of BpGH9 constructs (YFP-BpGH9 and YFP-CBM3a-BpGH9), enzymatic assays were conducted using the insoluble microcrystalline cellulosic substrate Avicel PH-101 (Sigma-Aldrich®). The enzymatic activities were tested at an enzyme concentration of 3µM in 10mM Tris/HCl Buffer pH 8.0 and with 5% (w/v) of Avicel at 37°C during 24h. For the assays, 70µl of the reaction medium were withdrawn at regular time intervals and added to 70µl of DNS (Dinitro salicylic acid solution). The mixture was heated at 95°C for 10 minutes [START_REF] Miller | Use of dinitrosalicylic acid reagent for determination of reducing sugar[END_REF]). The OD was then read at 540nm by spectrophotometry (Magellan, Tecan®), reflecting the reducing end of released sugars.

Affinity pull down assay

The functionality of the CBM3a module following fusion to the bi-modular wild type endoglucanase was ascertained by binding of the CBM to the microcrystalline ACCEPTED MANUSCRIPT / CLEAN COPY cellulosic substrate Avicel PH-101 according to the method by Stern with modifications [START_REF] Stern | Significance of relative position of cellulases in designer cellulosomes for optimized cellulolysis[END_REF]. The enzymes (YFP-BpGH9 and YFP-CBM3a-BpGH9) at 5µM were placed under orbital stirring (200 rpm /4°C) for two hours in presence of 5% (w/v) insoluble cellulose (Avicel). The mixture was then centrifuged for two minutes on a bench-top mini-centrifuge (Extragen). The supernatant was then recovered and the pellet was washed with 10 mM Tris/HCl buffer, pH8.0 containing 0.05% (v/v) Tween®20 (Sigma) in order to remove the non-specifically bound proteins. The mixture was centrifuged again for two minutes on a bench-top mini-centrifuge. The supernatant was eliminated and the pellet was taken up with 10 mM Tris/HCl buffer, pH8.0. The fractions containing the pellets (P) and the supernatants (S) were denatured for 3 minutes at 95°C in loading buffer (SDS 2%

(w/v); 0.08 M Tris-HCl; pH 6.8; 10% glycerol (v/v), ß-mercaptoethanol 0.06% (v/v))

then loaded onto an SDS-PAGE gel containing 12% acrylamide under denaturing conditions. (https://www.nikoninstruments.com/fr_FR/Produits/Logiciels/NIS-Elements-

2.7

ACCEPTED MANUSCRIPT / CLEAN COPY

Advanced-Research/NIS-Elements-Viewer).

Confocal imaging

Multicolour images of colonies were acquired with a Leica SP8 inverted confocal microscope (Leica) and a 63× oil-immersion objective (NA 1.4) or a 20x oil immersion (NA 0.75) driven by the Leica Acquisition Suite software. The excitation and emission wavelengths for Nile Red were 488 and 565/25, respectively; for autofluorescence from chlorophyll, they were 561 and 700/50 nm.

Cytometry

Cytometry analyses were carried out on a Beckman Coulter CytoFLEX flow cytometer on the same cell suspension treated with BpGH9 constucts and observed in fluorescent microscopy (see 2.7). For other enzymes 150µL of microalgal cell suspension were treated with 75µl of hemicellulase (20mg/ml, Merck-Sigma®), cellulase (20mg/ml, Merck-Sigma®), CtGan43A (2mg/ml, Nzytech®), BsGan53A

(1mg/ml, Nzytech®) and BtAbn43A (1mg/ml, Nzytech®). The measurements of frontal diffusion ("Forward SCatter" or FSC) and lateral diffusion ("Side SCatter" or SSC) were taken with a blue laser at 488nm. A 660nm filter was used to detect the fluorescence emission of chlorophyll in the microalgae. The flow rate was fixed at 10µL/min and the recording was done on 1000 events.

Results and discussion

B. braunii is a microalga which forms colonies in which cells are embedded in an ECM mainly composed of polymerized hydrocarbons in which are trapped the liquid hydrocarbons excreted by the cells [START_REF] Hirose | Active hydrocarbon biosynthesis and accumulation in a green alga, Botryococcus braunii (race A)[END_REF]. By separating the cells from the ECM one can assume that extraction of the hydrocarbons should be feasible while keeping the cells alive for continuing the microalgae culture, making possible to envisage the development of a semi-continuous process. Such semi-continuous ACCEPTED MANUSCRIPT / CLEAN COPY process cannot be considered with most of microalgae that must be killed prior to recover their hydrocarbon production as lipids usually accumulate in lipid bodies inside the cell.

The cell wall, the retaining wall and the colony sheath are all composed of polysaccharides whose partial hydrolysis is a potential strategy for releasing the hydrocarbons from the colonies. To this aim, different glycosidases were chosen according to the carbohydrate composition of these colony components. On the one hand, arabinanases and galactanases are obvious candidates to be active on the retaining wall and colony sheath which consists of arabinose and galactose residues.

Therefore the endo-1,5-arabinanase from Bacteroides thetaiotaomicron (BtAbn43A) [START_REF] Cartmell | The structure and function of an arabinan-specific α-1, 2-arabinofuranosidase identified from screening the activities of bacterial GH43 glycoside hydrolases[END_REF], the endo-1,4-galactanase from Bacillus subtilis (BsGAn53A) [START_REF] Nakano | Purification and characterization of an exo-1, 4-β-galactanase from a strain of Bacillus subtilis[END_REF] and the exo-1,3-galactanase from Clostridium thermocellum (CtGan43A) [START_REF] Ichinose | Characterization of an exo-β-1, 3-galactanase from Clostridium thermocellum[END_REF][START_REF] Jiang | Crystal structure of 1, 3Gal43A, an exo-β-1, 3-galactanase from Clostridium thermocellum[END_REF] were selected and tested. On the another hand cellulases and hemicellulases are expected to be active on the cell wall made of 1,3 and 1,4-glucans, so commercial cellulases and hemicellulases and the cloned cellulase from Bacillus pumilus (BpGH9) [START_REF] Ogonda | Characterization and engineering of two new GH9 and GH48 cellulases from a Bacillus pumilus isolated from Lake Bogoria[END_REF] were included in the assay.

Binding of BpGH9 cellulase on B.braunii

The endo-β-1,4-D-glucanase BpGH9 from B. pumilus (NCBI Gene databank AVG70969) was chosen in order to genetically fuse this cellulase with various functional modules for detection (YFP) or binding (CBM3a). This enzyme was previously isolated and identified in our laboratory from a new strain of B. pumilus collected from the hot springs of Lake Bogoria in Kenya. It consists of a catalytic domain flanked by a CBM3c at its C-terminal end. It was previously shown that this enzyme was very tolerant to fusion at either the N-terminus or the C-terminus of the ACCEPTED MANUSCRIPT / CLEAN COPY catalytic domain [START_REF] Ogonda | Characterization and engineering of two new GH9 and GH48 cellulases from a Bacillus pumilus isolated from Lake Bogoria[END_REF].

Fusion of BpGH9 with YFP and CBM3a

The BpGH9 was shown to be active on cellulose substrates (carboxymethylcellulose, Na-CMC and phosphoric acid swollen cellulose, PASC) but very weakly on crystalline cellulose (Avicel) despite the presence of the CBM3c module in its structure [START_REF] Ogonda | Characterization and engineering of two new GH9 and GH48 cellulases from a Bacillus pumilus isolated from Lake Bogoria[END_REF]. To our knowledge the presence of crystalline cellulose in the cell wall of B. braunii has not been checked but has been identified in different green microalgae. If such crystalline cellulose exists in the cell wall of B.

braunii, the fusion of BpGH9 with the CBM3a from Clostridium thermocellum (CtCBM3a), known to have high affinity for such cellulose, should improve the BpGH9 activity by fixing the enzyme to its polymeric substrate.

Moreover, since the discovery of the green fluorescent protein (GFP) from the jellysfish Aequorea victoria, fluorescent proteins (FP) have been largely used for biotechnological applications such as cell imaging and protein interaction studies. A set of GFP variants that are fluorescing along the visible spectrum is now available like BFP (blue), CFP (cyan) and YFP (yellow). In the carbohydrate field fluorescent proteins have been fused with CBM for localizing exopolysaccharides, controlling the accessibility of cellulose to cellulases and hemicelullases, or imaging complex carbohydrates [START_REF] Kawakubo | Analysis of exposed cellulose surfaces in pretreated wood biomass using carbohydrate-binding module (CBM)-cyan fluorescent protein (CFP)[END_REF].

To test the presence of microcrystalline cellulose and the effect of CtCBM3a on the BpGH9 activity, two constructs comprising fused YFP and BpGH9 with (YFP-CBM3a-BpGH9) or without (YFP-BpGH9) CtCBM3a were expressed in E. coli.

Enzymatic and affinity pull down assays on Avicel

Before testing the BpGH9 constructs on B. braunii cells, it was necessary to verify that adding YFP to CBM3a-BpGH9 and BpGH9 did not impair the fixation to ACCEPTED MANUSCRIPT / CLEAN COPY crystalline cellulose nor the endocellulase activity.

A pull-down assay was used to show the affinity of different constructs of BpGH9 for insoluble crystalline microcellulose (Avicel PH-101). When YFP-BpGH9 was mixed with Avicel (Figure 1), most of the protein was found in the supernatant, showing that YFP-BpGH9 possesses low affinity for Avicel. In contrast the YFP-CBM3a-BpGH9 construct was located mainly in the pellet fraction, demonstrating good affinity for insoluble microcrystalline cellulose. Thus adding YFP to the BpGH9 constructs did not modify the affinity of the original constructs [START_REF] Ogonda | Characterization and engineering of two new GH9 and GH48 cellulases from a Bacillus pumilus isolated from Lake Bogoria[END_REF]. supernatant soluble fractions).

The activity of the constructs was determined on Avicel for checking that addition of YFP does not impair with the enzymatic activity and the effect of CBM3a. As shown on figure 2, the YFP-BpGH9 construct retains activity and the activity is increased when fused with CtCBM3a (YFP-CBM3a-BpGH9).

ACCEPTED MANUSCRIPT / CLEAN COPY

Fluorescence microscopy

The YFP-CBM3a-BpGH9 and YFP-BpGH9 constructs were incubated with B. braunii

Evaluation of enzymatic colony disruption by flow Cytometry

Cytometry is the method of choice for determining size of cells in suspension as the quantity of scattered light (Forward Scatter or FSC) increases with cell size [START_REF] Peniuk | Identification and quantification of suspended algae and bacteria populations using flow cytometry: applications for algae biofuel and biochemical growth systems[END_REF]. We therefore used this technique to evaluate the impact of glycosidases on the organization of B. braunii colonies. Indeed if enzymes are able to disaggregate the B. braunii colonies, the cell suspension should evolve from large colonies to smaller ones and eventually to single cell. By injecting a control cell suspension of B. braunii in the cytometer three populations P1 (Large, 18.8%), P2 (Medium, 29.7%) and P3 (small, 42.0%) were discriminated according to the scattered light (Figure 4). ACCEPTED MANUSCRIPT / CLEAN COPY the cell wall were active by increasing the P3 population from around 40% for the untreated cells to 60-75% (Figure 5). The three enzymes (cellulase, hemicellulase and YFP-BpGH9) were almost as active but fusion of CtCBM3a to BpGH9 (YFP-CBM3a-BpGH9) even further increased the enzyme efficiency by around 15%.

Concerning the enzymes targeting the colony retaining wall and sheath, the endo-1,5-arabinanase (BtAbn43A) was almost as efficient as the cellulases. The endo-1,4-galactanase (BsGan53A) and the exo-1,3-galactanase (CtGan43A) were also effective but in a less extent, with an increase in P3 population from 40% (control) to 45-50%. Surprinsingly the enzymes supposed to act on the cell wall (cellulase, hemicellulase and BpGH9) were as much or even more effective than those supposed to act on the retaining wall and colony sheath (BsGan53A, BtAbn43A, CtGan43A). This demonstrates the importance of targeting the cell wall for releasing the cells from the To confirm the effect of enzymes, the cell suspension treated with cellulase and hemicellulase were inspected by fluorescence microscopy. The presence of colonies was revealed by staining the lipids and hydrocarbons present in the ECM with Nile Red and the cell healthiness was controlled by verifying the autofluorescence from chlorophyll. The untreated cells consisted in colonies (Figure 6b) with cells surrounded by hydrocarbons as demonstrated by the presence of a green color due to Nile red (false color) in comparison to cell suspensions treated with cellulase (Figure 6d) and hemicellulase (Figure 6f) where cells appeared relatively more isolated. The autofluorescence from chlorophyll (red color) indicated that the cells were still alive after 1 h enzymatic treatment. [START_REF] Wang | Simultaneous detection of viability and concentration of microalgae cells based on chlorophyll fluorescence and bright field dual imaging[END_REF] ACCEPTED MANUSCRIPT / CLEAN COPY

  BpGH9 and YFP-CBM3a-BpGH9 recombinant enzymesRecombinant strains of E. coli BL21(DE3) expressing the BpGH9 variants (YFP-BpGH9 or YFP-CBM3a-BpGH9) were grown in 1 L of LB medium supplemented with ampicillin (resistance antibiotic) at 37°C to 0.6 of OD 600nm (Optical Density measured at =600nm) and IPTG at 0.5 mM was added to induce the expression at 30°C overnight under stirring (200 rpm). Then the culture was centrifuged and the pellet was frozen and resuspended in 20 ml of lysis buffer 20mM Tris-HCl pH 8.0 containing 10mM Imidazole, 5mM DNaseI, 1mg/ml lysozyme and protease inhibitors ACCEPTED MANUSCRIPT / CLEAN COPY cocktail (Sigma-Aldrich®). After sonication and centrifugation, the recombinant proteins with His-tag contained in supernatant (soluble fraction) were purified by IMAC: 300 µl of Ni-NTA Superflow (Qiagen), preliminary equilibrated into 20mM Tris-HCl pH 8.0 containing 10 mM imidazole, were added to the supernatant and stirred

  Fluorescence microscopy B. braunii cell suspension was incubated with a 10µM enzyme solution of YFP-BpGH9 or YFP-CBM3a-BpGH9 with a 2:1 ratio (v/v). The mix loaded between blade and coverslip was observed at ×40 lens with optical microscope at optical fiber Nikon Ni-E, in transmission light to observe the colonies. A TRITC filter (excitation: 543/22 nm; emission: 593/40 nm) was used to observe chlorophyll auto-fluorescence and a FITC filter (excitation: 482/35 nm; emission: 536/40 nm) was used to observe YFP fluorescence. The pictures of chlorophyll fluorescence and Bright Field Dual Imaging were analyzed to estimate the cell viability with Nis-Elements Viewer software (Wang et al., 2021).

Fig. 1 .

 1 Fig. 1. Cellulose based affinity pull down assay for YFP-BpGH9 (95 kDa) and

Fig. 2 .

 2 Fig. 2. Comparison of the enzymatic activities of YFP-BpGH9 and YFP-CBM3a-

  cell suspension and analyzed by fluorescence microscopy to verify the effect of CtCBM3a on the fixation of the construct to B. braunii cells and thus highlight the presence of microcrystalline cellulose. By comparing pictures 3c and 3d corresponding to the YFP signal of the BpGH9 constructs with and without fused CtCBM3a respectively, it appears that YFP-CBM3a-BpGH9 is localized at the cell surface (see arrow and square box in figure3c), suggesting binding to crystalline cellulose present in the cell wall. In absence of CtCBM3a the localization seems much more diffuse and may be due to weaker unspecific binding or binding of the native CBM3c present in BpGH9 to amorphous or soluble cellulose (Figure3d).

Fig. 3 .

 3 Fig. 3. Fluorescence microscopy observations of cellular localization of YFP-

Fig. 4 .

 4 Fig. 4. Distribution of colonies size in B. braunii cell culture before enzyme

Fig. 5 .

 5 Fig. 5. Quantification of the B. braunii colonies disorganization by flow

Fig. 6 .

 6 Fig. 6. Botryococcus braunii colonies and cell suspensions with enzymatic

Acknowledgment

The authors are grateful to Gweninna Cueff for her technical support in fluorescence ACCEPTED MANUSCRIPT / CLEAN COPY microscopy and Emmanuelle Courtois for her help in flow cytometry. We also thank the Affilogic company (Nantes, France) for providing the YFP gene.

We acknowledge France-BioImaging infrastructure supported by the French National Research Agency (ANR-10-INBS-04).

This work was funded by the University of Nantes within the interdisciplinary project framework program.

Declaration of competing interest

None.

Author contributions


Adil Mouahid

Magalie Claeys-Bruno

Isabelle Bombarda

Sandrine Amat

Andrea Ciavarella

Emmanuelle Myotte

Jean-Paul Nisteron

Christelle Crampon

Elisabeth Badens

Valorization of handmade argan press cake by supercritical CO2 extraction

teaching and research institutions in France or abroad, or from public or private research centers.


Lisa Baboin

Servane Berton

Dylan Dunand

Quentin M Dutertre

Sabrina Gilardi

Jean-Baptiste R Guy

Bérangère Leys
email: berangere.leys@imbe.fr

Comparative approach of multivariate statistics to decipher trade off in temporal datasets Approche statistique multivariée pour décrire les données temporelles long terme (millénaire)

Keywords: vegetation, fire, long-term, co-inertia, MFA, PCA

Introduction

Paleorecords are replete with examples of long-term biotic responses to past climate change, and disturbances such as fire, herbivores, insect outbreaks or ice storms to cite a few [START_REF] Whitlock | Fire History Reconstructions Based on Sediment Records from Lakes and Wetlands[END_REF][START_REF] Whitlock | Charcoal as a fire proxy[END_REF][START_REF] Mclauchlan | Reconstructing disturbances and their biogeochemical consequences over multiple timescales[END_REF]. One particularly useful set of records are those preserved in lake and marine sediments, recording both past environmental changes and corresponding biotic responses (e.g. [START_REF] Leys | Global fire history of grassland biomes[END_REF][START_REF] Genet | Modern relationships between microscopic charcoal in marine sediments and fire regimes on adjacent landmasses to refine the interpretation of marine paleofire records: An Iberian case study[END_REF]. The now frequent challenges in palaeoecological studies are to better understand both the trends and the breaking points of biotic variables in response to disturbances. Recently there has been increasing focus on the need for conservation of ecological and evolutionary processes in the face of climate change based on long-term records. The lake sedimentary archives, due to their anoxic environment, preserve the biotic and abiotic factors of the ecosystems particularly well [START_REF] Mclauchlan | Reconstructing disturbances and their biogeochemical consequences over multiple timescales[END_REF]. Generally, the sediments are deposited since the formation or the outcrop of the wetland, i.e.,

Abstract

Paleorecords are replete with examples of longterm biotic responses to past climate change, and disturbances such as fire, herbivores, insect outbreaks or ice storms. The now frequent challenges in palaeoecological studies are to better understand both the trends and the breaking points of biotic variables in response to disturbances. The aim of this article is to expand the capacity of new and existing methods to provide greater insight into ecosystem trajectories and functioning. Our analyses focus on biomes where fire is a key structural disturbance for vegetation establishment and evolution. We aim to determine: 1) explanative variances between biotic and abiotic variables at both short and millennial time scales, and 2) whether a temporal relationship exists between fire regimes and plant diversity change in both systems. Our statistical approach focused on PCA (Principal Component Analysis), co-inertia, MFA (Multiple Factor Analysis) and Hill & Smith methods, which provide us new information about our data, and bring new conclusions to the former studies. We advise to preferentially use the MFA when the environmental variables are numerous, while the co-inertia is a better tool to explain variance of the datasets.

Material and methods

Study sites

The two site cases have been chosen to understand the charcoal production used to illustrate the relationships between fire and vegetation diversity, at both short and long-time scales.

(1) The Flint Hills ecoregion (37°17'00"N 96°40'31"W) is the largest remaining contiguous tallgrass prairie ecosystem in North America, encompassing over 50,000km 2 . The current climate conditions provide enough moisture to support woody plants, and grassland is frequently and extensively burned throughout the region to maintain open conditions [START_REF] Reichman | Konza Prairie: a tallgrass natural history[END_REF]). The study site of Konza Prairie (39°05'N, 96°35'W) is in the Flint Hills region of northeastern Kansas (hereafter, "Konza"). Konza is a 3,500 hectares native tallgrass prairie preserve. Sediments in traps from Konza Prairie (LTER) represents the last 4 years of vegetation composition, fire activity and other environmental parameters (climate, herbivores) in the charcoal production (table 1).

(2) Lac de Creno (1,310m a.s.l.; 42°12'17"N, 08°56'45"E) is in the southeastern part of the Rotondo massif (western Corsica, west Mediterranean basin). Macrofossils of Pinus laricio Poir. provide evidence for its growth around the Lac de Creno since 13,200 cal year BP, which is consistent with its natural origin in Corsica. Sediments from Lac de Creno in Corsica (France) expend the Holocene period and from which a reconstruction of vegetation composition and fire history is available (table 2). All details are available in [START_REF] Leys | Historical range of fire frequency is not the Achilles' heel of the Corsican black pine ecosystem[END_REF] and [START_REF] Leys | Wildfires and geochemical change in a subalpine forest over the past six millennia[END_REF].

Statistical approaches

PCA

Principal component analyses (PCA), standardized by taxa with log-transformed concentration data, were used to visualize the relationships among taxa inferred from macrofossils accumulation rates (table 2). The log-transformation allow to minimize extreme value and stabilize the variance within the data, which is particularly required in this case study where number of macroremains can vary of a factor 25 from one taxa to another [START_REF] Ammann | Quantification of biotic responses to rapid climatic changes around the Younger Dryas -a synthesis[END_REF]. To limit the biases of around 20,000 years for most moraine lakes in Europe, and continuously. They are cut into thin slices (0.5cm or 1cm) to reconstruct past environments over time steps ranging from a few years to a few decades depending on the rate of sedimentation (which depends on the production of organic matter in the lake, and inputs from the watershed) [START_REF] Scheffer | Catastrophic shifts in ecosystems[END_REF][START_REF] Leys | A comparison of charcoal measurements for reconstruction of Mediterranean paleo-fire frequency in the mountains of Corsica[END_REF][START_REF] Leys | Global fire history of grassland biomes[END_REF]. Thus, it is possible to quantify both the post-disturbance response of the vegetation, and the millennial trajectories (stability and changes) of the vegetation and the disturbance regimes. For instance, the simple analysis of correlation between the biomass burned (through charcoal records) and the vegetation (by pollens) of the last millennia in central and southern Europe has clearly shown that fires have been a major factor in the change of vegetation 4,500 years ago leading to the establishment of meadows and scrubland, the reduction of mesophyte forests and the extension of arable and pastoral land [START_REF] Connor | A long-term perspective of biomass burning in the Serra da Estrela, Portugal[END_REF]. Recent work on the Iberian Peninsula has shown more precisely that some of the changes observed in the millennial trajectories of vegetation in response to the fire regime constitute change points. Quasi-permanent transitions in vegetation status are characterized by shifts from wooded to open vegetation and from a fireadapted system (xerophilic bushes and fireadapted pines) to a fire-resistant system fire (Pinus nigra J.F.Arnold. and the mesophytes) [START_REF] Connor | A long-term perspective of biomass burning in the Serra da Estrela, Portugal[END_REF]). The challenge is to expand the capacity of new and existing methods to provide greater insight into ecosystem trajectories and functioning. Here we examine Mediterranean and grassland fire and vegetation diversity histories by developing alternative approaches based on multivariate analyses. These two case studies allow to analyze temporal datasets at both decennial and millennial scales. Our analyses focus on biomes where fire is a key structural disturbance for vegetation establishment and evolution. We aim to determine: 1) explanative variances between biotic and abiotic variables at both short and millennial time scales, and 2) whether a temporal relationship exists between fire regimes and plant diversity change in both systems. To achieve these aims, we will present different and complementary statistical approaches using objective criteria. Finally, we discuss the likely drivers of fire regime and diversity change on millennial and decennial timescales at the light of the different multivariate analyses. relationships between the local fire-episodes regime and the local vegetation inferred from macrofossil assemblages, CHAR background (proxy of the burning area) and FRI (proxy of local fire episodes) were added passively in the PCA ordination plots. All ordinations erosions events that could have created artefactual increase of taxa abundances though increase of matter in the lacustrine system, we used the taxa accumulation rate, which correct the taxa abundance by the accumulation rate of sediments through time. To visualize the [START_REF] Husson | Factoextra: extract and visualize the results of multivariate data analyses[END_REF]).

The MFA is a symmetrical ordination based on correlation, and this particular analysis was specifically chosen to ordinate the different variables (not assumed to be explanative in the first place) with no risk of overfitting. We plotted the MFA results using the fviz_ mfa() function from the factoextra package (Kassambara & Mundt 2019). We graphically presented the quality of the representation (cos2) of each variable for the four first axes of the MFA, i.e. the proportion of the variable represented by each axis using the corrplot() function from the corrplot package [START_REF] Wei | Package "corrplot[END_REF]. To analyze the relationships among the four groups of variables, we extracted the RV coefficients from the MFA, measuring the similarity (squared correlation) between each pair of groups. Then, we tested these coefficients using the coeffRV() function from the FactoMineR package.

were carried out in R Studio (version 4.1.1), package ade4 [START_REF] Dray | The ade4 package: implementing the duality diagram for ecologists[END_REF], using the function dudi.pca().

Co-inertia

We performed a co-inertia analysis [START_REF] Dray | Co-inertia analysis and the linking of ecological data tables[END_REF] based on a Correspondence Analysis (CA) on vegetation data and a normalized Principal Component Analysis (PCA) on fire data to assess the covariance between these two components (table 2). The PCA was performed using the CA's rows weight to match co-inertia analysis requirement. The co-inertia analysis was performed with the coinertia() function from the ade4 package [START_REF] Dray | The ade4 package: implementing the duality diagram for ecologists[END_REF] on the last 6,000 years of history were fire and vegetation data were the most complete.

To enhance the interpretation of co-inertia results we performed a Monte-Carlo test [START_REF] Heo | A permutation test of association between configurations by means of the RV coefficient[END_REF] with 9,999 permutations on both CA and PCA. It allowed us to assess the correlation between vegetation and fire data. The function RV.rtest() from the ade4 package was used.

Hill and Smith

We used multivariate analyses to visualize the relationships among environmental parameters, fire parameters, and charcoal measurements. Because our dataset included both quantitative and qualitative variables (table 1), we used a Hill and Smith analysis [START_REF] Hill | Principal component analysis of taxonomic data with multi-state discrete characters[END_REF]) to identify a specific set of variables that avoid redundancy. listed variables except solar radiation and air temperature for climate parameters). MFA axis 1 (hereafter MFA 1) 1 is represented by vegetation at 21.50%, while the second axis (hereafter MFA 2) is represented by charcoals at 14.15%. The relationships between the fire and climate groups follow two different trajectories given the explanative variables of interest. First, the fire variables were positively correlated with the evapotranspiration variable which brings together the measurements of maximum temperature, minimum temperature, solar radiation rate and evapotranspiration. Conversely, the variables negatively correlated to fires

Results and discussion

MFA pinpointed new relationship between fire and climate parameters

At Konza Prairie, from the precedent study, the Hill and Smith analysis (Figure 1) demonstrated no direct relationships between charcoal production and fire variables < 500m around the trap, as indicated by non-significant correlations (i) between different measurements of charcoal and (ii) between total, non-arboreal charcoal or NA/T ratio and fire parameters (burn area at 500m distance from the trap, fuel burn estimation, fire frequency and time since last fire). I n a ddition, t he authors performed a random forest analysis (more details in [START_REF] Leys | Wildfires and geochemical change in a subalpine forest over the past six millennia[END_REF]) which highlighted that total charcoal or NA/T ratio are most strongly predicted using fire parameters at a larger spatial scale and with environmental variables, both of which varied during each of the four years of the study. Charcoal variables, including Total charcoal count and NA/T ratio, did not correlate with other fire parameters, vegetation cover, landscape, or climate variables.

Here, we performed an MFA (Figure 2) to test whether the charcoal data (all morphotypes and 125µm) in one hand and the fire parameters (buffer at 300m, all other parameters were strongly correlated) on the other hands are explained by the two other categories: climate and vegetation (table 1, all relationship among fire and vegetation displays a weak explanative percentage of variance explained (4%).

The co-inertia explores the covariances between both fire and vegetation categories, based respectively on PCA for charcoal parameters (FRI and CHARa) and CA for vegetation data. From the PCA, axis 1 is well explained by the Fire Return Interval (FRI) while axis 2 is well explained by the charcoal accumulation rate (Figure 3 B). From the CA, axis 1 is explained positively with Quercus and negatively with Alnus glutinosa (L.) Gaertn and Juniperus communis L., while axis 2 is positively correlated with Alnus cordata (Loisel.) Duby and negatively with Berberis (Figure 3 A). Combined, co-inertia axis 1 explained 60% of the variance, the second axis explained 11%.

The graphical representation of the co-inertia results allows to associate at each observation represented by the score of the CA in the ordination plot, with an arrow representing the predicting trend from PCA ordination (Figure 4). The longer the arrow, the more the observation (sample with vegetation assemblage) was unexpected given the fire condition at this time. For instance, the fire conditions were consistent over the last millennia [START_REF] Leys | Historical range of fire frequency is not the Achilles' heel of the Corsican black pine ecosystem[END_REF], although the vegetation assemblages at 127 (125-129) cal year BP differed by the presence of Juniperus communis (Figure 4 B). Besides, at 5,422 (5,344-5,579) cal year BP, the charcoal accumulation rate was particularly high given the vegetation assemblage. This result suggests that the vegetation is not following the expected assemblages given the fire regime recorded, maybe reflecting the beginning of a fire regime change appearing before a vegetation change (Figure 4 B). On the other side, at 4,148 (4,045-4,230) cal year BP, the arrow is not even visible, meanings that the vegetation was consistent with the fire regime (Figure 4 B).

To strength the results statistically, we can calculate a p-value through Monte-Carlo test on the RV-coefficients (RV.rtest() in ade4 package). Given the non-significance of our results of our analysis we decided to notshow this part here.

were humidity and precipitation measurements. In addition to precedent results, the MFA pinpoint different relationships between charcoal, vegetation and climate groups. A positive correlation between the charcoal variables and the wind measurement appears positively correlated with charcoal variables.

A positive correlation appears between the charcoal variables and the wind measurement.

The RV coefficient, which measures the similarity between pairs of variables, were 12% between the vegetation and fire variable groups, and 7% between the climate and vegetation groups. Thus, fire parameters seem to correlate more the vegetation parameters than does the climate.

Co-inertia allows to identify time period where fire played a major role in the vegetation assemblage

The onset of the Holocene in Corsica (~11,700 cal year BP) was marked by a rapid shift in the treeline, the establishment of P. laricio-dominated woodlands with low species turnover, and a long-term increase in taxa richness as a result of successive expansions of broadleaved deciduous trees. In spite of fire-return intervals (FRIs) fluctuating between 30 and 490 years during the Holocene, P. lariciodominated woodlands persisted for several millennia, and fires likely played an ecological role in the functioning of these woodlands. The 12,000-year record of mean FRI is of 80 years between fires; i.e., frequency of 12.5 fires 1000 year-1 [START_REF] Leys | Historical range of fire frequency is not the Achilles' heel of the Corsican black pine ecosystem[END_REF]).

Previous analysis with PCA method on the

Conclusion

Multivariate analyses can bring new information on palaeoecological data, and complete efficiently the description of long-term trajectories. These analyses found their spot to answer key questions relative to ecological questions, on both long-and short-time windows studied. We advise to preferentially use the MFA when the environmental variables are numerous, while the co-inertia is a better tool to explain variance of the datasets. We presented chosen multivariate analyses, although we strongly encourage the use of all multivariate analyses that answer the best to the dataset studied and their related questions.

Figure 1 -

 1 Figure 1 -Ordination plots from Hill and Smith multivariate analysis of numerical data in function of fire type. (WU = wildfire burn unplanned for a given year; PP = prescribed burn planned; WP = wildfire burn planned for a given year).

Figure 2 -

 2 Figure 2 -Multiple factor analysis (MFA) of 4 parameters: charcoal, climate, fire and vegetation.

Figure 3 -

 3 Figure 3 -Direction of the CA variables (A) and the PCA variables (B).

Figure 4 -

 4 Figure 4 -Scores of all the observations on the co-inertia axis (A); scores of the observations n o 20, 198 and 244 on co-inertia axis (B).

Table 1 -Groups of data used for statistical analyses for the site of Konza Prairie: charcoal measurements, fire parameters, vegetation and landscape data, and climate.

 1

	Parameter	Name	Unit	Formula	Sources
	types
	Charcoal	Morphotypes: Cell,	pieces		Trap content
		Porous, Fibrous,
		Sponge, Branch, Dark
		Non-Arboreal	pieces	Cell + Porous + Fibrous
		Total	pieces	Sum of all morphotypes
		Non-Arboreal/Total	pieces	Ratio of non-arboreal charcoal pieces on total
				amount of charcoal pieces
		125µm-250µm	pieces		Trap content
		250µm-1mm	pieces		Trap content
	Fire	100 to 500m	km 2	Sum of area burn of watershed within the 100	Konza website
		buffer area burn		(to 500) m radius of a trap
		watershed burn	km 2 .watershed-1		Konza website
		Konza area burn	km 2	Sum of area burn of watersheds
		FlintHills area burn	km 2		FlintHills annual report
		month of burn			Konza website
		Fire return interval	years	Average fire return intervals of watersheds within	Konza website
				the 500m radius distance of a given trap
		Fire frequency	fire.100years-1	Inverse of fire return interval multiplied by 100
		Type of fire	3 classes		Konza website
		Time since last fire	year	Average number of years since last fire of
				watershed burn within the 500m radius distance
				of a given trap
		Fuel burn index		Sum of 500m buffer area multiplied by time
				since last fire
	Vegetation	Woody	5 classes		Field survey
	and landscape	Herbaceous	5 classes		Field survey
		Shrubbery	yes/no		Field survey
		Height	dm and 2 classes		Field survey
		Bare Soil	5 classes		Field survey
		Limestone rocks	yes/no		Field survey
		Bison Manure	yes/no		Field survey
		Elevation	m		Field survey
		Landscape position	3 classes		Field survey
	Climate	Wind Speed	m.s-1	Average on 8 days following the date of burn	Konza Prairie
					Meterorological station
		Relative Humidity	%	Average on 8 days following the date of burn	Konza Prairie
					Meterorological station
		Precipitation	mm	Average on 8 days following the date of burn	Konza Prairie
					Meterorological station
		Solar Radiation	W	Average on 8 days following the date of burn	Konza Prairie
					Meterorological station
		Air temperature	°C	Average on 8 days following the date of burn	Konza Prairie
		(min and max)			Meterorological station
		Mean Air temperature °C	Average on 8 days following the date of burn	Konza Prairie
					Meterorological station
		Soil temperature	°C	Average on 8 days following the date of burn	Konza Prairie
		(min and max)			Meterorological station
		Evapotranspiration	mm	Average on 8 days following the date of burn	Konza Prairie
					Meterorological station

Table 2 -Description of all variables used in the following analyses for Lac de Creno.

 2

	Parameter	Name	Description	Unit
	types
	Age		210 Pb and 137 Cs measurements were	cal. year BP
			used to build an accurate age-depth model
	Charcoal	CHAR area	measurements are reported as charcoal accumulation rates Charcoal particles > 250µm² were identified. Charcoal	mm2 cm-2 year-1
			(CHAR a )
		CHAR background	2 Components were derived from Char area : CHAR peak which	mm2 cm-2 year-1
			represents the charcoal peaks for local fire episodes. (CHAR p )
			CHARbackground which indicated the charcoal background
			for regional area burned. (CHAR b )
	Fire	Fire Return Interval (FRI) Number of fire between two consecutive years (derived from	year.fire-1
			CHAR p )
		Fire Frequency (FF)	Number of fires per unit of time, smoothed over a 1000-year	year
			smoothing window.
	Vegetation Plant macrofossil	Plant macrofossils were extracted by	number of fragments cm-2.year-1
			water-sieving (250-µm mesh size) and identified to genus,
			species when possible

Acknowledgments

We gratefully thank Franck Torre, Eric Meineri and Marie Finocchiaro for their insights and the interesting discussions while preparing the manuscript. We also thank Mathis Degand and Manon Berchet for their implication on the project and their help with statistical tests realization.

Author contribution

BL conceived and ran the research project. All authors contributed equally to data analysis and writing.


Klara Borowa

Marion Wiese

Dalila Tamzalit

Claudine Allen

A Marketplace for Industrial Case Studies in Software Engineering

Keywords:

Case studies are valuable for both sides of the Software Engineering community, the practitioners and the researchers. To perform such research, collaboration between them is necessary. However, establishing such partnerships is not straightforward. We identified a set of challenges that must be overcome and propose a research plan with the goal of creating a marketplace for industrial case studies.

INTRODUCTION

A case study is an empirical examination of a phenomenon in its real-life context [START_REF] Per Runeson | Case study research in software engineering: Guidelines and examples[END_REF]. Typical methods of collecting data for case studies include surveys (interviews, questionnaires, etc.) and artifact analysis (source code, tests, and meta-data repositories, etc.). Case studies are extremely valuable for the field of Software Engineering since they provide both researchers and practitioners with valuable practical insights that cannot be observed in a controlled experimental environment. To gather data for such studies, cooperation between researchers and practitioners is essential.

Establishing collaborations to perform case studies is not a straightforward task [START_REF] Leigh | The practical challenges of case study research: Lessons from the field[END_REF]. Various factors make this a challenge:

(1) Using personal networks The most obvious method would be to use one's personal network to reach potential collaborators. Frequently, this approach may be enough [START_REF] Verdecchia | Architectural Technical Debt: A Grounded Theory[END_REF]. However, it has the following disadvantages: When performing case studies, researchers' and practitioners' goals may diverge significantly [START_REF] Sherman | Conducting a Long-Term Case Study in a Software Firm: An Experience Report[END_REF]. Researchers and practitioners operate on different Technology Readiness Levels (TRLs) [START_REF] John | Technology readiness levels[END_REF]. TRLs range from TRL 1 ("Basic Principles Observed and Reported") to TRL 9 ("Actual system "flight proven" through successful mission operations"). Researchers usually work on TRLs from 1 to 3, whereas practitioners require practical and applicable results, i.e., TRLs from 7 to 9.

(3) Data vaporization

After the data is collected and a paper is published, the data may be made public for future use. However, this is not always the case. Sharing case study protocols is not the norm, nor does there exist a space dedicated to storing such data. This means that valuable data may get lost, and potential future research can not be accomplished.

Several other concerns and challenges, including internal politics [START_REF] Leigh | The practical challenges of case study research: Lessons from the field[END_REF], use of employee time, individual participant biases as well organizations' concerns regarding the use of their data, also negatively impact researchers' ability to produce high-quality case studies [START_REF] Sherman | Conducting a Long-Term Case Study in a Software Firm: An Experience Report[END_REF].

Our goal is to improve this situation by creating a service that:

(1) Allow researchers and practitioners to find each other to create collaborations.

RESEARCH METHOD

We plan to first perform the following steps described in the subsections: gather researchers' and practitioner's requirements, build a requirement matrix to identify key requirements and friction points. On this basis, we will design and implement a case study marketplace service. An overview of the research plan is given in Figure 1.

Practitioners' requirements

To gather information about the practitioners's requirements, we plan a two-step approach. Firstly, we plan to interview practitioners to obtain qualitative data. This will be followed by a survey that would support our findings with quantitative data. This research will focus on the following questions:

(1) What do practitioners hope to gain from case studies?

(2) What leads practitioners to participate in case studies (Do's)?

(3) What deters practitioners from doing case studies (Dont's)?

Researchers' requirements

To obtain researchers' requirements, we plan to obtain qualitative data from a focus group discussion, quantitative data from a survey, and additionally perform a Systematic Literature Review to inspect their current approach to case studies. Our focus group and survey will aim to answer the following questions:

(1) What do researchers hope to gain from case studies?

(2) What demands (requirements) do researchers place on industrial partners? (3) What are their experiences with case studies? What worked?

What did not work?

The systematic literature review, will summarize the latter:

(1) How do researchers find participants for their case studies? Do they report this information?

(2) What kind of research questions do researchers usually want to answer with case studies? (3) What data collection methods do software engineering researchers use in case studies? (4) Are the case study protocols and data shared? In what form?

Requirements matrix

We plan to summarize our findings in the form of a requirement matrix. The requirements will be divided into the following categories.

(1) Mutual points -requirements that match from both groups.

(2) Distinct points -non-contradictory requirements that should be satisfied to find a collaborator from one of the groups. (3) Friction points -contradictory requirements, which create problems that have to be addressed and solved.

Design and implementation

After an in-depth analysis of the key requirements from both researchers' and practitioners' points of view, we will proceed to design and implement the Marketplace for Industrial Case Studies.

( 2 )

 2 Allow practitioners to share their open problems and research needs.(3) Save case study protocols and data for future use. (4) Allow researchers and practitioners to share structured feedback on the case studies.