Agent-Based Modelling of the Evolution of Hydro-Sedimentary Connectivity: The Case of Flash Floods on Arable Plateaus

Abstract

Land use and landscape structure play an important role in the functioning of flash floods on the arable plateaus of northern France. Landscape structures have changed considerably over the last decades with an increase in runoff-producing surfaces and an enlargement of the plots. This evolution results in an increase in runoff volumes accompanied by an increasingly easy diffusion of runoff on the slopes. There is therefore potentially an increasingly frequent and important spatial connectivity from the plots to the thalwegs, which can lead to the formation of flash floods. This study proposes to model this diachronic evolution of connectivity in a small agricultural basin of Seine Maritime using a multiagent system (MAS) and to develop synthetic indicators characterising these spatial links in the flow processes. The model outputs show that spatial connectivity has been steadily increasing over the past 70 years due to the enlargement of the parcel grid and the growth of runoff surfaces. For example, for the same 20 mm/h rainfall, the connectivity indicator increases from 40.99% (in 1947) to 78.33% (in 2015). This observation is observed for all levels of rainfall intensity, including the lowest. This modelling, carried out for a 116 ha basin in arable farming, can be transposed to all small agricultural basins.

1. Introduction

Flash floods observed in northern France (and especially the Paris Basin) correspond to rapid and turbid flows that affect dry valleys. They occur following long winter rains or under the effect of violent storms [1,2].

The structure of the landscape also plays an important role in these hydrological phenomena, both in the genesis of runoff and in its path through the basin. By landscape structure, we mean all the material objects that characterise the landscape and the interactions that link them, including the occupation of the land, the parcel of land, the boundaries of the parcels, the road system, etc.

In the basins of the Pays de Caux, this landscape structure has changed considerably over the last few decades, leading to profound transformations. The main driving force behind these changes is the modification of agricultural practices, which intensified as they did throughout France during the second half of the 20th Century. The landscape consequences, from which the Pays de Caux has not escaped, are the retreat of meadows and orchards, the increase in cultivated areas, the enlargement of cultivated plots, and the removal of features deemed obsolete: hedges and ponds, in particular.

The move towards specialised cropping systems (maize, flax, wheat, etc.) at the expense of the traditional system (mixed farming) has contributed to increasing the vulnerability of the soil by leaving it bare during periods of heavy rainfall.

Finally, this agricultural intensification has generated a proliferation of practices that weaken the soil by making it very sensitive to runoff and erosion. More generally, this rationalisation of landscapes is the cause for a more general degradation of the environment: deterioration of water quality, silting of rivers, impacts on aquatic habitats, and more generally on biodiversity [3,4,5].

Measuring the impact of this evolution on the sensitivity of basins to runoff and flash flooding processes is a major issue. Various previous works have been based on the use of distributed modelling tools to reproduce the flow of runoff on a slope or in small agricultural basins [6,7,8,9,10,11,12,13,14].

At the same time, many authors have studied in detail the impact of landscape organisation on the links between flow-producing areas and the overall hydrological behaviour of the catchment. This is the “hydrological connectivity” that characterises the interactions between the surfaces and networks that produce runoff and convey it to the outlet [10,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29].

With the increase in computer memory capacity and the growing development of spatial analysis processes, methods derived from distributed artificial intelligence offer another alternative for modelling flow transfer in a watershed. These methods offer great possibilities. One of the most widely used approaches to simulate flow in a watershed is the cellular automaton (CA) [6,30]. One of the first cellular automaton-based models applied to flow simulation was developed by Murray and Paola [31]. This work [31] was followed by the application of numerous cellular automata models in a wide variety of environments [32,33,34]. Parsons and Fonstad [35] combined Manning’s equation and the principle of conservation of mass to allow sufficient interaction to represent the movement of water in a river. They were able to simulate with some degree of accuracy a flood hydrograph that fairly represents the observed hydrograph. RuiCells [6] was developed for the simulation of erosive runoff phenomena within small watersheds and for intense turbid flood phenomena.

Another approach to simulating flow in a watershed is the use of multiagent models, which differ from CA due to their use of a mobile entity called “agent”. Multiagent models provide a different view of the temporal and spatial dynamics of the flow in a watershed. Unlike the cell used in a CA, the agent is mobile, and its environment will change depending on its movements. The agent’s neighbourhood structure can vary in time and allows it to have great behavioural flexibility. To date, not many of these models have been used to simulate the flows of water and sediment in streams. However, Reaney [36] used agent-based modelling techniques in hydrology. Fleurant [37] presents a model of pollutant transfer in porous media using a multiagent approach. Rakotoarisoa et al. [38] was able to develop an agent-based model featuring “hydrological agents” and apply it to a small wine catchment. His model was able to correctly reproduce the hydrograph observed by the measurement stations. Similar to the model of [35], this work focussed on the integration of hydrological functions in order to have a correct flood hydrograph. These authors focussed on the spatial behaviour at a fine scale. However, the high degree of accuracy in hydrological parameters outshines the spatial aspect.

Reulier [39,40] has looked further into the spatial consideration of flows in bocage watersheds. Hydrological agents representing water flows could then be used to trace the path taken by water, but rainfall has not yet been fully integrated as a parameter. In our approach involving flash floods, we propose leveraging the capability of agent-based models to provide information on the spatial dynamics of flows. We are thus be able to recreate the path of surface runoff and have detailed information on its path through the landscape during a flood: genesis of the flood following a rainfall intensity that exceeds the infiltration capacity of the soil (origin of the water supplying the runoff); flow trajectory; interaction with an infiltrating or runoff surface; and interaction with various landscape objects. Subsequently, we are able to provide spatialised indicators, especially with respect to connectivity.

Note that this work models spatial connectivity to simulate water passages at all points in space. This was not previously performed in other works.

The objectives of this article are threefold: i. to implement a model to measure the effect of changing landscape structures on hydrological connectivity; ii. to test the model on a small catchment area sensitive to runoff and fast flows by conducting a diachronic analysis over a 70-year period; and iii. to develop synthetic indicators to characterise the variations in connectivity over time.

2. Materials and Methods

For this research work, we followed a specific approach composed of several steps (Figure 1). The first step aims at clarifying the questions that we wish to answer and the identification of the processes to be modelled. In our case, the questions revolve around the quantification of hydrological connectivity and are presented in the following sections. Then, we proceed to the conceptualisation of the system. This involves formalising the hypotheses established in the previous step so that the “concepts” that comprise the model are well described. At the same time, we can then collect the data we need to feed the model. Once this conceptual model is well defined, we can proceed to the implementation phase (computer coding). Once the model is coded and ready to be executed, we can compare its outputs with the reality on the ground (validation) and finally use the model to answer the questions. In our case, this work leads to the creation of spatial indicators that can characterise the hydrological connectivity.

2.1. Case Study: Presentation of the Study Catchment Area

To address the issue of rapid flooding on arable land plateaus, the choice was made to work on the Etretat slope, which has a physiognomy (morphology, landscape, outlet to the sea, etc.) that is fairly representative of the coastal valleys of the Upper Normandy chalk plateau.

The basin covers a predominantly agricultural area of 133 km² located in the Pays de Caux, near Cap d’Antifer. The main valley, 25 km long, is a dry valley of rather exceptional dimensions in the region. At the outlet of this basin, the town of Etretat, a world-renowned tourist town, is sensitive to various risks: storm surges, rising groundwater, and rapid flooding. The catchment area has silty soils that are prone to siltation and during long winter rains or spring and summer storms, runoff processes can become significant and form turbid flows that concentrate in the valleys. These are small, flash floods known locally as mudflows.

The Etretat catchment area is composed of a group of small dry valleys, mainly agricultural, with similar hydrological behaviour. For our study, one of these sub-basins, considered as representative, was chosen: the Glape basin (116 ha) (Figure 2). We chose to work on this catchment because it is one of the most sensitive areas to this type of phenomenon (flash floods) in France due to the morphology of dry valleys and the instability of the soil.

2.2. Identification of the Landscape Structure in the Selected Pilot Catchment

To assess the reality of the landscape changes and their consequences on the flash flooding processes in the study area, a diachronic analysis was carried out on the Glape basin.

The characterisation of the landscape structure is based on the use of images (aerial photographs and orthorectified images) available free of charge from the IGN (National Institute of Geographic Information). To better understand the evolution of the landscape over the last sixty years, three dates were chosen: 1947, 1994, and 2015 (Figure 3).

After orthorectification and georeferencing, digitisation was carried out to identify the landscape structure for the three different dates. The entities that were chosen to constitute the typology are the following: water surfaces, cultivated surfaces, meadows, wooded surfaces, gardens, orchards, and buildings.

2.3. Presentation of the MAS Model

To understand the evolution of the relationship between landscape entities and spatial dynamics of flows, a model developed under multiagent systems was used. The multiagent approach is characterised by its ability to “bring out collective behaviours that are the result of individual actions and interactions”. Despite some promising works [36,37,38,39,41,42,43,44], the use of MAS in the analysis of spatial flow dynamics remains rare.

The principle of MAS is based on the design, construction, and modelling of a complex system composed of individualised entities that can act autonomously while interacting with each other [41]. These entities are called agents [41]. This type of modelling allows for better analysis of a complex system through the use of behavioural rules and simple interactions [45,46].

For the study of physical processes involving flash floods, the multiagent system approach differs from classical hydrological models (such as SWAT, HEC-HMS) in its ability to provide information on the spatial dynamics of flows [39,40,42,43].

More concretely, this approach allows us to rebuild the course of surface runoff and to have detailed information on its path through the landscape during the flood: genesis of the flood following a rainfall intensity that exceeds the infiltration capacity of the soil (origin of the water feeding the runoff); flow trajectory; interaction with an infiltrating or runoff surface; and interaction with various objects in the landscape [36,39].

For the presentation of the model, the ODD (Overview, Design concepts, Details) protocol [47] was chosen.

2.4. Objectives

The overall objective of the model is to spatially quantify the hydrological connectivity of a watershed according to its landscape structure. The aim is to provide answers to the following questions:

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Where is runoff occurring in the basin?

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Who? Which parcels discharge runoff that enters the basin outlet?

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When? What are the triggers and what are the consequences on the flows?

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How did this happen? How has the evolution of the landscape during the last seventy years affected the spatial dynamics of surface runoff?

2.5. Implementation of the Model (Netlogo)

The Netlogo platform was chosen for it is ease of use, its dedicated programming language, and its relative flexibility concerning geographical data (Figure 4).

2.6. Description of the MAS Model

The MAS model is essentially based on the LASCAR (Landscape Structure and Runoff) model [39,48] coupled with the model of [38].

Respectively developed for bocage and vineyard applications, the models have been modified in order to adapt the model to the landscape characteristics of the Glape basin. A brief description of the model is given together with an explanation of the additions that have been made.

2.6.1. Input Data

The input data come mainly from GIS files, which have been processed beforehand (digitisation, georeferencing, orthorectification).

• A digital terrain model (DTM) representing the topography in raster format. The data used come from the RGE Alti^® (Référentiel à Grande Echelle) with a resolution of 5 m × 5 m provided by the IGN.
• A “flow direction” raster file, which for each cell identifies the cell in its vicinity that has the greatest downward slope, based on the DTM (resulting from a GIS processing in ArcMap).
• Land use, derived from the digitisation of the images and aerial photographs described in the previous paragraphs, in vector format.
• The location of the facilities (fascines, hedges, ponds), in vector format.
• The location of roads in vector format, from the IGN BDtopo.

2.6.2. Entities

Two main types of agents (Figure 5) are used in the model:

• Hydrological agents that represent the flow of water in the form of “water packets” [42]. These are mobile agents, called “turtles” [39], which can move on the land cells. Under Netlogo, the term “turtles” is used to designate these agents. (In the rest of the report, the terms “agentdrops” and “turtles” refer to the same entity: the “hydrological agent”.)
• Immobile terrain agents, also called “field cells”, each representing a portion of the space and possessing topographic and hydrological characteristics resulting from information coming from the input data, in particular, the digital terrain model (DTM). In Netlogo, these agents are referred to as “patches” (The terms “cell”, “field cell”, and “patch” refer to the same entity: the “field unit”).

Each type of agent has a number of attributes, and is able to perform certain actions throughout the simulation. These attributes and actions are represented in Figure 5 by means of a class diagram.

The Hydrological Agent

The hydrological agent, named here “Agentdrops”, is an individual entity that moves “like a portion of flow in the simulation environment” [40]. These agents do not necessarily die on contact with the ground but can continue to exist, thus forming the surface flow. These agents are located in space and therefore have spatial coordinates (x, y) that make them easy to locate at any time during the simulation. In order to give a better picture of the hydrological processes (runoff and infiltration), each “agent-drop” contains a discrete volume of water (represented by the variable stock_in_water). These hydrological agents also carry with them information that will be used as indicators when evaluating the connectivity of the spaces at the end of the simulation. This is made possible by the ability of the agents to memorise the name of the patch on which they are located at the beginning of the simulation (start-patch variable), i.e., the zone where the flow was initiated.

As the simulation progresses, the agentdrops that are at a given time in the same place (on the same terrain cell) will “merge” to form a single agentdrop. This “merging” is carried out by means of an action specific to agentdrops, the concatenate action. All the attributes of these agentdrops will be combined and assigned to a new “agentdrop”. This “merging” saves computing time and makes it possible to work with increasingly fine spatial resolutions. This aggregation also makes it possible to bring out interesting behaviours that could not otherwise be observed.

In addition to the concatenate action, the drip agents perform two main actions during the simulation: the infiltrate action and the runoff action. These last two actions are conditioned by hydrological (infiltration capacity, rain intensity) and topographical (altitude) parameters that require an interaction with the land cells.

The Field Unit

The spatial environment in which the “agentdrops” evolve is composed of a network of two-dimensional square cells that encompass the entire basin under study.

This grid structure is based on the resolution of the digital terrain model (DTM). The resolution is 5 m × 5 m (resolution of the RGE Alti provided by the IGN). Different attributes characterise these terrain cells. Some of them come directly from the input data in GIS format: spatial coordinates, altitude, direction (the direction towards which a drip agent located on the cell should move), target (the neighbouring patch towards which the drip agent moves based on the information provided by the direction data), land use (pond, building, wood, grass, crop, garden, or orchard). The outlet and issue variables are “true or false” (Boolean) variables that indicate whether the patch concerned is an outlet or an issue. The issue patches correspond to roads, buildings, or gardens. If the patch is neither an outfall nor an issue, it is given the value “false” for these two attributes.

Other attributes are parameters, which can be set according to the needs of the modelling. The usable_reserve attribute represents the infiltration capacity for each land cell, which is different for each type of land use and according to the modelling hypotheses that are taken (simulation of winter or spring runoff, simulation for a particular date, etc.). Finally, some attributes have been designed to be output variables that are used to feed the different types of connectivity indicators. The connected variable is used to indicate whether the agentdrop emitted from a patch was able to reach the outlet at the end of the simulation. The attributes volume_of_water_start and volume_of_water_finish, respectively, designate the stock_in_water carried by the agentdrop that originates on the patch, and the stock_in_water of this same agentdrop when it arrives at the outlet (the volume_of_water_finish is equal to zero if the agentdrop does not reach the outlet). The attributes connectivity_V and connectivity_S are used to calculate the degree of connectivity of each parcel according to the proportion of water volume reaching the outlet (connectivity_V) or the percentage of connected surface (connectivity_S). Finally, the attributes volume_total and volume_max indicate, respectively, the sum of the stock_in_water of all the agents passed over the patch during the simulation and the maximum stock_in_water among the stock_in_water of the agents that passed over the patches during the simulation.

The terrain cells are affected by two main actions: i. the rain action, which simulates rain at the very beginning of the simulation (the patch creates a drop agent); ii. the calculate_connectivity action, which groups together all the operations for calculating connectivity indicators from the results of the simulation. The calculation mode of these attributes referring to connectivity is explained in the following paragraphs.

Interactions between Agents and Cells

The hydrological agent (drop agent) and the field cell interact constantly during the simulation. Each agentdropper knows at each moment the identity of the patch on which it is located (patch-here attribute). In the same way, each patch can interact with all the agentdrops present on it (agentdrop-here attribute). Each agentdropper knows the name of the patch on which it is located at the beginning of the simulation (start_patch attribute). In addition, each agent-merge generates lists of variables (list_start_patch attribute). Each list contains all the start-patches of all the agents that have merged.

2.6.3. Spatial and Temporal Scale

The Space

The simulation environment is discretised into 5 × 5 m cells based on the regular square grid of the digital terrain model. The small size of the catchment under study ensures this fine resolution (116 ha).

The Time

The simulation is based on a succession of iterations during which the agents will perform actions. The speed of flow is not taken into account in the model. The “time step” is therefore not represented by a temporal unit (seconds or minutes) but by an iterative unit (designated by the term tick in the Netlogo platform).

2.7. Running a Simulation

2.7.1. Initialisation

Before launching a simulation, an initialisation phase is required. The information from the GIS files is then integrated and transformed into attributes specific to each land cell (altitude, land use, etc.). The values of the input parameters are also chosen beforehand.

The most important parameters are rain intensity (mm/h) and infiltration rate (mm/h). The infiltration rate is different for each type of land use, the landscape structure specific to each basin, and to the simulated time period (historical or current).

2.7.2. Simplification Assumptions

In order to be able to take into account the hydrological characteristics of different types of land use and to be able to integrate rainfall as a relevant input variable, simplification assumptions have been made concerning the model. These simplifications are explained here so that the results can be correctly interpreted.

Assumption 1.

The first assumption is the following. It is assumed that rain falls instantaneously at the beginning of the simulation and that runoff (if any) does not start until after this time. Rain and runoff are therefore not simultaneous. If, for example, we want to simulate a rainy episode with an intensity of 30 mm/h, at the beginning of the simulation the 30 mm of rain will fall instantaneously on the basin. This rainfall is materialized by the creation of agentdrops on each land cell. All of these newly created drops will have a water stock value equal to 30 mm. This simplified hypothesis avoids the creation of too many drops. It is also sufficient to highlight the spatial connectivity at the watershed scale.

Assumption 2.

A second simplifying assumption comes in parallel to the first assumption mentioned above: the useful reserves of each land cell do not empty throughout the simulation. This assumes that for a field agent belonging to a surface with an infiltration rate equal to 10 mm/h, the model will assign to this field agent a useful reserve equal to 10 mm. This useful reserve may decrease as the simulation progresses (due to the infiltration of drip agents), but in no case will it be renewed.

Assumption 3.

These two assumptions can only be accepted if a third one is respected: the duration of the simulated event does not exceed 1 h. This implies that the use of the model, in the present version, is only fully suitable for small catchment areas with a concentration time not exceeding one hour.

Assumption 4.

The last hypothesis concerns the infiltration capacities. Delahaye [49] proposed a parameterization in the Ruicells cellular automaton [6] during the simulation of a spring flood on a catchment of the Seine–Maritime department (Villers). Our simulation is set up with the same parameters. (For crops, it was based on the Benkhadra model [50] combined with field observations; for grasslands on experimental data [49]; and for buildings, on the literature concerning sparsely populated areas [51]).

The values of the infiltration parameters to be considered are therefore the following: infiltration rate of grasslands and woods: 50 mm/h; infiltration rate of habitats (building and garden): 5 mm/h; infiltration rate of crops: 1 mm/h (in this configuration, the agricultural soils are degraded with a completely formed surface crust).

2.7.3. Simulation (Functions and Actions)

After initialization of the model, the “rain” action is executed. This action consists in the creation of one (1) drop agent on each terrain cell

Then, for each iteration, the agentdrops perform a succession of actions (Figure 6):

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The concatenate action: The stock_in_water variables of all the agentdrops present on the same patch are added together and the start-patch variables are grouped into a list named list_start_patch. The ndrops attribute is used to count the number of agentdrops that have merged to form the new agentdrop. At each “merger”, the ndrops variable of the agentdrops that are going to merge is added and then assigned to the ndrops variable of the newly formed agentdrop.

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The infiltrate action: the agentdrop inspects the usable_reserve variable of the patch it is on and compares it to its stock_in_water variable. If the usable_reserve is greater than the agent’s stock_in_water variable, the agent dies by infiltration. The stock_in_water value is then subtracted from the usable_reserve of the patch. If, on the other hand, this usable_reserve is lower than its stock_in_water, the agentdrop does not infiltrate and can continue its path. The value of the usable_reserve of the patch is still subtracted from the stock_in_water of the agentdrop. The usable_reserve of the patch becomes zero because it is saturated.

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The runoff action: if the agentdrop is still “alive” at this stage, it proceeds to the runoff action, which consists of moving towards a neighbouring “target” patch. The presence of an obstacle induces a blockage or a deviation for the agentdrop.

When the drip agent is located on the “outlet” patch, it transmits the information gleaned during the start_patch simulation via list_start_patch and then dies.

2.8. Quantifying Hydrological Connectivity: Development of Spatial Indicators

In the model, different indices have been set up to assess the connectivity within the catchment. As soon as a drop agent reaches the outfall, its starting patch is considered to be connected to the outfall [52].

Three types of connectivity indicators have been developed:

The simple connectivity indicator Ic. This is an indicator that immediately concerns the land cells. It is a true or false variable.

The connectivity indicator according to the share of connected areas$I{c}_s$ is an indicator at a parcel scale. The unit of study is therefore the plot. This indicator calculates, for each plot, the number of connected patches. By multiplying this number by the area of a patch, the connected area (S_C) can be calculated. By relating this area to the total area of the patch (S_T), we obtain the connectivity indicator according to the percentage of connected area $I{c}_s$.

$$I{c}_s=\frac{S_C}{S_T}\times 100$$

where $S_c$ is the connected area and $S_T:$ is the total area of the plot.

The connectivity indicator by volume of water connected$I{c}_v$ maps the proportion of the volume of water discharged from the plot that reaches the outfall in relation to the total volume of precipitation discharged. For example, if the stock_in_water of the drop is 15 mm when it arrives at the outlet and its list_start_patch is composed of three patches, each of these three patches is assigned a value of volume_water_finish equal to 15/3 = 5 mm.

The indicator is then calculated as the quotient between these two values.

$$I{c}_v=\frac{V_c}{V_T}\times 100$$

where $V_c$ is the volume of runoff from the plot that reaches the outlet and $V_T:$ is the volume of precipitation falling on the whole plot at the beginning of the simulation.

Figure 7 shows an example of the application of each of these indicators to the Glape basin (modelling a 5 mm rainfall event applied to the basin with the 1994 landscape configuration). While the $Ic$ indicator is distinguished by its cellular scale, the $I{c}_s$ and $I{c}_v$, which are both at the parcel scale, do not show much difference in spatial distribution and are therefore both applicable if one wants to focus on parcel connectivity.

3. Results and Discussion

3.1. Landscape Evolution for the Glape Catchment Area

Figure 8 shows the evolution of the landscape structure of the Glape catchment. In 1947, the proportion of cultivated land and grassland was roughly equal (46% cultivated land and 43% grassland). The average size of cultivated plots was 1 ha. Apart from the proximity of inhabited areas (houses and gardens), hedges did not exist in this open field landscape, typical of the silty plateaus of northern France.

In 1994, the area devoted to agricultural activities increased significantly (65% in 1994, +19 points). Among these crops, a few plots were set up on long-established meadows. The average size of the plots was now 1.6 ha. Grassland now represented only 23% of the area of the basin. There was also a slight increase in urbanised areas, especially downstream from the catchment area.

In 2015, the evolution of land use was still very marked, with 73% of land under cultivation and a net decrease in grassland (13%). The average size of agricultural plots was increasing (equal to 2.8 ha, i.e., three times larger than the 1947 plots).

As far as urban expansion is concerned, although the surface area of urbanised areas had not increased significantly (1% of the total surface area of the basin, i.e., almost the same proportion as in 1994), the number of dwellings had increased considerably. Moreover, these newly built dwellings were located downstream from agricultural plots likely to produce runoff.

We are therefore witnessing not only an evolution of the landscape that favours the production of runoff (increase in cultivated areas), but also an increase in the vulnerability of the system by an overexposure of stakeholder infrastructure (construction of new dwellings in areas exposed to hazards, downstream from the agricultural plots).

The analysis did not take into account the diachronic evolution of linear features (hedges, ditches, etc.) because the basin under study is an open field landscape, occupied by large-scale cultivation and where the density of these features is very low or even absent.

3.2. The MAS Model to Identify the Intensity of Connectivity

Before proceeding to the diachronic simulation, it is necessary to verify whether the MAS reconstructs the water paths and thus the connectivity between the plots in the basin. To perform this validation, the model is tested by reconstructing the flow paths of an actual episode that has been documented.

3.2.1. Description of the 24 August 2015 Episode

On 24 August 2015, the inhabitants of Le Glape were once again confronted with runoff from the plots upstream from Rue de la Mare Tina (Figure 9). The meteorological station of Poterie Cap d’Antifer located just near the pond records the following data: a cumulative rainfall of 95.7 mm following 19 August allowed the formation of a driving crust. The 18 mm rainfall that occurred on 24 August, preceded by a 12.5 mm rainfall the day before, finally triggered the runoff. Even though it was located less than 5 km away, the measurement point did not capture the epicentre of the storm. The testimonies collected from the residents mention a rainstorm bringing more than 40 mm of rain in two hours.

The flood originated on the cultivated plots upstream from the pond called “Tina Pond” (Figure 9). The flow followed the street of Tina Pond before joining the street of Oursel farm (where it was reinforced by meeting the flow coming from the latter). As the topography becomes a little higher as it follows the road, the runoff left the road by branching off and passing through the dwellings (in particular, the B and B and “Oursel farm”). Thereafter, the runoff emerged beyond the dwellings to reach the road to Gonneville. This is where it was reinforced by the inflow from another plot and ended by completely flooding the road, preventing traffic.

3.2.2. Simulation of the Episode by the Multiagent Model

To represent the rainfall of 24 August, the “rain intensity” parameter is set at 20 mm/h (i.e., the average hourly rain intensity measured by the residents). For the infiltration velocities, the parameterisation presented in the model description is used.

The simulation follows the methodological protocol presented above; however two additional attributes are calculated for each cell in order to obtain a map of water circulation at any point in space:

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The total volume attribute, which indicates the sum of the water_stocks of all the drip agents that passed over the patch during the simulation;

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The volume_max attribute, which represents the maximum water_storage among the water_storage of the agentdrops that are passed over the patches during the simulation.

The model reconstructs well the dynamics of the water circulation and the hydrological connections between the different parcels in the basin. It is this property that is useful for the rest of the demonstration.

3.3. Comparison of Model Outputs for Different Landscape Structures

3.3.1. Experimental Design

Once the applicability of the model is approved, it can be applied to the different landscape structures described above (1947, 1994, and 2015) by testing different rainfall scenarios.

Thus, the experimental plan is as follows:

The main output of the model that is mapped and presented here is the $I{c}_v$ (connectivity indicator according to the volume of water connected). Global results are also calculated for each simulation (total connected area, total volume reaching the outlet, etc.).

Nine scenarios are analysed based on the following six parameters:

• The intensity of the rainfall, which varies among the following values: 5, 20, and 40 mm/h;
• The landscape structure for the three different dates: 1947, 1994, and 2015.

3.3.2. Analysis of Model Outputs in the Glape Basin

Figure 10 shows the evolution of indicator $I{c}_v$ over the years according to the different types of rainfall.

Table 1. Evolution of the connectivity indicator Ic_s.

Ics Global	5 mm	20 mm	40 mm
1947	21.80%	43.04%	51.72%
1994	52.70%	70.53%	75.42%
2015	67.06%	80.74%	84.51%

and

Table 2. Evolution of the connectivity indicator Ic_v.

Icv Global	5 mm	20 mm	40 mm
1947	21.86%	40.99%	50.03%
1994	52.17%	68.25%	73.76%
2015	66.73%	78.33%	82.74%

show the values of the indicators on a global scale (the indicators are related to the whole catchment area and not to the surface of a parcel).

In general, it can be seen that connectivity increases significantly from 1947 to 2015. For a rainfall of 5 mm, the connectivity increased from 21% in 1947 to 67% in 2015. This is also the case for other rainfall events. For a 20 mm rainfall, the connectivity increases from 43% (in 1947) to 80% (in 2015). Similarly, for a 40 mm rainfall, it increases from 52% (in 1947) to 85% (in 2015). This is true for both types of indicators ($I{c}_s$ and $I{c}_v$). However, the behaviour of this connectivity differs for the three dates. Indeed, in 1947, the connectivity for a 5 mm rainfall is completely different from the connectivity for a 40 mm rainfall. For 2015, this difference is smaller. This means that for the current landscape configuration, connectivity tends to remain strong regardless of the rainfall intensity of the event.

Table 3. Evolution of connected areas.

Connected Surfaces	5 mm	20 mm	40 mm
1947	25.2 ha	49.7 ha	59.7 ha
1994	60.8 ha	81.4 ha	87.0 ha
2015	77.4 ha	93.2 ha	97.5 ha

and Figure 11 show the evolution of the connected areas according to the years and the types of rainfall. The slope of the connectivity curve is steeper for 5 mm rainfall (slope = 0.77) than for 40 mm rainfall (slope = 0.56). This suggests that the evolution of the landscape structure from 1947 until now increasingly favours connectivity, especially for low intensity rainfall. This means that low rainfall, which previously would have favoured small-scale runoff trapped before reaching the outlet, can now cause much larger flows as the contributing connected areas increase.

Furthermore, the difference between the connected areas for a 40 mm rainfall and for a 5 mm rainfall tends to decrease over the years (Figure 12). This is also the case for the difference between the connectivity for a 40 mm rainfall and for a 20 mm rainfall. This only supports the observation made earlier: the evolution of the landscape to the current configuration means that connectivity tends to remain high regardless of the rainfall intensity of the event (even for low intensity rainfall).

3.3.3. Note and Interpretation of Model Outputs

Looking at the results, as expected, the increase in the value of the indicator over the 3 years seems to be related to the evolution of the landscape and the cultivation practices, especially the reduction in grasslands at the expense of croplands. A small part of these results can also be explained by urbanisation over the years.

We can also see that the indicators did not change much in 2015 for 20 and 40 mm (this is the same case for 1994, but more obvious for 2015). This is an interesting finding revealed by the model, probably due to the fact that 20 mm of rain is enough to put the whole network into operation.

The results found so far tend to show a strong increase in hydrological connectivity. However, it should be noted here that the simulations do not take into account the developments that have taken place over time. Some of them have been implemented, notably by the basin syndicate (fascines, grassed strips, etc.) in order to minimise the impacts of rapid flooding. The results should therefore be taken with the understanding that the model is likely to overestimate connectivity by not taking these features into account. However, the aim here was to analyse the effect of landscape evolution on connectivity, and in a second phase it will be possible to insert the development features to test their effectiveness in reducing connectivity.

3.4. Discussion

3.4.1. Conceptualization and Development of the MAS Model

In this multiagent model, the transition rules were developed to be simple and easy to implement, with various simplifying assumptions. Like most multiagent models, this makes it a tool that can be transposed and used in various problems. The comments of [53] have emphasized this simplicity of CA/MAS models compared to approaches based on physical equations. However, this point of view needs to be discussed. Certainly, the behavioural rules used to represent water and its path are often simple, but practice shows that the implementation of the model can introduce unexpected complexity into its overall behaviour. This is what makes these approaches so valuable. The complexity results mainly from the interactions between runoff generation, water flow, and infiltration.

The instantaneous rainfall (Assumption 1) and short concentration time (Assumption 3) seem to be sufficient for the work on our small watershed, provided that we keep about the same surface size, given the fine resolution of the DTM. These assumptions are also adapted to our region where most rainfall events are short and intense, such as thunderstorms, generating fast and sudden floods. This confirms the fact that the model presented in this paper is particularly adapted to the study of flash floods.

From the moment we want to free ourselves from these hypotheses, which can be limiting, the main obstacle to overcome is the memory capacity of computers. Indeed, a point that must be considered in cellular automaton or multiagent system type models is the computing time and the hardware requirements necessary to run the simulations. The simplifying assumptions that have been adopted allow us to run a simulation by creating only one (and only one) hydrological agent on each field cell during the rainfall simulation. Considering the resolution of our DTM, the model creates about 110,000 hydrological agents at the same time. With this, the simulation time needed with a good computer is already very long. With the ever-increasing evolution of computer memory, it will be possible to eliminate these assumptions with more powerful machines.

The choice aimed at not using the unit of flow measurement (m³/s) because our model is not intended to plot a flood hydrograph. Rather, its objective is to quantify connectivity based on synthetic spatial indicators. However, it is technically possible to calculate the discharge (m³/s) even with the “ticks” of the model. This has already been performed for the SMA model of [38], in which the authors were able to correctly reconstruct flood hydrographs and compare them to actual measurements. To this purpose, we considered the time step “ticks” as being a time step with a classical unit of time (the second, for example—in practice, however, it can be the time step corresponding to the hydrometric data that we have). We name this time step dt. Then, we assigned a displacement speed to the hydrological agent (by giving it a certain value or by using a hydrological formula—Manning’s equation, for example). We can then calculate, at each time step, the distance that is covered by the hydrological agent in one tick. Each agent then moves over this distance carrying its volume of water. Finally, to determine the discharge (in m³/s) at the outlet (or at any point where we wish to calculate it), we divided the sum of the volumes of water brought by all the agents on this point by the simulation time step dt. Although this goes beyond the objective of this paper, it would be interesting in other circumstances to consider using this technique.

3.4.2. Consideration of Soils

Recall that the purpose of this paper is to present a model capable of assessing (the evolution of) hydrological connectivity as a function of landscape structure. In contrast to other works [54,55], the question of incision is not addressed here. The morphology favours concentration and the slopes in small valleys are often higher than 3%, which is the minimum slope to observe incision processes [56] The soils here are thick with very good infiltration capacity (>60 mm/h), if not degraded on the surface.

Brown leached soils from loess cover most of the watershed. They have a silty texture with low clay content and reduced organic matter content. They are sensitive to crusting (battance phenomenon) because they have poor stability. Under the action of rainfall, the surface degrades, leading to a decrease in infiltration capacity [57,58,59,60]. The soil passes from a fragmentary state to a smoothed facies by dispersion of aggregates and welding together of particles (structural crust stage) and then sedimentation in puddles (sedimentary crust). The infiltration capacity during these different phases can drop from 60 mm/h to 1 or 2 mm/h [61].

To focus on the question we are interested in (i.e., the effect of land use on connectivity), assumptions were made, notably in assumption 4 (infiltration rate of crops = 1 mm/h, i.e., in this configuration, the agricultural soils are degraded with a completely formed surface crust). This means that the soil condition is already completely crusted during the simulation. For other uses, it is possible to apply the model with some adaptations.

3.4.3. Consideration of Rain

It can be seen in the rainfall data from the closest station (Figure 2) that extreme events exceeding 40 mm/day are quite frequent (some even reach 70 mm/day). Note that we can distinguish two types of flash floods typical of the Seine–Maritime and northwestern France: the flash floods qualified as “winter event”, which are generally observed from October—associated with long and repeated rains—and the “spring” events, which are mainly related to thunderstorms with a strong intensity. The latter generally occur between April and August. Spring floods are generally observed in small watersheds, such as ours (which are located downstream from larger watersheds). The rainfall associated with this type of phenomenon is characterised by a very high intensity but is often very punctual [49,62,63]. In this case, rainfall amounts vary from 40 to 70 mm, with strong amplitude of the storm duration. This is the case of the event presented in this article (24 August 2015), which is a spring phenomenon (rainstorm bringing more than 40 mm of rain in two hours). The rainfall simulated in our model fully represents these types of phenomena. (This makes the model and its assumptions even more adapted to our watershed).

4. Conclusions

This article proposes a method to evaluate the role of the evolution over time of landscape structures resulting from flash flood phenomena. The arable plateau of the Pays de Caux is taken as an example because its silty soils are sensitive to slaking, runoff, and erosion, and the small rural basins are regularly affected by flash floods.

An agent-based model was developed on the Netlogo platform. It simulates the flow of runoff between agricultural plots and measures the connectivity between them. From this model, it is possible to study the variation in this connectivity over time as a function of the evolution of land use, the organisation of runoff surfaces (aggregation, dispersion), and the constraints and obstacles that the drip agents encounter on their path. The model also allows the calculation of indices to qualify the state of this connectivity.

The first tests were carried out on a small catchment of 116 hectares by simulating the evolution of connectivity between 1947 and 2015 for different rainfall intensities (5, 20, and 40 mm/h). The results show both a strong increase in connectivity over time linked to the transformations of the basin, but also a convergence of the hydrological response for all rainfall intensities. Over time, the connectivity of the basin becomes strong even for small rainfall intensities (5 mm/h). This is an important conclusion because it is an argument that can orient the development and, in particular, intervene on the key plots that are responsible for this growth of sensitivity.

Obviously, the hydrological parameters used are quite simple because on these silty soils the infiltration capacity quickly becomes very low with the formation of the slaking crust. Water circulates quite freely throughout this open-field landscape because there are networks that allow water to circulate from plot to plot to the outlet (ditches, roads, etc.) and few obstacles inhibiting the free flow of water. Transposing this model to more complex landscapes will require adaptations.