# A path towards precision border irrigation combining hydrodynamic modelling and in-field sensor-based support

Paul Vandôme, Gilles Belaud, Mohamed Amine Berkaoui, Cédric Guillemin, François Charron, Crystèle Leauthaud

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Paul Vandôme, Gilles Belaud, Mohamed Amine Berkaoui, Cédric Guillemin, François Charron, et al. A path towards precision border irrigation combining hydrodynamic modelling and in-field sensor-based support. Agricultural Water Management, 2025, 316, pp.109518. 10.1016/j.agwat.2025.109518. hal-05193232

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# A path towards precision border irrigation combining hydrodynamic modelling and in-field sensor-based support

Paul Vandôme<sup>D</sup>, Gilles Belaud<sup>D*</sup>, Mohamed Amine Berkaoui, Cédric Guillemin, François Charron, Crystèle Leauthaud

G-EAU, Univ. Montpellier, Institut Agro, Cirad, INRAE, AgroParisTech, BRGM, IRD, Montpellier, France

## ARTICLE INFO

Handling Editor - Enrique Fernández

**Keywords:**

Border irrigation

IoT-based water management

Surface irrigation model

Precision irrigation

## ABSTRACT

Surface irrigation is often described as low performing insofar as its practice is labour intensive and involves the use of large water flows that are difficult to quantify and manage. However, this method remains predominant worldwide, and modernisation towards localised irrigation systems is not always feasible nor advisable. To support border irrigation management, we previously developed a low-cost sensor for surface irrigation management, which remotely informs the farmer of water arrival downstream of his field and therefore of the moment to stop irrigation. The objectives of this article were: (i) to determine the optimal position of this sensor lengthwise in the field throughout the season, and (ii) to compare the influence of management scenarios (current farmer's practices, sensor-based and time-based cutoff) on irrigation performance. To this end, an integrated agro-hydraulic model was developed to simulate surface water flow dynamics throughout the season including variations in infiltration and roughness. The model was run using monitoring data from the border irrigation of a hay field during a whole season in Southern France. The results showed that the optimal sensor position can change significantly over the course of the season, depending on inflow rates, initial soil moisture and Manning's roughness. Sensor-based irrigation control was found to be more efficient than current farming practices, with an estimated water-saving potential of 33%, and more effective than an optimised fixed cutoff time in limiting water losses induced by variability or uncertainty in the initial conditions. For some irrigation events, water savings could reach 50%. The methods and findings should serve as a basis for larger-scale studies integrating the adoption of sensors and real-time data for surface irrigation management.

## 1. Introduction

Surface irrigation is still by far the most widely used irrigation technique in the world (Pereira and Gonçalves, 2018; FAO, 2020). Its performance is generally described as poor, as its practice is labour intensive and requires large amounts of water that are used with a poor application efficiency. In the case of border irrigation, water is applied by the overflow of a canal at the highest point of the field and then flows down a slight slope to the lower point. The dynamics of the water flow are driven by the geometric variables of the field, the irrigation practices (flow rate, duration), and the properties of both the crop and substrate. Many studies have shown that it is possible to improve the performance of border irrigation by optimising the topography (González-Cebollada et al., 2016), the dimensions of the borders (Anwar et al., 2016; Nie et al., 2021a) and the practices by adjusting irrigation duration according to soil characteristics and inflow rates (Morris et al., 2015; Nie et al., 2019). To this end, several

numerical models have been developed, the most commonly used being field-scale and event-based models representing the advancement of the water front in one dimension, such as SISCO (Gillies and Smith, 2015), WinSRFR (Bautista et al., 2009, 2016) and SIRMOD (Walker, 2003).

Research has particularly focused on the optimisation of cutoff times (Ghorbanian et al., 2024), i.e. the time at which the water supply is turned off, firstly because of its significant effect on irrigation performance, and secondly because of the convenience of fixed irrigation schedules in advance. However, this approach may have some limitations under real conditions. Xu et al. (2019) showed for example that the temporal variation of infiltration and roughness in different seasons had significant impacts on surface water advance times and performances. Furthermore, variations in inflow rates are practically unavoidable in surface irrigation systems, for reasons both internal (actual flow is often unknown, e.g. due to a lack of measurement

<footnote>* Corresponding author.
E-mail address: gilles.belaud@supagro.fr (G. Belaud).</footnote>
systems) and external (collective water management rules, water al-
location restrictions, etc.) to the farm. Also, while cutoff times may be
considered as a maximum duration when water can be used, there is
an increasing interest to reduce these durations, first to save water, and
second to minimise the impacts of excessive irrigation.

In these circumstances, the search for a cutoff distance ratio (CR),
defined as the ratio of the advance distance at cutoff to the total
field length, rather than a cutoff time, may help to mitigate uncer-
tainties (Salahou et al., 2018). However, to our knowledge, there is
no clear comparison of both strategies applied at seasonal scale, where
infiltration, roughness and discharge vary considerably and are mostly
unknown.

The feasibility to use real-time monitoring and control was explored for furrows (Koech et al., 2014) and border irrigation (Smith et al., 2016), with a field implementation in different farms, using ultrasonic flow depth sensors and a commercial communication system. In the case of linear advance, measuring the time when the front reaches the middle of the field allows to calculate when to stop irrigation at the optimal time, and this can be applied even though the roughness is not determined accurately (Smith and Uddin, 2020). The benefit of realtime sensing is to adjust the irrigation parameters using actual field conditions, which may be unknown accurately, such as roughness or infiltration rate. Nie et al. (2021b) suggested to use a larger ratio (0.75) to determine the optimal cutoff time. However, this requires specific conditions implying linear advance, then a rather advanced procedure in order to evaluate the optimal cutoff time has as a function of the mid-distance time or the time to reach 75% of the plot.

Other than these technical issues, the adoption of improved moni-
toring practices for irrigation is a challenge for farms with low financial
and technical capacities. Recent developments in the fields of on-board
electronics and long-range communication networks have led to the
development of new wireless sensor networks for agriculture (Hamami
and Nassereddine, 2020). A proof-of-concept of an integrated system
with automatic soil-water sensors and a gate controlled by moisture
depletion was published for border irrigation (Pramanik et al., 2022).
Surveys and workshops with farmers revealed the potential of even
simpler technologies (Vandôme et al., 2024), such as a sensor alerting
of the arrival of water at the downstream side of the field at the desired
cutoff time. By making sensor-based irrigation control economically
and technically accessible, these new technologies are likely to spread
widely beyond the world of precision agriculture and might be adopted
in surface irrigation systems. Yet, the benefit of adopting such practices
on border irrigation performance remains to be evaluated. More specifi-
cally, where should the sensor be located in the field to meet crop water
requirements while optimising application efficiency? How do these
optimal locations evolve over the course of the season? And to what
extent is this practice beneficial compared with the cutoff practices
traditionally used?

In light of these considerations, the objectives of this study were
(i) to determine the optimal longitudinal position of a basic water
detection sensor for border irrigation control throughout the season
and (ii) to compare the effects of sensor-based control with the use of
the fixed cutoff time method on application efficiency and satisfaction
of water requirements for border irrigation. To do so, we developed a
new integrated model (Surflrri) coupling a surface water flow simulator
with dynamic crop and soil models and different irrigation strategies
for irrigation duration. These strategies were evaluated using field
monitoring data from Southern France, representative of actual border
irrigation practices, over a full irrigation season.

## 2. Material and methods

### 2.1. Overall approach

We addressed these objectives through an original approach com-
bining the monitoring and simulation of surface irrigation water flows

of a hay field at the time scale of the cropping season. The rapid
growth of the crop under fluctuating climatic conditions and the regular
changes in the irrigation inflow rates over the course of the season
make it difficult to optimise border irrigation strategies on such a
time scale. To account for this seasonal variability in initial conditions,
we integrated models of surface water flow, vegetation growth and
soil water content, which allowed dynamic simulations of the changes
in both Manning's roughness and soil moisture. The optimisation of
irrigation strategies was then based on this integrated model, that
took into account the seasonal variability in hydrodynamics processes,
to explore suitable and scalable management scenarios for the cutoff
of border irrigation. The overall methodology is illustrated in Fig. 1,
showing the logics between the main steps detailed below.

2.2. Study area

The irrigated territory of the Crau (600 km²), South of France, counts 14 000 ha of border irrigated hay by water distributed through a network of open channels from the Durance river. The hay meadows, which are multispecific and permanent, are harvested three times a year for a total yield of around 10 tons ha⁻¹. Surface irrigation is traditionally practiced on open-ended borders that range in length from 100 m to 500 m and slope from 0.2% to 0.4%. The irrigation schedule, mainly imposed by the Water User Associations, is based on a frequency of eight to ten days during the months from March to October, during which irrigation management is labour-intensive (Merot et al., 2008a). With applied irrigation volume of around 20,000 m³ ha⁻¹ year⁻¹, of which 60% to 80% is drained and percolated, the irrigation efficiency of the Crau hay is low (Merot et al., 2008b), and the increasing pressure on water resources in the region raises the question of the system's sustainability. However, those percolated volumes largely contribute to the recharge of the Crau aquifer, which provides domestic water for 300,000 residents and irrigation water for around 5000 ha of micro-irrigated orchards (Saos et al., 2006; Olioso et al., 2013; SINERGI, 2020). Given this fragile balance, the search for tools to better understand and manage border irrigation is essential.

The experimental farm of Institut Agro, located within the area (43.643748N, 5.016744E, WGS84), produces hay on 150 ha. The cropping system, and particularly the irrigation practices, are representative of that found within the Crau plain. A number of studies have been carried out, providing data and references used in this study.

2.3. *Surflrri model*

### 2.3.1. *Model overview*

The aim of the Surflrri model is to simulate water flows and crop
development for a surface irrigated system over a time period. It
includes flow transfers during border irrigation events on scales rang-
ing from the field to the irrigation scheme, including irrigation and
drainage networks. It was built by coupling several pre-existing field
level models for crop and water flows: (i) an infiltration and sur-
face water flow simulator (adapted from Calhy model, Bader et al.
(2010)); (ii) a leaf area index (LAI) variation simulator to simulate the
seasonal crop development (adapted from SPFC model, Mailhol and
Merot (2008)) and (iii) a seasonal soil water content variation simulator
(adapted from SPFC, Mailhol and Merot (2008)). The coupling of
the simulators and the spatio-temporal discretisation of the integrated
Surflrri model (Villafañe, 2018) were carried out using the open-source
OpenFluid platform (Fabre et al., 2010), in which the specific module
Surflrri was coded in C++. Fig. A.8 shows the simulators specifically
developed for surface irrigation (soil water content, vegetation growth,
and surface water flow, which includes the management of inflow), as
well as input data, output variables and links between all simulators.
Details of all the variables and parameters are given in Table A.3.
<figure><img src="image_3.png" /><figcaption>Fig. 1. Overall methodology of the study: main steps, from left to right. Methods are detailed in the following sections.</figcaption></figure>

### 2.3.2. Simulation of surface water flow during irrigation

Considering the low width to length ratio of the plots, which are laser-levelled, the 1D-approach of WinSRFR was chosen. Some adaptations were needed in order to account for varying roughness as a function of crop stage, as well as initial soil moisture, which results from daily soil water balance. WinSRFR was used for comparison or calibration on specific events.

Following Bader et al. (2010) For infiltration, the formulation of Green and Ampt was chosen. It has the great advantage to consider explicitly the role of initial soil moisture on the flow dynamics. Run-off is classically represented by the diffusive wave equation, simplified form of the Saint-Venant's equations (Vieira, 1983):

$$ \frac{\partial h}{\partial t} + \frac{\partial q}{\partial x} = -f \qquad (1) $$

and

$$ S = S_b - \frac{\partial h}{\partial x} \qquad (2) $$

with h water depth (m), q discharge per unit width (m²/s), f infiltration rate (m/s), S hydraulic gradient, S_b bed slope. Functions h, q and f depend on time t and distance x.

The hydraulic gradient is given by the Manning equation, in which the hydraulic radius can be approximated by the water depth:

$$ S = n^2 \frac{q^2}{h^{10/3}} \qquad (3) $$

with n Manning roughness coefficient at time t (s m⁻¹/³).

Finally, the Green and Ampt model was used to simulate infiltration depending on topsoil saturation:

$$ F < Z \cdot (\theta_s - \theta_i) \Rightarrow f = K_s \cdot \left[ 1 + \frac{(\theta_s - \theta_i) \cdot (H_f - h)}{F} \right] \qquad (4) $$

$$ F \geq Z(\theta_s - \theta_i) \Rightarrow f = K_s \cdot \left[ 1 + \frac{h}{Z} \right] \qquad (5) $$

with F the infiltrated depth (mm) at time t between x - δx and x, Z the thickness of the top soil horizon (mm), θ_s the soil moisture content at saturation (m³ m⁻³), θ_i the instant soil moisture (m³ m⁻³), K_s the soil hydraulic conductivity (m s⁻¹) and H_f the capillary suction at the wetting front (m). The set of equations was discretised in space and time, as described in Bader et al. (2010).

### 2.3.3. Simulation of vegetation and soil water content variations

In the case of hay, vegetation height and density are highly variable throughout the year, due to harvest and plant growth. This impacts the flow resistance. Using the daily leaf area index of the plot, LAI, as a proxy of plant development, the roughness coefficient was calculated from the experimental relationship of Mailhol and Merot (2008):

$$ n = 0.05 + a \cdot [1 - e^{-LAI}] \qquad (6) $$

with a an empirical parameter.

The daily changes in vegetation development were expressed through varying LAI in time (daily) depending on climate (adapted from Mailhol et al., 1997):

$$ LAI = LAI_{max} \left[ \left( \frac{\sum TT}{t_m} \right)^\beta e^{\frac{\theta}{a} \left( 1 - \left( \frac{\sum TT}{t_m} \right)^a \right)} - (1 - WSI^\lambda) \right] + LAI_0 \qquad (7) $$

with LAI_max the maximum LAI, LAI_0 the initial LAI, TT the cumulative sum of temperatures until t, t_m the cumulative temperature threshold to reach LAI_max, and WSI the water stress index, being the ratio between actual evapotranspiration and maximum evapotranspiration. At each mowing operation, the sum of the temperatures was reset to 0.

Initial soil moisture θ_i also affects how water flows during an irrigation event, as more water can be stored in drier soils (and conversely, less in initially wetter soils). The soil moisture simulator was built as a reservoir model based on the water balance principle, adapted from the SPFC model by Mailhol and Merot (2008). For the days with no irrigation, the available soil water content decreases with the actual evapotranspiration ETa. In case of irrigation during the day, this amount is increased by the depth of water D_rz stored in root zone. This amount is obtained from F (cumulated infiltration during the irrigation event, Eqs. (4) and (5)) calculated in each point, bounded by the storage capacity of the soil, and averaged over the plot length:

$$ D_{rz} = \frac{1}{L} \int_{x=0}^{L} \min(Z(\theta_{FC} - \theta_i); F(x, T_{\infty})) dx \qquad (8) $$

where Z is the root zone thickness, θ_{FC} is the soil moisture at field capacity, L the plot length, and T_∞, taken as a few times of T_i, is the time required to ensure that all the water on the plot was infiltrated.

The instantaneous total available soil water depth (TAW_i for day i) was calculated at each daily time step by adding the irrigation water depth stored in the root zone (D_rz), in case of irrigation event at day i, and subtracting the actual evapotranspiration (ETa) of the day:

$$ TAW_{i+1} = TAW_i - ETa + D_{rz} \qquad (9) $$

Eq. (8) ensures that the available soil water content remains lower than the soil capacity TAW = Z(θ_{FC} - θ_{WP}), where θ_{WP} is the soil moisture at permanent wilting point. Finally, changes in instantaneous humidity and soil saturation deficit were calculated as follows:

$$ \theta_i = \theta_{WP} + \frac{TAW_i}{Z} \qquad (10) $$

$$ \Delta\theta = \theta_s - \theta_i \qquad (11) $$

Eqs. (1)-(11) involve a number of parameters and characteristics which must be set either from direct measurements performed in the fields (e.g., root depth Z) or in laboratory (such as soil characteristic moistures θ_{FC} and θ_{WP}), while some others should be obtained by inverse modelling applied to specific irrigation events. For instance, the hydraulic conductivity K_s, one of the most sensitive parameters, should preferably be set from inverse modelling, due to the high variability of local hydraulic conductivity obtained from infiltration tests (Ram et al., 2012). In order to evaluate the sensor-based cut-off time strategy, a reference situation will be designed from field observations (Section 2.4).

### 2.3.4. Performance indicators

Performance indicators can be calculated for each event and each plot, or aggregated at larger time (e.g., season) and space scales
(e.g. group of plots, irrigation scheme). In this study, we explored the detail of each event, focussing on two performance indicators at the plot scale.

The application efficiency (AE) allows to distinguish the fraction of water available for plants, stored in the soil after irrigation, from the fraction of lost water, which includes tailwater runoff and deep percolation. The application efficiency was thus computed as the ratio between the volume of water stored in the soil and the volume of water applied at each irrigation event:

$$AE = \frac{D_{rz}}{D_{app}} \cdot 100 \qquad (12)$$

Secondly, the requirement efficiency (RE) was used to evaluate the filling level of the soil total available water. The RE was thus calculated as the ratio between instant available water content and the total available water:

$$RE = \frac{D_{rz}}{D_{req}} \cdot 100 \qquad (13)$$

with $D_{rz}$ the water depth stored in the root zone (mm) and $D_{req}$ the water depth required to fill the total available water TAW (mm). A value of 100 means that the total water storage capacity is satisfied. A value below 100 means that the TAW was not fully refilled after irrigation for a part of the plot — usually the most downstream part.

## 2.4. Field implementation

In order to evaluate the strategies of irrigation time control, we built a reference situation representative of plots and actual practices in the area. Within the experimental farm, we selected a plot of average size (0.83 ha), 208 m long, 40 m wide and levelled with a slope of 0.36%. It was equipped for the monitoring of irrigation over a complete season, from March to October 2021. Data were processed during winter 2021–2022.

### 2.4.1. Monitoring of input variables

Daily climate data (reference evapotranspiration $ET_0$, precipitation $P$) were obtained from the Domaine du Merle weather station, located within the experimental farm (43.642532N, 4.993516E). The irrigation schedule (schedule and duration of the events, $T_i$) was recorded using a water detection sensor (float system with data logger, EL-USB, Lascar electronics) positioned at the top of the field, at the canal overflow location. Installed in this way, the data logger recorded the periods during which irrigation was in progress (float in high position) throughout the irrigation season. The schedule was validated with the irrigation manager who also provided the hay mowing schedule.

The flow rates delivered to the plot ($Q_i$) were estimated from continuous monitoring (two-minute time step) of the water level upstream of the weir ($h_{up}$) feeding the distribution canal. The water depths were recorded by a pressure probe (Diver probe, SDEC), and the values were compensated with the atmospheric pressure measured continuously by a barometric probe. Flow rates were finally calculated by applying the stage-discharge relationship of the structure (sharp-crested rectangular weir with no lateral contraction (Eq. (14)):

$$Q_i = \mu \cdot l \cdot \sqrt{2g \cdot h_{up}^{3/2}} \qquad (14)$$

with $Q_i$ the inflow rate (m³ s⁻¹), $\mu$ the weir discharge coefficient (Bazin, 1898), $l$ the width of the weir (m), $g$ the gravitational constant (m³ kg⁻¹ s⁻²) and $h_{up}$ the water depth upstream of the weir (m). Bazin's weir law was validated by flow gauging (ISO 748 standard) with an electromagnetic current meter (BFM 801, Hydreka).

### 2.4.2. Parameters setting

The characteristics of the experimental plot, considered as homogeneous, are summarised in Table 1. The slope (S) was obtained from the elevation profile measured using a differential GPS (Emlid Reach-RS2) along 5 lines lengthwise, 30 points in each line. The soil consisted of a superficial horizon of loam with a thickness of Z = 650 mm (Andrieux, 1981) corresponding to the root exploration zone. This soil may be classified as a calcic luvisol with an agricidal upper horizon (Mailhol and Merot, 2008). The boundary with the highly draining subsoil of fractured pounding pebbles marked the limit of the system, therefore the loamy superficial horizon was the only one considered in this study. The total available water was calculated from the characteristic soil moisture contents ($\theta_{FC}, \theta_{WP}$) identified by Mailhol and Merot (2008). Infiltration parameters (hydraulic conductivity $K_s$ and capillary suction at the wetting front $H_f$) were obtained by fitting the Green & Ampt infiltration model with experimental data from the monitoring of an irrigation event (June 2022). The plot is a permanent grassland, with no tillage, so the soil structure is stable and unchanged throughout the season. In addition, $H_f$ can be considered as a soil parameter obtained from pedo-transfer functions (Alastal and Ababou, 2019). Therefore, $K_s$ and $H_f$ are assumed constant throughout the season. During this monitoring, the progress of the water along the plot was measured at regular time intervals (10 min) using benchmarks, with coordinates measured after irrigation with the GPS. Flow depths and recession were measured at three control points ($X_1$ = 16 m, $X_2$ = 79 m, $X_3$ = 138 m) using pressure probes (Diver 0–10 m, Schlumberger). $K_s$ and $H_f$ were estimated by minimising the square error for Green and Ampt infiltration model using the EVALUE method of WINSRFR 5.1.1 software (Bautista et al., 2009). Comparison between measured and simulated flow depths with WINSRFR after the adjustment of the parameters (Fig. 2) gave Nash–Sutcliffe efficiency coefficients of 0.98, 0.92 and 0.55 at the respective measuring stations $X_1$, $X_2$ and $X_3$. Finally, the parameters needed to simulate LAI variations (Eq. (7)) determined by Mailhol and Merot (2008) in similar experimental conditions were retained.

### 2.5. Simulation strategy

We first sought to determine the ideal positioning of the sensor lengthwise in the field (width band considered to be homogeneous) according to the conditions of the irrigation event, i.e. mainly as a function of the initial soil moisture, the roughness of the crop cover and the inflow rate. The Surflrri model was used to simulate the evolution of these variables over time using data measured during the 2021 irrigation season at the experimental plot described above. The model was then forced with distance-based cutoff ranging from 60 to 100% of the plot length ($\delta x = 5\%$) to simulate the use of a water sensor at these different positions ($WS_x$) (Fig. 3a). For each $WS_x$, the application efficiency (AE) and the requirement efficiency (RE) were computed. The position of the $WS_x$ sensor was considered optimal if the simulation resulted in the highest application efficiency while ensuring that the total available soil water was filled (RE = 100%). The operation was repeated for each of the thirteen irrigation events over the season, so that each date was matched by a set of optimal cutoff distance and time ($WS_x, T_{co}$).

Inflow rates can be highly variable from one irrigation event to another, due to the farmer's practices (distribution of flow rates within the farm, absence of measurement tools), or to water allocation restrictions which can be regular (official WUA calendars) or exceptional (e.g. restrictions of 25% by drought decree in August 2022). The aim was then to compare the scenarios of irrigation cut-off control when faced with the variability of the inflow rate (Fig. 3b). To this end, we forced the Surflrri model with the optimal conditions previously calculated with initial inflow rate ($Q_i$), so that irrigation cutoff was controlled by: (i) the sensor optimally positioned lengthwise throughout the season on the one hand (ii) the corresponding optimal cutoff time on the other hand. The effect of inflow rate variability on irrigation performance was then tested for both scenarios by first increasing the applied flow rates by 30% ($Q_i + 30\%$), then decreasing them by 30% ($Q_i - 30\%$).
<figure><img src="image_4.png" /><figcaption>Fig. 2. Comparison of flow depth hydrographs measured and simulated with WINSRFR software after adjustment of the infiltration parameters.</figcaption></figure>

<table><caption>Table 1
Summary of the experimental field parameters.</caption><thead><tr><th>Width (m)</th><th>Length (m)</th><th>Slope (m/m)</th><th>Z (mm)</th><th>θ<sub>FC</sub> (m<sup>3</sup>/m<sup>3</sup>)</th><th>θ<sub>WP</sub> (m<sup>3</sup>/m<sup>3</sup>)</th><th>θ<sub>s</sub> (m<sup>3</sup>/m<sup>3</sup>)</th><th>H<sub>f</sub> (m)</th><th>K<sub>s</sub> (m s<sup>-1</sup>)</th><th>LAI<sub>o</sub> (m<sup>2</sup> m<sup>-2</sup>)</th><th>LAI<sub>max</sub> (m<sup>2</sup> m<sup>-2</sup>)</th></tr></thead><tbody><tr><td>40</td><td>208</td><td>3.6110<sup>-3</sup></td><td>650</td><td>0.28</td><td>0.12</td><td>0.5</td><td>0.56</td><td>8.0810<sup>-6</sup></td><td>2</td><td>7.7</td></tr></tbody></table>

<figure><img src="image_5.png" /><figcaption>Fig. 3. Method for the search of the optimum irrigation cutoff times and distances, and the evaluation of the changes in performance depending on the water management scenario.</figcaption></figure>

# 3. Results

## 3.1. Reference situation

The reference situation (simulation of year 2021) was built using the mean inflow and actual irrigation durations, with parameters as reported in Table 1. Fig. 4 presents the seasonal variations of Manning's roughness coefficient *n* (resulting from plant growth and harvests), daily soil moisture *θ*, as well as inflows to the plot (irrigation depth

and rain). The measured inflow rates (*Q*<sub>i</sub>) were in the range of 100 to 180 l s<sup>-1</sup> (σ = 19.2 l s<sup>-1</sup>, CV = 14%), which indicated a high degree of inter-event variability. The roughness (*n*), simulated as a function of the state of the vegetation, ranged between 0.29 and 0.35 s m<sup>-1/3</sup> during the growing season (σ = 0.02 s m<sup>-1/3</sup>, CV = 6%). Daily soil moisture ranged from 16% to θ<sub>FC</sub> = 28% after significant rainfall and irrigation events. The evolution of θ, and notably the range of variation of soil moisture just before irrigation events, is in line with the one reported by Merot et al. (2008a), which was obtained from regular soil
<figure><img src="image_6.png" /><figcaption>Fig. 4. Variations in initial irrigation conditions over the season in the reference situation. Water inflows and mowing dates were measured locally, soil moisture and roughness were simulated using Surflirri.</figcaption></figure>

moisture measurements with a neutron probe. These values will be used to explore the sensitivity of irrigation performance to the initial soil moisture, with the different cut-off strategies.

The temporal variability of roughness was mainly explained by the three mowing operations that took place on June 9, July 27 and September 17. The highest values were found for mature hay, and the lowest for freshly mown hay. Finally, simulation results gave an initial moisture content ($\theta_i$) ranging from 0.16 to 0.26 m$^3$ m$^{-3}$ ($\sigma$ = 0.03 m$^3$ m$^{-3}$, CV = 13%). The highest soil moisture levels, closer to field capacity ($\theta_{FC}$ = 0.28), were found in autumn and spring, or when irrigation frequency was higher. Conversely, the lowest moisture contents, closer to the wilting point ($\theta_{WP}$ = 0.12), were found when irrigation events were more widely spaced, and even more so during the dry season from June to September.

## 3.2. Optimised cutoff time thanks to in-field water sensor

### 3.2.1. Search for the optimal sensor position over the irrigation season

The results of the search for optimal irrigation distance and cutoff times over the course of the irrigation season are presented in Table 2. Simulation of the evolution of the initial parameters over time allowed to determine the optimal scenarios, i.e. those for which the application efficiency (AE) was maximum while ensuring the complete filling of the total available soil water (RE = 100%). The optimum position of the water sensor ($WS_x$) was found ranging between 80% and 90% of the length of the field. The corresponding optimal cutoff times showed a rather wide range from 2 to 4.6 h ($\sigma$ = 0.65 h, CV = 20%). Under these conditions, the requirement efficiency reached 100% for all events, and the average application efficiency of the season was 28%, with AE ranging from 9% to 41% depending on the irrigation event.

### 3.2.2. Comparison of border irrigation performance using sensor-based cutoff with reference situation

The performance of border irrigation obtained by optimising the position of the sensor was compared with the performance simulated

on the basis of usual practices (Fig. 5). The “actual management” scenario thus represents the application efficiencies and applied irrigation volumes based on irrigation times measured under real field conditions, while the “sensor-based management” scenario involves the use of a sensor optimally positioned lengthwise the field, which controls the irrigation cut-off for each event. The simulation results showed that in both scenarios, the water requirements to fill the TAW were met, so that RE was 100% at the end of each event of the season in both situations. Nevertheless, the sensor-based management led to application efficiencies equal to or higher than those achieved with actual management for all events. As the water depths ultimately stored in the root zone were otherwise the same, these differences in AE resulted in large disparities in the irrigation volumes applied, which were always equal or lower with the use of the sensor. On average, AE was 56% higher and applied volumes reduced by 33% over the irrigation season in the sensor-based management scenario.

A comparison of successive irrigation events of July 16 and August 01 provides a good illustration of the combination of factors affecting this optimum from one irrigation to the next: (i) hay mowing led to a reduction in Manning of almost 15%, (ii) the time interval between the two irrigations due to mowing during the dry season led to a reduction in $\theta_i$ of almost 20%, (iii) the inflow rate decreased by 50%. To achieve equivalent levels of performance, the optimal $T_{co}$ on August 01 would be almost twice the duration $T_{co}$ simulated 15 days earlier.

## 3.3. Sensitivity of strategies to unmeasured irrigation conditions

### 3.3.1. Impacts of inflow rate variability depending on management scenarios

Finally, the distinction was made between the sensor-based and the time-based cutoff management scenarios and we simulated the impacts of variability in inflow rates on irrigation performance in both cases (Fig. 6). The initial inflow rate ($Q_{in}$) corresponded to the inflow rates measured over the course of the irrigation season. Applying the optimal cutoff time (optimal $T_{co}$) and sensor positioning (optimal $WS_x$) in these
<table><caption>**Table 2**
Evaluation of optimal cutoff time and sensor position lengthwise the field over the irrigation season.</caption><thead><tr><th>Irrigation sch.</th><th>Qi (l s<sup>-1</sup>)</th><th>n (s m<sup>-1/3</sup>)</th><th>θ<sub>i</sub> (m<sup>3</sup>/m<sup>3</sup>)</th><th>Optimal T<sub>co</sub> (h)</th><th>Optimal WS<sub>x</sub> (%)</th><th>RE (%)</th><th>AE (%)</th></tr></thead><tbody><tr><td>30/03/21</td><td>158</td><td>0.344</td><td>0.172</td><td>2.63</td><td>85</td><td>100</td><td>39</td></tr><tr><td>12/04/21</td><td>120</td><td>0.349</td><td>0.232</td><td>3.67</td><td>85</td><td>100</td><td>16</td></tr><tr><td>21/04/21</td><td>104</td><td>0.350</td><td>0.252</td><td>4.62</td><td>90</td><td>100</td><td>9</td></tr><tr><td>27/05/21</td><td>159</td><td>0.350</td><td>0.167</td><td>2.60</td><td>85</td><td>100</td><td>41</td></tr><tr><td>16/06/21</td><td>158</td><td>0.294</td><td>0.162</td><td>2.79</td><td>90</td><td>100</td><td>40</td></tr><tr><td>28/06/21</td><td>151</td><td>0.316</td><td>0.186</td><td>2.73</td><td>85</td><td>100</td><td>34</td></tr><tr><td>08/07/21</td><td>131</td><td>0.336</td><td>0.206</td><td>3.63</td><td>90</td><td>100</td><td>23</td></tr><tr><td>16/07/21</td><td>178</td><td>0.346</td><td>0.206</td><td>2.08</td><td>80</td><td>100</td><td>32</td></tr><tr><td>01/08/21</td><td>127</td><td>0.298</td><td>0.168</td><td>3.94</td><td>90</td><td>100</td><td>34</td></tr><tr><td>12/08/21</td><td>133</td><td>0.318</td><td>0.214</td><td>3.43</td><td>90</td><td>100</td><td>22</td></tr><tr><td>20/08/21</td><td>128</td><td>0.332</td><td>0.219</td><td>3.21</td><td>85</td><td>100</td><td>23</td></tr><tr><td>29/08/21</td><td>142</td><td>0.345</td><td>0.210</td><td>2.97</td><td>85</td><td>100</td><td>25</td></tr><tr><td>23/09/21</td><td>132</td><td>0.307</td><td>0.206</td><td>3.48</td><td>90</td><td>100</td><td>24</td></tr></tbody></table>

Optimal sensor positioning WS<sub>x</sub> was determined as resulting in the best AE while ensuring RE = 100%.

<figure><img src="image_7.png" /><figcaption>**Fig. 5.** Simulated effects of sensor-based management on the performance of border irrigation compared with current practices.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Fig. 6.** Sensitivity of application efficiency (a) and requirement efficiency (b) to inflow rate variability depending on management scenarios. Qi, Qi<sub>+30</sub> and Qi<sub>-30</sub> are respectively the inflow rates initially measured in field, increased by 30% and decreased by 30%. The values represent average performance and the error bars the standard deviation over the irrigation season.</figcaption></figure>
conditions (Table 2) resulted in an average AE of 28% and an average RE of 100%.

By increasing inflow rates by 30% ($Q_{i,+30}$): (i) time-based cutoff (optimal $T_{co}$) led to an average decrease in AE of 6% over the season, and RE remained equal to 100%; (ii) sensor-based cutoff (optimal $WS_\chi$) slightly increased average AE (+2%) over the season, and RE remained equal to 100%.

By decreasing the inflow rates by 30% ($Q_{i,-30}$): (i) time-based cutoff increased average AE by 6% but did not allow to meet soil water requirements and average RE dropped by almost 30%; (ii) sensor-based cutoff led to lower AE (-5%) on average but allowed the soil water requirements to be reasonably met with an average RE of 96% over the irrigation season.

### 3.3.2. Impacts of soil moisture variability depending on management scenarios

In order to evaluate the sensitivity to the soil moisture before irrigation, performance indicators were evaluated for three initial moistures: wet soil ($\theta$ = 25.2%, which was the maximum initial value among all irrigation events), soil at critical depletion ($\theta$ = 20.6%, reference), dry soil ($\theta$ = 16%, which was the minimum initial value among all irrigation events). Note that these moistures are consistent with those reported in Merot et al. (2008b), measured throughout an irrigation season in the experimental farm. While irrigations are generally performed when water content is at 50% of TAW, water access or labour constraints can force irrigations to be delayed (water content at 40% of TAW and below) or after a rainfall (wet soil condition).

Indicators AE and RE were evaluated for irrigation events as a function of cutoff time (Fig. 7). As expected, application efficiency (values on left Y-axis) curves (wet, reference, dry) are decreasing functions with respect to irrigation duration (cutoff time), while requirement efficiency (values on right Y-axis) increase with irrigation duration. The cutoff times corresponding to cutoff distances of 80% and 90% of plot length are also indicated, for each initial moisture. These points correspond to the times at which sensors (positioned at 80% or 90% of plot length) would send an alert.

The results show that the performance clearly depends on initial soil moisture. For the cutoff time based on the reference situation, e.g. 3.6 h (AE = 23%, RE = 95%), the efficiency is higher for the dry soil (since more water is stored in the soil) but the requirement efficiency RE falls to 84%, due to the fact that the downstream part of the plot has received little water. Therefore, in order to obtain the same requirement efficiency as for the reference, one would need to increase the cutoff time up to 4.1 h. This time corresponds roughly to the time necessary for the water front to reach 80% of the plot (3.95 h). If we consider the initially wet soil, the requirement efficiency of 95% would be reached with a cutoff time of 3.18 h, which is around 12% less than for the reference moisture. This time is also very close to the time obtained with a sensor placed at 80%.

The same observation can be done with the times to reach RE = 100% (TAW totally refilled). In that case, Fig. 7 shows that these times correspond to the cutoff distance ratio of 90%. This is a remarkable result: putting the sensor at a given position yields a quite constant requirement efficiency — in this case RE = 95% with the sensor at 80% of plot length, RE = 100% with the sensor at 90% of plot length, whatever the initial moisture.

# 4. Discussion

## 4.1. Sensitivity of irrigation performance to variations of roughness and moisture

The Surflrrri integrated model allowed to simulate temporal hydrodynamic variations of border irrigation in a permanent meadow over the course of the season. By coupling a surface water flow simulator with crop and soil water models, we were able to estimate variations in

infiltration and Manning's roughness coefficient over time. The results showed that initial soil moisture deviated noticeably from its mean over the course of the season, with values that were rather close to characteristic soil moistures ($\theta_{WP}$ for dry soil, $\theta_{FC}$ for wet soil). This behaviour is consistent with the dynamics of volumetric water content measured in the field under similar conditions by Merot et al. (2008b). As shown in Fig. 7, the initial soil moisture has a strong impact on application efficiency, and on the necessary time to reach a given position.

The variations in Manning's roughness coefficient *n* is also an important factor affecting the irrigation performance, although it showed a relatively small deviation [0.29–0.35] from the mean value of 0.33. The higher roughness results in a lower velocity and therefore increased the necessary irrigation time. Here, the lowest *n* gives an optimal irrigation time decreased by about 0.25 h compared to the highest *n*. This involves a significant volume of water (up to 200 m³/ha per irrigation event) and illustrates the importance of roughness on irrigation efficiency. This remark is in line with Xu et al. (2019) who showed that temporal variations of this magnitude in Manning's roughness coefficient could have significant consequences on the performance of border irrigation. Therefore, predicting the evolution of *n* with time is an important issue. Here, we linked the roughness coefficient with LAI simulated with the vegetation simulator (Eq. (7)). The sensitivity to errors in LAI, which may be quite large at large LAI values (El Hajj et al., 2016), is actually limited due to the extinction law in Eq. (6). Importantly, the evolution of *n* faithfully reflected the development stages of a permanent pasture, with maximum values reached at the time of hay maturity, and minimum values when the grass was short, following mowing operations. The results coincide with the values of *n* obtained by Robertson et al. (2004) ranging from 0.20 to 0.36 for a pasture, without succeeding in identifying a relationship between the height of the vegetation and *n*, and those obtained by Bader et al. (2010) ranging from 0.20 to 0.43 under similar experimental conditions. We suppose that the relatively high minimum of *n* obtained by simulation could reflect a roughness increased by crops residues left at the surface of the field.

A number of studies in laboratory and field conditions suggested relationships between Manning coefficient and the “blocage factor” of the vegetated cover (Rudi et al., 2020), which can be obtained from measurable physical properties (see e.g. Vinatier et al., 2017). This may be an interesting perspective to reduce the uncertainty on roughness determination.

Ultimately, these results highlight the intra-seasonal heterogeneity of the initial conditions impacting the performance of border irrigation, and the importance of integrating their dynamics when searching for optimisation of practices.

## 4.2. Sensor-based irrigation management: expected gains on irrigation performance

In the area, farmers' experience guides practices, and especially decision-making on the cutoff: at the start of the irrigation event, the farmer estimates approximatively how long it will take for the water to advance downstream of the field, then makes several return visits to the field to check progress before stopping when he considers that there will be sufficient inertia to cover the remainder of the field. This practice has the inconvenience of being (i) very labour-intensive, as irrigation is carried out 24/7; (ii) very irregular, as the variability of initial conditions and the irrigator's lack of availability can easily lead to insufficient irrigation or, conversely, over-irrigation. The potential of a sensor-based cutoff strategy was assessed by simulating the performance of border irrigation under various scenarios. Comparison with actual practices showed that sensor-based management should make it possible to significantly improve application efficiency while maintaining requirement efficiency equal to 100%, thus making it possible to reduce the volumes of irrigation applied by around 30%
<figure><img src="image_9.png" /><figcaption>Fig. 7. Sensitivity of border irrigation performance to initial soil moisture. Plain lines: application efficiency; dotted lines: requirement efficiency.</figcaption></figure>

without affecting crop production. The average AE obtained by sim-
ulating traditional practices (18%) was in the range described in the
literature for the region (Mailhol and Merot, 2008; Olioso et al., 2013).
Furthermore, the analysis of the sensitivity of irrigation performance to
inflow rates variation depending on the management scenarios showed
that the use of an in-field sensor would reduce performance gaps in
comparison with the use of a cutoff time optimised under initial condi-
tions. With increased inflow rates, the water front reached the sensor
position faster, thus reducing irrigation time with regard to cutoff time
which resulted in over-irrigation. When inflow rates were lowered, the
water front took longer to reach the sensor, which allowed the total
available water to be properly refilled, unlike the use of a cutoff time.
The use of in-field water detection sensors therefore appears to be
beneficial compared with traditional cutoff time, insofar as it allows
better flexibility to the intra- and inter-event unpredictability of surface
irrigation.

Conceptually, this study provides elements for better understanding irregular and generally low values of border irrigation application effi- ciency in field conditions, beyond optimised scenarios. It is interesting to see how the variability of initial conditions, certainly associated with labour constraints, may lead the farmer to frequently over-irrigate in order to overcome the risk of water requirements that would not be sat- isfied. This pattern was similarly observed in other contexts (Masseroni et al., 2022). From this perspective, and because models are unable to predict everything, the development of new technologies such as wireless sensor networks (Hamami and Nassereddine, 2020) represents an opportunity for surface irrigation management, which has been relatively forgotten by precision agriculture. This study highlights the benefits of using a real-time surface water detection sensor to support farmers’ decision making for border irrigation cutoff. Future studies should investigate the possibilities of data acquisition to adjust the model in real time, for example by positioning several sensors to validate surface water advance. Beyond this binary data, the production of more complex data such as hydraulic pressure or soil moisture in real time represent many opportunities to improve the parameterisation of surface irrigation models and the optimisation of irrigation strategies closer to actual field conditions.

4.3. *Applications of the model, limitations and perspectives*

The integration of this temporal variability of factors affecting surface water flow (Qᵢ, n, θᵢ), within our integrated Surflrri model simulating border irrigation, made it possible to determine optimal irrigation management scenarios that evolve over the course of the season. The results showed that throughout the season, the optimal cutoff time was highly variable, with durations that could double from one irrigation event to the other. These results are in line with the field experience of farmers in the area, who are well aware that on the same field the water velocity can differ greatly from one irrigation to the next. This variability also illustrates how difficult it is for farmers to manage these flows accurately. The use of the Surflrri model, through the production of “optimal management tables”, could thus repre- sent a valuable decision-making tool for optimising border irrigation strategies. Further studies should include statistical analyses in order to identify a simplified relationship that would allow the optimum position of the sensor to be estimated on the basis of simple field inputs (e.g. water level at the weir, canopy height, soil water status).

In its present version, the model has some limitations which could
be of importance in some cases. Indeed, it did not consider the soil
moisture heterogeneity after irrigation, since the daily soil moisture
is averaged at the plot scale. It had a limited impact in our case,
where the requirement efficiency was close to 100%, but it may be of
importance in the case of restrictions imposing limited inflow to the
plots. This could result in heterogeneity in crop development, which
was not considered here. The crop model was also designed for pasture,
with a specific relationship linking roughness to LAI. The inclusion
of other crop models is an important perspective in order to widen
the applicability of the model. The 1D approach of surface flow is
another limitation. In a recent study, Costanzo et al. (2024) developed
the concept of precision surface irrigation based on microtopography
measurements and 2D modelling. However, their results also showed
that 1D and 2D (such as WinSRFR) provided quite close results, when
compared based on integrated indicators. For the purpose of our study,
the 1D approach was clearly the easiest to set-up, and appropriate to
compare the overall performance of irrigation in terms of application
efficiency and requirement efficiency, but more complex configurations
or poorly levelled plots would require the use of the 2D approach to
evaluate the best sensor position.
<table><caption>**Table A.3**
Notations for the variables and parameters used in the Surflrri model.</caption><thead><tr><th>Notation</th><th>Definition</th><th>Discretisation</th><th>Unit</th></tr></thead><tbody><tr><td colspan="4"><strong>Input variables</strong></td></tr><tr><td>ET<sub>o</sub></td><td>Penman-Monteith reference evapotranspiration</td><td>d</td><td>mm</td></tr><tr><td>P</td><td>Rainfall</td><td>d</td><td>mm</td></tr><tr><td>T</td><td>Daily mean temperature</td><td>d</td><td>°C</td></tr><tr><td>T<sub>i</sub></td><td>Irrigation duration</td><td>d, e</td><td>h</td></tr><tr><td>Q<sub>i</sub></td><td>Inflow rate</td><td>d, e</td><td>m<sup>3</sup> s<sup>-1</sup></td></tr><tr><td>Mowing</td><td>Crop mowing schedule</td><td>d</td><td>Date</td></tr><tr><td colspan="4"><strong>Plot descriptors and parameters</strong></td></tr><tr><td>S</td><td>Slope of the field strip</td><td>p</td><td>m m<sup>-1</sup></td></tr><tr><td>L</td><td>Length of the field strip</td><td>p</td><td>m</td></tr><tr><td>ω</td><td>Width of the field strip</td><td>p</td><td>m</td></tr><tr><td>Z</td><td>Thickness of the top soil horizon</td><td>p</td><td>mm</td></tr><tr><td>θ<sub>s</sub></td><td>Soil moisture content at saturation</td><td>p</td><td>m<sup>3</sup> m<sup>-3</sup></td></tr><tr><td>θ<sub>FC</sub></td><td>Soil moisture content at field capacity</td><td>p</td><td>m<sup>3</sup> m<sup>-3</sup></td></tr><tr><td>θ<sub>WP</sub></td><td>Soil moisture content at permanent wilting point</td><td>p</td><td>m<sup>3</sup> m<sup>-3</sup></td></tr><tr><td>TAW</td><td>Total available soil water</td><td>p</td><td>mm</td></tr><tr><td>K<sub>i</sub></td><td>Soil hydraulic conductivity</td><td>p</td><td>m s<sup>-1</sup></td></tr><tr><td>H<sub>f</sub></td><td>Capillary suction at the wetting front</td><td>p</td><td>m</td></tr><tr><td>LAI<sub>max</sub></td><td>Maximum leaf area index</td><td>p</td><td>m<sup>2</sup> m<sup>-2</sup></td></tr><tr><td>LAI<sub>0</sub></td><td>Initial leaf area index</td><td>p</td><td>m<sup>2</sup> m<sup>-2</sup></td></tr><tr><td>α, β</td><td>Empirical shape parameters for LAI</td><td>p</td><td>–</td></tr><tr><td>λ</td><td>Crop sensitivity to water stress</td><td>p</td><td>–</td></tr><tr><td colspan="4"><strong>Simulated variables</strong></td></tr><tr><td>ET<sub>c</sub></td><td>Crop evapotranspiration</td><td>d</td><td>mm</td></tr><tr><td>ET<sub>a</sub></td><td>Actual evapotranspiration</td><td>d</td><td>mm</td></tr><tr><td>θ<sub>i</sub></td><td>Instant soil moisture content</td><td>d, e, x</td><td>m<sup>3</sup> m<sup>-3</sup></td></tr><tr><td>Δθ</td><td>Soil saturation deficit</td><td>d, e, p</td><td>m<sup>3</sup> m<sup>-3</sup></td></tr><tr><td>LAI</td><td>Leaf Area Index</td><td>d</td><td>m<sup>2</sup> m<sup>-2</sup></td></tr><tr><td>TT</td><td>Cumulative sum of temperatures (thermal time)</td><td>d</td><td>°C</td></tr><tr><td>WSI</td><td>Water Stress Index</td><td>d</td><td>–</td></tr><tr><td>n</td><td>Manning roughness coefficient</td><td>d</td><td>s m<sup>-1/3</sup></td></tr><tr><td>h</td><td>Water depth at the surface of the field during irrigation</td><td>e, x</td><td>mm</td></tr><tr><td>q</td><td>Surface flow per unit width</td><td>x, e</td><td>m<sup>3</sup> s<sup>-1</sup></td></tr><tr><td>F</td><td>Infiltrated depth at spatial grid level</td><td>x, e</td><td>mm</td></tr><tr><td>f</td><td>Infiltration rate</td><td>x, e</td><td>m<sup>3</sup> s<sup>-1</sup></td></tr><tr><td>D<sub>app</sub></td><td>Depth of water applied</td><td>d, p</td><td>mm</td></tr><tr><td>D<sub>ra</sub></td><td>Depth of water run-off drainage</td><td>d, p</td><td>mm</td></tr><tr><td>D<sub>f</sub></td><td>Depth of water infiltrated</td><td>d, p</td><td>mm</td></tr><tr><td>D<sub>rz</sub></td><td>Depth of water stored in the root zone</td><td>d, p</td><td>mm</td></tr><tr><td>D<sub>p</sub></td><td>Depth of water percolated</td><td>d, p</td><td>mm</td></tr><tr><td>TAW<sub>i</sub></td><td>Instant available soil water</td><td>d, p</td><td>mm</td></tr><tr><td>D<sub>req</sub></td><td>Depth of water required to fill the TAW</td><td>d, p</td><td>mm</td></tr><tr><td>AE</td><td>Application efficiency</td><td>d, p</td><td>–</td></tr><tr><td>RE</td><td>Requirement efficiency</td><td>d, p</td><td>–</td></tr></tbody></table>

Note: for discretisation, 'd' stands for daily information (seasonal variation), 'e' stands for 'event' (variable calculated at each Surflrri simulation time step), 'p' stands for 'plot', 'x' means that the variable is discretised along the plot length.

Irrigation efficiency is often considered at plot and event scales. By considering the overall efficiency throughout the season, this work showed the importance of considering the temporal scale. However, the authors are aware that the optimisation of irrigation efficiency at the sole plot level is subject to limitations because of scale effects. Water-saving measures may have important side effects (Grafton et al., 2018; Lankford et al., 2020), as it is the case for the Crau irrigated territory. Water flows considered as “losses” (tailwater runoff, deep percolation) when evaluating application efficiencies at field level may indeed be considered, depending on the scale and perspective, as beneficial return flows. For instance, the Crau aquifer is mainly recharged by border irrigation percolation water flows (Olioso et al., 2013; SINERGI, 2020), and runoff flows may be reused at farm or irrigation scheme level, not considered here. The simulation platform Openfluid (with the specific simulator Surflrri presented here) could be used to simulate flows and performance indicators for an irrigation scheme comprising many plots and canals, with possible reuse of drainage run-off. Tests at larger scales are in progress (e.g. Pignard, 2022, for an irrigation scheme with around 60 plots). The expected results are an evaluation of the overall performance gains permitted by a wide adoption of the sensor-based cutoff strategy.

## 5. Conclusion

Sensor-based cutoff was studied through modelling and field experimentation for border irrigation. To this end, an integrated model (Surflrri) was developed, based on the coupling of a surface water flow simulator with dynamic crop and soil models. The model could simulate both initial moisture before irrigation, which has a large impact on irrigation performance, and roughness variations over the season. It can be used to improve irrigation scheduling and to adapt irrigation duration according to the season and the available discharge. We showed the benefit of using a simple real-time water detection sensor installed in the field: it could improve average application efficiency by more than 50%, while maintaining the maximum requirement efficiency. This improvement would represent a water saving of 33% on surface irrigation volumes at the field level under the conditions of our experiment, which is representative of border irrigation as practiced over the 10,000 ha of hay in the Crau plain, in the South of France. Compared with a predefined cutoff time, the use of an in-field sensor-based cutoff makes it possible to limit water losses arising from variability or uncertainty in the initial irrigation conditions. The rapid development of new wireless sensor network technologies for agriculture thus represents a real opportunity to optimise surface irrigation management, which
<figure><img src="image_10.png" /><figcaption>Fig. A.8. Surflrri model overview.</figcaption></figure>

until now has been relatively forgotten by digital innovation. Future
studies should seek to assess the benefits and impacts of adopting such
technologies at different spatial scales, considering the overall water
saving but also potential non-beneficial side effects.

CRediT authorship contribution statement

**Paul Vandôme:** Writing – original draft, Validation, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Gilles Belaud:** Writing – review & editing, Writing – original draft, Validation, Supervision, Software, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. **Mohamed Amine Berkaoui:** Writing – review & editing, Validation, Software, Data curation. **Cédric Guillemin:** Data curation. **François Charron:** Resources, Data curation, Conceptualization. **Crystèle Leauthaud:** Writing – review & editing, Supervision, Resources, Funding acquisition, Conceptualization.

Declaration of competing interest

The authors declare the following financial interests/personal rela-
tionships which may be considered as potential competing interests:
Gilles Belaud reports financial support was provided by Thematic Re-
search Agency for Science and Technology. If there are other authors,
they declare that they have no known competing financial interests or
personal relationships that could have appeared to influence the work
reported in this paper.

Acknowledgements

This paper is part of the first author's PhD project, funded by the CIRAD and the Occitanie Region (France). The work was carried out as part of HubIS project (EU's PRIMA programme 2019, grant ANR-19- P026-0006-02). Field experimentations and model development were also funded by the Water Agency Rhône-Méditerranée and Corse, as well as Région Sud-PACA (Fiche Action B, Contrat de Nappe).

**Appendix. Appendix section**

See Table A.3 and Fig. A.8.

Data availability

Data will be made available on request.

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