# Simulating generic agrivoltaic systems with ORCHIDEE: Model development and multi-case study insights

Lia Rapella, Nicolas Viovy, Jan Polcher, Davide Faranda, Jordi Badosa,

Philippe Drobinski

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## To cite this version:

Lia Rapella, Nicolas Viovy, Jan Polcher, Davide Faranda, Jordi Badosa, et al. Simulating generic agrivoltaic systems with ORCHIDEE: Model development and multi-case study insights. Agricultural and Forest Meteorology, 2025, 371, pp.110589. 10.1016/j.agrformet.2025.110589. hal-05345173

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# Simulating generic agrivoltaic systems with ORCHIDEE: Model development and multi-case study insights

Lia Rapella<sup>a,b,∗</sup>, Nicolas Viovy<sup>b</sup>, Jan Polcher<sup>a</sup>, Davide Faranda<sup>b,c</sup>, Jordi Badosa<sup>a</sup>, Philippe Drobinski<sup>a</sup>

## ARTICLE INFO

Dataset link: https://cds.climate.copernicus.eu
/#!/home

**Keywords:**

Agrivoltaics

Water–food–energy nexus

Land–surface modelling

Energy–water–carbon interaction

## ABSTRACT

Agrivoltaics (AVs) has emerged as a promising solution to address the competing demands for land, energy, and food production within the Water-Energy-Food-Ecosystem (WEFE) nexus. However, its effects depend on climate, crops and local conditions, requiring large-scale models capable of capturing these variations. For this purpose, our study introduces a new regional-scale AV model, at the interface with regional climate models and the Organizing Carbon and Hydrology In Dynamic Ecosystems (ORCHIDEE) land surface model, to explore the interactions between climate, AV systems and crops within the WFEF nexus. The model is applied to two AV configurations across three distinct climates (dry, wet, and climatological) over the Iberian Peninsula and The Netherlands, using two generic crop types. The results reveal that in arid regions with high solar radiation, such as in the southern Iberian Peninsula, AV systems offer many advantages, particularly in dry years: increased crop productivity, enhanced food security and better use of water and land, while producing renewable energy. In contrast, in The Netherlands, characterized by abundant rainfall and lower solar radiation, AV systems tend to reduce crop productivity, and the gains in terms of water and land use are less marked. These findings highlight the model ability to assess AV systems by capturing regional specificity and varying responses to different climatic contexts. They suggest that optimizing AV system designs involves a nuanced approach, carefully balancing the synergies across energy production, agricultural productivity, and resource use while managing the trade-offs inherent to different climatic conditions.

## 1. Introduction

In the perspective of a “net-zero” carbon economy, the transition to a renewable energy system must occur in conjunction with a profound transformation of the agri-food sector, which needs to be adapted to a changing climate. Among the adapting and mitigating solutions to the climate-water-energy-food nexus, agrivoltaics (AVs) may play a key role. AVs is a food-energy producing ecosystem that involves the simultaneous use of land areas for both solar photovoltaic (PV) power generation and agriculture (Dupraz et al., 2011). The deployment of this hybrid system could lead to significant benefits across the water-energy-food nexus, as it could allow to simultaneously reach these targets: power carbon-neutral farms, make the agricultural sector more resilient and sustainable, and support the clean energy transition (Herrero, 2020). AVs could be a big energy player, as the installation of AV systems over less than 1% of global croplands has the potential to satisfy the total global energy demand Adeh et al. (2019). The

expected growth in global population, and the consequent increase in food and energy demand, will exacerbate the already existing competition for land (Valle et al., 2017; Adeh et al., 2019; Dinesh and Pearce, 2016). Approximately 12% of the global land surface is currently covered by cultivated crops (AlMamun et al., 2022), and the development of PV infrastructures requires an increasing number of large-scale spaces (Amaducci et al., 2018). Building PV panels over crop fields avoids competition between solar and agriculture in land use (Valle et al., 2017), especially in regions characterized by land scarcity, such as small islands, and/or densely populated (Amaducci et al., 2018; Herrero, 2020; Dinesh and Pearce, 2016). Furthermore, this combined use can help mitigate the impacts of climate change on agri-food systems, which we expect to be affected by a warmer and drier future climate (Barron-Gafford et al., 2019), and contribute to a higher climate resilience of agricultural activities, representing an important instrument for realizing a sustainable and circular food-energy economy in rural and farmers communities (Amaducci et al.,

<footnote><sup>a</sup> LMD-IPSL, Ecole Polytechnique, Institut Polytechnique de Paris, ENS, Université PSL, Sorbonne Université, CNRS, Palaiseau, France</footnote>

<footnote><sup>b</sup> LSCE-IPSL, Université Versailles Saint Quentin, Université Paris Saclay, CEA, CNRS, Saclay, France</footnote>

<footnote><sup>c</sup> London Mathematical Laboratory, 8 Margravine Gardens, London, W6 8RH, British Islands, United Kingdom</footnote>

<footnote>* Corresponding author at: LMD-IPSL, Ecole Polytechnique, Institut Polytechnique de Paris, ENS, Université PSL, Sorbonne Université, CNRS, Palaiseau, France. E-mail address: lia.rapella@lmd.ipsl.fr (L. Rapella).</footnote>
2018). Indeed, AVs, especially in dry land environments, are reported to increase land use efficiency and enhances water management (Al-Mamun et al., 2022; Barron-Gafford et al., 2019; Amaducci et al., 2018), by minimizing evaporation from the soil surface. PV panels, with their shielding, reduce heat stress, especially during periods of intense heatwaves, and, by using systems that regulate their tilts, optimize the distribution of solar radiation over crops (Herrero, 2020; Barron-Gafford et al., 2019; Amaducci et al., 2018; Dupraz et al., 2011). This leads to improved crop productivity and reduced water consumption and soil degradation (Barron-Gafford et al., 2019; Dupraz et al., 2011). Moreover, they protect crops against hazardous events, such as hail and frost, which can endanger crop yields (Herrero, 2020; Dupraz et al., 2011). At the same time, PV panels make farms energy self-sustaining and climate-neutral (Herrero, 2020), and, in these conditions, they even increase their electrical yield (Dinesh and Pearce, 2016), owing to the underlying microclimate (Barron-Gafford et al., 2019; Adeh et al., 2019) and the possibility of modifying their tilt (Valle et al., 2017), both aspects that optimize the working conditions of PV panels. Despite the positive perspectives of installing AV systems, there are still issues that need to be investigated, as the benefits may not occur for every type of crop/soil or in every period of the year, and not all the effects of modifying light/water availability, temperature, wind and humidity – the main factors that influence crop productivity – are well known (Trommsdorff et al., 2021). Various studies suggest that the presence of PV panels may lead to variations in crop productivity depending on factors such as the season, latitude, cultivated species and crop cycle length (Marrou et al., 2013). Therefore, to thoroughly assess its long-term sustainability, a more in-depth analysis is required, at local scale with dedicated experiments and through the use of modelling tools. Models, in particular, play a crucial role in predicting the behaviour of crop ecosystems and identifying optimal conditions for AV systems.

Existing research has primarily focused on optimizing panel layout to enhance crop production (and/or the electrical PV performance), considering variables like panel height, spacing, and the impact of irradiation on crop shading, tested through specific arrangements or field experiments (Sarr et al., 2023). To achieve this goal, models for radiation interception and energy production by PV farms have been integrated with models for crop productivity, enabling the simulation of an AV system (Dupraz et al., 2011; Dinesh and Pearce, 2016; Amaducci et al., 2018; Potenza et al., 2022). These modelling studies, designed at a metre-scale resolution, analyse and validate the performance of specific installations, assessing their impact on crop yields and requiring optimization. However, transitioning from small-scale models to the scale of regional climate models could provide insights into how AV configurations interact with different climatic conditions, crop types, and locations, allowing for a more comprehensive assessment of AV systems beyond fine-resolution models. This work aims to fill this gap.

Our objective is to develop a regional-scale sub-grid AV model designed to explore the interconnections between climate, the AV system and crops. This model will enable a comprehensive evaluation of the efficacy and efficiency of AV configurations within the context of the climate-water-energy-food nexus. The AV module will be interfaced with regional climate models and the Land Surface (LS) model ORCHIDEE (Organizing Carbon and Hydrology In Dynamic Ecosystems), being used for the first time to simulate the functioning of an AV system. This exploration aims to delve deeper into the advantages and challenges presented by AV systems in promoting a sustainable nexus between climate, water resources, energy production and food security. The first part of our paper, delineated in Section 2, focuses on the development of the AV model. As mentioned above, our approach involves coupling a PV model with ORCHIDEE to construct the AV module. Fig. 1 provides a visual depiction of this process. The PV layer, by simulating the effects of PV panels, alters the solar radiation and the wind speed taken from atmospheric forcings. Subsequently, these altered variables, along with key atmospheric data, such as

air temperature and precipitation, required by ORCHIDEE, serve as inputs to the hydro-vegetation layer. Given ORCHIDEE capability to quantify terrestrial water and energy balances at the land surface, this integration allows for a comprehensive simulation of crop ecosystem behaviour within an AV system. Net Primary Production (NPP), Water Use Efficiency (WUE), PV power (PV<sub>pow</sub>) are finally computed from the diagnostics at the output of our model, representing key indicators for the Water Energy Food Ecosystems (WEFE) nexus.

In this initial development of our model, we assume that the PV layer only modifies solar radiation and wind speed, while the other atmospheric variables shown in Fig. 1 remain unchanged. This assumption is based on several considerations. First, solar radiation is the primary driver of the energy balance, and changes in its intensity directly impact crop behaviour by influencing photosynthesis, soil temperature and overall energy distribution. Similarly, wind speed and the associated turbulence regulate plant transpiration as well as evaporation from soil, crop canopy and PV installations, playing a critical role in determining crop water use and soil moisture. Moving to air temperature, observational studies conducted in AV systems report little to no change in average daily air temperature (Marrou et al., 2013; Adeh et al., 2018; Armstrong et al., 2016; Edouard et al., 2023), likely due to compensatory effects, such as heating from panels being offset by cooling from vegetation. These findings support our decision to not modify air temperature in our model. However, we acknowledge that changes in air temperature due to surface temperature variations induced by PV panels could occur, even if such effects are not detectable in ORCHIDEE when used in offline mode (see Section 2.2), as soil-atmosphere feedbacks are not accounted for. Moreover, it is important to note that in ORCHIDEE, air temperature, rather than surface temperature, governs photosynthesis processes (Schulz et al., 2001). Surface temperature is the result of the energy balance at the surface, but it does not directly represent the temperature of the leaves, where photosynthesis occurs. When developing ORCHIDEE, air temperature was chosen for photosynthesis calculations because it is more stable and has a diurnal cycle of lower amplitude than surface temperature. Finally, challenges in modelling surface temperature are closely linked to difficulties in properly accounting for changes in longwave radiation within the energy balance, as it necessitates evaluating surface, air, and panel temperatures simultaneously. Regarding air humidity and the associated vapour pressure deficit, their values can be indirectly influenced by changes in transpiration and evaporation rates, which are in turn affected by the impact of PV panels on solar radiation and wind speed. Faced with such complex interactions we choose to keep air humidity and longwave radiation the same as without panels. Finally, including rainfall distribution further complicates the modelling process. For instance, PV panels can alter the spatial distribution of precipitation by intercepting raindrops or affecting water runoff patterns. However, these effects are difficult to quantify and detect within the resolution of regional climate models, as is the case in our study.

In Section 2.3, we apply our model to assess two AV configurations across three specific years, each representing different climate conditions (dry, wet, in the climatology), in the Iberian Peninsula and the Netherlands, focusing on two crop types. In particular, we compare the performance of the different configurations among themselves and against the situation without AV systems (Section 3).

## 2. Material and methods

Our model requires atmospheric variables as inputs, each defined by a specific spatial resolution. At each grid point, typically covering an area of a few square kilometres, the atmospheric forcings supply a single average value. Since the scale of the PV panels is significantly smaller, in order to capture alterations in the atmospheric variables due to their presence, employing a sub-grid modelling approach becomes necessary.
<figure><img src="image_5.png" /><figcaption>**Fig. 1.** Visual representation depicting the key components and processes integral to the AV module. The primary outcomes of the model include Net Primary production (NPP), Water Use Efficiency (WUE) and PV power ($PV_{pow}$) (see detailed definitions in the text). Different colours represent various elements: pink indicates the inputs, green denotes the processes, and purple signifies the outputs.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Fig. 2.** Visualization of the dual-layer sub-grid AV model. Within the selected spatial domain, each grid point is depicted as covered by crops (illustrated in green) and by regular arrays of PV panels (denoted by thick black lines). In the figure it is shown a zoom-view over a grid point in Spain.</figcaption></figure>

To begin with, we select a spatial domain and we envision its
complete coverage with bifacial PV fields. This arrangement results in
each grid point covered by regularly arranged PV rows adhering to
a specific geometry, representing the PV layer, as depicted in Fig. 2.
Average changes in solar radiation and wind speed are calculated at
the scale of the PV row, and, for solar radiation, we consider a panel
positioned at the centre of the row, to neglect edge effects. We assume
the panels have an infinitesimal thickness and that the row x-dimension
is significantly smaller than the row y-dimension, i.e. the row width is
considerably narrower than its length. Subsequently, these calculated
values are scaled up to the grid point level, and employed as input
values, for each respective grid point, within ORCHIDEE. Similar to
the approach taken for the PV layer, we set the hydro-vegetation layer
in ORCHIDEE to function in a manner where, at the soil level, each
grid point is entirely covered by crops. This strategy ensures that the
final model outputs reflect the average behaviour of the crops in an AV
system, maintaining the same spatial resolution.

2.1. *PV layer*

The PV collectors, characterized by a width *W* and length *L*, are tilted at an angle *β* (Appendix A) and elevated above the ground at a height *H*.<fnref n="1" /> These collectors are arranged in rows evenly spaced apart by the pitch *c* along the *x*-axis. Fig. 3 depicts a two-dimensional side view of two PV panels rows. The distance between the top edge of the front collector and the bottom edge of the back collector is denoted *D*, while the distance between the bottom edge of the collector and the ground is given by *H*<sub>min</sub>. The PV panels are displayed in the *portrait* mode, *i.e.* with the shorter side running parallel to the ground. To test our model, in Section 2.3, we will make use of three configurations, with the parameters values reported in Table 1. Specifically, we will deal with

<footnote n="1">¹ The height refers to the distance between the ground and the middle of the panel.</footnote>
<figure><img src="image_7.png" /><figcaption>Fig. 3. Two-dimensional view of two PV rows, along the x-axis. Key dimensions are labelled.</figcaption></figure>

**Table 1**

PV panels geometrical parameters for the PV layer. The last column shows the values for the configurations used in this study, ST and SAT.

<table><thead><tr><th>Symbol</th><th>Name</th><th>Value [ST/SAT]</th></tr></thead><tbody><tr><td>β</td><td>inclination angle [°]</td><td>{-60, +60}</td></tr><tr><td>W</td><td>width [m]</td><td>2.411</td></tr><tr><td>L</td><td>length [m]</td><td>1.130</td></tr><tr><td>H<sub>min</sub></td><td>height from panel bottom edge: H - (W sin|β|/2) [m]</td><td>{1.456, 2.5}</td></tr><tr><td>H<sub>max</sub></td><td>height from panel top edge: H + (W sin|β|/2) [m]</td><td>{2.5, 3.543}</td></tr><tr><td>H</td><td>height from panel centre [m]</td><td>2.5</td></tr><tr><td>c</td><td>pitch [m]</td><td>5.5</td></tr></tbody></table>

horizontal single-axis Sun Trackers (ST) and Sun Anti-Trackers (SAT) (Appendix B), with the row axis aligned in the North-South direction.

### 2.1.1. Solar radiation on the ground

The global solar radiation that reaches a horizontal plane at the surface of the Earth, $I_H$, is given by the sum of two components, direct radiation $I_b$ and diffuse radiation $I_d$:

$$I_H = I_b + I_d \quad (1)$$

The beam radiation is the fraction of the solar radiation that has not been scattered by the atmosphere, while the diffuse radiation represents the part that has changed its direction by scattering by the atmosphere. Starting from the total horizontal radiation, it is possible to compute the diffuse horizontal radiation by means of the clarity index $k_T$, defined as the ratio between $I_H$ and the extraterrestrial radiation incident on a horizontal plane.<fnref n="2" /> The diffuse radiation can be related to the global solar radiation through the following empirical relations, developed based on data collected from United States and Europe (Duffie and Beckman, 2013):

$$\frac{I_d}{I_H} = \begin{cases} 1 - 0.09 * k_T & \text{if } k_T \le 0.22 \\ 0.9511 - 0.1604 * k_T + 4.388 * k_T^2 & \text{if } 0.22 < k_T \le 0.80 \\ -16.638 * k_T^3 + 12.366 * k_T^4 & \text{if } k_T > 0.80 \end{cases} \quad (2)$$

In this work we will use the isotropic diffuse model (Liu and Jordan, 1963), which provides that the diffuse radiation has the same intensity whatever the incident angle.

In a PV field, the ground's view of the sky dome is restricted due to the presence of panels, which create shaded areas on the ground where only diffuse radiation is present, as the direct radiation is obstructed by the panels. The amount of radiation that hits the soil is therefore reduced by a geometrical factor, called view factor, which value spans

between 0 and 1. This parameter represents the fraction of radiation leaving a diffusive surface to directly reach a second surface (Marion et al., 2017). The average solar radiation that reaches the ground beneath the rows is determined by the following equation<fnref n="3" />:

$$I_G = f_{uns}(I_H - I_d) + I_d * V_{trr,sky} \quad (3)$$

where $V_{trr,sky}$ is the average view factor to the sky seen from the row-to-row space<fnref n="4" /> and $f_{uns}$ is the fraction of the ground (projected into x-dimension) which is not shaded,<fnref n="5" /> defined as (Mikofski et al., 2019)

$$f_{uns} = 1 - \min(1, \text{GCR}|\cos \beta + \sin \beta \tan \phi|) \quad (4)$$

In Eq. (4), GCR is the ground cover ratio defined as $W/c$ and $\phi$ is the projected solar angle on the vertical plane perpendicular to a surface (Appendix A).

### 2.1.2. Solar radiation on PV panels

When the solar radiation hits a surface with a horizontal inclination angle $\beta$, such as a PV panel, both direct and diffuse component undergo changes, and we have to take into account reflections phenomena that can occur with the ground or with obstacles in the nearby. Considering PV panels with front and rear surface reflectivity equal to 0.03 and 0.05, respectively, in our study we neglect reflection phenomena between adjacent rows and adjacent panels. A third component, the incident radiation diffusely reflected by the ground, $I_r$, has to be included, leading to the following equation for the solar radiation incident on a tilted surface:

$$I_{\beta} = I_{b\beta} + I_{d\beta} + I_{r} \quad (5)$$

A tilted collector has a reduced view of the sky, and, when displayed in multiple rows, this view is further reduced by the other panels, which act as obstacles thus shadowing each other. As for the radiation reaching the ground, the direct radiation only reaches unshaded panels areas. Considering bifacial panels, we have to compute $I_\beta$ for each side of the panel.

The direct component in Eq. (5) is given by

$$I_{b\beta} = (1 - a_{SH}) * R * I_b \quad (6)$$

where $a_{SH}$ represents the fraction of the panel shaded by the front row (Appendix C) and R is defined as the ratio of the beam radiation on a tilted surface to that on the horizontal surface (Appendix A). The diffuse components in Eq. (5) are defined as (Mikofski et al., 2019)

$$I_{d\beta} + I_{r} = I_{d} * V_{sky} + I_{gr,SH} * V_{ground} \quad (7)$$

<footnote n="2">² The extraterrestrial radiation is computed as $I_{H_0} = I_{sc}(1 + 0.033 * \cos(\frac{360\text{nm}}{365}) * \cos(\theta)$, where $I_{sc}$ is the solar constant equal to 1367 W m⁻², n is the day number and $\theta$ the solar zenith angle.</footnote>

<footnote n="3">³ We do not compute the reflection from the ground because it is quantified by ORCHIDEE.</footnote>

<footnote n="4">⁴ The detailed calculation of $V_{trr,sky}$ is presented in Appendix C.</footnote>

<footnote n="5">⁵ We assume that there is no shading caused by external objects, and that all modules are identical (no mismatch).</footnote>
with $V_{sky}$ and $V_{gr}$ view factors from the row to the sky and to the ground (Appendix C). In Eq. (7), $I_{gr,SH}$ is the reflected irradiance from the ground with shade and blocked sky (Mikofski et al., 2019):

$$I_{gr,SH} = I_{gr} \left( f_{uns} \left( 1 - \frac{I_d}{I_H} \right) + V_{rtr,sky} \frac{I_d}{I_H} \right) \quad (8)$$

where $I_{gr}$ is the ground reflected radiation incident on an horizontal surface assuming no shading and no blocking.

### 2.1.3. Wind speed

The airflow within an AV farm is a driving force for the PV production, as it regulates the PV module temperature (Leow et al., 2019). Additionally, it plays a crucial role for the turbulence which transports scalar variables such as heat transfer and water vapour distribution, thereby influencing evapotranspiration (Davarzani et al., 2014). Therefore, understanding the effects of the AV system on airflow and its subsequent impact on vegetation beneath the PV panels can be beneficial for making more precise predictions concerning the AV ecosystem. To formalize this concept, we take cues from canopy models developed for urban environments and forests.

Typically, for neutral atmospheric conditions, to analytically estimate the mean wind speed across an area, as a function of height, the standard logarithmic profile is employed (Tennekes, 1973)

$$u(z) = \frac{u^*}{\kappa} \ln\left(\frac{z-d}{z_0}\right) \quad (9)$$

In Eq. (9), z is the height above the ground, $u^*$ the friction velocity, $\kappa$ the Von Karman constant ($\kappa = 0.4$), $z_0$ and $d$ the roughness length and displacement height. In areas with obstructions, like urban areas, forests or extensive PV farms, accurate predictions using this methodology can be challenging. This difficulty arises from the complexities involved in precisely estimating $z_0$ and $d$ for these surfaces, and the impact of individual obstacles on the local wind resource. To address this challenge, various studies have been conducted to understand the relationship between the geometry of an urban/forest canopy and these aerodynamic parameters, and to address the flow inside the canopy, using both wind tunnel experiments and numerical simulations (Macdonald, 2000; Coceal and Belcher, 2004; Di Sabatino et al., 2008; Awol et al., 2022; Razak et al., 2013). The fundamental concept underlying urban canopy wind models involves conceptualizing buildings as idealized rectangular or cubic blocks arranged in regular or staggered arrays. These blocks are characterized by a plan area ratio $\lambda_p$, which represents the ratio of the plan area of the building as seen from above to the ground surface area ($A_d$), defined as the total area divided by the number of obstacles), and a frontal area ratio $\lambda_f$, denoting the ratio of the building's frontal area exposed to wind, $A_f$, to the ground surface area. In the forest canopy models, these density parameters can be substituted by the Leaf Area Index (LAI), defined, assuming a uniform vertical distribution of leaf area, as $LAI = a * h$, with a the leaf area density and h the canopy height. Combining these two approaches, we consider each panel as a three-dimensional obstacle, as sketched in Fig. 4, and we define the PV canopy density by means of $\lambda_f$. This allows us to approximate the wind profile within the AV farm, resembling the flow dynamics within a forest/urban canopy. To analyse the flow within the canopy, the spatially averaged mean wind speed over one cell of the array, i.e. over $A_d$, is typically used, and we assume its direction to be perpendicular to the rows. Therefore, we proceed as follows.

The initial step involves adjusting a wind speed from a regional wind climatology ($U(10)$, wind speed at 10 m) and scaling it down to the top of the “PV farm boundary layer”, which height corresponds to $H_{max}$ (see Table 1 and Fig. 4). According to Williams et al. (2023), the presence of the PV canopy also influences the wind above the PV panels, resulting in a reduced mean speed compared to configurations without panels. In fact, the presence of the PV panels implies that the atmosphere above them perceives a different roughness height. To compute it, we employ the approach outlined by Lettau (1969), which

derives a simple equation for the roughness length of an obstacle based on its geometry:

$$z_{0,PV} = \frac{1}{2} H \frac{A_f}{A_d} \quad (10)$$

where H is the PV panel height (Table 1 and Fig. 3). We calculate the ground surface area as the sum of the area directly below one panel and the area covering the row space in front of it, expressed as $A_d = L * c$. For the frontal surface area, we have $A_f = (H_{max} - H_{min}) * L$, where the dependence on $H_{max/min}$ causes $A_f$ to vary during the year due to changes in $\beta$ according to the Sun path. To obtain a constant value for $z_{0,PV}$, $A_f$ is averaged throughout the year. With this computation, we find $z_{0,PV}$ in the range [18–30] cm. This approach allows us to compute the reduction in wind speed at 10 m height caused by the presence of the panel. Our approximation, assuming equal friction velocity at both levels, is expressed by:

$$\tilde{U}(10) \approx U(10) \frac{\ln\left(\frac{10}{z_{0,PV}}\right)}{\ln\left(\frac{10}{z_0}\right)} \quad (11)$$

where $z_0$ represents the roughness height for momentum without PV panels, as provided by ORCHIDEE.<fnref n="6" /> Using Eq. (11), we determine the ratio $\tilde{U}(10)/U(10)$, which falls within the range [0.65–0.83], consistent with findings by Williams et al. (2023). This ratio serves as a basis for down-scaling to $H_{max}$, using:

$$U(H_{max}) = \tilde{U}(10) \frac{\ln\left(\frac{H_{max}}{z_{0,PV}}\right)}{\ln\left(\frac{10}{z_{0,PV}}\right)} \quad (12)$$

Finally, the last step involves examining the flow beneath the PV array. Wind tunnel experiments conducted to explore the flow behaviour in PV systems have shown that the decrease in mean wind speed relative to the free stream velocity above can be more or less pronounced depending on the maximum height of the PV farm (Williams et al., 2023; Smith et al., 2022). Regarding experimental studies, AL-agele et al. (2021) found a significant reduction in mean wind speed below PV panels canopy when placed at a height around 2 m. In contrast, experiments conducted by Marrou et al. (2013) with PV panels placed far above the ground ($H = 4$ m) did not show significant changes in the mean wind speed below the canopy. This results lead us to distinguish two cases, based on the PV panels height, $H$:

- $H \ge 3.5$ m. The assumption that the panels are positioned well above the ground suggests that there is adequate ventilation to keep the air masses in equilibrium with the external environment. Consequently, this setup would likely prevent any substantial changes in the mean wind speed experienced by the vegetation below (Marrou et al., 2013).

- $H < 3.5$ m. In this case, we embrace the idea that the presence of the panels influences the flow below them. The increased drag caused by the PV canopy likely slows down the air beneath the solar panels, resulting in a decrease in the mean wind velocity and in turbulence (Adeh et al., 2018; AL-agele et al., 2021; Glick et al., 2020; Williams et al., 2023; Smith et al., 2022).

Since in our configuration, due to the tracking system, the PV panels height is equal to 2.5, with a minimum $H_{min}$ of 1.456 m and a maximum $H_{max}$ of 3.543 m, we focus on the latter case ($H < 3.5$ m).

Therefore, beneath the canopy, we assume a simple exponential profile (Macdonald, 2000; Di Sabatino et al., 2008; Inoue, 1963):

$$U(z) = U(H_{max}) * \exp\left[\alpha_c\left(\frac{z}{H_{max}} - 1\right)\right] \quad (13)$$

Here, $U(z)$ denotes the wind speed at height $z$, and $\alpha_c$ is the canopy attenuation coefficient, dependent on the system packing density and

<footnote n="6">⁶ As done with $z_{0,PV}$, $z_0$ is averaged over the year.</footnote>
<figure><img src="image_8.png" /><figcaption>**Fig. 4.** Three-dimensional representation of the PV layer designed for wind calculations. The most important geometric factors are showcased. On the left side of the figure, the PV rows are depicted as solid parallelepipeds. On the right, $A_f$ denotes the projection of the panel surface area onto the vertical plane.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Fig. 5.** Schematic diagram of the wind methodology.</figcaption></figure>

proportional to canopy porosity. In our model, we take $a_c$ equal to $\lambda_f = A_f/A_d$ (Macdonald, 2000). To compute the average wind profile $U_{crop}$ beneath the canopy, we integrate Eq. (13) from $z=0$ to $z=H_{min}$, averaging over the height span $H_{min}$, yearly averaged. Fig. 5 provides a visual representation of the wind methodology. As explained in Section 1, we assume that air temperature and air humidity at 2 m (T and Q in Fig. 5) remain unaffected by the presence of the panels. Therefore, our model do not change the air temperature and humidity gradients relative to the soil surface, but only affects the turbulence that influences diffusion. We emphasize that $U(H_{max})$ does not reflect the actual velocity at $H_{max}$. Eq. (12) neglects the inclusion of the displacement height $d$, differently from what specified in Eq. (9), which would otherwise result in $U(H_{max})$ being approximately close to zero. In fact, in our model, $U(H_{max})$ solely represents a virtual velocity – an intermediate parameter between $\bar{U}(10)$ and the velocity below the panels, essential for the down-scaling process in our model.

## 2.2. Hydro-vegetation layer: ORCHIDEE land surface model

To explore the crop ecosystem behaviour, we integrate the PV layer with the hydro-vegetation layer, represented by ORCHIDEE, the Institut Pierre Simon Laplace LS model. ORCHIDEE simulates terrestrial water and energy balances at the land surface, alongside the vegetation and soil carbon cycle (Krinner et al., 2005). It consists of two primary modules: SECHIBA and STOMATE. SECHIBA handles thermodynamic and hydrological processes at half-hourly intervals, computing key surface variables and fluxes like soil temperatures (Wang et al., 2016) and water content (de Rosnay et al., 2003) in an 11-layer scheme, and the vegetation photosynthesis (Vuichard et al., 2019). STOMATE operates daily, managing carbon dynamics, involving processes such as vegetation respiration, soil carbon dynamics and vegetation phenology, constrained by nutrient availability (Vuichard et al., 2019). The model

relies on various environmental drivers, such as temperature, solar radiation, humidity, and atmospheric CO$_2$ concentration, extracted from input files known as forcing files. It can operate in a coupled set-up, where the atmospheric forcings impact the land surface and viceversa, or in offline mode as a stand-alone land surface model. In this study, since we are solely interested in changes in the land surface, ORCHIDEE operates in offline mode, without interacting with the climate. Table 2 summarizes the variables needed in the forcing files, and more details are provided in Appendix D. A specific spatial resolution is not required, and it is automatically adopted from the forcing data. ORCHIDEE represents the land surface through 13 Plant Functional Types (PFTs) and bare soil. The PFT is a set of plant species that exhibit similar behaviour in carbon and water exchange. Although each PFT shares identical governing equations, they vary in parameters, which define the plant-specific behaviour. For our model, we focus on the PFT Herbaceous, specifically its sub-classes C3 and C4 crops. In the standard version of ORCHIDEE used here, there is a simplified representation of C3 and C4 crops, which differ from a standard grassland by a specific phenology and improved photosynthetic capacities. The C3 crop type in our simulations represents winter crops such as wheat, while the C4 crop type represents summer crops such as maize.

C3 and C4 refer to two different photosynthetic pathways (Bräutigam and Gowik, 2016):

- C3 plants, including most crops like wheat, rice, and soybeans, typically thrive in moderate temperatures and do not require high light intensity for optimal growth.

- C4 plants, such as corn (maize) and sugarcane, are better adapted to high temperatures and dry conditions. They exhibit better tolerance to higher temperatures and drought compared to C3 plants (Taylor et al., 2011).
<table><caption>**Table 2**

Definition of the forcing atmospheric variables.</caption><thead><tr><th>Symbol</th><th>Definition</th></tr></thead><tbody><tr><td>SW<sub>down</sub></td><td>surface incident shortwave radiation [W m<sup>-2</sup>]</td></tr><tr><td>LW<sub>down</sub></td><td>surface incident longwave radiation [W m<sup>-2</sup>]</td></tr><tr><td>U</td><td>wind speed module at 10 m [m s<sup>-1</sup>]</td></tr><tr><td>P</td><td>surface pressure [Pa]</td></tr><tr><td>T</td><td>air temperature at 2 m [K]</td></tr><tr><td>Q</td><td>near surface air humidity</td></tr><tr><td>Rain<sub>f</sub></td><td>rainfall rate [kg m<sup>-2</sup> s<sup>-1</sup>]</td></tr><tr><td>Snow<sub>f</sub></td><td>snowfall rate [kg m<sup>-2</sup> s<sup>-1</sup>]</td></tr></tbody></table>

As introduced at the beginning of Section 2, we enforce complete crop coverage at each grid point. This is possible because the vegetation can be prescribed by a map giving the fraction of each PFT in each pixel or it can be prescribed as a fixed fraction everywhere. Thus, we assign the PFT as either 100% C3 crop type or 100% C4 crop type. Since ORCHIDEE operates in the off-line mode, this imposition does not affects the results.

Among the diverse variables quantifiable by ORCHIDEE, the outputs of interest to analyse the crop behaviour include Gross Primary Production (GPP), NPP, Leaf Area Index (LAI) and EvapoTranspiration (ET), given by the sum of evaporation and Transpiration (Tr).

## 2.3. Simulations set-up

We apply the model outlined in Section 2 to two distinct case studies: the Iberian Peninsula (IP) and the Netherlands (NL). These regions within the European context exhibit diverse climatic conditions. Panel a of Fig. 6 shows the day-time hourly solar radiation averaged over the period 2011–2020. Notably, as the latitude increases, its value decreases: the Netherlands experiences significantly lower solar radiation compared to the Iberian Peninsula. Moving to panel b of the same figure, the annual count of dry days – defined as days with no precipitation – averaged across the same time frame, is showcased. The Iberian Peninsula emerges as a dry area, particularly in the South-East part, characterized by a Mediterranean-type climate. Conversely, the Netherlands exhibits a typically humid climate, experiencing precipitation throughout all the year. To generate the forcing files needed by ORCHIDEE, we utilize ERA5-Land ERA5-Land (2024), the latest climate reanalysis published by the European Centre for Medium-Range Weather Forecasts. These data-sets are publicly accessible through the Copernicus Climate Data Centre (Copernicus, 2022) on a regular latitude–longitude grid, with a resolution of 0.1° x 0.1°. We specifically extract hourly data for two regions: 10°W–4°E, 36°N–44°N, covering the Iberian Peninsula (IP), and 3°E–8°E, 50°N–54°N for the Netherlands (NL), showed by the black boxes in panel a, Fig. 6. We select the years 2015, 2018 and 2020. The year 2020 serves as a benchmark in climatology (cli). Meanwhile, 2015 marked a notably *dry* (wet) period for the Iberian Peninsula (Netherlands), whereas the inverse is observed in 2018. This reflects the behaviour of cyclonic patterns over Europe, particularly the North Atlantic Oscillation (NAO) and the Scandinavian (SCA) patterns, which are known to be the primary drivers of precipitation across Europe (Casanueva et al., 2014). In summer, if the NAO and SCA are in the negative phase, Northern Europe receives more precipitation, while the rest of Europe is more susceptible to drought. This pattern was notably observed in 2020 and more intensely in 2015, with the summer months characterized by extremely low Summer NAO and SCA index values (Ionita et al., 2016). Conversely, in 2018, we experienced a positive NAO throughout almost the entire year. In its positive phase, the summer NAO is associated with anticyclonic conditions over Northern Europe, resulting in sunny, warm and dry conditions, which could be related to summer droughts in Northern Europe. Selecting years with various climatic conditions allows us to test the performance of the AV systems under more extreme climatic conditions.

We run simulations for two PV configurations, ST and SAT, as introduced in Section 2.1. Among the variables listed in Table 2, SW<sub>down</sub> and U are modified according to the PV model presented in Section 2.1.

To ensure that the model reaches a stable state within the ORCHIDEE framework, a preliminary phase known as model spin-up is necessary. This involves running the model for a period representative of the time preceding the simulation’s initialization. Accordingly, we execute a warm up simulation spanning a decade (2005-2014), and we use it as the basis for subsequent simulations. Then, restart simulations are performed over the period 2005-2020, and we take into account only the years 2015, 2018 and 2020. We note that achieving equilibrium in soil carbon typically requires several thousand years, while forest biomass takes several hundred years. However, in our case, since we are not focusing on soil carbon and considering that biomass in grasslands and crops does not accumulate from year to year, a decade is sufficient to reach equilibrium for pools such as soil water and biomass, which drive GPP, NPP, LAI, and ET. In addition to the AV simulations, we run a set of simulations with forcing files generated utilizing atmospheric variables without applying the PV layer. This set of simulations models conditions without PV panels, serving as the control in our analysis. For the output files we require a 3-h temporal resolution.

As explained in Section 2.2, we force ORCHIDEE to operate as if the entire spatial domain were covered by crops. However, this represents an unrealistic situation, not only because of urban areas within the territory, but also because some regions, especially in the Iberian Peninsula, are unsuitable for the agriculture due to harsh climatic conditions and poor soil quality. To exclude these areas, we filter our data using the PFT which corresponds to the actual distribution of vegetation types within the territory. We thus select only the grid points with at the least 10% coverage of agricultural crops, C3 and C4 combined.

## 3. Results

To analyse the performance of the simulated system and to compare the behaviour of different AV configurations against the control, key performance indicators, tailored to the specific characteristics of each AV system, are used. These indicators are linked to the Water-Energy-Food-Ecosystem (WEFE) nexus, focusing on aspects such as land productivity, water use efficiency, and PV energy yield. Based on these indicators, in the next sections we explore the following nexus: food-climate, water-food, food-energy. For the sake of brevity and simplicity, in this section the Sun Tracking and Sun Anti-Tracking configurations will be referred to as ST and SAT, respectively, and the two types of crops as C3 and C4.

### 3.1. Food-climate nexus

Fig. 7 shows the annual NPP, grid point by grid point, for the Iberian Peninsula (panels a-b) and the Netherlands (panels c-d), comparing the AV configurations to the control for both types of crops across the three years analysed. Over the Iberian Peninsula, the ST provides overall a greater performance than the SAT. For C4 (Fig. 7 b), the ST configuration shows a significantly higher mean value than the control.<fnref n="7" /> Additionally, the distribution shifts from a dense lower tail in the control to a more concentrated shape around the mean, bringing the mean and median closer (see Fig. F.1 in Appendix F). For C3 (Fig. 7 a), ST performs best during the dry year, increasing the mean NPP by 38%. Its distributions are narrower each year, reducing maximum NPP while raising the lower tail, preventing areas with low food production. The distributions remain bimodal but with closer modes, leading to a more homogeneous distribution and reducing productivity gaps.

<footnote n="7">⁷ Significance assessed using the Cramér-von Mises test and the bootstrap method at the 95% level.</footnote>
<figure><img src="image_10.png" /><figcaption>**Fig. 6.** Panel a: Day-time hourly SW<sub>down</sub> [W m<sup>-2</sup>] averaged over the years 2011–2020. Panel b: annual count of precipitation-free days [#] averaged over the years 2011–2020. The variables are taken from the ERA5-Land data-sets. The spatial domain covered in both panels is 15°W-38°E, 27°N-60°N. The black boxes in panel a delineate the areas analysed in this study: 10°W-4°E, 36°N-44°N (IP) and 3°E-8°E, 50°N-54°N (NL). The blue contour in panel b delineates the Atlantic area in the Iberian Peninsula.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>**Fig. 7.** Violin plot of the yearly NPP [gC m<sup>-2</sup> y<sup>-1</sup>], grid point values, over the Iberian Peninsula (panel a: C3, panel b: C4) and the Netherlands (panel c: C3, panel d: C4), for each configuration analysed. The dots show the mean value for each configuration. The dashed black lines correspond to the control mean value for each year.</figcaption></figure>

The bimodal distributions reflect the spatial NPP patterns across the Iberian Peninsula. Following De la Mata et al. (2012), we divided the region into two sub-areas (Fig. 6 b). In the humid, Atlantic-influenced northern belt, PV panels reduce annual NPP (Fig. 8 a-b). Conversely, in the drier Mediterranean zone, shading mitigates extreme low NPP values, enhancing overall performance (Fig. 8 c). Similarly, C4 shows significant NPP increases under ST (Fig. 8 d). In the Netherlands, ST leads to an opposite effect compared to the Mediterranean area. Annual NPP is significantly lower than in the control, especially during wet years (Fig. 7 c-d), as reduced solar radiation and frequent precipitation favour crops and prevent low productivity zones. Comparing control NPP, the Mediterranean area has significantly lower values than the Netherlands, with most dry-year control distributions in [300-500] gC m<sup>-2</sup> y<sup>-1</sup> versus [600-800] gC m<sup>-2</sup> y<sup>-1</sup> in the Netherlands (Figs. 8 c-d, 7 c-d). In the Netherlands, control NPP is more homogeneous, with reduced variability, particularly in wet years. For C3, transitioning from control to SAT and ST further decreases variability, ensuring that lower-tail values increase during dry and climate years (Fig. 7 c).

The differential impact of the ST configuration on crop productivity is evident in the seasonal evolution of LAI. Fig. 9 depicts the annual LAI cycle for low and high NPP areas, focusing on C4 and C3 in the Iberian Peninsula and the Netherlands. These areas are defined

yearly based on the 10th and 90th percentiles of the control annual NPP. For C3 in the Iberian Peninsula, ST benefits low NPP areas by increasing LAI, while in high NPP areas, these gains diminish, reducing LAI. The effect is strongest during the dry year, with LAI exceeding control values year-round in low NPP areas. The peak shifts from May (control) to June, and the growing season extends until October (August in control). For C4, in low NPP areas, peak LAI shifts from June (control) to July in dry years and from July to August in wetter years. C4 plants, with efficient water use and CO<sub>2</sub> fixation, thrive in warmer conditions. The ST enhances this, prolonging their growth and productivity. In the Netherlands, both SAT and ST reduce productivity, with lower LAI than the control for C3 and C4. However, during dry years, low NPP areas show a positive effect: peak LAI shifts from June to July for C3 and from July to August for C4, with increased LAI in the latter part of the year. A similar pattern to LAI is observed in the annual cycle of autotrophic respiration (R<sub>a</sub> = GPP - NPP) (not shown). The effectiveness of ST in low NPP areas of the Iberian Peninsula during the growing season is further highlighted by the GPP/R<sub>a</sub> ratio (Fig. F.3 in Appendix F). The significantly higher GPP/R<sub>a</sub> values compared to the control (Fig. F.3, a, e, i and c, g, k), especially in summer, indicate that the temperature-driven reduction in R<sub>a</sub> under ST leads to lower respiration, enhancing biomass accumulation and potentially increasing long-term crop productivity.
<figure><img src="image_12.png" /><figcaption>**Fig. 8.** IP. Violin plot of the annual NPP [gC m⁻² y⁻¹], grid point values, for each configuration analysed. Panels a-b Atlantic area (C3 and C4) panels c-d Mediterranean area (C3 and C4). The dots show the mean value for each configuration.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>**Fig. 9.** LAI annual evolution averaged over two selected areas (low and high crop NPP), across various configurations, for the Iberian Peninsula (upper figure) the Netherlands (lower figure), for dry and wet year.</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>Fig. 10. Violin plot of the yearly WUE relative change, grid point values, over the Iberian Peninsula (panel a: C3, panel b: C4) and the Netherlands (panel c: C3, panel d: C4), for each configuration analysed. The dots show the mean value for each configuration. The dashed grey line corresponds to the 0 value.</figcaption></figure>

## 3.2. Water-food nexus

Water Use Efficiency (WUE = GPP/ET [gC m⁻² mm⁻¹]) measures how effectively an ecosystem converts water into yield (Pohanková et al., 2018). A higher WUE indicates greater efficiency, as less water is required for the same yield. Fig. 10 shows the relative annual WUE change for AV configurations versus the control, grid point by grid point, for the Iberian Peninsula (panels a-b) and the Netherlands (panels c-d). All AV configurations significantly increase WUE, particularly ST, with a stronger effect in the Mediterranean region, mirroring NPP trends. Changes in WUE stem from crop-level water cycle modifications. While higher GPP usually increases transpiration due to stomatal opening, improved light and wind conditions under AV reduce water stress, maximizing photosynthesis while limiting transpiration and evaporation losses. Indeed, when defining WUE as GPP/Tr, the pattern remains similar but with lower values, indicating reduced water loss beyond transpiration alone. Comparing the annual cycles of GPP/Ra and soil moisture stress (vᵢₜ) for the Iberian Peninsula (Figs. 11 and F.3), low NPP areas show increased GPP/Ra under SAT/ST while maintaining lower soil moisture stress than the control, improving water use efficiency. A strong correlation between crop productivity and soil moisture stress is also evident when comparing Figs. 9 and 11. Moving from control to SAT and ST, high NPP areas show a decrease in LAI, while low NPP areas experience an increase in both LAI and vᵢₜ. This reduced variability across values suggests improved efficiency in the phenological cycle, enhancing stability and control over crop productivity and water use, particularly under ST.

## 3.3. Food-energy

The Land Equivalent Ratio (LER) is commonly used to assess the efficiency of land use in AV systems compared to monoculture. It is defined as:

$$LER = \frac{NPP_{AV}}{NPP_{control}} * (1 - LL) + \frac{PV_{pow,AV}}{PV_{pow, std}} \quad (14)$$

where PVpow,AV [Wh] is the PV power generated in an AV system, and PVpow, std is the output of a standard PV farm (Appendix E). This study

uses a fixed-tilt south-facing array (β = 20°, W = 4.57 m, c = 6 m, H = 0.8 m), with yearly values for NPP and PVpow. The Land Loss (LL), which refers to portion of land unusable for agriculture (e.g. support structures, maintenance areas), is set at 10%. An LER > 1 indicates more efficient land use in AV systems than monoculture. As shown in Fig. 12, ST achieves the highest land-use efficiency, particularly for C3 during the dry year. While SAT also performs well, with most grid points above LER = 1, its values remain consistently lower than ST, confirming its lower efficiency. Comparing regions, LER values in the Netherlands are lower than in the Iberian Peninsula, highlighting AVs greater land-use advantage in the Mediterranean region.

## 4. Discussion

The present study is limited to the analysis of the impact of PV installations on solar radiation and near surface wind. The lack of knowledge of the impact of these infrastructures on atmospheric conditions close to the surface have lead us to use simple assumptions which will be the subject of future studies.

To compute the solar radiation on the ground and on the PV panels surface, we employed standard methods that have been validated and successfully used for modelling the irradiance and the PV power (Mikofski et al., 2019; Holmgren et al., 2018; Mavromatakis et al., 2010). This does not hold for the wind speed model. Experimental studies assessing the impact of AV farms on wind speed are limited (Marrou et al., 2013; Adeh et al., 2018). The lack of meteorological data presents a challenge in evaluating the accuracy of our predictions across various AV sites and determining the extent to which AVs affects wind speed profiles. Indeed, the flow within the PV canopy is highly complex and spatially variable, influenced by various factors such as changes in wind direction, which our model does not detect. In our model, to compute the mean wind speed within the canopy we relied on simplified assumptions from urban/vegetation canopy models, mostly based on numerical simulations, and on computational fluid dynamics simulations of specific PV configurations without tracking mechanisms (such as Macdonald, 2000; Smith et al., 2022; Williams et al., 2023). Therefore, this approach provides only a mean and qualitative understanding of wind behaviour as it is experienced from the vegetative
<figure><img src="image_15.png" /><figcaption>**Fig. 11.** $v_{lw}$ annual evolution averaged over two selected areas (low and high crop NPP), across various configurations, for the Iberian Peninsula, for dry and wet year.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>**Fig. 12.** Violin plot of the yearly LER, grid point values, over the Iberian Peninsula (panel a: C3, panel b: C4) and the Netherlands (panel c: C3, panel d: C4), for the SAT and the ST configuration. The dots show the mean value for each configuration.</figcaption></figure>

surface. It does not take into account the cooling effects of the wind on the inner layer below the PV array nor the heating effects on the panel surface. Moreover, while there is a general agreement in experimental and modelling studies that below a certain threshold height the presence of PV panels reduces both mean wind velocity and turbulence, this threshold is not clearly defined. The threshold we set at $H = 3.5$ m is approximate. To better understand these effects, further studies with various AV configurations are needed, particularly to explore the combined influence of height and row spacing on wind behaviour, as well as more on-site observations. Additionally, a more detailed analysis of the effects when PV panels are positioned farther from the ground would be beneficial.

To conclude, regarding ORCHIDEE, it is important to acknowledge that the crop parametrization has intrinsic limitations. The model uses generic field parameters, which may not accurately capture the nuances of very local and specific sites. However, this is acceptable for our purposes, as we are conducting assessments and perspective studies rather than evaluations of specific and localized sites.

Within the context of the WEFE nexus, three specific interconnections -food-climate, water-food and food-energy- were analysed. In the Mediterranean region of the Iberian Peninsula, these interactions exhibit strong synergies. AV systems, especially in the ST configuration, demonstrate several benefits. They ensure higher overall crop productivity, exhibit a more efficient phenological cycle and achieve a more efficient water and land use. The reduced variability in the NPP allows for more controlled crop productivity, and the substantial increases in crop productivity in areas with low productivity aligns with the AVs objective to enhance food security, by contributing to more stable and predictable agricultural output. The reduction in solar radiation due to the shading provided by the PV panels, along with a decrease in wind speed, creates a more favourable microclimate for crops in our model. This aspect is especially beneficial during drought periods or in years characterized by adverse weather conditions when water availability becomes critical, as is often the case in arid regions. The reduced evapotranspiration, resulting from the shading provided by the panels, not only contributes to more efficient water use but could also have
long-term implications for soil health and crop resilience. In fact, these microclimatic changes could make crops more resistant to prolonged drought periods, a factor that is becoming increasingly important due to climate change, which is driving rising temperatures and a gradual reduction in water resources. This suggests that AV systems, in addition to improving agricultural productivity in the short term, have the potential to mitigate risks posed by extreme weather conditions, while ensuring overall ecosystem stability, particularly in arid and semi-arid environments. Furthermore, the dual land use for both agriculture and energy production helps alleviate the competition between these sectors, contributing to a more sustainable use of available resources. This synergy is one of the key features of AV systems, as it allows for the simultaneous production of both food and renewable energy without compromising agricultural production, a critical aspect for achieving long-term sustainability goals.

On the other hand, in the Netherlands, AV systems generally tend to decrease crop productivity, and the improvements in LER and WUE relative to the control are less pronounced than those observed in the Iberian Peninsula. Nevertheless, it is important to note that the control NPP is significantly higher than in the Mediterranean area, and water scarcity is not a major concern in the region, even though water savings remain beneficial. The primary benefit of AV systems in the Netherlands would lie in reducing competition for land use. In fact, producing renewable energy without displacing agricultural land is a crucial benefit in a densely populated and agriculturally intensive region like the Netherlands. These observations suggest that there is no unequivocal “win-win” scenario with AV systems in the Netherlands: while AVs offers some advantages, such as enhanced land-use efficiency and renewable energy production, it also comes with trade-offs, including decreases in crop productivity. As a result, the implementation of such systems requires a tailored approach that balances the specific agricultural and energy needs of the region, taking into account local climatic conditions.

Our results indicate that AV systems, especially with the ST configuration, offer significant benefits within the WEFE nexus in regions characterized by a dry climate and abundant solar radiation, such as the Mediterranean area of the Iberian Peninsula. Conversely, in regions typically characterized by lower radiation and abundant precipitations, the reduction in solar radiation due to the AV system can hinder crop productivity, preventing a win-win situation across each aspect of the nexus. This disparity highlights that the benefits of AV systems are not uniformly distributed across different climatic and geographical contexts and that trade-offs are necessary when implementing AV systems, as the benefits vary by regions. Moreover, an in-depth evaluation of the relative importance of each interconnections within the WEFE nexus should be conducted according to the specific regional context, ensuring that the implementation of AV systems is tailored to maximize their positive impacts. Policymakers and stakeholders should consider localized adaptation strategies to fine-tune AV installations based on crop type, regional climate, and water availability. Finally, the socioeconomic impacts of AV – such as changes in agricultural practices and potential economic benefits or drawbacks for farmers – should be considered. Understanding these aspects is essential for ensuring the acceptance and successful implementation of AV systems across diverse regions, contributing to the promotion of more sustainable, inclusive, and resilient agricultural practices. As a final remark, we emphasize that our decision to present results for only three specific years does not compromise the validity of our findings. These years serve as representative examples, but the results can be readily extrapolated to other years within the current climatic conditions (see Fig. F.4 in Appendix F).

## 5. Conclusion

This study underscores the potential of AVs to reshaping the interconnections between climate, energy, water, and food security within

the WEFE nexus. Our work is among the first to integrate a regional-scale AV model with a land surface model, allowing for a comprehensive simulation of AV systems effects on crop productivity and water/land use under varying climatic conditions. The findings highlight the capacity of AV systems, particularly in dry regions with abundant solar radiation, like the Mediterranean area of the Iberian Peninsula, to enhance land use efficiency, optimize water management, and sustain food security while supporting renewable energy goals. In contrast, the performance of AV systems in regions with lower solar radiation and abundant precipitation, such as the Netherlands, reveals the complexity and context-specific nature of these systems. The trade-offs between energy production and agricultural productivity suggest that a uniform approach may not be suitable for AV deployment. Instead, region-specific strategies are essential to maximize the benefits of AV systems and address the unique challenges of each area. Our research contributes a novel perspective by moving beyond fine-scale assessments to explore the broader regional impacts of AV systems. This approach suggests how AV configurations can be optimized across different climatic zones, with the caveat that these systems must be not only technically feasible but also socially and economically viable. Overall, this work represents a significant step forward in understanding the role of AV systems in a sustainable, climate-resilient future, offering a basis for future research and policy development in the transition to a net-zero carbon economy.

## CRediT authorship contribution statement

**Lia Rapella:** Writing – original draft, Methodology, Investigation, Formal analysis, Conceptualization. **Nicolas Viovy:** Writing – review & editing, Supervision, Data curation, Conceptualization. **Jan Polcher:** Writing – review & editing, Supervision, Methodology, Conceptualization. **Davide Faranda:** Writing – review & editing, Supervision, Formal analysis, Conceptualization. **Jordi Badosa:** Writing – review & editing, Methodology, Conceptualization. **Philippe Drobinski:** Writing – review & editing, Supervision, Methodology, Formal analysis, Conceptualization.

## Declaration of competing interest

The authors 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 work has been carried out at the Energy4Climate Interdisciplinary Center (E4C) of IP Paris, which is in part supported by 3rd Programme d'Investissements d'Avenir [ANR-18-EUR-0006-02]. This work is done in the frame of the AgriPV-ER project (22-PETA-0007), which has the funding support from France 2030, PEPR TASE (https://www.pepr-tase.fr/), through ANR, and by the Foundation of Ecole polytechnique (Chaire "Défis Technologiques pour une Énergie Responsable") financed by TotalEnergies. We are grateful to Etienne Drahi and Pierre Souquet, from TotalEnergies, for their insightful discussions and feedback, which have greatly contributed to the development of this work.

## Appendix A. Angles

The amount of solar radiation that reaches the Earth is not uniform everywhere, but it depends on the latitude and on the longitude of the location. Moreover, due to the rotation and revolution motions of the Earth, same locations during different periods see the Sun from different positions. To accurately locate the position of the Sun are used the so called solar angles. In this section we will briefly describe all the angles necessary to the calculate the position of the Sun in the sky and the Sun-PV panel system geometry.
- $\lambda$, the latitude angle [°], positive in the northern hemisphere and negative in the southern hemisphere, is defined as the angle forming with respect to the equator centre. Together with the longitude angle, $\mu$ [°], it is used to specify every location on the Earth (Karafil et al., 2015).

- $t_s$, the local solar time, in hours:

$$t_s = t_{sm} + e \qquad (A.1)$$

where $t_{sm} = t_u + \lambda/15$ is the mean solar time, with $t_u$ the universal time. The parameter $e$ is the equation of time (expressed in minutes, to be converted in hours dividing by 60) (Tasdemiroglu (Maleki et al., 2017)):

$$e = 9.87 \sin(2B) - 7.53 \sin(B + 78.7) \qquad (A.2)$$

with $B = 360(n - 81)/365$ ($n$ is the day number).

- $\omega$, the hour angle [°], which takes into account the rotation of the Earth of $15^\circ/hour$ around its polar axis (+15° in the morning, -15° in the afternoon). It is defined as the angle between the local meridian and the meridian plane of the Sun, which results displaced east or west with respect to the local meridian.

$$\omega = 15(t_s - 12) \qquad (A.3)$$

- $\delta$, the solar declination angle [°], i.e. the angle between the sun at solar noon and the plane of the equator. It is due to the $23.45^\circ$ shift of the Earth's rotational angle with respect to the orbital plane. The value of $\delta$ can be approximated by the Cooper equation:

$$\delta = 23.45 \sin \left( 360 \frac{284 + n}{365} \right) \qquad (A.4)$$

- $\alpha$, the solar altitude angle [°], i.e. the angular position of the Sun with respect to the horizontal.

$$\sin \alpha = \sin \lambda \sin \delta + \cos \lambda \cos \delta \cos \omega \qquad (A.5)$$

- $\theta$, the zenith angle [°], the angle between the Sun and the vertical, i.e. the angle of incidence of the direct radiation on a horizontal surface. By direct inspection, this angle is the complementary of the altitude angle, $\theta = 90 - \alpha$. Therefore, it obeys the following rule:

$$\cos \theta = \sin \lambda \sin \delta + \cos \lambda \cos \delta \cos \omega \qquad (A.6)$$

- $\gamma_s$, the solar azimuth angle [°], the angular displacement from the north of the beam radiation projection on the horizontal plane.

$$\gamma = \operatorname{sign}(\omega) \left| \arccos \left( \frac{\cos \theta \sin \lambda - \sin \delta}{\sin \theta \cos \lambda} \right) \right| \qquad (A.7)$$

The sign function gives $+1/-1$ when $\omega$ is positive/negative (afternoon/morning).

- $\gamma_p$, the surface azimuth angle [°], which shows the deviation of the line normal to the plane from the local meridian. Both azimuth angles are assumed to be negative from north to west and positive from north to east.

- $\beta$, the surface inclination angle [°], the angle between the surface and the horizontal plane.

- $\Theta$, the solar incident angle [°] on the inclined surface, i.e. the angle between the direct radiation and normal line on that surface.

$$\cos \Theta = \cos \theta \cos \beta + \sin \theta \sin \beta \cos (\gamma_s - \gamma_p) \qquad (A.8)$$

By means of $\Theta$ and $\theta$, it is possible to compute the beam radiation tilt factor $R$, i.e. the ratio of the beam radiation on a tilted surface to that on the horizontal surface, defined as

$$R = \frac{\cos \Theta}{\cos \theta} \qquad (A.9)$$

- $\phi$, the projected solar angle [°] on the vertical plane perpendicular to a surface, satisfying the following relationship (see Table A.1)

$$\tan \phi = \cos (\gamma_s - \gamma_p) \tan \theta \qquad (A.10)$$

<table><caption>**Table A.1**

Definition of the angles necessary to calculate the position of the Sun in the sky and the Sun-PV panel system geometry.</caption><thead><tr><td>Symbol</td><td>Name</td></tr></thead><tbody><tr><td>λ</td><td>latitude[°]</td></tr><tr><td>t<sub>s</sub></td><td>solar time [hours]</td></tr><tr><td>ω</td><td>hour angle [°]</td></tr><tr><td>δ</td><td>solar declination angle [°]</td></tr><tr><td>α</td><td>solar altitude angle [°]</td></tr><tr><td>θ</td><td>zenith angle [°]</td></tr><tr><td>γ<sub>s</sub></td><td>solar azimuth angle [°]</td></tr><tr><td>γ<sub>p</sub></td><td>surface azimuth angle [°]</td></tr><tr><td>β</td><td>surface tilt [°]</td></tr><tr><td>Θ</td><td>solar incident angle [°]</td></tr><tr><td>φ</td><td>projected solar angle [°]</td></tr></tbody></table>

## Appendix B. Sun tracking and sun anti-tracking

In PV farms, the tilt of the panels is often regulated according to the position of the Sun. Sun Tracking (ST) allows PV panels to follow the path of the sun throughout the day. This dynamic orientation optimizes the angle of the panels to ensure they receive maximum sunlight exposure, potentially increasing the overall energy output. By direct inspection, the ST angle is the one who minimizes the beam angle of incidence with the module normal. On the other hand, in a Sun Anti-Tracking (SAT) system panels are oriented away from direct sunlight. In the context of AVs, this could allow plants to receive more irradiance.

We computed the ST angle as

$$\beta_{ST} = \arctan (x_p/z_p) \qquad (B.1)$$

where $x_p$ and $z_p$ are the $(x, z)$ solar coordinates projected on the tracking plane of rotation (Anderson and Mikofski, 2020).

In the SAT configuration we want the panels to be ideally parallel to the beam ray. To achieve this, we add $90^\circ$ to the ST angle in the morning hours and subtract $90^\circ$ in the afternoon (after the daily maximum in the solar elevation angle). In both cases, we restrict the angles values to the range $-60^\circ/ + 60^\circ$ due to structural constraints. To avoid row-to-row shading during early morning and late afternoon hours, we further restrict the range of motion of the panels by applying backtracking (Holmgren et al., 2018). By convention, the sign for tracking angles follows the right-hand rule. In our setup, where the arrays point south, rotations towards west are considered positive, while rotations towards east are negative.

## Appendix C. Viewfactor

The amount of diffuse and reflected radiation that hits an inclined surface is limited by a geometrical factor, called view factor (unitless), which value spans between 0 and 1. This parameter represents the fraction of radiation leaving a diffusive surface to directly reach a second surface, i.e. the fraction of the radiation leaving a surface that is incident on a receiving surface (Marion et al., 2017). If a stand-alone surface is horizontal, it is able to get the radiation from the whole sky (view factor equal to 1), while a tilted collector has a reduced view of the sky, leading to a reduction in the solar radiation that can reach it. When PV panels are displayed in multiple rows, the view of the sky from a single collector is further reduced by the other panels.

We then have to take into account two types of view factors:

- the view factor of the surface to the sky (fraction of sky that is visible from the panel surface)

- the view factor of the surface to the ground (fraction of ground that is visible from the panel surface)
<figure><img src="image_17.png" /><figcaption>Fig. C.1. 2D view of two PV rows, highlighting the angles necessary to determine $V_{rtr,s}$ for the diffuse radiation incident on ground beneath the PV panels. The thick black (red) segments represent the shaded (unshaded) area at the ground.</figcaption></figure>

Considering bi-facial PV panels, each of these view factors has a front and a rear component. Moreover, their values can vary significantly based on whether the diffusive surfaces are shaded or exposed to direct sunlight.

A similar reasoning holds when the solar radiation on the ground is computed. The diffuse radiation reaching the ground is reduced because the area beneath the PV panels has a limited view of the sky-dome.

In our computation, we do not consider reflection from adjacent PV panels (i.e in the same row), from the supporting system and neither from nearby objects that there could be in the proximity of the PV field. Finally, we underline that we consider the values of the view factor equal for every row and not varying with the distance along the collector width.

For the view factors calculation, we make use of the open-access library PVlib (Holmgren et al., 2018).

### C.1. Solar radiation on the ground

To determine the view factor to the sky from the ground beneath the rows, we follow the methodology outlined in Marion et al. (2017). This factor considers the obstruction of the sky caused by the assumed infinitely long array rows. Acknowledging that increased distance reduces the blocking effect, we limit the calculation to 10 rows on each side of the focal row,<fnref n="8" /> resulting in a 2D geometry analysis. Assuming flat and level ground and isotropic radiation, the row-to-row (rtr) spacing is divided into n segments (100), each defined by their position x relative to the row centre (positive x indicating rightward, negative x indicating leftward). Each segment is associated with a pair of angles $\psi_i$ that delimit its view of the sky, as depicted in Fig. C.1. The fraction of the sky dome visible from each ground segment is calculated as:

$$V_{ns} = \frac{1}{2}(\cos \psi_1 - \cos \psi_2) \qquad (C.1)$$

To obtain the view factor across the length between adjacent rows, $V_{rtr,s}$, we integrate $V_{ns}$ over the entire row-to-row distance.

### C.2. Solar radiation on the PV panels

As mentioned at the beginning of this section, to calculate solar radiation on tilted bifacial panels, multiple view factor components are necessary. Following the methodology outlined in Mikofski et al.

(2019), the following view factor contributions are considered for each panel side:

- View factors from the panel to the sky for shaded ($V_{SH}^{sky}$) and unshaded ($V_{L}^{sky}$) areas of the PV panels.

- View factors from the panel to the ground for shaded ($V_{SH}^{ground}$) and unshaded ($V_{L}^{ground}$) PV panels areas.

- $V_{rtr,s}$ as defined in the preceding sub-section, which constrains the reflected radiation from the ground.

Similar to a ground point, each spot on the panel surface has a limited view of the sky, due to the presence of the front row. As depicted in Fig. C.2, this view is delimited by two angles, $\psi_{top}$ and $\psi_{bottom}$, defined accordingly to equations (12) and (13) in Mikofski et al. (2019). The view factors are defined as follows:

$$V_{SH}^{sky} = \frac{V_{SH}^{sky}(x_{SH}) + V_{SH}^{sky}(a_{SH} = 0)}{2} \qquad (C.2)$$

$$V_{L}^{sky} = \frac{V_{L}^{sky}(x_{SH}) + 1}{2} \qquad (C.3)$$

$$V_{SH}^{ground} = \frac{V_{SH}^{ground}(x_{SH}) + 1}{2} \qquad (C.4)$$

$$V_{L}^{ground} = \frac{V_{L}^{ground}(x_{SH}) + V_{L}^{ground}(a_{SH} = 1)}{2} \qquad (C.5)$$

Here, $a_{SH}$ represents the fraction of the panel shaded by the front row, defined as $a_{SH} = 1 - \frac{1}{\text{GCR}(\cos \beta\alpha + \sin \beta \tan \phi)}$, and $x_{SH}$ denotes the point on the panel separating light from shadow. Eqs. (C.2)–(C.5) compute the view factors using equations (10) and (11) from Mikofski et al. (2019), determining view factors for each row point x by using the angles $\psi_{top}$ and $\psi_{bottom}$ and integrating over shaded/unshaded sections. The cumulative view factors to the sky $V_{sky}^{front}$ and ground $V_{ground}^{front}$ are then computed by summing shaded/unshaded components multiplied by $a_{SH}$ and $(1 - a_{SH})$.

$$V_{front}^{sky} = a_{SH} * V_{SH}^{sky} + (1 - a_{SH}) * V_{L}^{sky} \qquad (C.6)$$

$$V_{front}^{ground} = a_{SH} * V_{SH}^{ground} + (1 - a_{SH}) * V_{L}^{ground} \qquad (C.7)$$

To compute the values for the rear side, $V_{rear}^{sky}$ and $V_{rear}^{ground}$, the procedure is repeated using the complementary angle of $\beta$.

## Appendix D. ORCHIDEE forcings

As requested by ORCHIDEE, the atmospheric variables in the forcing files must meet specific constraints. Therefore, we made the following modifications.

<footnote n="8">⁸ Adding more rows results in changes of the order of 0.001%, which are negligible.</footnote>
<figure><img src="image_18.png" /><figcaption>Fig. C.2. 2D view of two PV rows, highlighting the angles necessary to determine the PV surface view factors.</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>Fig. F.1. Histogram distribution of yearly C4 NPP for the control and ST configuration across the three years analysed in our study. For each distribution, the vertical dashed line represents the mean value, while the solid line indicates the median value.</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>Fig. F.2. Spatial distribution of yearly control NPP for the climatological year over the Iberian Peninsula, for C3 (panel a) and C4 (panel b). The blue contour delineates the Atlantic area in the Iberian Peninsula.</figcaption></figure>

<figure><img src="image_21.png" /><figcaption>Fig. F.3. GPP/R<sub>a</sub> annual evolution averaged over two selected areas (low and high crop NPP), across various configurations, for the Iberian Peninsula, for dry and wet year. The shaded area represents the 95% confidence interval obtained using the bootstrap method.</figcaption></figure>
<figure><img src="image_22.png" /><figcaption>Fig. F.4. Annual average NPP [gC m⁻² y⁻¹] for the Iberian Peninsula (panel a: C3, panel b: C4) and the Netherlands (panel c: C3, panel d: C4), over the period 2006-2020, for each configuration analysed.</figcaption></figure>

- Surface incident shortwave radiation $SW_{down}$ [W m⁻²]. In the ERA5-Land data-set we have the surface solar radiation down- wards, S [J m⁻²], which represents the total amount of solar radiation stored from the beginning of the forecast time to the end of the forecast step. To convert from J m⁻² to W m⁻² the accumulated values must be divided by the accumulation time expressed in seconds. In this case, since we have hourly time-steps, we make the following conversion:

$$SW_{down} = \begin{cases} \frac{S_h}{3600} & \text{if } h = 01 \text{ UTC} \\ \frac{S_h - S_{h-1}}{3600} & \text{otherwise} \end{cases} \qquad (D.1)$$

where 3600 are the number of seconds in one hour, and $S_h$ and $S_{h-1}$ are the values of S at hour h and h − 1, respectively.

- Surface incident longwave radiation, $LW_{down}$ [W m⁻²]. We make the same conversion as above.

- Module of the wind speed at 10 m, U [m s⁻¹]. To obtain the module of the horizontal wind speed at 10 m we combine the u-component of wind with the v-component:

$$U = \sqrt{u^2 + v^2} \qquad (D.2)$$

- Near surface air specific humidity, Q. We compute Q starting from P, T and the dewpoint temperature $T_d$ (Weedon et al., 2014).

- Rainfall rate, $Rain_f$ [kg m⁻² s⁻¹]. The ERA5-Land data-set provides the total precipitation $TP$ [m]. First, to obtain the precipitation rate in kg m⁻² s⁻¹ we do the following conversion:

$$TP[\text{kg m}^{-2}\text{s}^{-1}] = \begin{cases} \frac{TP \cdot 1000}{3600} & \text{if } h = 01 \text{ UTC} \\ \frac{(TP_h - TP_{h-1}) \cdot 1000}{3600} & \text{otherwise} \end{cases} \qquad (D.3)$$

Then, we calculate the rainfall rate to be equivalent to the precipitation rate when T exceeds zero, and zero otherwise.

- Snowfall rate, $Snow_f$ [kg m⁻² s⁻¹]. We calculate the rainfall rate to be equivalent to the precipitation rate when T is less than or equal to zero, and zero otherwise.

## Appendix E. PV power

The PV power, $PV_{pow}$ [W], produced by a PV module is calculated as described by Mavromatakis et al. (2010), Pérez et al. (2019). It is defined by the equation:

$$PV_{pow} = P_{nom} * P_{R} * I_{N} \qquad (E.1)$$
where $P_{nom}$ denotes the nominal power of the PV module, which is set to 550 W. To obtain $PV_{nom}$ over a specific time period, i.e. the energy produced, we integrate Eq. (E.1) over the related time-steps. $I_N$ denotes the total solar radiation incident on the panel normalized by its value under standard test conditions (1000 W m⁻²), while $P_R$ is the so-called performance ratio of the PV cell, i.e. the ratio between the real power output and the theoretical one, a dimensionless parameter that takes into account the thermal losses, computed as

$$P_R = 1 - 0.005(T_c - T_N) \qquad (E.2)$$

with $T_c$ the cell temperature and $T_N$ the reference temperature for the cell, equal to 25°C. To evaluate $T_c$, the dependence on the solar radiation and the wind speed is taken into account:

$$T_c = a_1 + a_2 T + a_3 S + a_4 V \qquad (E.3)$$

The values of the parameters are fixed as $a_1 = 4.3$ °C, $a_2 = 0.943$, $a_3 = 0.028$ m² W⁻¹°C and $a_4 = -1.528$ s m⁻¹ °C.

In our analysis, we focus on the annual PV power per grid point. Assuming each grid point fully covered by PV panels, $P_{nom}$ in Eq. (E.1) is multiplied by the total number of PV panels per grid point.

## Appendix F. Supplementary figures

See Figs. F.1–F.4.

## Data availability

The data that support the findings of this study are openly available. ERA5 is the latest climate reanalysis being produced by ECMWF as part of implementing the EU-funded Copernicus Climate Change Service (C3S), providing hourly data on atmospheric, land-surface and sea-state parameters together with estimates of uncertainty from 1979 to present day. ERA5-Land data are available on the C3S Climate Data Store on regular latitude-longitude grids at 0.11° × 0.11° resolution. https://cds.climate.copernicus.eu/#!/home.

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