Crop Yield Responses to Reduced Solar Radiation in Agrivoltaic Systems: Crop-Specific Patterns and Shading Thresholds

Abstract

Crop yield responses to reduced solar radiation are central to the design of agrivoltaic systems, yet crop-specific patterns and critical shading thresholds remain insufficiently characterized across diverse environments. This study evaluates yield responses across a global dataset of 546 observations from 66 studies, including agrivoltaic, shading, and agroforestry systems. Relative yield was analyzed in relation to reduction in solar radiation (RSR), crop type, and environmental variables using exploratory analysis, multiple linear regression, and tree-based ensemble models. Crop responses varied systematically across crop types. Fruits, berries, and fruity vegetables maintained or increased yield under lower shading levels, while forages, leafy vegetables, cereals, and tubers showed gradual declines, and maize and grain legumes exhibited the strongest sensitivity. Across models, yield responses were non-linear, with relatively stable yields at lower shading levels followed by accelerated declines beyond approximately 50–60% RSR. Climatic conditions further influenced these patterns, with crops in higher-radiation and warmer environments maintaining yields more effectively under partial shade. These findings demonstrate that crop yield responses depend on crop type, shading intensity, and environmental context, providing an agronomic basis for crop selection and agrivoltaic system design.

1. Introduction

Crop productivity is fundamentally governed by the availability of solar radiation, which drives photosynthesis and biomass accumulation. Variations in light intensity influence key physiological processes, including stomatal conductance, carbon assimilation, and resource allocation within the plant [1,2]. Experimental studies across major crops have shown that reduced radiation can alter plant morphology, decrease photosynthetic efficiency, and ultimately affect grain or biomass yield [3,4]. However, the relationship between light availability and yield is not strictly linear. Moderate reductions in radiation may be partially compensated by physiological and structural adjustments, while more severe or prolonged shading can lead to substantial declines in productivity [4]. These findings highlight the importance of understanding how crops respond to varying levels of shade under different environmental conditions.

Shading effects have been widely studied in agroforestry and intercropping systems, where competition for light between plant species can influence crop performance. Research on maize, wheat, and soybean systems has demonstrated that light interception, canopy structure, and spatial arrangement play critical roles in determining yield outcomes under shaded conditions [3,5,6]. While these systems differ from agrivoltaic configurations, they provide important insights into how reduced radiation influences crop growth and resource use efficiency. Such studies establish that crop responses to shading are highly context-dependent, varying with species, developmental stage, and environmental factors [1,2,3,4].

Agrivoltaic systems extend this concept of modified light environments by integrating agricultural production with photovoltaic (PV) energy generation on the same land area [7]. In these systems, solar panels create structured patterns of partial shading that alter microclimatic conditions, including light distribution, temperature, and soil moisture [8,9]. Beyond improving land-use efficiency, agrivoltaics has been shown to influence both agricultural and energy outcomes. Field studies have demonstrated that the presence of PV panels can reduce plant water stress, moderate extreme temperatures, and improve water-use efficiency, particularly in arid and semi-arid environments [10]. These microclimatic modifications position agrivoltaic systems as a promising approach for enhancing the resilience of food and energy systems under changing climatic conditions.

Crop responses to agrivoltaic shading remain highly variable and depend on both environmental conditions and crop characteristics. Experimental studies have reported that some crops, particularly those sensitive to heat and water stress, can maintain or even increase productivity under partial shading, while others experience yield reductions due to insufficient light availability. For example, lettuce grown under PV panels has been shown to maintain productivity through adjustments in radiation use efficiency under partial shade [11]. Similarly, tomatoes and other heat-sensitive crops have been observed to exhibit increased productivity and delayed senescence under moderated radiation conditions [12]. In contrast, light-demanding or fast-growing species may experience yield reductions under reduced radiation, although produce quality may improve in some cases due to reduced sunscald and more favorable microclimatic conditions [9]. These findings indicate that shading in agrivoltaic systems does not have a uniform effect on agricultural productivity, but instead produces a range of outcomes that are strongly crop-specific.

In addition to crop production, agrivoltaic systems can support other agricultural and ecological functions. Grazing systems beneath solar panels have been implemented to reduce vegetation management costs while providing shade that improves animal welfare [13,14]. Agrivoltaic sites may also support biodiversity and ecosystem services, including pollinator habitats that benefit agricultural landscapes [15]. While these applications demonstrate the multifunctional potential of agrivoltaic systems, understanding crop yield response to shading remains central to optimizing system design for agricultural production.

The role of shade is therefore central to agrivoltaic system design, directly influencing both agricultural productivity and energy generation. While moderate shading may benefit certain shade-tolerant crops, higher levels of radiation reduction can lead to substantial yield declines [16]. Despite its importance, current understanding of shade effects remains incomplete. While the meta-analysis by Laub et al. (2022) [16] provides a comprehensive synthesis of crop yield responses to shading, it primarily draws on intercropping and artificial shading experiments, with relatively limited representation of agrivoltaic field systems. Moreover, the aggregation of crop types and experimental conditions can mask variability in crop-specific responses, and the analysis does not explicitly capture interactions between shading and environmental factors such as climate and water availability. In addition, more recent agrivoltaic studies, including those published after 2022, are not comprehensively integrated into existing syntheses. These limitations constrain the ability to derive crop-specific and context-dependent insights needed for optimizing agrivoltaic system design.

This study addresses this gap by analyzing crop yield responses to reduced solar radiation across a global dataset integrating agrivoltaic, artificial shading, and agroforestry systems. This study builds on and extends previous datasets by incorporating additional agrivoltaic field observations, including studies and data published after 2022 and up to October 2024, and integrating diverse experimental systems into a unified analytical framework. We hypothesize that crop yield responses to shading follow consistent, crop-specific patterns characterized by nonlinear responses and identifiable threshold behavior across environmental conditions. Specifically, this study quantifies crop yield responses as a function of reduction in solar radiation (RSR), crop type, and climatic conditions, enabling the identification of crop-specific response functions and critical thresholds in yield decline. In particular, we aim to characterize how yield responses vary across crop groups and environmental contexts, and to identify threshold ranges of RSR beyond which yield reductions become pronounced. The findings provide an agronomic basis for crop selection and system design, supporting more effective and context-specific deployment of agrivoltaic systems.

2. Materials and Methods

2.1. Dataset

The dataset used in this study is mainly adopted from the meta-analysis by Laub et al., “Contrasting yield responses at varying levels of shade suggest different suitability of crops for dual land-use systems” [16]. This meta-analysis provides a comprehensive collection of crop yield responses under varying levels of shade and serves as a strong foundation for evaluating shade–yield relationships in agrivoltaic systems [17].

The original dataset compiled observations from peer-reviewed studies that examined crop yields under controlled shading conditions, with inclusion criteria based on crop type, shading levels, and climatic context. To extend the dataset with a specific focus on agrivoltaic systems, additional data were collected from field-based agrivoltaic experiments.

Additional data were obtained from the National Renewable Energy Laboratory (NREL) InSPIRE Agrivoltaics Data Portal [18]. The portal was filtered to include only field experiments and exclude modeled studies. Studies published between April 2022 and October 2024 were screened, resulting in 114 candidate studies. Inclusion criteria similar to those used by Laub et al. were applied, with the exception that studies from all climatic regions were considered. Data from selected studies were extracted from text, tables, and figures. When numerical values were not explicitly reported, data were digitized from figures using WebPlotDigitizer (version 5.2) [19]. This process yielded an additional 95 observations from eight agrivoltaic studies.

To ensure consistency with the original meta-analysis, crop yields were standardized by defining the unshaded control as 100% yield [17]. This standardization resulted in the response variable “relative yield under shading,” which enables direct comparison across studies. Crops were categorized into the nine crop types defined by Laub et al.’s work: berries, fruits, fruity vegetables, leafy vegetables, C₃ cereals, maize, tubers/root crops, grain legumes, and forages (including grasses, forage legumes, and multispecies forage stands).

The final dataset includes 66 studies representing 52 crop species, with a total of 546 observations (395 excluding unshaded controls). Among these, 142 observations correspond to shading from solar panels, allowing for direct analysis of agrivoltaic systems.

Additional environmental and contextual variables were incorporated to account for climatic and site-specific conditions influencing crop performance. These include plant hardiness zone, average temperature, and average daily rainfall. Plant hardiness zones were assigned based on the United States Department of Agriculture (USDA) classifications of average extreme minimum temperatures. When studies reported temperature and rainfall during the experimental period, those values were used directly. If such data were not provided but the study period was specified, temperature and rainfall were estimated using the Open-Meteo Historical Weather API [20]. Observations lacking sufficient temporal or geographic information were retained, with missing values recorded as NA.

A shade measurement variable was included to account for differences in how shading was quantified across studies. Some experiments reported reductions in photosynthetically active radiation (PAR) or total solar radiation, while others reported percentage shade without specifying measurement methods. Additional geographic variables, including city, region, and country, were also incorporated to provide spatial context.

A complete list of studies included in the dataset is provided in Appendix A (

Table A1. Studies included in the agrivoltaic crop yield dataset, grouped by experimental system.

Reference	Crop/System	Study Type
Agrivoltaic Systems
[11]	Lettuce	Agrivoltaic field study
[21]	Lettuce	Agrivoltaic modeling + field
[22]	Mixed crops	Mobile PV system
[23]	Cropland	Semi-transparent PV
[24]	Maize	AVS field experiment
[25]	Tomato	AVS field study
[26]	Multiple crops	AVS cultivation study
[27]	Soybean	AVS modeling study
[28]	Broccoli	AVS field study
[29]	Multiple crops	AVS comparison study
[30]	Cropland	AVS system design
[31]	Ginger, kale	AVS thesis study
Artificial Shading Experiments
[32]	Maize	Artificial shading
[33]	Potato	Artificial shading
[1]	Soybean	Controlled light study
[2]	Maize	Isotope tracer shading
[4]	Wheat	Long-term shading
[34]	Wheat	Shading experiment
[35]	Maize	Density + shading
[36]	Wheat	Radiation reduction
[37]	Soybean	Shade + irrigation
[38]	Soybean	Light manipulation
[39]	Maize	Light intensity study
[40]	Squash	Light + moisture
[41]	Soybean	Radiation deficit
[42]	Bean	Shade levels
[43]	Chickpea	Light + water stress
Agroforestry and Intercropping Systems
[44]	Forages	Agroforestry shading
[45]	Forages	Agroforestry study
[46]	Legumes	Shade response
[47]	Wheat	Alley cropping
[48]	Apple + crops	Intercropping system
[49]	Alfalfa	Agroforestry system
[50]	Forages	Shade comparison
[6]	Corn, soybean	Tree competition
[51]	Wheat	Agroforestry system
[52]	Crops	Tree-based system
[53]	Agroforestry crops	System design
[54]	Soybean, maize	Intercropping
[55]	Wheat	Tree age effects
[56]	Forage	Alley cropping
[57]	Cereals	Agroforestry competition
[5]	Maize	Tree shading
[58]	Wheat, lupin	Windbreak shading
Horticultural and Shade Net Studies
[59]	Apple	Anti-hail net shading
[60]	Blueberry	Colored nets
[61]	Pepper	Shade study
[62]	Blackberry	Shade nets
[63]	Blackberry	Canopy shading
[64]	Apple	Net shading
[65]	Sugar beet	Dynamic shade
[66]	Clover	Shade adaptation
[67]	Pepper	Shade levels
[68]	Apple	Shade + water stress
[69]	Apple	Net protection
[70]	Grass-clover	Shade material
[71]	Citrus	Heat + shade
[72]	Lemon	Shade screen
[73]	Strawberry	Light effects
[74]	Blackcurrant	Net shading
[75]	Forage mix	Shade treatments
[76]	Grapevine	Light + temperature

).

Crop yield was treated as the response variable and is expressed as a percentage relative to the unshaded control. This standardized measure, referred to as relative yield under shading, enables comparison of yield responses across studies with differing baseline conditions.

The dataset includes a range of explanatory variables describing crop characteristics, shading conditions, environmental factors, and experimental context. Crop identity is represented both at the species level (52 crops) and through aggregation into nine crop types: berries, fruits, fruity vegetables, leafy vegetables, C₃ cereals, maize, tubers/root crops, grain legumes, and forages.

Shading was primarily quantified using RSR, expressed as the percentage reduction in incoming radiation relative to unshaded conditions. Due to variation in reporting across studies, a shade measurement variable was included to distinguish between measurements based on PAR, direct percentage reduction in RSR, or reported shade levels without specified methodology. In addition, shade types were categorized into six groups: solar panel, cloth, nets, nets combined with cloth, intercropping systems, and not specified.

Environmental variables were incorporated to account for climatic influences on crop performance. These include average temperature (°C) during the experimental period and average daily rainfall (mm day⁻¹). Global horizontal irradiance (GHI), measured in kWh m⁻², was included as an indicator of total incoming solar radiation. Climate zone was classified using the Köppen–Geiger system, and plant hardiness zone was assigned based on USDA classifications of average extreme minimum temperature.

Experimental context was further described using experiment type, which distinguishes between artificial shading and intercropping systems. Geographic variables, including city, region, and country, were also included to capture spatial variation in environmental conditions.

A summary of classification systems, including climate zone and plant hardiness zone codes, is provided in Appendix B.

2.2. Data Preparation

The dataset was refined to ensure consistency, comparability, and suitability for analysis across studies with differing reporting standards. The climate zone variable, originally recorded as broad categories such as “temperate” and “subtropical”, was reclassified using the Köppen–Geiger climate classification system to provide a more detailed representation of climatic conditions. This system includes five primary climate groups (A, B, C, D, and E), with additional highland classifications included where applicable, further subdivided based on precipitation patterns (f: fully humid, s: dry summer, w: dry winter, m: monsoon) and temperature regimes (a, b, c, d).

Data preprocessing steps were applied to improve clarity and analytical compatibility. Variables not relevant to the analysis were removed, and variable names were standardized to ensure consistency across the dataset and compatibility with statistical software. For the shade type variable, entries recorded as “.” in the original dataset indicated that the corresponding studies did not specify the shading method. To retain these observations, such entries were recoded as “Intercropping” for intercropping experiments and “Not Specified” for artificial shading experiments, rather than being treated as missing values.

Missing environmental data were addressed to enable inclusion of all observations in the modeling framework. Specifically, missing values for temperature and rainfall were imputed using location-specific historical averages obtained from publicly available climate databases (Open-Meteo [20]), corresponding to the study location and typical crop growing period. Imputation was applied only where environmental data were unavailable from source studies. This approach allowed for the incorporation of environmental variability while maintaining a consistent dataset for analysis.

2.3. Analytical Framework

This study combines exploratory data analysis, multiple linear regression, and tree-based ensemble models to examine the effects of shading on crop yield. These approaches were used in a complementary manner to identify, quantify, and validate relationships between yield, shading intensity, and environmental variables.

Exploratory data analysis was first conducted to identify patterns, trends, and potential relationships between variables, and to inform model specification. Crop yield, expressed as relative yield compared to an unshaded control, was treated as the response variable. Predictor variables included RSR, crop type, climatic zone, plant hardiness zone, temperature, rainfall, and other environmental and experimental factors.

Multiple linear regression (MLR) was used to estimate the effects of shading and associated variables on crop yield while controlling for confounding factors. The exploratory analysis informed model specification, including the inclusion of a quadratic temperature term to capture non-linear relationships and interaction terms between RSR and crop type to account for crop-specific responses.

Model selection was performed using stepwise regression based on the Akaike Information Criterion (AIC), with comparison to models selected using the Bayesian Information Criterion (BIC) to evaluate model parsimony. The final model was chosen to balance explanatory power and interpretability, retaining the primary agronomic drivers identified in the exploratory analysis. Climatic variables were evaluated separately due to their importance, and climate zone was included in the final specification based on its contribution to model fit. The final model includes RSR, crop type, climate zone, and the interaction between RSR and crop type.

To improve model assumptions, a square root transformation of yield was applied. Diagnostic plots, including residuals versus fitted values and Q–Q plots, indicated improved normality and reduced heteroscedasticity following transformation, and the final model was fitted using the transformed response variable.

Tree-based ensemble models, including Random Forest, Histogram Gradient Boosting (HGB), and Extreme Gradient Boosting (XGBoost), were applied to capture nonlinear relationships and interactions that may not be fully represented in the regression framework. These models were used to assess the relative importance of predictors and to evaluate the consistency of observed patterns across modeling approaches.

The dataset was randomly partitioned into training and test sets using an 80:20 split to evaluate out-of-sample predictive performance. Model accuracy was quantified using the coefficient of determination ($R^2$), root mean square error (RMSE), and mean absolute error (MAE). For ensemble models, five-fold cross-validation was additionally performed on the training data to assess model stability and reduce the risk of overfitting. These evaluation procedures ensure that model results reflect generalizable relationships rather than dataset-specific patterns.

3. Results

3.1. Dataset Characteristics

The dataset comprises observations of crop yield responses to varying levels of RSR across a wide range of experimental conditions and environmental settings. A complete list of all studies included in the dataset is provided in Appendix A (Table A1). Five numerical variables were considered: relative yield, RSR, average temperature, average daily rainfall, and GHI.

The mean relative yield across all observations was 85.65% (±31.86), with values ranging from 4% to 292%. RSR had a mean of 29.06% (±25.89), spanning a range from 0% to 94%. Average temperature during the growing period was 19.10 °C (±5.45), with values between 5.3 °C and 29.8 °C. Average daily rainfall had a mean of 2.8 mm (±2.29), ranging from 0.03 mm to 12.15 mm. GHI averaged 1527.1 kWh/m² (±231.36), with a range of 868.3 to 2137 kWh/m².

The dataset includes nine crop types, with forages representing the largest proportion of observations (21.43%), followed by grain legumes (19.60%), maize (12.27%), and leafy vegetables (10.44%). Fruity vegetables were the least represented crop type (4.21%).

Experimental conditions were primarily based on artificial shading (76.92% of observations), with the remaining observations derived from intercropping systems (23.08%). A broad range of climatic conditions was represented, with Mediterranean (Csa) climates accounting for the largest share of observations (19.05%), followed by humid subtropical (Cfa and Cwa) and humid continental (Dwa) climates. Plant hardiness zone 6b was the most common, representing 19.05% of observations (see Appendix B for classification details).

Shade type varied across studies, with 33.18% of observations reported as not specified. Among identified categories, cloth (28.5%), nets (25.23%), and solar panels (10.75%) were the most common. Shade measurements were most frequently reported as PAR (38.43%) or general shade percentage (37.84%), while 23.73% of observations explicitly reported RSR.

Overall, the dataset captures substantial variability in crop type, climatic conditions, and shading intensity, providing a strong basis for examining crop yield responses to reduced solar radiation across different agronomic systems.

3.2. General Yield Response to Shading

Yield responses to reductions in solar radiation were compared across different shade types and experimental systems to assess whether observed patterns depend on how shading is implemented.

Yield loss per unit RSR shows similar distributions across shade types (Figure 1). The relationship between relative yield and RSR also follows comparable patterns across shading approaches (Figure 2). Minor variation is observed for combined net and cloth systems, though the overall response remains consistent across shading methods.

A one-way ANOVA indicated statistically significant differences in yield loss per unit RSR among shade types ($F=5.92$, $p<0.001$). Post hoc comparisons using Tukey’s HSD test showed that these differences were limited to specific pairwise contrasts, primarily involving the “not specified” category, which differed significantly from cloth- and net-based systems. In contrast, most other pairwise comparisons were not statistically significant, indicating substantial overlap in yield response across shading methods. These results suggest that while shading type contributes to variation in yield response, the overall patterns remain broadly comparable across most shading approaches. The distinct behavior of the “not specified” category may reflect variability in reporting methods across studies.

A similar comparison across experimental systems shows consistent patterns (see Appendix C Figure A3). Yield loss distributions and yield–RSR relationships are comparable between artificial shading and intercropping experiments, although yield declines tend to be slightly more pronounced in intercropping systems, where competition for light may intensify the effects of reduced radiation.

Overall, these findings indicate that crop yield responses are primarily associated with the level of RSR rather than the specific shading method or experimental design. This supports combining observations from different study systems when evaluating yield responses under agrivoltaic conditions.

3.3. Crop-Specific Yield Responses to Shading

Crop yield responses to RSR vary substantially across crop types. Differences in yield loss per unit RSR are shown in Figure 3.

Fruits, fruity vegetables, and berries exhibit, on average, neutral to positive responses under low to moderate RSR, indicating that these crops can benefit from partial shading. In contrast, maize and grain legumes show the largest yield declines, indicating strong sensitivity to reduced radiation. Forages, leafy vegetables, C3 cereals, and tubers/root crops show intermediate responses, with more gradual reductions in yield.

The variability in response also differs across crop types. Fruity vegetables and maize show a wide range of outcomes, indicating that responses depend on environmental conditions and management practices. Leafy vegetables, in contrast, show relatively consistent responses across observations.

The relationship between yield and RSR further highlights distinct response patterns (Figure 4). Fruits, berries, and fruity vegetables show stable or slightly increasing yield under low to moderate shading, followed by declines at higher levels of radiation reduction. This pattern suggests that moderate shading may reduce environmental stress before light limitation becomes dominant.

In contrast, C3 cereals, grain legumes, maize, and tubers/root crops show immediate declines in yield with increasing shading. Among these, maize and grain legumes exhibit the steepest declines, indicating strong dependence on high radiation levels. Forages and leafy vegetables show more gradual declines, consistent with greater tolerance to reduced light availability.

Based on these patterns, crop types can be grouped into three general response categories (Figure 3). Fruits, fruity vegetables, and berries fall into a shade-benefiting group. Forages, leafy vegetables, C3 cereals, and tubers/root crops form a shade-tolerant group. Maize and grain legumes represent a shade-sensitive group, with rapid declines in yield as radiation decreases.

These results show that crop yield responses to RSR differ systematically across crop types, with consistent patterns observed within each group.

3.4. Influence of Climatic Conditions on Yield Response

Climatic conditions further shape how crops respond to RSR. Yield loss per unit RSR was evaluated across climate zones and plant hardiness zones for each crop type (see Appendix C Figure A1 and Figure A2).

Differences in yield response across climate zones show that the effect of shading varies with environmental conditions. For several crop types, the magnitude of yield loss per unit RSR differs across climate classifications. Crops grown in warmer and higher-radiation environments tend to maintain more stable yields under moderate shading, whereas crops in cooler or lower-radiation environments show greater sensitivity to reduced radiation.

Patterns across plant hardiness zones show a similar trend. Crops in regions with milder winters and longer growing seasons generally exhibit more gradual yield declines with increasing shading, while those in more temperature-limited environments tend to show steeper reductions.

Although the magnitude of these differences varies among crop types, the overall pattern indicates that climatic conditions interact with radiation reduction to shape yield responses. These results show that crop response to shading is influenced not only by the level of radiation reduction, but also by background environmental conditions such as temperature and baseline irradiance.

Taken together, these findings indicate that crop performance under reduced radiation depends on both crop type and climatic context, highlighting the importance of considering local conditions when evaluating agrivoltaic systems.

Synthesis of Exploratory Findings

The exploratory analysis highlights several consistent patterns in crop yield responses to RSR under agrivoltaic conditions.

Crop types show clear differences in their response to shading. Fruits, fruity vegetables, and berries tend to maintain or increase yield under low to moderate shading. Forages, leafy vegetables, C3 cereals, and tubers/root crops show moderate declines, while maize and grain legumes exhibit the largest reductions as shading increases. These patterns correspond to three general response groups: shade-benefiting, shade-tolerant, and shade-sensitive crops.

Yield responses are also non-linear. Across crop types, moderate levels of shading are often associated with relatively stable yields, whereas higher levels of radiation reduction lead to sharper declines. This indicates that yield responses change with the level of shading rather than following a simple linear trend.

Climatic conditions further influence these responses. Differences across climate zones and plant hardiness zones show that temperature and baseline radiation affect how crops respond to shading. Crops grown in warmer or higher-radiation environments tend to maintain yields more effectively under moderate shading, while those in cooler or lower-radiation environments show greater sensitivity.

Variability in yield response also differs across crop types. Maize and fruity vegetables show a wide range of outcomes, while leafy vegetables display more consistent responses. This suggests differences in how crops adjust to shaded conditions.

Overall, these findings show that crop yield responses depend on crop type, the level of radiation reduction, and climatic conditions. These patterns provide the basis for the modeling approaches presented in the following sections, where these relationships are examined quantitatively.

3.5. Multiple Linear Regression Model

The MLR model was used to quantify the relationships identified in the exploratory analysis. The model explains approximately 58% of the variance in square-rooted yield ($R^2=0.5836$, adjusted $R^2=0.5585$), indicating a moderate level of explanatory power across different crops and environmental conditions. Model coefficients, standard errors, and confidence intervals are presented in

Table 1. Estimates, standard errors, p-values, and 95% confidence intervals for each variable in the MLR model. The intercept represents the expected $\sqrt{\mathrm{Yield}}$ when RSR is 0, the crop type is the reference category, and the climate zone is the reference category.

Variable	Coefficient	Std. Error	p-Value	95% Confidence Interval
Intercept	10.029	0.837	<0.001	(8.386, 11.673)
RSR	0.008	0.012	0.505182	(−0.015, 0.031)
Crop Type (C3 cereals)	0.426	0.577	0.460817	(−0.708, 1.560)
Crop Type (Forages)	0.353	0.571	0.536542	(−0.768, 1.474)
Crop Type (Fruits)	0.407	0.577	0.481059	(−0.727, 1.541)
Crop Type (Fruity vegetables)	1.253	0.688	0.069209	(−0.099, 2.606)
Crop Type (Grain legumes)	0.235	0.566	0.678409	(−0.878, 1.347)
Crop Type (Leafy vegetables)	−0.201	0.612	0.732297	(−1.412, 0.993)
Crop Type (Maize)	0.310	0.588	0.598447	(−0.845, 1.464)
Crop Type (Tubers/root crops)	0.330	0.644	0.608399	(−0.935, 1.595)
Climate Zone (BSh)	−0.750	0.768	0.329250	(−2.258, 0.758)
Climate Zone (BSk)	0.309	0.674	0.647076	(−1.016, 1.634)
Climate Zone (BWh)	−0.048	0.743	0.948901	(−1.507, 1.411)
Climate Zone (BWk)	0.051	0.788	0.948586	(−1.498, 1.600)
Climate Zone (Cfa)	−0.369	0.670	0.581729	(−1.686, 0.947)
Climate Zone (Cfb)	−0.284	0.692	0.682171	(−1.644, 1.076)
Climate Zone (Csa)	−0.183	0.681	0.788516	(−1.521, 1.155)
Climate Zone (Csb)	0.785	0.770	0.308902	(−0.729, 2.298)
Climate Zone (Cwa)	−0.106	0.667	0.873610	(−1.417, 1.205)
Climate Zone (Cwb)	−0.716	0.884	0.418647	(−2.453, 1.022)
Climate Zone (Dfa)	1.028	0.702	0.143534	(−0.351, 2.406)
Climate Zone (Dfb)	−0.397	0.679	0.558775	(−1.731, 0.937)
Climate Zone (Dwa)	−0.575	0.677	0.396372	(−1.905, 0.755)
Climate Zone (Dwb)	−0.848	0.745	0.255520	(−2.313, 0.616)
RSR × Crop Type (C3 cereals)	−0.055	0.015	<0.001	(−0.085, −0.025)
RSR × Crop Type (Forages)	−0.045	0.012	<0.001	(−0.070, −0.021)
RSR × Crop Type (Fruits)	0.006	0.015	0.699174	(−0.024, 0.036)
RSR × Crop Type (Fruity vegetables)	−0.052	0.014	<0.001	(−0.080, −0.024)
RSR × Crop Type (Grain legumes)	−0.084	0.013	<0.001	(−0.110, −0.058)
RSR × Crop Type (Leafy vegetables)	−0.023	0.014	0.099085	(−0.050, 0.004)
RSR × Crop Type (Maize)	−0.083	0.013	<0.001	(−0.109, −0.057)
RSR × Crop Type (Tubers/root crops)	−0.059	0.017	<0.001	(−0.093, −0.026)

.

The lack of a statistically significant main effect for RSR indicates that a single uniform relationship between shading and yield is not supported across all crops. Instead, the significant interaction terms between RSR and crop type indicate that the effect of shading varies systematically by crop type.

Clear differences in shade sensitivity were observed across crop groups. Grain legumes and maize show the strongest negative interactions with RSR (p < 0.001), indicating that yield declines rapidly as shading increases. Tubers/root crops and C₃ cereals also show significant negative interactions, though with smaller magnitudes. These patterns indicate that these crops are particularly sensitive to reduced radiation.

In contrast, fruits show a positive interaction with RSR, although not statistically significant, suggesting that their yields are less negatively affected by shading compared to the reference group (berries). Leafy vegetables also show relatively stable responses, with non-significant interaction terms indicating a weaker dependence on shading intensity.

Forages and fruity vegetables show intermediate responses. Both exhibit significant negative interactions with RSR, indicating sensitivity to shading, but less pronounced than for maize and grain legumes. These patterns are consistent with the response groupings identified in the exploratory analysis.

Climate zone effects are smaller and not statistically significant at the 0.05 level. However, variation in coefficients and improved model fit with climate zone included suggest that environmental conditions contribute to differences in yield response, even if individual effects are not clearly separated within the dataset.

The consistency of interaction effects and their agreement with ensemble models reinforces the interpretation that crop-specific responses govern yield under reduced radiation.

Overall, the model demonstrates that crop yield responses to shading are primarily driven by crop-specific sensitivity rather than a uniform effect of reduced radiation. The presence of strong interaction effects highlights that agrivoltaic system performance depends on selecting crops with appropriate shade tolerance characteristics. Crops such as maize and grain legumes are more vulnerable to yield reductions under shading, while fruits and certain vegetable crops exhibit greater tolerance and may be more suitable for integration into agrivoltaic systems.

3.6. Tree-Based Ensemble Models

To complement the MLR analysis, three tree-based ensemble models—Random Forest, HGB, and XGBoost—were used to examine relationships between crop yield, shading, and environmental variables. Model performance on the held-out test set is summarized in

Table 2. Predictive performance of ensemble models on the test dataset. All models show similar performance, indicating consistent relationships between predictors and crop yield.

Model	Test ${\mathit{R}}^2$	RMSE	MAE
Random Forest	0.60	17.32	11.85
HGB	0.59	17.56	12.20
XGBoost	0.59	17.63	12.18

.

All three models achieved similar predictive performance, explaining approximately 55–60% of the variation in crop yield. This consistency suggests that the observed relationships are not dependent on a specific modeling approach. Cross-validation results further support this, with comparable performance across models (see Appendix D 

Table A4. Five-fold cross-validated $R^2$ values for the ensemble models. Comparable performance across models indicates that the observed yield–shade relationships are not dependent on a specific modeling approach.

Model	Cross-Validated ${\mathit{R}}^2$ (Mean ± SD)
Random Forest	$0.53\pm 0.16$
HGB	$0.54\pm 0.15$
XGBoost	$0.53\pm 0.20$

).

Across all models, RSR consistently emerged as the most influential predictor of yield. Climatic variables, including rainfall, GHI, and temperature, contributed to secondary variation, followed by crop type and climate zone (see Appendix D 

Table A5. Comparison of influential predictors identified across ensemble models. Despite differences in importance metrics, all models consistently identify RSR as the dominant driver of yield variation, followed by climatic variables and crop type.

Feature	Random Forest	HGB	XGBoost
	(Importance)	(Permutation)	(Gain)
RSR	0.420	highest	1450
Average daily rainfall	0.116	moderate	–
GHI	0.104	high	–
Average temperature	0.076	moderate	–
Crop type: Fruits	0.053	moderate	2910
Crop type: Grain legumes	0.020	lower	1765
Crop type: Maize	0.016	–	1320
Climate zone: Csb	0.029	lower	1650
Climate zone: Cfa	0.018	lower	–
Climate zone: Dwa	–	–	3120
Hardiness zone: 7b	0.035	lower	1780
Hardiness zone: 9a	0.012	lower	–

). Despite differences in how importance is measured, the same set of key variables was identified across models.

Partial dependence plots (PDPs) (Figure 5) show a clear nonlinear relationship between yield and RSR. Yield remains relatively stable under low to moderate shading, followed by a sharp decline beyond approximately 50–60% RSR. This threshold-like behavior is consistent across models and represents an important pattern for agrivoltaic system design. Although this pattern appears consistently, its magnitude and onset vary by crop type, as indicated by the significant interaction effects in the regression analysis, suggesting that while a general nonlinear response to shading exists, the sensitivity to radiation reduction differs across crops.

Climatic variables modify this relationship. Higher GHI is associated with improved yield outcomes under shading, indicating that crops in high-radiation environments are better able to maintain yield under partial shade. Threshold analysis based on the Random Forest prediction surface showed that the estimated RSR threshold increased by approximately 5.05 percentage points for every 100 kWh m⁻² increase in GHI ($R^2=0.846$), indicating that higher-radiation environments can tolerate greater reductions in solar radiation before yield declines become pronounced. This threshold is defined as the level of radiation reduction at which predicted yield declines by 10% relative to unshaded conditions. This relationship is further illustrated in Appendix D Figure A4.

Interactions between shading and temperature further highlight context-dependent responses. Under moderate shading (approximately 20–50% RSR), higher temperatures are associated with improved yield relative to cooler conditions. However, beyond the identified threshold (approximately 60% RSR), yield declines regardless of temperature, indicating that radiation availability becomes the limiting factor.

Overall, the ensemble models support three main findings. First, shading intensity is the primary driver of crop yield response. Second, crop type and environmental conditions influence how strongly yield responds to shading. Third, yield responses are nonlinear, with a clear threshold beyond which shading leads to substantial yield loss. These results provide quantitative support for selecting crops and designing agrivoltaic systems within appropriate shading ranges, recognizing that while general threshold behavior exists, the response varies across crop types.

4. Discussion

This study provides a comprehensive assessment of crop yield responses to RSR across a wide range of crop types, climatic conditions, and experimental systems. By integrating observations from agrivoltaic, artificial shading, and agroforestry studies into a unified framework, the analysis extends beyond crop- or site-specific studies and enables a broader understanding of crop responses to reduced radiation. Together, these results show that crop yield responses can be interpreted within a unified framework based on radiation reduction, allowing direct comparison across diverse agronomic systems.

A central finding is that crop responses to shading are strongly crop-dependent. Fruits, fruity vegetables, and berries generally maintain or improve yield under low to moderate shading, whereas forages, leafy vegetables, C₃ cereals, and tubers/root crops show moderate declines, and maize and grain legumes exhibit the most pronounced yield reductions. These patterns support a classification of crops into shade-benefiting, shade-tolerant, and shade-sensitive groups. Similar distinctions in crop response have been reported in previous studies of shading and agrivoltaic systems [16], and the present analysis extends these findings across a broader range of environments and experimental conditions.

The observed differences across crop types can be interpreted in terms of plant physiological responses to light and microclimate. Moderate shading can reduce canopy temperature and evapotranspiration, improving water-use efficiency and alleviating heat stress, particularly for crops sensitive to high radiation or temperature [1,2]. This helps explain the stable or positive yield responses observed in fruits and certain vegetables. In contrast, crops such as maize and grain legumes are strongly dependent on high radiation levels for photosynthesis and biomass accumulation, making them more susceptible to yield declines under reduced light availability [3,4]. Differences in variability across crop types further suggest variation in physiological plasticity, with some crops better able to adjust to shaded environments than others.

Another key finding is the non-linear nature of yield responses to shading. Across crop types, yields remain relatively stable under low to moderate reductions in solar radiation, followed by increasingly rapid declines at higher levels of shading. This behavior is consistent with previous studies showing that moderate radiation reductions can be partially compensated, while more severe shading leads to substantial productivity losses [1,4]. The identification of an approximate threshold around 50–60% RSR suggests a critical limit beyond which light availability becomes the dominant constraint on crop productivity. This threshold is consistent with previous findings suggesting yield declines under high levels of shading [1,4].

While this threshold-like behavior is consistently observed, its magnitude and onset vary across crop types, reflecting differences in crop-specific sensitivity to reduced radiation. This has direct implications for agrivoltaic system design, as it defines a general operating range within which shading can be applied without substantial yield penalties, while highlighting the need for crop-specific considerations.

Climatic conditions further modify these responses. Crops grown in environments with higher baseline irradiance or warmer temperatures tend to maintain yields more effectively under moderate shading, while those in cooler or lower-radiation environments show greater sensitivity. These findings are consistent with studies showing that microclimatic changes induced by shading, including reduced temperature and altered moisture conditions, can influence crop performance [8,10]. As a result, crop suitability for agrivoltaic systems is likely to vary by location, and site-specific conditions must be considered when evaluating system performance. This interpretation is further supported by quantitative threshold analysis, which shows that the estimated RSR threshold increases by approximately 5 percentage points for every 100 kWh m⁻² increase in GHI, indicating that higher-radiation environments can tolerate greater levels of shading before yield declines become pronounced.

The consistency of these patterns across different experimental systems is also notable. Despite differences in how shade is generated, including PV panels, shade nets, and intercropping systems, similar yield responses were observed when expressed as a function of radiation reduction. Comparable effects of reduced radiation have been reported in agroforestry and intercropping studies [5,6], supporting the use of RSR as a common basis for comparing crop responses across systems. Although structural differences exist between agrivoltaic and other shading systems, the consistent response to radiation reduction across systems supports the use of RSR as a unifying variable.

The modeling results reinforce these findings. Both MLR and tree-based ensemble models identified similar relationships between yield, shading, crop type, and environmental variables. Across all models, RSR emerged as the primary driver of yield response, while crop type and climatic conditions influenced the magnitude and direction of this response. The agreement between modeling approaches increases confidence that the observed relationships reflect underlying agronomic processes rather than model-specific artifacts.

The absence of a uniform main effect of shading, combined with strong crop-specific interaction effects, further indicates that shading cannot be treated as a single agronomic factor, but instead operates through crop-dependent responses to radiation reduction.

The consistency of these relationships across modeling approaches indicates that they reflect underlying agronomic processes rather than model-specific artifacts. While yield responses are broadly consistent across shading systems when expressed as a function of radiation reduction, the slightly stronger declines observed in intercropping systems suggest that additional factors beyond simple shading may influence crop performance. In intercropping systems, crops experience direct competition for light, water, and nutrients, as well as structural interactions within the canopy that can amplify the effects of reduced radiation. Unlike agrivoltaic or artificial shading systems, where shading is externally imposed, intercropping introduces biotic competition that may intensify yield reductions under similar levels of radiation reduction. These differences indicate that while RSR serves as a useful unifying variable, system-specific processes such as competition can modify the magnitude of yield responses.

At the same time, the integration of data from multiple experimental systems highlights important considerations for interpretation. Differences in how shading is generated and measured across studies, including variation in light quality and temporal distribution of shade, are not fully captured by a single measure of radiation reduction. In particular, shading from PV panels differs from that of shade nets or cloth in its spectral composition, as PV panels can alter the ratio of red to far-red light reaching the crop canopy. Changes in light quality can influence plant morphogenesis, including stem elongation, leaf expansion, and canopy architecture, which may in turn affect yield responses beyond the effects of radiation reduction alone. In addition, agrivoltaic field studies represent a smaller portion of the available data, with many observations derived from artificial shading or intercropping systems. While this integration enables broader analysis, it also suggests that further work is needed to refine the understanding of crop responses under specific agrivoltaic configurations. As a result, although the analysis captures generalizable responses to reduced radiation, these findings highlight opportunities for further refinement when applying them to specific agrivoltaic system designs that account for system-specific configurations.

Variability in data reporting and environmental measurements across studies also introduces uncertainty. Differences in how radiation, temperature, and rainfall are measured, as well as the need to estimate missing environmental variables in some cases, may influence the precision of model estimates. Similarly, grouping crops into broader categories, while necessary due to limited data for individual species, may mask variation within crop types, including differences among cultivars and management practices.

The results of this study provide direct support for the assumptions outlined in the Introduction. First, crop yield responses to RSR are clearly crop-specific, as evidenced by the distinct response groups observed across crop types. Second, the relationship between yield and radiation reduction is strongly non-linear, with relatively stable yields under lower levels of shading followed by increasingly rapid declines at higher levels. Third, the identification of a consistent threshold range of approximately 50–60% RSR supports the presence of threshold behavior in crop responses to shading. While the exact magnitude and onset of this threshold vary across crop types and environmental conditions, the overall pattern remains consistent, indicating that these assumptions provide a useful framework for understanding crop performance under agrivoltaic systems.

Future research should build on these findings by expanding the availability of field-based agrivoltaic data across a wider range of crops, climates, and system configurations. Controlled experiments that compare different photovoltaic designs under similar environmental conditions would improve understanding of system-specific effects. Incorporating additional environmental variables, such as soil moisture, soil temperature, and evapotranspiration, would further clarify the mechanisms underlying crop responses to shading. Improved standardization in the measurement and reporting of radiation and microclimatic conditions would also strengthen future analyses.

Overall, this study shows that crop yield responses to RSR depend on the interaction between crop characteristics, shading intensity, and climatic context. These findings provide a foundation for selecting appropriate crops and designing agrivoltaic systems that balance energy production with agricultural productivity under diverse environmental conditions.

5. Conclusions

This study provides a comprehensive assessment of crop yield responses to RSR across diverse crop types, climatic conditions, and experimental systems. The results demonstrate that crop responses to shading are strongly crop-dependent and exhibit consistent non-linear behavior, with relatively stable yields under lower levels of shading followed by more rapid declines beyond an approximate threshold of 50–60% RSR.

Climatic conditions further modify these responses, with crops in higher-radiation and warmer environments generally maintaining yields more effectively under moderate shading. The consistency of these patterns across modeling approaches and experimental systems indicates that RSR provides a robust basis for comparing crop responses across agronomic contexts.

These findings highlight the importance of crop-specific and context-dependent design in agrivoltaic systems. Rather than applying uniform shading strategies, system design should consider both crop sensitivity and local environmental conditions to maintain productivity while enabling energy generation. Overall, this study provides a generalizable framework for evaluating crop performance under reduced radiation, supporting the development of more efficient and adaptable dual land-use systems.