# AI-driven remote sensing for environmental characterization and rice crop modeling in water-limited regions

Edgar S. Correa, Francisco C. Calderon, Julian D. Colorado

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Edgar S. Correa, Francisco C. Calderon, Julian D. Colorado. AI-driven remote sensing for environmental characterization and rice crop modeling in water-limited regions. 2025. hal-05041011

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# Al-driven remote sensing for environmental characterization and rice crop modeling in water-limited regions

Edgar S. Correa

e_correa@javeriana.edu.co

UMR AGAP Institut, Univ. Montpellier, CIRAD, INRAE, Institut Agro

Francisco C. Calderon

Pontificia Universidad Javeriana, Cra. 7 No. 40-62, 110311, Bogota

Julian D. Colorado

Pontificia Universidad Javeriana, Cra. 7 No. 40-62, 110311, Bogota

## Research Article

**Keywords:** Crop modeling, Satellite-based genotype-by-environment (GxE), water use efficiency (WUE), rice, food security

**Posted Date:** April 16th, 2025

**DOI:** https://doi.org/10.21203/rs.3.rs-6440110/v1

**License:** © This work is licensed under a Creative Commons Attribution 4.0 International License.
Read Full License

**Additional Declarations:** No competing interests reported.
AI-driven remote sensing for environmental
characterization and rice crop modeling in
water-limited regions

Edgar S. Correa¹,²,³*, Francisco C. Calderon³ and
Julian D. Colorado³,⁴

¹UMR AGAP Institut, Univ. Montpellier, CIRAD, INRAE, Institut Agro,
Montpellier, France.

²CIRAD, UMR AGAP Institut, F-34398, Montpellier, France.

³Pontificia Universidad Javeriana, Cra. 7 No. 40-62, 110311, Bogota, Colombia.

⁴Omics Science Research Institute, iOMICAS, Pontificia Universidad Javeriana, Cali,
760031, Colombia.

*Corresponding author(s). E-mail(s): e_correa@javeriana.edu.co;
Contributing authors: calderonf@javeriana.edu.co;
coloradoj@javeriana.edu.co;

**Abstract**

Advancing our understanding of environmental interactions in rice crops con-
tributes to food production in water-limited regions. This paper proposes an
integrated crop modeling architecture, demonstrating how machine-learning
(ML) models enhance classic Mechanistic Crop Modeling (MCM) estimations
by learning directly from environmental data. Here, we quantify the impact of
noise-induced uncertainty on the CERES-Rice crop growth model, particularly
relevant for drought-tolerant varieties that exhibit complex adaptation mecha-
nisms, such as Nerica 4. Environment characterization is achieved through a novel
3D Gaussian Mixture Model (GMM), offering enhanced precision and scalabil-
ity when coupled with remote-sensing satellite-derived environmental data. By
coupling both MCM and ML models, we achieved higher estimations for grain
yield (R² = 0.99) and biomass (R² = 0.8) in the northwest Tambacounda
region of Senegal in Africa, providing reliable estimates of 30% grain conversion
efficiency and 2.18kg/hamm water use efficiency from an environment char-
acterized by sandy soils with high saturated hydraulic conductivity (1.1cm/h)
and the lowest regional precipitation (513mm, 49%).

**Keywords:** Crop modeling, Satellite-based genotype-by-environment (GxE), water use efficiency (WUE), rice, food security.
# 1 Introduction

Food security is a global concern, with challenges ranging from climate change and water deficits to soil degradation and changes in land use. Addressing these challenges at the regional scale with a growing population is crucial to ensuring self-sufficient food systems and mitigating the effects on food production [1–5].

Agriculture plays a crucial role in food production and, at the same time, contributes significantly to global greenhouse gas (GHG) emissions, with estimates ranging from 10% to 30% of total human-induced emissions [6, 7]. Rice cultivation in flooded fields, contributes significantly to global greenhouse gas emissions, primarily through the production of methane (CH4) [8]. Flooded paddies create anaerobic conditions in the soil, which promote the decomposition of organic matter by microorganisms, releasing methane [9]. Historically, rice has been cultivated in flooded conditions [10, 11]. However, hybrid drought-resistant rice has developed intricate adaptation mechanisms, demonstrating efficient water use, short growing cycles, and deep roots, performing well in environments with low water content [12–15]. In this context, aerobic rice is an alternative crop grown in well-drained, unflooded soils, particularly in regions with limited water availability or where irrigation is not sustainable, relying primarily on rainfall [16].

A major challenge in quantifying biomass and crop efficiency in non-industrialized agriculture is the significant lack of resources, technology, and infrastructure, such as meteorological stations with high spatial and temporal resolution [17, 18]. Earth Observation (EO) technologies have democratized access to technology, developing satellite-driven databases that enable the study of regions with limited infrastructure.[19–22]. Building on this foundation, recent advancements in artificial intelligence (AI) have enabled a set of tools for addressing global food security challenges. AI applies computational techniques, such as machine learning (ML), multispectral image processing, and pattern recognition, to model, optimize, and automate processes such as crop monitoring, yield prediction, and resource management [23–30].

The mathematical representation of crop growth under diverse environmental conditions provides a powerful approach for assessing food production, overcoming the challenges of large-scale field experiments [31–35]. However, the use of crop models at regional scale in uncontrolled conditions face the challenge of accurately capturing how plants respond to environmental factors like soil type, climate, farming practices, and biotic interactions. Plant growth and development operate across multiple scales, from cellular processes to ecosystem-level interactions, a challenge intensified by the complex adaptation mechanisms of diverse drought-tolerant cultivars [12, 36].

Mechanistic crop models (MCMs) have been widely used for decades in the field of agronomic research, with over 70 models developed in the last 40 years to simulate crop growth and yield under diverse conditions [31, 37]. The growth and development of rice depend on the accumulation of heat over time, quantified through Growing Degree Days (GDD), which the MCM uses to simulate crop growth [38, 39]. While these models have proven valuable, still rely on empirical elements and parameters with limited biological relevance, and numerous mechanisms remain poorly understood. Significant efforts are required to quantitatively link genotype to phenotype and address model limitations to improve the accuracy of modeling studies [34, 38]. Moreover, crop model
estimations inherently involve uncertainties arising from model structure, parametriza-
tion, and input data, such as climate variables [40]. A systematic review of 277 studies
conducted between 1991 and 2019 across 82 countries and 460 locations assessed uncer-
tainty in crop model outputs, specifically grain yield. The review identified that 52%
of studies focused on input uncertainty related to climate change projections, 28%
addressed model parameter uncertainties, and 20% examined model structure uncer-
tainties, often through multi-model ensembles. However, uncertainty associated with
meteorological variables remains under-explored, despite its relevance. Random fluctu-
ations, or noise, inherent in physical systems and instruments, arise from factors such
as thermal effects, radiation, degradation, and instrumental failure [41, 42]. Address-
ing these uncertainties is essential to enhance the reliability of crop models [40]. For
instance, a review of 140 studies using the CERES model under various conditions,
including well-managed fields with appropriate irrigation and fertilization, reported
simulated root mean square errors (RMSE) for rice grain yield ranging from 200 to
1,672 kg/ha. Notably, the normalized RMSE varied between 11.8% and 25.6% across
more than 500 rice stations in China [43, 44]. In contrast, drought-tolerant rice varieties
have been less widely studied with the CERES-Rice model. In a controlled experiment
with sixteen upland rice genotypes, RMSEn values ranged from 0.76 to 1.06 [45]. A
rainfed field experiment in Senegal, however, reported a mean model calibration effi-
ciency of 0.66 for 21 rice varieties [46]. If such uncertainties inherent in the model are
not critically addressed, they could lead to not fully representative recommendations
for policymakers and stakeholders, particularly when developing adaptation strategies
[40].

These results highlight the need for further refinement in crop modeling, a task
increasingly supported by advances in plant physiology, mathematics, computational
tools, and AI. This progress is enabling the development of more mechanistic models
through detailed response functions [32, 39, 47]. A new paradigm called 'simulation
intelligence' has emerged, integrating elements from both mechanistic crop models
(MCMs) and data-driven methods based on machine learning (ML) [48]. The surro-
gate models based on ML have gained prominence in plant and crop sciences due to
their potential to achieve both high-accuracy estimation and the capability to explain
plant responses [48] [49] [50]. Combining MCM and ML, given their intrinsic comple-
mentarity, allows for three main modeling approaches: parallel, serial, and modular
structures, that can be adopted to represent complex agricultural interactions [51-55].

In this context, MCM and ML strategies should complement each other to improve
the understanding of plant responses to environmental variability, ensuring high-
accuracy estimations and reliable recommendations for policymakers and stakeholders.
This is particularly critical for large agricultural regions where field conditions are
heterogeneous and cannot be strictly controlled [31, 48, 49, 56].

Figure 1 presents a framework for a novel approach that integrates the mechanistic
crop model (MCM) CERES-Rice with machine learning (ML), aiming to enhance
the accuracy of MCM simulations by addressing uncertainties caused by instrumental
noise. This study specifically examines the temperature variable (°C), which plays a
crucial role in thermal time calculations within the MCM [57–59]. The focus aligns with
the broader discussion of thermal time as a fundamental concept governing fluctuations
<figure><img src="image_2.png" /><figcaption>**Fig. 1** High accuracy yield estimation by coupling the mechanistic crop model with ML.</figcaption></figure>

in plant development rates between crop models [31, 38]. The ML module processes time series data using an auto-regressive model with exogenous inputs (ARX) [60] [61]. The inputs to the ARX model include environmental variables and MCM estimations within the time window from sowing to harvest. The connection between the MCM and ML is implemented through a filter configuration designed to achieve high-accuracy estimations of grain yield (kg/ha), biomass (kg/ha), number of tillers, and number of grains per hectare. This configuration serves as an analogous compensation method to the traditional Kalman filter used in dynamic systems [62]. The case study focuses on the rainfed experiment conducted in the Casamance and Eastern Senegal for the Nerica 4 (N4) cultivar.

This article presents how integrating machine learning (ML) with the CERES-Rice model provides deeper insights into drought resilience in the region, along with comprehensive environment characterization, which allows for a better understanding of the varying environmental factors that influence crop performance. Using the drought-adapted rice variety Nerica 4 as a case study, this study compares it with traditional mechanistic crop modeling (MCM). This integration is achieved by analyzing water use efficiency and grain conversion efficiency across distinct environmental conditions. The ability of each model to capture drought adaptation is evaluated through genotype-by-environment (G×E) interactions and the accuracy of the modeling approach in representing this response. The high-accuracy calibration and validation of key crop parameters such as grain yield, biomass, number of grains, tillers, and phenology serve as a robust foundation for informed analysis, recommendations, and decision-making. Furthermore, this study exposes how ML integration enables the estimation of consistent water use efficiency and grain conversion efficiency for aerobic rice at a regional scale in drought-prone environments.
# 2 Materials and setup

## 2.1 Study area

Senegal is located on the west coast of Africa and includes the Sudano-Sahelian zone. The Casamance region, comprising Ziguinchor, Sédhiou, and Kolda, spans approximately 28,350 square kilometers, while the Senegal Oriental region (also known as the Tambacounda region) covers around 42,364 square kilometers. Together, these regions cover a total of 70,714 square kilometers.

### Soil Data

DB1 consists of 9 experiments, each associated with soil properties determined through laboratory tests conducted at a depth of 30 cm [46]. In contrast, DB2 is sourced from SoilGrids, with a spatial resolution of 250 meters. This dataset covers the entire study region and provides soil property data at three depth intervals: 15 cm, 30 cm, and 100 cm, which are used as inputs for the crop growth model [63]. The measured properties include soil texture, key nutrients, and other relevant factors. Table 1 summarizes the soil information available from both DB1 and DB2. The nomenclature displayed in DB1 is associated with the DSSAT software platform and the CERES-Rice model. The crop growth model requires soil hydraulic properties, including permanent wilting point (SLLL), field capacity (SDUL), saturation (SSAT), and saturated hydraulic conductivity (SSKS), which are calculated using Saxton and Rawls pedotransfer functions [64–67].

<table><caption>Table 1 Physicochemical soil properties in the DB1 and DB2 databases.</caption><thead><tr><th></th><th>DB1 - Field experiment</th><th>DB2 - Satellite</th></tr></thead><tbody><tr><th scope="row">Soil texture</th><td>SLCL - Clay content (%)<br>SLSI - Silt Content (%)<br>Soil Sand (%)<br>SBDM - Bulk density (g/cm3)<br>SLCF - Coarse fraction (%)</td><td>Clay (g/kg)<br>Silt (g/kg)<br>Sand (g/kg)<br>Bulk (cg/cm3)<br>Coarse (cm3/dm3)</td></tr><tr><th scope="row">Macronutrients</th><td>SLNI - Soil Nitrogen (%)<br>SLOC - Total organic Carbon (%)</td><td>Nitrogencg/kg)<br>Total Carbon(dg/kg)</td></tr><tr><th scope="row">Others</th><td>SLHW - PH (unitless)</td><td>PH (unitless)</td></tr></tbody></table>

### Climate Data

Crop modeling requires meteorological data inputs to characterize crop responses to environmental conditions. The MCM depends on key variables such as minimum and maximum temperature (°C), solar radiation (MJ/m²/day), wind speed (m/s), relative humidity (%), and precipitation (mm/day), which are also sourced from the rainfed rice study [46]. To apply the model at a regional scale, all these variables are obtained from the NASA POWER dataset [68].
## 2.2 Environments Definition

To study crop development in response to the environment (GxE), it is crucial to define the environmental types within the study area. This definition is independent of the cultivar's response, as each cultivar's behavior varies based on its genetic composition [69] [70]. In this study, environments are characterized regionally by key factors, such as soil type and climate.

<figure><img src="image_3.png" /><figcaption>Fig. 2 Environment characterization methodology based on Climate and Soil data.</figcaption></figure>

Figure 2 illustrates the methodology for environmental characterization, aimed at defining soil and climate types at a regional scale. This approach employs a clustering strategy, where soil and climate data are clustered independently. Principal component analysis (PCA) is first applied to reduce the dimensionality of the data, accounting for multiple variables. The optimal number of clusters is determined using silhouette scoring, a technique that evaluates the quality of clustering by measuring the cohesion and separation of the data points. For the clustering stage, the Gaussian Mixture Model (GMM) algorithm is employed in three-dimensional space, using the first three PCA dimensions. The resulting clusters are represented by deformed ellipsoids, as shown in Figure 2-c. This GMM approach is then compared to the traditional clustering algorithm [71–75]. The output of this process is a detailed map categorizing each region based on its soil and climate types. Following this, spatial correlation analysis is performed to generate all possible combinations of these types, resulting in distinct environmental classifications that allow for the analysis of plant responses to specific environmental conditions.

## 2.3 Mechanistic Crop Growth Model (MCM)

To model crop development in response to environmental conditions, the CERES-Rice mechanistic crop model is used to approximate plant behavior and identify plant responses. Field-based crop measurements, including phenological parameters such as anthesis and maturity stages in days, as well as productivity attributes such as biomass and grain yield in kilograms per hectare, are crucial for assessing crop performance. Parameters in the context of crop modeling are measurable factors or variables that influence plant growth and yield, such as the timing of phenological stages, the number
of tillers, and the number of grains per square meter. These parameters are critical to establishing the environmental and agronomic conditions under which a crop develops, and they are essential to ensure accurate calibration and prediction of the model. The calibration of the model is performed using data from a rainfed rice study in Senegal [46], which provides field-based insights into environmental factors and crop responses.

## Noise base uncertainty in MCM

Figure 3 presents the methodology for simulating noise from the database. The case study of this research focuses on temperature due to its importance in the mechanical crop growth model (MCM) for biomass accumulation, which is estimated daily based on thermal time. Satellite-based data were used to quantify the model error and uncertainty. Figure 3-b illustrates the noise modeling process through a convective filtering approach applied to the variable. A moving average filter with a window size of 21 is used, employing MATLAB signal processing module. The noise is modeled by subtracting the filtered signal from the initial database signal, and this noise is represented by a Gaussian distribution. Finally, additive Gaussian white noise is generated with a distribution consistent with that of the initial database. For each sample in the original dataset, 100 new data points are generated as a data augmentation approach to overcome the disadvantage of having a reduced dataset from field experiments, forming a time series to feedback into the crop growth model. For 9 sites experiments from [46] with an average window of 106 days for the short-cycle rice, corresponding to the N4 variety, a total of 95,400 data points are available, which is optimal for modeling time series with machine learning.

<figure><img src="image_4.png" /><figcaption>Fig. 3 Gaussian white noise with the same variance as meteorological database: a) data collection from remote sensing, b) database noise modeled with a Gaussian distribution using the MATLAB signal processing toolbox, c) data augmentation based on Gaussian white noise for the temperature variable.</figcaption></figure>

## 2.4 AI architecture

The linear auto-regressive with exogenous inputs (ARX) model is widely used in time-series forecasting due to its effectiveness in capturing the dynamics of temporal
data. In this study, we extend the ARX model to the Nonlinear auto-regressive with exogenous inputs (NARX) framework by utilizing a feedforward neural network. The primary objective is to approximate the function $f(x)$, where $f(x)$ is derived from the mechanistic crop model (MCM) CERES-Rice that has been adjusted based on filed observations. Specifically, the function $f(x)$ is driven by key variables such as biomass, grain yield, the number of grains, and the number of tillers, all of which are critical components of the crop growth and development process.

The auto-regressive component of the NARX model relies on Time Lagged Data (TLD), which involves using past values of the input variables from environment to predict future outputs. This approach effectively integrates the temporal dependencies within the data, where past observations of environment influence the current state of the crop dynamic system, this allows for the prediction of organic matter cumulation dynamics of biomass and grain yield.

By incorporating time-lagged data, the model reduces noise and disturbances, leading to a more precise characterization of the underlying process. Such improvements enhance accuracy, enabling reliable predictions of crop performance and yield across diverse environmental conditions.

<figure><img src="image_5.png" /><figcaption>**Fig. 4** NARX model using a feedforward neural network to approximate the function from MCM adjusted by GY observed.</figcaption></figure>

## Dataset to train and validate the ML

Crop observation data originate from a rainfed experiment conducted across nine sites for the N4 cultivar [46]. The field-based rainfed study collected data on grain yield, biomass, grain number, and tiller number at maturity. These experimental data serve as ground truth for evaluating model performance.

From this field experiment, the mechanistic model generates temporal dynamics for each variable from sowing to maturity, forming the basis for training the ML module. A total of 954 data points were obtained from the nine sites, averaging 106 samples per site. The dataset for ML model calibration and validation consists of 95,400 data points, generated by taking the full time series for each site and augmenting it 100
times using additive Gaussian white noise. The dataset for ML calibration includes data from five of the nine field experiment sites, incorporating the variability of noise from each available meteorological station. Of this dataset, 70% of the noisy data is used for ML model calibration, while 30% is used for validation. Finally, once the ML model is calibrated and validated with noisy data, it is further validated using the four remaining sites from the original field experiment dataset.

## 2.5 Large scale insilico Simulation

The crop model simulates the accumulation dynamics of organic matter in response to environmental conditions. Simulations incorporate climate and soil data spanning 20 years (2000-2019), with a fixed sowing date in the second week of July, consistent with regional averages [46]. The in silico data set comprises 10,100 simulations, each executed daily in seven phenological stages: (i) germination, (ii) tillering, (iii) panicle initiation, (iv) panicle emergence, (v) anthesis, (vi) grain filling, and (vii) maturation.

Each simulation quantifies grain yield, biomass, grain number, and tiller count. The Water Stress Photosynthesis Deficit (WSPD) factor quantifies the impact of soil water availability on crop photosynthesis by assessing the relations between soil moisture and evapotranspirative demand using the Penman-Monteith equation. WSPD is calculated daily, ranging from 0 (no stress) to 1 (severe stress), directly influencing photosynthetic efficiency, biomass accumulation, and yield formation. Higher values indicate increased water stress, leading to reduced carbon assimilation and compromised growth [76]. Finally, the crop model outputs, combined with environmental data, are processed through the Machine Learning module to generate the final crop yield estimate.

# 3 Results

This section presents key findings from the analysis of factors influencing plant performance, including organic matter accumulation and crop yield at the regional scale. A novel aspect of this study is the exploration of noise-induced uncertainty in the CERES-Rice crop growth model, which is addressed through the integration of Machine Learning (ML) and MCM to enhance yield prediction accuracy. The results also include large-scale simulations, which highlight the value of this approach in refining performance forecasting, assessing the efficiency of the cultivar in converting biomass into grain and evaluating water use efficiency for yield production.

## 3.1 Environmental monitoring at regional scale

Environmental characterization was conducted in two stages: soil categories and climatic conditions. The variance of the twelve soil variables is explained by three principal components (PCA), accounting for 94.55% of the total variance. The optimal number of soil groups, determined using the silhouette metric, is two for k-means and three for the Gaussian Mixture Model (GMM). Figure 5-a-b illustrate the two and three clusters based on the three principal components for k-means and GMM. Figure 5-c-d presents the values of the twelve soil variables for each group. The second soil type in cyan is the same for both clustering approaches. It is a sandy soil, with
<figure><img src="image_6.png" /><figcaption>**Fig. 5** Soil categories in the region using K-means and the Gaussian Mixture Model. a-b) 3D PCA clusters, c-d) twelve soil variables for each cluster, e-f) spatial distribution of each soil group in the Casamance and Eastern Senegal.</figcaption></figure>

higher values for pH and saturated hydraulic conductivity (SSKS). It is a soil with low water retention capacity, allowing water to pass through it when fully saturated, which influences water infiltration and drainage. The first soil type identified using K-means in Figure 5-c has a higher content of silt and clay, greater organic matter and nitrogen content, and higher values for hydraulic properties related to water retention, including water holding capacity (SLLL), field capacity (SDUL), and saturated upper limit (SSAT), compared to the second soil type.

Using GMM, soil with higher water retention capacity is better differentiated into two groups, as shown in Figure 5-d. Soil type 1 has higher levels of pH, bulk density, silt, and clay, along with intermediate levels of hydraulic properties related to water retention (SLLL, SDUL, and SSAT). It also has lower values of nitrogen and organic carbon. Soil type 3 exhibits the highest values for SLLL, SDUL, SSAT, and clay content, as well as higher levels of nitrogen and organic carbon, and lower pH compared to soil type 1. Figure 5-e-f shows the spatial distribution of each soil group in the Casamance and Eastern Senegal for each clustering approach.

Figure 6-a-b illustrate the clusters based on the three principal components. The variance of the eleven climate variables is explained by three principal components (PCA), accounting for 75.94%. The optimal number of clusters, determined using the silhouette metric, is two with k-means and four with GMM. Climate type 2, represented by the color cyan, is identified using both clustering approaches and is predominantly located in the northern part of the study area, as shown in Figure 6-e-f. This climate is characterized by having 49% less accumulated rainfall, 18% lower average relative humidity, and higher values of solar radiation, average temperature, and maximum temperature compared to the groups located in the southern part of the region.
<figure><img src="image_7.png" /><figcaption>**Fig. 6** Climate conditions in the region. a-b) 3D PCA clusters, c-d) eleven climate variables features for each cluster, e-f) spatial distribution of each climate group in the Casamance region.</figcaption></figure>

Using GMM, the climate in the southern part of the region is better differentiated into three groups, as shown in Figure 6-f. Climate 1, represented in purple, is the most representative of the southern region. In Figure 6-b, it is observed that it has lower dispersion in the 3D space of the principal components, compared to climate 4 and 3, represented in black and green. Climate 1 has higher average solar radiation values with lower variability in solar radiation, while maintaining similar values for average, minimum, and maximum temperature. Climate 3 has the lowest solar radiation values, with the highest variability in solar radiation, and it also exhibits the lowest average maximum temperature, highest average minimum temperature, and highest average wind speed, and is located near the coastal region of the study area.

Figure 7 illustrates the identification of 12 environments based on combinations of soil and climate types. Figure 7-a shows the four environments associated with soil type 1, which covers 51.13% of the region. Environments 1 and 2 are the most prevalent, accounting for 30% and 18%, respectively. Figure 7-b presents the four environments related to soil type 2, representing 43.13% of the region, with environments 5 and 6 being the most prominent, accounting for 21% and 20%, respectively. Finally, Figure 7-c depicts the four environments associated with soil type 3, which constitutes 4.75% of the region.

Environments 1 and 2 exhibit a higher water retention capacity due to their high clay and silt content. Environment 1 experiences higher precipitation, along with intermediate radiation with lower variability. In contrast, Environment 2 experiences lower precipitation but is characterized by maximum values of radiation, average temperature, and maximum temperature. Environments 5 and 6, with sandy soils, have
<figure><img src="image_8.png" /><figcaption>**Fig. 7** Environmental categories in the Casamance and Eastern Senegal region: a) Four environments with soil type 1, b) Four environments with soil type 2, c) Four environments with soil type 3.</figcaption></figure>

the lowest water retention capacity with the highest saturated hydraulic conductivity. They also share a similar pattern of high radiation and low precipitation in the northern region compared to the southern region.

Environments 4, 8, and 12 represent 8% of the region, encompassing all three soil types with climate type 4, which exhibits a higher variability in solar radiation compared to climate types 1 and 2, along with the lowest wind speed. Environments 3, 7, and 11, each representing at least 1% of the region, also encompass the three soil types and climate type 3, which is characterized by the highest variability in solar radiation, as well as maximum wind speed and average minimum temperature.

<figure><img src="image_9.png" /><figcaption>**Fig. 8** Uncertainty in the variables grain yield, biomass, number of grains, and number of tillers: a) Daily dynamics of biomass accumulation in the Kolda 2014 location (KOLD1401). b) Crop growth model uncertainty across 9 experimental points from field experiments.</figcaption></figure>
## 3.2 Crop Growth Model uncertainty

Biomass accumulation dynamics, influenced by environmental factors, are calculated daily from sowing to maturity using the mechanistic crop growth model (MCM) CERES-Rice, as shown in Figure 8-a. Biomass rate estimation is an integrative process calculated based on growing degree days, which depend on temperature and day length. By researching the effect of Gaussian white noise on the temperature data, we can quantify the uncertainty associated with grain yield, biomass, number of grains, and number of tillers. The uncertainty calculation is performed on the final day of the cycle, at the point of maturation and harvest.

Figure 8-b shows the noise-based uncertainty in the temperature variable in nine samples from the experiment by Gerardeaux et al. [46] for the N4 cultivar. The uncertainty in biomass ranges from 266 to 680 kg/ha, representing 13.67%; grain yield ranges from 183 to 425 kg/ha, representing 8.62%; the number of grains per hectare ranges from 612 to 1416, representing 13.66%; and the number of tillers per hectare ranges from 23 to 52, representing 20.65%.

## 3.3 Enhancing Crop Growth Prediction with ML

Figure 9-a presents the performance of the CERES-Rice model calibration reported by Gerardeaux et al. [46] (MCM1) for the N4 cultivar, in terms of phenological variables: anthesis and maturity, as well as variables of organic matter accumulation: biomass, grain yield, number of grains, and number of tillers. The reported results integrate the crop parameter G2 with a value of 0.063, associated with the grain weight in grams. The model calibration estimates biomass with an RMSE of 3127 kg/ha, an average of 4484 kg/ha, and a low R² of 0.011. The grain yield and number of grains are underestimated with an RMSE of 905 kg/ha and 4134 grains/ha, with averages of 1275 kg/ha and 4344 grains/ha, respectively. In contrast, the number of tillers is

<figure><img src="image_10.png" /><figcaption>**Fig. 9** Cultivar N4 performance: Biomass, grain yield, number of grains, number of stems, anthesis, and maturity, a) MCM1 CERES-Rice reported by Gerardeaux et al. [46] b) MCM CERES-Rice manually calibrated c) MCM CERES-Rice and ML approach.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>**Fig. 10** In silico grain yield simulations for the Casamance and Eastern Senegal regions across the 7 most representative environments: a) Mechanistic Crop Model (MCM) CERES-Rice, and b) MCM coupled with a Machine Learning approach.</figcaption></figure>

overestimated, with an RMSE of 353 and an average of 155. The phenological error shows an RMSE of 8 days for anthesis with an average of 71 days, and an RMSE of 7 days for maturity with an average of 99 days.

Figure 9-b presents the performance of the CERES-Rice model with manually adjusted crop parameters, ensuring that the values align with the cultivar's defined range (Supplementary materials: Table S1). Specifically, the crop parameter G2 is set to a maximum value of 0.03. The empirical calibration is validated through Genetic Algorithm optimization, which runs the model 8,280 times and evaluates 920 possible crop parameter combinations. The results of the Genetic Algorithm are consistent with the empirical calibration (Supplementary materials: Table S2). The RMSE for biomass decreases by 338 kg/ha, and the R² metric improves by 48%. The grain yield and number of grains are overestimated, with R² improving by 1.42% and 22.9%, respectively. The RMSE for the number of tillers is 45, showing an 87.3% increase in accuracy compared to MCM1. The phenological error shows an RMSE of 1 days for anthesis with an average of 71 days, and an RMSE of 8 days for maturity with an average of 99 days.

Figure 9-c illustrates the performance of the integrated crop growth model coupled with machine learning approach, aimed at simulating organic matter accumulation across multiple variables. The model exhibits precision in predicting grain yield, achieving an R² value of 0.99 based on calibration data from five sites and validation data from four independent sites. In addition, the model has an R² of 0.80 for both biomass and the number of grains. Notably, the model also shows a significant enhancement in the prediction of tiller numbers, with a 35% reduction in RMSE, resulting in an RMSE of 14 tillers with an average of 155 tillers.

## 3.4 Nerica 4 yield and efficiency at regional scale

Figure 10 shows the in silico production of the grain yield for 7 million hectares in the Casamance and Eastern Senegal regions. Figure 10-a illustrates the yield predictions
<figure><img src="image_12.png" /><figcaption>**Fig. 11** Harvest Index: a) Mechanistic Crop Model (MCM) CERES-Rice, and b) MCM coupled with a Machine Learning approach.</figcaption></figure>

using the mechanistic crop model (MCM). The grain yield estimate has a mean of 3158.2 kg/ha with a variation of 251.46 kg/ha. Figure 10-b presents the results from the ML-MCM approach. The grain yield estimate has a mean of 1033.3 kg/ha with a variation of 267.59 kg/ha. The Machine Learning approach leads to a 67.28% decrease in mean and an 6.91% increase in variation. The spatial distribution of yield differs between the traditional mechanistic model approach and the Machine Learning-based approach.

Traditional MCM predicts higher yields in environment 1, which represents 33% of the region, with an average of 3340 kg/ha. This environment experiences higher precipitation, intermediate radiation of 19.1 MJ/m²/day with a lower variability of 3.4 MJ/m²/day, a wind speed of 163.1 m/s with a variation of 59.69 m/s, and exhibits higher water retention capacity due to its high clay and silt content. In contrast, the model shows lower yields in environments 4, 8, and 12, averaging around 3080 kg/ha.

The estimate with ML-MCM shows higher yields in environments 4, 8, and 6. Environments 4 and 8 represent 3% and 2%, respectively, and include soil types 1 and 2 with climate type 4, which exhibits a mean solar radiation of 18.55 MJ/m²/day with variability of 3.6 MJ/m²/day, along with the lowest wind speed of 110 m/s and the lowest variance of 41.38 m/s. Environment 6 represents 20% of the region, located in the northern part of the studied area, with an average yield of 1113 kg/ha. It presents the highest radiation of 19.6 MJ/m²/day, low accumulated precipitation of 513 mm, and a sandy soil with the highest saturated hydraulic conductivity of 1.2 cm³/cm³, resulting in soils with low water retention capacity.

Figure 11 illustrates the efficiency of the Nerica 4 cultivar in converting biomass into grain, quantified by the Harvest Index (HI). Figure 11-a presents the HI using the MCM model, identifies environment 1 as exhibiting the highest HI values, with a peak average HI of 0.504, representing 30% of the area in the southeastern region. This environment is characterized by 51% higher cumulative precipitation (840 mm), lower solar radiation (19.1 MJ/m²/day), and an average temperature of 26.4°C. The soils in this region are defined by high bulk density and clay content, with hydraulic
<figure><img src="image_13.png" /><figcaption>**Fig. 12** Water Use Efficiency : a) Mechanistic Crop Model (MCM) CERES-Rice, and b) MCM coupled with a Machine Learning approach.</figcaption></figure>

properties that support water retention: Wilting Point (SLLL) = 0.2 cm³/cm³, Upper Limit (SDUL) = 0.3 cm³/cm³, and Saturation (SSAT) = 0.4 cm³/cm³.

Figure 11-b shows that the machine learning (ML) approach identifies the highest HI values in Environment 6. The highest HI is 0.422, representing 20% of the area in the northwest region. This environment experiences 49% lower cumulative precipitation (513.2 mm), higher solar radiation (19.6 MJ/m²/day), and an average temperature of 28.3°C. The soil is sandy with high saturated hydraulic conductivity (SSKS), indicating a low water retention capacity that allows for rapid water infiltration when fully saturated. This characteristic significantly influences water infiltration and drainage dynamics.

Figure 12 illustrates the efficiency of water use for yield production, quantified by the Water Use Efficiency (WUE) indicator. Figure 12-a shows that the Nerica 4 cultivar exhibits the lowest WUE, with an average value of 0.2147 kg/H.mm in Environment 6, while the highest WUE recorded in the region is 0.2421 kg/H.mm. In contrast, Figure 12-b reveals that the ML-based approach identifies Environment 6, a dry region with low water retention capacity, as having the highest WUE, peaking at 2.65 kg/ha.mm. In contrast, the lowest average WUE recorded is 1.31 kg/ha.mm in Environment 12, which accounts for 3% of the region and is characterized by high values of hydraulic properties (SLLL, SDUL, SSAT), clay content, and organic carbon. This WUE corresponds to the Nerica 4 hybrid, which demonstrates efficient performance in water-limited environments.

Figure 13 presents five distinct drought stress patterns, which were derived from the accumulated stress across the seven phenological stages, as calculated by the CERES-Rice model. Stress typically occurs towards the end of the cycle, during the grain filling and maturation stages. Pattern 1 is more intense and also presents a lower intensity of stress in stage 4, which corresponds to flowering. This stress pattern is found in environments two and six, which represent 38% of the region and are located in the north with soil types 1 and 2, having two different soil compositions: sandy-loam with 56.6 g/kg of sand and 21.6 g/kg of clay, and loamy-silty with 44.9 g/kg of sand and
26 g/kg of clay, respectively. Pattern 2 occurs in environment 10, also in the northern part of the region, where soil type 3 is present. This soil is loamy-silty, containing 39.1 g/kg of sand and 26.9 g/kg of clay, with lower sand content and higher nitrogen and organic carbon levels. Pattern 3 occurs in environments 5, which represent 21% of the region in the southern part, where rainfall is more intense and radiation is lower. This environment feature soil types 2. Pattern 4 is also found in the southern part of the region in environment 9 and 1, but with soil type 3 and 1 and lower stress intensity compared to pattern 3. Finally, stress pattern 5 occurs in environments 4, 8, 12, 3, 7, and 11. A common feature of these environments is that they have climate types 3 and 4, with minimal solar radiation, and are located in the coastal region of Ziguinchor.

# 4 Discussion

By investigating the interaction between environmental factors such as temperature, rainfall, soil texture, and hydraulic properties, this research explores how these factors influence crop yield and biomass accumulation under varying conditions on the regional scale. The clustering approach using a Gaussian Mixture Model (GMM) in the 3D space of the Principal Component Analysis (PCA) demonstrates an enhanced capability to identify distinct soil types and climate settings, surpassing traditional clustering algorithms used in environmental characterization, such as hierarchical clustering and K-means [71–75]. This method efficiently differentiates environmental conditions through the region and, when integrated with satellite-derived databases, facilitates scalable analysis at the regional level, enabling the assessment of cultivar efficiency and productivity.

To the best of the author's knowledge, this work presents the first quantification of noise-induced uncertainty in mechanistic crop model CERES-Rice, with a particular focus on temperature. In addressing model limitations and their scope of applicability [31], we highlight the challenges posed by the inherent uncertainty within these models, which remain difficult to calibrate due to the complexities of biological systems [35, 77], intensified with new varieties exhibiting intricate adaptation mechanisms. This complexity suggests that many underlying mechanisms are not yet fully understood, emphasizing the need for advanced tools to explore these uncertainties [32, 48, 49], particularly in non-industrial agriculture under uncontrolled conditions

<figure><img src="image_14.png" /><figcaption>**Fig. 13** Drought stress patterns across the seven phenological stages for all environments in the region.</figcaption></figure>
on the regional scale. To address these gaps, we propose integrating time series mod-
eling with a machine learning technique that does not have assumptions and learns
directly from the environment and the observed data. By harnessing daily environ-
mental inputs and ecophysiological model-based dynamics, this integration enhances
the accuracy of traditional crop model estimates. This integration achieves R² values
of 0.99 for grain yield and 0.80 for both biomass and grain number in the rainfed
experiment. This research also investigates the plant response of the Nerica 4 cultivar,
a hybrid rice variety resulting from the cross between African rice (Oryza glaberrima)
and Asian rice (Oryza sativa). Known for its high grain yield performance under sub-
optimal water resource conditions, Nerica 4 demonstrates adaptability to poor soils
and limited water environments, attributed to its deep root system and short growth
cycle, with key traits including enhanced productivity and resistance to disease and
pests [15, 78]. This pattern aligns with machine learning (ML) estimates, revealing a
key finding: the ML-based approach identifies Environment 6, a dry region with low
water retention capacity, as exhibiting: (i) A yield of 1113 kg/ha with the highest grain
conversion efficiency in the region at 30%. (ii) The highest water use efficiency (WUE)
with an average of 2.179 kg/H·mm. This elevated WUE is consistent with the findings
of 41 cases of aerobic rice, where the WUE values range from 2 to 15 kg/H·mm [14],
reflecting the adaptability of Nerica 4 cultivar to drought conditions.

In contrast, traditional mechanistic crop model (MCM) estimates indicate a
maximum WUE of 0.2421 kg/H·mm, consistent with findings from 56 studies on flood-
irrigated rice, which report significantly lower WUE values ranging from 0.028 to 0.125
kg/H·mm [79]. These results highlight the superior water use efficiency of aerobic
rice systems compared to conventional flooded cultivation methods, and the limita-
tion of traditional mechanistic crop model to capture the efficiency and productivity
of drought resistance rice crops. This aligns with the challenges of accurately repre-
senting the Nerica 4 cultivar in rainfed rice studies using the state of the art model
parametrization [46]. Mechanistic crop models assume that drought effects begin when
soil water content decreases below saturation, as represented by the WSPD parame-
ter in the CERES-Rice model. WSPD serves as a limiting factor for organic matter
accumulation and directly influences biomass-to-grain conversion efficiency [57–59]. As
shown in Figure 13, environments 6, which exhibit the highest WSPD values, estimate
a lower water use efficiency (WUE) and a reduced harvest index (HI). These results are
consistent with flooded rice cultivars but not with drought-resistant, adapted varieties
as Nerica 4 [12, 13, 80].

5 Conclusion

The integration of the unsupervised Gaussian Mixture Model (GMM) in 3D with
Principal Component Analysis (PCA) represents a significant advancement in environ-
mental characterization, surpassing conventional clustering methods such as K-means
and hierarchical clustering. This approach enables a more precise identification of
distinct environmental compositions, including soil types and climate settings, refin-
ing our understanding of regional variability. When coupled with satellite-derived
databases, it enhances large-scale assessments, providing a scalable and data-driven
framework for improved environmental characterization and optimize decision-making
in precision agriculture.

A key contribution of this study is quantifying noise-induced uncertainty in the CERES-Rice crop model, with a particular focus on temperature variability. This approach addresses the complexities of modeling crop responses under fluctuating environmental conditions. By integrating machine learning with a multivariate time series approach, the study enhances the accuracy of mechanistic models, particularly in capturing crop yield and biomass dynamics, learning directly from environmental data, and reducing reliance on assumptions commonly embedded in traditional models. The research highlights the need for a more comprehensive crop modeling approach that combines both mechanistic and data-driven techniques, emphasizing the importance of refining modeling mechanisms to better capture the complexities of drought-resistant varieties and their adaptation to diverse environmental stressors. The complexities of drought-resistant crop varieties, such as their intricate water use mechanisms and adaptive traits, are not always captured adequately by traditional models, leading to significant gaps in predictions. Furthermore, the integration of machine learning techniques, although promising, faces challenges.

Our results, which achieve R² values of 0.99 for grain yield and 0.80 for biomass and grain number, demonstrate the power of this integrated approach to deliver high-accuracy recommendations to policymakers and stakeholders. The exceptional adaptability of the Nerica 4 cultivar to drought conditions is consistently confirmed by machine learning-based estimates. The findings align with the superior water use efficiency (WUE) of aerobic rice systems like Nerica 4, compared to traditional flooded rice varieties. This research challenges traditional crop models, which do not fully capture the efficiencies of drought-resistant varieties like Nerica 4, as reported in the state of the art, particularly in rainfed environments at regional fields. This study also highlights the limitations of mechanistic crop models, particularly in capturing the complexities of drought resistance and water use efficiency in aerobic-adapted cultivars. Our results call for improved model mechanisms that better reflects the behavior of drought-tolerant crops under varying environmental stressors. The proposed machine learning coupling approach represents a significant advance in accurately estimating key variables such as grain conversion efficiency and water use efficiency (WUE) in aerobic rice.

Future work should focus on advancing multiscale modeling to improve the representation of crop-environment interactions. Technological advancements will be essential for enhancing model precision and capturing complex stress responses. Integrating machine learning and multiscale measurement systems into mechanistic modeling offers promising pathways for optimizing resource use in agricultural systems.

## Acknowledgements

The authors express their deep gratitude to the UMR AGAP Institute (Genetic Improvement and Adaptation of Mediterranean and Tropical Plants) and the School of Engineering at Javeriana University for their support and for granting access to
research facilities. They also extend thanks to CIRAD for providing a Ph.D. scholarship that significantly contributed to this work. The authors sincerely appreciate the valuable contributions of Myriam Adam and Maria Camila Rebolledo in formulating the research project, assisting and supporting crop model applications, and supervising this work. Special acknowledgment is extended to Edward Gerardeaux for supplying crop parameters and observational data for the rice variety NERICA 4, as detailed in Gerardeaux et al. (2021).

## Funding

This research was funded by the Agropolis Fondation through the CropModAdapt project (Contract No. 2201-026) and the ClimBeR initiative - France-CGIAR action plan on climate change (ICARDA Agreement No. 200303).

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