Improving Wheat Yield Prediction with Multi-Source Remote Sensing Data and Machine Learning in Arid Regions

Abstract

Wheat (Triticum aestivum L.) is one of the world’s primary food crops, and timely and accurate yield prediction is essential for ensuring food security. There has been a growing use of remote sensing, climate data, and their combination to estimate yields, but the optimal indices and time window for wheat yield prediction in arid regions remain unclear. This study was conducted to (1) assess the performance of widely recognized remote sensing indices to predict wheat yield at different growth stages, (2) evaluate the predictive accuracy of different yield predictive machine learning models, (3) determine the appropriate growth period for wheat yield prediction in arid regions, and (4) evaluate the impact of climate parameters on model accuracy. The vegetation indices, widely recognized due to their proven effectiveness, used in this study include the Normalized Difference Vegetation Index (NDVI), the Enhanced Vegetation Index (EVI), and the Atmospheric Resistance Vegetation Index (ARVI). Moreover, four machine learning models, viz. Decision Trees (DTs), Random Forest (RF), Gradient Boosting (GB), and Bagging Trees (BTs), were evaluated to assess their predictive accuracy for wheat yield in the arid region. The whole wheat growth period was divided into three time windows: tillering to grain filling (December 15–March), stem elongation to grain filling (January 15–March), and heading to grain filling (February–March 15). The model was evaluated and developed in the Google Earth Engine (GEE), combining climate and remote sensing data. The results showed that the RF model with ARVI could accurately predict wheat yield at the grain filling and the maturity stages in arid regions with an R² > 0.75 and yield error of less than 10%. The grain filling stage was identified as the optimal prediction window for wheat yield in arid regions. While RF with ARVI delivered the best results, GB with EVI showed slightly lower precision but still outperformed other models. It is concluded that combining multisource data and machine learning models is a promising approach for wheat yield prediction in arid regions.

1. Introduction

Wheat (Triticum aestivum L.) is one of the most important staple crops globally, providing food security and economic stability for millions of people [1]. The worldwide agricultural sector consumes over 70% of freshwater [2]. In order to fulfill the future food demands by the year 2050, it is necessary to increase food production by 60% in industrialized nations and by 100% in emerging ones [3]. In recent decades, human activities and climate change have caused a decline in water resources, putting the earth’s ability to sustain itself under extreme strain [4,5]. The combination of extended periods of drought and a growing need for agricultural products is causing water shortages and a lack of available area for farming, ultimately endangering food production. Wheat is a highly important and productive cereal crop and a major food source in many developing countries, including Pakistan, which ranks in the top ten largest producers of wheat in the world [6]. Wheat serves as a major source of calories and protein for the global population [7,8]. In Pakistan, wheat is grown across diverse climatic regions, but the arid and semi-arid regions, particularly in the southern and western parts of the country, are becoming increasingly important for wheat production [9]. Precise crop productivity predictions in advance are crucial for the functioning of the grain circulation market, the prevention of famines, and the maintenance of food security [10,11]. Early prediction of crop yield helps manage field activities like fertilization, irrigation scheduling, pest control, and harvesting planning, ultimately improving resource utilization and reducing environmental impacts [12]. Pakistan produces about 3.2% of the world’s wheat, an amount which translates to an estimated 25.2 to 28.8 million tons annually, and Bahawalnagar is one of the top wheat-producing districts in Pakistan [13]. The assessment of wheat production in Bahawalnagar must be conducted promptly and accurately due to its significant influence on agricultural progress and regional food security.

Empirical statistical models and process-oriented crop growth models have been utilized by the majority of researchers over the past few decades in order to enhance agricultural productivity predictions [14,15]. Traditional statistical models use regression equations to empirically predict crop yield by linking weather parameters like temperature, precipitation, and solar radiation with recorded yields at different times and places [16,17]. The regression equations show the impact of climate on crop yield; however, their explanatory capacity remains debated. These models have limited spatial generalization, making them difficult to apply to wider regions. Process-based crop models, such as the Decision Support System for Agrotechnology Transfer (DSSAT) developed at the University of Florida, the Agricultural Production Systems Simulator (APSIM) created by the Agricultural Production Systems Research Unit in Australia, and the Modeling Crop Water and Land Allocation (MCWLA) from the Chinese Academy of Sciences, are widely used to simulate and predict crop yield [18,19,20]. These models can reliably simulate agricultural yield but require a lot of parameters from climate variables, fertilizers, irrigations, soil, and hydrological factors. Running the models with these inputs is time consuming, expensive, and difficult to scale up or deploy in a developing nation [21,22,23]. Arid regions require models that overcome the limitations of linear assumptions together with constrained spatial generalization to accurately model nonlinear remote sensing and climate–crop-yield relationships [24]. Process-based modeling requires large amounts of soil information, hydrological descriptions, and management data, all of which is typically unavailable for arid and developing regions, impeding the expansion potential [25,26]. ML can use noisy multisource data such as remote sensing and climate data to develop nonlinear models that require minimal initial assumptions [27]. The optimal solution for predicting wheat yields in arid regions comes from ML because of its efficient computation alongside scalability features and the ability to process spatiotemporal patterns.

Remote sensing technology has emerged as a promising tool for improving the accuracy and timeliness of crop yield predictions by providing spatial data on vegetation health and environmental factors, with resolution varying depending on the platform used, such as high-altitude or low-altitude remote sensing [28]. Climate factors are the key inputs for the two crop modeling techniques. Increased vegetation growth status indicators like the Normalized Difference Vegetation Index (NDVI), the Enhanced Vegetation Index (EVI), and the Atmospheric Resistance Vegetation Index (ARVI) can improve crop yield estimates [29,30]. These indices are available at longer temporal and larger spatial resolutions due to rapid remote sensing progression [31]. Machine learning excels in data mining and agricultural studies, classifying crop types and predicting yields [32,33]. Crop productivity is influenced by various factors that change over time and across different geographical locations. The effective management of such multidimensional data ensures reliable and robust analysis [34]. Machine learning can be effectively utilized to estimate crop yield by using remote sensing data, resulting in improved accuracy and efficiency of the models [35,36]. Recent studies have increasingly focused on integrating multisource remote sensing data with machine learning models for wheat yield prediction. However, there appears to be limited research specifically addressing the application of these integrated approaches to arid regions.

Most studies to date have primarily focused on single remote sensing indices, such as NDVI, for screening vegetation health and predicting yields [37]. NDVI has been well utilized in crop yield prediction [38], without explicitly considering the vegetation structure, climate extremes, and soil moisture, all of which are critical in arid areas [38]. Although several studies have used remote sensing and meteorological data to estimate winter wheat yields in wet locations, similar techniques face substantial problems in dry areas. High atmospheric interference, particularly frequent dust storms, and minimal plant cover make accurate vegetation index retrieval difficult in arid regions [39]. Furthermore, the geographical variety of dry environments produces variances in crop development patterns, making it difficult to determine which growth stage time frame is optimum for yield estimation [40]. These constraints highlight the need for an optimal prediction framework that tackles these region-specific difficulties, prompting the creation of a more robust and accurate wheat yield forecast model. Also, to date, the impact of combining multiple remote sensing indices, such as the EVI and the ARVI, with climate data and machine learning approaches is still not well studied in arid regions. Additionally, there are a limited number of studies that indicate the optimal time frame for crop yield prediction in arid regions [41].

Predicting crop yield on a wider spatial scale typically necessitates a substantial volume of data and intricate data manipulation, both of which imply significant expenses to obtain and process extensive datasets. Fortunately, Google Earth Engine (GEE), a free, cloud-based geospatial computing platform developed by Google, is available for large-scale environmental data analysis and processing. This platform enables the processing of extremely large datasets, often at the petabyte level, to analyze and visualize geospatial data [42,43,44]. The primary objective of this study is to develop a predictive model for wheat yield in arid regions by combining multisource remote sensing data with advanced machine learning techniques. The specific objectives are to (1) assess the performance of multiple remote sensing indices (NDVI, EVI, ARVI) to predict wheat yield at different growth stages, (2) evaluate the predictive accuracy of four machine learning models, (3) determine the appropriate time frame during wheat growth season for yield prediction in arid regions, and (4) evaluate the impact of climate parameters on model accuracy. Utilizing GEE’s extensive computing capabilities for large-scale data analysis, all the data were preprocessed to extract pertinent features before being used to train and assess the performance of the chosen machine learning models. This method offers a strong foundation for predicting wheat production in dry locations by enabling an integrated evaluation of climate and remote sensing data.

2. Materials and Methods

2.1. Description of the Study Area

The region selected for this study comprises the Bahawalnagar District of the Punjab Province in Pakistan (30.36°N latitude and 72.48°E longitude), with an area of 8878 square kilometers (Figure 1). The selected region is an arid region with varying temperatures and rainfall [45]. Summer temperatures often exceed 45 °C, with cooler winters having temperatures ranging between 5 °C and 20 °C. Rainfall is sparse, averaging around 150–250 mm annually, with most precipitation occurring during the monsoon season from June to September, thus being insufficient for the needs of crops without supplemental irrigation. The district’s agricultural activities are largely dependent on irrigation, with water sourced primarily from the Sutlej River and canal irrigation systems. Wheat and cotton are major crops of the selected region. Holding the status of Pakistan’s top wheat producers and its representative arid climate, the region of Bahawalnagar is an ideal location for this research. The growing season of wheat is nearly five months in duration, from the start of November to early or mid-April of the following year.

2.2. Data Sources

This study utilized several data sources from 2013 to 2023 to delineate wheat crop regions and assess the yield in the Bahawalnagar District. Initially, all data were resampled to a uniform spatial resolution of 10 × 10 m and a temporal resolution of one month. Subsequently, all variables were further obscured according to the wheat cultivation regions. Data processing was mostly conducted using Google Collab, the GEE platform developed by Google LLC, CA, USA, and ArcGIS, developed by the Environmental Systems Research Institute (Esri), CA, USA. The distribution of the utilized variables is illustrated in Figure 2 and examined in detail below.

2.2.1. Ground Truth Data

A multidimensional approach was used to produce a complete ground truth dataset comprising crop type information. Geospatial data were obtained by field surveys with GPS units, which recorded geographical coordinates for accurate spatial reference. Crop management areas were identified and captured using historical true-color satellite images. Field surveys were conducted over eleven years (2013–2023), complemented by conversations with local farmers to learn about previous crop management approaches. This method produced a strong ground truth dataset of 300–400 data points per crop each year, reflecting wheat and cotton farming areas throughout the Bahawalnagar District.

2.2.2. Remote Sensing Data

Wheat planting area classification and yield estimation were carried out using remote sensing data from the Landsat 8 Operational Land Imager (OLI) and the Sentinel-2 Multispectral Instrument (MSI). Landsat 8 OLI data (2013–2014) and Sentinel-2 MSI data (2015–2023) yielded spatial resolutions of 30 and 10 m, respectively. To ensure the data’s dependability and precision, a variety of preprocessing procedures were implemented, including atmospheric and geometric corrections, and a cloud cover filter was developed using the CFMask and QA60 algorithm [46]. The CFMask technique was used to remove clouds from Landsat 8 OLI and QA60 from the Sentinel-2 MSI data, ensuring the correct surface reflectance. In addition, atmospheric correction was conducted using LaSRC for Landsat 8 and Sen2Cor for Sentinel-2, and a geometric correction was implemented within the study area boundary to achieve an exact image alignment. GEE was used to access and process the data, taking advantage of its huge remote sensing datasets and computational capabilities to process and analyze large amounts of data efficiently.

2.2.3. Climate Data

Climate variables, such as temperature and precipitation, are the key drivers of crop productivity [47]. Extreme temperatures and droughts have a negative influence on crop growth in the context of climate change [48]. Climatic variables for crop yield estimation, including monthly maximum temperature (Tmax), minimum temperature (Tmin), and downward solar surface shortwave radiation (Srad), from the Terra Climate dataset were selected. The Terra Climate dataset is a high-resolution global climate dataset providing monthly climate and hydrological variables at a spatial resolution of approximately 4 km, designed for use in terrestrial modeling and monitoring [49].

2.2.4. Wheat Yield Data

Wheat yield data, in kilograms per hectare (kg ha⁻¹), were collected from the Crop Reporting Services (CRS) of the Agriculture Department, Government of Punjab, Pakistan, from 2013 to 2023. A thorough statistical analysis was performed to confirm the data’s trustworthiness and robustness. To ensure the integrity and correctness of the dataset, an outlier detection and removal technique with a statistical criterion of ±3SD to evaluate observations was employed [50]. Yield values beyond this range were excluded from the analysis.

2.3. Yield Estimation

For wheat yield estimation in the study region, four distinct machine learning models were employed, viz. Random Forest (RF), Bagging Trees (BTs), Gradient Boosting (GB), and Decision Trees (DTs). These models were selected based on their proven ability to handle high-dimensional data, robustness to noise, and suitability for complex regression tasks like crop yield prediction. While other models exist, these were prioritized due to their performance in prior studies and their adaptability to varying environmental and phenological conditions in arid regions. To ensure a robust and reliable model performance, the dataset was divided into two subsets. The models were trained on 80% of the data and tested on 20% of the data. The model underwent training using data spanning from 2013 to 2020. It was subsequently tested on data from 2021 and 2022 and, finally, employed to forecast the yield for 2023. The model exhibiting the greatest coefficient of determination (R²) and the smallest Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) was selected as the optimal one. The categorization of wheat was conducted using supervised classification, where 80% of randomly selected training points were employed, and the remaining 20% were used to assess the accuracy of the classification. The workflow overview depicts the sequential process of data preprocessing, feature selection, model training, evaluation, and the ultimate selection of the best model and most relevant features for yield prediction. Figure 3, below, shows the workflow adopted in this study for crop classification and wheat yield prediction. All the processes were carried out in GEE, including extracting features (NDVI, ARVI, EVI, and climatic variables), training the model, and evaluating and predicting wheat yield using machine learning models.

Table 1

Description of the vegetation indices used in this study.

Feature	Formulation	References
Normalized Difference Vegetation Index (NDVI)	(NIR − R)/(NIR + R)	[51]
Enhanced Vegetation Index (EVI)	EVI = G × ((NIR − RED)/(NIR + C1 × RED − C2 × BLUE + L))	[52]
Atmospheric Resistance Vegetation Index (ARVI)	(NIR − (2 × R − B))/(NIR − (2 × R − B))	[53]

2.3.1. Machine Learning Methods for Predicting Crop Yield

In this study, we focused on widely recognized vegetation indices, i.e., NDVI, EVI, and ARVI (Table 1), based on previous studies that revealed these indices to be highly effective for wheat yield prediction, particularly for winter and spring wheat [54,55,56]. The primary aim was to evaluate which of these indices would yield the most accurate results in the study area. Although numerous other vegetation indices exist, our selection was due to their proven effectiveness in capturing crop health and productivity in arid regions, and their relevance to wheat yield estimation. We incorporated the climatic variables of maximum and minimum temperatures and solar radiation into our analysis. These variables were identified as the most influential factors affecting wheat yield in the study region, based on data provided by the district extension department. Given the region’s dependency on canal irrigation, which ensures a relatively stable water supply, and the minimal variability in precipitation over the study period, parameters such as rainfall and drought indices were considered less critical for yield estimation. Instead, greater emphasis was placed on factors like temperature and solar radiation, both of which have a more direct and significant impact on wheat growth and yield in the study area. While vegetation indices are capable of capturing stress conditions such as drought, our focus on temperature and solar radiation reflects their stronger direct correlation with wheat yield in this specific context. This region is flat, with minimal variation in terrain elevation.

We applied four advanced machine learning algorithms, i.e., RF, DTs, BTs, and GB, and evaluated their performance across three vegetation indices (NDVI, EVI, ARVI) and multiple climate parameters. This comprehensive approach allowed for a robust comparison of the models and indices, ensuring a thorough assessment of their predictive capabilities for wheat yield estimation in varying environmental conditions. The model achieving the highest precision was ultimately selected for yield estimation.

DTs is a nonlinear model used for classification and regression [57]. It creates a hierarchical structure with root, internal, and leaf nodes and split features to forecast outcomes. DTs is resilient to noise, nonparametric, and interpretable, making it appropriate for crop yield prediction [58].

RF is an ensembled method that creates numerous DTSs using randomly selected characteristics and data points [59]. It reduces overfitting and manages high-dimensional data to improve model accuracy and interpretability [60].

GB creates a set of weak models, often DTs, by repairing flaws in earlier models [61]. It iterates to minimize the loss function, producing a robust model that is resistant to overfitting, provided that proper learning rates and iterations are used [62].

BTs, or bootstrap aggregating trees, improve DTs’ stability and accuracy by generating bootstrapped data subsets and aggregating their predictions [62]. This technique decreases variance, prevents overfitting, and enables parallel processing, laying the groundwork for more sophisticated algorithms such as RF [63].

The RF, BT, GB, and DT models were chosen for their robustness, interpretability, and ability to deal with nonlinear connections and noisy data in big datasets. These models are computationally more efficient in GEE than neural networks and support vector machines (SVMs), both of which need significant processing power and parameter adjustment [64]. Previous research has demonstrated their improved performance in predicting agricultural production, particularly when incorporating multiple-source remote sensing and climatic data.

2.3.2. Optimal Wheat Training Time for Yield Estimation

Accurate wheat yield prediction in arid regions requires finding the optimal time window at which models should be trained, since different crop developmental stages have different contributing information for yielding [65]. To assess the optimal training period for wheat yield prediction in the Bahawalnagar District, three distinct time windows were tested, each corresponding to critical growth stages of wheat: (1) December to March 15, covering the Tillering (T) stage through to Grain Filling (GF); (2) January to March 15, spanning the Stem Elongation (SE) stage to GF; and (3) February to March 15, focusing on the Heading (HD) stage through to GF, as shown in Figure 4 below. During these important wheat phenological phases, environmental and physiological variables have a substantial impact on yield formation. Early phases, such as tillering and stem elongation, govern vegetative development and biomass buildup, both of which are critical for yield potential. The transition to the grain filling stage is essential, since it immediately influences grain quantity and size, making it a solid predictor of eventual yield results. Identifying the best time frame throughout these phases improves forecast accuracy by capturing important growth dynamics and climatic interactions. We evaluated these different time windows to know which period would offer the most reliable features for yield prediction in this arid region because of the temporal change of weather and other factors such as humidity. This time window for wheat varies across regions due to differences in climate, topography, and agronomic practices. Therefore, it is essential to select these time windows based on the local crop calendar, which reflects region-specific phenological stages and environmental conditions.

2.3.3. Model Evaluation for Yield Estimation

We partitioned the dataset into 80% for training and 20% for testing, aligning with standard practices in machine learning to ensure robust model evaluation. To assess the model’s performance, we employed evaluation metrics. Three primary metrics were utilized to evaluate the effectiveness of the machine learning models: R², RMSE, and MAE [66], all of which can be calculated by the equations given below. The MAE metric quantifies the average absolute differences between predicted and actual yields, providing insights into the model’s overall prediction accuracy. The use of MAE is prevalent in yield estimation studies, as it offers a straightforward interpretation of prediction errors. RMSE measures the square root of the average squared differences between predicted and actual yields, placing greater emphasis on larger errors. This metric is particularly useful in agricultural studies, where larger deviations can have significant implications. R² indicates the proportion of variance in the actual yields that is predictable from the model’s predictions, serving as a measure of the model’s explanatory power. High R² values suggest that the model effectively captures the underlying patterns in the data.

(1)${\mathrm{R}}^2={\displaystyle \frac{{({{\displaystyle \sum }}_{i=1}^{\mathrm{n}}\left(y_i-{\overline{y}}_i\right)\left(f_i-{\overline{f}}_i\right))}^2}{{{\displaystyle \sum }}_{i=1}^n{\left(y_i-{\overline{y}}_i\right)}^2 {{\displaystyle \sum }}_{i=1}^n{\left(f_i-{\overline{f}}_i\right)}^2}}$

(2)$RMSE=\sqrt{{\displaystyle \frac{1}{n}}{{\displaystyle \sum }}_{i=1}^n{\left(y_i-{\overline{f}}_i\right)}^2}$

(3)$MAE={\displaystyle \frac{1}{n}}{{\displaystyle \sum }}_{i=1}^n\left|y_i-{\overline{f}}_i\right|$

where n is the sample count, $y_i$ is the observed wheat yield, ${\overline{y}}_i$ is the mean value, and $f_i$ is the predicted winter wheat yield, while ${\overline{f}}_i$ is the mean value. Through a comprehensive analysis of these metrics across all four models, the model exhibiting the highest generalization to unknown data and providing the most precise wheat yield forecasts for Bahawalnagar was selected. Cross-validation ensures that the chosen model can identify underlying data patterns without merely memorizing specifics, while evaluation metrics provide a quantitative assessment of model performance using indices extracted from satellite imagery (NDVI, ARVI, and EVI).

3. Results

3.1. Crop Classification

The wheat classification for the Bahawalnagar District from 2013 to 2023 was performed using the GEE platform, with the Random Forest (RF) model as the primary classification algorithm. While RF was the most effective method, other machine learning models were also tested for comparison to ensure the robustness and reliability of the results. Two classes were defined for the classification: wheat and others. The training points that gave the classifier model a spectral signature for those data were divided into two groups: 80% for training and 20% for testing. During testing, this categorization’s producer accuracy was 87%. The spatial distribution of wheat for the years 2013, 2018, and 2023 is illustrated in Figure 5. The classification maps in Figure 5 reveal a substantial increase in the wheat cultivation area over the decade. In 2013, the area under wheat cultivation was 133,747 hectares. By 2018, this area had increased to 153,071 hectares, and, by 2023, it had reached 180,146 hectares. This growth trend indicates an expansion in wheat farming practices within the district. The bar plot in Figure 6 further elucidates this trend. From 2013 to 2023, the area under wheat cultivation shows a consistent upward trajectory, with minor annual fluctuations. For instance, a slight decrease in the cultivated area was observed in 2019, where it dropped to 146,907 hectares from the previous year’s 153,071 hectares. However, the overall trend remained positive, with significant increases in subsequent years. Quantitatively, the wheat cultivation area grew by approximately 34.7% over the ten years, from 133,747 hectares in 2013 to 180,146 hectares in 2023. The most notable increase occurred between 2019 and 2020, with the area jumping from 146,907 hectares to 164,714 hectares, an increase of 17,807 hectares or approximately 12.1% by area coverage. This substantial rise can be attributed to improvements in agricultural practices, better irrigation facilities, and potentially favorable government policies supporting wheat cultivation.

3.2. Yield Estimation

3.2.1. Model Performance for Estimating Yields

The different models’ performance was assessed based on the December–March 15 training period (Figure 7). Specifically, the R² values for NDVI, ARVI, and EVI were 0.59, 0.62, and 0.54, respectively, for the BT model. RF produced slightly lower R² values of 0.57 for NDVI, 0.60 for ARVI, and 0.53 for EVI, showing a strong ability to explain yield variations, although somewhat less effectively than BTs. Conversely, DT models demonstrated the lowest R² values, indicating that they were the least successful in explaining yield variance across all indices. Lower values of RMSE indicate a lower model error in terms of average magnitude. The lowest RMSE scores were achieved by RF, suggesting higher accuracy in yield estimates. For example, the RMSE for RF was 1852.65 kg ha⁻¹ for NDVI, 1556.1 kg ha⁻¹ for ARVI, and 1704.37 kg ha⁻¹ for EVI. BTs followed closely, with RMSE values of 2163.87 kg ha⁻¹ for NDVI, 1867.32 kg ha⁻¹ for ARVI, and 2015.59 kg ha⁻¹ for EVI. GB and DT models performed relatively worse, resulting in higher RMSE values, which reflected less accurate yield estimates. Regarding MAE, RF scored the lowest MAE across all indices: 1052.37 kg ha⁻¹ for NDVI, 755.82 kg ha⁻¹ for ARVI, and 904.09 kg ha⁻¹ for EVI. BTs ranked second in terms of accuracy, with MAE values of 1185.75 kg ha⁻¹, 889.2 kg ha⁻¹, and 1037.47 kg ha⁻¹ for NDVI, ARVI, and EVI, respectively. GB and DT models had higher MAE scores, indicating less precise estimates. The results indicate that RF and BTs were the best-performing models for estimating wheat yields in this arid region, consistently outperforming DTs and GB across all indices.

Then model performance was again tested for the growth period from January to March in the arid region, and the evaluation metrics of R², RMSE, and MAE are shown in Figure 8. Among all vegetation indices, BTs performed the best, followed by RF during this growth period. BTs achieved R² values of 0.71, 0.75, and 0.65 using NDVI, ARVI, and EVI, respectively, indicating an excellent ability to explain yield variations. RF performed similarly well, with R² values of 0.68 for NDVI, 0.72 for ARVI, and 0.63 for EVI. Conversely, DT and GB models had the lowest R² values using NDVI and ARVI indices. In terms of RMSE, RF achieved the lowest values, resulting in the most accurate estimates. Specifically, RF had RMSE values of 1370.92 kg ha⁻¹ for NDVI, 1089.27 kg ha⁻¹ for ARVI, and 1230.10 kg ha⁻¹ for EVI, indicating high accuracy in yield prediction. BTs followed with RMSE values of 1548.76 kg ha⁻¹ for NDVI, 1267.11 kg ha⁻¹ for ARVI, and 1407.94 kg ha⁻¹ for EVI, demonstrating slightly larger errors than those of the RF models. DT and GB models had higher RMSE values, indicating a poorer performance in yield estimation accuracy. Regarding MAE, RF emerged as the top performer with the lowest MAE values across all indices: 859.63 kg ha⁻¹ for NDVI, 577.98 kg ha⁻¹ for ARVI, and 718.81 kg ha⁻¹ for EVI. BTs had slightly higher MAE values of 948.55 kg ha⁻¹ for NDVI, 666.90 kg ha⁻¹ for ARVI, and 807.73 kg ha⁻¹ for EVI. DT and GB models recorded even higher MAE scores, demonstrating their relatively lower accuracy in yield estimation. These results indicate that RF and BTs were the most effective models for predicting wheat yields during the growth period from January to March. RF consistently prevailed over other models in all evaluation metrics, generating yield estimates with high levels of accuracy and consistency.

Finally, the performance of the models for predicting wheat yields during the arid region’s February to March growth period was evaluated, as shown in Figure 9. RF achieved the highest R² values across all vegetation indices: 0.78 for NDVI, 0.82 for ARVI, and 0.72 for EVI. Bagging Trees (BTs) also delivered good results, with R² values of 0.77 for NDVI, 0.81 for ARVI, and 0.70 for EVI, only slightly behind RF. The R² values of Decision Trees (DTs) ranged from 0.40 (NDVI) to 0.58 (EVI), and Gradient Boosting (GB) performed similarly, with R² values of 0.37 (NDVI) to 0.74 (EVI), indicating a lower success in explaining yield variability. RF produced the lowest RMSE values, indicating the highest accuracy in yield predictions. Specifically, the RMSE values for RF were 889.2 kg ha⁻¹ for NDVI, 622.44 kg ha⁻¹ for ARVI, and 755.82 kg ha⁻¹ for EVI. BTs followed closely, with RMSE values of 933.66 kg ha⁻¹, 666.9 kg ha⁻¹, and 800.28 kg ha⁻¹ for NDVI, ARVI, and EVI, respectively. DT and GB models had higher RMSE values, indicating less accurate predictions. In terms of MAE, RF, again, performed the best, with the lowest values of 666.9 kg ha⁻¹ for NDVI, 400.14 kg ha⁻¹ for ARVI, and 533.52 kg ha⁻¹ for EVI. BTs followed with slightly higher MAE values of 711.36 kg ha⁻¹, 444.6 kg ha⁻¹, and 577.98 kg ha⁻¹ for NDVI, ARVI, and EVI, respectively. The MAE values for DT and GB models were higher, indicating greater deviations from the observed yields. The results demonstrated the superior performance of RF and BTs for yield prediction during the February to March growth period in the arid region. RF consistently provided the most accurate predictions across all metrics (R², RMSE, and MAE) and for all vegetation indices. While DT and GB models were capable of providing yield estimates, their accuracy was significantly lower. These findings highlight the importance of model selection, with RF emerging as the most effective model for estimating wheat yields in arid agricultural regions during this growth period.

Figure 10 illustrates the scatter plot of the estimated and observed wheat yield, generated using the RF model with ARVI as the vegetation index during the February to March 15 growth period. The plot features the best-fit line (red), the 1:1 line (green dashed), and a mean deviation of 100.36 kg/ha, highlighting the model’s performance with an R² value of 0.82. A clear linear relationship is shown when comparing the observed versus the predicted yield. This indicates that the RF model effectively predicted wheat yield in this period. The points on the plot are closely aligned with the 1:1 line, indicating that applying the RF model with the ARVI index could successfully replicate the trends in wheat growth and estimate the yields reliably. The importance of predictor variables for wheat yield prediction with the RF model during the February to March 15th growth period under the arid environment is shown in Figure 11. The feature importance values were derived using the mean decrease in accuracy (permutation importance) and the mean decrease in impurity (Gini importance). The importance of critical predictors related to wheat yield predictions in this environment followed the order of ARVI > Tmax > Srad > Tmin. ARVI was more critical for wheat yield prediction in arid regions than EVI and NDVI. It was designed to minimize atmospheric effects, such as aerosol and cloud interference, which can be more pronounced in arid areas. As a result, ARVI’s robustness against atmospheric noise gave it an edge over NDVI for accurate vegetation monitoring. In arid environments, vegetation is often subjected to water stress and other environmental factors that can significantly affect crop growth. ARVI is more sensitive to these stresses than NDVI because it accounts for atmospheric interference that can mask the true vegetation conditions.

3.2.2. Spatial Patterns of Wheat Yield Predicted

The spatial distribution of observed and predicted wheat yield (in kg ha⁻¹) for the 2023 growth season of Bahawalnagar is depicted in Figure 12. The comparison of observed and predicted yield maps revealed a strong alignment regarding the distribution pattern of the yield, demonstrating that the RF model could predict the spatial variability in wheat yield across the tehsils of Bahawalnagar. Spatial heterogeneity in wheat yield in the Bahawalnagar District was apparent and related to local variation in soil properties, water availability, and microclimatic conditions. Among all the tehsils, Haroonabad tehsil had the highest predicted yield due to better conditions for cultivating wheat, including better water management and soil fertility. However, Chishtian and Minchinabad showed relatively lower average yields than the other tehsils, possibly because the conditions in terms of availability of water or soil characteristics were not that favorable. Moreover, the spatial yield patterns predicted by the RF model reflected the yield variability observed in the district well. Consequently, this spatial distribution of predicted yields could be important for guiding targeted agricultural interventions (e.g., precision irrigation or fertilization strategies) in areas where yields were predicted to be low. The overall results confirmed the predictive capability of the RF model, together with the ARVI, to predict wheat yield across a broad spatial extent.

4. Discussion

4.1. Arid Region Yield Estimation Model Performance with Different Indices

Four machine learning models (RF, GB, DTs, and BTs) were compared to predict wheat yield in an arid region based on three different remote sensing indices (NDVI, EVI, and ARVI). The evaluation was based on three different temporal windows: T-GF, SE-GF, and HD-GF. The RF model demonstrated the best performance across all other models in the growth period of February–March. For instance, when using the ARVI index in the February–March window, the RF model achieved an R² value of 0.82, which was substantially higher than the R² values of 0.72 for the NDVI and 0.76 for the EVI index. Furthermore, the RF model had an RMSE of 0.12 for ARVI which is low enough for practical application in yield prediction and management. These results indicate that ARVI is a better and more reliable predictor of wheat yield in this arid region [67]. The MAE for ARVI was the lowest. The RF model showed better predictive accuracy consistently for all the indices, strengthening its applicability in yield estimation for areas exhibiting diversified environmental factors aligned with previous findings [68,69].

In arid regions, where dust and haze severely interfere in the atmosphere, the performance differences of NDVI, EVI, and ARVI are particularly meaningful. Although NDVI is highly utilized, it is not always reliable in arid environments because of its sensitivity to atmospheric conditions [70]. This limitation was also reflected in this study, where NDVI exhibited a lower correlation with wheat yield than ARVI, especially in the early growth stages (December–January). In all evaluated temporal windows, the performance of the ARVI index, which was developed to minimize atmospheric effects, especially in aerosol interference areas, was better than that of the NDVI. This finding is consistent with previous studies that suggest that areas with high atmospheric particle concentrations—which are typical of arid and semi-arid regions like Bahawalnagar—provide an enhanced ARVI performance [71,72]. Furthermore, EVI also performed well, but was worse in terms of prediction accuracy than ARVI. Because EVI is less sensitive to atmospheric conditions [73], it has previously been demonstrated to be advantageous for monitoring vegetation over large areas. However, the added sensitivity of ARVI to vegetation stress gave a more reliable yield estimation tool, especially for the post-flowering period (February–March) when the effects of water stress and soil fertility limitation are most pronounced. We compared the predicted yields from our model to the observed yields from field sites randomly selected in the Bahawalnagar District to further assess model reliability. A scatter plot (Figure 10) of predicted versus observed yields was plotted, and a correlation was observed with an R² of 0.80 for the RF model with ARVI, showing that the model was statistically sound and performed efficiently for practical use. This result conforms to a previous study for wheat yield prediction [65].

The other machine learning models, like DT and GB models, had an R² value of 0.60 for DTs with NDVI and 0.65 for GB with EVI. The RMSE and MAE values of these models indicated that these models were not capable of capturing the complex, nonlinear relationship between vegetation indices and arid region wheat yields. This result is consistent with previous findings that simpler machine learning models, such as DTs, are poorly suited for crop yield prediction, as they have the propensity to overfit or underfit the data, especially in environments with strong interactions between variables [74]. Although the BT model outperformed both DTs and GB, its R² of 0.74 for ARVI and 0.68 for NDVI was still behind that of RF, suggesting that ensemble models helped but did not outperform RF. The bagging’s capacity to reduce variance by bootstrapping was not good enough to outperform the RF model in capturing the variability in wheat yield data. These results are consistent with the literature and corroborate the usefulness of machine learning and remote sensing technologies to enhance crop management and food security in water-scarce environments [75,76,77]. While previous studies using vegetation indices (e.g., NDVI, EVI) and machine learning models have achieved moderate wheat yield prediction accuracy in arid regions, their reliability was compromised by atmospheric interference (e.g., aerosols, dust) and temporal sensitivity during critical growth stages [78,79]. This study advanced the field by combining the RF model with the ARVI, which greatly reduced air distortions typical in arid settings and resulted in a stronger performance. In the future, the work could be extended to incorporate more remote sensing indices, climatic data, and soil moisture information to refine future yield prediction models in such areas, which involve diverse agricultural challenges for higher accuracy of forecasts. These advancements will be significant for optimizing farming practices and improving the use efficiency of resources in arid and semi-arid regions.

4.2. Yield Estimation Model Performance in Different Time Windows

Wheat enters an early growth phase spanning December in the study region, characterized by vegetation indices relating to plant establishment and early canopy development. The RF and BT models worked reasonably well in this window, but not as strongly as during later growth phases. The R² value of the BT model using ARVI was 0.62, and the R² value of the RF model using ARVI was 0.60. However, this was a moderate performance relative to the other indices. The BTs with ARVI had an RMSE of 1867.32 kg ha⁻¹, and the RF with ARVI had an RMSE of 1556.1 kg ha⁻¹, which was a comparatively higher error for the predictions, considering the role of early-stage soil moisture variations and atmospheric circumstances. Also, as compared to the DT model, having an R² of 0.50 and an RMSE of 2889.9 kg ha⁻¹, the performance was poor. These results demonstrate the need for models more complex than DTs to capture the intricate relationships between early-stage vegetation indices and wheat yield. The R² for the GB model, 0.45, was barely better but still far behind that of the BT and RF models which achieved R² values of 0.59 and 0.57, respectively.

In the January–March window, the predictive ability of the models improved considerably as the wheat crop shifted into the more important vegetative and reproductive stages (tillering and heading). Using ARVI, the RF model proved to be significantly better than the other models, with an R² of 0.72. The reduced RMSE of 1089.27 kg ha⁻¹ clearly showed a smaller prediction error in this critical growth phase, and this is consistent with previous findings that mid-growth stages are better at predicting the final yield potential and also for crop modeling [80,81]. Alternatively, the predictive accuracy of EVI was improved compared to the NDVI, while the predictive accuracy of the NDVI was still low. This suggests that EVI’s reduced sensitivity to atmospheric interference, especially in the reproductive crop stages, was more reliable for indicating plant health than NDVI in this period [82]. The BT model had a bigger improvement over the December–March window, but still less than RF.

More importantly, the February–March window was critical for the final yield prediction during the grain filling stage, when environmental factors such as water stress and temperature fluctuations are the most critical determinants of yield [83,84]. The time period when yield is most sensitive to water availability and other environmental stress factors is the most informative time for crop yield prediction models. This window, as expected, was the best performer across all models and indices. The performance of the RF model using ARVI was the highest, with an R² of 0.82, explaining 82% of wheat yield variation. An improvement in the accuracy of prediction was marked, as the RMSE decreased to 622.44 kg ha⁻¹. For this model, the MAE was 400.14 kg ha⁻¹, which was much better than that of previous time windows. This is in line with previous studies that report grain filling stages as important grain yield prognostic periods when used in combination with remote sensing [85,86,87]. ARVI turned out to be more effective than NDVI and EVI because of its sensitivity to stress factors (drought or heat) that usually strengthens for the grain filling period [88]. In this window, the BT model performance also improved, with an R² of 0.81 and an RMSE of 666.9 kg ha⁻¹, though still below that of RF which has an advantage in tackling complex, nonlinear interactions of environmental factors affecting wheat yield.

The temporal performance of the models suggests that yield estimation accuracy increased as the wheat crop went through successively later growth stages. During the early growth phase (December–March), predictions were less accurate, probably because this period offers less variation in vegetation cover and environmental stress. The remote sensing indices, however, became more effective at discriminating the water stress, soil conditions, and other climatic factors that determined the final day of the crop at the growth stages when the crop reached the reproductive and grain filling stages (January–March and February–March). A significant finding in this study is that the RF model had a superior predictive performance in the February–March window, which corresponds to the grain filling and the maturity stages of the wheat crop. RF’s high performance (particularly with ARVI) indicates that RF could capture complex interactions between the environmental variables and that, therefore, it is a powerful tool to predict wheat yield in water-scarce regions. The temporal performance of the yield estimation models agrees with past research. For example, mid to late stages of growth, including grain filling, are the most reliable timing for remote sensing yield prediction, primarily due to the higher sensitivity of these growth stages to environmental stresses that directly affect yield [89,90]. Arid regions require models that emphasize the reproductive phases of crops, as those phases are the most significant contributors to the final yield outcomes [91,92]. In earlier phases, yield predictions are not accurate, as the early phase depicts slight environmental variation, thus causing the yield prediction process to be potentially false [93].

Previous studies using remote sensing and machine learning for wheat yield prediction in arid regions frequently neglect important development stage specificity, resulting in unsatisfactory accuracy. This study performs a temporal analysis of the model performance, and the results show that the grain filling stage window is the optimal period for wheat yield estimation in arid regions, with the most accurate prediction being achieved by the RF model using ARVI. Late-stage vegetation signals better reflect cumulative environmental constraints (e.g., water scarcity, soil fertility) impacting the final yield. This discovery is consistent with wider crop phenology concepts, but it adds new validation for wheat in arid regions, underlining the significance of temporally tailored remote sensing approaches to improve prediction robustness and limit air influence. These results emphasize the need to consider an appropriate time window in remote-sensing-based yield prediction models and a late growth stage (e.g., grain filling) to ensure the robustness of yield forecasts.

4.3. Uncertainties in the Study

Several sources of uncertainty exist in this study, including uncertainties in the data quality, environmental variability, and agricultural system complexity. Remote sensing indices and climatic variables are the predictors for yield, but also the key sources of uncertainty in remote-sensing-based yield estimation [94]. The spatial and temporal resolution of satellite imagery is a major factor. Relatively low spatial resolutions lack the capacity to detect small spatial variations in crop health and yield potential. Low temporal resolutions lack the capacity to detect small variations in crop health and yield potential over time. Such low resolutions could cause errors of spatial averaging that might decrease the accuracy of yield predictions, particularly in heterogeneous agricultural landscapes. Furthermore, remotely sensed data quality was sometimes poor, due to cloud cover or atmospheric interference. Satellite sensors could be obstructed by clouds, aerosols, and other atmospheric conditions, leaving poor or contaminated data, resulting in gaps in the time series. Methods like cloud masking and data interpolation could reduce problems with the dataset, but they always contribute to some degree of uncertainty [95]. Terra Climate provides essential climatic variables but at a coarser resolution, which might overlook localized environmental heterogeneity. These discrepancies can influence the accuracy of yield predictions, particularly in heterogeneous agricultural systems. Future studies could explore advanced data fusion techniques to harmonize such datasets, thereby reducing uncertainty and improving model reliability.

In this study, the RF and the GB models were strong models, capturing the complex relationships between features and yield outcomes. However, these models have some limitations that may lead to uncertainty. They managed to execute well with nonlinear discoveries but depended on the supposition that crop growth and environmental trends would be constant with time in the next planting periods [96]. However, we show that this assumption did not hold in regions experiencing climatic shifts or extreme weather events, a phenomenon which could result in wrong predictions. Despite their predictive accuracy, explaining the models’ error is not straightforward. For example, if the environmental conditions or feature interactions changed a little but were not well represented in the training data, the predictions could be wrong. However, the lack of transparency could create uncertainty about how the models arrived at their predictions, and how generalizable the predictions are to other regions and time periods. Arid regions are regions with highly variable environmental conditions, including, among others, extreme temperatures, irregular rainfall patterns, and droughts [97]. These variations could lead to large bias in the yield prediction models, especially due to spatial heterogeneity in soil properties, crop growth, and water availability [98]. The model included climatic variables but did not explicitly take soil moisture stress into account, although it could change dramatically over short distances, especially under dry conditions [99]. Integrating soil moisture models with remote sensing data could improve model predictions of yield under such conditions, but also introduce uncertainty with respect to how those models estimate soil moisture.

The temporal dynamics of crop growth was another vital source of uncertainty. Multiple factors, such as planting date, growth duration, and phenological stages, were spaced out over time from year to year and would affect wheat growth [100]. For instance, a delay in the growth period resulting from late rainfall or a long dry spell could impact the crop’s response to climatic factors as growth approached completion. Our study also utilized three yield estimation periods (December to March, January to March, and February to March). However, the time windows identified here characterized distinct crop growth stages and the optimal time window for accurate yield prediction may not be the same in other climatic years. For example, wheat could grow much earlier or later than its average beginnings due to climatic anomalies. In that case, those temporal windows within the study period might not represent the crop yield potential sufficiently, leading to prediction errors. Model uncertainty is inherent in all models, particularly those based on historical data. Machine learning models’ predictions rest on the assumption that the pattern of future environmental conditions is similar to the past. However, historical data may not fully represent extreme events, such as heat waves, unpredictable rainfall patterns, or flooding, a phenomenon which can lead to potential errors in predicting yields in the future under changing climatic conditions. To address some of these concerns, machine learning models might be enhanced by including climate change predictions and seasonal forecasts, increasing their resistance to future climate variability and catastrophic weather occurrences. By addressing these sources of uncertainty, the accuracy of yield estimation models can be further increased, leading to better decision-making tools for farmers in arid regions.

5. Conclusions

This work aims to increase the accuracy of wheat yield estimation in arid regions using Landsat and Sentinel-2 satellites, remote sensing climatic data, and machine learning models. The results indicate that wheat yield predictions within arid environments could be effectively made using climatic variables and vegetation indices, such as NDVI, EVI, and ARVI. Particularly, the optimal input variables and timeframes for prediction accuracy were found to significantly affect the model performance depending on the different indices, time windows, and feature combinations. The results show that varying accuracy in the yield prediction was obtained when NDVI, EVI, and ARVI were used as input features along with climatic variables in the machine learning models. The RF model using ARVI achieved the highest performance with an R² of 0.82, explaining 82% of wheat yield variation during the HD to GF stage, while improving prediction accuracy by reducing the RMSE to 622.44 kg ha⁻¹ and the MAE to 400.14 kg ha⁻¹. The best performance of predictive models presented in this study was obtained for the February–March HD to GF stage time window, coinciding with important crop growth stages, especially the reproductive phase, which is most sensitive to environmental stress during yield formation. Model accuracy depended on temporal variations in crop emergence timing and rainfall patterns, reinforcing the need to align yield prediction windows with crop phenology. An analysis of feature importance showed that climatic variables contributed greatly to the yield prediction. Several sources of uncertainty influencing yield estimation were identified, including data quality issues (e.g., spatial resolution of remote sensing data) and cloud cover. Moreover, uncertainties in predictions could be induced by the inherent limitations of machine learning models themselves, particularly the difficulty of generalizing these models in extreme climatic conditions. To reduce such uncertainties, the study points out the necessity for more granular data, including soil moisture and microclimatic conditions. However, despite these uncertainties, the results of this study demonstrate the promise of remote-sensing-based machine learning models for yield estimation in water-scarce and arid regions, holding great potential for agricultural decision making, resource management, and food security. Future work should aim to enhance data resolution, incorporate more environmental variables, and enhance machine learning models for spatial and temporal intricacies.

Author Contributions

Conceptualization, A.R., M.A.S. and M.Z.; methodology, A.R. and M.A.S.; software, A.R.; validation, M.S. and S.M.; formal analysis, M.A.S. and N.E.M.; resources, M.Z. and M.S.; data curation, A.R. and S.M.; writing—original draft preparation, A.R.; writing—review and editing, Y.M. and Y.H.; supervision, M.A.S. and M.Z. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

The original contributions presented in the study are included in the article; further inquiries can be directed to the corresponding author.

Acknowledgments

We would like to express our sincere thanks to the anonymous reviewers.

Conflicts of Interest

The authors declare no conflicts of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Table

Figure 1. Study area maps of (A) Pakistan, (B) the Punjab province, and (C) the Bahawalnagar District and tehsils.

Figure 2. The distribution of NDVI (A), ARVI (B), EVI (C), Tmax (D), Tmin (E), and Srad (F) for the available data (2013–2023) over a monthly period. Tmax: monthly maximum temperature (°C); Tmin: monthly minimum (°C); Srad: downward surface shortwave radiation (W/m2).

Figure 3. Flowchart of the crop classification and yield estimation in GEE.

Figure 4. Time windows for training wheat yield prediction models in the Bahawalnagar District: (A) December–March 15, (B) January–March 15, and (C) February–March 15.

Figure 5. Spatial distribution of wheat in the Bahawalnagar District for the years 2013, 2018, and 2023.

Figure 6. The trend of wheat cultivation in the Bahawalnagar District from 2013 to 2023 was calculated using satellite imagery. The error bar represents the percentage error between the area calculated by the classifier and the area by the CRS.

Figure 7. R2 (A), RMSE (B), and MAE (C) values of four models for wheat with different indices in the December to March 15 growth periods in the arid region. The error bar shows the percentage error, not the standard error. The top and bottom of the line represent the value plus and minus 15%, respectively.

Figure 8. R2 (A), RMSE (B), and MAE (C) values of four models for wheat yield prediction using different vegetation indices in the January to March 15 growth periods in the arid region. The error bar shows the percentage error, not the standard error. The top and bottom of the line represent the value plus and minus 15%, respectively.

Figure 9. R2 (A), RMSE (B), and MAE (C) values of four models for wheat yield prediction using different vegetation indices in the February to March 15 growth periods in the arid region. The error bar shows the percentage error, not the standard error. The top and bottom of the line represent the value plus and minus 15%, respectively.

Figure 10. A scatter plot showing the correlation between the observed and predicted wheat yield in the Bahawalnagar District using the RF model, with ARVI as the selected index, during the February to March 15 growth period of wheat. The plot includes the best fit line (red), the 1:1 line (green dashed), and the calculated mean deviation (100.36 kg/ha).

Figure 11. The importance of predictor variables for wheat yield prediction using the RF model from February to March 15 in an arid environment.

Figure 12. Spatial distribution of observed and predicted wheat yields (kg ha−1) in 2023 in the Bahawalnagar District. (A) Yield observed in the district, (B) yield predicted by RF. The wheat growth period chosen for projection was from February to March 15th, using ARVI as an index.

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