UAV-based RGB imagery and supervised–unsupervised machine learning for estimating sorghum biomass and grain yield under water and nitrogen stress

Precision agriculture emerged as a key strategy for rational management of water and nutrients amid growing food demand driven by global population expansion. Therefore, timely monitoring of field crops is crucial in maintaining adequate nutrient and water levels in the crop fields. Vegetation indices are increasingly being studied for their use in plant nutrient management and in guiding fertilizer recommendations. However, these indices were not adequately evaluated for nutrient management of crops grown with different water and nitrogen application levels. This study investigated the potential application of RGB imagery from low-cost Unmanned Aerial Vehicles (UAVs), combined with machine learning techniques, for quantifying water and nutrient stress in sorghum [ Sorghum bicolor (L.) Moench] crop performance. The field experimental setup at Prairie View A&M University, located in Southeast Texas, applied four irrigation levels (0, 75, 100, and 125% of irrigation; the 100% irrigation level is a fully irrigated treatment with no water stress) and four nitrogen application rates (0, 90, 180, and 360 kg N ha −1). The RGB images were captured before harvesting the grain sorghum. Image segmentation for filtering sorghum crops from soil and weeds was performed using K-means clustering and a Convolutional Neural Network (CNN). The vegetation indices, including the Green-Red Vegetation Index (GRVI), Green Leaf Index (GLI), and Excess Green Index (ExG), derived from the segmented images were used to predict sorghum grain and biomass yields using multiple linear regression, Partial least squares regression, Ridge regression, and XGBoost. The results indicated that no single model consistently outperformed the others across both segmentation approaches and response variables, suggesting that the predictive information in the RGB indices is meaningful with selected ML approaches. For example, biomass prediction using ridge regression yielded a Pearson correlation coefficient (r) of 0.65 and an RMSE of 0.72 for K-means clustering-derived indices. The models exhibited moderate, stage-specific predictive performance, with no single regression method consistently outperforming the others across both segmentation approaches and response variables. Because imagery was acquired only once during the late reproductive period, the RGB indices primarily reflected canopy condition, maturity, and senescence at that time. The findings demonstrate the feasibility of a low-cost, single-date UAV RGB workflow for late-season sorghum assessment, while emphasizing the need for multi-temporal imagery and independent validation before application to season-long stress diagnosis or operational yield forecasting.

Global food demand is projected to grow by 30%–62% as the population is expected to reach 9.8 billion by 2050 (United Nations, 2017; Kraklow et al., 2025). This increasing food demand places additional pressure on agricultural systems that are already highly vulnerable to climate-related stresses, including drought. Drought is the foremost natural disaster causing agricultural production loss (Veettil et al., 2024b; Veettil et al., 2026). For example, three-fourths of the global harvested area witnessed a production loss of 166 billion U.S. dollars due to severe drought from 1983 to 2009 (Kim et al., 2019). In addition, from 1961 to 2014, droughts resulted in 3.0%–10.4% and 3.1%–12.2% reductions in maize and soybean yields globally (Matiu et al., 2017). Such evidence indicates that future increases in drought frequency and severity may pose serious risks to global agricultural production (Veettil and Mishra, 2020). In addition to water limitation, nutrient deficiency, particularly nitrogen stress, remains a key factor constraining crop growth and yield (Fares et al., 2026; Safian et al., 2022). Thus, developing efficient approaches to monitor crop stress and improve resilience to water and nutrient limitations is critical in the face of a warming climate. Water stress has been shown to reduce leaf area and growth rate, limit dry matter accumulation, and alter biomass partitioning by increasing the root-to-shoot ratio (Wang et al., 2017). Furthermore, crops are often more sensitive to water stress during later developmental stages, emphasizing the need for effective management interventions throughout the crop growth cycle.

Nutrient deficiency limits nutrient absorption in plants, leading to unmet nutrient demand and severely impairing nutrient utilization efficiency (Sun et al., 2024). Nitrogen is an essential nutrient for plants and a crucial component of proteins, which are made up of amino acids (Thapa et al., 2024; Thapa et al., 2025; Veettil et al., 2024a). These amino acids play a vital role in catalyzing chemical reactions and transporting electrons. As a result, nitrogen is present in many major parts of the plant body. Nitrogen deficiency reduces crop dry matter accumulation and impairs annual yield improvement, and phosphorus insufficiency reduces the soil phosphorus levels and causes soil nutrient imbalances (Thuynsma et al., 2014; Li B. et al., 2019). If crops cannot absorb sufficient fertilizer during their growth period, nutrient use efficiency will be significantly reduced, thereby impeding grain yield formation. It is important to note the critical role of nitrogen in improving food quality, increasing photosynthesis, increasing leaf area production and leaf area duration, and increasing net assimilation rate (Leghari et al., 2016).

Currently, AI is playing a significant role in improving crop health through real-time monitoring (Fares et al., 2026). Low-altitude, versatile unmanned aerial vehicles (UAVs) are becoming increasingly popular because of their ability to carry and capture RGB (Red, Blue, Green) and hyper- and multispectral imagery for visual analysis. Many UAV-based studies have been conducted to investigate crop phenotypic variation, including plant height, canopy cover, chlorophyll content, and water- and nutrient-stress symptoms (Chu et al., 2016; Zhou et al., 2020). Although image and analysis accuracy can be improved by using hyperspectral or multispectral cameras, the cost of the entire process exceeds the capacity of a marginal farmer (Osroosh et al., 2018). RGB images provide a high-throughput approach for quantifying vegetation indices by capturing canopy reflectance in the visible red, green, and blue bands, which can be processed to assess plant vigor, greenness, and spatial variability (Li S. et al., 2019; Janani and Jebakumar, 2023). These image-derived indices are widely used in agricultural and environmental studies for non-destructive monitoring of crop growth, stress responses, nutrient status, and overall vegetation health (Gerardo and Lima, 2023).

During the growing season, phenotyping at an earlier stage allows more time to make decisions to improve yield (Varela et al., 2021). However, collecting information repetitively over time requires significant effort and labor. Many studies have evaluated crop yield data from RGB imagery collected on a single-date flight. Recent studies have demonstrated that RGB imagery collected during a single UAV flight can yield acceptable crop-yield predictions when acquired at an appropriate growth stage. For example, Zeng et al. (2021) substantially predicted wheat yield from RGB indices collected at flowering. Ma et al. (2023) showed that CNN models can predict wheat yield directly from single-date RGB images, with limited training samples. Heinemann et al. (2025) found that single-date RGB predictions were most effective during grain filling, although multi-date data generally improved accuracy. These findings indicate that one-time RGB UAV data collection can be a practical and cost-effective approach for predicting crop yield or biomass, provided that flight timing and image-derived features are carefully selected. The relationship between UAV-derived vegetation indices and crop productivity is strongly dependent on image-acquisition timing. Images collected during vegetative growth may capture canopy establishment, leaf-area development, and early responses to water and nitrogen availability. Multi-temporal observations capture complementary physiological information and frequently produce more robust yield predictions than a single observation. Under post-flowering water limitation, susceptible plants can undergo premature senescence, whereas stay-green plants retain photosynthetically active leaf area for longer and may sustain grain filling (Kyratzis et al., 2017; Harris et al., 2007; Prey et al., 2022).

Machine learning models can be applied to predict grain and biomass yields using vegetation indices derived from RGB images, offering a rapid, non-destructive approach to crop monitoring (Zhou et al., 2017). These RGB-based indices capture variations in canopy color, cover, and vigor that are closely associated with plant growth and yield potential. By integrating such indices with machine learning algorithms, yield prediction can be improved through better identification of complex, non-linear relationships between crop traits and final productivity (Prey et al., 2022).

Grain sorghum [ Sorghum bicolor (L.) Moench] is significantly utilized for feed, fuel, construction material, and various industrial applications (Thapa et al., 2025; Anami et al., 2015). Sorghum is drought-resistant, tolerant to waterlogging, and considered a viable substitute for maize in water-scarce environments (Hadebe et al., 2017). Although sorghum is preferred by growers for its tolerance to drought and nutrient deficiencies, many reports indicate that stress conditions can result in more than 50% grain loss compared to optimal growth conditions (Assefa et al., 2010).

Despite increasing interest in UAV-based crop monitoring, three important research gaps remain. Many sorghum remote-sensing studies employ a single image-segmentation or feature-extraction approach, leaving limited evidence on how an unsupervised method such as K-means clustering compares with supervised CNN semantic segmentation when both are applied to consumer-grade UAV RGB imagery. This is important because the two segmentation strategies differ substantially in their training requirements, computational complexity, and capacity to distinguish crop pixels. In addition, relatively few studies have systematically compared multiple linear and nonlinear regression approaches for estimating both sorghum grain yield and aboveground biomass under simultaneous water and nitrogen gradients. Also, a few studies have quantitatively compared multiple linear and nonlinear machine-learning models for estimating both sorghum grain yield and aboveground biomass under combined water and nitrogen stress using only single-date, late-season UAV RGB imagery, and field-based evidence remains limited regarding the use of low-cost, consumer-grade UAV RGB systems to support precision irrigation and nitrogen management in sorghum production under humid subtropical conditions. To address these gaps, this study used a 2-year split-plot field experiment at the Prairie View A&M University Research Farm in Southeast Texas, with four irrigation levels and four nitrogen application rates.

The overarching goal of this study was to investigate the impact of varying irrigation and nitrogen application levels on the sorghum crop using various AI techniques. The specific objectives are (1) to investigate the effects of four irrigation levels, including rainfed, deficit (75%), full (100%), and excess (125%) irrigations, and four nitrogen application levels: Zero nitrogen (0% N), Reduced nitrogen (50% recommended N), Recommended nitrogen (100% recommended N), and High nitrogen (200% recommended N) on sorghum grain, biomass yield, and vegetation indices; (2) to predict grain and biomass yield from vegetation indices using different machine learning algorithms and to evaluate their comparative performance. The ML-based predictions include multiple linear regression (MLR), partial least squares regression (PLSR), ridge regression, and XGBoost. PLSR and Ridge regression were more suitable than MLR, given the limited dataset, reducing instability in coefficient estimates and improving model robustness. PLSR reduces the original predictors to a smaller set of latent components that explain the maximum common variation between the predictors and the response. Ridge regression reduces multicollinearity, a common problem in MLR that reduces predictive power. XGBoost can also be helpful in data-limited settings as it can model complex nonlinear relationships and interactions. Here, vegetation indices from the RGB indices are derived using two methods: unsupervised K-means clustering and supervised convolutional neural networks (CNN). Instead of representing a season-long stress-monitoring system, the study evaluates the feasibility and limitations of a low-cost, single-date UAV RGB workflow for late-season sorghum assessment under combined water and nitrogen stress. The results provide baseline evidence for developing affordable precision-agriculture methods, while recognizing that multi-temporal imagery and independent external validation will be required before the approach can support operational irrigation and nitrogen decisions.

Experimental design

The sorghum field experiment was conducted during the summer (May–August) of 2023 and 2024 at Prairie View A&M University’s research farm (Latitude: 30°5′33.95″N, Longitude: 95°58′43.14″W), located in the vicinity of Greater Houston, Texas. Prairie View receives an annual rainfall of 1,118 mm, with 60% falling between June and October (Veettil et al., 2022). The study area features a humid subtropical climate, with a yearly average temperature of 17.2 °C. Summers are hot, whereas winters are comparatively colder. July has the highest average air temperature, at 35 °C, and January is the coldest month, with an average air temperature of 3 °C. We installed a WatchDog 2000 series Portable Weather Station (Spectrum Technologies, Inc., Aurora, IL, United States) in the field during the experimental season to monitor rainfall, solar radiation, wind speed, humidity, and air temperature at 15-min intervals. The soil at the site is classified as a Wockley fine sandy loam (fine-loamy, siliceous, semiactive, hyperthermic Plinthaquic Paleudalfs) (Veettil et al., 2024a; Veettil et al., 2025). The selected soil characteristics of the experimental site are provided in Table 1.

Approximately 40 plants were established in each subplot, resulting in approximately 1,920 plants across the 48 subplots in each season. Grain yield and aboveground biomass were determined from four plant representatives of the center row in each subplot to minimize border effects.

The factorial combination of four irrigation levels, four nitrogen rates, and three replications yielded 4 × 4 × 3 = 48 experimental subplots per season. The same experimental structure was evaluated in 2023 and 2024, producing 96 plot-year observations for statistical and machine-learning analyses. Each plot-year record contained the season, replica (block), irrigation treatment, nitrogen treatment, plot-level vegetation indices, grain yield, and aboveground biomass.

The 100% irrigation treatment was defined as the amount required to replenish the calculated crop water deficit based on the IrrigWise soil-water-balance procedure. The 75% treatment imposed moderate deficit irrigation, whereas the 125% treatment received 25% more than the calculated requirement. The 125% treatment was included to test whether water application above the calculated requirement produced an additional yield or resulted in diminishing returns. This treatment also represents practical over-irrigation that can result from uncertainty in evapotranspiration estimates and nonuniformity in irrigation systems. It should not be interpreted as a recommended irrigation practice.

Nitrogen was applied as urea at rates of 0, 90, 180, and 360 kg N ha −1. The rate of 180 kg N ha −1 was the recommendation for the expected grain yield of 8,000 lbs acre −1 (8,967 kg ha −1) from Texas AgriLife Extension (https://soiltesting.tamu.edu/). Accordingly, the four treatments represented 0, 50% of the recommended rate, the full recommended rate, and twice the recommended rate, respectively. The zero-nitrogen treatment served as an unfertilized control for assessing crop performance without additional nitrogen fertilizer; the 50% treatment represented reduced-input management; the recommended treatment represented standard production practice; and the 200% treatment tested whether excessive nitrogen produced additional biomass or grain-yield benefits under contrasting water availability. The field experimental layout is illustrated in Figure 1. The dataset consisted of 48 plot observations collected across two growing seasons.

Irrigation management

The irrigation water requirement was monitored using the Irrigwise model (Awal et al., 2021), which calculates evapotranspiration using the Penman-Monteith method and accounts for field capacity, permanent wilting point, and crop coefficient (Kc) at each growth stage. The weather variables, including precipitation, temperature, solar radiation, wind speed, and relative humidity, were obtained from the weather station installed in the experimental field for calculating the ET. We considered Kc at five stages of sorghum growth: planting, 10% field coverage, full coverage (70%), initial maturation, and the end of the season, to represent the crop’s water stress at different growth stages. Additionally, the field capacity and permanent wilting point calculations considered both the initial and final stages of root growth. The supplementary irrigation allowed us to maintain the plant’s available water level above the management-allowable deficit and close to field capacity. As mentioned, the irrigation amount is calculated only for the 100% irrigation. The 75% and 125% irrigation levels were managed by adjusting the irrigation duration.

Statistical analysis

The effects of irrigation level and nitrogen application rates on sorghum biomass and yield were investigated using Analysis of Variance (ANOVA). Tukey’s mean separation test was performed to differentiate the effects of irrigation and nitrogen level. ANOVA and Tukey test were conducted using RStudio.

RGB-based vegetation indices calculation

The UAV platform and RGB camera model used in this study to collect images are a DJI Mavic mini (Nanshan District, Shenzhen, Guangdong, China). The UAV was flown manually at approximately 20 m above ground level, with the camera oriented downward in a nadir configuration. The nominal ground sampling distance was approximately 0.7 cm/pixel. Each RGB image was captured approximately over the center of each subplot. The images were subsequently cropped without resampling to isolate the experimental plots, resulting in variable image dimensions while retaining the nominal spatial resolution. No automated flight path, orthomosaic, or ground control points were used because each plot image was analyzed independently.

Only one UAV survey was conducted in each growing season. Imagery for each plot in this study was collected during two growing seasons using a drone at 20 m altitude on 30/6/2023 and 27/6/2024. Thus, the image dataset was single-temporal within each year and did not include observations from the vegetative, booting, flowering, or earlier grain-filling stages. This sampling design allowed evaluation of a low-cost, single-flight workflow. The vegetation indices listed below (Table 2) are derived from RGB imagery and are commonly used to assess canopy greenness, crop vigor, and vegetation cover. GRVI, GLI, and ExG were selected because they describe complementary contrasts among the visible red, green, and blue channels that are available from consumer-grade RGB cameras. Chlorophyll absorbs red and blue light more strongly than green light; therefore, irrigation- and nitrogen-induced changes in chlorophyll, canopy cover, and senescence alter RGB responses. GRVI, GLI, and ExG quantify complementary green–red–blue contrasts, enabling treatment-related differences in canopy greenness and vegetation fraction to be detected using visible imagery (Motohka et al., 2010; Meyer and Neto, 2008). VARI enhances vegetation greenness while reducing illumination effects, whereas TGI uses the triangular relationship among the red, green, and blue bands as an indirect indicator of leaf chlorophyll content. Together, these indices provide useful inputs for crop monitoring, stress assessment, and yield prediction studies. The image segmentation, the sorghum crops segmented from weeds and soil classes, were separated using unsupervised K-means clustering and supervised CNN approaches, described in the following sections.

Image segmentation using K-means clustering

K-means clustering is an unsupervised machine learning technique used for image segmentation, where pixels are grouped into a specified number of clusters (K) based on the similarity of their features. The core idea of the K-means clustering algorithm is that, for a dataset to be divided into K classes, the similarity between classes should be minimized, and the similarity within classes should be maximized (Tian et al., 2019). The steps include (1) random selection of K initial cluster centers from the data set, (2) calculation of the distance of each remaining point to each cluster center, and classification of each point into the category of the nearest cluster center, (3) recalculation of the arithmetic mean, and adjusting the cluster center. In this study, we considered three segments, including the sorghum crop, weeds, and soil. The indices are only calculated for the sorghum segments.

Image segmentation using convolutional neural network

Convolutional Neural Networks (CNN)-based segmentation was performed using DeepLabV3 with a MobileNetV3-Large backbone (Torchvision implementation). Similar to the K-means method, each image was processed separately. The selected images from each replication were divided into smaller tiles, saved as standard RGB images, and used for annotation and CNN training. Pixel-level annotations were produced in CVAT, a web-based tool, considering Sorghum and Weeds as separate classes. Soil/background pixels were treated as an implicit third class (Background/Soil) by leaving them unlabeled. CVAT polygon annotations were exported to XML and converted into single-channel label masks with the following class codes: 0—soil, 1—Sorghum, 2—Weeds.

All image tiles and their masks were resized to 256 × 256 pixels for training. The segmentation model was initialized with pre-trained weights, and we modified the final classifier layer to predict three output classes. The training batch size was small (batch size = 1), and Batch Normalization layers were replaced with Group Normalization to improve the training stability. A small validation subset was separated from the annotated tile set in order to track the model performance. A probability threshold of 0.25 was applied to the sorghum class to mitigate underprediction of crop pixels. After segmentation, pixels classified as sorghum were retained for vegetation index calculation, but pixels of weeds and soil/background were discarded. Then, the sorghum-only masks were applied to calculate GRVI, VARI, GRI, ExG, GLI, and TGI from the RGB imagery for subsequent statistical and machine-learning analyses.

K-means and CNN segmentation were selected to compare unsupervised and supervised methods with different data and computational needs. K-means is simple and efficient because it groups similar pixels without labeled training data. However, its performance can be affected by shadows and color similarities between sorghum and weeds. CNNs learn spectral, textural, and spatial features from labeled images, which can improve the separation of sorghum from soil, weeds, shadows, and crop residues but require more annotation and computational resources. Comparing these methods allowed us to examine whether CNN segmentation improved vegetation index extraction and the prediction of grain yield and biomass compared with the simpler K-means approach.

The segmentation accuracy was computed using manually annotated RGB image tiles. The CNN- and K-means-derived masks were compared with the reference masks using IoU, mIoU, Dice/F1-score, precision, recall, and pixel/overall accuracy (PA/OA). IoU and Dice are similarity measures between the predicted sorghum area and the reference area. Precision is the number of pixels correctly identified as sorghum. Recall is the number of reference sorghum pixels that are successfully detected. PA/OA is the percentage of all correctly classified pixels, and mIoU is the mean IoU for the sorghum and background classes.

Multiple linear regression

Multiple linear regression (MLR) quantifies the linear relationship between the explanatory (independent) variables and the response (dependent) variable. Here, we used vegetation indices derived from the RGB images to predict sorghum biomass and yield. The equation of MLR is as follows Equation 1, where Xj represents the j th predictor and βj quantifies the association between that variable and the response. We interpret βj as the average effect on Y of a one-unit increase in Xj, holding all other predictors fixed. The biomass and grain yield data are randomly split to 70% train and 30% test across the seasons 2023 and 2024.

Partial least squares regression

Partial least squares (PLS) regression is a supervised, multivariate statistical technique that quantifies the relationship between the predictor and response variables. Similar to Principal Component Regression (PCR), PLS is a dimension-reduction method that first identifies a new set of features F 1, …, F M that are linear combinations of the original features, and then fits a linear model via least-squares using these M new features. While supervised dimension reduction in PLS can reduce bias, it can also increase variance. PLS aims to identify directions that explain both the response (Y) and the predictors (X) by analyzing the covariance structure. Unlike ordinary least squares regression, which can be unstable in the presence of multicollinearity and high-dimensional predictors, PLSR simultaneously decomposes X and Y into a set of orthogonal latent components that capture the shared information relevant for prediction. PLSR was trained using 70% of the dataset and evaluated on the remaining 30% independent test dataset. Internal cross-validation (CV) was applied during model training to determine the optimal number of latent components using the one-sigma selection criterion.

Ridge regression

Ridge regression is a regularized version of ordinary least squares (OLS) that reduces model overfitting by adding a penalty term to the regression coefficients. Multicollinearity occurs when independent variables are highly correlated, leading to unstable coefficient estimates and inflated variances in OLS models. Ridge regression addresses this issue by adding a penalty term to the least squares objective function, which shrinks the regression coefficients toward zero and reduces their variance. Unlike multilinear regression, ridge regression estimates the coefficients by minimizing a penalized residual sum of squares (Equation 2): where y i is the response variable, X i represents the predictor variables, β j are the regression coefficients, n is the number of observations, p is the number of predictors, and λ ≥ 0 is the regularization parameter controlling the amount of shrinkage. Here, the λ is calculated using 10-fold cross-validation.

XGBoost

Extreme Gradient Boosting (XGBoost) is an ensemble learning method based on gradient-boosted decision trees, designed to improve prediction accuracy while controlling model complexity. XGBoost builds an ensemble of weak prediction trees sequentially, where each new tree minimizes the errors made by the previous trees through gradient optimization. The method is highly effective for handling nonlinear relationships, multicollinearity, and high-dimensional datasets. In addition, XGBoost incorporates regularization parameters to reduce overfitting and improve model generalization. Five-fold cross-validation with early stopping was used during model tuning to determine the optimal number of boosting iterations and reduce overfitting. The model parameters included a learning rate (η) of 0.05, a maximum tree depth of 3, a minimum child weight of 1, a subsampling ratio of 0.8, a column subsampling ratio of 0.8, and a maximum of 2,000 boosting iterations.

Model performance evaluation

All model analyses were performed by splitting the data into 70% for training and 30% for testing (randomly sampled across both seasons). Also, indices were standardized before model training. The test results were analyzed using the following statistics. Pearson correlation (r), root mean square error (RMSE), and Percent bias (PBIAS). In the case of r, relationship values range from −1 to +1 depending on the value sign, and there is no correlation between the two variables when this value is equal to 0. For example, the Pearson correlation between sorghum grain yield is calculated as Equation 3, where Yp represents the predicted yield, Y p ¯ is the average yield predicted Ym and Y m ¯ is the measured and the average measured yield, respectively.

RMSE measures how far predictions fall from measured true values using Euclidean distance. The equation for calculating the RMSE is as follows Equation 4. where n is the total number of data points, x i is the actual observations of yield, and y i is the predicted yield.

Percent bias (PBIAS) measures the average tendency of the predicted yield to be larger or smaller than the measured values (Equation 5). where x i is the actual observations of yield, and y i is the predicted sorghum yield.

Effects of nitrogen and irrigation levels on grain and biomass yield

The distribution of sorghum yield and biomass with respect to the nitrogen and irrigation application rates is illustrated in Figure 2. The boxplots a and b illustrate the distribution of grain yield (t ha −1) across four irrigation and nitrogen levels, respectively. In both cases, median yield (indicated by the horizontal line within each box) generally increases with higher treatment levels, suggesting a positive response of yield to increased water and nitrogen inputs. The interquartile range reflects variability within the middle 50% of observations. At 100% irrigation level, grain yield exceeds 125%. The individual dots denote outliers, highlighting occasional extreme yield responses under certain treatment conditions. In the case of biomass, the effects of applications were more evident. For example, for irrigation levels, biomass increased by 2–3 t ha −1 from 75% to 125% irrigation. The ANOVA results for sorghum yield (Table 3) show that irrigation and nitrogen had very significant effects (P < 0.001). Irrigation explained a bigger part of the variability (F = 27.63) than nitrogen (F = 15.19).

The season alone did not have a significant effect on yield. The interaction between Season and Irrigation, on the other hand, was very important, indicating that the yield response to irrigation varied across seasons. The interaction between Season and Nitrogen had a small effect (Table 3). Figure 3 shows that Tukey’s mean separation test makes these differences even clearer. Yield increased significantly from irrigation level 1 to higher levels, with level 3 producing the highest mean yield and differing significantly from level 1. The stronger sorghum response to irrigation than to nitrogen indicates that water availability was the primary production constraint under the experimental conditions (Thapa et al., 2025). However, grain yield did not increase consistently between the 100% and 125% irrigation treatments in the present study, although biomass showed a clearer response. This divergence suggests that water application above the calculated crop requirement promoted vegetative growth without producing a proportional improvement in grain allocation.

Statistics of vegetation indices derived from K-means and CNN approaches

Vegetation indices are quantified from RGB images collected during the 2023 and 2024 sorghum growing seasons. The segmentation is performed using K-means and CNN approaches. The vegetation indices derived for sorghum crops using K-means and CNN approaches for the first plot in 2023 are illustrated in Figures 4, 5, respectively. These maps clearly demonstrated the effectiveness of the approaches in excluding soil and weeds, and in calculating indices only for sorghum crops. GRVI and VARI showed relatively similar distributions of positive values, with values less than 0.35. Similarly, GRI values exceeded 0.25. TGI exhibits a much broader range of values, indicating greater sensitivity to chlorophyll concentration and leaf structural variability. As in the K-means approach, CNN-based calculations derived vegetation indices only for sorghum crops, excluding soil and weeds. GRVI values generally ranged from approximately 0.02–0.32, with most pixels concentrated between 0.10 and 0.25, indicating moderate green reflectance consistent with actively growing sorghum. GRI indicated a range of 1–1.9. The distribution of vegetation indices across irrigation and nitrogen application levels is shown in boxplots (Figures 6, 7).

Figure 6 shows the distribution of indices derived using K-means clustering, where boxplot panels a–f indicate the effects of irrigation levels. GRVI and VARI showed much variation in median across treatments. However, the treatment levels 3 and 4 showed a wider range. Boxplot panels (g–l) show the distribution of the same vegetation indices across four nitrogen levels. Compared to irrigation, nitrogen treatments appear to produce more noticeable shifts in several indices, particularly VARI, GRI, and TGI. VARI shows a gradual increase in median values as nitrogen levels rise, suggesting enhanced vegetation vigor and canopy density with greater nitrogen availability. The presented patterns suggest that RGB-derived vegetation indices derived from K-means segmentation of crop areas effectively capture variability associated with both irrigation and nitrogen management practices. In the case of CNN (Figure 7), GRVI shows a gradual decrease in median values from irrigation levels 1 to 4, suggesting reduced canopy greenness or vegetation vigor as irrigation levels increase.

The comparison between K-means and CNN segmentation illustrates a trade-off between operational simplicity and class discrimination capacity. K-means requires no manually labeled training data and, therefore, represents an accessible approach for low-cost field applications (Xu et al., 2020). However, because clustering is based primarily on pixel similarity, its classifications can be affected by shadows, exposed soil, and spectral similarity between sorghum and weeds. CNN segmentation can incorporate spatial and contextual information, producing visually sharper crop boundaries (Persello et al., 2019).

The accuracy assessment indicated that CNN outperformed K-means across all metrics (Table 4). For example, the sorghum IoU for CNN was 0.308, and for KNN it was 0.126. However, moderate IoU and precision indicate that misclassification persisted, and the results reflect apparent performance on the tiles used during model development. The CNN showed a relatively high OA of 0.799 but a lower IoU of 0.308, mainly because background pixels outnumbered sorghum pixels. Precisely classifying these non-sorghum pixels increased the overall accuracy. But IoU more strictly measures the overlap between the predicted and reference sorghum areas by accounting for both false positives and false negatives. The high recall (0.774) shows that the CNN detected most labeled sorghum pixels, while its lower precision (0.346) indicates that some background pixels were incorrectly classified as sorghum. Therefore, despite its high OA, the CNN’s sorghum segmentation performance was moderate.

Correlation between vegetation indices and yield

The correlation between vegetation indices and biomass and grain yield was analyzed using a correlation matrix (Figure 8). Most RGB-based vegetation indices showed negative correlations with sorghum biomass and grain yield for the K-means clustering and CNN-based indices. This may be due to the image collection after the reproduction stage of sorghum plants. For example, in K-means clustering, biomass was negatively correlated with GRVI, GRI, ExG, GLI, and TGI (r = −0.17 to −0.36), and yield was also negatively correlated with these indices (r = −0.21 to −0.32). In the case of CNN, where biomass was negatively correlated with GRVI (−0.59), VARI (−0.20), GRI (−0.36), ExG (−0.38), and GLI (−0.54), and yield followed a similar pattern. Most RGB vegetation indices were negatively correlated with biomass and grain yield. RGB data were collected only once during the late reproductive period, when RGB canopy signals were likely influenced by chlorophyll degradation, leaf senescence, and panicle exposure. During grain filling, assimilates and nitrogen are remobilized from vegetative tissues to developing grain, while the timing and rate of leaf senescence may vary among irrigation and nitrogen treatments. Sorghum plants that accumulated greater biomass or achieved higher yield could therefore have been more developmentally advanced at the time of imaging and thus displayed lower greenness index values. The observed negative correlations cannot be interpreted solely as direct inverse relationships between crop greenness and productivity. They may also reflect treatment-related differences in phenology and senescence.

Predicting grain and biomass yield using vegetation indices

This study used four methods: MLR, PLSR, Ridge, and XGBoost regression methods to predict the sorghum yield using the vegetation indices. Overall, the results showed no clear superiority of any single model, as all four approaches produced comparable predictive performance. For example, MLR, in the case of the K-means clustering-based yield prediction approach, showed a correlation coefficient (r) of 0.53, an RMSE of 0.79, and a PBIAS of 8.08 (Figure 9). Similarly, Ridge Regression showed an r value of 0.53. However, PLSR and XGBoost showed an r value of 0.33 and 0.39, respectively, indicating the highest PBIAS in the case of XGBoost. In the case of biomass, r values were comparatively higher than yield prediction (Figure 10). Here, MLR indicated the lowest r value (0.48), and the highest r value is observed for the Ridge regression (0.65), and the lowest RMSE is also observed for the Ridge regression. XGBoost also showed a higher value of correlation in the analysis.

CNN-based vegetation indices derived model evaluation results showed moderate variation in sorghum yield prediction accuracy among the four approaches (Figure 11). In all methods, the fitted regression lines deviated from the 1:1 line, especially at higher observed yield values, suggesting that the models have limited ability to fully capture yield variability across the entire range.

Similarly, in biomass prediction, the strongest relationships between predicted and measured biomass were observed with correlation coefficients of 0.62 and 0.67 for MLR and PLSR, respectively (Figure 12). The RMSE values suggest that XGBoost had the lowest absolute prediction error, although its correlation remained weak. The PBIAS values were positive across all four models, indicating a general tendency toward underprediction according to the PBIAS definition used in this study. The fitted regression lines in all panels deviated from the 1:1 line, especially at higher biomass values, indicating that the models did not fully reproduce the observed variability across the biomass range. Overall, the results suggest that the MLR and PLSR models provided relatively better biomass predictions than Ridge and XGBoost, although prediction bias remained substantial in most cases. Compared with previous UAV-based crop modeling studies, the predictive performance in this study was moderate, indicating that RGB-derived vegetation indices can explain a meaningful but still limited proportion of sorghum yield and biomass variability. For example, in bioenergy sorghum, Li et al. (2022) reported moderate biomass prediction accuracy using UAV-derived data, consistent with the present findings. Tunca et al. (2025) reported stronger sorghum biomass estimation using a random forest model, and Khodjaev et al. (2025) found that optimized RF and XGBoost models outperformed linear models for wheat yield estimation, likely because those studies used multi-temporal and more comprehensive UAV-derived predictors rather than RGB indices alone. The competitive performance of PLSR and ridge regression is consistent with their ability to manage collinearity among vegetation indices. MLR also remained competitive in some cases, suggesting that the available predictive structure was predominantly linear. XGBoost produced a low biomass RMSE in one model but a comparatively weak correlation.

The negative relationships between the RGB indices and yield or biomass do not mean that reduced canopy greenness improved crop productivity. As sorghum approaches maturity, nitrogen and other resources are transferred from leaves and stems to the sorghum grain. This leads to more visibility of non-green plant tissues in the collected images. Therefore, plots that had already accumulated greater biomass or produced more grain may have been at a more advanced stage of maturity and appeared less green when the UAV images were collected. Differences in crop maturity and senescence among the irrigation and nitrogen treatments may thus have weakened or even changed relationships that could have been positive at earlier growth stages.

The low R 2 values indicate that the RGB vegetation indices captured a limited portion of the variability in sorghum yield and biomass. First, imagery was acquired near crop maturity, when canopy senescence, chlorophyll degradation, panicle exposure, and increasing non-photosynthetic tissue altered canopy color and weakened the relationship between greenness and accumulated yield or biomass. Second, RGB vegetation indices may have approached saturation under dense, nearly closed canopies, reducing their sensitivity to differences among high-yielding plots. Finally, the single RGB survey captured canopy conditions only at a single growth stage and could not capture the dynamic effects of irrigation and nitrogen on crop establishment, vegetative growth, flowering, and grain filling throughout the season. In addition, segmentation errors and the relatively small sample size may have further limited model performance, particularly for the more complex XGBoost model. Therefore, these results can be interpreted as evidence of a modest, stage-specific relationship rather than an accurate field-scale prediction. The modeling framework presented in this study is not sufficiently accurate for operational yield forecasting or irrigation and nitrogen recommendations. The incorporation of multi-temporal RGB imagery with canopy height, texture, multispectral or thermal data, larger datasets, and independent validation across seasons is required to improve model accuracy.

The principal limitation of this study is that only a single UAV RGB survey was conducted in each growing season. The dataset does not capture the temporal progression of irrigation and nitrogen responses from canopy establishment through all the growth stages. Late-season RGB imagery may introduce a specific physiological source of uncertainty. The single-date design also limits the model’s generalizability. The reported performance represents the particular acquisition stage, cultivar, field environment, illumination conditions, and irrigation–nitrogen treatments evaluated in this experiment. The moderate-to-weak correlations indicate that the proposed low-cost RGB approach is not sufficiently accurate for operational grain yield or biomass prediction. Its performance was likely limited by the single late-season image acquisition, small sample size, and limited spectral information available from RGB bands. The models should not be assumed to provide equivalent accuracy at earlier growth stages or in other locations and seasons. Future research should include UAV capture at all vegetative growth stages. Models based on individual stages should be compared with models that integrate multi-temporal features, including temporal changes in vegetation indices, canopy cover, texture, and UAV-derived plant height.

This study showed that low-cost UAV RGB imagery, combined with K-means or CNN-based segmentation and regression modeling, can estimate sorghum grain yield and biomass under different irrigation and nitrogen treatments. The results indicated that water availability was the main constraint on sorghum yield, while irrigation and nitrogen applied beyond recommended levels produced diminishing gains in grain yield. Although sorghum is relatively tolerant of stress, greater water and nutrient availability generally improved crop performance.

CNN segmentation generally isolated sorghum pixels more effectively and strengthened the relationships between RGB indices and productivity, suggesting that image segmentation and feature quality may be as important as model complexity. Several vegetation indices were negatively related to grain yield and biomass, but these relationships were specific to the late-season image-acquisition stage and should not be generalized to earlier growth stages. No regression model performed best in every case. MLR, PLSR, and ridge regression generally benefited from CNN-derived indices, whereas XGBoost offered no consistent advantage. Consumer-grade UAV RGB imagery provides a practical and affordable option for stage-specific sorghum assessment. The findings of this study are not interpreted as evidence of a robust or field-ready yield-estimation system. The approach demonstrated only preliminary feasibility for using low-cost UAV RGB imagery for stage-specific sorghum assessment under the conditions evaluated. Future studies should integrate multi-temporal imagery with multispectral or hyperspectral data, canopy structural features, weather and soil variables, larger datasets, and independent validation across seasons and locations to improve prediction accuracy and model transferability.