The advancement of precision agriculture is fundamentally reliant on the accurate and timely monitoring of crop growth status. As a staple global food crop, precise monitoring of wheat growth is of paramount importance for ensuring food security. Traditional growth monitoring methods primarily depend on manual field surveys and ground-based sensors. While these approaches can provide relatively accurate data, they suffer from low efficiency, high costs, and an inability to conduct large-scale, real-time monitoring. They fail to capture the dynamic changes occurring throughout the wheat growth cycle and thus cannot meet the demands of modern, precision agricultural management. With the progression of agricultural modernization, the application of unmanned drone technology combined with machine learning algorithms in crop growth monitoring has garnered increasing attention. Unmanned drones offer distinct advantages such as high flexibility, low operational costs, and rapid data acquisition, enabling the swift collection of high-resolution remote sensing imagery. This provides a powerful tool for the fine-scale monitoring of wheat growth status. Simultaneously, machine learning algorithms, leveraging their robust data processing and pattern recognition capabilities, can effectively mine latent information from the data to establish high-precision growth inversion models.
In my investigation, I focus on the critical heading stage of winter wheat. This period coincides with the peak leaf area index and the rapid accumulation of dry matter in the ear, making the crop highly sensitive to water and nitrogen stress. Minor variations in environmental conditions or management practices during this phase can lead to significant fluctuations in seed setting rate and grain weight, resulting in pronounced spatial heterogeneity. Therefore, elucidating the spatial distribution of wheat growth at the heading stage and its driving factors constitutes a core requirement for implementing precise field management. In this study, I utilize an unmanned drone to acquire hyperspectral imagery at the field scale during the heading stage. Concurrently, I collect in-situ measurements of key winter wheat growth parameters, including Leaf Area Index (LAI), chlorophyll content (SPAD), plant height (H), and above-ground biomass (AGB). A Comprehensive Growth Indicator (CGI) is constructed based on the Coefficient of Variation (CV) method. Through correlation analysis between vegetation indices and the CGI, and subsequent calculation of the Variance Inflation Factor (VIF), optimal vegetation indices are selected as input variables for machine learning models. By evaluating multiple performance metrics, the optimal model is identified and used to generate a growth inversion map for the heading-stage winter wheat. Furthermore, the relative importance of the input variables is analyzed to provide deeper insights for field management.
The core of my methodology involves the fusion of high-dimensional spectral data captured by an unmanned drone with multi-parameter ground truth data. The unmanned drone platform, equipped with a high-precision hyperspectral imager, allows me to obtain detailed spectral reflectance information across hundreds of contiguous bands. This rich spectral dataset is far superior to traditional multispectral data for capturing subtle physiological changes in crops. The subsequent integration of this spectral information with physically measured growth parameters through a robust statistical framework forms the basis for a comprehensive and accurate assessment of crop health and vigor at a fine spatial resolution.
To construct a holistic representation of winter wheat growth that moves beyond single-parameter assessments, I employed the Coefficient of Variation (CV) method to integrate the four measured parameters: LAI, SPAD, H, and AGB. The CV method is an objective weighting technique that assigns weights based on the relative dispersion of each indicator. An indicator with a higher coefficient of variation is considered to provide more discriminative information about the growth status across the field. The process is defined as follows:
First, for each growth indicator \(X_i\), its standard deviation \(\sigma_i\) and mean \(\bar{X}_i\) are calculated from the sample data. The coefficient of variation \(CV_i\) for the \(i\)-th indicator is then computed as:
$$CV_i = \frac{\sigma_i}{\bar{X}_i}$$
The weight \(W_i\) assigned to each indicator is determined by normalizing its CV value relative to the sum of all CVs:
$$W_i = \frac{CV_i}{\sum_{j=1}^{n} CV_j}$$
where \(n\) is the total number of indicators (in this case, 4).
Each original indicator value \(X_{i,sample}\) for a given sample is normalized to a [0,1] scale (\(U_i\)) to eliminate unit differences before combination. Finally, the Comprehensive Growth Indicator (CGI) for each sample is calculated as the weighted sum of its normalized indicators:
$$CGI = \sum_{i=1}^{n} (W_i \cdot U_i)$$
Applying this method to my dataset yielded the following objective weights for each parameter: AGB (0.411), LAI (0.334), H (0.166), and SPAD (0.089). The resulting CGI formula for my study is:
$$CGI = 0.411 \times U_{AGB} + 0.334 \times U_{LAI} + 0.166 \times U_{H} + 0.089 \times U_{SPAD}$$
The descriptive statistics for the individual growth parameters and the synthesized CGI are summarized in Table 1. The CGI demonstrated a smaller coefficient of variation (0.108) compared to key individual parameters like LAI (0.202) and AGB (0.211), indicating that it provides a more stable and integrated measure of overall crop status across the field.
| Growth Indicator | Min | Max | Mean | Std. Dev. | Coefficient of Variation |
|---|---|---|---|---|---|
| LAI | 1.670 | 4.700 | 3.366 | 0.679 | 0.202 |
| SPAD | 34.933 | 50.533 | 45.468 | 2.828 | 0.062 |
| H (cm) | 34.960 | 59.660 | 45.079 | 5.049 | 0.112 |
| AGB (kg/m²) | 0.123 | 0.716 | 0.434 | 0.092 | 0.211 |
| CGI | 0.501 | 0.791 | 0.642 | 0.069 | 0.108 |
Vegetation indices (VIs), which are mathematical combinations of spectral reflectance from specific bands, are powerful proxies for various biophysical and biochemical plant properties. From the high-dimensional hyperspectral data captured by the unmanned drone, I calculated a suite of established and optimized VIs. The formulas for these indices are listed in Table 2, where \(R_{\lambda}\) represents the reflectance at wavelength \(\lambda\).
| Vegetation Index (Abbr.) | Formula | Primary Reference Bands |
|---|---|---|
| Difference Vegetation Index (DVI) | $$DVI = R_{NIR} – R_{Red}$$ | NIR, Red |
| Normalized Difference Vegetation Index (NDVI) | $$NDVI = \frac{R_{NIR} – R_{Red}}{R_{NIR} + R_{Red}}$$ | NIR, Red |
| Kernel NDVI (kNDVI) | $$kNDVI = \tanh(NDVI^2)$$ | Derived from NDVI |
| Optimized Soil Adjusted Vegetation Index (OSAVI) | $$OSAVI = \frac{(1+0.16)(R_{NIR} – R_{Red})}{R_{NIR} + R_{Red} + 0.16}$$ | NIR, Red |
| Ratio Vegetation Index (RVI) | $$RVI = \frac{R_{NIR}}{R_{Red}}$$ | NIR, Red |
| Optimal Vegetation Index (VLOPT) | $$VLOPT = \frac{R_{750} – R_{705}}{R_{750} + R_{705} – 2 \times R_{445}}$$ | 750 nm, 705 nm, 445 nm |
| Enhanced Vegetation Index (EVI) | $$EVI = 2.5 \times \frac{R_{NIR} – R_{Red}}{R_{NIR} + 6 \times R_{Red} – 7.5 \times R_{Blue} + 1}$$ | NIR, Red, Blue |
| Excess Green Index (EXG) | $$EXG = 2 \times R_{Green} – R_{Red} – R_{Blue}$$ | Green, Red, Blue |
| Triangular Vegetation Index (TVI) | $$TVI = 0.5 \times [120 \times (R_{NIR} – R_{Green}) – 200 \times (R_{Red} – R_{Green})]$$ | NIR, Red, Green |
| Visible Atmospherically Resistant Index (VARI) | $$VARI = \frac{R_{Green} – R_{Red}}{R_{Green} + R_{Red} – R_{Blue}}$$ | Green, Red, Blue |
| New Vegetation Index (NVI) | $$NVI = \frac{R_{800} – R_{670}}{R_{800} + R_{670} + 0.5 \times R_{550}}$$ | 800 nm, 670 nm, 550 nm |
To evaluate the effectiveness of the synthesized CGI compared to single parameters, I performed a Pearson correlation analysis between all VIs and each growth metric. The results, presented in Table 3, clearly demonstrate the superiority of the CGI. All 11 VIs showed statistically significant correlations with the CGI, with correlation coefficients ranging from 0.456 to 0.612. When comparing the maximum correlation coefficient achieved by any single parameter with that achieved by the CGI for each VI, the CGI showed an improvement ranging from 16.7% to 40.0%. For instance, the NVI’s correlation with CGI (0.570) was significantly higher than its best correlation with a single parameter (0.407 with LAI). This confirms that the CGI, by integrating multiple aspects of growth, provides a more comprehensive and strongly related target variable for spectral modeling compared to any individual agronomic parameter.
| Vegetation Index | Correlation Coefficient (Pearson’s r) | ||||
|---|---|---|---|---|---|
| LAI | SPAD | H | AGB | CGI | |
| DVI | 0.296* | 0.180 | 0.206 | 0.403** | 0.514** |
| NDVI | 0.414** | 0.104 | 0.320** | 0.293* | 0.527** |
| kNDVI | 0.437** | 0.186 | 0.213 | 0.271* | 0.510** |
| OSAVI | 0.403** | 0.113 | 0.285* | 0.294* | 0.515** |
| RVI | 0.412** | 0.107 | 0.327** | 0.291* | 0.527** |
| VLOPT | 0.243 | 0.218 | 0.195 | 0.365** | 0.456** |
| EVI | 0.376** | 0.183 | 0.169 | 0.384** | 0.537** |
| EXG | 0.456** | 0.188 | 0.204 | 0.377** | 0.594** |
| TVI | 0.485** | 0.164 | 0.226 | 0.374** | 0.612** |
| VARI | 0.393** | 0.109 | 0.330** | 0.326** | 0.540** |
| NVI | 0.407** | 0.258** | 0.270* | 0.359** | 0.570** |
* Significant at p < 0.05 level; ** Significant at p < 0.01 level.
Before model construction, it is crucial to address potential multicollinearity among the predictor VIs, as highly correlated inputs can destabilize models and obscure the interpretation of individual variable importance. I calculated the Variance Inflation Factor (VIF) for each VI, where a VIF value greater than 10 indicates severe multicollinearity. Based on a threshold of VIF < 10, I selected four VIs with acceptable independence: DVI (VIF=2.1), kNDVI (VIF=3.8), VLOPT (VIF=1.5), and NVI (VIF=4.2). These four indices served as the input feature set for the subsequent machine learning models.
I implemented three prominent machine learning algorithms to establish the relationship between the spectral features from the unmanned drone and the ground-based CGI: Random Forest (RF), Boosted Regression Trees (BRT), and eXtreme Gradient Boosting (XGBoost). The dataset was randomly split into 70% for training and 30% for independent testing. Model hyperparameters were optimized using grid search combined with 10-fold cross-validation on the training set. The performance of the final models was evaluated using the Coefficient of Determination (R²), Root Mean Square Error (RMSE), and Mean Absolute Error (MAE), defined as:
$$R^2 = 1 – \frac{\sum_{i=1}^{n}(y_i – \hat{y}_i)^2}{\sum_{i=1}^{n}(y_i – \bar{y})^2}$$
$$RMSE = \sqrt{\frac{1}{n}\sum_{i=1}^{n}(y_i – \hat{y}_i)^2}$$
$$MAE = \frac{1}{n}\sum_{i=1}^{n}|y_i – \hat{y}_i|$$
where \(y_i\) is the measured CGI, \(\hat{y}_i\) is the predicted CGI, \(\bar{y}\) is the mean of measured CGI, and \(n\) is the number of samples.
The performance metrics for the three models on both the training and test sets are compared in Table 4. The BRT model emerged as the most effective for predicting the winter wheat CGI. It achieved the highest R² (0.561) and the lowest RMSE (0.052) and MAE (0.047) on the training set. More importantly, it maintained superior performance on the independent test set (R²=0.415, RMSE=0.066, MAE=0.055), outperforming both the RF and XGBoost models. This indicates that the BRT model, which builds an ensemble of trees in a sequential manner to correct the errors of previous trees, generalizes better to unseen data for this specific task using unmanned drone-derived features.
| Model | Training Set | Testing Set | ||||
|---|---|---|---|---|---|---|
| R² | RMSE | MAE | R² | RMSE | MAE | |
| Random Forest (RF) | 0.504 | 0.051 | 0.046 | 0.397 | 0.067 | 0.055 |
| Boosted Regression Trees (BRT) | 0.561 | 0.052 | 0.047 | 0.415 | 0.066 | 0.055 |
| XGBoost | 0.498 | 0.053 | 0.047 | 0.374 | 0.069 | 0.055 |
To understand which spectral features contributed most to the predictive power of the models, I analyzed the relative importance of the four input VIs. The results, aggregated from the three machine learning algorithms, are presented in Table 5. A clear and consistent pattern emerged across all models: the New Vegetation Index (NVI) was assigned the highest relative importance, followed by the Difference Vegetation Index (DVI). The NVI, which strategically incorporates a green band reflectance (\(R_{550}\)) into its denominator alongside the standard red-edge type formulation, appears to capture a unique spectral signature highly relevant to the integrated physiological and structural status represented by the CGI. This finding aligns perfectly with the earlier correlation analysis, where NVI also showed one of the strongest correlations with CGI. The high importance of indices like DVI and NVI underscores the critical role of the near-infrared (NIR) region, to which these indices are highly sensitive. The NIR region is directly related to the internal cellular structure of leaves and canopy biomass, making it a robust indicator of overall crop vigor and a key spectral region leveraged by unmanned drone sensing.
| Vegetation Index | Random Forest | Boosted Regression Trees | XGBoost | Average Importance |
|---|---|---|---|---|
| New Vegetation Index (NVI) | 38.2 | 42.5 | 35.8 | 38.8 |
| Difference Vegetation Index (DVI) | 31.5 | 28.1 | 33.4 | 31.0 |
| Kernel NDVI (kNDVI) | 20.1 | 18.9 | 22.5 | 20.5 |
| Optimal Vegetation Index (VLOPT) | 10.2 | 10.5 | 8.3 | 9.7 |
Applying the optimal BRT model to the entire unmanned drone hyperspectral scene allowed me to generate a high-resolution spatial distribution map of the winter wheat CGI across the field. The predicted CGI values ranged from 0.570 to 0.740. Using the natural breaks classification method, the growth status was categorized into five levels (I to V, with V representing the best growth). The spatial analysis revealed a distinct “center superior, periphery inferior” distribution pattern. Level III (moderate-good growth) occupied the largest contiguous area (approximately 35.4%), located centrally. The poorest growth areas (Level I) were predominantly concentrated along the western and outer edges of the field, accounting for about 27.3% of the area. The best growth zones (Levels IV and V) appeared as smaller, scattered patches within the central core, totaling 26.1%.
This spatial heterogeneity can be attributed to micro-environmental variations under unified management. The central areas likely benefit from more consistent and optimal soil moisture and nutrient distribution due to proximity to irrigation infrastructure and more uniform application of soil amendments. In contrast, edge zones may experience marginal effects such as slight water deficit, potential salinity ingress, or suboptimal soil conditions, leading to reduced growth vigor. The unmanned drone-based map precisely captures these subtleties, which would be difficult to discern through conventional scouting.
In conclusion, this study demonstrates an effective framework for field-scale winter wheat growth monitoring by integrating unmanned drone-acquired hyperspectral imagery with multi-parameter ground measurements and machine learning. The key findings are: First, the Comprehensive Growth Indicator (CGI) constructed using the Coefficient of Variation method proved to be a more robust and representative metric than any single growth parameter, exhibiting stronger correlations with a wide array of vegetation indices. Second, among the evaluated machine learning models, the Boosted Regression Tree (BRT) algorithm provided the most accurate and stable inversion model for estimating the CGI from spectral data, with a test set R² of 0.415. Third, interpretability analysis of the models identified the New Vegetation Index (NVI) as the most important predictive variable, highlighting the value of specific band combinations involving NIR, red, and green regions for assessing integrated crop status. Finally, the spatial distribution map generated by the model revealed clear within-field variability, characterized by better growth in central areas and poorer growth along the edges, providing actionable insights for site-specific management.
This research underscores the significant potential of unmanned drone hyperspectral remote sensing as a core tool in precision agriculture. The methodology offers a scientifically grounded, efficient, and high-resolution approach for comprehensive crop status assessment. It provides a foundation for timely interventions such as variable-rate fertilization or irrigation, ultimately aiming to optimize resource use, enhance crop productivity, and contribute to sustainable agricultural practices. The framework established here is readily transferable to the growth monitoring of other crops, paving the way for more intelligent and data-driven farming systems.