The study was conducted in Xiaogang village, Fengyang County, Chuzhou city, Anhui Province, China (longitude 117°46′7″E, latitude 32°48′52″N) ( Figure 1A ), which is characterized by a subtropical monsoon climate, an average annual temperature of 15.4°C, and an average annual precipitation of 1179.2 mm. The soil predominantly consists of clay with medium fertility on flat terrain. The experimental area included 36 plots, measuring 2 m × 8 m each. The rice varieties tested were Runzhuxiangzhan (V1), Runzhuyinzhan (V2), and Hongxiangnuo (V3), with each plot replicated three times. Four nitrogen gradient treatments were applied with nitrogen application rates of N0 (0 kg/hm²), N1 (100 kg/hm²), N2 (200 kg/hm²), and N3 (300 kg/hm²). Phosphorus (90 kg/hm²) and potash (135 kg/hm²) fertilizers were applied once as basal fertilizer ( Figure 1B ). The experiment spanned from June 2020 to October 2020. The plants experienced no drought or flooding during the seedling stage and favorable conditions of abundant sunshine and moderate temperatures during the mid-growth stage, which are conducive to rice growth and development. Field management practices followed local cultivation methods and pest control technologies.

To thoroughly investigate the relationships between the independent and dependent variables, four machine learning models were selected for comparison: PLSR, PCR, SVM, and RR.

PLSR (Geladi and Kowalski, 1986) is a multivariate linear statistical method that focuses on finding a hyperplane that minimizes the variance between the response and independent variables. It projects predictor and observed variables into a new space to derive a linear regression model, known as a bilinear factor model, due to the presence of both data X and Y in this new space.

PCR (Kawano et al., 2018) employs PCA for predictive data mining, transforming original variables into principal components that are linear combinations of the original variables and mutually independent. Regression analysis is then performed on these principal components to derive the regression equation, which is subsequently applied to the original variables.

SVM (Suykens and Vandewalle, 1999) operates as a supervised learning model utilized for analyzing data in classification and regression analysis. The core concept involves identifying the optimal classification hyperplane for two types of samples in the original space when they are linearly separable. In instances where linear separability is not achievable, the samples are projected into a high-dimensional feature space where an optimal hyperplane is determined. This hyperplane classifies the samples, aiming to minimize the distance within similar classes and maximize the distance between distinct classes.

RR (Ivanda et al., 2021) serves as a technique for estimating the coefficients of a multiple regression model in scenarios where the independent variables exhibit high correlation. This is achieved by incorporating an L2 regularization term into the OLS loss function. The L2 regularization term is calculated as the product of the sum of the squares of the coefficients and a regularization parameter λ (lambda).

In this study, 70% of the sample data (n=25) were selected as the modeling set for each growth stage, and 30% of the sample data (n=11) were used as the validation set to construct the rice AGB estimation model. The coefficient of determination (R²), root mean square error (RMSE), and mean absolute error (MAE) were used to evaluate the model accuracy. The closer R² is to 1, the lower the RMSE and MAE are, and the higher the accuracy of the estimation model is. R², RMSE and MAE are calculated using Equations 1–3, respectively:

Note: x i , y i , and x ^ are the actual measured value, predicted value and average value of the measured data, respectively; n is the number of samples.

To fully explore the sensitivity of the different orders of rice canopy spectra and to compare the effects of spectral transformations on AGB, FD and SD transformations were carried out on the basis of OS, and their correlations with rice AGB were investigated ( Figure 3 ).

During the full growth stage, the correlation between OS and AGB showed a consistent trend from negative to positive as the band increased, with the maximum correlation at 720 nm. The correlation curve between FD and AGB shows a continuous fluctuation trend in the 400 ~ 900 nm band, among which the 680 ~ 750 nm band has the highest correlation, with a correlation coefficient between 0.60 ~ 0.85. The correlation curve between SD and AGB was similar to that between FD and AGB, but the fluctuations were more severe.

In summary, the derivative spectrum of the different orders were compared with the maximum absolute value of the AGB correlation coefficient ( Figure 4 ). Except for the tillering stage, the maximum values in the other four periods all occurred at FD. Comprehensive analysis revealed that the FD could better reflect the growth status of rice, so the FD was used as the input variable of the feature screening algorithm for subsequent construction of the AGB estimation model.

An AGB estimation model utilizing PLSR, PCR, SVM, and RR was developed to evaluate the effectiveness of the band screening algorithms. This model incorporated characteristic bands selected by both the Boruta algorithm and the RFE algorithm, as well as the full band as input variables. The diversity and scope of the characteristic bands selected by these feature screening algorithms during different growth stages are summarized in Table 1 . Detailed feature selection results are shown in Appendix 2 .

The Boruta algorithm demonstrated remarkable stability, with the number of characteristic wavelengths in each growth stage not exceeding 40. In contrast, the RFE algorithm showed more significant fluctuations, with 3 characteristic wavelengths identified at both the tillering and booting stages and 439 at the maturity stage, indicating substantial variance in the number of wavelengths identified across different growth stages. Notably, the characteristic wavelengths identified by both screening algorithms predominantly fall within the “red edge” spectral range, highlighting their importance in estimating rice AGB.

This study employs three types of model input variables: first derivative full band (FD-FB), the characteristic bands selected by the Boruta algorithm (FD-Boruta), and the characteristic bands selected by the RFE algorithm (FD-RFE). Sixty AGB estimation models were developed for various growth stages using four machine learning algorithms (PLSR, PCR, SVM, RR), with R² ( Figure 5 ), RMSE ( Table 2 ) and MAE ( Appendix 1 ) serving as the model evaluation metrics.

Initially, the AGB estimation abilities of different feature selection algorithms were compared within the same model framework. In the PLSR model, the estimation precision for FD-Boruta and FD-RFE was found to be comparable, with R² values ranging from 0.43 to 0.70, and RMSE values between 464.34 and 2515.77 kg/hm² and 493.81 and 2407.61 kg/hm², respectively. These results are more accurate than those obtained using FD-FB, with R² values improving by 0 to 0.06 and RMSE values decreasing by 29.47 to 148.91 kg/hm². Among the PCR models, FD-Boruta exhibited the highest estimation accuracy, followed by FD-RFE, with FD-FB showing the least accuracy. The R² accuracy of FD-Boruta improved by 0.03, 0.19, 0.02, 0.01, and 0.04, respectively, compared to FD-RFE. In contrast, the R² accuracy of FD-RFE improved by 0.02, 0.05, 0.07, and 0.01 compared to FD-FB. The outcomes for the SVM and RR models were analogous, although the performances of the three algorithms varied significantly. R² ranged from 0.58 to 0.71 for FD-Boruta, 0.22 to 0.74 for FD-RFE, and 0.19 to 0.60 for FD-FB.

Second, the estimation accuracy of AGB by different models under the same feature selection algorithm was compared. For the model constructed with FD-Boruta inputs, when the estimation accuracy was similar, FD-Boruta-PCR demonstrated more stable performance. The estimation outcomes of models based on FD-RFE varied significantly. FD-RFE-PLSR and FD-RFE-PCR provided more precise estimates of rice AGB, whereas the FD-RFE-SVM and FD-RFE-RR models exhibited overfitting in certain stages. The models based on FD-RFE generally showed poor performance, with model R² values below 0.65, and the accuracy of the FD-FB-SVM and FD-FB-RR models varied greatly.

Finally, the performance of all model combinations was assessed for estimating AGB effects across different growth stages. In the tillering stage, FD-Boruta-SVM yielded the best estimation, with an R² of 0.66 and an RMSE of 34.33 kg/hm². During the jointing stage, FD-Boruta-SVM achieved the highest estimation accuracy, with an R² of 0.65 and an RMSE of 985.55 kg/hm², while FD-FB-SVM showed the lowest accuracy, with an R² of 0.32 and an RMSE of 1412.37 kg/hm2. In the booting stage, the estimation accuracies R² of models using FD-FB and FD-RFE inputs were both above 0.7, with FD-RFE-SVM and FD-Boruta-PCR performing the best, achieving R² values of 0.74 and 0.72, respectively, and RMSE values of 1311.04 kg/hm² and 1290.24 kg/hm², respectively. At the heading stage, FD-Boruta-PCR had the highest estimation accuracy, with an R² of 0.71, while FD-FB-SVM had the lowest accuracy, with an R² of 0.30. In the maturity stage, the AGB estimation accuracy of all the models decreased, with R² values ranging from 0.19 to 0.53.

In conclusion, models built using the Boruta algorithm are more reliable and exhibit greater stability, among which FD-Boruta-PCR is the most stable, followed by FD-Boruta-PLSR. Considering the model estimation accuracy, the booting period is the most accurately estimated, with R² values exceeding 0.7.

An in-depth analysis of the correlation between spectral information and AGB will facilitate a comprehensive understanding of the growth status of rice. This study performed a correlation analysis between different orders of derivative spectrum and AGB at different growth stages of rice. Generally, the correlation between the derivative spectrum of various orders and AGB tended to increase and then decrease throughout the growth stage, potentially due to the influence of the rice growth cycle (Xu et al., 2023). From the tillering stage to heading stage, as the chlorophyll content in rice leaves increases and the vegetation canopy structure becomes fully developed, the canopy becomes richer in spectral information, which can more accurately reflect crop characteristics (Ren et al., 2018). In the mature stage, as stems and leaves progressively wither and yellow, the chlorophyll content drops sharply, the spectral characteristics obtained are less able to accurately represent crop growth, leading to a decrease in the correlation between the canopy spectrum and AGB (Yang and Chen, 2004; He et al., 2019; Zhang et al., 2019).

Within the 680~750 nm band range, the correlation between the canopy spectrum and AGB reached its maximum value in different stages ( Figure 3 ). This occurs because this band serves as the transition region between the infrared and near-infrared bands, where spectral reflectance transitions rapidly from a low negative correlation to a high positive correlation. This shift is attributed to strong absorption and reflection (Kanke et al., 2016; Xu et al., 2022). The correlation between FD and AGB was generally greater than that between OS and SD at the different fertility stages ( Figure 4 ). This observation aligns with the findings of Liang et al. (2018) and Tong et al. (2023). As a method for analyzing spectral information, derivative transform can diminish noise and enhance data accuracy (Li and Xie, 2015). FD reflects the slope of the spectrum, while SD represents the change in the slope of the reflection spectrum. While SD identifies more absorption peaks, it also introduces noise and may result in errors (Shen et al., 2022). Therefore, FD is strongly correlated with AGB and can be effectively utilized for estimating rice AGB.

In the realm of feature selection, prior research has demonstrated that employing screened feature variables for model construction enhances the estimation power, inversion accuracy, and utility of the original models (Gao et al., 2019; Sun et al., 2021). For example, Yu et al. (2023) used the SPA algorithm to extract sensitive bands in rice canopy spectral data, and combined with PROSAIL to establish a rice AGB estimation model, achieving high accuracy (R²=0.69). This study yielded similar findings, the characteristic band had a greater estimation ability than the original band. The difference is that previous research is usually based on OS and does not involve derivative transform. Therefore, whether the estimation model constructed by derivative transformed spectrum is better than OS remains to be determined. This study performs SG smoothing and derivative transform on OS and selects characteristic bands based on the optimal derivative spectrum. The results show that the Boruta algorithm is more robust than the RFE algorithm, and the selected feature bands are more sensitive, which is conducive to constructing subsequent rice AGB estimation model.

Under identical conditions, the most accurate AGB estimates were achieved using feature bands selected by the Boruta algorithm. This superiority of the Boruta algorithm is attributed to its ability to identify bands of features that are genuinely relevant to the dependent variable, thereby enhancing the prediction accuracy of the model (Kursa and Rudnicki, 2010), a conclusion that aligns with the findings of Degenhardt et al. (2019). However, the RFE algorithm exhibited suboptimal performance in the jointing, heading, and maturity stages. This could be due to the RFE algorithm generates feature subsets with corresponding accuracy by continuously building models. This process may result in retaining a large number of features, leading to significant collinearity between bands and diminishing the model’s estimation accuracy (Paul et al., 2015; Chen et al., 2018), echoing the research results of Lin et al. (2023). The poorest performance was observed when the entire band was utilized as an input variable, attributed to the presence of redundant information and increased collinearity among bands, which impaired the model’s estimation capability (Hansen and Schjoerring, 2003; Pan et al., 2017).

Compared with the RFE algorithm, the Boruta algorithm identified fewer feature bands ( Table 1 ); however, the resulting estimation model was more stable. This stability may be due to the characteristic bands determined by the Boruta algorithm being more effective and independent (Poona et al., 2016). Additionally, when comparing feature bands screened by both the Boruta and RFE algorithms, it was noted that their intersection predominantly occurred in the “red edge” region. This could be due to the band encapsulates rich crop information and is highly correlated with AGB (Horler et al., 1983; Filella and Penuelas, 1994), consistent with the findings of Cheng et al. (2017), who assessed the estimation effects of eight vegetation indices on rice canopy composition AGB and found the red edge index to be particularly sensitive to leaf AGB, achieving the highest estimation accuracy.

Another aspect of interest is that the characteristic bands identified by the Boruta algorithm, which are relatively evenly distributed across the spectrum, are predominantly found at wavelengths of 420 nm, 644 nm, 750 nm, and 842 nm. These characteristic bands are mainly located in areas sensitive to crop AGB response and are relatively evenly distributed. During the tillering stage, the characteristic bands are primarily located in the “red edge” region, which may be due to the low vegetation coverage at this time and the spectrum response is not obvious (Kokaly and Clark, 1999; Clevers et al., 2001). In the jointing stage, characteristic wavelengths are observed in the near-infrared region, likely due to the increase in rice canopy biomass, making the wavelength response in this region more pronounced and easier to detect during the selection process (Datt, 1998). From the heading to the maturity stage, a few characteristic wavelengths in the blue light region are identified, possibly because the chlorophyll content in the leaves gradually decreases, leading to increased spectral reflectance in the blue light region (Yan-lin et al., 2004). Thus, the Boruta algorithm effectively mines the spectral information of the rice canopy, and the selected characteristic bands align with the spectral response changes in the rice canopy, thereby enhancing the accuracy of AGB estimation.

The performances of various models were meticulously compared, with the PCR model emerging as the most reliable and stable for estimating AGB. The differences between the R² values for the modeling set and the validation set are minimal, ranging from 0 to 0.1. Both the RMSE and MAE are lower for the PCR model than for the other models. This superior performance of the PCR model can be attributed to its foundation in predictive data mining technology through principal component analysis (PCA), which efficiently reduces the dimensionality of independent variables, mitigates the effects of multicollinearity among variables, and enhances the model’s adaptability (Suryakala and Prince, 2019). In the PLSR model. Models constructed with three different input variables all demonstrated the ability to estimate rice AGB, particularly at the booting stage, when the R² of the validation set exceeded 0.6. This performance is likely due to the robust adaptability of the PLSR algorithm, its ability to diminish the dimensionality of spectral data, its ability to effectively handle complex collinear relationships between independent variables, and its overall enhancement of the model’s estimation accuracy (Helland, 2001). In the SVM model, estimation models built on FD-RFE and FD-FB inputs exhibited overfitting at the jointing, heading, and maturity stages. Due to the excessive number of FD-RFE and FD-FB, when fitting as sample data, the noise interference in the model is large, resulting in an increase in estimation error. Even some noise may be recognized as characteristic frequency bands by machine learning algorithms, destroying the preset classification rules and significantly affecting the accuracy of model estimation (Cherkassky, 1997; Shafaei and Kisi, 2017; Raja et al., 2022). FD-Boruta has a small number but high estimation potential and can solve collinearity problems well when combined with the SVM algorithm. Similar outcomes were also observed in the RR model. This may be because the RR algorithm cannot automatically select important feature variables when fitting sample data. Therefore, when the amount of input sample data is large, it is easily affected by outliers, thereby reducing the model’s predictive ability. It may also be that because determining optimal ridge parameters is critical when building an estimation model, poor parameter selection can lead to overfitting of the model, thereby reducing its interpretability (Smith and Campbell, 1980; Forrester and Kalivas, 2004). Moreover, this study demonstrates that the model achieves the highest estimation accuracy during the booting stage. This can be ascribed to the booting stage, which is the primary period for increases in rice chlorophyll and is characterized by high vegetation coverage and the absence of panicles. At this juncture, noise interference is minimized, and the spectral information collected is purer and more precise, providing advantageous conditions for estimating rice AGB (Chang et al., 2005; Takai et al., 2006; Kawamura et al., 2018).