# Potato Leaf Chlorophyll Content Estimation through Radiative Transfer Modeling and Active Learning

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}values of model validation accuracy for the potato whole plantation period and three single growth periods are 0.742, 0.683, 0.828, and 0.533, respectively with RMSE values of 4.207, 4.364, 2.301, and 3.791 µg/cm

^{2}. Compared with the LCC inversion accuracy through LUT with a cost function, the validation accuracies of the GPR_PROSPECT-AL hybrid model were improved by 0.119, 0.200, 0.328, and 0.255, and the RMSE were reduced by 3.763, 2.759, 0.118, and 5.058 µg/cm

^{2}, respectively. The study results indicate that the hybrid method combined with the radiative transfer model and active learning can effectively select informative training samples from a data pool and improve the accuracy of potato LCC estimation, which provides a valid tool for accurately monitoring crop growth and growth health.

## 1. Introduction

^{2}of 0.91 by using the NAOC Proba/CHRIS hyperspectral data [12]. Additionally, machine learning (ML) methods use a wider range of spectral features to deal with complex regression problems. Wang et al. employed random forest (RF) techniques to identify specific wavelengths in the spectrum that are sensitive to chlorophyll content in rice canopy leaves. Then, they developed a partial least squares regression model to estimate the chlorophyll content of maize leaves [13]. Ban et al. established an estimation model of LCC based on rice chlorophyll content using partial least squares regression (PLSR), support vector regression (SVR), and artificial neural network (ANN) methods [14]. Such methods are relatively simple and easy to use, but the empirical relationship between the two is susceptible to external factors (e.g., sensor, vegetation type, and background reflectance) [15]. However, the use of the radiation transfer model (RTM) is one of the various techniques for the quantitative inversion of vegetation physicochemical characteristics that has gained increasing attention. It follows specific physical laws, quantitatively describes the relationship between canopy structural parameters and canopy spectral reflectance, and is unaffected by vegetation. Currently, the main inversion methods based on RTM are (1) parametric inversion [16], (2) nonparametric inversion [17], (3) inversion based on physical methods such as look-up table (LUT) [18], and (4) hybrid methods [19]. Among them, the hybrid method uses RTM-generated data to train a machine-learning model to express the relationship between the two. It combines the simplicity of empirical statistical methods with the versatility of physical models. It provides more accurate and faster inversion of the biophysical and chemical parameters of reference crops than other methods [20]. Xu et al. coupled RTM with the Bayesian network model (BNM) for rice canopy chlorophyll content and leaf area index inversion [21]. Pascual-Venteo et al. compared two spectral dimension reduction strategies, namely GPR-20PCA and GPR-20BR. They found that the inversion results using the PCA strategy were slightly superior to band ordering with all variables. This suggests that the GPR-20PCA model exhibits higher fidelity [22]. Zhu et al. demonstrated that the hybrid model, in combination with Gaussian process regression (GPR) and the physical model, can accurately retrieve the canopy water content of crops, thus confirming that the approach is suitable for estimating canopy water content [23]. Antonucci et al. demonstrated that the combination of the PROSAIL model and the ML Suna method can better estimate biophysical traits [24]. The above approaches demonstrate that integrating MLRAs (Machine Learning Regression Analysis) with RTMs can yield successful inversion models for estimating biophysical and chemical parameters in crops.

## 2. Materials and Methods

#### 2.1. Experimental Design

^{2}. Potato mid-tillage cultivation was conducted on 25 May. The base fertilizer was applied at the same time as the potato sowing on 13 May 2022, and the top dressing was applied on 2 June 2022. The distribution of the experimental plot is as follows (Figure 1).

_{2}O/ha were set, namely K0, K1, K2, K3, and K4, with three replicates and 30 plots. Potassium fertilizer was also applied at a 7:3 base fertilizer and topdressing ratio during the potato sowing and budding periods. Nitrogen and potassium fertilizers were both applied as base fertilizers in one go.

#### 2.2. Data Acquisition

#### 2.2.1. Spectral Measurement of Potato Leaves

#### 2.2.2. Determination of Leaf Chlorophyll Content

^{2}) was calculated according to Lichtenthaler’s method [36,37]. It was calculated using Equations (1) and (2):

^{2}.

#### 2.3. Data Analysis Flow and Methods

#### 2.3.1. PROSPECT-4 Model and LUT Generation

#### 2.3.2. Active Learning

#### 2.3.3. Gaussian Process Regression

#### 2.4. LCC Modelling and Accuracy Assessment

#### 2.4.1. LCC Inversion Based on LUT and Cost Function

#### 2.4.2. Hybrid Modeling Approach

#### 2.4.3. Model Accuracy Assessment

^{2}) and the RMSE were used as the indicators to evaluate model accuracy. The formulae for the relevant indicators are as follows (Equations (5) and (6)):

## 3. Results and Analysis

#### 3.1. Relationship between Measured LCC and Spectrum

#### 3.2. LUT Generation with PROSPECT-4 Model

#### 3.2.1. Global Sensitivity Analysis of PROSPECT-4 Model Input Parameters

#### 3.2.2. PROSPECT-4 Input Parameters and LUT Generation

^{2}; Cw: 0.001–0.08 g/cm

^{2}; and Cm: 0.0001–0.05 g/cm

^{2}. These parameters were defined based on relevant literature as well as measured data, and the model was then run to simulate the corresponding spectral reflectance of the leaves. Based on previous studies and related literature, 2000 simulations were chosen to establish the LUT in this study.

#### 3.3. Potato LCC Inversion

#### 3.3.1. GPR_PROSPECT Combined with AL Modeling Inversion

^{2}, NRMSE, and the efficiency of algorithm were used as evaluation metrics to assess different AL methods. Finally, the AL method with the highest R

^{2}, lowest NRMSE, and shortest time was adopted as the AL method used in this study. The number of training samples from different growth periods selected for the best AL technique was determined to be the optimal number of samples when the root mean square error (RMSE) was at its minimum. For the whole plantation period data, the R

^{2}of the GPR_PROSPECT-AL model based on the EBD algorithm was 0.742, the NRMSE was 9.743%, and the model runtime was 0.026 s, which had certain advantages. During the period of potato tuber formation, the GPR_PROSPECT-AL inversion model, utilizing the EBD algorithm, exhibited an R

^{2}value of 0.683, an NRMSE value of 0.118, and a computational time of 0.026 s. Similarly, during the potato tuber growth period, the inversion model based on RS yielded an R

^{2}value of 0.828, an NRMSE value of 0.088, and a computational time of 0.026 s. Lastly, during the potato starch accumulation period, the inversion model based on the EBD algorithm achieved an R

^{2}value of 0.553, an NRMSE value of 0.103, and a computational time of 0.003 s. Figure 6 shows the variation of RMSE values with the number of samples for different growth periods of potatoes when selecting the training samples based on the optimal AL algorithm. The selection results of training samples for the optimal AL method for chlorophyll modeling in different growth periods of potatoes were 172 for the whole plantation period, 163 for the tuber formation period, 129 for the tuber growth period, and 201 for the starch accumulation period.

^{2}of 0.978, RMSE of 2.869 µg/cm

^{2}, and NRMSE of 4.202%. When applying the AL method to the potato single growth period, R

^{2}reached 0.976, 0.965, and 0.944 during the potato tuber formation period (Figure 7b, n = 129), tuber growth period (Figure 7c, n = 163), and starch accumulation period (Figure 7d, n = 201), respectively.

#### 3.3.2. Chlorophyll Inversion Based on LUT CF Method

^{2}, respectively. Some of the minimal values are relatively higher than the measured LCC ranges of 8.716–45.718, 25.304–51.123, 8.716–34.828, and 10.526–33.4967 µg/cm

^{2}. This could be attributed to the smaller sample size in the single growth period, localized search by the CF, or an incomplete improvement of the inversion’s ill-posedness by the CFs. However, most optimal simulated spectral reflectance values correspond well with the measured LCC values. Hence, the above results of the optimal spectral selection are utilized for model validation.

#### 3.4. Validation of Inversion Model for Potato Chlorophyll Content

^{2}= 0.742, RMSE = 4.207 µg/cm

^{2}, and NRMSE = 9.921%. In Figure 9a

_{1}, the validation results for the LUT_PROSPECT CF model are shown with a validation accuracy of R

^{2}= 0.623, RMSE = 7.970 µg/cm

^{2}, and NRMSE= 21.539% for the whole plantation period. The research findings indicate that when using the AL method, the validation accuracy of the whole plantation period inversion model increases by 0.119 compared to the traditional LUT inversion method, demonstrating the effectiveness of the AL method in enhancing model precision. The validation accuracy of the GPR_PROSPECT-AL model for potato during a single growth period is R

^{2}= 0.683, 0.828, and 0.533, as shown in Figure 9b–d. The validation accuracy of the LUT CF algorithms is shown in Figure 9b

_{1}–d

_{1}, where the R

^{2}values from the tuber formation phase to the starch accumulation period are 0.483, 0.500, and 0.278, respectively. It can be seen that the potato LCC model constructed based on the AL method (Figure 9a–d) was superior to the model constructed by the LUT CF method, which is because the AL method can select samples in a large number of simulated datasets that better match the measured data, thus improving the inversion accuracy.

## 4. Discussion

#### 4.1. AL for Hybrid Retrieval Methods

#### 4.2. Analysis of Potato LCC Hybrid Inversion Model Construction

^{2}, whereas the R

^{2}values increased by 0.119, 0.200, 0.328, and 0.255, respectively. The results indicate that although hybrid model may not alleviate the limitations of the RTM, it offers the primary advantage of providing a comprehensive training database for ML regression models without the need to collect large amounts of data in the field.

## 5. Conclusions

- (1)
- This study demonstrated that the AL algorithm was able to screen the modeling samples efficiently. Based on the measured labeled dataset of potatoes at different growth periods, this study constructed effective modeling samples of potato LCC at different growth periods from the simulated data pool. The training samples were 172, 163, 129, and 201 for the whole plantation, tuber formation, tuber growth, and starch accumulation periods, respectively. The EBD algorithm in the AL algorithm was more efficient in the sample screening process. Based on whole- and single-fertility validation data, six different AL methods were used in this study to screen the training set from the simulated dataset. Each AL method converged faster to the lower error bound than a random sampling strategy. Diversity criteria (EBD, ABD, and CBD) generally performed the best both in terms of reaching high accuracies as well processing time.
- (2)
- Compared with the LUT CF method, the hybrid model constructed using GPR_PROSPECT-AL has higher modeling accuracy. This indicates that the RTM-based simulation can generate a sufficiently large training dataset and can be used for inverse LCC model training, while the AL approach helps to optimize the training samples for the RTM simulation and improves the accuracy of the model.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Analysis of chlorophyll content distribution and spectral reflectance changes at different growth periods. (

**a**) Spectral reflectance maps at different potato growth periods; (

**b**) Correlation between LCC and leaf spectra at different potato growth periods.

**Figure 5.**Analysis of spectral curves of potatoes from different datasets. (

**a**) Measured spectral curves of potatoes; (

**b**) Simulated spectral curves of potatoes.

**Figure 6.**Selection results of training samples for optimal AL method for chlorophyll modeling in different growth periods of potatoes. (

**a**) Selection results of AL methods for the whole plantation period; (

**b**) Selection results of AL method during tuber formation period; (

**c**) Selection results of AL method for tuber growth period; (

**d**) Selection results of AL method for starch accumulation period.

**Figure 7.**Scatter plot of measured and estimated LCC for GPR_PROSPECT-AL model at different potato growth periods. (

**a**) GPR_ PROSPECT-AL model for potato whole plantation period; (

**b**) GPR_PROSPECT-AL model for potato tuber formation period; (

**c**) GPR_PROSPECT-AL model for potato tuber growth period; (

**d**) GPR_PROSPECT-AL model for potato starch accumulation period.

**Figure 8.**Spectrum selected from LUT based on CF and measured data. (

**a**) Spectrum selected by the normal distribution-LSE during potato whole plantation period; (

**b**) Spectrum selected by the normal distribution-LSE during potato tuber formation period; (

**c**) Spectrum selected by the normal distribution-LSE during potato tuber growth period; (

**d**) Spectrum selected by the Laplace distribute during potato starch accumulation period.

**Figure 9.**Scatter plots of validation accuracy of different models for potato LCC. (

**a**–

**d**) validation accuracy of GPR_PROSPECT-AL models of potato whole plantation period, tuber formation period, tuber growth period, and starch accumulation period, respectively; (

**a**–

_{1}**d**) are the validation accuracies of LUT-PROSPET CF models of potato whole plantation period, tuber formation period, tuber growth period, and starch accumulation period, respectively.

_{1}Parameter | Unit | Min | Max | Samples |
---|---|---|---|---|

Chlorophyll content (Cab) | µg/cm^{2} | 0 | 70 | 2 |

Equivalent water thickness (Cw) | g/cm^{2} | 0.0001 | 0.08 | 2 |

Leaf structure (N) | — | 1.5 | 2.5 | 2 |

Dry matter content (Cm) | g/cm^{2} | 0.0001 | 0.05 | 2 |

AL Selected Criterions | AL Algorithms | Equation | Literatures |
---|---|---|---|

Diversity Criteria Methods | Euclidean distance-based diversity (EBD) | ${\mathrm{d}}_{\mathrm{E}}={\Vert {\mathrm{x}}_{\mathrm{u}}-{\mathrm{x}}_{\mathrm{l}}\Vert}_{2}^{2}$ | [43] |

Angle-based diversity (ABD) | $\angle \left({\mathrm{x}}_{\mathrm{u}},{\mathrm{x}}_{\mathrm{l}}\right)={\mathrm{cos}}^{-1}\left(\frac{<{\mathrm{x}}_{\mathrm{u}},{\mathrm{x}}_{\mathrm{l}}>}{\Vert {\mathrm{x}}_{\mathrm{u}}\Vert \xb7\Vert {\mathrm{x}}_{\mathrm{l}}\Vert}\right)$ | [46] | |

Cluster-based diversity (CBD) | clustering algorithm | [47] | |

Uncertainty Criteria Methods | Pool of regressors (PAL) | ${\mathsf{\sigma}}_{\mathrm{y}}^{2}=\frac{1}{\mathrm{k}}{\sum}_{\mathrm{i}=1}^{\mathrm{k}}{\left({\mathrm{y}}_{\mathrm{i}}-\overline{\mathrm{y}}\right)}^{2}$ | [43] |

Residual regression AL (RSAL) | $\mathrm{e}\left(\mathrm{x}\right)=\mathrm{y}-\stackrel{\u02c6}{\mathrm{y}}$ | [45] | |

Entropy query by bagging (EQB) | $\mathrm{H}\left(\mathrm{x}\right)=-{\sum}_{\mathrm{i}=1}^{\mathrm{k}}\mathrm{p}\left({\mathrm{x}}_{\mathrm{i}}\right)\mathrm{logp}\left({\mathrm{x}}_{\mathrm{i}}\right)$ | [44] |

Measured Datasets | Tuber Formation Period | Tuber Growth Period | Starch Accumulation Period | Whole Plantation Period | |
---|---|---|---|---|---|

Data collection Date | 21 July 2022 | 8 August 2022 | 28 August 2022 | — | |

LCC (µg/cm^{2}) | Sample size | 60 | 60 | 60 | 180 |

Min | 25.565 | 8.797 | 10.526 | 8.797 | |

Max | 51.123 | 34.828 | 33.846 | 51.123 | |

Mean | 38.344 | 21.813 | 22.186 | 29.960 | |

CV (%) | 0.471 | 0.844 | 0.743 | 0.998 | |

LCC for N treatment (µg/cm^{2}) | Sample size | 30 | 30 | 30 | 90 |

Min | 25.565 | 8.797 | 13.945 | 8.797 | |

Max | 46.192 | 33.473 | 33.846 | 46.192 | |

Mean | 35.879 | 21.135 | 23.896 | 27.4945 | |

CV (%) | 0.407 | 0.826 | 0.589 | 0.962 | |

LCC for K treatment (µg/cm^{2}) | Sample size | 30 | 30 | 30 | 90 |

Min | 25.854 | 14.689 | 10.526 | 10.526 | |

Max | 51.123 | 34.828 | 28.357 | 51.123 | |

Mean | 38.489 | 24.759 | 19.442 | 30.825 | |

CV (%) | 0.464 | 0.575 | 0.649 | 0.931 |

**Table 4.**Optimal active learning (AL) method selection for chlorophyll modeling in potato different growth periods.

AL | Whole Plantation Period | Tuber Formation Period | Tuber Growth Period | Starch Accumulation Period | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

GPR_PROSPECT-AL | GPR_PROSPECT-AL | GPR_PROSPECT-AL | GPR_PROSPECT-AL | |||||||||

R^{2} | NRMSE | Time | R^{2} | NRMSE | Time | R^{2} | NRMSE | Time | R^{2} | NRMSE | Time | |

RAL | 0.701 | 0.107 | 0.022 | 0.481 | 0.154 | 0.022 | 0.726 | 0.116 | 0.016 | 0.312 | 0.212 | 0.035 |

RS | 0.732 | 0.012 | 0.022 | 0.517 | 0.148 | 0.02 | 0.828 * | 0.088 | 0.026 | 0.256 | 0.195 | 0.033 |

PAL | 0.743 | 0.099 | 0.031 | 0.481 | 0.154 | 0.029 | 0.792 | 0.097 | 0.031 | 0.266 | 0.214 | 0.032 |

ABD | 0.729 | 0.104 | 0.031 | 0.51 | 0.151 | 0.031 | 0.632 | 0.129 | 0.038 | 0.214 | 0.218 | 0.033 |

CBD | 0.725 | 0.103 | 0.032 | 0.518 | 0.148 | 0.028 | 0.815 | 0.09 | 0.028 | 0.232 | 0.218 | 0.033 |

EBD | 0.742 * | 0.099 | 0.026 | 0.683 * | 0.118 | 0.03 | 0.804 | 0.092 | 0.031 | 0.533 * | 0.147 | 0.003 |

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## Share and Cite

**MDPI and ACS Style**

Ma, Y.; Qiu, C.; Zhang, J.; Pan, D.; Zheng, C.; Sun, H.; Feng, H.; Song, X.
Potato Leaf Chlorophyll Content Estimation through Radiative Transfer Modeling and Active Learning. *Agronomy* **2023**, *13*, 3071.
https://doi.org/10.3390/agronomy13123071

**AMA Style**

Ma Y, Qiu C, Zhang J, Pan D, Zheng C, Sun H, Feng H, Song X.
Potato Leaf Chlorophyll Content Estimation through Radiative Transfer Modeling and Active Learning. *Agronomy*. 2023; 13(12):3071.
https://doi.org/10.3390/agronomy13123071

**Chicago/Turabian Style**

Ma, Yuanyuan, Chunxia Qiu, Jie Zhang, Di Pan, Chunkai Zheng, Heguang Sun, Haikuan Feng, and Xiaoyu Song.
2023. "Potato Leaf Chlorophyll Content Estimation through Radiative Transfer Modeling and Active Learning" *Agronomy* 13, no. 12: 3071.
https://doi.org/10.3390/agronomy13123071