# Estimation of the Total Soil Nitrogen Based on a Differential Evolution Algorithm from ZY1-02D Hyperspectral Satellite Imagery

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Soil Sample Acquisition and TN Content Determination

#### 2.3. ZY1-02D/AHSI Remote Sensing Image Collection and Pre-Processing

#### 2.4. Methodology

#### 2.4.1. Spectral Reflectance Transformation

#### 2.4.2. Selection of Spectral Feature Variables

- (a)
- Initializing the population: M individuals, each made up of an n-dimensional vector, are created uniformly and randomly in the solution space. The vector and the j-th dimensional value assigned to the i-th individual, respectively, are given in Equations (5) and (6):$$\begin{array}{c}{\mathrm{X}}_{\mathrm{i}}\left(0\right)=\left({\mathrm{x}}_{\mathrm{i},1}\left(0\right),{\mathrm{x}}_{\mathrm{i},2}\left(0\right),{\mathrm{x}}_{\mathrm{i},3}\left(0\right),\dots ,{\mathrm{x}}_{\mathrm{i},\mathrm{n}}\left(0\right)\right)\\ \mathrm{i}=1,\text{}2,\text{}3,\dots ,\text{}\mathrm{M}\end{array}$$$$\begin{array}{c}{\mathrm{X}}_{\mathrm{i},\mathrm{j}}\left(0\right)={\mathrm{L}}_{\mathrm{j}\_\mathrm{min}}+\mathrm{rand}\left(0,1\right)\left({\mathrm{L}}_{\mathrm{j}\_\mathrm{max}}-{\mathrm{L}}_{\mathrm{j}\_\mathrm{min}}\right)\\ \mathrm{i}=1,\text{}2,\text{}3,\dots ,\text{}\mathrm{M};\mathrm{j}=1,\text{}2,\text{}3\dots ,\text{}\mathrm{n}\end{array}$$
- (b)
- Mutation operation: The DE algorithm implements an individual mutation operation through a difference strategy. Equation (7) shows the vector mutation operation for each individual:$${\mathrm{W}}_{\mathrm{i}}\left(\mathrm{G}+1\right)={\mathrm{X}}_{\mathrm{c}1}\left(\mathrm{G}\right)+\mathrm{Z}({\mathrm{X}}_{\mathrm{c}2}\left(\mathrm{G}\right)-{\mathrm{X}}_{\mathrm{c}3}\left(\mathrm{G}\right))$$
- (c)
- Crossover operation: the mutated individuals are subject to the crossover operation shown in formula eight:$${\mathrm{U}}_{\mathrm{i},\mathrm{j}}\left(\mathrm{G}+1\right)=\left\{\begin{array}{cc}\hfill {\mathrm{W}}_{\mathrm{i},\mathrm{j}}\left(\mathrm{G}+1\right)\hfill & \hfill \mathrm{i}\mathrm{f}\text{}\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{d}\text{}\left(0,1\right)\le \mathrm{C}\mathrm{R}\hfill \\ \hfill {\mathrm{x}}_{\mathrm{i},\mathrm{j}}\left(\mathrm{G}\right)\hfill & \hfill \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{s}\mathrm{e}\hfill \end{array}\right.$$
- (d)
- The operation for selecting the next generation of individuals is shown in Equation (9):$${\mathrm{X}}_{\mathrm{i}}(\mathrm{G}+1)=\left\{\begin{array}{cc}\hfill {\mathrm{U}}_{\mathrm{i}}\left(\mathrm{G}+1\right)\hfill & \hfill \mathrm{i}\mathrm{f}\text{}({\mathrm{U}}_{\mathrm{i}}\left(\mathrm{G}+1\right)\le \mathrm{f}{(\mathrm{X}}_{\mathrm{i}}\left(\mathrm{G}\right))\hfill \\ \hfill {\mathrm{X}}_{\mathrm{i}}\hfill & \hfill \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{s}\mathrm{e}\hfill \end{array}\right.$$

#### 2.4.3. Construction and Evaluation of the TN Content Estimation Model

^{2}), the mean absolute error (MAE), and the root mean square error (RMSE) were used to evaluate the accuracy of the prediction model. Lower MAE and RMSE values and higher R

^{2}values correspond to more precise model estimation [47].

## 3. Results

#### 3.1. Statistical Description of the TN Content of the Sampling Points

#### 3.2. TN Content Spectral Features Analysis and Spectral Transformation Processing

#### 3.2.1. Spectral Features Analysis of TN Content

#### 3.2.2. Spectral Transformation Processing

#### 3.3. Selection of TN Spectral Characteristics

#### 3.4. TN Content Model Estimation Results

#### 3.4.1. Results of All Bands Based on the Individual Spectral Reflectance Transformation

^{2}ranged from 0.45 to 0.59, the MAE ranged from 0.11 to 0.13 g/kg, and the RMSE ranged from 0.15 to 0.17 g/kg. SVM was the best model for estimating the TN content based on all bands after combining the data from the training and test set models.

^{2}was 0.59, the MAE was 0.11 g/kg, and the RMSE was 0.15 g/kg for the test set.

#### 3.4.2. Results of the LASSO Feature Selection Based on the Individual Spectral Reflectance Transformations

^{2}value of the MLR training set models ranged from 0.53 to 0.67, and higher R

^{2}values corresponded to lower MAE and RMSE values. The training set R

^{2}value for the SVM varied from 0.54 to 0.62, and the lowest values of MAE and RMSE were 0.10 and 0.14 g/kg, respectively. According to the outcomes of the test set models, the SVM model made the best predictions, followed by the PLSR and MLR models. The R

^{2}of the SVM for the test set ranged from 0.47 to 0.61, the MAE ranged from 0.11 to 0.13 g/kg, and the RMSE ranged from 0.14 to 0.17 g/kg. Combining the training and test set model results, the SVM was the optimal model for TN content estimation based on the LASSO feature selection.

^{2}= 0.61, MAE = 0.11 g/kg, and RMSE = 0.14 g/kg.

#### 3.4.3. LASSO-Selected Spectral Band Combinations for the Four Spectral Reflectance Transformations

^{2}of 0.80; nevertheless, when compared with the other models, the test set model did not perform as well (LBC: LASSO-selected spectral band combination). In terms of the test set accuracy, the LBC–PLSR and LBC–SVM models both outperformed the LBC–MLR, with the LBC–SVM model outperforming the LBC–PLSR model in terms of prediction outcomes. The LBC–SVM model, with test set model metrics of R

^{2}= 0.57, MAE = 0.12 g/kg, and RMSE = 0.15 g/kg, was the best model for TN content estimation among the LASSO-selected feature band combinations. The scatter plots of the LBC–SVM model’s TN content measurements fitted to the predicted values are shown in Figure 8.

#### 3.4.4. DE Secondary Feature Selection from LASSO-Selected Spectral Band Combinations Based on Four Spectral Reflectance Transformations

^{2}= 0.85, MAE = 0.08 g/kg, and RMSE = 0.09 g/kg, while the corresponding values for the test set were R

^{2}= 0.72, MAE = 0.08 g/kg, and RMSE = 0.12 g/kg (Table 8). The LBC–DE–MLR and LBC–DE–PLSR models were comparable in predictive ability but inferior to the LBC–DE–SVM model. The LBC–DE–SVM was the best model for TN content estimation based on the LBC–DE quadratic feature selection (Figure 9). Moreover, compared with Figure 6, Figure 7 Figure 8, the fitted scatter plots of both the training set and test set models in Figure 9 were closer to the 1:1 line. The results show that the LBC-DE-SVM model had a better TN content estimation ability than the other models.

## 4. Discussion

#### 4.1. Role of Spectral Reflectance Transformation Processing

#### 4.2. The Role of Spectral Feature Extraction

^{2}value using LASSO feature selection: 0.61; best R

^{2}value of models using all bands: 0.59). This was mainly because the LASSO feature selection method could extract the characteristic spectral bands of TN according to the subtle relationship between TN and spectral reflectance and then achieve the purpose of eliminating redundant spectral variables and estimating the accuracy using the model. The model prediction results based on LBC–DE were noticeably superior to those based on the LBC, as shown in Figure 9 (best R

^{2}value for LBC–DE: 0.72; best R

^{2}value for LBC: 0.57). This implies that the LBC contained a significant amount of redundant information. The DE technique eliminated non-essential variables and retained valuable information, which enhanced the model’s estimation capacity.

#### 4.3. Estimated Model Comparison and Best Model TN Content Mapping

## 5. Conclusions

- (1)
- The transformation of the spectral reflectance data can highlight some of the enhanced spectral information. However, the best spectral data pre-processing methods for different estimation models differ, where even the optimal spectral transformation methods for the training and test sets of the same model are different. Suitable spectral reflectance transformation methods can be selected for different prediction models in the TN content estimation studies in other regions to improve the estimation accuracy.
- (2)
- Using the LASSO method for feature variable selection for full-band data not only reduced the spectral data redundancy and simplified the model but also improved the estimation accuracy of the model. Compared with individual spectral reflectance data, the LBC contained more valid spectral information and concentrated a large amount of noise information. This study used a combination of the DE algorithm and the prediction model to extract feature variables from the LBC, which can achieve the purpose of retaining valid information in the LBC and eliminating invalid information and can provide a reference for future research in making full use of the spectral reflectance transform and feature data for TN content estimation.
- (3)
- Compared with ground-based hyperspectral data and airborne hyperspectral data, ZY1-02D/AHSI hyperspectral satellite image data have the advantages of wide image coverage, the automatic acquisition of hyperspectral remote sensing image data, and a short return cycle, and thus, it can enable the dynamic, rapid, and large area estimation of TN content.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Maps of the research site. (

**a**) Map of China, where the blue area is Henan Province; (

**b**) map of Henan Province; (

**c**) hyperspectral ZY1-02D/AHSI image of the research area, together with the locations of the soil sampling sites (in this study, only the reflectance data of satellite images in cultivated areas were extracted for experimentation, excluding buildings and other areas).

**Figure 4.**Spectral reflectance profiles for different TN contents: (

**a**) original reflectance, (

**b**) inverse reflectance, (

**c**) natural logarithm of the reflectance, and (

**d**) first-order derivative reflectance.

**Figure 5.**LASSO algorithm TN feature band selection results: (

**a**) OR–LASSO, (

**b**) IR–LASSO, (

**c**) NLR–LASSO, and (

**d**) FDR–LASSO.

**Figure 6.**Scatter plots of measured and predicted TN contents based on individual spectral reflectance conversions of the best estimation model for all bands: (

**a**) OR–SVM training set model; (

**b**) OR–SVM test set model.

**Figure 7.**Scatter plots of the measured and predicted values of the best estimation model for TN content based on the LASSO feature selection: (

**a**) OR–LASSO–SVM training set model; (

**b**) OR–LASSO–SVM test set model.

**Figure 8.**Scatter plots of the measured and predicted values of the best estimation model for TN content based on the LBC: (

**a**) LBC–SVM training set model; (

**b**) LBC–SVM test set model.

**Figure 9.**Scatter plot of the measured and predicted values of the best estimation model for TN content based on LBC–DE: (

**a**) LBC–DE–SVM training set model; (

**b**) LBC–DE–SVM test set model.

**Figure 11.**Map of the best model (LBC–DE–SVM) for estimating the TN content in the agricultural areas of the study area: (

**a**) agricultural distribution in the study area and (

**b**) spatial distribution of the TN content.

Items | Parameters |
---|---|

Date of launch | 12 September 2019 |

Spectral bands | 76 (VNIR), 90 (SWIR) |

Spectral range (nm) | 400–2500 |

Spectral resolution (nm) | 10 (VNIR), 20 (SWIR) |

Spatial resolution (m) | 30 |

Swath width (km) | 60 |

Revisit cycle (d) | 3 |

Set | N | Max (g/kg) | Min (g/kg) | Mean (g/kg) | SD (g/kg) | CV |
---|---|---|---|---|---|---|

Whole set | 595 | 1.80 | 0.37 | 1.01 | 0.22 | 0.22 |

Training set | 476 | 1.80 | 0.37 | 1.01 | 0.22 | 0.22 |

Test set | 119 | 1.71 | 0.43 | 1.02 | 0.24 | 0.23 |

Reflectance Representation | n | Wavelengths (nm) |
---|---|---|

OR | 77 | 396–405, 439–227, 542, 577, 619, 696–705, 756–774, 791, 808, |

842, 894, 920, 945–954, 988–997, 1014–1073, 1123–1139, 1190, | ||

1224, 1308, 1341–1442, 1493, 1526, 1594, 1644–1678, 1711–1745, | ||

1779, 1812–1880, 1930–1981, 2014–2048, 2081–2098, | ||

2132–2199, 2267, 2300–2401, 2450–2501 | ||

IR | 17 | 395–404, 422, 447, 697, 1526, 1778–1795, 1845–1880, 1929–1947, |

1998, 2451, 2484–2501 | ||

NLR | 19 | 404, 422, 447, 697, 757, 1375, 1425, 1526, 1594, 1644, |

1845–1880, 1930–1947, 2048, 2199, 2484–2501 | ||

FDR | 141 | 404–430, 447–490, 524–559, 576–628, 645–705, 722–1106, |

1139–1173, 1207–1274, 1307–1324, 1357–1594, 1627, 1660–1795, | ||

1828–2132, 2165–2199, 2233–2317, 2350–2501 | ||

Total | 254 |

**Table 4.**Estimation results of the TN content for all bands based on individual spectral reflectance transformations.

Model | Reflectance | Training Set | Test Set | ||||
---|---|---|---|---|---|---|---|

R^{2} | MAE (g/kg) | RMSE (g/kg) | R^{2} | MAE (g/kg) | RMSE (g/kg) | ||

MLR | OR | 0.68 | 0.10 | 0.13 | 0.29 | 0.15 | 0.19 |

IR | 0.69 | 0.10 | 0.12 | 0.22 | 0.16 | 0.20 | |

NLR | 0.69 | 0.10 | 0.12 | 0.28 | 0.15 | 0.19 | |

FDR | 0.68 | 0.10 | 0.13 | 0.27 | 0.16 | 0.20 | |

PLSR | OR | 0.51 | 0.12 | 0.16 | 0.54 | 0.12 | 0.16 |

IR | 0.54 | 0.12 | 0.15 | 0.55 | 0.12 | 0.15 | |

NLR | 0.53 | 0.12 | 0.15 | 0.54 | 0.12 | 0.16 | |

FDR | 0.50 | 0.12 | 0.16 | 0.47 | 0.13 | 0.17 | |

SVM | OR | 0.60 | 0.10 | 0.14 | 0.59 | 0.11 | 0.15 |

IR | 0.61 | 0.10 | 0.14 | 0.58 | 0.11 | 0.15 | |

NLR | 0.61 | 0.10 | 0.14 | 0.58 | 0.11 | 0.15 | |

FDR | 0.58 | 0.10 | 0.14 | 0.45 | 0.13 | 0.17 |

Model | Reflectance | Training Set | Test Set | ||||
---|---|---|---|---|---|---|---|

R^{2} | MAE (g/kg) | RMSE (g/kg) | R^{2} | MAE (g/kg) | RMSE (g/kg) | ||

LASSO–MLR | OR | 0.62 | 0.11 | 0.14 | 0.49 | 0.13 | 0.16 |

IR | 0.53 | 0.12 | 0.15 | 0.56 | 0.12 | 0.15 | |

NLR | 0.54 | 0.12 | 0.15 | 0.55 | 0.12 | 0.15 | |

FDR | 0.67 | 0.10 | 0.13 | 0.32 | 0.15 | 0.19 | |

LASSO–PLSR | OR | 0.55 | 0.12 | 0.15 | 0.54 | 0.12 | 0.16 |

IR | 0.52 | 0.12 | 0.15 | 0.57 | 0.12 | 0.15 | |

NLR | 0.53 | 0.12 | 0.15 | 0.55 | 0.12 | 0.15 | |

FDR | 0.51 | 0.12 | 0.16 | 0.48 | 0.13 | 0.17 | |

LASSO–SVM | OR | 0.58 | 0.11 | 0.14 | 0.61 | 0.11 | 0.14 |

IR | 0.54 | 0.12 | 0.15 | 0.56 | 0.12 | 0.15 | |

NLR | 0.62 | 0.10 | 0.14 | 0.58 | 0.11 | 0.15 | |

FDR | 0.57 | 0.11 | 0.15 | 0.47 | 0.13 | 0.17 |

Model | Training Set | Test Set | ||||
---|---|---|---|---|---|---|

R^{2} | MAE (g/kg) | RMSE (g/kg) | R^{2} | MAE (g/kg) | RMSE (g/kg) | |

LBC–MLR | 0.80 | 0.08 | 0.10 | 0.23 | 0.19 | 0.24 |

LBC–PLSR | 0.52 | 0.12 | 0.15 | 0.54 | 0.12 | 0.16 |

LBC–SVM | 0.65 | 0.10 | 0.13 | 0.57 | 0.12 | 0.15 |

Reflectance | MLR | N | PLSR | N | SVM | N |
---|---|---|---|---|---|---|

Representation | Wavelengths (nm) | Wavelengths (nm) | Wavelengths (nm) | |||

OR | 404, 542, 576, 619, 765–774, | 33 | 705, 757, 1880, 2132 | 4 | 447, 954, 1139, 1308, 1341, | 11 |

791, 954, 1023, 1056, 1139, | 1375, 1425, 1812, 2317, | |||||

1190, 1308, 1442, 1526, 1644, | 2451 | |||||

1745, 1812–1845, 1880, 1930- | ||||||

1947, 1981, 2031–2048, 2082- | ||||||

2098, 2183–2199, 2267, 2301, | ||||||

2451 | ||||||

IR | 396, 697, 1526, 1795, 1880, | 7 | 1526, 1880, 1930–1947, 2451, | 7 | 404, 422, 1795, 1862, 2484, | 6 |

1998, 2501 | 2484–2501 | 2501 | ||||

NLR | 697, 757, 1425, 1526, 1880, | 9 | 422, 1526, 1593, 1880, 1947 | 5 | 404, 4222, 1644, 1880, 1947 | 5 |

1930, 2199, 2484–2501 | ||||||

FDR | 413, 490, 551–559, 594–628, | 49 | 413, 447–456, 551–559, 576- | 45 | 482, 525, 594–602, 619, 622, | 28 |

654–662, 679–688, 722–731, | 602, 619, 757, 808–842, 877, | 679–688, 705, 748, 834, | ||||

757, 834, 851, 868–877, 894, | 894, 928, 946, 980, 1073, | 877–885, 1073, 1089, 1224, | ||||

1073–1089, 1156–1173, 1257, | 1139, 1173, 1277, 1241, 1375, | 1526, 1745, 1778–1795, 1880, | ||||

1375, 1442–1476, 1526, 1678- | 1442, 1510–1526, 1678, 1728, | 1930, 2098, 2183, 2233, | ||||

1728, 1762, 1795, 1947–1981, | 1829–1846, 1880, 1930–1947, | 2301, 2501 | ||||

2048, 2081, 2199, 2267, | 1981, 2048–2098, 2132, 2183, | |||||

2367–2417, 2451 | 2367 | |||||

Total | 98 | 61 | 50 |

Model | Training Set | Test Set | ||||
---|---|---|---|---|---|---|

R^{2} | MAE (g/kg) | RMSE (g/kg) | R^{2} | MAE (g/kg) | RMSE (g/kg) | |

LBC–DE–MLR | 0.64 | 0.10 | 0.13 | 0.65 | 0.10 | 0.14 |

LBC–DE–PLSR | 0.57 | 0.11 | 0.15 | 0.60 | 0.11 | 0.14 |

LBC–DE–SVM | 0.85 | 0.08 | 0.09 | 0.72 | 0.08 | 0.12 |

Model | Training Set | Test Set | Model | Training Set | Test Set |
---|---|---|---|---|---|

OR–MLR | 0.014 | 0.032 | FDR–LASSO–MLR | 0.014 | 0.033 |

IR–MLR | 0.014 | 0.034 | OR–LASSO–PLSR | 0.013 | 0.029 |

NLR–MLR | 0.014 | 0.033 | IR–LASSO–PLSR | 0.012 | 0.028 |

FDR–MLR | 0.014 | 0.033 | NLR–LASSO–PLSR | 0.012 | 0.028 |

OR–PLSR | 0.012 | 0.027 | FDR–LASSO–PLSR | 0.012 | 0.025 |

IR–PLSR | 0.012 | 0.028 | OR–LASSO–SVM | 0.012 | 0.027 |

NLR–PLSR | 0.012 | 0.028 | IR–LASSO–SVM | 0.012 | 0.027 |

FDR–PLSR | 0.012 | 0.025 | NLR–LASSO–SVM | 0.013 | 0.028 |

OR–SVM | 0.012 | 0.028 | FDR–LASSO–SVM | 0.010 | 0.021 |

IR–SVM | 0.012 | 0.028 | LBC–MLR | 0.015 | 0.041 |

NLR–SVM | 0.012 | 0.028 | LBC–PLSR | 0.012 | 0.028 |

FDR–SVM | 0.010 | 0.021 | LBC–SVM | 0.012 | 0.025 |

OR–LASSO–MLR | 0.013 | 0.031 | LBC–DE–MLR | 0.014 | 0.031 |

IR–LASSO–MLR | 0.012 | 0.027 | LBC–DE–PLSR | 0.013 | 0.028 |

NLR–LASSO–MLR | 0.013 | 0.028 | LBC–DE–SVM | 0.015 | 0.030 |

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## Share and Cite

**MDPI and ACS Style**

Zhang, R.; Cui, J.; Zhou, W.; Zhang, D.; Dai, W.; Guo, H.; Zhao, S.
Estimation of the Total Soil Nitrogen Based on a Differential Evolution Algorithm from ZY1-02D Hyperspectral Satellite Imagery. *Agronomy* **2023**, *13*, 1842.
https://doi.org/10.3390/agronomy13071842

**AMA Style**

Zhang R, Cui J, Zhou W, Zhang D, Dai W, Guo H, Zhao S.
Estimation of the Total Soil Nitrogen Based on a Differential Evolution Algorithm from ZY1-02D Hyperspectral Satellite Imagery. *Agronomy*. 2023; 13(7):1842.
https://doi.org/10.3390/agronomy13071842

**Chicago/Turabian Style**

Zhang, Rongrong, Jian Cui, Wenge Zhou, Dujuan Zhang, Wenhao Dai, Hengliang Guo, and Shan Zhao.
2023. "Estimation of the Total Soil Nitrogen Based on a Differential Evolution Algorithm from ZY1-02D Hyperspectral Satellite Imagery" *Agronomy* 13, no. 7: 1842.
https://doi.org/10.3390/agronomy13071842