# Simulating Heat Stress of Coal Gangue Spontaneous Combustion on Vegetation Using Alfalfa Leaf Water Content Spectral Features as Indicators

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## Abstract

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## 1. Introduction

^{2}= 0.7, RMSE = 8.485). Krishna et al. [41] predicted RWC according to the water deficit stress status of rice genotypes based on spectral indices, multivariate techniques, neural network techniques, and existing water-band indices. They proposed new water-band indices—the ratio index (RI) and normalized difference ratio index (NDRI)—for this purpose. In previous studies, the water indicators obtained by remote sensing technology have been used to qualitatively analyze plant water condition over an entire monitoring period to determine environmental stress level on vegetation. However, the accuracy and timeliness of the results are usually insufficient.

## 2. Materials and Methods

#### 2.1. Experimental Design

#### 2.2. Data Acquisition

#### 2.2.1. Spectral Data

#### 2.2.2. Leaf Water Content

#### 2.3. Methods

#### 2.3.1. Spectral Feature Construction

**Raw spectral data processing:**MATLAB 2017a (MathWorks, Natick, MA, USA) was used to average the spectral curves collected for each treatment in the heat-stress test to reduce the differences within groups. Then, a one-dimensional Gaussian filter was applied to the mean spectral curve along the spectrum direction to smooth it. The sliding window was set to 5, as shown in Figure 2 and Supplementary Figure S1.

**First derivative spectrum:**Differential processing of a spectrum can reduce the influence of background information such as field noise and soil on spectral data [44]. The direct difference method was used to calculate the first-derivative spectrum of spectral reflectance to highlight the target spectral features. Equation (4) was used to calculate the first derivative of the spectrum.

**Spectral reflectance index:**The spectral reflectance index was constructed using the two-band combination method of raw and first-derivative spectral reflectance and compared with the conventional index (Table 1). The two-band combination method included the ratio vegetation index ($RVI\text{}({\lambda}_{1},\text{}{\lambda}_{2})$), normalized difference vegetation index ($NDVI\text{}({\lambda}_{1},\text{}{\lambda}_{2})$), and difference vegetation index ($DVI\text{}({\lambda}_{1},\text{}{\lambda}_{2})$). These are commonly used in remote sensing monitoring. The selection range of any band combination was between 340 and 2500 nm, and their formulas [45] are as follows:

#### 2.3.2. Spectral Feature Selection

**Correlation analysis:**The Pearson correlation coefficient (Equation (8)) was used to correlate the spectral parameters (raw spectrum, first-derivative spectrum, and vegetation index) with plant leaf water content indicators (LFMC, EWT, and RWC). Pairwise analysis selected highly correlated spectral features in the appropriate band range.

**Lasso regression:**The Lasso (least absolute shrinkage operator) regression model was proposed by Robert in 1996 and has become an important regression model in the field of machine learning [54]. The method is a compression estimator that constructs a penalty function to obtain a relatively refined model. This makes it compress some regression coefficients; that is, the sum of the absolute value of the forcing coefficient is less than a fixed value. Through regularization, the regression coefficients of some independent variables are compressed to zero, then the variable selection is completed. At the same time, Lasso regression retains the advantage of subset contraction and is a biased estimation model (Equation (9)) for dealing with data with multicollinearity.

#### 2.3.3. Assessment of Heat Stress by SF-LSTM

#### 2.3.4. Validation

^{2}) and root mean square error (RMSE) were used as indicators of its accuracy [26] (Equations (16) and (17)). Accuracy is defined as the degree of consistency between the model results and the true categories (Equation (18)). Ten-fold cross-validation was adopted for the training set [56].

## 3. Results

#### 3.1. LFMC, EWT, and RWC Time Series Analysis

#### 3.2. Correlation Analysis of Spectral Features and Leaf Water Content

#### 3.2.1. Correlations between Raw Spectrum, Derivative Spectrum, and Leaf Water Content Data

#### 3.2.2. Correlation between Spectral Reflectance Indices and Leaf Water Content

#### 3.3. Optimal Spectral Features

^{2}-value of the Lasso regression model constructed with FDS (1661), RVI (1525,1771), DVI (1412,740), and NDVI (1447,1803) as independent variables was 0.77 with an RMSE of 0.05. Although the spectral features were reduced, the model accuracy was still high.

#### 3.4. SF-LSTM Estimation of Heat-Stress Level

## 4. Discussion

#### 4.1. Leaf Water Content

#### 4.2. Spectral Features

#### 4.3. Heat Stress Estimation

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Field of simulation experiment of heat stress in alfalfa and (

**b**) schematic diagram of the heating equipment.

**Figure 2.**Schematic diagram of one-dimensional Gaussian filtering along the spectrum direction, with a sliding window of 5.

**Figure 4.**Time series of equivalent water thickness (EWT), live fuel moisture content (LFMC), and relative water content (RWC) in the control and experimental groups at leaf level from 16 October–15 November 2020; letters a, b, c, d and e are labeled to show significant differences between treatments within each measurement date.

**Figure 5.**Coefficients of correlation between EWT, RWC, LFMC, and the raw leaf and first-derivative spectral data.

**Figure 6.**Coefficients of correlation between EWT, RWC, and LFMC with RVI (λ1, λ2), NDVI (λ1, λ2), DVI (λ1, λ2), and ratio/normalized difference/difference vegetation indexes constructed from raw spectral data. (

**a**) Correlation between EWT and RVI (RVI band combinations based on raw reflectance relationship with EWT); (

**b**) Correlation between EWT and DVI; (

**c**) Correlation between EWT and NDVI; (

**d**) Correlation between RWC and RVI; (

**e**) Correlation between RWC and DVI; (

**f**) Correlation between RWC and NDVI; (

**g**) Correlation between LFMC and RVI; (

**h**) Correlation between LFMC and DVI and (

**i**) Correlation between LFMC and NDVI.

**Figure 7.**(

**a**) Use of 10-fold cross-validation to determine the regular coefficient (lambda, λ) of the Lasso model; (

**b**) predicted and actual values of LFMC by Lasso regression.

**Figure 8.**Loss and accuracy of the SF-LSTM model training set and validation set under different classification strategies and time series lengths.

Water-SRIs | Acronym | Equation ^{1} | Reference |

Water index | WI (900, 970) | ${R}_{900}/{R}_{970}$ | [46] |

Water index | WI (1300, 1450) | ${R}_{1300}/{R}_{1450}$ | [47] |

Normalized difference water index | NDWI | $({R}_{870}-{R}_{1260})/({R}_{870}+{R}_{1260})$ | [48] |

Moisture stress index | MSI | ${R}_{1610}/{R}_{842}$ | [49] |

Vegetation-SRIs | Acronym | Equation ^{1} | Reference |

Normalized difference vegetation index | NDVI | ${(\mathrm{R}}_{858}-{\mathrm{R}}_{645}{)/(\mathrm{R}}_{858}{+\mathrm{R}}_{645})$ | [50] |

Normalized difference infrared index | NDII | $({R}_{858}-{R}_{645})/({R}_{858}+{R}_{645})$ | [51] |

Simple ratio vegetation index | SR | ${R}_{800}/{R}_{680}$ | [52] |

Photochemical reflectance index | PRI | $({R}_{570}-{R}_{531})/({R}_{570}+{R}_{531})$ | [53] |

^{1}${R}_{\lambda}$ = reflectance at wavelength ${\lambda}_{}$.

**Table 2.**Coefficients of correlation (r) between existing spectral reflectance indices and leaf water content.

Water-SRIs | r | Vegetation-SRIs | r | ||||
---|---|---|---|---|---|---|---|

EWT | RWC | LFMC | EWT | RWC | LFMC | ||

WI (900,970) | 0.34 | −0.39 | −0.64 * | SR | −0.37 | −0.33 | −0.57 * |

WI (1300,1450) | 0.44 | −0.39 | −0.7 * | NDVI | 0.39 | −0.33 | −0.57 * |

NDWI | 0.22 | −0.57 * | −0.59 * | NDII | 0.33 | −0.44 | −0.63 * |

MSI | −0.35 | 0.42 | 0.64 * | PRI | −0.44 | 0.31 | −0.5 |

Lasso Regression | Regression Coefficients | R^{2}^{_}CV | RMSE_CV | |
---|---|---|---|---|

Spectral Parameters | ||||

RS (1889) | 0 | 0.77 | 0.05 | |

FDS (1661) | 29 | |||

RVI (1525,1771) | 30.93 | |||

DVI (1412,740) | 0.19 | |||

NDVI (1447,1803) | −2.76 | |||

Equation ^{1} | $y=29{x}_{1}+30.93{x}_{2}+0.19{x}_{3}-2.76{x}_{4}$ |

^{1}y = LFMC; ${x}_{1}$ = FDS (1661);${x}_{2}$ = RVI (1525,1771);${x}_{3}=$ DVI (1412,740);${x}_{4}$ = NDVI (1447,1803).

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Wang, Q.; Zhao, Y.; Yang, F.; Liu, T.; Xiao, W.; Sun, H.
Simulating Heat Stress of Coal Gangue Spontaneous Combustion on Vegetation Using Alfalfa Leaf Water Content Spectral Features as Indicators. *Remote Sens.* **2021**, *13*, 2634.
https://doi.org/10.3390/rs13132634

**AMA Style**

Wang Q, Zhao Y, Yang F, Liu T, Xiao W, Sun H.
Simulating Heat Stress of Coal Gangue Spontaneous Combustion on Vegetation Using Alfalfa Leaf Water Content Spectral Features as Indicators. *Remote Sensing*. 2021; 13(13):2634.
https://doi.org/10.3390/rs13132634

**Chicago/Turabian Style**

Wang, Qiyuan, Yanling Zhao, Feifei Yang, Tao Liu, Wu Xiao, and Haiyuan Sun.
2021. "Simulating Heat Stress of Coal Gangue Spontaneous Combustion on Vegetation Using Alfalfa Leaf Water Content Spectral Features as Indicators" *Remote Sensing* 13, no. 13: 2634.
https://doi.org/10.3390/rs13132634