Influence of Time-Lag Effects between Winter-Wheat Canopy Temperature and Atmospheric Temperature on the Accuracy of CWSI Inversion of Photosynthetic Parameters

Abstract

When calculating the CWSI, previous researchers usually used canopy temperature and atmospheric temperature at the same time. However, it takes some time for the canopy temperature (Tc) to respond to atmospheric temperature (Ta), suggesting the time-lag effects between Ta and Tc. In order to investigate time-lag effects between Ta and Tc on the accuracy of the CWSI inversion of photosynthetic parameters in winter wheat, we conducted an experiment. In this study, four moisture treatments were set up: T1 (95% of field water holding capacity), T2 (80% of field water holding capacity), T3 (65% of field water holding capacity), and T4 (50% of field water holding capacity). We quantified the time-lag parameter in winter wheat using time-lag peak-seeking, time-lag cross-correlation, time-lag mutual information, and gray time-lag correlation analysis. Based on the time-lag parameter, we modified the CWSI theoretical and empirical models and assessed the impact of time-lag effects on the accuracy of the CWSI inversion of photosynthesis parameters. Finally, we applied several machine learning algorithms to predict the daily variation in the CWSI after time-lag correction. The results show that: (1) The time-lag parameter calculated using time-lag peak-seeking, time-lag cross-correlation, time-lag mutual information, and gray time-lag correlation analysis are 44-70, 32-44, 42-58, and 76-97 min, respectively. (2) The CWSI empirical model corrected by the time-lag mutual information method has the highest correlation with photosynthetic parameters. (3) GA-SVM has the highest prediction accuracy for the CWSI empirical model corrected by the time-lag mutual information method. Considering time lag effects between Ta and Tc effectively enhanced the correlation between CWSI and photosynthetic parameters, which can provide theoretical support for thermal infrared remote sensing to diagnose crop water stress conditions.

Keywords: CWSI; photosynthetic rate; stomatal conductance; time-lag effects; transpiration rate; winter wheat.

Figure 1

(a) ESC equations fitted to S-G filter-smoothed Ta; (b) CCE equation fitted to S-G filter-smoothed Tc.

Figure 2

(a) Time-lag parameters of T1 (fully irrigated), T2 (mild water stress), T3 (moderate water stress), and T4 (severe water stress) calculated by time-lag peak-finding method. (b) Coefficient of determination (R²) for T1, T2, T3, and T4 fitted by the time-lag peak-finding method.

Figure 3

Time-lag parameters and corresponding coefficients for fully irrigated treatment. (a) is the time-lag parameter calculated by the time-lag cross-correlation method and the cross-correlation coefficient between Ta and Tc after the corrected time-lag; (b) is the time-lag parameter calculated by the time-lag grey correlation analysis and the time-lag grey correlation coefficient between Ta and Tc after the corrected time-lag; (c) is the time-lag parameter calculated by the time-lag mutual information method and the mutual information coefficient between Ta and Tc after the corrected time-lag. Circles indicate the results of the time-lag cross-correlation method under the four moisture treatments; cross sign indicates the results of the time-lag grey correlation analysis under the four moisture treatments; squares indicate the results of the time- lag mutual information method.

Figure 4

Time-lag parameters and corresponding coefficients for mild water stress treatment. (a) is the time-lag parameter calculated by the time-lag cross-correlation method and the cross-correlation coefficient between Ta and Tc after the corrected time-lag; (b) is the time-lag parameter calculated by the time-lag grey correlation analysis and the time-lag grey correlation coefficient between Ta and Tc after the corrected time-lag; (c) is the time-lag parameter calculated by the time-lag mutual information method and the mutual information coefficient between Ta and Tc after the corrected time-lag. Circles indicate the results of the time-lag cross-correlation method under the four moisture treatments; cross sign indicates the results of the time-lag grey correlation analysis under the four moisture treatments; squares indicate the results of the time- lag mutual information method.

Figure 5

Time-lag parameters and corresponding coefficients for moderate water stress treatment. (a) is the time-lag parameter calculated by the time-lag cross-correlation method and the cross-correlation coefficient between Ta and Tc after the corrected time-lag; (b) is the time-lag parameter calculated by the time-lag grey correlation analysis and the time-lag grey correlation coefficient between Ta and Tc after the corrected time-lag; (c) is the time-lag parameter calculated by the time-lag mutual information method and the mutual information coefficient between Ta and Tc after the corrected time-lag. Circles indicate the results of the time-lag cross-correlation method under the four moisture treatments; cross sign indicates the results of the time-lag grey correlation analysis under the four moisture treatments; squares indicate the results of the time- lag mutual information method.

Figure 6

Time-lag parameters and corresponding coefficients for severe water stress treatment. (a) is the time-lag parameter calculated by the time-lag cross-correlation method and the cross-correlation coefficient between Ta and Tc after the corrected time-lag; (b) is the time-lag parameter calculated by the time-lag grey correlation analysis and the time-lag grey correlation coefficient between Ta and Tc after the corrected time-lag; (c) is the time-lag parameter calculated by the time-lag mutual information method and the mutual information coefficient between Ta and Tc after the corrected time-lag. Circles indicate the results of the time-lag cross-correlation method under the four moisture treatments; cross sign indicates the results of the time-lag grey correlation analysis under the four moisture treatments; squares indicate the results of the time- lag mutual information method.

Figure 7

Heat map of the CWSI theoretical model and Pn before and after considering time-lag effects.

Figure 8

Heat map of the CWSI empirical model and Pn before and after considering time-lag effects.

Figure 9

Heat map of the CWSI theoretical model and Tr before and after considering time-lag effects.

Figure 10

Heat map of the CWSI empirical model and Tr before and after considering time-lag effects.

Figure 11

Heat map of the CWSI theoretical model and gs before and after considering time-lag effects.

Figure 12

Heat map of the CWSI empirical model and gs before and after considering time-lag effects.

Figure 13

Training set for attention-LSTM.

Figure 14

Validation set for attention-LSTM.

Figure 15

Training set for GRU-attention.

Figure 16

Validation set for GRU-attention.

Figure 17

Training set for CNN-BILSTM.

Figure 18

Validation set for CNN-BILSTM.

Figure 19

Training set for GA-SVM.

Figure 20

Validation set for GA-SVM.

Figure 21

Training set for Bayes-LSTM.

Figure 22

Validation set for Bayes-LSTM.

Figure 23

Training set for PSO-LSTM.

Figure 24

Validation set for PSO-LSTM.

Figure 25

Overview of the experimental site.

Figure 26

Canopy temperature of winter wheat under four moisture treatments.

Figure 27

Dynamic variations in (a) u (m·s⁻¹); (b) G (W·m⁻²); (c) RH (%); (d) Ta (°C); (e) Rs (W·m⁻²).

Figure 28

Pn (µmol/(m²·s)), gs (mol/(m²·s)), and Tr (mmol/(m²·s)) in winter wheat.

Figure 29

The blue circle represents the trajectory of the VPD (kPa) and the corresponding CTD (°C) over the course of a day; The blue line represents the outcome of a linear regression analysis of the relationship between VPD (kPa) and CTD (°C) between 13:00 and 15:00.