**3. Results**

### *3.1. Vegetation Index Response for Yellow Rust Disease*

The responses of the 14 VIs and corresponding two-stage vegetation indices (nVIs) are shown in Figure 3, where their mean and difference values are compared for healthy and yellow rust-infected wheat. The values of the re-normalized difference vegetation index (RDVI), and red-edge disease stress index (REDSI) were reduced by 100 times to maintain the same magnitude as that of the other indices. On the single-stage indices, according to the difference information of each vegetation index in healthy and diseased wheat, RDVI, REDSI, enhance vegetation index (EVI), soil adjusted vegetation index (SAVI), and normalized red-edge3 index (NREDI3) were most suitable for discriminating healthy and yellow rust-infected wheat (Figure 3a). Among them, the difference value of RDVI for healthy and disease samples was the largest, reaching 5.5. However, the magnitude of the difference value in the entire single-stage VIs was relatively small, except for RDVI and REDSI.

**Figure 3.** Mean and difference values for healthy wheat and yellow rust infected wheat. (**a**) Single—stage vegetation indices and (**b**) normalized two—stage vegetation indices.

Regarding the normalized two-stage indices, the difference between health samples and yellow rust infection samples was evident, specifically for the normalized REDSI (nREDSI), normalized visible atmospherically resistant index (nVARIgreen), normalized difference vegetation index reg-edge 1 (nNDVIre1), and normalized plant senescence reflectance index (nPSRI1). Among them, the difference between healthy and diseased samples in nREDSI was up to 1.1 (Figure 3b). The two-stage nVIs (using images from both 2 April and 12 May 2018) exhibited a greater difference between healthy and yellow rust-infested wheat compared with the corresponding single-stage VIs (using the images from 12 May). This confirms that nVIs are closely related to the pathological progress of the crop, which can more clearly reflect leaf wilting, leaf tissue death, and canopy structure changes caused by the yellow rust pathogen.

### *3.2. Meteorological Data Processing and Selection*

Each type of meteorological data was averaged by month to obtain its monthly average value. Then, the meteorological factors from March to May 2018 were spatially interpolated using an inverse distance weighted method in the ArcGIS software for subsequent continuous spatial pixel-scale analysis [9]. All meteorological factors were interpolated at a spatial resolution of 10 m, which matches the resolution of the Sentinel-2 satellite imagery. Figure 4 presents the results of meteorological data spatial resolution in May Finally, based on continuous meteorological data, meteorological characteristics were extracted for wheat yellow rust habitat monitoring.

**Figure 4.** Spatial interpolation of meteorological data in Ningqiang county in May 2018. (**a**) Average temperature (TEM; 0.1 ◦C), (**b**) average relative humidity (RHU; %), (**c**) average sunshine hours (SSD; 0.1 h), (**d**) average wind speed (WIN; 0.1 m/s), (**e**) average of precipitation (PRE; 0.1 mm).

### *3.3. VIs and Meteorological Features Sensitivity of Yellow Rust Monitoring*

We observed a strong correlation between VIs as well as wheat physiological and, biochemical parameters caused by the development of yellow rust; however, correlations and multiple collinearities among different VIs limit the extraction of sensitive information for wheat yellow rust discrimination. Therefore, we selected the single- and two-stage VIs most sensitive to reflect the state of the crop after being stressed by disease using the important criterion in the RF method. The selected single-stage vegetation index, normalized two-stage vegetation index, and meteorological data were used to determine the important features for yellow rust detection (Figure 5).

**Figure 5.** Variable importance of vegetation indices and meteorological factors in identifying yellow rust-infected wheat. (**a**) Vegetation indices (VIs) and normalized VIs (nVIs) based on a single- and two-stage imagery; (**b**) meteorological data from March to May 2018.

> The relative importance of the three features for wheat yellow rust discrimination were analyzed using the RF method (Figure 5). According to the importance ranking of spectral VIs (Figure 5a), we selected the features with variable importance greater than 0.05 for subsequent analysis. In terms of single-stage VIs, the RDVI, REDSI, VARIgreen, NREDI3, RGR, PSRI1, NDVIre1, SAVI, and EVI were selected; for nVIs, the nREDSI, nVARIgreen, nPSRI1, nNDVIre1, nNREDI1, nNREDI2, nSAVI, and nNREDI3 were selected. For meteorological data, the SSD\_03, PRE\_05, RHU\_04, PRE\_04, RHU\_05, WIN\_03, WIN\_04, TEM\_03 and SSD\_05 were selected. To avoid information redundancy of selected features, we used the analysis of variance (ANOVA) method to optimize important features (Table 3). For VIs, the EVI, NREDIre1, PSRI1, and SAVI showed no significant differences (ρ > 0.05); and for nVIs, the differences of nNREDI3, nNREDI2, and nSAVI with other nVIs were insignificant (ρ > 0.05).

> The variable importance values of the vegetation indices based on a single image and two images taken at different times in the discrimination of wheat yellow ruts differed. The five most important vegetation indices were selected for subsequent analysis. For single-stage imagery, the RDVI, REDSI, NREDI3, RGR, and VARIgreen were most sensitive to wheat yellow rust (Figure 5a, indigo histogram); for two-stage imagery, nREDSI, nVARIgreen, nPSRI1, nNREDI1, and nNDVIre1 were most sensitive to wheat yellow rust (Figure 5a, magenta histogram). This is generally consistent with the results shown in Figure 3b and allows us to distinguish between healthy wheat and yellow rust infection. Similarly, the meteorological features of WIN\_03, WIN\_04, TEM\_03, and SSD\_05 were excluded using ANOVA.

> Figure 5b demonstrated the importance ranking of meteorological features. Due to the strong correlation between the same type of meteorological data, we selected the features above the average value (0.07) of all variable importances for yellow rust identification. Accordingly, five of the most important meteorological features were selected for monitoring wheat yellow rust on a regional scale: average sunshine hours in March (SSD\_03),

average relative humidity (RHU\_04, RHU\_05) in April and May, and average

(PRE\_04, PRE\_05) in April


and **Table 3.** ANOVA for vegetation indices feature sets (VIs and nVIs).

May.

precipitation

Note: "a" indicates the difference is significant at the 0.95 confidence level, "b" indicates the difference is significant at the 0.99 confidence level, and "c" indicates the difference is significant at the 0.999 confidence level; "VARIg" = VARIgreen, "nVARIg" = nVARIgreen," and "mete" = meteorological.

### *3.4. Wheat Yellow Rust Monitoring Based on Spectral Vegetation Indices*

Monitoring models for wheat yellow rust were built using the LDA, SVM, and ANN algorithms. The RDVI, REDSI, NREDI3, RGR, and VARIgreen were selected for use in single-stage monitoring models; nREDSI, nVARIgreen, nPSRI1, nNREDI1, and nNDVIre1 were selected for use in two-stage monitoring models. Table 4 presents the classification results of the three algorithms using the different VIs.

**Table 4.** Classification accuracies of three classification algorithms using single- and two-stage vegetation indices (VIs and nVIs, respectively; n = 19).


Note: P.a = producer's accuracy, U.a = user's accuracy, OA = overall classification accuracy.

For the single-stage vegetation index model, the overall classification accuracy and kappa coefficient were 63.2% and 0.18 for the LDA algorithm, respectively; 73.7% and 0.42 for the SVM algorithm, respectively; and 63.2% and 0.23 for the ANN algorithm, respectively. For the nVIs models, the overall classification accuracy and kappa coefficient were 68.4% and 0.32 for the LDA algorithm, respectively; 78.9% and 0.55 for the SVM algorithm, respectively; and 68.4% and 0.32 for the ANN algorithm, respectively. Based on these results, the classification accuracy of wheat yellow rust monitoring models using nVIS as the input features is better than that of models using VIs; the overall accuracy is improved by 5.2%. Compared with the VIs model, the P.a of healthy wheat identification and yellow rust wheat exceeded 57.1% and 83.3%, respectively, for nVIs. Among the algorithms, SVM performed the best.

### *3.5. Wheat Yellow Rust Monitoring Based on Meteorological Data and Spectral Information*

The classification results of the three algorithms based on both vegetation indices (VIs and nVIs) and meteorological data are shown in Table 5. For the single-stage vegetation index model, the overall classification accuracy and kappa coefficient were 68.4% and 0.32 for the LDA algorithm, respectively; 78.9% and 0.55 for the SVM algorithm, respectively; and 73.7% and 0.45 for the ANN algorithm, respectively. For the two-stage models, the overall classification accuracy and kappa coefficient were 73.7% and 0.42 for the LDA algorithm, respectively; 84.2% and 0.65 for the SVM algorithm, respectively; and 78.9% and 0.55 for the ANN algorithm, respectively.

**Table 5.** Classification accuracies for three classification algorithms using single- and two-stage vegetation indices (VIs and nVIs, respectively) combined with meteorological data (n = 19).


According to these results, the accuracies of wheat yellow rust monitoring models with the nVIs and meteorological data as the input features are higher than those based on VIs and meteorological data. This is consistent with the results based on the pure VIs model (see Section 3.4). Among the three algorithms, SVM again had the highest classification accuracy. Moreover, the U.a of healthy and yellow rust wheat identification was 83.3% and 84.6%, respectively; the P.a of yellow rust reached 91.7% in the nVIs and meteorological model (nVIs\_meteorological data). The results confirm that the inclusion of meteorological data improves model accuracy and offers the potential for crop disease monitoring on a regional scale.

### *3.6. Mapping Wheat Yellow Rust Using the Optimal Monitoring Model*

Figure 6 shows a map of wheat yellow rust in Ningqiang county, Shaanxi Province during the filling period based on the optimal model (SVM algorithm using two-stage spectral vegetation indices and meteorological data). The wheat yellow rust infected region is highly consistent with the field observation, which verifies the feasibility of the model for crop disease monitoring. This remote sensing method has the potential for effective, rapid (near real-time), and a spatially continuous regional monitoring of crop disease, offering substantial labor-, time-, and cost-savings.

**Figure 6.** Mapping wheat yellow rust disease in Ningqiang county during the filling period (May 2018) based on the support vector machine (SVM) algorithm using two-stage spectral vegetation indices and meteorological data.
