the variable is not measured in the "on-the-go" mode.

## *2.4. Statistical Analysis*

The Multiplex data of the three measurement modes at each sampling stage, year, and cultivar obtained under the varied N supply were subjected to analysis of variance (ANOVA) using SAS software (SAS Institute, Cary, NC, USA). Moreover, the means for each treatment were compared using the least significant di fference (LSD) test at the 95% level of significance. Relationships between the Multiplex indices and N status indicators were determined. All of the in-situ samples were divided into two groups by a stratified random sampling method, with approximately 2/3 of the data used for model calibration and the remaining for model validation. Simple linear regression analyses were performed with SPSS 20.0 (SPSS Inc., Chicago, Illinois, USA). The coe fficient of determination (R2) was calculated for comparison. The relationships between Multiplex indices and N status indicators established at di fferent growth stages were validated. The root mean square error (RMSE) and the relative error (RE), shown in Equations (1) and (2), between the predicted and observed values were used for evaluation.

$$\text{RMSE} = \sqrt{\frac{1}{n} \sum\_{i=1}^{n} \left( y\_i - \hat{y}\_i \right)^2} \tag{1}$$

$$\text{RE}(\%) = \frac{RMSE}{\overline{y}} \times 100 \tag{2}$$

where *yi*, *y*<sup>ˆ</sup>*i*, and *y* were the observed, predicted, and mean value, respectively.

In order to evaluate normalized vegetation indices for improving the estimation of N nutrition indicators, the well-fertilized plots were used as N su fficient reference to calculate the NSI index. The NSI index equals to the ratio of Multiplex indices of the plots receiving normal N rates and the well-fertilized plots. In this study, the treatment with the largest shoot dry matter was defined as the well-fertilized plot, corresponding to the treatment of 130 or 160 kg N ha−1.

Finally, the NNI diagnostic results of validation data using Multiplex indices were compared to the observed NNI by areal agreemen<sup>t</sup> and Kappa statistics [52]. Both used the same diagnostic criteria: N was deficient when NNI < 0.95, N was optimal when NNI is between 0.95–1.05, and N was in surplus when NNI > 1.05. The areal agreemen<sup>t</sup> (%) and Kappa statistics were used to determine the accuracy of the diagnostic results. The areal agreemen<sup>t</sup> indicates the percentage of two groups sharing a common category or diagnostic class [53]. The Kappa statistic is a more robust measure of the agreemen<sup>t</sup> of two classifications by correcting the agreemen<sup>t</sup> that occurs by chance. When Kappa equals 1, it indicates that the two categorization systems are identical. Kappa ≥ 0.60 indicates a satisfactory agreement, while the Kappa < 0.4 indicates weak agreemen<sup>t</sup> [54].

## **3. Results**

#### *3.1. Comparison of the Three Measurement Modes*

The three aforementioned measurement modes were applied for each treatment plot. The results were compared to determine the best measurement mode. The abbreviation of the measurement mode is added to the variable as a prefix. For example, AC\_SFR\_G represents the Multiplex index SFR\_G obtained from above the canopy.

Figure 1 shows box plots of Multiplex indices obtained from the three measuring modes at two phenological stages. Since FLAV and ANTH are the log transformation values of FER\_RUV and FER\_RG, only FLAV and ANTH were selected for the analysis to avoid duplication. During both the PI and SE growth stages, the mean values of the Multiplex indices (except for the BRR\_FRF) obtained using the OG mode were significantly higher (P ≤ 0.05) than the leaf-borne indices measured in the LS mode, whereas the latter were significantly higher than the measurements obtained in the AC mode. In addition, substantial large data ranges were shown in the NBI\_G and NBI\_R indices measured in motion and the leaf-borne BRR\_FRF value.

The ANOVA results are listed in Table 3, indicating the sensitivities of the Multiplex indices to five N rates (0, 70, 100, 130, and 160 kg N ha−1). N fertilization treatment e ffects were significant for most of the Multiplex variables measured in the OG mode whereas the opposite was true for the leaf-borne measurements. Comparatively, the N treatment e ffects were more significant for the readings obtained in the OG mode than those collected in the AC mode, while the measurements collected using the LS mode showed the minimum sensitivity to N rate changes. As an example, Figure 2 further demonstrates the comparison of the selected Multiplex indices at each N application rate for cultivar KY 131 in 2013. From Figure 2 we can also see that the indices measured using the OG mode could better distinguish the e ffects of N supply compared to the other two modes. Especially, the Multiplex indices measured in the OG mode performed consistently better than the others for di fferentiating high N-application treatment (≥100 kg ha−1) e ffects. Similar results were achieved for the variety LJ 21, or for the experiments conducted in 2012.

In conclusion, the ANOVA analysis results showed that most of the Multiplex variables obtained in the OG mode were more sensitive to N supply, followed by the AC modes, while measurements made in the LS mode were the least influenced by N supply (Table 3, Figure 2). Thus, only the results of the OG mode were used for further analysis and discussion.

**Figure 1.** Box plots of selected Multiplex index values for the above canopy, on-the-go, and leaf scale measuring modes at the panicle initiation and stem elongation stages in 2013: Simple fluorescence ratio under green excitation (SFR\_G) (**a**), simple fluorescence ratio under red excitation (SFR\_R) (**b**), flavonol (FLAV) (**c**), blue–green to far-red fluorescence ratio (BRR\_FRF) (**d**), anthocyanins (ANTH) (**e**), nitrogen balance index under UV and red excitation (NBI\_R) (**f**), and nitrogen balance index under UV and green excitation (NBI\_G) (**g**). Within the same growth stage, different lowercase (panicle initiation stage) or uppercase letters (stem elongation stage) above or below the boxes indicate that the Multiplex index values differed significantly according to the least significant difference test at P ≤ 0.05.


*Remote Sens.* **2019**, *11*, 1847
