**3. Results**

### *3.1. Grain Yield and Spike Number*

The highest grain yield as well the highest number of spikes per m<sup>2</sup> was observed for location C (Kryłów) in both years (Table 3). This was mainly due to the very favorable soil conditions where the research sites were located in both years in (Table 1). In 2017, soil conditions were very good and uniform within the very flat field (denivelation of less than 2 m). This caused very low yield variability (SD = 0.63) within this field. In 2018, soil conditions were slightly less favorable and more variable, but still quite uniform in comparison to soil conditions in the other two locations (A and B). In location A (Bro˙zówka), the average grain yield of winter wheat was much higher (8.33 <sup>t</sup>·ha−1) in 2017 than the yield of winter triticale in 2018 (5.10 <sup>t</sup>·ha−1). The main reason for the much lower grain yield as well as the lower spike number per m<sup>2</sup> (458 spikes in 2017 versus 317 in 2018) was the shorter tillering time in 2017/2018, related to the later sowing date of winter triticale when compared to winter wheat (2016/2017). Moreover, we must mention that winter wheat is usually sown later than winter triticale. In both years in location A, yield variability within this field was quite high, mainly due to the undulated surface of the field (denivelation of about 20 m), which determined the soil variability. In location B, in both years, a grain yield of about 5 t ha−<sup>1</sup> and a spike density of about 400 spikes per m<sup>2</sup> were relatively low and very variable within the field. The main reason for such high within-field variability of the grain yield traits was the variable soil texture (Table 1), which caused varied water availability for plants. A shortage of water usually occurred in later growth stages, especially during heading and grain filling. This caused very low-weight grains and, despite quite large numbers of spikes, grain yield was very low. Such a situation was especially visible in the sandy parts of the fields in location B.

#### *3.2. Changes in NDVI over the Vegetation Season and in Research Locations*

Due to cloud cover, the availability of useful satellite images from Sentinel-2 was limited to 4–6 scenes per season during intensive growth of winter cereals, i.e., from half of March to half of July. Despite this limitation, it was possible to evaluate changes in VI values during the growing seasons. The most substantial differences between the average and a range of NDVI values for the three locations were observed from the end of March to the beginning of April. For location A, mean values

of NDVI in both years were very low (0.3–0.4) until the beginning of April. The main cause of these low NDVI values in location A were lower air temperatures and consequently growing degree days (from sowing date to the end of April in 2017: location A—283, B—298, and C—451; in 2018: A—415; B—501, and C—605) during early spring than in the other two locations (Figure 2). The highest values of NDVI (of about 0.7 at the beginning of April) were observed in location C. This was caused by warmer conditions in both autumn and early spring as well as by more favorable soil conditions, which caused more intensive plant growth. The very high values of NDVI (0.7 or higher) in location C were observed for a much longer time, even until the end of June, in comparison to the other two locations. Consequently, this longer and more intensive crop growth in location C allowed us to obtain higher grain yields. In location B, NDVI values in early spring were at a medium level (higher than in location A and lower in comparison to location C) and very variable depending on the season at the later growth stages. In all locations, in 2017, a maximum NDVI value was achieved in very late June and much earlier in 2018, at the end of April (Figure 4, Table 4).

**Figure 4.** Mean values of NDVI values for six fields (three locations: A—Bro˙zówka, B—Zdziechów, and C—Kryłów in two years: 2017 and 2018).

#### *3.3. Relationships between NDVI and Grain Yield and Spike Number*

One of the aims of the study was to determine the dates and plant growth stages when the relationships between VI values and grain yield, as well as number of spikes, were the strongest. The strongest correlations were achieved at various growth stages (Tables 5 and 6).

For fields located in northeastern Poland, the highest correlation coe fficients between grain yield and as well as number of spikes and NDVI were observed at the end of May (approximately shortly before or during the heading stage) in both years. On the basis of the regression slope values, it can be concluded that an increase in NDVI by 0.1 unit corresponded to the increase in grain yield by about 1.5–1.6 t·ha−<sup>1</sup> in both years (Figures 5 and 6).

**Figure 5.** Relationships between grain yield (charts in the left side), number of spikes per square meter (charts in the right side) and NDVI values for three locations (A—Bro˙zówka, B—Zdziechów, C—Kryłów) for the dates when the correlations reached maximum values in 2017. Regression equations and the value of the R<sup>2</sup> coefficient are given for each relationship.

**Figure 6.** Relationships between grain yield (charts in the left side), number of spikes per square meter (charts in the right side) versus NDVI for three locations (A—Bro˙zówka, B—Zdziechów, C—Kryłów) for the date when their correlations reached maximum values in 2018. Regression equations and the value of the R<sup>2</sup> coefficient are given for each relationship.

In location B, the strongest relationship between NDVI and grain yield was registered in late June of 2017 (end of milk maturity of winter wheat) and in the second half of May 2018 (shooting and heading of winter triticale). In this research site, the relationships were the strongest among the three examined locations, i.e., the R<sup>2</sup> value was about 0.70–0.75 (Figures 6 and 7). Moreover, the relationship between NDVI and the number of spikes was slightly weaker. The increase in NDVI by 0.1 unit was related to an increase in grain yield of about 8.0 t·ha−<sup>1</sup> in 2017 and about 2.5 t·ha−<sup>1</sup> in 2018.

**Figure 7.** Values of correlation coefficients between vegetation indices and grain yield (t·ha−1) in three locations (A—Bro ˙zówka, B—Zdziechów, C—Kryłów) on the selected dates in years 2017 (charts in the left side) and 2018 (charts in the right side).

In location C in 2017, the strongest correlation between NDVI and both grain yield and number of spikes was observed, respectively, on 21 June and 11 July (milk and dough maturity). In 2018, the strongest relationships between NDVI and both grain yield and spike number per square meter were obtained at the end of April and June. Due to a lack of data (clouds), it was not possible to verify this relationship at the end of May. The relationship was much stronger in 2018 than in 2017, mainly due to the considerably higher within-field variability of soil and consequently grain yield variability (Coefficient of Variation—CV) for grain yield was 6% and 16%, respectively, for 2017 and 2018). Based on the regression equations (Figures 5 and 6), it was evaluated that an increase in NDVI by 0.1 unit was related to the increase in grain yield by about 1.0 t·ha−<sup>1</sup> in 2017 and about 2.1 t·ha−<sup>1</sup> in 2018. For all six site years, the strongest correlation between NDVI and grain yield and number of spikes was observed on similar dates and at similar growth stages. This is because the number of spikes per square meter usually very strongly affects grain yield.

#### *3.4. Relationships between the Other Vegetation Indices and Grain Yield and Spike Number*

Regression analyses performed to evaluate the strength of the relationship between the vegetation indices (SAVI, mSAVI, mSAVI2, GEMI, IPVI, RVI) and grain for each crop in 2017 and 2018 (Figure 7) indicated that the strongest relationships were observed for most of the VIs on the same dates. In location A, the highest correlations were observed at the end of May (end of shooting stage) in 2017, and from late May to mid-June (heading stage) in 2018. In location B, in 2017, the value of the correlation coe fficients di ffered for individual VIs on several dates, while, in 2018, the strongest relationships were achieved in mid-May (beginning of heading stage) and at the end of June (milk maturity stage) for all VIs. The highest di fferentiation in the correlation coe fficient values for the relationship between various VIs and yields was observed at the end of June and beginning of July (milk maturity stage) of 2017 in location C. In 2018, in all locations, the correlation coe fficients had similar values for all VIs across the whole season.

The vegetation indices (VI) are ranked by order of decreasing correlation (data not shown) with yield as follows: SAVI, MSAVI, NDVI, MSAVI2, IPVI, RVI, GEMI. This ranking was carried out by averaging the R<sup>2</sup> values from all of the measurement dates and research areas. The strength of the correlation of VIs with the number of ears was evaluated in the same way as above, and the order of decreasing correlation was as follows: NDVI, SAVI, MSAVI, MSAVI2, IPVI, RVI, GEMI.
