**4. Discussion**

Constant field monitoring using RS methods is important not only for grain yield prediction, but also for the assessment of the site-specific conditions of plant development during the growing season [31,32]. This may allow us to introduce site-specific managemen<sup>t</sup> of the field, and thus increase yields or save inputs.

#### *4.1. Relationships between NDVI and Grain Yield*

Our results for winter cereals, which constitute the majority of crop production in Central Europe, proved moderate and strong relationships (R<sup>2</sup> in range of 0.35–0.81 for all fields in two seasons, Figures 5 and 6) between the NDVI and grain yield of winter wheat and triticale for all of the studied fields. At location A, the correlation coe fficient grew from mid-March to the end of May, when it reached the highest value. From the beginning of June to mid-July, we noticed a decrease in this correlation. The highest correlation coe fficients are observed from the beginning of June to mid-July due to the growth stages such as heading, milk maturity, or dough maturity for location B. At the site C, we can see high rates of milk maturity at the end of June. A similar tendency, though with lower correlation values, can be observed when comparing the number of spikes per square meter. Similar results were achieved by Benedetti and Rossini (1993) [4] in Italy and by Smith et al. (1995) [5] in Western Australia for wheat. In both studies, AVHRR/NOAA satellite data were used for the calculation of NDVI. In Italy, R<sup>2</sup> coe fficient values for the relationship between NDVI and grain yield ranged from 0.24 to 0.749, and for Australia they ranged from 0.46 to 0.72. Ali et al. (2019) [17] observed higher R<sup>2</sup> values of 0.878 and 0.926 for the relationship between the grain yield of winter and bread durum wheat and NDVI when the values of this index were derived from Landsat images. In turn, Labus et al. (2002) [6] achieved low R<sup>2</sup> values ranging from 0.00 to 0.69 when wheat yield prediction was based on NDVI derived from AVHRR/NOAA satellite data. In our study, very low R<sup>2</sup> values were obtained in April and May, and higher R<sup>2</sup> values were mainly close to the heading stage and at the end of the growing season (Tables 5 and 6). Therefore, while comparing many di fferent studies, we can expect that, regardless of the research region, the relationship between NDVI and the grain yield remains at a similar level depending on the growth stage of the studied cereal.

#### *4.2. Determination of Dates and Plant Growth Stages When Relationship between NDVI and Grain Yield Was the Strongest*

Veloso et al. (2017) [10] found, for southeastern France, that NDVI reached maximum values in the second half of May, while, in Poland, depending on the research location, the highest NDVI values were reached from the end of April to the end of June (Figure 4). The site-related di fferences in the absolute NDVI values and the date at which they reached their maximum may primarily be influenced by the environmental conditions, mainly weather and soil conditions. This, in turn, closely depends on the climate in a specific region (amount of rainfall, growing degree days) and the amount of nitrogen applied. In the study of Naser et al. (2020) [33], much stronger correlations between NDVI, measured using a ground sensor, and the grain yield of winter wheat were observed for dryland than for irrigated conditions. The reason for such results was the greater range of absolute NDVI values for dryland in comparison to irrigated conditions. In that study, the highest correlations were observed after anthesis for both types of conditions. Very strong relationships between NDVI, measured using a ground spectrometer, and wheat yield were observed in a study where the e ffect of various nitrogen doses (from 0 to 210 kg/ha) was investigated [34]. The strongest correlations (R<sup>2</sup> up to 0.96) were achieved at the heading stage. According to Satir and Berberoglu (2016) [35], the strength of the relationship between satellite-derived NDVI and the yields of wheat, corn and cotton was modified by soil conditions, e.g., soil salinity. This is because soil surface and soil water content can a ffect the values of vegetation indices, as well as the fact that water availability for plants is limited in high-salinity conditions. A better prediction of grain yield in the variable soil conditions of south Turkey can be achieved not only using prediction models such as NDVI, but also other spectral indices such as Normalized Di fference Water Index (NDWI), Soil-Adjusted Vegetation Index (SAVI) or Tasseled Cap Wetness Index (WETNESS). The highest prediction accuracy for wheat was using the model which includes NDVI, NDWI and WETNESS. Prediction of wheat yield based on satellite-derived NDVI was improved if auxiliary data such as grain yield from previous seasons were included in models [36]. Dempewolf et al. (2013) [12] obtained the highest R<sup>2</sup> values of 0.964 for NDVI and the yield of wheat grown in Pakistan six weeks before harvest. In our studies, the highest R<sup>2</sup> value was observed at the end of April, i.e., about 12 weeks before harvest in the case of the field located in southeastern Poland. These results are similar to those of Kussul et al. [13] (2014), obtained in Ukraine, where a good prediction of winter wheat yields was possible even 2–3 months before harvest. The latest date (beginning of July) when the correlation coe fficient for the relationship yield versus NDVI was the highest was observed in location B (Zdziechów) in central Poland in 2017. Similar results were obtained in Hungary by Nagy et al. (2018) [15] and Lopresti et al. (2015) [11] in Argentina, where good yield prediction was possible six weeks before harvest. Ali et al. (2019) [17] observed the highest correlation between NDVI and yield for winter bread wheat from stem elongation to the milk maturity of the grain, i.e., 6–17 weeks before harvest. In summary, the choice of the date of the yield estimation with the best accuracy does not depend only on long-term field and satellite measurements. Environmental, weather, and soil conditions should also be taken into account. As shown above, a yield estimation can be properly performed even between 3 months and 6 weeks before harvest, depending on the research region and the field-specific conditions.

#### *4.3. Relationship between Other VIs and Grain Yield*

According to Purevdorj et al. (1998) [37], SAVI and its modifications usually show higher correlations with grain at the beginning of the growing season compared to NDVI. According to Ren et al. (2018) [38], SAVI, with its modifications, should be used to estimate vegetation coverage at low vegetation density on arable land. In our study, the value of the correlation coe fficient for the relationship between SAVI and grain yield was similar to the relationship with NDVI for both seasons and locations. Moreover, only in locations A and C in 2017 were the correlations between SAVI and grain yield stronger in early spring. For location A, during two vegetative seasons, we saw an increase in the correlation coe fficient at the beginning of the growing season and a decrease in the cereals' subsequent growth stages. For location B, the correlation coe fficient increases until the beginning of June and slightly decreases until the end of July. In tested area C, an increase in the correlation coe fficient value is noticed until mid-June, followed by a sharp decline by the end of July.

Ali et al. (2019) [17] selected NDVI and SR (referred to RVI in our study) as better VIs in comparison to EVI, SAVI, GNDVI, and GCI. Their conclusion was that SAVI never exhibited the strongest correlation with yield in comparison with other VIs, although, its correlation with grain yields was, most frequently, significant and strong. On the contrary, our research results proved that SAVI (and its modifications) and NDVI are ranked as VIs with the highest correlations with yield and number of spikes.

Moreover, Ali et al. (2019) [17] obtained R<sup>2</sup> values of about 0.8 for durum and bread wheat yield and NDVI, EVI, and SR. We achieved Pearson's correlation values of 0.4 between winter wheat and triticale yield and SAVI, but 0.3 with mSAVI, NDVI, IPVI, RVI (SR), and GEMI. These di fferences most probably arise from a di fferent method being used for the collection of yield data.
