**1. Introduction**

Satellite remote sensing (RS) helps in the mapping of current crop status and the assessment of biophysical parameters. Currently, RS data are publicly accessible due to the availability of an unprecedented amount of Free Sentinel data from the Copernicus Program, established by the European Space Agency [1]. Constellations of the Sentinel-2 satellites (2A and 2B) can be also used for precision farming applications [2]. Thanks to the high spatial resolution (pixel size of 10 m), relatively short revisit time (about 5 days) and multispectral sensors, it is possible to observe and analyze the crop status using vegetation indices (VIs). For the purpose of such an evaluation, satellite Sentinel-2 images of two radiation bands, red (650–680 nm) and NIR (785–900 nm), are usually used [2].

Recently, many research results on yield evaluation based on data from the Sentinel-2 satellites [3–8] as well as from other satellite sources has been available. However, studies in which significant relationships between NDVI and the grain yield of cereals were proved have been carried out since the 1980s [3–6]. Most of these studies were done at a regional level and low-resolution satellite imagery was used (mainly using AVHRR/NOAA - Advanced Very High Resolution Radiometer/National Oceanic and Atmospheric Administration sensors with pixel sizes of 1 km).

Research on the evaluation of the relationships between VIs from high-resolution satellite sensors (e.g., QuickBird) and the grain yield and crop status of cereals has become more common since the year 2000 [7–10], due to the availability of new sources of satellite data. Such of studies were conducted at di fferent spatial scales from one field scale (evaluation of within-field yield variability) to a whole country level. Many studies refer to Vis in relation to wheat grain yield because of the high importance of this crop. In most studies, Normalized Di fference Vegetation Index (NDVI) [5] has been used as a predictor of grain yield. The highest accuracy of grain yield forecast was possible at di fferent growth stages, even 2–3 months before harvest [11–16]. Recently, other VIs besides NDVI have been used as grain yield predictors. Ali et al. (2019) [17] studied the relationship between six vegetation indices (NDVI, EVI—Enhanced Vegetation Index, SAVI—Soil-Adjusted Vegetation Index, GNDVI—Green Normalized Vegetation Index, GCI—Green Chlorophyll Index and SR—Simple Ratio), derived from Landsat 5, 7 and 8 satellite imagery and a grain yield of durum and bread wheat in one 11 ha field in Italy, during five consecutive years (2010–2014). Most frequently, NDVI and SR were characterized as having the strongest relationship with yields.

Most of the studies that examined relationships between satellite-derived VIs and the grain yield of cereals were conducted at a regional level and did not analyze the relationships of VIs with other yield components such as the number of spikes. Nowadays, the common availability of satellite images of relatively high spatial resolution allows us to evaluate these relationships even at the within-field level. The results of such an evaluation can be useful for site-specific crop management, including variable fertilization, which should be based, besides soil nutrient availability, on the prediction of grain yields.

The aim of this study was to evaluate the relationships between vegetation indices derived from Sentinel-2 imagery and grain yield and the number of spikes per square meter of winter wheat and triticale. These two crops were selected because of their high cropping area among cereals in Poland. Recently, winter wheat has been grown on about 1.9 M hectares and winter triticale on 1.1 M hectares [18]. Moreover, the aim was to determine the dates and plant growth stages when the above relationships were the strongest at the individual field scale, thus allowing an accurate yield prediction.
