*2.4. Spectral Vegetation Indices*

The selection of the vegetation indices (VIs) used for the winter wheat and triticale yield analysis depended on several factors. First of all, we only considered the same satellite data spatial resolution. Another factor determining our choices was the prevalence in the literature and the comparability with the yield of cereal crops. The VIs were calculated on the basis of the reflectance of wavelength bands registered by Sentinel-2 at spatial resolution 10 m (squared pixels 10 × 10 m). The Normalized Di fferential Vegetation Index (NDVI) allows us to determine the indirect absorption of photosynthetic radiation on a landscape scale. NDVI calculation is based on the contrast between the largest reflection in the near-infrared band and the absorption in the red band. In the case of this index, the di fference in reflection in the near-infrared and red bands is divided by their sum. This approach compensates for the di fferences in the radiation amounts in both bands. It is believed that NDVI is more sensitive to small amounts of vegetation [22,23].

$$\text{NDVI} = \frac{\text{NIR} - \text{RED}}{\text{NIR} + \text{RED}}$$

Another VI used in this study was the Soil-Adjusted Vegetation Index (SAVI). This indicator was designed to minimize the e ffect of soil reflection on red and near-infrared radiation by adding an estimated background correction factor [24].

$$\text{SAVI} = \frac{(1 + \text{L})(\text{NIR} - \text{RED})}{\text{NIR} + \text{RED} + \text{L}}$$

where L is a canopy background adjustment factor. An L value of 0.5 was adopted to minimize soil brightness variations and eliminate the need for additional calibration for di fferent soils.

In the literature, modifications of the SAVI index, known as modified SAVI (mSAVI) and modified SAVI 2 (mSAVI2), are often used. These two VIs also include the soil background correction factor [25]:

$$\text{mSAVI} = \frac{(1 + \text{L})(\text{NIR} - \text{RED})}{\text{NIR} + \text{RED} + \text{L}}$$

where L is:

$$\text{L} = 1 - \frac{2 \times \text{s} \times (\text{NIR} - \text{s} \times \text{RED})(\text{NIR} - \text{RED})}{\text{NIR} + \text{RED}},$$

and:

$$\text{mSAVI2} = \frac{\left(2 \times \text{NIR} + 1 - \sqrt{\left(2 \times \text{NIR} + 1\right)^2 - 8 \times \left(\text{NIR} - \text{RED}\right)}\right)}{2}$$

Crippen (1990) proposed the Infrared Percentage Vegetation Index (IPVI), which simplifies the calculation by eliminating the subtraction of the red radiation value in the NDVI indicator counter. This simplification of a new VI calculation proved to be important for fast image processing [26].

$$\text{IPVI} = \frac{\text{NIR}}{\text{NIR} + \text{RED}}$$

In 1992, Pinty and Verstraete proposed the Global Environmental Monitoring Index (GEMI), a new nonlinear crop status indicator, which includes a correction factor adjusted by the effect of soil reflectance and atmospheric background [27].

$$\text{GEMI} = n(1 - 0.25n) - \frac{\text{RED} - 0.125}{1 - \text{RED}}$$

where:

$$n = \frac{\left[2 \times \left(\text{NIR}^2 - \text{R}^2\right) + 1.5 \text{NIR} + 0.5 \text{R}\right]}{\text{NIR} + \text{RED} + 0.5}$$

The last VI used in this study for a comparison with NVDI was the Ratio Vegetation Index (RVI), sometimes also referred to as the Simple Ratio (SR). This VI is a ratio of NIR and red reflectance [28].

$$\text{RVI} = \frac{\text{NIR}}{\text{RED}}$$

The investigated Vis, except RVI, are normalized and placed on a comparative scale. These indices have values from −1 to 1, where values close to −1 indicate water, or any inanimate matter, values from 0 to 0.20 relate to barren rock, sand, barren soil and plants at an early stage of growth, values of 0.20–0.50 relate to sparse vegetation such as shrubs and grasslands, while values above 0.60 indicate crops at their peak growth stages.
