# Monitoring Within-Field Variability of Corn Yield using Sentinel-2 and Machine Learning Techniques
## 1 Introduction  
Crop yield is defined as the total production per unit area and is commonly measured in tons per hectare [1]. Such yield changes spatially and temporally within-field zones based on local spatial variability in soil physical and chemical properties, management practices and localized damage due to pests and pathogens [2; 3; 4]. Information on within-field yield variability supports farmers to improve their management decisions, profit, land rental, and for insurance assessment as well [5; 6]. The first step in PA is yield monitoring, which is one of the fundamental elements for delineating management zones (MZ) based on previous yield maps [7]. Delineating MZ requires information on soil characteristics and archived management practices for the field, while yield monitoring evaluates the final result of these practices at the end of the growing season. Satellite remote sensing (RS) offers a wide range of indications for crop and vegetation parameters, such as Leaf Area Index (LAI) [8; 9], leaf nitrogen accumulation [10], the fraction of absorbed photosynthetically active radiation (FPAR) [11] and crop biomass [8; 12; 13; 14]. Most of these applications were on the large scale of a region or country compared with few applications at a field scale. The most common reasons for this trend are the high cost of obtaining and processing RS data on a field scale, research funders such as governments and organizations are focusing on total production, and a lack of ground truth data and measurement accuracy [5]. Traditional methods for crop yield monitoring such as quadratic frame sampling are time-consuming, destructive, laborious, and not accurate for large fields where spatial variability becomes an issue [2]. Currently, the availability of crop yield monitoring systems mounted to harvesters can provide yield maps but obviously only at the end of the season. Therefore, the rapid development in RS and the need for crop yield monitoring and prediction attracts the attention of many researchers to investigate within-field variability through satellite and aerial RS data [15; 16; 17; 18; 19]. In most yield monitoring studies using RS data, two main strategies have been typically proposed. The first method integrates RS data with meteorological data and plant physiological models to monitor crop development and then crop yield [20; 21]. The other method relies on RS data to predict the yield for crops that have a direct relation between biomass and the harvest index [22]. The harvest index is the ratio between grain yield and above ground crop biomass. The first method is complicated and requires a lot of inputs, while the latter method does not provide an explanation of physiological process [23]. The development of empirical equations between vegetation indices (VIs) and crop yield is a simple and operational way to assess within-field variability [24; 25], whereas the developed equations have spatial and temporal constraints to apply in another field or another season [19; 26; 27]. A large number of VIs have been developed to describe crop growth and subsequently yield. Some well-known ones are the Normalized Difference Vegetation Index (NDVI), Soil Adjusted Vegetation Index (SAVI), Enhanced Vegetation Index (EVI), Green Normalized Difference Vegetation Index (GNDVI), Green Atmospherically Resistant Vegetation Index (GARVI), and Normalized Difference red edge (NDRE) [16; 28; 29; 30; 31; 32]. Specific modifications by differential weighting of some bands (in particular of the near-infrared range) have been applied to provide specific indices for crop yield monitoring, like the Wide Dynamic Range Vegetation Index (WDRVI) [33; 34] and the Green Chlorophyll Vegetation Index (GCVI) [35]. Selecting the most suitable VI and crop age for yield assessment is an important step in crop yield empirical model development [16]. Predicting corn (_Zea mays_ L.) grain yield and assessing its spatial and temporal variability have been investigated in several studies [24; 26; 36; 37; 38; 39; 40]. [PERSON] et al.