# Monitoring Within-Field Variability of Corn Yield using Sentinel-2 and Machine Learning Techniques
## 1 Introduction
[5] introduced a yield prediction method based on Landsat 5 and Landsat 7 satellite imagery and weather data used as inputs with crop model simulations. This approach was tested between different fields based on farmers reports in the USA and the overall R\({}^{2}\) for corn was 0.35. [PERSON] et al. [41] reported that GNDVI derived from aircraft imagery at mid-grain filling stage provided the highest correlations (0.7 to 0.92) with corn grain yield in a plots experiment. [PERSON] et al. [42] used the greenness index derived from the Advanced Very High Resolution Radiometer (AVHRR) imagery to predict corn yield at the Hungarian county scale with 90% accuracy in late July (70 days before harvesting). A recent study was performed in Brazil and the USA to investigate different VIs derived from Sentinel-2 images to predict corn grain yield at a field scale. The collected images were in the range of \(\pm\)20 days from flowering. This study showed that NDRE, GNDVI, and NDVI presented high performance to forecast field variability and provided an R\({}^{2}\) value of 0.32 for the universal corn yield estimation equation [19]. Currently, various agricultural models based on RS imagery have been developed using Machine Learning (ML) techniques [43; 44; 45]. ML techniques potentially provide a higher accuracy and a more robust performance compared to conventional correlations as they learn to model complexity through training. Therefore, variance is explained through either parametric or nonparametric approaches. Parametric approaches are simpler, need less data for training, but are less suited for complex problems. Nonparametric models are harder to interpret with regards to input features, need more time and more data for training, and can suffer from overfitting, but by making no assumptions in the underlying function, they are more flexible [46]. A note must be made about deep learning methods. Applications of deep learning to imagery in the literature have proven to give added accuracy and improve results. In this study, deep learning methods were not considered because of the implicit complexity to the deep learning approach. The complexity lies in defining the architecture of the hidden layers that require testing combinations of pooling layers and convolutional layers with the respective parameters. The ML methods tested in this investigation only require tuning a few parameters. It is certainly worth testing deep learning methods, but this was not the focus of this research. In this work we tested three regression methods. One is a common multiple linear Regression (MR), and two are ML algorithms, Random Forests (RF) and Support Vector Machines (SVM). The two ML approaches are more effective as they are not affected by collinearity and non-normal distribution of the variables, can handle overfitting, and do not require scale normalization. They are nonparametric models, as opposed to MR, and therefore have the drawback that they add complexity to interpretation. Recently, ML algorithms have emerged with big data technologies to create new opportunities in the agricultural domain [47]. Applying ML algorithms on crop yield estimation from RS data is a flexible approach and capable of processing a large number of inputs with the increase in data volumes due to higher resolution and the shorter revisit times of new satellite sensors [48]. [PERSON] et al. [45], compared different ML techniques to estimate the LAI of soybean using Unmanned Aerial Vehicle (UAV) imagery and reported that RF was the most suitable technique when the sample plots and variations in LAI were relatively large. [PERSON] et al. [49] reported that RF was extremely robust against noise compared with other ML techniques in estimating winter wheat biomass using near-surface spectroscopy. [PERSON] et al.