# Defining the Ideal Phenological Stage for Estimating Corn Yield Using Multispectral Images
## 1 Introduction  
Estimating yield is a critical agronomic parameter for assisting the national and international market in terms of demand, transport capacity, and storage of agricultural products. It is possible to commercialize and ascertain prices by predicting crop yields and considering the quantity of product that will be generated prior to the harvest [1]. Yield can be estimated by combining the collection of biophysical parameters sampled in the field [2] and the information obtained using remote sensing techniques [3]. These techniques consist of analyzing the spectral response of crops and the targets present on the surface, which are obtained with multispectral sensors attached to satellites, remotely piloted aircrafts, or field machinery [4]. A critical aspect of yield mapping is that it can detect areas with lower yield potential, which may eventually be associated with nutritional deficiencies of the plants or soil. Multispectral images that are used to estimate yield follow scientific methodologies [5]. However, determining the period at which images should be obtained, the definition of spectral bands, and the ideal vegetation indices for constructing prediction models that are conditioned to the spectral characteristics of the different phenological stages of crops, remains a challenge [6]. This occurs because each crop has agricultural variations, including the type of management required for the structural changes inherent to each type of crop,such as the time of cultivation [7]. For example, annual and perennial crops exhibit distinct phenological stages and different spectral responses, and their conditions are influenced by canopy geometry, biomass, leaf area index, and leaf senescence [7]. Specifically, during the vegetative and reproductive phases, the maize crop experiences stress that can reduce yield. Depending on the moment of image acquisition for stress detection, it is uncertain whether the spectral responses detect the condition affecting a plant, especially when using a limited data set; thus, yield mapping becomes unfeasible. In recent studies, spectral models for yield estimation based on machine learning and MODIS [8], Landsat 8 [9], and aerial [10] showed greater accuracy with the use of images obtained in the phenological stage, called the reproductive phase (R2 and R3), that is, the period that varies from 12 to 18 days after the fertilization when the culture presents a significant gain in biomass. However, these models are often developed in the late stage and do not precisely estimate the absolute value of yield; decades of agricultural remote sensing studies indicate that for any crop, the spectral bands always have a high sensitivity to agronomic parameters that correlate with the production factors, making them potential predictor variables. Based on the aforementioned findings, in this study, we assume that the actual contribution of spectral models for estimating yield is related to how useful they are for management practices of maize crops, in addition to the potential accuracy of the absolute value of production. The application of the current spectral models for yield prediction [11; 12] have limitations owing to the fact that these methodologies [13] only recommend estimations at advanced phenological stages of maize development, that is, stages in which interventions in the crop will only make a slight difference in the final yield [11]. Therefore, given the hypothesis that it is possible to estimate the yield of corn using multispectral orbital images and algorithms based on machine learning, the objective of this study was to evaluate whether there is an ideal phenological stage that accurately estimates yield in a timely manner for applying management practices that will increase the productive potential of the crop.