# A Geographically Weighted Random Forest Approach to Predict Corn Yield in the US Corn Belt
## 1 Introduction  
Corn, as an important crop in the world, is mostly used for human food, ethanol production, and livestock feed [1]. The United States (US) is the largest corn producer and accounts for more than 36% of global corn production [2]. The majority of the corn produced by the US is from the Corn Belt, which consists of 12 Midwestern states where corn is usually grown in rotation with soybean [3]. The changing climate poses a threat to crop yield and the agricultural systems [4]. Additionally, the rapid growth of the global population also poses a challenge for global food security [5]. An accurate and timely yield estimation plays a significant role in agricultural economics and global food security because it can provide more information to different stakeholders such as farm managers, crop specialists, and governments and facilitate their decision making (e.g., importing/exporting grains, planting, irrigation, fertilizing, and harvesting) [6; 7; 8]. Crop yield prediction has attracted significant research attention [6; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29] and can date back to 1964 [30]. There are two primary categories of crop yield models: physical models and statistical models [31]. Physical models use physiological conditions of crops and predict yield by incorporating the underlying processes such crop health, soil nutrients, and water availability [24]. Physical models usually provide better estimates of crop yield if the underlying crop conditions provided are accurate; however, these models are not widely used due to their complexity [32]. Physical models require fine-grained data, whichlimits the use of these models in large-scale applications, since it is difficult to compile the required detailed data for large study areas [31]. On the other hand, statistical models are widely used due to their simplicity and good performance [12; 33; 34]. Crop yield is affected by several factors such as genotype [17], weather [33], water management practices [35], soil moisture [14], and soil nutrients [36]. We can use these factors as the input to predict crop yield. In the early stages, soil-based parameters were mainly used to predict crop yield at the field level since other datasets were not available. With the development of data acquisition technologies, remote sensing and climate data have been widely used for crop yield prediction [28]. Recently, a significant amount of research has been conducted on crop yield prediction [11; 15; 19; 20; 25; 31; 34; 37; 38]. Different studies have used different datasets such climatic data [33], remote sensing data [21], and other biophysical data [23] to predict crop yield. Climatic variables such as temperature, precipitation, evapotranspiration, and vapor pressure deficit are related to crop growth as they can affect crop yield prediction [39]. Remote sensing data can provide information on both biotic and abiotic factors, such as temperature, precipitation, soil moisture, vegetation health, and water stress. One advantage of remote sensing data is their good availability. Early research [22] has demonstrated the effectiveness of remote sensing data in crop yield predictions. Since then, many studies [9; 31; 40] have been conducted on using satellite-derived information for crop monitoring and yield prediction. Remote sensing data can capture several crop characteristics such as crop health [41], diseases [42], and primary productivity [43]. The use of vegetation indices (VIs) derived from remote sensing data are more popular in crop yield prediction [44]. Compared with raw reflectance values, VIs are more sensitive to vegetation conditions and can better capture the changes in vegetation conditions such as crop growth, health, or stress [23].