## 1 Introduction  
Aerating stored grains may best be described as using low-volume airflow rates to cool a grain mass down to a specified temperature [1]. The airflow rates in English units are between 0.1 and 0.3 cubic feet per minute per bushel, which is equivalent to about 0.12-0.36 m\({}^{3}\)/min/metric ton (MT). These airflow rates are distinguished from grain drying, which utilizes airflow rates that are several orders of magnitude greater than those used for aeration [1, 2]. Development for most stored product insects ceases at about 15 \({}^{\circ}\)C [3, 4], which can be used as a target temperature for utilizing aeration to cool a grain mass. Aeration can be an important component of integrated pest management (IPM) programs for stored grains, as it is a non-pesticide option that could mitigate development of insecticide resistance in stored product insects. Throughout most of the temperate regions of the world, hard red winter wheat is planted in autumn and harvested during the summer months of the next year. One of the obvious requirements for using aeration is availability of electricity and the hours that the ambient outside air is below the 15 \({}^{\circ}\)C threshold necessary to cool the grain mass, for slowing or halting development of insects. Theoretical engineering calculations state that 120 h below a specified threshold are necessary to cool the grain mass to that temperature at an airflow rate of 0.12 m\({}^{3}\)/min/MT [5]. A controller wired into the electrical system of the bin can be set to operate when ambient temperatures fall below the desired threshold [6; 7; 8]. The aeration system can be configured to bring the ambient air into the bottom of the grain mass where a cooling front is then produced that can gradually cool the grain from the bottom of the bin to the top. These hours assume that the aeration fan is properly sized to match the bin capacity and can deliver this cooling front throughout the grain mass. Historical weather data, available from the USA National Oceanic and Atmospheric Administration (NOAA) National Climatic Data Center ([[https://www.ncdc.noaa.gov](https://www.ncdc.noaa.gov)]([https://www.ncdc.noaa.gov](https://www.ncdc.noaa.gov))), have been utilized to predict the hours below this insect developmental threshold temperature for corn, wheat, and rice stored in different regions of the USA [9; 10; 11; 12; 13]. A program written in Q-Basic, which required maximum and minimum temperatures for a given day, along with sunrise and sunset times, was utilized for these studies and published [9]. The sunrise and sunset times were obtained from the website of the USA National Weather Service ([[https://www.weather.gov](https://www.weather.gov)]([https://www.weather.gov](https://www.weather.gov))). For most regions of the USA, the hours below 15 \({}^{\circ}\)C in September were best used to predict success of aeration in a given location. The Q-Basic program [9] could predict hourly temperatures but perhaps a simpler method is necessary to further promote the concept of aeration, particularly for international use. A common method to determine degrees days was developed several decades ago [14; 15] and has become widely implemented in agriculture (e.g., [15]). The model functions by approximating the temperature diurnal course using a sine wave delimited by the maximum and minimum daily temperature readings from a weather station, and then calculates degree day or hour accumulations by integrating under the sine curve. The model may subsequently be tied to key phenological events in the life history of a pest, as has been done for _Ophionyia simplex_ ([PERSON]), the asparagus miner [15]; _Lobesia botrana_ ([PERSON] and [PERSON]), the grape berry moth [16]; and even postharvest pests such as _Dinoderus minutus_ (F.), the powderpost beetle [17]. However, to date, a degree-day calculation method has not been used to model potential efficacy of grain aeration.