An integral model to calculate the growing degree-days and heat units, a spreadsheet application

The concept of heat units is used in several phenological studies like the prediction of sowing and harvesting dates, crop yield, length of plant stages, and maturity state. However, calculation of heat units as growing degree-days requires a summation process that is not easily performed like direct-substitution equations. The aim of this work was to develop a simple integral model to calculate the heat units as growing degree-days. The development involved two steps; the first step was applying a non-iterative sinusoidal fit to the discrete temperature data to get a fitting equation of each station in the two datasets, CLIMWAT 2 and FAOCLIM 2. The second step was to integrate each temperature equation to calculate the heat units, either by the average temperature or by both the minimum and maximum temperatures. The results showed that the sinusoidal model properly fits the temperature profiles in most of the studied stations (Most of the stations got the fit with R2 > 95% and 98.4% of the stations had <2 °C root mean squared error). Additionally, the results showed no significant differences (in accuracy) between the developed integral model and the conventional summation methods of calculating the heat units, while the new model is faster and easier in application. Finally, it is recommended to use the new integral model with the fitted average temperature due to its accuracy and simplicity.