Investigation of Bi-sinusoidal model efficacy in estimation of hourly temperature in different climates of Iran

Abstract
Background and objectives
Access to hourly temperature due to the more detailed analysis of plant growth processes is of fundamental importance in crop modeling and freezing studies. Also, hourly data is needed for more accurate analysis of climate change effect and atmospheric hazard phenomena on the growth and development of plants. The Bi-sinusoidal model is a precise method in daily temperature modeling which, while considering the sinusoidal nature of temperature variations, is very accurate in detecting the time of minimum and maximum temperature of the day. So far, the accuracy of this method has not been studied in different climates of Iran. The objective of this research is to evaluation of Bi-Sinusoidal model for estimation of hourly temperatures from maximum and minimum daily temperature in different climates of Iran.
Materials and methods
For investigation of the efficiency of Bi-sinusoidal model, the data of meteorological stations in different climates from ultra-dry to very humid climates were used. For this purpose, daily and three-hour recorded temperatures at eight stations include: Ahwaz, Ardabil, Bushehr, Gorgan, Mashhad, Rasht, Tehran and Zahak in 2000 and 2005 were used. In this model, sunrise time is considered as the occurrence time of minimum temperature and maximum temperature occurrence is assumed after passing two-thirds of daytime length. These times can be accurately calculated with astronomical calculations. All the modelling calculations were performed in MATLAB software environment. To evaluate the mean error and mean bias of the model, RMSE and MBE indices were used, respectively.
Results
The results showed that in arid and extra-arid stations, RMSE vary between 1.5 to 2 and in humid and sub-humid stations it’s close to 3 Celsius degrees. Also, it seems that the performance of this model is not related to the season, in other words, the hourly temperature error estimation in hot and cold months is not significantly different. The MBE showed that the model underestimate hourly temperature in warm months and overestimate in cold months. However, the bias error is negligible in most of the months and is less than 0.5 degrees. Variation of actual and modelled temperature showed that circadian fluctuation of temperature in dry region is more similar to sinusoidal changes than humid area.
Conclusion
Investigation of circadian temperature fluctuation showed that this model has some trouble in detection of occurrence time of minimum and maximum temperature in humid stations that this is one of the main sources of this model error. But this model simulates the sinus trend of temperature variations properly. According to development of this model based on ordinary circadian temperature fluctuation, in days with the meteorological phenomena such as warm and cold advection to the region, or in rainy days, the model accuracy in estimating hourly temperatures maybe reduced.