Application of linear splines to simulate daily changes in insolation

Abstract

The paper shows the possibility of using linear splines in modeling the daily change in solar radiation. The calculations were based on the generally accepted cosine expression used for modeling insolation changes on the surface of lakes and the ocean. The equation parameters are set for the conditions of Sevastopol (44°35'N, 33°30' E): the maximum height of the sun above the horizon is about 68 degrees, the day length is 15 hours. The model curve was divided into three sections. For the early morning hours and late evening, the sunlight intensity is low and is below the “compensation point” of photosynthesis. So these areas were not considered during modeling. Three sites: the increase in irradiation from 6 to 12 hours, the maximum irradiation from 12 to 14 hours, and the decrease in irradiation from 14 to 20 hours are described by linear equations. It is shown that the deviations in the description of the data of the dependence of the sunlight intensity on the time of day by linear splines from the generally accepted formula in the form of a cosine do not exceed 5%. An example of experimental data of linear growth of productivity of A. platensis culture is given. Based on the assumption that the growth rate of microalgae culture is proportional to the amount of energy absorbed, the linear increase in productivity can be explained by a linear increase in the intensity of sunlight.