Mathematical model of extensive green roof with a steep type of phytocenosis

Abstract

A mathematical model of the influence of weather conditions on the development of plants of a green roof with steppe type of phytocenosis for the eastern region of Ukraine with a sharply continental type of climate was developed. The main factors are the average annual relative humidity, temperature, percentage of sunny days and wind speed. By the method of least squares three equations are obtained for three groups of plants having the same phenotype. The analysis of the equations shows that the coefficients under various factors are comparable, which shows the same importance of taking into account all the factors. The smallest coefficients for all factors correspond to the group of plants II. These plants are the most resistant to weather influences. Plants of group III are characterized by insignificantly higher values of coefficients – within 0 ... 18.2%. Thus, plants of group III have approximately the same resistance to weather conditions. Plants of group I are characterized by values of coefficients that are 1.8 ... 2.1 times greater than group II, and the value of the free member is 4% less than group II. Thus, the first group is most prone to weather conditions and, with an average value of ambient air properties, has a lower score. These plants are more likely to lose their decorative qualities and require more frequent replacement or planting. The sensitivity of the plants to the action of the wind is established. This factor can have a negative impact on the decorative properties of plants. The action of wind is proposed to be adjusted using a parapet. When perforated parapet in the summer, the effect of the wind increases, which reduces decorative, but increases the «cooling effect». With a blind parapet, the effect of the wind decreases, the decorative nature of the plants increases, but the "cooling effect" decreases. This fact must be taken into account when using the green roof.