Development of a mathematical model for forecasting pastural fertility to remote sensing data

Abstract

Variants of developing a mathematical model for predicting pasture fertility based on the use of remote sensing data from the Earth and ground based measurements on test field plots are presented. The NDVI data, which is a time series with pronounced seasonal features in the form of one or two maxima, are the basis for obtaining the vegetation index forecast model (NDVI) from the currently available measurements. To predict the parameters of this maximum, we used the position on the time axis, width, amplitude, and its shape. Using various model regressions over the entire available time interval, it is possible to obtain models, for example, in the form of rational and polynomial functions. As model, in addition to the rational and polynomial ones presented above, we used the following functions with characteristic impulse behavior: Cauchy, arctg (x)’, Verhulst, Gompertz differential functions (derivatives) with left and right asymmetries, as well as the sum fs and the product fp of logistic functions Verhulst. Of all the options on the evaluation interval [56 and 180] days, the model in the form of the sum of the Verhulst logistic functions with 7 evaluated parameters turned out to be more effective. The results show that all parameters are statistically significant, and the corrected determination coefficient is large enough: 0.9545. However, to parameterize the model, observations are needed “on the decline” of the time series - 150-180 days from the beginning of the year. The use of mathematical models is necessary for managing pasture plots and the need for timely management decisions of various kinds - alternating corrals, mowing terms for grass stands, and fertilizing. To generate reliable information about the state of pastures, the use of remote monitoring is relevant.