Simulation of vegetation conditions using differences of current NDVI values from average long-term indicators

Currently, one of the important tools for increasing crop production is the introduction of precision farming systems. As an obligatory element of such systems, production process control has been successfully used in recent years. Such control is implemented by modeling the responsiveness of the vegetative mass to changes in actual environmental conditions. In domestic and foreign literature, there are many examples of the development of mathematical models of plant growth and development that take into account external influences. It is shown that the predictive models allow us to respond in a timely manner to changing growing conditions. In turn, this helps to quickly make optimal agronomic decisions. In this work, for the first time, the relationship between the difference (anomaly) of the average annual and current seasonal indicators of NDVI (normalized difference vegetation index) and the process of plant growth and development, taking into account the influence of existing conditions, was established for the first time. It is shown that the conditions for the adequacy of approximation, when leveling noisy time series, are completely satisfied by the Gauss-Laplace function. As a mathematical expectation, the average values of the highest NDVI values of the vegetative period of the crop should be used. Mathematical models of the influence of photosynthetic, meteorological, and soil-climatic factors on NDVI anomalies in a particular phase of plant development have been obtained. Our goal was to develop predictive models of the vegetation process of grain crops, based on a comparison of the average long-term indicators of NDVI with its current seasonal values. The influence of actual conditions was taken into account. The research was carried out on the fields of the «Integration» center of the Oryol State Agrarian University (Oryol Procince). In 2021, winter wheat ( Triticum aestivum L.) cultivar Moskovskaya 39 occupied an area of 48.1 ha, spring barley ( Hordeum vulgare L. sensu lato) cultivar Raushan - 17.4 ha. Data for calculation of NDVI values were obtained from the CosmosAgro geoportal, as well as using an Agrofly Quadro 4/17 unmanned aerial vehicle (Agrofly International, Russia). Data noise compensation was performed by approximating time series with the Gauss-Laplace function. The adequacy of the regression models for the approximation of NDVI time series was assessed using the Fisher F -test and the average error of the approximation coefficient; the accuracy of the predictive models was confirmed by the Mean Absolute Percentage Error (MAPE) indicator. As a result, time series of the average NDVI value for the studied crops were obtained based on long-term observations, and the current NDVI values in the growing season 2021 were calculated. The distribution of time series of the vegetation index has been established. It was close to normal. The maximum (peak) values of NDVI are determined. They amounted to 0.71 for winter wheat and 0.54 for spring barley and fell in June, regardless of the crop. The purpose of leveling the noisy NDVI time series of crops during the growing season is most fully satisfied by the asymmetric Gauss-Laplace function. As a mathematical expectation, the average value of the highest NDVIs for the crop vegetation period was used. Mathematical models were obtained based on the NDVI anomaly index. These models describe the influence of photosynthetic, meteorological, soil, and climatic factors on the crop state during a particular phenophase. The mean absolute error of the proposed models was 9.23 for spring barley and 5.68 for winter wheat. Thus, the proposed characteristic ΔNDVI can be used as an independent variable (optimization criterion) in factorial models for predicting the dynamics of the vegetation process.