A large number of abiotic and biotic factors which are characterized by complicated functional relationships generally influence agrocenosis. Ultimately, the technology of sugar beet growing, as well as other agricultural crops is aimed at high-quality products obtaining. However, the full realization of this task can only take place under condition of totality tasks decision by certain elements of system process which are important for achieving this goal and are impossible fully exploring without the use of mathematical modeling.

In plant systems modeling perspective, the main data matrix is constructing computational algorithms mechanisms and patterns of functioning the beet crop rotation is a numerical expression of indicators of biological processes, which is a function of abiotic, biotic and anthropogenic factors additive action.

Recently, works of many domestic and foreign scientists are devoted to the mathematical models creation, however, they worth noting as many models are created indirectly bind to environmental conditions and in most cases just simulate some relationship between the productivity and the number of chemical fertilizers or different structural elements of plants, and so on. In our opinion, such approaches to the creation of plant growth and development of mathematical models is wrong and need further improvement. Particularly, it is necessary to pay more attention to the study of climatic conditions influencing s the amount of active temperatures, rainfall amount, GTC on plant growth and development, with complex mathematical models, and to inspect the accuracy of the results.

The obtained mathematical models can be used not only to simulate and forecast sugar beet processes of plants growth and development, but also for database management of sugar beet growing process productivity working.

Experimental researches were conducted on the experimental field of Bila Tserkva National Agrarian University during 2011-2014. Technology of sugar beet growing on test plots was common for the forest-steppes of Ukraine, except for the elements that were studied.

On the basis of research and study the influence of rainfall and the amount of active air temperatures on the mass of sugar beet root crops is established that coefficient of multiple regression is high (0.97), and a coefficient of determination is high (0.93), which shows how well the experimental data are described of real equation.

According to the results of previous studies on the analysis of complex agroecological factors on sugar beet root crop the mass,
on 01.07, foliar feeding is providing the similar reaction of plants on weather and climate conditions changing in the later periods
(on 01.09).

So, we have received the following regression equation that determines the dependence of the mass of roots of sugar beet (MR) from the amount of precipitation in the previous month (P) and the sum of active temperatures (T): MR = - 8519.83 + 263.76 T – 15.33 P. All coefficients of the equation are significant on the 5% level (p-level <0,05). This equation explains 93% (R² = 0,93) variation of the dependent variable.

There has been developed the mathematical models of culture growth and development on the basis of studies on the influence of weather conditions on sugar beet plant growth, development and productivity with the use foliar feeding of micronutrients and hybrids growing of the longest growing season by the optimum planting density - 100 thousand/ha.

During the analysis high coefficients of multiple regression (0,85-0,97) and coefficients of determination (0,73-0,93) were received, which indicates not only the link between the studied traits, but also stating that experimental data is quite accurately describes of the real equation. These models show that the relationship between the mass of roots and leaves, depending on the amount of active temperatures and precipitation during the growing season, and allows a high degree of accuracy to predict the parameters of these indicators of sugar beet plants.

Key words: sugar beet, processes of growth and development, mathematical modeling, climatic factors.