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The article investigated and formed the imperatives of the impact of the external natural environment on the grain yield in the south of Russia, forcing to abandon the simplified classical concepts and methods of analysis. The author's research concept defines quantitative risk analysis, as a category, inverse forecast, which is possible only on the basis of economic and mathematical modeling. The modern theory of assessing measures of economic risks, forecasting and managing them is still far from adequate to the real needs of practical agricultural management. This determines the main feature of modern risk, which is its total and comprehensive nature. It is difficult to manage risks in regions with frequent droughts, which are classified as areas of risk farming. The methodology of studying risks in the field of agriculture is based on the study of the dynamics of the natural environment of growing crops, the conjuncture uncertainty of the external economic environment, the variability of land management technologies. Climatic and agrometeorological conditions are becoming an important factor affecting crop yields. The yield series accumulates information about the fluctuation of weather conditions and their influence on the yield, they contain information about certain regularities that synergy relates to the concept of “long-term memory”. The paper describes the features of the spectrum of climatic conditions affecting socio-economic indicators, the growth and yield of grain (winter wheat) in southern Russia, as well as the results of the implementation of the author-hybrid approach to the fractal and linguistic forecasting of winter wheat yield in southern Russia.