Polymodal distribution of water discharge probability in river systems

Relevance. Statistical studies of water discharge in river systems conducted by various authors have shown that forms of distribution of river discharge probability density are polymodal. There are various hypotheses for the origin of this polymodal distribution. For example, in dynamic systems the formation of attractors is possible, or under conditions of perturbation of the initial data singular numbers can be transformed into a polymodal structure. However, the proposed hypotheses of formation of polymodal distribution of transformation intensity of elements of an open system are not always applicable to specific objects and are limited to certain conditions. Therefore, it is proposed to apply the universal theory of formation of polymodal distribution of transformation intensity of open systems to study water discharge distribution in river systems. Aim. To confirm the compliance of river flow modes with universal transformation principles in unifying the polymodal statistical probability distribution of water discharge in river systems. Object. Samples of water discharge intensity of hydrographic open systems of the Velikaya and Oka rivers in different seasonal period. Method. Determined on the basis of the derived universal equation of modes of unified polymodal probability density distributions for transformation of any open systems. Each mode in the unified polymodal distribution of river runoff corresponds to a certain universal principle of transformation of an open system under external influence. Its universality is based on the constants of the ratio of time parameters (internal time of transformation of system elements and external time of impact on the system) associated with the "golden" proportion. Soil evaporation and moistening reduce the flow rate and is an internal transforming process depending on atmospheric temperature, and precipitation is an external factor that increases river runoff. Results. Certain modes of polymodal distribution of water discharge fully correspond to universal states of transformation of open systems under external influence. For each seasonal period, the modes correspond to different, previously established principles of systems transformation. Conclusions. Based on a sample of water discharge in river systems, using the unification equation of polymodal distribution, it is possible to determine the state of the river system transformation in the present time and, knowing the parameters of external influence, to predict its future development.