The results of studies in the area ofnumerical weather prediction and climate theory are presented. These results were obtained by the team of researchers of the Siberian school of mathematical modeling of atmosphere and ocean dynamics established by academician G.I. Marchuk. Academician V.P. Dymnikov played an enormous role in the development of this school by enriching it with new approaches and ideas. His contribution to the Siberian school of mathematical modeling was most strongly pronounced concerning three problems: numerical weather prediction for the Siberian region, the modeling of the climate system dynamics, and the mathematics and theory of climate.