The Effects of El Ni\~no on the Global Weather and Climate

This paper studies the chaotic behavior of hydrosphere and its influence on global weather and climate. We give mathematical arguments for the sea surface temperature (SST) to be unpredictable over the global ocean. The impact of SST variability on global climate is clear during global climate patterns, which involve large-scale ocean-atmosphere fluctuations similar to the El Ni\~no-Southern Oscillation (ENSO). Sensitivity (unpredictability) is the core ingredient of chaos. Several researches suggested that the ENSO might be chaotic. It was Vallis [1] who revealed unpredictability of ENSO by reducing his model to the Lorenz equations. Interactions of ENSO and other global climate patterns may transmit chaos. We discuss the unpredictability as a global phenomenon through extension of chaos "horizontally" and "vertically" in coupled Vallis ENSO models, Lorenz systems, and advection equations by using theoretical as well as numerical analyses. To perform theoretical research, we apply our recent results on replication of chaos and unpredictable solutions of differential equations, while for numerical analysis, we combine results on unpredictable solutions with numerical analysis of chaos in the advection equation.