  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.
