The sea surface temperature (SST) variability is clearly affected by global climate patterns, which involve large-scale ocean-atmosphere fluctuations similar to the El Nino-Southern Oscillation (ENSO). We give mathematical arguments for the SST to be unpredictable over oceans. Sensitivity (unpredictability) is the core ingredient of chaos. Several researches suggested that the ENSO might be chaotic. It was Vallis (Science 232:243-245, 1986) who revealed unpredictability in ENSO by reducing his model to the Lorenz equations. We discuss the unpredictability for SST as an extendable phenomenon through coupled Vallis ENSO models 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.