Understanding the simple mechanism of variable solar irradiance ocean warming/cooling allows for effective attribution, detection, and prediction of ocean-related extreme weather events based on solar activity level and duration. Modern and historical solar and ocean data were used to find the ocean warms from rising and high solar activity over any duration, and vice-versa, such as cooling from low activity during the Dalton Minimum. Equatorial ocean heat content and sea surface temperature are sensitive to daily total solar irradiance (TSI) variation and level, and to the upwelled heat accumulation from prior days sub-surface absorbed solar energy penetration. Equatorial evaporation from the absorbed solar energy performs as the pump of Earth’s hydrological system, sourcing atmospheric rivers and associated extreme weather events, follows a solar cycle pattern. Decadal scale ocean warming and post-solar cycle maximum El Nino events were empirically found to occur after solar activity rises above a decadal average of 120 sfu F10.7cm, equivalent to 94 v2 SIDC sunspot number and 1361.25 W/m2 LASP SORCE TSI. HadSST3 was found to linearly vary with the annual change in TSI, nominally at 0.5°C/W/year, varying with rate of TSI change. An empirical F10.7-TSI-SST model was derived combining a F10.7cm-SORCE TSI correlation model and the HadSST3-TSI sensitivity factor, predicated on the SWPC Solar Cycle 24 panel 2016 F10.7cm flux forecast. The author used this model in December of 2015 to uniquely and successfully predict the 2016 HadSST3 temperature fall to within 0.03°C. Cross correlation analysis indicate solar minimum La Nina events result from insufficient TSI over time, producing less equatorial evaporation, less cloud cover and precipitation, causing drought in the US. The Solar Modern Maximum that peaked in late 2003 warmed the ocean creating 20th century climate change via higher than average solar activity, higher than the 1361.25 W/m2 decadal TSI warming threshold. The 2003 European heat wave was forced by cumulative high solar activity warming of the AMO, and from high TSI during the heat wave. The 2013/14 Cold Wave is partly attributable to periods of lower than solar minimum level irradiance from October 2013 through February 2014. Future extremes depend on the duration of future solar cycle activity extremes.