Sea-level rise does not seem to depend on ocean temperature, and certainly not on CO2
Whereas our CMIP5 analysis supports the hypothesis that seasonal-to-interannual sea level variability will increase relative to changes in ocean temperature variability due to nonlinearity of the EOS, the EOS alone does not constrain future sea level variability to increase in a warming ocean. From this perspective, future sea level variability could also remain constant with reduced temperature variability. Indeed, CMIP5 models diverge substantially in the projected amount of sea level variability increase because of the uncertainty in ocean temperature variability changes (respectively, stippling in Figs. 1c, d and 4c, d; see also shading in Fig. 6). Certainly also contributing to future sea level and temperature variability changes in CMIP5 are changes in the variability of atmospheric forcing. Because such forcing impacts variability in the oceans locally as well as globally, the effects of atmospheric changes are difficult to separate from those of increased oceanic thermal expansion and stratification in coupled climate model simulations. For this reason, we consider how thermal expansion and stratification impact sea level and thermocline variability (a proxy for temperature variability) in an analytic, reduced-gravity ocean model prescribed with future warming but otherwise unchanged atmospheric forcing.