Steric sea level change ($\Delta {\eta }_{\mathrm{steric}}=-\int \Delta \rho /\rho dz$)

Steric sea level change results from changes of seawater mass density at fixed ocean mass. To first order, thermal expansion gives $\Delta {\eta }_{\mathrm{thermal}}=\int \alpha \Delta Tdz$; changes in salinity give a halosteric contribution. The reference column, pressure and equation of state must be specified.

Thermosteric sea level change is the thermal expansion part of steric sea level change. For a uniform layer of depth $H$, conservation of mass gives $\rho H=(\rho +\Delta \rho )(H+\Delta \eta )$, hence $\Delta \eta \simeq -H\Delta \rho /\rho =H\alpha \Delta T$.