Abstract. With recently improved instrumental accuracy, the change in the heat content of the oceans and the corresponding contribution to the change of the sea level can be determined from in situ measurements of temperature variation with depth. Nevertheless, it would be favourable if the same changes could be evaluated from just the sea surface temperatures because the past record could then be reconstructed and future scenarios explored. Using a single column model we show that the average change in the heat content of the oceans and the corresponding contribution to a global change in the sea level can be evaluated from the past sea surface temperatures. The calculation is based on the time-dependent diffusion equation with the known fixed average upwelling velocity and eddy diffusivity, as determined from the steady-state limit. In this limit, the model reduces to the 1966 Munk profile of the potential temperature variation as a function of depth.

There are no adjustable parameters in the calculation and the results are in good agreement with the estimates obtained from the in situ data. The method allows us to obtain relevant timescales and average temperature profiles. The evaluation of the thermosteric sea level change is extended back to the beginning of accurate sea surface temperature records. The changes in sea surface temperature from 1880 until the present time are estimated to have produced a thermosteric sea level rise of 35 mm. Application to future IPCC scenarios gives results similar to the average prediction of more complex climate models.