We present the first analysis of global and hemispheric surface warming trends that attempts to quantify the major sources of uncertainty. We calculate global and hemispheric annual temperature anomalies by combining land surface air temperature and sea surface temperature (SST) through an optimal averaging technique. The technique allows estimation of uncertainties in the annual anomalies resulting from data gaps and random errors. We add independent uncertainties due to urbanisation, changing land-based observing practices and SST bias corrections. We test the accuracy of the SST bias corrections, which represent the largest source of uncertainty in the data, through a suite of climate model simulations. These indicate that the corrections are likely to be fairly accurate on an annual average and on large space scales. Allowing for serial correlation and annual uncertainties, the best linear fit to annual global surface temperature gives an increase of 0.61±0.16°C between 1861 and 2000.