The HadCM3 AOGCM has been used to undertake an ensemble of four integrations from 1860 to 1999 with forcings due to all major anthropogenic and natural climate factors. The simulated decreasing trend in average Arctic sea ice extent for 1970--1999 (-2.5% per decade) is very similar to observations. HadCM3 indicates that internal variability and natural forcings (solar and volcanic) of the climate system are very unlikely by themselves to have caused a trend of this size. The simulated decreasing trend in Arctic sea ice volume (-3.4% per decade for 1961--1998) is less than some recent observationally based estimates. Extending the integrations into the 21st century, Arctic sea ice area and volume continue to decline. Area decreases linearly as global-average temperature rises (by 13% per K), and volume diminishes more rapidly than area. By the end of the century, in some scenarios, the Arctic is ice-free in late summer.