This variability has always been there and will continue to operate in the future too. The anthropogenic contribution to global warming is small for a specific year, but because of the persistent warming the sum becomes large in the long run. The natural variability is hard to predict because we don't know all the mechanisms controlling the variations. But what we do know is that the natural variations follow different time scales, from diurnal to decadal scales and all the way up to multidecadal and 100.000 years ice-age cycles.
A large part of the annual to decadal variations is linked to The north-atlantic oscillation (NAO). This is an index describing the relationship between low-pressure and high-pressure systems in the North-Atlantic. A positive NAO-index will usually lead to a warming of the Barents Sea, but the connection between heat content in the Barents Sea and the NAO-index changes through time and is not necessarily that simple. In the Norwegian Sea a positive NAO-index will lead to a stronger North Atlantic Current positioned closer to the coast.
The North-Atlantic is a region with large multidecadal variability, and the main frequency is at about 70-80 years. Historical data supports that this multidecadal variability has been present for a long time. The long term variations in the Barents Sea seem to follow the index of The atlantic multidecadal oscillation (AMO). Even though the mechanisms behind this oscillation are uncertain, it is strongly linked to the main circulation patterns in the Atlantic ocean.
Climate models provide an estimate of anthropogenic global warming, given specific scenarios of amount of greenhouse gases released to the atmosphere. The scenarios usually project a slow increase in temperature with a given uncertainty. The natural variability will add to the long-term trend, and on a short timescale will the importance of natural variability will be larger than the global warming.