[caveat: this is my opinion and in no way should be used for any decision-making]
Given the level of disruption caused by the 2010 eruption of Eyjafjallajökull there has been an inevitable level of concern from many readers/commenters on the likelihood of future air travel plans being affected by any eruption in Bardarbunga.
Unfortunately we have no way of forecasting any possible disruption on any particular day, as there are so many variables. Remember that, while Eyja was particularly bad in terms of disruption, Grimsvötn in 2011 caused much less, despite being a much larger eruption.
Variables – For a start, you need an eruption and there hasn’t been one yet!
However, let’s take the case that there is one. The type of eruption (small, large, explosive, ashy, gassy, wet, dry, blocky, squidgy, under ice, under water, on land) can greatly affect the nature of any flight disruption due to the height that the eruptive column reaches, and the type and density of the particles that are ejected into the atmosphere.
Then there’s the weather, which plays a huge part in determining where any ash cloud goes. Wind directions and strengths differ not only from hour-to-hour, and day-to-day, but also at varying altitudes. Winds all the way from ground level to 50,000 feet can affect ash dispersal. Column height is therefore an important factor in determining which airspace is affected; as well as directional changes, it’s mostly the case that the higher the column, the further the ash is carried from the volcano.
Forecasting – If an eruption happens, the variables (eruption type and weather) become quickly known. They are fed into a computer model that provides a forecast of where and how the ash cloud will propagate.
While advances in meteorology allow detailed models to be produced, the models can also be verified and contributed to by a number of observation means, such as both persistent and periodic monitoring from space. There are ground-based radars in Iceland that can provide high-quality data about the nature and behaviour of an ash cloud.
Using real data and model predictions, forecasters have a good idea of the dispersion of the ash and where it is at its most dense. Appropriate warnings (NOTAMs) are issued to operators and air traffic control authorities. For an idea of how it works, and who is involved, have a look at this UK Civil Aviation Authority page:
The UK Met Office operates the London Volcanic Ash Advisory Centre (VAAC) with responsibility for overseeing the eastern North Atlantic (including Iceland), the British Isles and Scandinavia. In the unlikely event that ash was to disperse westwards, then the Montreal VAAC would also be involved.
The Met Office uses a programme known as NAME for prediction. Some details can be found here:
Programmes such as NAME allow more flexible use of airspace than during the Eyja eruption, with the result that potential disruption to air traffic should be reduced (for an equivalent eruption) without any erosion of safety.
Safety in the air – In the 1980s two Boeing 747s separately encountered heavy volcanic ash (from Galunggung in Indonesia, and Redoubt in Alaska) and in both cases all four engines stopped. While these were very serious incidents, both times the crew got the engines started again and made safe landings.
In 62 years of jet airliner operations, just two non-fatal incidents due to encountering volcanic ash is not a bad statistic.
Advice? – I am loathe to give any other than to say ‘Contact your airline’ if there is an eruption that might threaten your journey.