Stochastic modelling of rainfall for the island of Ireland

This paper analyses a recently created continuous 305-year (1711–2016) monthly rainfall series for the island of Ireland. The findings are as follows. The excess skewness in the monthly series may be eradicated by using a Box-Cox transformation with parameter equal to 0.6: a value very similar to that found for the U.K. and its regions. There is no evidence of either an overall stochastic trend or of evolving monthly seasonal patterns, but positive linear trends are found for January, March, and December and a negative linear trend is found for July. Analysis of the seasonal and annual series (which require no transformation) confirms the implication from the monthly data that winters have become progressively wetter and summers progressively drier, with the positive linear trend for winter being twice the size of the negative summer trend. Since there is no trend in either spring or autumn rainfall, annual rainfall shows a positive linear trend. Given that the rainfall series exists for over three centuries, breaks and structural shifts in the model were investigated. Five breaks were identified, three of which occurred in the early portion of the series during the eighteenth century. However, trends were found to be much more stable from the middle of the nineteenth century. For the seasonal series, only a single break, at 1790 for the winter series, was found: it was only after this break that winters became wetter; before then, winter rainfall had a negative trend. In terms of predictability, predictions from the model were found to be more volatile during the second half of the eighteenth century and again from 1976 onwards.