We estimate the frequency of Saharan mineral dust outbreak events observed over the North Atlantic island of La Palma based on in situ nightly atmospheric extinction measurements recorded almost continuously since 1984 by the Carlsberg Meridian Telescope at the Roque de los Muchachos observatory. The outbreak frequency shows a well-defined seasonal peak in the months of July to September, during which time the occurrence of Saharan dust events (SDEs) is approximately 28\pm6%. We find considerable year-to-year variability in the summertime SDEs frequency, observing a steady reduction between 1984 and 1997, followed by a period of relative mean stability from 1999 to 2012. We investigated changes in the atmospheric extinction of the SDEs as an indicator of strength of the episodes and found that this parameter approximately follows the SDE frequency, however, instrumental limitations prevented us from deriving precise conclusions regarding their long-term changes. A lagged correlation analysis between SDE properties and the El Ni\~{n}o Southern Oscillation (ENSO), North Atlantic Oscillation (NAO), and Sahel rainfall index (SRI) was performed. We found that 55\pm4% of the year-to-year variations in July-September SDE frequency may be reproduced by a lagged relationship to the NAO conditions during the preceding October-December period, and 45\pm4% may be reproduced by a negative correlation to the SRI during the preceding February-April period. Based on these relationships it may be possible to obtain an approximate indication of the strength of the upcoming summertime dust season over the North Atlantic around half a year in advance.