Long-term evolution of a transgressive migrating dune using reconstruction of the EOF method

The advance of the Valdevaqueros transgressive dune has resulted in gradual invasion of the adjacent road and ecosystem. Despite restoration and control activities performed within the last decades, strong winds have favoured dune destabilisation. Topographic surveys of five profiles were carried out in the research area from 1995 to 2006 to study the dune evolution. It was found that the average migration rate is 17.5 m/year, with a maximum of 38.0 m/year in the most active profile. The Empirical Orthogonal Functions method (EOF) is applied herein to identify tendencies in the aforementioned profile, separating spatial from temporal variations. Four spatial and temporal eigenfunctions account for 99.94% of the total data variability. The analysis of the individual eigenmode contributions allows us to identify particular and independent physical interpretations. The first eigenfunction represents the equilibrium dune profile. The second individual eigenmode shows pivot points separating different behaviours, which indicate a positive sand balance from the windward side towards the crest and the dune slip face. Finally, the third and fourth spatial and temporal modes reveal a slope increase and identify parallel dune advances, respectively. Although the dune sand budget (138 m3/m·year) is similar to the sand extraction rate (147 m3/m·year) over the research period, sand is still extending inland. Some different sustainable and less costly steps should, therefore, be taken to mitigate the dune invasion.