Periodicities in mean sea-level fluctuations and climate change proxies: Lessons from the modelling for coastal management

• Replication of published periodicities in global tidal and past climate data sets.
• Modelling chaotic-deterministic limit cycles based on half a sunspot cycle.
• Inclusion of anthropogenic warming within natural cycles.
• Three-fold increase in the likelihood of extreme events with anthropogenic warming.
• Planning and management consequences of these risk cycles for coastal communities.

The question of whether sea levels and global temperatures are accelerating or decelerating is a major source of current debate. Single taper and multi-taper spectral analysis from seventeen globally distributed tidal stations and twenty climate proxies show aggregate significant common periodicities in mean sea level fluctuations and the climate proxies of approximately 7 yr, 13 yr, 23 yr, 32 yr, 41 yr, 53 yr, 66 yr, 88 yr, 105 yr and 132 yr, respectively. These periods are shown to strongly correlate with an harmonic sequence of n, m = n + n/4 and p = n + n/2n for n = 5.5 yr and this synchronicity allows for a climate state function to be defined by Lotka–Volterra limit cycles. Such a model can include both anthropogenic warming and complex natural cycles, based on past evidence, and these cycles can form or bifurcate into extreme events close to critical values. The model suggests that accelerating sea levels can be in-phase, but lag decelerating global temperatures or vice versa, so a ‘pause’ in global warming should not be surprising. Further, the model can simulate the uneven regional effect of climate responses and replicate the chaos apparent in monthly sea-level records. The approach poses ‘a planner's dilemma’ whereby the likelihood of a present 1 in 100 yr positive extreme event can either be caused by anthropogenic warming within shorter cycles or by a stationary mean in a longer cycle. We simply show that for rising average temperatures in a double period cascading model, there would be a three-fold increase in the likelihood of an equivalent 1 in 100 yr positive extreme event relative to present over a 20 yr period. A consequence to the ‘planner's dilemma’ is the ‘manager's risk imperative’ where risk cycles can be quantified into strategic GIS maps of potential future inundations: identifying vulnerability, defining possible economic impacts and underpinning response strategies that are legally defensible and transparent to a range of stakeholders.