On the time lag between sea-level rise and basin infilling at tidal inlets.

Tidal inlets are a common feature along the world's coastline. Inlet-adjacent coastlines have for millennia supported communities and livelihoods, and therefore, projected climate change driven variations in catchment-estuary-coast (CEC) system drivers (e.g., sea-level rise (SLR)) are likely to lead to substantial socio-economic impacts. One important SLR-driven process that affects inlet-adjacent shoreline change is basin-infilling (i.e., sediment import to the estuary from the coast to satisfy the SLR-driven increase of estuarine accommodation space). Due to the slow morphological response to hydrodynamic forcing, however, there is a time lag between basin infilling and SLR, which, in numerical models that simulate century-scale evolution of CEC systems, is represented by a basin infilling lag factor (M). To date, an indicative M value has only been derived for small tidal inlet systems (M ~0.5), and due to the lack of M estimates for larger systems, studies have been using M ~0.5 indiscriminately. Here, for the first time, we derive indicative M values for small, medium, and large tidal inlet systems (M ~0.5, ~0.25 and ~0.15 respectively) via analytical considerations. Subsequently, to investigate the consequences of using sub-optimal M values on twenty-first century projections of inlet-adjacent shoreline change, we apply a probabilistic, reduced complexity model (G-SMIC), under four IPCC AR6 climate scenarios, to three CEC systems representing small, medium and large systems. Results show that, in general, shoreline change projections are substantially lower(higher) when M values smaller(larger) than the indicative M for a given system are used. When smaller-than-optimal M values (0.25 and 0.15) are used for the small tidal inlet, both mid- and end-century shoreline retreats are under-estimated by 50-75% (across the four climate scenarios), relative to projections obtained with the optimal M value. For the medium-sized inlet, shoreline retreats for both future periods are over-estimated by ~100% with the larger-than-optimal M value of 0.5, while they are under-estimated by ~40-75% (across climate scenarios) with the smaller-than-optimal M value of 0.15. When the two higher-than-optimal M values (0.25 and 0.5) are used for the large tidal inlet system, shoreline retreat is over-estimated by ~ 65-240% (across climate scenarios) for both future periods. In terms of absolute values, these under/over-estimations increase in time and with the severity of emission scenario.