On the need for a new generation of coastal change models for the 21st century

The combination of climate change impacts, declining fluvial sediment supply, and heavy human utilization of the coastal zone, arguably the most populated and developed land zone in the world, will very likely lead to massive socio-economic and environmental losses in the coming decades. Effective coastal planning/management strategies that can help circumvent such losses require reliable local scale (<~10 km) projections of coastal change resulting from the integrated effect of climate change driven variations in mean sea level, storm surge, waves, and riverflows. Presently available numerical models are unable to adequately fulfill this need. A new generation of multi-scale, probabilistic coastal change models is urgently needed to comprehensively assess and optimise coastal risk at local scale, enabling risk informed, climate proof adaptation measures that strike a good balance between risk and reward.


Numerical Modelling of Climate Change Driven Coastal Change
At present, climate change impacts on coastal change are commonly estimated via: (a) one-dimensional, physically based, but simple models (e.g. Bruun Rule 26 ); (b) highly scale-aggregated models with limited process descriptions (e.g. ASMITA 27 , CASCADE 28 ); and (c) extensive time integration of micro-scale processes using process-based morphodynamic models [29][30][31] . For the convenience of the reader, all coastal change models mentioned above and below are listed by model category in Table 2.
Straightforward applications of simple techniques such as the Bruun rule, while potentially being adequate for first-pass assessments at regional to global scale, are unlikely to produce results that are sufficiently reliable to support local scale coastal management/adaptation decisions with US $ billions at stake 32,33 . Highly aggregated models such as ASMITA and CASCADE essentially drive the models toward a prescribed end-state (i.e. equilibrium condition). Due to the empirically based (usually with data from one or two data rich locations) severe aggregation inherent in these models, they do not provide much insight on processes governing morphological evolution, and their general applicability is also somewhat tenuous. Attempts to date with fully process-based models (e.g. Delft3D, Mike21, CMS) forced with concurrent water level, wave, and riverflow forcing have only been able to produce accurate results for simulation lengths less than about 5 years 5,34-36 . Therefore, it appears that currently available modelling approaches are unable to provide sufficiently reliable predictions of integrated climate change impact on coastal change, and that new models underpinned by 'out-of-the-box' thinking are urgently needed.
As climate change impacts on sandy coasts will manifest themselves at various different spatio-temporal scales (~10 m to ~100 km and days to centuries; see Table 1), ideally what is required for climate change impact assessments is a multi-scale coastal change model that concurrently simulates the various physical processes occurring at different spatio-temporal scales, while also accounting for inter-scale morphodynamics.
Process-based modelling. To simulate coastal hydrodynamics relevant for episodic (ST), medium-term, and long-term (LT) morphodynamics, a process-based multi-scale model needs to incorporate both cross-shore (vertically non-uniform) and longshore (mostly vertically uniform) hydrodynamics. Ideally, therefore, the model would need to be a process based model capable of simulating nearshore hydrodynamics in at least a quasi-3D fashion. Previous attempts at quasi-3D representation of nearshore coastal hydrodynamics have been successful (e.g 37 .), and therefore, this is not a major challenge. However, modelling morphological change that may occur under the combined forcing of waves and currents (including riverflow effects at coastal inlets), especially at time scales of more than a few years, still remains a significant challenge 34,38 . Although, there have been numerous attempts since the early 1990s to overcome this challenge, these have met with only partial success, at best 29,[38][39][40] . The most recent attempt, which used a combination of parallel computing and wave input reduction techniques, achieved a 30-year morphodynamic simulation with combined wave-tide forcing 41 , with a computing time of 5-19 days (depending on the parallel computing/input reduction combination used). While this is a huge improvement from what was possible 10 years ago, achieving a 100 year wave-tide-riverflow forced simulation within a few minutes (or hours) using traditional process-based models still seems very far away.
Perhaps a completely different approach is required to solve this problem. For example, the solution could lie in a novel concept in which morphological change is simulated using a non-gridded technique. In such a model, for instance, a traditional computational grid may still be used to compute time varying quasi-3D nearshore water level, velocity and transport fields, but these quantities would then be spatially and temporally aggregated in areas of interest where potentially mobile morphological features exist (e.g. sand bars, channels, mounds, ebb/   www.nature.com/scientificreports www.nature.com/scientificreports/ flood deltas etc.). These aggregated hydrodynamic forcing fields may subsequently be used, in combination with an appropriate morphodynamic acceleration factor, to rapidly simulate the spatio-temporal evolution of only the morphological features of interest over a few tidal cycles. If successful, such an approach would enable morphodynamic simulations that are much faster, and consequently much longer, than what the present state-of-the-art would allow.

Reduced complexity modelling. While new ideas and increasing computational power might enable
~100-year long process-based model simulations in the future, still, their inherent slowness, will probably render this type of models unwieldy for the multiple simulations (~1000) required to derive probabilistic estimates of coastal change; a mandatory requirement of emerging risk informed coastal zone management/planning frameworks 42,43 . An effective approach to circumnavigate this problem is to develop physics based, yet simple and fast numerical models known as reduced complexity models. This approach adopts simplified descriptions of fundamental system physics and delivers estimates of system response to forcing. It is a well-grounded and fast approach that lends itself to multiple simulations (thousands of simulations in minutes), enabling probabilistic estimates of system response.
While a few such reduced complexity numerical models have been developed since the turn of the century [44][45][46][47] , no concerted efforts have yet been made to develop a reduced complexity model that is capable of providing rapid, probabilistic estimates of coastal change resulting from the integrated effect of climate change driven variations in coastal forcing. Such an attempt, which would undoubtedly be a challenging undertaking, could for example follow the basic approach outlined below.
Relevant concepts adopted in existing non-process based LT coastal evolution models (e.g [48][49][50][51][52][53][54][55] .) could be used to develop a reduced complexity model to obtain rapid, probabilistic estimates of future LT nearshore morphological change. This model can then potentially be combined with an existing ST reduced complexity models, such as the Probabilistic Coastal Recession (PCR) model 45 , which provides probabilistic estimates of contemporary and/ or future ST storm erosion volumes. Concepts adopted in existing non-process based models of ST coastal change (e.g [56][57][58][59] .) may also be strategically used in the model development depending on local geomorphic conditions and/or the target coastline indicator (e.g. MSL contour, toe/top of dune, vegetation line).
The main result that can be expected from the application of such an LT/ST integrated, 2D reduced complexity coastal change model is a series of coastline positions (alongshore) with a range of exceedance probabilities (e.g. 0.9, 0.5, 0.1, 0.01) for every year of the simulation. These probabilistic results could then be combined with, for e.g. spatial maps of property value to derive economic risk maps.
It is important to note that the confidence with which any of the above discussed novel modelling approaches can be applied to address real-world situations depends very much on rigorous model validation against field measurements. The non-availability of (or lack of free access to) long term morphological and hydrodynamic data has been for decades a frustrating bottleneck in terms of achieving robust validation of, especially, longer term coastal change models. However, the recent emergence of open source satellite image based global data sets of coastal morphology and topography 24,60-64 and the general worldwide trend towards open source in-situ data (e,g. EMODNET, CEFASWavenet, SISMER, SHOM, Open Earth, DUCK FRF, Narrabeen-Collaroy) represents a step-change in the availability of/access to long term data, greatly improving opportunities for the validation of long term coastal change models.
While the economic damage (consequence) that can be caused by climate change driven coastal change (hazard) can be very high, foregoing land-use opportunities in coastal regions is also costly (opportunity cost), with both sides of the equation depending not only on climate change impacts but also on economic considerations such as future changes in coastal property values, and return on investments in the coastal zone etc 65 . Developing effective policies and strategies for future coastal land-use planning purposes is therefore a delicate balancing act. Quantitative coastal risk assessments are also invaluable to the insurance and re-insurance industries for determining optimal insurance premia, with follow-on effect on coastal property values, and subsequently on the value-at-risk [65][66][67][68][69][70] . Projections of future coastal change provided by a new generation of multi-scale, probabilistic coastal change models such as those discussed above will readily support comprehensive coastal risk assessment and optimisation, enabling risk informed, climate proof adaptation measures that optimises the balance between risk and reward.