Beach-dune modelling in support of Building with Nature for an integrated spatial design of urbanized sandy shores

The long-term physical existence of sandy shores critically depends on a balanced sediment budget. From the principles of Building with Nature it follows that a sustainable protection of sandy shores should employ some form of shore nourishment. In the spatial design process of urbanized sandy shores, where multiple functions must be integrated, the knowledge and the prediction of sediment dynamics and beach-dune morphology thus play an essential role. This expertise typically resides with coastal scientists who have condensed their knowledge in various types of morphological models that serve different purposes and rely on different assumptions, thus have their specific strengths and limitations. This paper identifies morphological information needs for the integrated spatial design of urbanized sandy shores using BwN principles, outlines capabilities of different types of morphological models to support this and identifies current gaps between the two. A clear mismatch arises from the absence of buildings and accompanying human activities in current numerical models simulating morphological developments in beach-dune environments.


Introduction
Coastal dunes on sandy shores provide multiple ecosystem services to urbanized coastal areas: they protect against flooding by offering a buffer against storms and a higher ground to live on (a regulating ecosystem service), provide drinking water by collecting and filtering water in the coastal freshwater lens (production service) and provide an attractive environment for leisure and beach tourism (cultural service). A good spatial design for an urbanized beach-dune area takes the full spectrum of these functions into account. However, these desired ecosystem services can only exist by the grace of the supporting ecosystem services. Therefore, a truly integrated spatial design not only combines all desired functions into a favourable spatial arrangement, it must also explicitly take into account and use the supporting ecosystem services. Numerous coastal morphological models have been developed by coastal scientists and coastal engineers for various purposes. However, it is often unclear for spatial designers what can be expected from these models with respect to level of detail of the simulation, accuracy, temporal and spatial scales of problems for which models are suitable. Furthermore, models describe certain aspects more accurately than others because modelers develop their models with a certain purpose in mind.
To our knowledge, modelers so far have never specifically considered the information needs of spatial designers when developing beach-dune models.
Therefore, this paper identifies morphological information requirements in the spatial design process of urbanized sandy shores using BwN principles.
It also outlines the capabilities and limitations of different types of morphological models to simulate impacts of constructions on beach-dune development. To bridge the 'language gap' between spatial designers and mor-phological modelers, we have attempted to avoid jargon, or explain it, and illustrate different approaches through examples from the ShoreScape 1 project. Hereby, we aim to match the morphological information requirements of spatial designers and morphological model capabilities to identify knowledge gaps where current models do not match information needs for integrated spatial design of urbanized shores.

Morphological information needs for integrated spatial design of urbanized shores
An integrated spatial design of urbanized sandy shores requires understanding and prediction of sediment dynamics and morphological change in interaction with a (possibly) dynamic built environment (Van Bergen et al, 2020). The specific morphological information needs vary during the different phases of the design process, as outlined below.
In the 'inquiry and analysis' phase of the design process, design requirements and context are explored to grasp the parameters of the urban and eco-morphological spatial systems involved. In the case of a BwN approach, this requires information on the dynamic context. That is not just spatial characteristics of the system at a given time, as can be represented in a Geographical Information System (GIS), but of the full system's behaviour.
For instance, considering a specific nourishment scheme, which beach width variation over time, or which combinations of dune height and width can be expected to develop in areas of a planned waterfront design? What are characteristic bed level profiles across the beach-dune zone during this development? Which morphodynamic mechanisms exist to direct the location and amount of erosion and deposition using buildings placed at the beach (such as already present on Fig. 1 for recreational use)? Additionally, in this phase of the design process rules of thumb are desired that summarize interactions of buildings with wind-driven sediment flows. For instance, a simple formula describing the relation between inter-building spacing and the amount of blockage of wind-driven sediment flow. Similarly, what would be the sediment blockage factor of raised buildings as a function of their vertical distance above the beach?
The above type of information is important for understanding landscape and urban processes and to identify parameters for the exploration of possible futures. Integrated spatial designs for urbanized shores with wide beaches, rapidly eroding shorelines and large spatial variations therein, such as at 1 ShoreScape is a research project that aims to develop knowledge, tools and design principles for the sustainable co-evolution of the natural and built environment along sandy shores.
the Sand Motor (figure 1), will most likely differ from those with more gradual advancing shoreline positions and slowly seaward advancing dune fronts.
In the subsequent phase of 'design feasibility', different spatial arrangements are tested and combined into one design. Interactions of urban design and morphological development are studied by so called 'rapid prototyping'.
For example, when planning for beach housing in a dune formation zone, various layouts are explored by systematically varying the types and configurations of buildings and the timing of their placement. A combination of several design aspects will lead to variants and plausible solutions, ready to fit the dynamic context and urban program.
Finally, in the phase of 'design optimization', interactions between different design aspects are studied in detail and optimized. Now decisions have to be made that have financial consequences and thus require a higher level of accuracy and precision of morphological information. For example, when considering sea level rise, a proposed nourishment scheme and arrangement of beach houses should guarantee natural growth of the dunes, such that flood safety levels and natural values provided by the dunes will be maintained. This requires detailed information about, amongst others, the amount of sand in the dunes over time, including a prediction of its topographic evolution, to enable the application of models that test flood safety levels through time.
This optimization process will lead to a favourable solution, underpinned by quantitative tests based on the output of morphological modelling.

Model types for evaluating morphodynamics of the beachdune system on urbanized sandy shores
In the context of simulating topographic changes (related to sand transport by wind and water) in a beach-dune environment, the term 'model' or 'morphodynamic model' refers to a simplified version of reality that, in its very essence, incorporates topography (bed elevation) and the sediment transport processes that change it. Models differ in how they incorporate sediment transport processes. Broadly, we can identify three types of models, differing in their simplification approach: conceptual models, physical models ((scaled) lab experiments), and numerical simulation models. For a beach dune environment, numerical simulation models can be split into process-scale models and rule-based behavioural models. In the following, we will explain these different modelling approaches, what type of information they can provide as well as their present, or inherent, limitations.

Conceptual models
In the context of morphodynamic modelling, a conceptual model refers to a schematization of the beach dune systems in a qualitative manner. It describes, in words, how beach-dune topography changes under the influence of one or more factors (such as wind, waves, or sediment surplus), often with the help of diagrams and sketches. Relations between factors and bed level changes are often described in terms of positive or negative feedback. Conceptual models can be based on a combination of phenomenological knowledge, derived from field observations, and theory (first principle physics, analogies). For example, Psuty (2004)   Rules of thumb also are conceptual models and have a quantitative element to them. For example, in a given region, initiation of sand-drift dikes 2 2 A sand-drift dike (stuifdijk) is an artificially created linear dune ridge, initiated by erecting long lines of reed bundles and willow on coastal sandflats to capture windblown sand, often accompanied by planting marram grass at a later stage. Traditional Dutch coastal maintenance practice (see Boeschoten, 1954).
will be unsuccessful when the sandflat is less than 1.3 m above mean sea level (Boeschoten, 1954). Rules of thumb are often based on empirical relations that may be derived from field monitoring or lab experiments (physical models), although they may as well form a way of schematizing insights derived from numerical simulation models. Empirically derived, as well as process-scale modelling-derived rules of thumb can form input for rule-based morphodynamic simulation models.
A conceptual model generally forms the basis for developing a numerical simulation model by providing the elements that may be quantified in numerical simulation models. Conceptual morphological models themselves do not provide quantitative information on rates of change, sediment volumes, or specific complications that could arise from interventions. Morphological experts may use conceptual morphological models to provide: -a fast overview of possible, first order impacts on morphology of interventions/designs or objects -rules of thumb for indicating types of natural topographic evolution to be expected in different zones of the beach dune system.

Physical models -scaled lab experiments
A physical model is a tangible representation of a natural system, simplified, but still faithfully reflecting important relationships between relevant processes. Observations and measurements in a physical model can be used to infer information about the behaviour of the natural system itself. As physical models are often built on a reduced spatial and temporal scale, they are also called scale models.
In coastal studies, physical models are mostly used to examine hydrodynamics and morphodynamics and are generally developed in a laboratory setting. For instance, Boers et al. (2009) used a wave basin to study storm erosion of a scaled dike-and-dune system; wind flow around buildings or over dunes can be studied in wind tunnels (e.g. Fackrell, 1984;Wiggs et al., 1996).
Occasionally, physical experiments are located in a field setting.  Even though the small-scale flow structures will be parameterized, the wide range of spatial scales limits the simulated time to several minutes.
Computational times typically take hours or days.
-Obtain system knowledge through CFD, which can result in rules of thumb.
Even though computers become increasingly powerful, solving turbulent wind flow at the required level of detail and fast enough for a long-term morphological evolution of quantitative accuracy, is not yet realistic. Average flow simulations can be used but result in a lack of physics on smaller scales.
Note that most morphological models used in coastal engineering applications are hydro-morphodynamic models that use a more schematized way of CFD modelling, with cell sizes of tens to hundreds of meters and often only depth-averaged fluid flow instead of the full 3D flow field. These models can be applied to simulate the development of the submerged nearshore seabed and can be used, for instance, to evaluate the longer-term shoreline evolution of mega-nourishments due to waves and currents.
A preliminary result of the use of CFD modelling in the ShoreScape project is shown in Fig. 4

Rule-based coastal morphodynamic models
Like CFD models, rule-based morphodynamic models describe the beach-dune topography using a large number of cells on a regular grid, usu- So far, the DUBEVEG (Dune, Beach and VEGetation) model (Keijsers et al., 2016, Galiforni-Silva et al., 2018, 2019 is the only attempt to simulate beachdune development solely using a CA approach. It includes the main processes involved in the dynamics of the beach-dune system, such as wind-driven sediment transport, vegetation growth and decay, hydrodynamic erosion and supply, and groundwater depth. Model rules are applied with a weekly time step, under the assumption of a given long-term average wind-driven sand transport. This results in short computing times, making the model suitable for long-term morphodynamic studies over tens of years. The main advantages of CA modelling are its flexibility and range of modelling possibilities with a relatively low computational effort. Rules can be simple and are usually easily adaptable. For instance, DUBEVEG only needs sediment transport rules without separate rules for fluid flow (air or water), contrary to CFD models where repeated fluid flow computations are an essential and computationally intensive component.
A limitation of the beach-dune CA model is that total aeolian sediment supply is user-specified, either derived from other models or from long-term monitoring data. This implies that the total wind-driven sediment volume increase, totalled over the simulated period, is imposed by the user and not an outcome of the interacting processes in the model. Also, because CA models focus on interactions at a certain location (e.g. changes in sand transport around a dune), rather than the movement of objects through space (e.g. the transport of sand grains), the model does not simulate sand fluxes as required for commonly used model validation methods (e.g. comparison to a measured sand flux). CA model outcomes can therefore only be validated at a higher level of aggregation, such as overall trends and spatial patterns in morphology. Hence model outcomes cannot be used as a quantitatively accurate prediction or reproduction of beach-dune topography at a given time.
Following from all advantages and limitations, CA models for beachdune dynamics are currently useful as exploratory rather than predictive tools. Their characteristics make them suitable for: -Investigating underlying principles of archetypical situations (e.g. can dune formation be explained solely from shadow zone effects and avalanching when slopes become too steep?).

Matching morphological information needs and morphological model capabilities
A BwN approach for developing integrated spatial designs for urbanized sandy shores requires morphological modelling at both small and large scales. It requires models to predict the larger scale evolution of the coastline under different nourishment strategies as well as the evolving topography of beach and dunes on smaller scales. For the latter, understanding shorter term interactions of wind-driven sediment transport, vegetation growth, dune development, human use and the built environment are essential to simulate the long-term consequences for the upper beach and dune evolution. Understanding and modelling these complex interactions, where sediment has to move from the submerged domain to the subaerial domain and interact there with the biotic system and the socio-economic system is at the frontiers of coastal modelling (Lazarus et al, 2016).
In the 'inquiry and analysis' phase of spatial design, conceptual models, physical scale models, and CFD models all contribute to meeting identi- banized shores, such as seawalls, is much more advanced (e.g. Smallegan et al., 2016;Muller et al, 2018) In the phase of 'design feasibility', it is 'rapid prototyping' that puts high demands on the computational time of long-term morphological simulations (covering several years to tens of years). It requires numerical models that can quickly evaluate morphological effects of multiple spatial design alternatives, considering the interaction of buildings and sediment flows, as well as interaction with vegetation development (all of which influence dune formation). This makes CA models currently the most suitable type of model, even though they do not yet include rules for interactions of buildings with wind-driven sand transport. Also, it has been observed that activities related to the recreational use of the beach, such as beach raking or beach traffic, may affect vegetation growth and hence dune development, as does local mechanical removal of aeolian sand deposits by property owners (Jackson and Nordstrom, 2011). Respective relations are still lacking in current beach-dune morphological models.
Regarding the phase of 'design optimization', expressed morphological information requirements seem to be rooted in the tradition of static spatial designs, where the final design can be highly detailed and precise. However, in the case of BwN-based spatial designs, the final design is not a static situation but an inherently dynamic, evolving situation and a static end situation will never exist. Regarding the assessment of flood defence functionality of future dune landscapes, adaptive approaches may be needed (cf. Vuik et al, 2018).
Moreover, the assessment of the safety level of a dune with hard objects in or on top of it, is still a difficult issue (e.g. Boers et al., 2009). Apart from the difficulties of knowing details of future beach-dune topography, even predicting the total amount of sand in a dune area is still a major challenge. No models are available yet for accurate prediction of long-term sediment supply to the dunes. Recent efforts in coupling subaqueous and subaerial domains in numerical model studies (e.g. Roelvink and Costas, 2019;Hallin, 2019) help to obtain quantitative insight in the time-varying amount of sand supply that is delivered by the waves and tides and can be picked up by wind for continued onshore transport. In short, present-day capabilities of morphological models to support design optimization are still limited.

Conclusion
Using 'Building with Nature' principles in the spatial design of urbanized sandy shores asks for a new design approach. A recognition of the interconnectedness between urban and morphological spatial systems implies the need for dynamic and adaptive, instead of static, designs. Combining the demand for multi-functionality -flood protection, nature, recreation and economy -while at the same time explicitly considering and utilizing sediment dynamics, requires truly integrated spatial design. This poses new challenges to morphological models supporting it.
Numerical models (computer models) able to accurately predict the morphological effects of interaction between wind-driven sediment dynamics and buildings are currently lacking. This is most severely felt in the phases of 'design feasibility' and 'design optimization', where alternatives like conceptual and physical models -particularly useful in the 'inquiry and analysis' phase -are less suitable. In the 'design optimization' phase, a gap exists between model capabilities and morphological information needs as it is difficult to accurately predict the long-term sediment supply to dunes with numerical models. Finally, the observed influence of human activities on urban beaches on vegetation development is currently absent in all morphological models. Hence predicted location and/or rate of new dune formation will be inaccurate for urbanized beaches.
To conclude, arriving at integrated spatial designs for the sustainable protection of urbanized sandy shores using BwN principles requires morphological models that can go beyond the hydro-morphological simulation of nourishment behaviour alone and can include interactions with how humans use the beach.