Projections of shoreline change for California due to 21st century sea-level rise

Set up model structure as discussed in Vitousek and others (2017, 2021, and 2023) for the California coast. The structure included defining cross-shore transect locations, from CSTs and CDIP, as locations for the one-dimensional numerical models simulating the shoreline position given changing sea level and wave forcing. The assimilation scheme outlined in Vitousek and others (2023; 2021, section 2.3), was set up to use an ensemble of 200 members (Nens = 200). The model was set up to assimilate SDS observations and calibrate itself for a majority portion of the historical data period (1995-2015), reserving 5 years of SDS observations (2015-2020) for validation of the model. Although the uncertainty in the SDS positions (with RMS error of 10 m) is generally larger than traditional surveys (RMS error of centimeters to meters), the larger observational uncertainty is handled within the context of the Kalman filter.
A representation of the landward boundary of the beach was hand-digitized from aerial imagery in Google Earth. This boundary was used in models at individual transects to classify the landward end of the sandy beach. This sandy beach limit separates the beach from other landscapes, such as vegetated or urban landscapes, in model simulations (representing a coarse categorization of sandy versus not-sandy beach). This limit was digitized from the most recent, cloud-free imagery available at the time of digitization (between October 2014 and March 2020 across the region). Imagery was viewed in Google Earth at a minimum 1:300 scale, and digitized at an average horizontal vertex spacing of 10-20 m. The landward edge or boundary of the sandy beach was visually identified in the imagery using several criteria, dependent on the landscape, by the presence of infrastructure or buildings; changes in vegetation; or established dune systems. If multiple criteria were present, the feature encountered first (as the landward boundary of the beach) was generally used.

Obtained SDS observations from all available satellite imagery in the study area (Vos and others, 2019a; 2019b, 2020), at model transect locations. Data for transects along sections of beach adjacent to river mouths and inlets should be understood to be highly dynamic and include more uncertainty.

Shoreline change models were run within Matlab to correct SDS observations for synoptic wave setup as predicted with empirical runup equations as described in Vitousek and others (2021; 2023). The model was run sequentially for three periods: a hindcast/calibration period (1995-2015), a validation period (2015-2020), and projection period (2020-2100). The hindcast period serves as the calibration period, assimilating available data including SDS observations, to automatically-tune and optimize parameters at every transect. The model was started on 01 Jan 1995, using a SDS for the initial condition. This shoreline can appear ‘spikey’, as it is only derived and shown at discrete transect locations. In rare circumstances, the initial shoreline comes from observations at two different instances in time on neighboring transects, which can also lead to spikiness. Any uncertainty in both modeled and observed shoreline position is accounted for and adjusted in the Kalman filter for subsequent time steps, while refining model parameters (see Vitousek and others, 2021; 2023).
Depending on location and availability of SDS data, transects were run in 3 configurations: “full model” configuration included all model parameters; “cross-shore only” configuration excluded longshore transport in locations where this was applicable (for example, when the beach was short or enclosed, or if there was too much curvature on the shoreline for the long-shore transport term to be resolved); and a “rate only” configuration shows where only historical rates of shoreline change are used (usually due to limited SDS data). Note that the model was not run in areas without beach and these are labeled as "cliff only" transects.
As the models are run in an ensemble, uncertainty was defined as 95 percent confidence intervals determined by the band that enclosed the middle 95 percent of model trajectories in the ensemble illustrating impacts from variable projected wave conditions (see Vitousek and others, 2023). This uncertainty encapsulates long-term changes as well as episodic changes and reflects decades of data (Vitousek and others, 2023). However, shoreline changes and erosion from extreme storms can lie outside this band of trajectories, and so to illustrate the potential impact of extreme storms, the maximum landward ensemble trajectory for wave heights of certain intensities (return periods of 1-year, 20-year and 100-years, representative of extreme coastal storm impacts) are also provided. For locations where “rate only” model configurations were used, episodic changes are not projected, and potential storm erosion uncertainty is not available.
The impact of large historical events may affect the model output in certain locations; in highly dynamic regions that have experienced large episodic shoreline change (such as near headlands or river mouths), SDS may have higher uncertainty as well as model projections.
Data were assimilated during the validation period (2015-2020). While several processes are implicitly included with each location, the model does not explicitly account for all coastal processes. In dynamic areas including around river mouths, capes, inlets, and at the end of spits, uncertainty is greater. An estimate of this potential uncertainty due to unresolved processes was derived from comparing shoreline predictions for this period to observations. This comparison showed an RMS error of less than 15 m most of the study area (on the order of SDS positional error), with higher values in the dynamic areas mentioned above (Vitousek and others, 2023). The confidence bands of the unresolved process uncertainty are based on 2x the root-mean-square error of the un-assimilated model versus observations during this validation period. This unresolved process uncertainty is separate from and not mathematically additive to model uncertainty. Unresolved process uncertainty is not available at locations that do not have enough data for validation (for example, “rate only” and some “cross-shore only” transects).
To run any shoreline model, as a simplified representation of shoreline evolution, certain assumptions about the behavior of the model need to be made, since the effect of these assumptions over long projection periods can lead to different outcomes (Vitousek and others, 2017; 2021; 2023). To explore the importance and impact of certain key model assumptions, the model was run for different cases representing end-members of model behavior bracketing a spectrum of possible solutions. Key aspects of model behavioral assumptions were investigated in combination: the extent or boundary of the beach (that is, where parameters derived from observed shoreline movement may or may not remain valid over long periods of time), and parameters accounting for shoreline accretion. For the first aspect, the shoreline model does not differentiate different landscapes in terms of shoreline evolution and erodibility. In natural settings, derived parameters from assimilated historical records may arguably hold (or be modified) for areas landward of the beach to include dunes and vegetated areas. But it is similarly arguable that parameters would not hold when encountering hardened infrastructure. Therefore, the model was run for two different cases to show solutions bracketing this behavioral assumption: 1) allowing the shoreline to evolve/erode without impediment/constraint as determined by its historical behavior or 2) limiting the shoreline erosion to the landward end of the modern-day beach. Similarly, modern-day, long-term, cross-shore shoreline change rates (particularly for developed, accreting beaches) may be reflective of human intervention/nourishments, and it is exceedingly difficult to project how interventions/nourishments may progress and/or persist in the future. Therefore, the model was run for two different cases to show end-member solutions of cross-shore accretion (and possibly reflective of generalized coastal management options) in the future: 1) retaining the model-derived residual long-term shoreline change rate (Vitousek and others, 2017; 2021; 2023) for future projections and 2) suppressing the residual shoreline trend by setting this parameter to 0 when it is estimated to be positive (accretionary). The latter case only suppresses the residual trend of the process; it does not affect accretion or erosion due to longshore transport: accretion (and erosion) due to alongshore sediment transport are still reflected in the modeling results. These different end-member solutions are combined for four different model cases. In model cases where a landward model boundary is imposed, model shoreline uncertainty is not shown landward of the boundary; however, potential storm erosion uncertainty is still projected landward. Also note that in these cases when a model boundary is imposed, there are rare locations where the initial shoreline was located landward of the model boundary (occurred in dynamic areas, as landward boundary was digitized from imagery dated after initialization periods); in these locations, when the historical or modeled shoreline is landward of boundary, beach width was then 0 m, long-short transport was neglected, and the resultant projected shoreline was held at imposed model boundary. When historical or modeled shoreline was oceanward of model boundary, all model parameters (as defined per transect) were used and resultant projections are displayed normally.
It is important to note that historical impacts of nourishment are captured in the SDS observations, and so impacts are implicitly included in the calibration and shoreline projections. However, as mentioned above, we provided no assumptions about the persistence or policy of this practice. Model parameters derived during the calibration period and projection periods are preserved and used without adjustment in those model cases.
Projected SLR curves through 2100 (relative to 2000; Vitousek and others, 2023) are used in model scenarios for this study’s SLR scenarios of 1.0 m SLR and higher; final shoreline projections for these scenarios are taken at 2100. For SLR scenarios of 0.25 m – 0.75 m, final shoreline positions are taken at the corresponding dates for the target SLR scenario along a SLR projection of curve of 1.0 m by 2100. See Vitousek and others (2023) for details. For the hindcast period (1995-2015), SLR is extrapolated linearly backwards from 2000 to the beginning of the model (January 1995) based on a historical rate.

Organized model projections into groups by model case, numbered thusly: In model case 1, shorelines are allowed to evolve and erode without limitation/impediment and long-term shoreline change rate parameters derived by the model are preserved with no adjustments; in model case 2, shorelines are not allowed to evolve and erode past current boundaries and change rate parameters are preserved; in model case 3, shorelines are allowed to erode without limitation while cross-shore residual long-term shoreline change rates are set to 0; and in model case 4, shorelines are not allowed to erode past current boundaries and cross-shore residual accretionary change rates are set to 0. Projections are presented in both KMZ and shapefile formats. KMZs and shapefiles include the initial shoreline, landward model boundary locations (applied in model cases 1 and 2), final shoreline projections for SLR scenarios, model uncertainty (representing 95 percent of the ensemble model spread and robust model uncertainty). Files also include unresolved process uncertainty, as an estimate of uncertainty for unresolved processes and other sources of error not explicitly included in the model, as well as uncertainty with potential storm erosion, shoreline change hazard zones, and extreme storm hazard zones. KMZs also include transect information including all model parameters calibrated at each respective site. Null projection and model parameter values are listed as NaN.
File names indicate state and model parameters; for example, ShorelineChange_projctn_CA_Case1.kmz contains shoreline projections in California for case 1 (no landward limitation to shoreline evolution, and no adjustments to model accretion parameters).
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