CoSMoS (Coastal Storm Modeling System) Southern California v3.0 projections of shoreline change due to 21st century sea level rise
Summary: This dataset contains projections of shoreline positions and uncertainty bands for future scenarios of sea-level rise. Projections were made using CoSMoS-COAST, a numerical model forced with global-to-local nested wave models and assimilated with LIDARlidar-derived shoreline vectors.
Details: Projections of shoreline position in Southern California are made for scenarios of 0.0, 0.5, 1.0, 1.5, 2.0 and 5.0 meters of sea-level rise by the year 2100. Projections are made at CoSMoS Monitoring and Observation Points, which represent shore-normal transects spaced 100 m alongshore. The newly developed CoSMoS-COAST model solves a coupled set of partial differential equations that resembles conservation of sediment for the series of transects. The model is synthesized from several shoreline models in the scientific literature: One-line model formulations (Pelnard-Considere, 1956; Larson and others, 1997; Vitousek and Barnard, 2015) account for longshore transport, equilibrium shoreline-model formulations (Yates and others, 2009) account for wave-driven cross-shore transport, and equilibrium beach-profile formulations (Bruun, 1954; Davidson-Arnot, 2005; Anderson and others, 2015) account for long-term beach-profile adjustments due to sea-level rise. The model uses an extended Kalman filter data-assimilation method to improve the fit of the model to lidar-derived observed shoreline positions. As with previous studies (for example, USGS National Assessment of Shoreline Change), the available shoreline data are spatially and temporally sparse. The data-assimilation method automatically adjusts model parameters and estimates the effects of unresolved processes such as natural and anthropogenic sediment supply. The data-assimilation method used in CoSMoS-COAST has been improved over the original method of Long and Plant (2012). The new method ensures that the coefficients of the equilibrium shoreline-change model retain their preferred sign. Without this improvement, the data-assimilation method was subject to instability. Data assimilation is performed only on days of the simulations where shoreline data are observed. For the shoreline projection period (2015–2100), no such data are available and thus no data-assimilation can be performed. Some of the model components are ignored for certain transects and geographic locations. For example, on small pocket beaches longshore transport is assumed negligible and, therefore, is not computed via the model. Generally, projections were not made at transects where the shoreline is armored and sandy beaches are not present. The formulations that comprise the shoreline model are only valid for sandy beaches. Furthermore, they become invalid as the beach becomes fully eroded and possibly undermines coastal infrastructure. Hence, we have specified a maximally eroded shoreline state that represents the interface of sandy beaches and coastal infrastructure (for example, roads, homes, buildings, sea-walls). If the beach erodes to this line, then it is not permitted to erode further. However, we note that the model can be run without specifying this unerodable line. The shoreline model uses a series of global-to-local nested wave models (such as WaveWatch III and SWAN) forced with Global Climate Model (GCM)-derived wind fields. Historical and projected time series of daily maximum wave height and corresponding wave period and direction from 1990 to 2100 force the shoreline model. The modeled wave predictions are a key input to the CoSMoS-COAST shoreline model because the calculation of both the longshore sediment-transport rate (obtained via the “CERC” equation developed by the Army Corp of Engineers; Shore Protection Manual, 1984) and equilibrium shoreline change (Yates and others, 2009) critically depends on the wave conditions. Notably, variations in nearshore wave angle can significantly affect the calculation of longshore transport. Thus, high-resolution modeling efforts to predict nearshore wave conditions are integral components of the shoreline modeling. Sea level vs. time curves are modeled as a quadratic function. Coefficients of the quadratic curves are obtained via three equations: (1) present sea level is assumed to be at zero elevation, (2) the present rate of sea-level rise is assumed to be 2 mm/yr, which is consistent with values observed at local tide gages, (3) future sea-level elevation at 2100 is either 0.5, 1.0, 1.5, 2.0 or 5.0 m based on the scenarios considered. We note that sea level only affects the equilibrium-profile changes derived via the Anderson and others (2015) model. The model uses a forward Euler time-stepping method with a daily time step. The longshore sediment-transport term has the option of using a second-order, implicit time-stepping method (Vitousek and Barnard 2015). However, for these modeling efforts, the forward Euler time-stepping method is sufficient and does not violate numerical stability determined by the Courant–Friedrichs–Lewy CFL condition when using a daily time step on 100 m-spaced transects. The model is composed of numerous scripts and functions implemented in Matlab. The main modeling routines have approximately 1,000-plus lines of code. However, many other functions exist that are necessary to initialize and operate the model. Overall the entire shoreline-modeling system is estimated to have approximately 10,000 lines of code. The modeling system is computationally efficient in comparison to traditional coupled hydrodynamic-wave-morphology models like Delft3D. Century-scale simulations for the entire 400 km coast of Southern California take approximately 20–30 minutes of wall-clock time. This limited computational cost allows the possibility of applying ensemble prediction. Significant uncertainty is associated with the process noise of the model and unresolved coastal processes. This makes estimation of uncertainty difficult. The uncertainty bands predicted here represent 95 percent confidence bands associated with the modeled shoreline fluctuations. Unresolved processes are not accounted for in the uncertainty bands and could lead to significantly more uncertainty than reported in these predictions. These results should be considered preliminary. Although some QA/QC has been completed, the results will improve through time as 1) more shoreline data become available to the data-assimilation method, 2) the models are improved, and 3) ensemble wave-forcing is applied to the model.
Refereces Cited: Anderson, T. R., Fletcher, C. H., Barbee, M. M., Frazer, L. N., and Romine, B. M., 2015. Doubling of coastal erosion under rising sea level by mid-century in Hawaii. Natural Hazards, 1-29.
Bruun, P., 1954. Coast erosion and the development of beach profiles. Technical Memorandum, vol. 44. 82 pp. Beach Erosion Board, Corps of Engineers.
Davidson-Arnott, R. G., 2005. Conceptual model of the effects of sea level rise on sandy coasts. Journal of Coastal Research, 1166-1172.
Hapke, C. J., Reid, D., Richmond, B. M., Ruggiero, P., and List, J., 2006. National assessment of shoreline change Part 3: Historical shoreline change and associated coastal land loss along sandy shorelines of the California Coast. US Geological Survey Open File Report, 1219, 27.
Larson, M., Hanson, H., and Kraus, N. C., 1997. Analytical solutions of one-line model for shoreline change near coastal structures. Journal of Waterway, Port, Coastal, and Ocean Engineering, 123(4), 180-191.
Long, J. W., and Plant, N. G., 2012. Extended Kalman Filter framework for forecasting shoreline evolution. Geophysical Research Letters, 39(13).
Pelnard-Considere, R., 1956. Essai de theorie de l'evolution des formes de rivage en plages de sable et de galets. Société hydrotechnique de France.
Shore Protection Manual, 1984. U.S. Army Corps of Engineers, Coastal Engineering Research Center, U.S. Government Printing Office, Washington, D.C.
Vitousek, S., and Barnard, P.L., 2015. A nonlinear, implicit one-line model to predict long-term shoreline change. Proceedings of the Coastal Sediments Conference 2015.
Yates, M. L., Guza, R. T., and O'Reilly, W. C., 2009. Equilibrium shoreline response: Observations and modeling. Journal of Geophysical Research: Oceans (1978–2012), 114(C9).
This work is one portion of on-going modeling efforts for California and the western United States. For more information on CoSMoS implementation, see https://walrus.wr.usgs.gov/coastal_processes/cosmos/
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