CoSMoS (Coastal Storm Modeling System) Southern California v3.0 projections of coastal cliff retreat due to 21st century sea-level rise

Summary: This dataset contains projections of coastal cliff-retreat rates and positions for future scenarios of sea-level rise (SLR). Projections were made using numerical and statistical models based on field observations such as historical cliff retreat rate, submarine slope, coastal cliff height, and mean annual wave power. Details: Cliff-retreat rate and position projections are for scenarios of 0, 0.5, 1, 1.5 and 2 meters of sea-level rise (SLR) by the year 2100. Projections were made at CoSMoS cross-shore transects(CST) spaced 100 m alongshore. Generally, projections were not made at transects where the sea cliff was armored or otherwise obstructed (for example, houses on the beach in front of the cliff, road between the beach and cliff), though some local exceptions apply where the obstruction was low enough to be easily overwashed. Spatial projections, such as those in the Google Earth KMZs, were made using a baseline sea-cliff edge from 2010. Two process-based, numerical cliff-profile evolution models were used to make projections: a soft-rock model by Walkden and Hall (2005, 2011) and a hard-rock model by Trenhaile (2000, 2009, 2011). Both models relate breaking-wave height and period to rock erosion, and distribute erosion vertically over a tidal cycle. Model behavior includes a variable beach slope that varies with the prevailing wave climate, wave run-up (Stockdon and other, 2006), and wave set-up that raises the water level during big-wave events and allows waves to impact the sea cliff with greater efficacy and frequency. The models were run on idealized cliff profiles extending from about 10 m water depth to 1 kilometer inland from the cliff edge. Profiles were extracted by overlaying the cross-shore transects on a high-resolution digital elevation model (DEM) covering the Southern California study area. Using aerial photography, the presence of a beach was recorded (yes or no) for all transects, and the cliff toe elevation (or beach/cliff junction) was digitized from the DEM profiles. Using historic cliff edge retreat rates by Hapke and Reid (2007), unknown coefficients within the cliff-profile models were calibrated using a Monte Carlo simulation (in other words, coefficients were tuned until the modeled mean retreat rate equaled the observed mean retreat rate for a given transect). This was successful for nearly 1,000 DEM profiles (about 45percent of all cliff transects). For those nearly 1,000 profiles, the profile models were run for two time periods: first, a period of 100–200 years using a historic rate of sea-level rise (2 mm/yr), and then for another 100 years using an accelerated mean rate of sea-level rise (5, 10, 15, or 20 mm/yr). The projected cliff-retreat rates are thus mean annual rates that represent the total retreat that occurred during this second time period. Each of the resulting nearly 5,000 model runs had one dependent (predicted mean annual cliff retreat for a given sea-level rise scenario) and multiple semi-independent variables that determined the magnitude of the dependent variable (such as historic retreat rate, shore platform slope, cliff height, cliff-toe/beach height, cliff-face slope, mean annual wave power, beach slope). This information was used to train a statistical model called an Artificial Neural Network (ANN). The ANN iteratively maps the independent variables to the dependent variable using linear algebra and a weighting system that gives importance to the variables that most strongly influence future sea-cliff retreat. In the end, the trained ANN is a standalone model that has learned, and can reproduce, the process-based cliff-profile model behavior. Independent tests between cliff profile model output and ANN output showed very good agreement (R-squared = 0.89 - 0.96; root-mean-square-error less than 0.1 m/yr). The trained ANN was then applied to each cross-shore transect, where observed independent variables such as sea cliff height, historic cliff retreat, mean wave power, shore platform slope, sea-level rise scenario, and cliff toe height were passed through the ANN to yield a prediction of future long-term cliff retreat rate. Two separate ANNs were trained: one to make predictions of the difference between future and historic cliff retreat rates (in other words, prediction = future cliff-retreat rate*historic cliff-retreat rate) and another to predict the mean trend, or acceleration, of cliff retreat as a function of sea-level rise (in other words, future cliff retreat = m*SLR + historic retreat rate, where the ANN predicts m). Training two separate ANNs allowed for two different predictions for each transect from the same training data. Of the 2,117 cliff transects, there were 8 for which a prediction could not be made, likely because values of independent variables fell outside of the range used to train the ANNs. A prediction was made for these 8 transects by interpolating from multiple neighboring transects for which results were available. Uncertainty was tallied using a RMSE approach. The RMSE approach represents cumulative uncertainty from multiple sources and assumes that different sources of error will, at times, cancel each other out. It is therefore not a 'worst-case uncertainty' (in other words, a straight sum of errors) but instead an average uncertainty. Sources of cumulative uncertainty included in the RMSE calculation are the base error of the historic retreat rates that the predictions are relative to (0.2 m/yr; Hapke and Reid, 2007), the difference between ANN and cliff-profile model predictions (about 0.1 m/yr), and the spread between the predictions using the two different ANN models (about 0.1 m/yr). Total RMSE increased with SLR rate and varied between 0.20 and 0.32 m/yr. Final cliff-retreat rates for a given SLR scenario are an average of the two different ANN predictions. The predictions were nominally smoothed using a Butterworth Filter to increase alongshore continuity and emphasize spatial trends in cliff retreat. References Cited: Hapke, C.J., and Reid, D., 2007. National Assessment of Shoreline Change, Part 4: Historical Coastal Cliff Retreat along the California Coast: U.S. Geological Survey Open-file Report 2007-1133. http://pubs.usgs.gov/of/2007/1133/ Stockdon, H.F., Holman, R. A., Howd, P. A., Sallenger Jr., A. J., 2006. Empirical parameterization of setup, swash, and runup, Coastal Engineering, Volume 53, Issue 7, Pages 573-588, ISSN 0378-3839, http://dx.doi.org/10.1016/j.coastaleng.2005.12.005. Trenhaile, A. S., 2000. Modeling the development of wave-cut shore platforms, Marine Geology, Volume 166, Issues 1–4, Pages 163-178, ISSN 0025-3227, http://dx.doi.org/10.1016/S0025-3227(00)00013-X. Trenhaile, A. S., 2009. Modeling the erosion of cohesive clay coasts, Coastal Engineering, Volume 56, Issue 1, Pages 59-72, ISSN 0378-3839, http://dx.doi.org/10.1016/j.coastaleng.2008.07.001. Trenhaile, A. S., 2011. Predicting the response of hard and soft rock coasts to changes in sea level and wave height, Climatic Change, Volume 109, Issues 3-4, Pages 599-615, ISSN 0165-0009, http://dx.doi.org/10.1007/s10584-011-0035-7. Walkden, M. J. A., and Hall, J.W., 2005. A predictive Mesoscale model of the erosion and profile development of soft rock shores, Coastal Engineering, Volume 52, Issue 6, Pages 535-563, ISSN 0378-3839, http://dx.doi.org/10.1016/j.coastaleng.2005.02.005.Summary: 本数据集包含针对海平面上升（sea-level rise, SLR）未来情景的海岸崖退速率与位置预测数据。预测基于现场观测数据（包括历史崖退速率、海底坡度、海岸崖体高度及年平均波浪功率），通过数值模型与统计模型完成。 Details: 崖退速率与位置预测对应到2100年时海平面上升0、0.5、1、1.5及2米的情景。预测基于沿岸间距100米的CoSMoS海岸横断剖面（CoSMoS cross-shore transects, CST）开展。通常情况下，对于已被防护或存在遮挡的崖体（例如崖前海滩上的建筑、海滩与崖体间的道路），不开展预测；但当遮挡物低矮且可被海浪轻易漫过的局部区域除外。空间预测（如Google Earth KMZ格式的数据）以2010年的海岸崖体基线边界为基准生成。 两款基于过程的海岸崖体剖面演化数值模型被用于开展预测：分别为Walkden与Hall（2005、2011）提出的软岩模型，以及Trenhaile（2000、2009、2011）提出的硬岩模型。两款模型均将破碎波高与波周期与岩石侵蚀速率相关联，并在潮汐周期内按垂直维度分配侵蚀量。模型涵盖随主导波浪气候动态变化的海滩坡度、波浪爬升（wave run-up，Stockdon等，2006），以及在大浪事件中抬升水位、使波浪更高效且更频繁地冲击海岸崖体的波浪增水（wave set-up）模块。 模型基于理想化的崖体剖面运行，剖面范围从水深约10米处延伸至崖体边界内陆1公里的区域。通过将海岸横断剖面叠加至覆盖南加州研究区的高分辨率数字高程模型（digital elevation model, DEM），提取得到所需剖面。利用航空摄影资料，为所有剖面记录海滩存在与否的信息，并从DEM剖面中数字化提取崖脚高程（或海滩-崖体交界点）。基于Hapke与Reid（2007）的历史崖体边界退蚀速率数据，采用蒙特卡洛模拟（Monte Carlo simulation）对崖体剖面模型中的未知系数进行校准（即不断调整系数，直至模型预测的平均退蚀速率与给定剖面的观测平均退蚀速率一致）。该校准过程在近1000个DEM剖面上取得成功（约占所有崖体剖面的45%）。针对这近1000个剖面，剖面模型分两个时段运行：第一时段为100~200年，采用历史海平面上升速率（2 mm/年）；第二时段为100年，采用加速后的平均海平面上升速率（5、10、15或20 mm/年）。因此，预测得到的崖退速率为第二时段内的年平均退蚀速率，代表该时段内的总退蚀量。 最终得到的近5000次模型运行结果中，每组数据包含1个因变量（给定海平面上升情景下预测的年平均崖退速率）与多个半自变量（这些变量决定因变量的大小，例如历史退蚀速率、岸台坡度、崖体高度、崖脚/海滩高程、崖面坡度、年平均波浪功率及海滩坡度）。利用这些数据训练一款名为人工神经网络（Artificial Neural Network, ANN）的统计模型。ANN通过线性代数与权重系统迭代实现自变量到因变量的映射，其中权重系统会对显著影响未来海岸崖体退蚀的变量赋予更高优先级。最终，经过训练的ANN成为一款独立模型，可学习并复现基于过程的崖体剖面模型的行为逻辑。 崖体剖面模型输出结果与ANN输出结果的独立测试显示二者一致性极佳（决定系数R²=0.89~0.96，均方根误差RMSE<0.1 m/年）。随后，将训练完成的ANN应用至每一个海岸横断剖面，将观测得到的自变量（如崖体高度、历史崖退速率、平均波浪功率、岸台坡度、海平面上升情景及崖脚高程）输入ANN，得到未来长期崖退速率的预测结果。 本研究共训练了两个独立的ANN：一个用于预测未来与历史崖退速率的差值（即预测值=未来崖退速率×历史崖退速率），另一个用于预测崖退速率随海平面上升变化的平均趋势或加速度（即未来崖退速率=m×SLR+历史崖退速率，其中ANN用于预测参数m）。通过训练两个独立的ANN，可基于同一套训练数据为每个剖面生成两种不同的预测结果。 在2117个崖体剖面中，有8个剖面无法生成预测结果，这可能是因为其自变量数值超出了ANN训练时使用的取值范围。针对这8个剖面，通过对已有预测结果的邻近多个剖面进行插值，生成其预测值。 不确定性采用均方根误差（root-mean-square error, RMSE）方法进行估算。该RMSE方法代表多源累积不确定性，并假设不同来源的误差有时会相互抵消，因此并非“最坏情形不确定性”（即误差的直接求和），而是平均不确定性。RMSE计算中纳入的累积不确定性来源包括：预测所参照的历史退蚀速率的基础误差（0.2 m/年；Hapke与Reid，2007）、ANN与崖体剖面模型预测结果的差值（约0.1 m/年），以及两个独立ANN模型预测结果的离散程度（约0.1 m/年）。总RMSE随SLR速率升高而增大，取值范围为0.20~0.32 m/年。 给定SLR情景下的最终崖退速率为两个独立ANN预测结果的平均值。为提升沿岸连续性并突出崖退的空间趋势，对预测结果采用巴特沃斯滤波器（Butterworth Filter）进行名义平滑处理。 参考文献： Hapke, C.J.，Reid, D.，2007. 《海岸线变化国家评估 第4部分：加利福尼亚海岸历史海岸崖体退蚀》：美国地质调查局公开报告2007-1133。http://pubs.usgs.gov/of/2007/1133/ Stockdon, H.F.，Holman, R.A.，Howd, P.A.，Sallenger Jr., A.J.，2006. 增水、激浪与波浪爬升的经验参数化，《海岸工程》，第53卷，第7期，第573-588页，ISSN 0378-3839，http://dx.doi.org/10.1016/j.coastaleng.2005.12.005. Trenhaile, A.S.，2000. 波蚀岸台发育模拟，《海洋地质》，第166卷，第1-4期，第163-178页，ISSN 0025-3227，http://dx.doi.org/10.1016/S0025-3227(00)00013-X. Trenhaile, A.S.，2009. 黏性黏土海岸侵蚀模拟，《海岸工程》，第56卷，第1期，第59-72页，ISSN 0378-3839，http://dx.doi.org/10.1016/j.coastaleng.2008.07.001. Trenhaile, A.S.，2011. 预测软硬岩海岸对海平面与波高变化的响应，《气候变化》，第109卷，第3-4期，第599-615页，ISSN 0165-0009，http://dx.doi.org/10.1007/s10584-011-0035-7. Walkden, M.J.A.，Hall, J.W.，2005. 软岩海岸侵蚀与剖面发育的中尺度预测模型，《海岸工程》，第52卷，第6期，第535-563页，ISSN 0378-3839，http://dx.doi.org/10.1016/j.coastaleng.2005.02.005.