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[1] A three-part algorithm is described and tested to provide robust bathymetry maps based solely on long time series observations of surface wave motions. The first phase consists of frequency-dependent characterization of the wave field in which dominant frequencies are estimated by Fourier transform while corresponding wave numbers are derived from spatial gradients in cross-spectral phase over analysis tiles that can be small, allowing high-spatial resolution. Coherent spatial structures at each frequency are extracted by frequencydependent empirical orthogonal function (EOF). In phase two, depths are found that best fit weighted sets of frequency-wave number pairs. These are subsequently smoothed in time in phase 3 using a Kalman filter that fills gaps in coverage and objectively averages new estimates of variable quality with prior estimates. Objective confidence intervals are returned. Tests at Duck, NC, using 16 surveys collected over 2 years showed a bias and root-mean-square (RMS) error of 0.19 and 0.51 m, respectively but were largest near the offshore limits of analysis (roughly 500 m from the camera) and near the steep shoreline where analysis tiles mix information from waves, swash and static dry sand. Performance was excellent for small waves but degraded somewhat with increasing wave height. Sand bars and their small-scale alongshore variability were well resolved. A single ground truth survey from a dissipative, low-sloping beach (Agate Beach, OR) showed similar errors over a region that extended several kilometers from the camera and reached depths of 14 m. Vector wave number estimates can also be incorporated into data assimilation models of nearshore dynamics.Citation: Holman, R., N. Plant, and T. Holland (2013), cBathy: A robust algorithm for estimating nearshore bathymetry, J. Geophys.

[1] Sea level rise during the 21st century will have a wide range of effects on coastal environments, human development, and infrastructure in coastal areas. The broad range of complex factors influencing coastal systems contributes to large uncertainties in predicting long-term sea level rise impacts. Here we explore and demonstrate the capabilities of a Bayesian network (BN) to predict long-term shoreline change associated with sea level rise and make quantitative assessments of prediction uncertainty. A BN is used to define relationships between driving forces, geologic constraints, and coastal response for the U.S. Atlantic coast that include observations of local rates of relative sea level rise, wave height, tide range, geomorphic classification, coastal slope, and shoreline change rate. The BN is used to make probabilistic predictions of shoreline retreat in response to different future sea level rise rates. Results demonstrate that the probability of shoreline retreat increases with higher rates of sea level rise. Where more specific information is included, the probability of shoreline change increases in a number of cases, indicating more confident predictions. A hindcast evaluation of the BN indicates that the network correctly predicts 71% of the cases. Evaluation of the results using Brier skill and log likelihood ratio scores indicates that the network provides shoreline change predictions that are better than the prior probability. Shoreline change outcomes indicating stability (−1 < rate < 1 m/yr) or erosion (rate < −1 m/yr) tend to occur for two sets of input scenarios. Stable shoreline change rates occur mainly for low rates of relative sea level rise and occur in low-vulnerability geomorphic settings. Rates indicating erosion result for cases where the rate of relative sea level rise is high and moderate-to-high vulnerability geomorphic settings occur. In contrast, accretion (rate > 1 m/yr) was not well predicted. We find that BNs can assimilate important factors contributing to coastal change in response to sea level rise and can make quantitative, probabilistic predictions that can be applied to coastal management decisions.Citation: Gutierrez, B. T., N. G. Plant, and E. R. Thieler (2011), A Bayesian network to predict coastal vulnerability to sea level rise,

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[1] Prediction of barrier-island response to hurricane attack is important for assessing the vulnerability of communities, infrastructure, habitat, and recreational assets to the impacts of storm surge, waves, and erosion. We have demonstrated that a conceptual model intended to make qualitative predictions of the type of beach response to storms (e.g., beach erosion, dune erosion, dune overwash, inundation) can be reformulated in a Bayesian network to make quantitative predictions of the morphologic response. In an application of this approach at Santa Rosa Island, FL, predicted dune-crest elevation changes in response to Hurricane Ivan explained about 20% to 30% of the observed variance. An extended Bayesian network based on the original conceptual model, which included dune elevations, storm surge, and swash, but with the addition of beach and dune widths as input variables, showed improved skill compared to the original model, explaining 70% of dune elevation change variance and about 60% of dune and shoreline position change variance. This probabilistic approach accurately represented prediction uncertainty (measured with the log likelihood ratio), and it outperformed the baseline prediction (i.e., the prior distribution based on the observations). Finally, sensitivity studies demonstrated that degrading the resolution of the Bayesian network or removing data from the calibration process reduced the skill of the predictions by 30% to 40%. The reduction in skill did not change conclusions regarding the relative importance of the input variables, and the extended model's skill always outperformed the original model.