The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

The history and technical capabilities of Argus

Environmental effects of the Deepwater Horizon oil spill: A review.

Sandy beaches occupy more than one-third of the global coastline1 and have high socioeconomic value related to recreation, tourism and ecosystem services2. Beaches are the interface between land and ocean, providing coastal protection from marine storms and cyclones3. However the presence of sandy beaches cannot be taken for granted, as they are under constant change, driven by meteorological4,5, geological6 and anthropogenic factors1,7. A substantial proportion of the world’s sandy coastline is already eroding1,7, a situation that could be exacerbated by climate change8,9. Here, we show that ambient trends in shoreline dynamics, combined with coastal recession driven by sea level rise, could result in the near extinction of almost half of the world’s sandy beaches by the end of the century. Moderate GHG emission mitigation could prevent 40% of shoreline retreat. Projected shoreline dynamics are dominated by sea level rise for the majority of sandy beaches, but in certain regions the erosive trend is counteracted by accretive ambient shoreline changes; for example, in the Amazon, East and Southeast Asia and the north tropical Pacific. A substantial proportion of the threatened sandy shorelines are in densely populated areas, underlining the need for the design and implementation of effective adaptive measures.

/pdf/sandy-coastlines-under-threat-of-erosion-56yom2q5qa.pdf

Sandy coastlines under threat of erosion

Sea level rise (SLR), a well-documented and urgent aspect of anthropogenic global warming, threatens population and assets located in low-lying coastal regions all around the world. Common flood hazard assessment practices typically account for one driver at a time (e.g., either fluvial flooding only or ocean flooding only), whereas coastal cities vulnerable to SLR are at risk for flooding from multiple drivers (e.g., extreme coastal high tide, storm surge, and river flow). Here, we propose a bivariate flood hazard assessment approach that accounts for compound flooding from river flow and coastal water level, and we show that a univariate approach may not appropriately characterize the flood hazard if there are compounding effects. Using copulas and bivariate dependence analysis, we also quantify the increases in failure probabilities for 2030 and 2050 caused by SLR under representative concentration pathways 4.5 and 8.5. Additionally, the increase in failure probability is shown to be strongly affected by compounding effects. The proposed failure probability method offers an innovative tool for assessing compounding flood hazards in a warming climate.

https://www.pnas.org/content/pnas/114/37/9785.full.pdf

Compounding effects of sea level rise and fluvial flooding

Evaluation of wave runup predictions from numerical and parametric models

The details of a large-scale laboratory experiment to study the turbulence generated by waves breaking on a fixed barred beach are presented. The data set includes comprehensive measurements of free surface displacement and fluid velocity for one random and one regular wave case. Observations of the time-averaged turbulent kinetic energy per unit mass, , show that the turbulence generated by wave breaking was greatest at the bar crest and did not fully dissipate prior to reaching the bed. This indicates that, even in a time-averaged sense, wave breaking turbulence may be important for near-bed processes. Onshore of the bar, turbulence was generally confined to the upper part of the water column and had dissipated once the waves reformed (approximately 1.5 wavelengths onshore of the bar crest). The turbulent structure was the same in the random and regular wave cases; however, the magnitude of was much less in the random wave case, despite similar offshore wave conditions. Additionally, three methods were used to separate the wave-induced and turbulent components of velocity:. ensemble averaging, high-pass filtering and a differencing method proposed by Trowbridge (1998 J. Atmos. Ocean. Technol. 15 290–8). The magnitude of varied by as much as a factor of 5 among these methods, but qualitatively, the cross-shore and vertical structure were independent of the method used. The differencing method agreed closely with ensemble averaging in terms of the magnitude and structure of time-averaged quantities and in the signature of the time-dependent turbulent kinetic energy. Given this agreement, the differencing method appears to be the most suitable for application to random waves, such as those observed in the field.

/pdf/large-scale-laboratory-observations-of-turbulence-on-a-fixed-59czc7shp1.pdf

Large-scale laboratory observations of turbulence on a fixed barred beach

[1] A shoreline change model incorporating both long- and short-term evolution is integrated into a data assimilation framework that uses sparse observations to generate an updated forecast of shoreline position and to estimate unobserved geophysical variables and model parameters. Application of the assimilation algorithm provides quantitative statistical estimates of combined model-data forecast uncertainty which is crucial for developing hazard vulnerability assessments, evaluation of prediction skill, and identifying future data collection needs. Significant attention is given to the estimation of four non-observable parameter values and separating two scales of shoreline evolution using only one observable morphological quantity (i.e. shoreline position).

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2012GL052180

Extended Kalman Filter framework for forecasting shoreline evolution

Large geomorphic changes to barrier islands may occur during inundation, when storm surge exceeds island elevation. Inundation occurs episodically and under energetic conditions that make quantitative observations difficult. We measured water levels on both sides of a barrier island in the northern Chandeleur Islands during inundation by Hurricane Isaac. Wind patterns caused the water levels to slope from the bay side to the ocean side for much of the storm. Modeled geomorphic changes during the storm were very sensitive to the cross-island slopes imposed by water-level boundary conditions. Simulations with equal or landward sloping water levels produced the characteristic barrier island storm response of overwash deposits or displaced berms with smoother final topography. Simulations using the observed seaward sloping water levels produced cross-barrier channels and deposits of sand on the ocean side, consistent with poststorm observations. This sensitivity indicates that accurate water-level boundary conditions must be applied on both sides of a barrier to correctly represent the geomorphic response to inundation events. More broadly, the consequence of seaward transport is that it alters the relationship between storm intensity and volume of landward transport. Sand transported to the ocean side may move downdrift, or aid poststorm recovery by moving onto the beach face or closing recent breaches, but it does not contribute to island transgression or appear as an overwash deposit in the back-barrier stratigraphic record. The high vulnerability of the Chandeleur Islands allowed us to observe processes that are infrequent but may be important at other barrier islands.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/2013JF003069

Inundation of a barrier island (Chandeleur Islands, Louisiana, USA) during a hurricane: Observed water‐level gradients and modeled seaward sand transport

[1] The rip current field resulting from the transformation of surface gravity waves over offshore submarine canyons is studied. Employing a wave transformation model and a wave-induced circulation model over observed bathymetry we find that wave height variations associated with undulations in the canyon contours cause rip current circulation cells with alongshore spacing of O(100m) even though the nearshore bathymetry displays no variations at these length scales. Further, the predicted rips correspond to observed rip currents during the Nearshore Canyon Experiment (NCEX). Motivated by these results we study the relationship between O(100 m) scale variations in offshore bathymetric contours and the resulting rip current field in the nearshore. To isolate the roles of possible bathymetric features, we construct a series of idealized case studies that include site characteristics found at NCEX that are conducive of rip current development, such as a curved shoreline, an offshore submarine canyon and undulations in the canyon contours. Our results show that the first two components are unable to produce the observed short-scale circulation systems, while wave refraction over undulations in the canyon walls at length scales of O(100 m) provides a sufficient disturbance to generate alongshore wave height variations that drive multiple rip currents for a variety of incident wave conditions. Rips are not generated when the wave period is short, or when the angle of incidence is large. Analysis of the alongshore momentum balances further demonstrates that the rip current locations are also strongly influenced by inertial effects. Hence, nonlinear processes are important within the rip current circulation cell and we find that nonlinear advective acceleration terms balance a large portion of the driving alongshore gradient in the mean water surface elevation in the vicinity of the rip currents with bottom friction accounting for the remainder. Away from the rips, the balance is between the wave forcing and the pressure gradient outside the surf zone and wave forcing and bottom friction inside the surf zone, as expected.

/pdf/offshore-controls-on-nearshore-rip-currents-2tytovm11f.pdf

Joseph W. Long

Papers

Evaluation of wave runup predictions from numerical and parametric models

Large-scale laboratory observations of turbulence on a fixed barred beach

Extended Kalman Filter framework for forecasting shoreline evolution

Inundation of a barrier island (Chandeleur Islands, Louisiana, USA) during a hurricane: Observed water‐level gradients and modeled seaward sand transport

Offshore controls on nearshore rip currents