A surge response function approach to coastal hazard assessment. Part 2: Quantification of spatial attributes of response functions

In response to the 2004 and 2005 hurricane seasons, surge risk assessment approaches have been re-evaluated to develop more rapid, reliable methods for predicting the risk associated with extreme hurricanes. Here, the development of dimensionless surge response functions relating surge to hurricane meteorological parameters is presented. Such response functions present an opportunity to maximize surge data usage and to improve statistical estimates of surge probability by providing a means for defining continuous probability density functions. A numerical modeling investigation was carried out for the Texas, USA coastline to develop physical scaling laws relating storm surge response with hurricane parameters including storm size, intensity, and track. It will be shown that these scaling laws successfully estimate the surge response at any arbitrary location for any arbitrary storm track within the study region. Such a prediction methodology has the potential to decrease numerical computation requirements by 75% for hurricane risk assessment studies.     

The effects of natural structure on estimated tropical cyclone surge extremes

The past 12 years have seen significant steps forward in the science and practice of coastal flood analysis. This paper aims to recount and critically assess these advances, while helping identify next steps for the field. This paper then focuses on a key problem, connecting the probabilistic characterization of flood hazards to their physical mechanisms. Our investigation into the effects of natural structure on the probabilities of storm surges shows that several different types of spatial-, temporal-, and process-related organizations affect key assumptions made in many of the methods used to estimate these probabilities. Following a brief introduction to general historical methods, we analyze the two joint probability methods used in most tropical cyclone hazard and risk studies today: the surface response function and Bayesian quadrature. A major difference between these two methods is that the response function creates continuous surfaces, which can be interpolated or extrapolated on a fine scale if necessary, and the Bayesian quadrature optimizes a set of probability masses, which cannot be directly interpolated or extrapolated. Several examples are given here showing significant impacts related to natural structure that should not be neglected in hazard and risk assessment for tropical cyclones including: (1) differences between omnidirectional sampling and directional-dependent sampling of storms in near coastal areas; (2) the impact of surge probability discontinuities on the treatment of epistemic uncertainty; (3) the ability to reduce aleatory uncertainty when sampling over larger spatial domains; and (4) the need to quantify trade-offs between aleatory and epistemic uncertainties in long-term stochastic sampling.     

The effect of uncertainty on estimates of hurricane surge hazards

It is shown here that uncertainty can significantly affect estimated surge levels over a wide range of annual exceedance probabilities (AEPs). For AEPs in the range of 1 × 10^?2–5 × 10^?2 in the New Orleans area, estimated surge values with and without consideration of uncertainty differ by about 0.5–1.0 m. Similarly, suppression of natural variability, such as using a single value for Mississippi River discharge in surge simulations, rather than allowing the discharge to vary probabilistically, is shown to produce deviations up to 1 m for the 1 × 10^?2 AEP in locations within the mainline river levees in this area. It is also shown that uncertainty can play a critical role in the analysis of very low probability events in the AEP range 1 × 10^?4–1 × 10^?6. Such events are typically used in designs of structures with major societal impacts. It is shown here that, for this range of AEPs along the west coast of Florida, the neglect of uncertainty can under-predict design surge levels by about 20 % compared to estimated surge levels that include uncertainty.     

Highly nonlinear wind waves in Currituck Sound: dense breather turbulence in random ocean waves

Ocean Dynamics - We analyze surface wave data taken in Currituck Sound, North Carolina, during a storm on 4 February 2002. Our focus is on the application of nonlinear Fourier analysis (NLFA)...     

Analysis of the coastal Mississippi storm surge hazard

Following the extreme flooding caused by Hurricane Katrina, the Federal Emergency Management Agency (FEMA) commissioned a study to update the Mississippi coastal flood hazard maps. The project included development and application of new methods incorporating the most recent advances in numerical modeling of storms and coastal hydrodynamics, analysis of the storm climatology, and flood hazard evaluation. This paper discusses the methods that were used and how they were applied to the coast of the State of Mississippi.     

Wave modelling - The state of the art

This paper is the product of the wave modelling community and it tries to make a picture of the present situation in this branch of science, exploring the previous and the most recent results and looking ahead towards the solution of the problems we presently face. Both theory and applications are considered.The many faces of the subject imply separate discussions. This is reflected into the single sections, seven of them, each dealing with a specific topic, the whole providing a broad and solid overview of the present state of the art. After an introduction framing the problem and the approach we followed, we deal in sequence with the following subjects: (Section) 2, generation by wind; 3, nonlinear interactions in deep water; 4, white-capping dissipation; 5, nonlinear interactions in shallow water; 6, dissipation at the sea bottom; 7, wave propagation; 8, numerics. The two final sections, 9 and 10, summarize the present situation from a general point of view and try to look at the future developments.     

Quantifying impacts of forecast uncertainties on predicted storm surges

In this paper, we propose a framework for quantifying risks, including (1) the effects of forecast errors, (2) the ability to resolve critical grid features that are important to accurate site-specific forecasts, and (3) a framework that can move us toward performance-based/cost-based decisions, within an extremely fast execution time. A key element presently lacking in previous studies is the interrelationship between the effects of combined random errors and bias in numerical weather prediction (NWP) models and bias and random errors in surge models. This approach examines the number of degrees of freedom in present forecasts and develops an equation for the quantification of these types of errors within a unified system, given the number of degrees of freedom in the NWP forecasts. It is shown that the methodology can be used to provide information on the forecasts and along with the combined uncertainty due to all of the individual contributions. A potential important benefit from studies using this approach would be the ability to estimate financial and other trade-offs between higher-cost “rapid” evacuation methods and lower-cost “slower” evacuation methods. Analyses here show that uncertainty inherent in these decisions depends strongly on forecast time and geographic location. Methods based on sets of surge maxima do not capture this uncertainty and would be difficult to use for this purpose. In particular, it is shown that surge model bias can play a dominant role in distorting the forecast probabilities.     

Winds and Waves in the Yellow and East China Seas: A Comparison of Spaceborne Altimeter Measurements and Model Results

Wind speed and wave height measured by satellite altimeters represent a good data source to the study of global and regional wind and wave conditions. In this paper, the TOPEX altimeter wind and wave measurements in the Yellow and East China Seas are analyzed. The results provide a glimpse on the statistical properties and the spatial distributions of the regional wind and wave conditions. These data are excellent for use in the validation and verification of numerical simulations on global and regional scales. The altimeter measurements are compared with model output of temporal statistics and spatial distributions. The results show that the model simulations are in good agreement with TOPEX measurements in terms of the local mean and standard deviation of the variables (wave height and wind speed). For the comparison of spatial distributions, the quality of agreement between numerical simulations and altimeter measurements varies significantly from cycle to cycle of altimeter passes. In many cases, trends in the spatial distributions of wave heights and wind speeds between simulations and measurements are opposite. The statistics of biases, rms differences, linear regression coefficients and correlation coefficients are presented. A rather large percentage (∼50%) of cases show poor agreement based on a combination of low correlation, large rms difference or bias, and poor regression coefficient. There are indications that wave age is a factor affecting the performance of wave modeling skills. Generally speaking, the error statistics in the wave field is correlated to the corresponding error statistics in the wind field under the condition of active wind-wave generation. The error statistics between the wave field and the wind field become less correlated for large wave ages. This revised version was published online in August 2006 with corrections to the Cover Date.     

A surge response function approach to coastal hazard assessment – part 1: basic concepts

This paper reviews historical methods for estimating surge hazards and concludes that the class of solutions produced with Joint Probability Method (JPM) solutions provides a much more stable estimate of hazard levels than alternative methods. We proceed to describe changes in our understanding of the winds in hurricanes approaching a coast and the physics of surge generation that have required recent modifications to procedures utilized in earlier JPM studies. Of critical importance to the accuracy of hazard estimates is the ability to maintain a high level of fidelity in the numerical simulations while allowing for a sufficient number of simulations to populate the joint probability matrices for the surges. To accomplish this, it is important to maximize the information content in the sample storm set to be simulated. This paper introduces the fundamentals of a method based on the functional specification of the surge response for this purpose, along with an example of its application in the New Orleans area. A companion paper in this special issue (Irish et al. 2009) provides details of the portion of this new method related to interpolating/extrapolating along spatial dimensions.