Development and uncertainty quantification of hurricane surge response functions for hazard assessment in coastal bays

Abstract

Reliable and robust methods of extreme value-based hurricane surge prediction, such as the joint probability method (JPM), are critical in the coastal engineering profession. The JPM has become the preferred surge hazard assessment method in the USA; however, it has a high computational cost: One location can require hundreds of simulated storms and more than ten thousand computational hours to complete. Optimal sampling methods that use physics-based surge response functions (SRFs) can reduce the required number of simulations. This study extends the development of SRFs to bay interior locations at Panama City, Florida. Mean SRF root-mean-square errors for open coast and bay interior locations were 0.34 and 0.37 m, respectively, comparable with ADCIRC errors. Average uncertainty increases from open coast, and bay SRFs were 10 and 12 %, respectively. Long-term climate trends, such as rising sea levels, introduce nonstationarity into the simulated and historical surge datasets. A common approach to estimating total flood elevations is to take the sum of projected sea-level rise (SLR) and present day surge (static approach); however, this does not account for dynamic SLR effects on surge generation. This study demonstrates that SLR has a significant dynamic effect on surge in the Panama City area, and that total flood elevations, with respect to changes in SLR, are poorly characterized as static increases. A simple adjustment relating total flood elevation to present day conditions is proposed. Uncertainty contributions from these SLR adjustments are shown to be reasonable for surge hazard assessments.

Appendix

The joint probability density function, f, in Eq. 1 for the JPM-OS is defined as:

$$f\left( {c_{\rm p} ,R_{\rm p} ,v_{f} ,\theta ,x_{\rm o} } \right) = \varLambda_{1} \varLambda_{2} \varLambda_{3} \varLambda_{4} \varLambda_{5}$$

(7a)

$$\varLambda_{1} = f(c_{\rm p} |x_{\rm o} ) = \frac{1}{{a_{1} (x_{\rm o} )}}{ \exp }\left[ { - \frac{{\Delta p - a_{\rm o} (x_{\rm o} )}}{{a_{1} (x_{\rm o} )}}} \right]{ \exp }\left\{ { - { \exp }\left[ { - \frac{{\Delta p - a_{\rm o} (x_{\rm o} )}}{{a_{1} (x_{\rm o} )}}} \right]} \right\}$$

(7b)

$$\varLambda_{2} = f(R_{\rm p} |c_{\rm p} ) = \frac{1}{{\sigma (\Delta p)\sqrt {2\pi } }}{ \exp }\left\{ { - \frac{{\left[ {\mu (\Delta p) - R_{\rm p} } \right]^{2} }}{{2\sigma^{2} (\Delta p)}}} \right\}$$

(7c)

$$\varLambda_{3} = f(v_{\rm f} |\theta ) = \frac{1}{{\sigma (\theta )\sqrt {2\pi } }}{ \exp }\left\{ { - \frac{{\left[ {\mu (\theta ) - v_{f} } \right]^{2} }}{{2\sigma^{2} (\theta )}}} \right\}$$

(7d)

$$\varLambda_{4} = f(\theta |x_{\rm o} ) = \frac{1}{{\sigma (x_{\rm o} )\sqrt {2\pi } }}{ \exp }\left\{ { - \frac{{\left[ {\mu (x_{\rm o} ) - \theta } \right]^{2} }}{{2\sigma^{2} (x_{\rm o} )}}} \right\}$$

(7e)

$$\varLambda_{5} = {\text{Rate}}\,{\text{of}}\,{\text{storm}}\,{\text{landfall}}\,{\text{occurrence}}\,{\text{per}}\,{\text{unit}}\,{\text{coastal}}\,{\text{length}}$$

(1f)

where f = probability density functions; a ₁, a ₂ = Gumbel coefficients; μ = mean of normal distribution; σ ² = variance of normal distribution; () indicates the parameter is a function of the variable in parentheses.