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A polynomial chaos framework for probabilistic predictions of storm surge events

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Abstract

We present a polynomial chaos-based framework to quantify the uncertainties in predicting hurricane-induced storm surges. Perturbation strategies are proposed to characterize poorly known time-dependent input parameters, such as tropical cyclone track and wind as well as space-dependent bottom stresses, using a handful of stochastic variables. The input uncertainties are then propagated through an ensemble calculation and a model surrogate is constructed to represent the changes in model output caused by changes in the model input. The statistical analysis is then performed using the model surrogate once its reliability has been established. The procedure is illustrated by simulating the flooding caused by Hurricane Gustav 2008 using the ADvanced CIRCulation model. The hurricane’s track and intensity are perturbed along with the bottom friction coefficients. A sensitivity analysis suggests that the track of the tropical cyclone is the dominant contributor to the peak water level forecast, while uncertainties in wind speed and in the bottom friction coefficient show minor contributions. Exceedance probability maps with different levels are also estimated to identify the most vulnerable areas.

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Funding

The work of P. Sochala is supported by a funding of BRGM (French Geological Survey) through its Institut Carnot sponsored by the ANR (French National Research Agency). This research was made possible in part by a grant from The Gulf of Mexico Research Initiative to the Consortium for Advanced Research on Transport of Hydrocarbon in the Environment (CARTHE) and by NSF 1639722 and NSF 1818847.

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Authors and Affiliations

  1. BRGM, 3 Avenue Claude Guillemin, 45060, Orléans, France

    Pierre Sochala

  2. Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, TX, 78712, USA

    Chen Chen & Clint Dawson

  3. Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, FL, 33149, USA

    Mohamed Iskandarani

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  1. Pierre Sochala
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  2. Chen Chen
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  4. Mohamed Iskandarani
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Correspondence to Pierre Sochala.

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Data are publicly available through the Gulf of Mexico Research Initiative Information & Data Cooperative (GRIIDC) at https://doi.org/https://data.gulfresearchinitiative.org (https://doi.org/10.7266/N73777BS).

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Appendix: Holland model

Appendix: Holland model

This parametric model [19] describes a symmetrical vortex and is derived by starting with an empirical analytical pressure field and by using the gradient wind equation to get the wind speed profile. The pressure field p is assumed to have an exponential profile,

$$ p(r,t)=p_{\mathrm{c}}(t)+(p_{\mathrm{a}}(t)-p_{\mathrm{c}}(t))\exp\left( -~\left( R_{\text{mw}}(t)/r\right)^{B}\right), $$
(28)

where r is the radial distance from the eye, t the time variable, pc(t) the central pressure, pa(t) the ambient pressure (at infinite radius), Rmw(t) the maximum wind radius (RMW), and B the Holland parameter. Plugging the pressure profile (28) into the gradient wind equation [21] and neglecting the Coriolis force (assumed to be small in the region of maximum winds) leads to the following tangential wind speed profile,

$$ v(r,t)=v_{\max}(t)\left[\left( R_{\text{mw}}(t)/r\right)^{B} \exp\left( -~\left( R_{\text{mw}}(t)/r\right)^{B}+1\right) \right]^{\frac{1}{2}}, $$
(29)

where the maximum wind speed \(v_{\max \limits }(t)\) has been introduced. This latter quantity is defined as v(r = Rmw,t) = (B(pa(t) − pc(t))/(ρae))1/2 with \(\rho _{\mathrm {a}}=1.18\text {kg/m}^{3}\) the air density, and e = 2.72 the Euler’s number. Assuming that the central pressure and the maximum wind speed are known, the ambient pressure in Eq. 28 is then computed with \(p_{\mathrm {a}}(t)=p_{\mathrm {c}}(t)+\rho _{\mathrm {a}} e v_{\max \limits }^{2}(t)/B\). The shape parameter B of the model determines the steepness of the eyewall and the strength of the winds far from the center. Its value ranges over the interval [0.5, 2.5] as mentioned in [49] and we set B = 1.

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Sochala, P., Chen, C., Dawson, C. et al. A polynomial chaos framework for probabilistic predictions of storm surge events. Comput Geosci 24, 109–128 (2020). https://doi.org/10.1007/s10596-019-09898-5

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