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Nonparametric Approach to Copula Estimation in Compounding The Joint Impact of Storm Surge and Rainfall Events in Coastal Flood Analysis

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Abstract

The joint probability modelling of storm surges and rainfall events is the main task in assessing compound flood risk in low-lying coastal areas. These extreme or non-extreme events may not be dangerous if considered individually but can intensify flooding impact if they occur simultaneously or successively. Recently, the copula approach has been widely accepted in compound flooding but is often limited to parametric or semiparametric distribution settings in a limited number of cases. However, both parametric and semiparametric approaches assume the prior distribution type for univariate marginals and copula joint density. In that case, there is a high risk of misspecification if the underlying assumption is violated. In addition, both approaches suffer from a lack of flexibility. This study uses bivariate copula density in the nonparametric distribution setting. The joint copula structure is approximated nonparametrically by employing the Bernstein copula estimator and Beta kernel copula density, and their performances are also compared. The proposed model is tested with 46 years of rainfall and storm surge observations collected on Canada's west coast. The marginal distribution of the selected flood variables is modelled using nonparametric kernel density estimation (KDE). Based on the different model compatibility tests, the Bernstein copula with normal KDE margins defined the joint dependence structure well. The selected nonparametric copula model is further employed to estimate joint and conditional return periods. It is found that flood hazard characteristics occurrence simultaneously is less frequent in AND-joint cases than in OR-joint cases. Also, the derived model is further used to estimate failure probability (FP) statistics to assess the variation of bivariate hydrologic risk during the project lifetime. It is found that FP statistics could be underestimated when neglecting the compound effect of storm surge and rainfall in the coastal flood risk.

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Data Availability Statement

Data used in the presented research are available at https://tides.gc.ca/eng/data (CWL data); https://wateroffice.ec.gc.ca/search/historical_e.html (Daily streamflow discharge records); https://climate.weather.gc.ca/ (Daily rainfall data).

Abbreviations

KDE:

Kernel Density Estimation

FP:

Failure Probability

CF:

Compound Flooding

JRP(s):

Joint Return Period(s)

PDF(s):

Probability Density Function(s)

CDF(s):

Cumulative Distribution Function(s)

EV:

Extreme value

GEV:

Generalized Extreme Value

SLR:

Sea Level Rise

MSE:

Mean Square Error

RMSE:

Root Mean Square Error

MAE:

Maximum Absolute Error

AIC:

Akaike Information Criterion

BIC:

Bayesian Information Criterion

HQC:

Hannan-Quinn Information Criterion

NSE:

Nash-Sutcliffe Model Efficiency

CWL:

Coastal Water Level

MLE:

Maximum Likelihood Estimation

DPI:

Direct Plug-in

AMISE:

Asymptotic Mean Integrated Squared Error

MK:

Mann-Kendall

CHS:

Canadian Hydrographic Service

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Acknowledgements

The work presented in the paper has been funded by the Natural Sciences and Engineering Council of Canada's discovery grant to the second author. We thank Fisheries and Ocean Canada for providing the coastal water level observations and Environment and Climate Change Canada for daily streamflow discharge records. Special thanks to Canadian Hydrographic Service for providing the tidal data.

Funding

This research was funded by the Natural Sciences and Engenirreing Research Council of Canada (NSERC) collaborative grant with the Institute for Catastrophic Loss Reduction (ICLR) to the second author (Slobodan P. Simonovic).

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  1. Department of Civil and Environmental Engineering, Western University, London, ON, N6A 5B8, Canada

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Shahid Latif (SL): Conceptualization, Methodology, Software, Visualization, Investigation, Validation, Writing-Original draft preparation. Slobodan P. Simonovic (SPS): Supervision. Conceptualization, Writing- Reviewing and Editing.

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Latif, S., Simonovic, S.P. Nonparametric Approach to Copula Estimation in Compounding The Joint Impact of Storm Surge and Rainfall Events in Coastal Flood Analysis. Water Resour Manage 36, 5599–5632 (2022). https://doi.org/10.1007/s11269-022-03321-y

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