Assessment of the joint impact of extreme rainfall and storm surge on the risk of flooding in a coastal area

Highlights

• Using copulas to capture asymptotic dependence when nonlinearity prevails.

• Characterizing tail behavior of the joint distribution is important when using copula.

• Dependence justification for extreme events shows that they are on the same scale.

• Copula provides a robust modeling framework when few extreme data are available.

• Comparison of flood inundation maps produced by univariate and bivariate analyses.

Abstract

In coastal areas, flood events can result from the interaction of several factors such as rainfall, river flow and the classical tidal asymmetry to mention but a few. Therefore, flood risk assessment in these areas involves not only the estimation of the extreme values of each variable, but also their probability of occurring simultaneously. This study investigates the combined effect and dependence between a “heavy” rainfall with a high tidal levels forcing on the occurrence and severity of floods in the urban neighborhood close to the estuary of the Bouregreg River (Morocco). The methodology used for this analysis is based on a bivariate copula model to evaluate the joint risk probability of flood events. The estimated joint probability is used to define the boundary conditions for a hydraulic model to quantify the water levels and the extent of floods caused by the combination of both extreme rainfall and storm surge. The considered variables reveal a not negligible correlation, and the copula approach seems to be suitable and enough flexible, for analyzing separately marginal distributions of the source variables and their structure of dependence. Results show that the joint probability of rainfall and tide both exceeding their critical thresholds remains low to moderate, and the biggest threat to this area might be caused by heavy rainfall. However, high tide adds an extra risk by reducing the capacity of the urban drainage in absorbing storm water; especially when rainfall intensity exceeds 100 years return period. Although rainfall and tide introduce a wide range of time scale meteorological forcing, this won’t prevent storm surge and extreme rainfall events resulting from climate change, to take place in the future, on the same day leading to some of the most critical flooding scenarios in this area.

Introduction

Estuarine hydrodynamic is controlled by the inflow of rivers, tides, the rainfall, the wind, and other oceanic events such as an upwelling, an eddy, and storms. Extreme or compound events related to all these factors, happening simultaneously or in close succession can create a situation where severe flooding may occur. This statement makes sense and is still valid even if the compound events are not all extreme per se, but only their combination (Xu et al., 2014, Lian et al., 2013, Leonard et al., 2014, Petroliagkis et al., 2016, Pappadà et al., 2017). Therefore, for more accurate assessment of flood risk in these areas, it is necessary to evaluate the dependence between these factors. There is, however, a lack of knowledge about the interaction between the hydrologic variables (rainfall, river flow, astronomical tide, storm surge…) and therefore the risk of flooding in estuarine environments is hardly quantifiable due to their dynamic nature and the complex interaction of tidal and catchment processes (Petroliagkis et al., 2016). As such, several joint probability theories have been recently incorporated into flood risk analysis including two or more hydrological variables. One of the most applied joint probability models in hydrology is the copula model. According to Sklar’s theorem (1959), any multivariate joint cumulative distribution function can be expressed in terms of univariate marginal distribution functions and a copula which describes the dependence structure between the variables. The most important feature of a copula model is the way it makes it possible to model the dependence structure independently of the marginal distributions.

Therefore, many recent studies have used copula model to highlight the importance of studying the combined effect of rainfall and tide processes in estuaries and coastal areas. Lian et al., 2013, Xu et al., 2014 investigated the joint probability and effect of the tidal level and rainfall on flood risk in a coastal city using copula-based model. They confirmed that some positive dependence exists between rainfall and tidal level, indicating that tidal level poses an additional risk of flooding. The presence of this structural and “statistical” dependence between rainfall and high tides (storm surge) has already been studied by Pugh, 1987, Coles et al., 1999, Svensson and Jones, 2002 who tried to quantify the strength of this dependence. All these studies confirmed the existence of a statistically significant dependence between extreme rainfall and extreme storm surge. Within the same spatial context, White (2009) combined traditional flood risk modeling techniques with statistical dependence to assess the relationship between river flow, tide and surge for Lewes, East Sussex, UK. He used then a one-dimensional hydraulic model to predict the joint probability of potential flood events occurring in Lewes. He concluded that a small amount of dependence between the extremes of river flow and sea level can have an important impact on the subsequent water levels in an estuary. Chen et al. (2012) established the joint distribution and calculated the coincidence probabilities of flood magnitudes and flood occurrence dates to analyze the risk of flood in the upper Yangtze River in China and the Colorado River in the United States using copula function, while Wahl et al. (2012) analyzed the statistical dependence between storm surges and wind waves in two tide stations in the German Bight using copula-based approach. Both studies confirmed that the copula concept represents a promising tool for studying multivariate problems in hydrology and coastal engineering. Similar conclusions were found by Ganguli and Reddy (2013) who used a copula-based methodology for probabilistic flood risks assessment and explored the performance of trivariate copulas in modeling dependence structure of flood properties considering peak flow, volume, and duration of flood hydrograph.

Zheng et al., 2013, Zheng et al., 2014 studied the interaction between extreme rainfall and storm surge using bivariate logistic threshold-excess model along the Australian coastline. They reported that a significant dependence was observed for most of the tide gauge locations. Daneshkhah et al. (2016) analyzed the joint distribution of flood event properties and quantified the associated uncertainty using pair-copulas. They stated that copula is an efficient tool that can be used for probabilistic flood hazard assessment. More recently, Sebastian et al. (2017) estimated the joint exceedance probabilities for peak surge and cumulative precipitation using Bayesian network based on Gaussian copulas to model the hydraulic boundary conditions in a coastal watershed.

An issue to mention here within those studies and which has been discussed only by few authors concerns the data selected for estimating hydrological and meteorological factors’ dependence. Hawkes (2008) for example, has discussed this issue and considered it as critical for dependence study. Indeed, Samuels and Burt (2002) modeled the dependence between peak river flows on the Taff at Pontypridd and sea levels at Cardiff in South Wales, UK, concluding that there was no correlation between the peak flows and the high sea levels. In contrast, a dependence analysis by Svensson and Jones (2004) for the same area found statistically significant dependence between daily mean river flow at Pontypridd and surge at Avonmouth. The contradictory conclusions may be due to the different datasets that were used, with peak river flow and peak sea level being used in Samuels and Burt (2002), and daily mean river flow and surge being used in Svensson and Jones (2004). Related to this, Zheng et al. (2013) stated that this could be because the use of peak sea level (which is in most cases dominated by astronomical tide) may lead to lower dependence compared to when using storm surge estimates directly, as it is only the latter quantity that is likely to be physically associated with extreme rainfall under the same meteorological conditions.

All these research studies have outlined the fact that univariate flood frequency analysis cannot provide a complete assessment of the occurrence probability of extremes if the underlying event is characterized by a set of interrelated random variables (Chebana and Ouarda, 2011, Masina et al., 2015). It becomes thus urgent and pressing to recognize that the risk posed by these events is likely to become more important in the future as existing coastal communities become threatened by rising sea levels and changing tidal regimes (Archetti et al., 2011, Zhang and Singh, 2007). Towns close to tidal rivers and estuaries like the ones we are dealing with in this study (Rabat and Salé, Morocco) are at risk from the combination of extreme rainfall, fluvial and tidal flooding (Egis, 2011, RMSI, 2012) that can almost ruin their entire assets in the near future and set back their urban development by years or even decades. The costs of protecting these cities from rising sea levels and storms are also likely to rise with increased precipitation resulting from climate change. Furthermore, the pressure for increased urbanization of low-lying areas is expected to create major flood risk problems for many coastal and estuarine towns (Zellou and Rahali, 2017, Petroliagkis et al., 2016, Bevacqua et al., 2017).

A storm on Thursday, the 23rd of February 2017 has dumped over 120 mm of rain in just a few hours, causing flooding in the coastal neighboring cities of Rabat and Salé. The most plausible way to explain this extreme event is to account for the variability of rainfall and storm tide.

The large amounts of precipitation that fell in the surrounding area, which are normally collected by urban drainage systems and headed toward the sea or the tidal river, were partially obstructed from spilling out into the sea by the storm surge, have then contributed to major flooding along the coastal area. Ignoring therefore the storm tide’s impact to flooding may necessarily lead to underestimation of the risk of flooding. This event emphasizes the importance of studying joint probabilities of extreme events and the fact that conventional univariate statistical analysis is not accurate to bring enough information regarding the multivariate nature of these events. Therefore, the present research focuses on bivariate flood frequency analysis including data preparation, parameter selection and methodology application. The source variable-pair presented here is the maximum annual 24 h rainfall and corresponding tide data. We present the application of the copula-based joint probability method to generate a combination of critical rainfall amounts and critical high tides exceeding both certain threshold values according to different return periods. Those values were applied as input to CAESAR-LISFLOOD (CL) model (Coulthard et al., 2002, Coulthard et al., 2013, Zellou and Rahali, 2017) to predict patterns of maximum water depth which may derive from different flood sources. CL model focus on the nearshore processes to replicate the tidewater hydrodynamics. Therefore, the model grid needs to be setup to include river channel, floodplain topography and nearshore bathymetry.

This study demonstrates that by putting emphasis on statistical dependence between seemingly independent variables, it is possible to investigate their multivariate extreme value distributions which are suitable for modelling the tails of multidimensional phenomena and the associated risk when these variables are above a certain critical threshold.

A parametric copula is initially fitted to the whole dataset to characterize the overall dependence structure and the tail behavior of that particular copula is extracted later. We estimate non-parametrically (Schmidt and Stadtmuller, 2006) the lower and upper tail copulas and show that the joint distribution of the rainfall and high tide level are rather upper tail dependent, a fact which cannot be detected by fitting a copula to the whole dataset. Huser et al. (2017) stated that, without firm knowledge about the tail properties of the data, it is safer (i.e., more conservative) in terms of risk of joint extremes to assume asymptotic dependence. We have proceeded, therefore, with the tails' estimation and characterization by giving a strong attention to appropriately capturing the tail extreme behavior before any joint probability evaluation. And since it is common for many environmental processes to exhibit weakening spatial dependence as events become more extreme (Huser and Wadsworth, 2018), very extreme joint risks tend to be strongly overestimated if the data exhibit decreasing dependence strength at more extreme levels (Ledford and Tawn, 1997, Davison et al., 2013). Therefore, the increase of upper tail dependence strength should be enough to explain why a copula is able to connect extreme rainfall to high tide level. The strong asymptotic dependence justification of extreme events should give evidence that concomitant extreme events are observed and both are at the same scale, and that copula provides a robust modeling framework especially when few extreme data are available.

Here due to limited data availability, the focus of rainfall using copula is much on extreme event itself when the rainfall amount changes and implicitly not on its temporal and spatial characteristics (Müller and Kaspar, 2010, Xiao et al., 2013) in order to estimate the dependence with tide levels, since it is widely accepted that extreme precipitation changes are one type of significant perspectives to scientifically assess the behaviors and changes of climatic systems (Allan and Soden, 2008, Kysely et al., 2011, Fan et al., 2012, Li et al., 2013, Rouge et al., 2013, Xu et al., 2014). This paper takes thus, into account, only the precipitation change when we analyze its associated risk.

The paper is organized as follows: The case study area, Bouregreg estuary, is presented in Section 2. Section 3 describes the methods and the data requirements, including a brief description of copula concept and their mathematical formulation. The results of the joint risk probability of extreme rainfall and tidal levels and the consequent inundation patterns are reported and discussed in Section 4. Finally, conclusions are given in Section 5.