Data collection

In order to carry out the hazard and risk assessment, the following data types have been compiled: bathymetry, topography, wind, waves, water levels, typhoon tracks and intensity, information on tsunamis from regional sources, climate change effects and exposure data.

Deep-water bathymetry data were derived by combining bathymetric data of the Republic of the Marshall Islands and Vicinity (Hein et al. 2007) and GEBCO 2008 global bathymetric data sets (resolution of ≈ 1 km × 1 km). Higher-resolution nearshore bathymetry data were collected with an echosounder, with a vertical resolution of 0.10 m, at a number of cross-shore transects over the reef flat and out to a depth of 80 m.

Detailed topographic data are essential to carry out coastal hazard and risk assessments on low-lying atoll islands. Unfortunately, no digital elevation data were available for the island from literature or other data sources. Therefore, high-resolution topographic data (maximum vertical resolution ≈ 10 cm) were collected with a GPS device (Trimble CenterPoint-RTX) at ≈ 1500 locations over the island and interpolated in order to create a digital elevation map of the entire island.

Tidal levels were derived based on the global TOPEX/Poseidon dataset (i.e. TPXO 8.0; Egbert and Erofeeva 2002) and were combined with information from the Kwajalein NOAA tidal gauge (station ID 1820000; lat. 8° 43.9′ N; lon. 167° 44.2′ E). A harmonic analysis was carried out on the measured water levels available every 6′. Residual water levels were derived as the difference between measured water levels at Kwajalein tidal gauge and predicted tidal water levels.

Offshore wave and wind conditions were extracted from the ERA-Interim (European ReAnalysis) global wave reanalysis (Dee et al., 2011). The data are six hourly, starting in 1979, and are available on a global grid with a resolution of 0.75° × 0.75° (≈ 80 × 80 km). The dataset contains information on winds (wind speed and direction) and wave conditions (wave height, period and direction). ERA-Interim global wave data were validated using wave data information available at Majuro via the NOAA website (National Oceanic and Atmospheric Administration).

The effect of typhoons was analysed based on historical typhoon tracks derived from the IBTrACS (“International Best Track Archive for Climate Stewardship”) database. Typhoon events between 1979 and 2015 are listed in the database.

No tsunami events caused by local sources (i.e. landslides or nearby earthquakes) have been previously reported. Most of the recorded tsunami waves were driven by mega thrust earthquakes (e.g. 2011 Tohoku tsunami) and resulted in minor impact to the RMI (i.e. limited to no island flooding). For example, tsunami waves generated by the Tohoku event in 2011 were estimated at less than 1 m in the RMI and occurred at low tide therefore not causing remarkable damages (Hess et al. 2015).

Sea level rise (SLR) projections were available through the Australian Bureau of Meteorology and Commonwealth Scientific and Industrial Research Organisation (CSIRO 2014). According to these projections, the mean sea level may increase 0.42 to 0.78 m by 2100, for the more conservative Representative Concentration Pathway (RCP) 2.6 scenario and the “business-as-usual” RCP 8.5 scenario, respectively. The intermediate RCP 4.5 and RCP 6.0 were also considered. Changes in wave conditions due to future climate change scenarios were derived from Hemer et al. (2013). According to these projections, an increase up to + 2% in wave height by the end of the century may be expected. No significant changes in wave direction are expected.

Since the scope of the present study is to assess impacts under specific warming levels (SWLs) compared to pre-industrial levels, projections of global temperature were used, available from CMIP5 GCMs (Coupled Model Intercomparison Project Phase 5, Global Climate Models) (Taylor et al. 2011). For each GCM, the initial time series were averaged to obtain annual mean series and were then bias-corrected according to the present day warming. Next, all model series were ensemble averaged to create time series of annual mean temperature spanning from 1970 to 2100 for all the studied RCPs. These were also used to estimate the years at which SWLs of 1.5, 2.0 and 2.5 °C are reached.

Exposure data (location, construction type and value in USD) were derived from PCRAFI 2015 (“Pacific Catastrophe Risk Assessment and Financing Initiative”).

Numerical models

Process-based numerical models were used to quantify and propagate the offshore forcing to nearshore and to compute the impacts over the island (Fig. 2).

Fig. 2 Multi-hazard and risk assessment methodology as applied in this study Full size image

The coupled hydrodynamics and waves Delft3D modelling system (Lesser et al. 2004) were used to compute wave conditions and storm surges resulting from wind wave events from the lagoon, as well as the generation and propagation of typhoons and tsunamis from the ocean. Wind waves from the lagoon, as well as due to typhoons, are not included in ERA-Interim due to the spatial resolution of this global dataset and therefore had to be simulated separately. Standard default parameters were used in the model.

Wind conditions from the ERA-Interim dataset were used to simulate wind-induced waves from the lagoon. A model covering the lagoon extent was built with a spatial resolution of 300 m.

The generation and propagation of typhoons were computed based on coupled Delft3D-FLOW and Delft3D-WAVE simulations. The model domain covered the area ranging between lon. 160 to 180° and Lat. − 5 to − 15° on a computational grid with a spatial resolution of 0.1°. Each individual typhoon track was simulated separately using a spider web grid, in order to generate the space- and time-varying wind and pressure fields within the model domain. No additional boundary condition was used to force the model. The same model setup was first validated in a different case study for Hawaii, and for which measurements were available (Hurricane Iniki, 1992). Based on the validated model, all tracks from the IBTrACS database and with a category of tropical storm or higher (i.e. categories 1 until 5) were modelled, resulting in a set of 30 simulated events.

Water levels generated specifically from the Tohoku tsunami event, the most recent recorded past event, were also simulated with Delft3D.

The offshore forcing was then translated into impacts on the island (i.e. flooding and erosion). The XBeach model (Roelvink et al. 2009; surf beat version) was used to propagate waves (i.e. short and infragravity) and water levels across the reefs towards the shore and to compute the flooding over the island (Fig. 2). The model has been successfully applied to compute wave transformation and water levels in reef environments (Pomeroy et al. 2012; Van Dongeren et al. 2013), including the nearby Roi-Namur island at Kwajalein Atoll (Quataert et al. 2015). Given the very similar settings, the model was selected for this application using the same parameters as in Quataert et al. (2015). Waves and water level boundary conditions for the XBeach model were derived from the ERA-Interim offshore wave data (i.e. for swell events) and from Delft3D simulations (i.e. for wind waves from the lagoon and typhoon events), as shown in Fig. 2. The model covered the entire island with alongshore resolution of 20 m and cross-shore resolution ranging between 50 m offshore and 1 m on the island. The model was forced with time-varying water levels and wave conditions in order to simulate a design storm with a duration of 30 h. The maximum in water level and wave condition of the design storm was dependent on the return period of the simulated event.

Storm erosion due to episodic (extreme) events and long-term land loss due to SLR were estimated separately by means of empirical formulas on nine representative cross-shore profiles of known steepness and sediment characteristics. Namely, the Van Rijn (2009) formula was used to provide an estimate of the dune erosion resulting from individual storms of different return periods, and the Bruun Rule (Bruun 1962) to assess the effect of coastal retreat induced by SLR. It is important to note that these formulas were originally derived for closed sandy coastlines. Although their application for this specific case study may stretch beyond their limit of validity, given the very specific geomorphological settings of Ebeye, we believe that the use of empirical formulas was the optimal solution in terms of computational times and accuracy.

Multi-hazard assessment

The two main coastal hazards at the island are flooding and coastal erosion. However, those hazards are generated by a number of inherently different, independent, hydro-meteorological events, namely, (a) wind waves and surge from the lagoon, (b) oceanic swell waves, (c) wind waves and surge during typhoon events and (d) tsunamis. Therefore, an important step of the methodology consists of the combination of those different processes.

An extreme value analysis based on a peak-over-threshold approach was at first carried out in order to derive wave heights and storm surge levels for different return periods (i.e. T = 1, 5, 10, 30 and 50 years) for each individual process. This resulted in a matrix of 15 conditions (i.e. 5 return periods and 3 processes, namely, wind waves, swell waves and typhoons). Since there was only evidence of one minor past tsunami at the island, no return period could be derived for tsunami events. Therefore, water levels generated from the past Tohoku event were treated as constant for the different return periods. In any case, tsunami events are a minor source of risks for the island, in comparison with swell waves and typhoons.

Each individual combination of wave height and storm surge level, for each individual process, was then used to compute the flooding and coastal erosion hazard over the island. An example of a flooding map, resulting from swell wave events with a return period of 10 years, in the present and in 2100, is shown in Online Resource 1. In order to reduce the number of scenarios and to combine the effect of different forcing mechanisms on each return period, maps were generated showing the greatest flood depth at each grid node and the greatest erosion distance at different representative cross-shore transects. This resulted in a total of five flood maps and five erosion maps corresponding to the different return periods (i.e. T = 1, 5, 10, 30 and 50 years) for each time horizon (current situation, 2030, 2050 and 2100). The SLR scenarios analysed were derived from different RCP scenarios, namely, RCP 2.6, 4.5, 6.0 and 8.5.

Relative percentages describing the portion of the island inundated by, an arbitrarily chosen, threshold water depth equal to 20 cm are summarised in Online Resource 2.

Risk assessment

Separate damage computations were carried out to quantify the effects of flooding and coastal erosion.

Direct damages due to flooding were estimated by combining inundation maps, exposure data and a depth-damage function describing the damages to houses and infrastructure at different flood depths. In particular, one depth-damage curve derived for America Samoa was selected and applied to all types of assets on the island (Paulik et al. 2015). Damages (D) for different return periods were derived and then integrated over the different probabilities of occurrence (P), to compute the expected annual damages (EAD), following Eq. (1). EAD describes an expected yearly averaged damage.

$$ \mathrm{EAD}=\underset{0}{\overset{1}{\int }}D(p)\cdot dP $$ (1)

EAD/m2 was also derived, to be used as a basis for the prioritisation of disaster risk reduction measures. Direct damages due to erosion were derived by multiplying the area loss by the estimated land value (400 USD/m2). The land value was estimated based on land reclamation costs, required to counteract island erosion.

Indirect and intangible damages were estimated as a percentage of the direct damages. Moreover, a separate indirect damage was added to account explicitly for the number of days when one of the major roads on the island (i.e. the causeway towards Gugeegue) is not accessible due to flooding and debris caused by wave overtopping. Inaccessibility of the road also results in additional indirect damages as inhabitants in Gugeegue are not able to reach their work place and students cannot attend school. The different sources of damage were then summed up to derive the total damages.

The population affected by flooding was estimated by overlaying flood maps and population maps. Expected annual affected people (EAAP) was computed similarly to the EAD, but using a 20 cm threshold depth value to consider individuals actually affected by flooding. This threshold takes into account the fact that local inhabitants have learnt to cope with minor and more frequent flooding events, which they do not necessarily consider as major problem.