We selected the Sofala province of Mozambique as our case study area. The area has recently seen two compound flood events from tropical cyclones, namely Idai in March 2019 and Eloise in January 2021, which both had a large impact on the area (UN OCHA, 2022, 2021). Furthermore, the proposed flood hazard framework was previously validated for this area for two historical flood events (Eilander et al., 2023a). In the absence of better local data and models, global models have been shown to be useful in supporting risk management in data-scarce areas (Ward et al., 2015), for instance for post-disaster response in this area by providing bulletins with flood impact forecasts from global models (Emerton et al., 2020). The largest city in the Sofala province is Beira, with more than 500 000 inhabitants and a large port connecting the hinterland with the Indian Ocean. While the city itself is mainly threatened by coastal and pluvial flooding, the deltas of the Pungwe and Buzi rivers are also susceptible to fluvial flooding (Emerton et al., 2020; van Berchum et al., 2020).

To simulate extreme flood events beyond what has been observed in historical time series we obtain extreme value distributions for each driver independently. Unless stated differently, marginal extreme values for each driver are based on extreme values distributions fitted to annual maximum events. Annual maxima are selected from a time series of 42 years based on the hydrological year commencing in August with a minimal 14 d separation between two events to ensure independent and identically distributed events. The marginal extreme value distributions are derived by fitting the Gumbel and general extreme value (GEV) distributions to the sampled annual maximum peaks using the L-moment method. The best fit is selected based on the minimum Akaike information criterion (AIC) (Mutua, 1994). For each flood driver, the time series is shown in Fig. A1, the fitted distribution is shown in Fig. A2, and the return values are listed in Table A1. A detailed description of each flood driver and its marginal extreme value distribution is provided in the following subsections.

A two-dimensional hydrodynamic SFINCS (Super-Fast INundation of CoastS) model is automatically set up with the globally applicable compound flood hazard framework as presented in Eilander et al. (2023a). SFINCS is selected as it is designed to efficiently simulate overland flow from compound flooding at limited computation costs and with good accuracy (Leijnse et al., 2021; Sebastian et al., 2021) and has been validated for two historical events for this case study region (Eilander et al., 2023a). Using this setup, we derive a maximum flood depth map for all combinations.

For each event in the model event set, flood impact is derived using the Delft-FIAT flood impact model (Slager et al., 2016). This step provides a response surface between the magnitude of the flood drivers and the impact obtained for each location of the case study area. This model combines the hazard maps with socioeconomic data on exposure and vulnerability to calculate distributed flood impacts per event. Exposure is here defined by assets and people in the floodplain and the vulnerability as the susceptibility of these assets and people to flooding. Hazard maps are derived as the maximum flood depth from the hydrodynamic simulations. As limited flooding is simulated in the simulation with only non-extreme flood drivers, which does not occur in reality, all hazard maps are bias-corrected with the flood depths of this simulation. This model bias in the hazard maps is likely due to inaccuracies in the absolute coastal elevation and river bathymetry. Exposure maps are automatically prepared at the same resolution as the hazard maps from global data sources using HydroMT (Eilander et al., 2023b). This procedure and the relevant datasets are described below.

We calculate impact in terms of damage and people affected. The potential damage is estimated per building and based on a country-specific potential damage per person multiplied by the number of residents per building. The country-specific damage per person is based on residential damage from Huizinga et al. (2017) and additionally accounts for direct non-residential damage (× 2.0) and indirect damage (× 1.2) using multiplication factors based on various studies (Wagenaar et al., 2019; Koks et al., 2015). The number of residents per building is obtained by downscaling the gridded population count dataset from WorldPop 2020 UN adjusted data (Bondarenko et al., 2020) based on the Google Open Buildings building footprints dataset (Sirko et al., 2021). The latter is preprocessed by rasterizing objects with an accuracy larger than 0.7 at a 10 m spatial resolution. The resulting potential building damage and population counts are shown in Fig. 3. The vulnerability is simulated based on a depth–damage function that provides the percentual potential damage as a function of the water depth. Here we use a depth–damage function based on a weighted average of depth–damage functions for different types of buildings from Huizinga et al. (2017). We assume no damage to buildings for water depths smaller than 15 cm, similar to other flood studies (e.g., Wing et al., 2017). The same threshold is used to determine the number of affected people from an event.

Different multivariate statistical approaches have been applied for hydrodynamic flood risk assessments but typically with only two flood drivers (Moftakhari et al., 2019; Bates et al., 2021; Wu et al., 2021). In this case study, we consider five flood drivers: discharge at the Buzi and Pungwe rivers, rainfall, storm surge, and wind setup. We therefore use the approach by Couasnon et al. (2022), in which the joint magnitude and temporal co-occurrence of extremes are simulated separately. The approach consists of four steps. First, we fit marginal distributions to annual maximum events of each driver (Sect. 2.2). Second, we fit a vine copula to the annual maxima of each driver to model their annual joint dependence. Third, we define the rate at which different combinations of annual maximum drivers co-occur within a given time window. Finally, we sample from the copula model and use the marginal distributions and the co-occurrence rate to generate the equivalent of 30 000 years of events. For the dependence and co-occurrence analysis, we extend the CoDEC dataset of tide and surge levels with additional simulations to cover the recent extreme events of Idai (2019) and Eloise (2021) (Eilander et al., 2023a). All flood drivers are forced with the same ERA5 meteorological reanalysis, hence providing a coherent dataset for this analysis.

Joint dependence of annual maxima. We use pair copula constructions (PCCs), also called vine copulas, to model the joint distribution of annual maxima of all drivers because they provide a highly flexible way to model multivariate dependencies. Vine copulas use the bivariate copula as building blocks to characterize the n-dimensional probability density function and a given structure to define the order in which these building blocks are assembled. More specifically, the n-dimensional copula density is calculated as the product of n(n-1)/2 bivariate (conditional) copulas (Bevacqua et al., 2017; Aas et al., 2009). From all the possible mathematically valid decompositions, we select the dimensional vine structure that minimizes the AIC. Each bivariate copula is selected from a set of 10 parametric copula models from the elliptical (Gaussian, Student t), Archimedean (Clayton, Gumbel, Frank, Joe), and BB (BB1, BB6, BB7, BB8) families, as well as the independence copula. This ensures that complex behavior, including upper-tail dependence, are properly captured, and modeled. We fitted a vine copula to the time series of annual maxima using the pyvinecopulib package in Python (Nagler and Vatter, 2021). The selected vine copula is shown in Table 2.

Flood risk is based on the product of exposure, vulnerability, and hazard over a range of exceedance probabilities. The risk is calculated from the empirical exceedance probability for annual damage from the stochastic event set (Sect. 2.5). For each event we derive the flood impact by linear interpolation of the simulated impacts based on its return values. We calculate the risk in terms of expected annual damage (EAD) and expected annual affected population (EAAP) as the exceedance probability integral of the flood impact using trapezoidal integration, i.e., the area under the flood impact versus exceedance probability curve (e.g., Ward et al., 2011).

Flood risk is calculated for a base scenario and three scenarios with risk reduction measures: levees, spatial zoning, and dry-proofing of buildings at three different protection levels. All risk reduction measures are implemented in the flood impact modeling as described below.

Levees. Current flood protection standards are estimated to be around a 2-year return level with the FLOPROS modeling approach (Scussolini et al., 2016). In this scenario we simulate levees with a protection standard at a 5-, 10-, and 50-year return level. No flooding occurs for fluvial or coastal drivers below this level, and above this level we assume complete dike failure. The measure is implemented by correcting the flood levels for scenarios below the protection level. In compound scenarios with rainfall, a minimum flood depth based on the return level of the univariate scenario with the same rainfall return level is maintained.

In this section we present the observed dependence and co-occurrence between all flood drivers. Figure 4 shows the pairwise joint annual maxima, the conditional Kendall's tau correlation coefficient, and fitted copula. The joint annual maxima that co-occur with other extremes are highlighted in orange. Each pair is conditioned based on the variables plotted in the panels above as indicated in the top left of each panel. For 6 out of the 10 pairs of drivers, a significant conditional dependence is found. The strongest dependence is found between the discharge in both rivers and between discharge in the Pungwe River and rainfall (τ = 0.43), followed by dependence between surge and wave setup (τ = 0.39). Figure 5 shows the distribution of single and compound annual maximum events. In total 141 events are found in 42 years during which at least one driver is extreme. From these events, 45 have more than one extreme flood driver, and these events have a maximum duration of 7 d. During three events (1986, 1992, and 2019) all five drivers co-occurred, one of those instances being during Tropical Cyclone Idai in 2019. The number of events increases to 160 (36 compound) if we decrease the maximum time lags between consecutive annual maxima to 2 d for all drivers, while it decreases to 139 (46 compound) if we increase these time lags to 5 d for all drivers.

In this section we discuss the flood hazard based on the 100-year univariate and compound event under the assumption of full statistical dependence (i.e., all 100-year flood drivers co-occur). Figure 6 shows the pluvial, coastal (combined surge and waves), and Buzi and Pungwe fluvial flood maps. While the pluvial flooding is most widespread, the flood depths are the smallest among the four univariate hazards. Coastal flooding, on the other hand, is the most limited in space but does hit the city of Beira. The fluvial flood maps for both rivers show large spatial extents and large water depths; this is especially the case for the Buzi River flood map where the discharge extremes are the largest. Similar patterns are observed for other return periods. In the left panel of Fig. 7, a compound flood hazard map is shown for the event where the 100-year conditions of all drivers co-occur, i.e., the full dependence event. The difference in flood depth between this full dependence compound 100-year flood hazard map and the maximum of each univariate 100-year flood hazard map shows where physical interactions between the drivers modulate the flood depth (see right panel in Fig. 7). In most places the interactions are relatively small compared to the flood depth. In terms of extent, the largest interactions are between the pluvial and fluvial flood drivers. In terms of flood depth, the largest interactions are between the coastal and fluvial drivers. The coastal and fluvial drivers cause the largest increase in flood depths around the upstream end of the Pungwe estuary. Interactions between pluvial and coastal drivers also increase the flood depth with ∼ 20 cm near Beira. Around the mouth of the Buzi estuary we find that the interactions cause a decrease in flood depth, while further upstream around the town of Buzi they cause an increase in flood depths. The water levels in the most downstream section of the Buzi River are higher in the compound scenario compared to the 100-year discharge scenario due to backwater effects. However, compared to the 100-year coastal scenario, water levels in the compound scenario are lower, as this river section changes from coastal-dominated to discharge-dominated. During these high-river-flow conditions, a lower volume of coastal water enters the river mouth. Further upstream, the water levels are always discharge-dominated and the water levels are larger in compound scenarios compared to all single driver scenarios due to backwater effects. This backwater effect causes water levels to increase more and over a larger area if the peaks of the flood drivers at the boundary happen with zero time lags instead of with the observed time lags, especially in the Buzi River but also in the Pungwe River (see Fig. A5).

In this section we compare flood risk from univariate flood drivers and compound flood drivers under different assumptions of statistical dependence. The left panel of Fig. 8 shows the flood risk profiles, i.e., the flood impact as a function of the return period, for each univariate flood driver. The univariate risk profiles show that coastal flooding causes the largest risk with an EAD of USD 40.53 million. This is due to the relatively large exposure in coastal areas. The risk curve also shows the steepest incline for events beyond the 100-year return period. This is due to the heavy tail of the marginal distribution for surge-related to tropical cyclone activity. Fluvial flooding of the Buzi is more severe in terms of flood depth and extent, but as its floodplains contain less exposure, the EAD is lower, at USD 5.38 million. This is similar for fluvial flooding of the Pungwe, where the EAD is USD 3.06 million because of even less exposure. Pluvial flooding does not cause much damage for events up to a 10-year return period but rapidly increases for more extreme events. The low damage for events up to a 10-year return period is mostly related to the flood depth threshold of 15 cm (Sect. 2.5), below which we assume flooding has no impact, in combination with the infiltration capacity of the soil (Sect. 2.4).

The right panel of Fig. 8 shows the compound flood risk profiles under different assumptions of statistical dependence between the joint annual maxima. Each risk profile is based on a stochastic event set with the same number of events based on the observed co-occurrence rates but with independence, full dependence, or observed dependence between the pairs of annual maximum flood drivers. Confidence intervals between the 0.05–0.95 quantiles are derived based on 30 realizations of 1000-year simulations. We report the median risk values and show the confidence interval between brackets. We find a risk based on observed dependence of USD 58.03 (55.45–60.43) million in terms of EAD and 29 990 (28 580–31 230) people in terms of EAAP. This EAD based on observed dependence is smaller than the USD 58.28 (55.51–61.09) million EAD based on full dependence and larger than the USD 57.71 (56.00–60.01) million EAD based on independence. The relative difference in EAD based on independence and observed dependence is 0.55 %. While the difference is small and not significant based on the used confidence intervals, the results indicate that taking into account the observed dependence will likely increase flood risk because of an increase in damage from rare events (12 % increase at the 100-year return period). In general, the difference in EAD between full dependence and independence is relatively small, namely 0.98 %, as the physical interactions between flood drivers mostly occur in locations with little flood exposure. When assuming a zero lag time between flood drivers, the risk is USD 58.19 (55.61–60.59) million EAD and 30 080 (28 690–31 330) EAAP. While this assumption results in notable differences in flood hazard (Sect. 3.2), the relative change in risk is small (0.28 %), as the differences are at locations with little flood exposure.

Here, we present the effectiveness of three distinct flood risk reduction measures: spatial zoning, dry proofing of buildings, and levees. Figure 9 shows the risk in terms of EAD and EAAP for these measures in absolute values on the left y axis and as a percentage of the base risk (i.e., without any risk reduction measure) on the right y axis. Zoning is the most effective risk reduction measure, with a reduction in EAD by USD 47.71 million (79.0 %) and EAAP by ∼ 22 000 (70.4 %) people at the middle protection level (i.e., 5-year return period). However, this is also the most drastic as it entails the relocation of 31 800 people living in the 5-year floodplain. In general, zoning and dry proofing reduce risk across all return periods and act against all flood drivers, whereas levees only reduce risk below the protection level and do not act against pluvial flood drivers. In terms of EAD, the low-protection-level zoning (2-year return period) and the middle-protection-level levee (10-year return period) measures are similarly effective with a risk reduction of 67.5 % and 71.2 % respectively, while dry proofing does not reach the same effectiveness across the simulated protection levels. In terms of EAAP, the low-protection-level zoning (2-year return period), the middle-protection-level dry proofing (75 cm), and the low-protection-level levee (5-year return period) measures are similarly effective with a risk reduction of 55.7 %, 56.1 %, and 49.4 % respectively.

In this paper, we applied the framework to one location, but it has two distinct features which make it globally applicable. Firstly, the schematizations of the hydrodynamic and impact model are automated and based on global datasets only. Secondly, the flood drivers (i.e., the model boundary conditions) are derived from global models. These features make it possible to easily apply the framework at a different location.

While the use of global open-source datasets and global models comes with the large benefit of global applicability of the model setup, the performance of the model will differ from case to case based on the local quality of the global data and skill of the global models. A validation for two events based on a comparison with flood extents derived from remote sensing and sensitivity analysis of the globally applicable model has been performed in a previous study (Eilander et al., 2023a). Based on a comparison with observed flood extents from remote sensing, we found that the model skill is not very sensitive to the river depth but is most sensitive to the Manning roughness and dynamic forcing. We also investigated the sensitivity of hydrodynamic interactions between flood drivers to river and estuarine bathymetry. Based on that analysis, we found that with a deeper estuary the transition zone (i.e., where hydrodynamic interactions between flood drivers amplify water levels) in the Pungwe estuary extends further inland, but this change is relatively small compared to the extent of the total transition zone.

Finally, it should be noted that the framework allows for integration of higher-quality (local) datasets which, if available, could improve the accuracy of the model. Datasets that would improve the risk assessment are for example a local lidar-based DEM, local observations of river bathymetry, observed damage from historical flood events, and observed time series of any flood driver. Furthermore, with sufficient coverage of (new) remote sensing missions, such as ICESat-2 (Ice, Cloud and land Elevation Satellite) and SWOT (Surface Water and Ocean Topography), it will become easier to quantify uncertainties in global datasets for local flood studies and go beyond sensitivity analysis.

The change in flood risk when accounting for compound events depends not only on the dependence between drivers but also on the co-occurrence rate, duration of and time lags between drivers, and the hydrodynamics of the estuaries (Harrison et al., 2022; Serafin et al., 2019). We used the method proposed by Couasnon et al. (2022) to assess flood risk based on joint magnitude and temporal co-occurrence of annual maxima in combination with hydrodynamic simulations. Here, we assume that the dependence can be estimated from all annual maxima. In our case study, where, apart from the significant wave height, the annual maxima of most drivers are within the same season, the correlation roughly captures the variability driven by seasonal climatological patterns (see Fig. A6). In locations with fewer co-occurring annual maxima or a less distinct wet season the approach might be less applicable. Future research should investigate how the selected dependence model and sampling strategy compares to other multivariate dependence models and sampling strategies (e.g., Zheng et al., 2014; Lucey and Gallien, 2022) to find out which approach is most appropriate for different applications. Furthermore, we simulated all combinations of flood drivers based on design events with fixed duration and time lags between drivers. Accounting for these in a probabilistic manner would rapidly increase the required number of simulations. Alternatively, the selection of simulations could be informed by the multivariate probability density function by selecting only the most likely combination (Moftakhari et al., 2019) or multiple combinations based on weighted random samples (Sadegh et al., 2018) for each multivariate return period. A brute force approach, which requires fewer assumptions but generally more computational resources (Winter et al., 2020; Wu et al., 2021), could be an interesting alternative to design-event-based approaches for coastal flood risk assessments with many flood drivers.

Here, we focused on compound flood risk based on current climate conditions. However, to assess risk reduction measures, it is important to account for changes in environmental, socioeconomic, and climate conditions. Changes in climate do not only translate to changes in the magnitude of flood drivers but may also affect the dependence between flood drivers (e.g., Gori et al., 2022). At the same time socioeconomic changes will also largely affect flood risk and without action might be the largest driver of change in future flood risk (Winsemius et al., 2015; Neumann et al., 2015).