Assessing flood risk at the global scale: model setup, results, and sensitivity

We simulated daily discharges and flood volumes (0.5° × 0.5°) using the global hydrological model PCR-GLOBWB (Van Beek and Bierkens 2009, Van Beek et al 2011), and its extension for dynamic routing, DynRout (PCR-GLOBWB-DynRout). Discharge arises from flood-wave propagation; in each cell the associated flood volume is stored in the channel or on the floodplain in case of overbank flooding. The suitability of these models is discussed in Winsemius et al (2013). In brief, the model runs on a daily time-step, which is sufficiently short for runoff generation and flood propagation. It is also capable of using a radiation-based potential evapotranspiration scheme. Two other important features are that the runoff scheme resolves infiltration excess as a non-linear function of soil moisture; and the routing differentiates river flow from overbank flow dynamically.

The models were forced by meteorological fields (precipitation, temperature, radiation) for 1958–2000 from the EU-WATCH project (Weedon et al 2011). The WATCH forcing data (WFD) were derived from the ERA-40 reanalysis product (Uppala et al 2006) via sequential interpolation to a horizontal resolution of 0.5° × 0.5°, with elevation corrections and monthly-scale adjustments of daily values to reflect CRU (temperature and cloud-cover) and GPCC (precipitation) monthly observations. They were also combined with new corrections for varying atmospheric aerosol-loading and separate precipitation gauge corrections. Specifically, we used the following datasets: air temperature, rainfall and snow (monthly bias-corrected by GPCC rainfall), and the Penman–Monteith based potential evaporation estimates. We aggregated all fields to daily values. Although WFD are available for 1901–2000, the pre-1958 dataset was developed by reordering the data for the later 1958–2000 period, prior to bias correction. Hence, we chose to use the later period, which represents actual years.

In Winsemius et al (2013), a 30-year time-series of daily flood volumes was used to derive the maximum flood volume per grid-cell, which was assumed to represent a 30-year return-period. In the current paper, we developed inundation maps for different return-periods based on the Gumbel distribution. From the daily flood volume time-series, we extracted an annual time-series of maximum flood volumes for hydrological years 1958–2000.⁷ For each cell, we then fit a Gumbel distribution through this time-series, based on non-zero data (extracting Gumbel parameters for the best-fit and the 5 and 95% confidence limits). For cells in which zero flood volume was simulated in one or more years, we also calculated the exceedance probability of zero flood volume. These Gumbel parameters were used to calculate flood volumes per grid-cell for selected return-periods (2, 5, 10, 25, 50, 100, 250, and 1000 years). Flood volumes were calculated conditional to the exceedance probability of zero flood volume. For those cells where fewer than five non-zero data points were available, flood volume was assumed to be zero.

The following step is the conversion of the coarse resolution flood volumes into high resolution (30'' × 30'') hazard maps showing inundation depths.

This is carried out using the GLOFRIS downscaling module described in Winsemius et al (2013). In brief, the module includes a high resolution digital elevation model (30'' × 30'') and a map of river cells at the same resolution. For each 0.5° × 0.5° grid-cell, the module iteratively imposes water levels, in steps of 10 cm, above the elevation of each river-cell in the 30'' × 30'' grid. It then evaluates which upstream connected cells on the high resolution grid have an elevation lower than the imposed water level in the river channel. These cells receive a layer of flood water, equal to the water level minus the elevation of the cell being considered. This process is iterated (with steps of 10 cm) until the flood volume generated for the cell in the low resolution model (0.5° × 0.5°) has been depleted.

We assumed that flood volumes with 2-year return-period would not lead to overbank flooding (Dunne and Leopold (1978) estimate bankfull discharge to have an average return-period of about 1.5 years). Hence, this flood volume is first subtracted from the flood volumes for the different return-periods (5, 10, 25 year, etc), before the inundation downscaling is carried out. In practice, this means that any systematic overestimation of 2-year flood volume (whether that be related to the input climate data, hydrological–hydraulic modelling, or the use of extreme value statistics) is subtracted from the flood volumes for all return-periods.

We have developed a flood impact module that estimates impacts per 30'' × 30'' grid-cell for different return-periods, and aggregates to any user-defined geographical unit (e.g. countries, basins). The module has been developed to accommodate new impact indicators required by end-users. To date, the following indicators have been integrated: affected population, affected GDP, affected agricultural value, economic urban asset exposure, and urban damage (see following paragraphs).

2.4.1. Affected population and affected GDP.

2.4.2. Economic urban asset exposure.

2.4.3. Urban damage.

2.4.4. Affected agricultural value.

Each impact indicator was calculated for the following return-periods: 2, 5, 10, 25, 50, 100, 250, 500, 1000 years, whereby the impact for a 2-year event is always zero. Annual expected impacts were then calculated as the area under the exceedance probability–impact curve (risk curve) (Meyer et al 2009).

PCR-GLOBWB has been validated in past studies on discharge (Van Beek et al 2011) and GRACE satellite data of terrestrial water storage (Wada et al 2012). Generally, the model shows fair to good performance. Here, we performed further validation for extreme discharges, since these are strongly related to the flooding process. We used observed daily discharge data from the Global Runoff Data Centre¹⁰, using gauging stations with daily data availability for more than 25 years (during 1958–2000), and an upstream area exceeding 125 000 km². For these stations, and their corresponding cells in PCR-GLOBWB, we estimated discharge for different return-periods. In figure 2, we show the relative error (%) between discharge with a return-period of 10 years (Q₁₀) based on observed and modelled datasets, whereby Q₁₀ is first adjusted for the absolute difference between Q₁₀ and Q₂ (similar to the adjustment made in flood volumes)¹¹. Generally, the relative error is reasonable (between −25 and +25% for 37 of the 53 stations). However, large differences can be seen regionally. For example, in several arid regions Q₁₀ is higher in the modelled data. Here, floods are known to re-infiltrate or evaporate from large wetlands such as the inner Niger Delta (Liersch et al 2012) and the Barotse floodplains and Kafue wetlands in the Zambezi (Winsemius et al 2006). Another example is regions where large amounts of water are extracted through reservoir control (e.g. Murray–Darling; see supplementary information 2, available at stacks.iop.org/ERL/8/044019/mmedia). To date, these processes have not been accounted for in our model cascade. In supplementary information 2 we show the Gumbel plots for the modelled and observed data at eight gauging stations covering a range of environmental conditions, and provide a more detailed discussion of the discharge validation results for those stations.

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We also compared our global impact results with reported fatalities and losses from Munich Re's NatCatSERVICE database (Munich Re 2013). To do this, we created inundation maps for each calendar year 1990–2000, and used these to model affected population and exposed urban assets per year. Results are shown in figure 3(a) (exposed population against recorded fatalities) and figure 3(b) (exposed urban assets against reported losses). There is a large absolute difference between these two sets of variables since, as we would expect, the majority of people affected by a flood do not suffer fatality, and not all exposed assets suffer losses. However, we demonstrate here the strong correlation between the variables over the years shown. For exposed population against fatalities, Pearson's r is 0.59, and for exposed urban assets against losses, r is 0.66 (based on de-trended data). This shows that the model cascade captures relative changes in impacts between years well.

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Reported data on global annual expected losses are not available. However, for Europe, the Association of British Insurers estimates current annual average losses from 'extreme flood events' in Europe to be $9–11.5 billion p.a.¹² (ABI 2005). Barredo (2009) examined direct economic flood losses in Europe recorded in the EM-DAT database of the Centre of Research on Epidemiology of Disasters (CRED) and Munich Re's NATHAN database, and found annual average losses of $4.1 billion p.a. A direct comparison of these estimates with our own is not straightforward for several reasons. Firstly, it is not clear exactly what loss categories are being referred to in the ABI report. Secondly, there is no definition of what are classed as 'extreme' flood events. Similarly, not all flood events are recorded in the databases. However, we here present a broad comparison with our results, which should be interpreted as an assessment of whether the modelled and reported data show damages in the same order of magnitude. If we assume a 100-year flood protection standard, which is common in Europe according to Wesselink et al (2012), our model suggests annual damages of $9.6 billion. This is within the range estimated by ABI, but higher than that of Barredo (2009). Given the large uncertainties described above, the order of magnitude of the different datasets is similar.

We also compared our simulated annual expected damages in England and Wales with estimates of Hall et al (2005), who used a more detailed country-specific assessment method. Hall et al (2005) simulated average annual damages between about $1 and 3.6 billion p.a. According to Hall et al (2006), roughly half of this relates to river flooding, i.e. $0.5–1.8 billion p.a. Floodplains in England and Wales are not protected against floods with a uniform return-period. In the Thames basin, for example, engineering schemes protect many urban areas against river floods with a return-period of 20–50 years, whilst in some areas there is little to no protection, and in some areas (e.g. London) it is significantly higher (Environment Agency 2009). This makes a direct comparison with our results difficult. However, assuming flood protection standards of 100 years and 10 years, our model simulates annual expected urban damages of ca $0.4 billion p.a. and $2.5 billion p.a. respectively, i.e. of the same order of magnitude as Hall et al (2005).

Initial results in terms of annual expected impacts are shown in table 1; note that these results assume no flood protection standards (e.g. dikes). In reality many regions are protected by infrastructural measures up to a certain design standard. Clearly, this will lead to an overestimation of impacts. In section 3.4, we provide the first assessment of the sensitivity to the assumption on flood protection standards. From hereon in, all values are shown in USD at purchasing power parity (PPP) in 2010 values.

The difference between annual expected urban damage and annual expected exposed urban assets is a factor six. Both indicators use the same input data for hazard and exposure, but the former uses a stage-damage function to represent vulnerability. As already stated, we used one stage-damage function for all countries, which is not a true representation of reality. However, it demonstrates the high sensitivity of the results to this assumption.

In figure 4, we show a sample of results spatially, in this case aggregated to the food producing units (FPUs) of IFPRI (International Food Policy Research Institute) and IWMI (International Water Management Institute) (Cai and Rosegrant 2002, Rosegrant et al 2002). Below, we briefly reflect on a number of spatial patterns. The annual expected impact results for all indicators are provided per country and per FPU in the accompanying shapefile in supplementary information 3 and 4 respectively (available at stacks.iop.org/ERL/8/044019/mmedia).

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In the left-hand panel of figure 4, values per FPU are shown as a percentage of the global total. Clear geographical differences can be seen between indicators. For example, whilst potential urban damages are highest in large parts of USA, Europe, the eastern coast of Australia, China, and Japan, a different pattern exists for affected population and affected agricultural value. In the latter two, whilst impacts are also very high in China, the percentage shares in USA and Europe are lower, whilst impacts are more highly concentrated in the Indian Subcontinent, south-eastern Asia, and parts of Africa.

In the middle panel of figure 4, annual expected impacts are shown for each FPU relative to the total population (for annual exposed population) or GDP (for other indicators) for that particular FPU. Whilst there are many regions in which impacts may be low in absolute terms, their impact on the given region may be very large. For example, whilst most FPUs in sub-Saharan Africa show low absolute impacts, there are many FPUs where the impacts are amongst the highest relative to their total population or GDP.

We assessed the sensitivity of the results to the extrapolation of flood volumes for different return-periods using the Gumbel distribution. To do this, we forced the inundation model with flood volumes obtained for the 5 and 95% confidence bounds of the Gumbel fit for different return-periods, and used the resulting inundation maps as input to the impacts module. The results are shown in figure 5, where blue lines indicate results based on the 5 and 95% confidence limits as a percentage difference compared to those based on the best-fit; this provides an illustration of the uncertainty in the extreme value statistics. Globally, the sensitivity is relatively small, with a range of ca −2 to +5% around the best-fit for exposed population, exposed GDP, and exposed agricultural value, and −5 to +10% for urban damage. The only impact indicator shown for which the depth component of the hazard map is used is the indicator urban damage. Hence, the results are more sensitive to the extrapolation of flood volumes when inundation depths are considered.

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In figure 4 (right-hand panel), we show this sensitivity per FPU, whereby the value shown per FPU is the range for the 5–95% confidence limits expressed as a percentage of the value based on the best-fit. For most regions the results are relatively insensitive, although again the results for urban damage are higher than for the other indicators. There are several FPUs (for example in North Africa, the Middle East, and around the Kalahari and Gobi deserts) that show a large sensitivity in percentage terms. However, these are FPUs in arid zones in which absolute impacts under the best-fit Gumbel parameters are very small, and where a small increase in absolute terms leads to a large increase in relative terms.

In figure 5, we show an impression of the sensitivity of the global results to the use of a climate forcing dataset that has been subjected to different processing methods. We ran the model cascade for the period 1961–1990 forced firstly with the WATCH forcing data (WFD-GPCC) described previously, and then with ERA-40 data (Uppala et al 2006), bias-corrected based on Sperna Weiland et al (2010). The latter dataset has been bias-corrected using a more simple method, and furthermore, no precipitation undercatch correction has been applied (for details of the procedure see supplementary information 5, available at stacks.iop.org/ERL/8/044019/mmedia). At the global scale, the difference in annual expected impacts between the simulations forced by the CRU-ERA40 data and the WFD-GPCC data is less than 10%. However, an analysis of the differences per FPU shows that the results are highly sensitive at this scale; these results and their discussion can be found in supplementary information 5. Briefly, they show large differences in extreme flood volumes, which appear to be linked to large differences in extreme precipitation between the two datasets. Further research is necessary to examine the influence of a larger range of climate forcing datasets on the impact results, but given the more sophisticated bias correction and the undercatch correction used to create the WFD-GPCC data, these can be assumed to provide the most reliable results.

The results above assume that all flood volumes exceeding a 2-year return-period have the potential to cause flooding, even though many areas are protected by infrastructural measures up to given design standards. Since no global database of protection standards exists, global risk estimates have not been able to incorporate this aspect, meaning that results are likely to be overestimations (in particular those related to high frequency events).

In their study of flood risk in Europe, Feyen et al (2012) accounted for flood protection by truncating the risk curve at a given exceedance probability (corresponding to an assumed protection standard), and estimating annual expected impacts as the integral of the remaining part of the curve. To assess the sensitivity of our results to the use of different protection standards, we also estimated total global impacts using this method. In figure 6, we show how annual expected urban damage decreases as the assumed protection standard increases. Clearly, flood risk estimates are highly sensitive to this parameter. For example, assuming protection standards of 5 and 100 years globally, total simulated annual expected urban damage falls by 41% and 95% respectively. We carried out the same analysis for the other impact indicators, and found very similar results; depending on the indicator, annual expected impacts fall by 48–50% and 95–97% respectively.

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Our model cascade provides a tool for assessing flood risk in terms of different impact indicators, and its relatively rapid nature allows for the calculation of impacts for many return-periods. However, we have identified several limitations to be addressed in future research. Next to improvements generic to most impact modelling frameworks (e.g. increased spatial resolution of input data, assessing the sensitivity of the results to a larger range of input data sources), we describe several of the main ones below.

Firstly, the hazard maps represent situations with no flood protection measures, whilst we have shown the results to be highly sensitive to such protection standards. Future improvements to the hydrological and hydraulic models will involve the parameterization of measures such as dikes and water retention areas. To date there is no database of such measures available at the global scale. In order to improve the model, we plan to carry out an extensive literature review of protection standards in order to derive spatially disaggregated first order estimates of protection standards at the global scale. Moreover, past research has shown that flood defence fragility (i.e. the reliability of the flood defences conditional on hydraulic loading) can be important in mediating risk (Dawson et al 2005). It would be useful to include simplified estimates of such fragility, using assumptions for broad-scale analyses such as those described in Hall et al (2005).

The modelling approach has been specifically set up to simulate large-scale river floods. To date, it does not include modules for assessing either coastal or pluvial floods, and is not able to capture local-scale flash flood events. In terms of overall risk, all of these floods are of high importance. Indeed, flash flood events often lead to loss of lives, even in areas where fatalities from large-scale river floods are low (e.g. Gaume et al 2009).

The current setup is limited in its treatment of vulnerability. The only impact indicator in the current setup for which vulnerability is explicitly considered is urban damage, and even for this indicator we have used one vulnerability function for all countries. Future model development must concentrate on identifying robust ways of modelling vulnerability at the global scale, for example using stage-damage functions such as those in the CAPRA vulnerability model¹³, and exploring the use of vulnerability indicators such as those employed by Peduzzi et al (2012), for example considering mortality as a function of total exposed population, and damage as a function of total exposed assets.

To date, we have only examined flood risk under current conditions, and not changes in risk under future scenarios. Generally, uncertainties in absolute flood risk estimates are large (Apel et al 2008, Merz et al 2010, De Moel and Aerts 2011), whilst estimates of relative changes in risk under different scenarios are more robust (e.g. Bubeck et al 2011). Given that our model cascade simulates interannual fluctuations in impacts similar to those in reported loss records, we are confident that it is a useful tool for assessing changes in global risk under future climate and socioeconomic scenarios.