As a first step (Fig. 1), an extensive literature review was conducted to develop flood vulnerability classes and associated curves based on construction types and building materials (Table 1). An increasing number of studies investigate multi-parameter damage models (e.g. Chinh et al., 2016; Wagenaar et al., 2018), but, given the large amount of data required to apply such models, we here only consider studies on river floods that apply stage-damage curves. For the class and curve development, we use studies from different regions that have focused on the vulnerability of individual construction types or building materials and which are preferably based on actual event data. Some additional studies, often more qualitative in nature, were used to further refine the flood vulnerability classifications of the different building materials and construction types (e.g. Kappes et al., 2012; Laudan et al., 2017; Neubert et al., 2008; Zhai et al., 2005). Apart from reviewing the literature, experts with a structural engineering background were consulted to confirm the coherence of the final classification and vulnerability curves.

Table 1 summarizes the studies used to derive construction type and building-material-based vulnerability classes and curves. In all of these studies, the construction type or (dominant) building material is clearly specified, and it is either the only indicator or one of the primary indicators for the description of the flood vulnerability. Four vulnerability classes can be identified from this literature, of which each class consists of similar construction types and building materials with comparable behaviour towards flooding. The four classes are (I) non-engineered buildings built with materials such as compacted mud and adobe block or informal buildings; (II) wooden buildings; (III) unreinforced masonry/concrete buildings with walls of burnt bricks or stone or concrete blocks; and (IV) reinforced masonry/concrete and steel buildings.

From the literature described in Table 1, we identified information to develop the stage-damage curve for each of these vulnerability classes. The stage-damage curves in most of the studies are concave, increasing steeply at low water depths (especially for the buildings made with more vulnerable materials), and with a decreasing slope at higher water depths. This overall concave shape was differentiated into curves for each of the four vulnerability classes, shown in Fig. 2, using information on threshold levels (e.g. the water depth at which most damage was incurred) from the studies in Table 1. We distinguish curves that go up to 2.5 m and up to 5 m (for buildings with one and two floors), as flood levels rarely reach higher levels. Housing built through informal channels dominates in Africa (World Bank, 2015), and self-constructed buildings using inexpensive materials and traditional manufacturing techniques are still very common (Alagbe and Opoko, 2013; Collier and Venables, 2015). Buildings of class I and II belong to this group and are assumed to be one floor only, as multiple-storey buildings would require higher quality materials and hiring a professional construction crew. The four vulnerability classes are described below:

Class I consists of non-engineered buildings built with materials such as compacted mud, (non-cemented) adobe blocks, and other traditional materials found in the natural environment or informal buildings (often using natural or scrap materials for the walls and roof covers). Buildings in this class can disintegrate and collapse easily when impacted by flood waters and thus are the most vulnerable to flooding. Literature shows that mud walls can collapse when flooded by about a metre of water (Maiti, 2007), and submersion tests illustrate that most adobe bricks completely dissolve when submerged for 24 h (Chen, 2009). Depending on the material mixture and mortar, the stability of these buildings can be increased, for example by adding cement. However, with the high level of the cement prices in Africa (Schmidt et al., 2012) this is rather a consideration for class I buildings in other regions. Buildings of class I are assumed to be one floor only.

In step 2 (Fig. 1), we reclassify the objects identified in the ImageCat database into the four vulnerability classes and distinguish between urban and rural areas. The exposure data developed by ImageCat are available on a 15′′×15′′ grid for several African countries. Each grid cell contains building counts for different construction types, as well as the total floor area and total building value of the cell's building stock. For the building numbers the Ethiopian census data on housing units were used directly in most regions as the building stock is mostly single-family housing. The living area was gleaned from sampling building footprint data and as with structural characteristics varies by development pattern. For a predominantly commercial pattern, building stock data are adjusted with exposure derived from building footprint data. The number of floors can vary by development pattern, but for the vast number of buildings it is single storey for most of the country. For highly urbanized areas the number of stories was adjusted through expert opinion of several country-based structural engineers (Huyck and Eguchi, 2017). In total, 22 construction types are differentiated in the ImageCat data. Table 2 shows how these can be reclassified into the four vulnerability classes used in our study. Further description of the construction types can be found in Sect. S1 in the Supplement. In the Ethiopian data nine of the types from Table 2 occur.

Most large-scale flood assessments focus on urban areas due to the availability of data and high potential damage. In countries with large differences between urban and rural living standards, such as developing countries, it can be expected that the share of more vulnerable buildings (i.e. class I and II) is higher in rural areas compared to urban areas (e.g. Fiadzo, 2004). To account for these differences, we classify each cell as urban or rural. If more than 50 % of the ImageCat objects in a cell belong to vulnerability class I or II, the area is assumed to be predominantly rural.

To check the assumption that the share of class I and II buildings in developing countries is higher in rural areas compared to urban areas, we examined these shares in the PAGER dataset (Jaiswal and Wald, 2008; Jaiswal et al., 2010). PAGER is a global residential and non-residential building inventory at the country level (usually but not exclusively expressed in proportions of people living or working in particular building structure typologies in urban and rural areas respectively), which is often used in earthquake research. PAGER provides information at a country level on the construction types that make up the total urban and rural building stock, though the information quality varies between countries. First, we reclassified the PAGER construction types into the four flood vulnerability classes used in our study (see Table S1 in the Supplement). Then, we calculated the percentage of buildings in PAGER's total urban and rural building stocks that are categorized as class I and II (Fig. 3). The building stock differences between urban and rural areas can be found to a changing degree in all groups. While there is a distinct gap suggested for Africa, PAGER has to rely there on very limited information (i.e. only two of the countries differentiate between urban and rural building stock without judging information from neighbouring countries). Nevertheless, the data for urban and rural building stock distribution compared by income level also indicate these differences in the built environment. In low- and lower-middle-income countries, the percentage of buildings in class I and II is indeed much higher in rural areas (36 %) than in urban areas (10 %). These differences are far less pronounced for higher-income countries. The chosen threshold to identify rural areas in the ImageCat dataset (>50 %) is larger than the average share we find in PAGER (Fig. 3). This means that cells identified as rural using the ImageCat data information about the built environment with the chosen threshold are quite likely to indeed be rural.

In remote sensing or land-use studies, accuracy assessments determine a process' accomplishment of classifying an image (e.g. satellite data, aerial photos). Such an assessment requires reference values that represent the ground truth of the region of interest. Preferably these values are from ground-collected data or hand-labelled high-resolution imagery validated by multiple interpreters (e.g. Goldblatt et al., 2018; Miyazaki et al., 2011). With these options out of the scope of this study, we examine the similarity between existing land-use products and classified areas in our approach. Compared to a strict accuracy assessment this holds the limitation of comparing already classified products. However, by benchmarking the classified ImageCat data against established and recently published products, we provide an assessment of how well areas are identified in comparison. To this end, we reviewed the quality of the urban–rural ImageCat map by visual comparison with satellite imagery and by overlap with other classification products, visually and by quantifying the agreement between classified areas of the ImageCat data and other products (Sect. 3.1). Two comparisons are made, one for urban and rural areas and one only for urban areas. Similar to an accuracy assessment, we express the performance of this overlap by calculating common comparison metrics from a confusion matrix such as overall accuracy, the kappa coefficient, and producer's and user's accuracy for the sampling cells as described in Fig. S1 in the Supplement. Overall accuracy and the kappa coefficient are metrics indicating the general agreement between the reference and comparison dataset. The latter two refer to the accuracy of individual classes of which the producer's accuracy describes the probability that, for example, an urban pixel is correctly classified and the user's accuracy that a pixel classified as urban is actually urban.

For Ethiopia, the comparison maps are from several global land-use datasets as there are no other maps on a national scale available for the country. For the reference map, the ImageCat data are assigned the reference categories urban, rural, and other land use for cells outside of settlements. From the comparison maps, GHS-SMOD is the only other product that also considers rural settlements, allowing for a comparison of both urban and rural classifications. GHS-SMOD is a relatively new product based on the high-resolution European Joint Research Centre (JRC)'s Global Human Settlement Layer (Pesaresi and Freire, 2016). For GHS-SMOD, built-up areas are combined with population grids to differentiate between three settlement classes: urban centres, urban clusters, and rural (Pesaresi and Freire, 2016). In order to compare to the ImageCat reference, the GHS-SMOD's urban centre and cluster cells were reassigned into a single urban class and rural cells were kept as is.

More products are available that provide a classification limited to urban areas but largely overlook rural areas, such as GRUMP (CIESIN, 2011), MOD500 (Schneider et al., 2009), the Global Urban Footprint (GUF) (Esch et al., 2017), and HBASE (Global Human Built-up And Settlement Extent) (Wang et al., 2017). GRUMP and MOD500 are widely used land-cover/land-use datasets, with GRUMP being a 30′′×30′′ grid of urban extent and MOD500 based on MODIS satellite data with a 500 m × 500 m resolution. GUF represents built-up areas based on satellite imagery with a 12 m × 12 m spatial resolution. HBASE is a 30 m × 30 m Landsat-derived dataset of the extent of built-up area and settlements. All these products are used in the second comparison, in which only the ImageCat settlements classified as urban remain in the reference map and all cells outside of these settlements are reassigned to other land use. From GHS-SMOD, the urban centre and cluster cells are again combined, but rural GHS-SMOD areas are excluded in this assessment.

Both the urban–rural and the sole urban classification comparisons between the ImageCat data and the other products follow a class-defined stratified random sampling scheme, meaning that per class 10 000 sample points were randomly placed over the cells in each reference class. As the original maps do not all share a common geospatial model, they were reprojected to a 15′′×15′′ raster, using the WGS-84 datum. The results of the assessments are discussed in Sect. 3.1.

In step 3 (Fig. 1), we determine the maximum damage of buildings in each vulnerability class. For a coherent set of input values, we use depreciated country-specific structural maximum damage estimates per square metre as provided by the JRC report of Huizinga et al. (2017), in which residential construction costs are estimated per country using a non-linear relationship between construction costs and GDP per capita. This maximum damage value needs to be further differentiated between the four different vulnerability classes used in our study and then multiplied by an estimate of the building footprint area per cell. This is achieved by applying the following formula for each cell: 1Di=∑1kS⋅Nk,i⋅Ak,i⋅Fk, where Di is total structural maximum damage in a given cell (i); S is structural maximum damage per square metre in Ethiopia; N is the number of buildings belonging to vulnerability class k and cell i; A is the object area, meaning the building footprint for each vulnerability class k and cell i; and F is the maximum damage adjustment factor for vulnerability class k.

The factors A and F are derived as follows.

Building footprint area (A). As data on the footprint of different building types are not directly available, we estimated these based on floor area and number of floors derived from the ImageCat data. ImageCat provides estimates of floor areas for each construction type, based on sampling of building footprints, OpenStreetMap data, interviews with local contractors and experts, and literature review (Huyck and Eguchi, 2017). The country data descriptions also provide information on the typical number of floors, based on sampling. For each construction type, we divided the average floor area from the ImageCat data with the number of floors and calculated the footprint area per class (A) as the average from the construction types belonging to each class.

Our assumptions on the number of floors are derived from information in the ImageCat country data descriptions. Since buildings of construction types belonging to vulnerability class I or II rarely exceed one floor, we assumed they have one floor in both urban and rural areas. The construction of class III and IV buildings with more than one floor requires a higher skill level, mainly found in professional construction workers available in urban areas. Considering these characteristics, most class III buildings can be assumed to have one floor in rural areas. However, as most buildings in urban areas have more than one floor, we assumed class III buildings in urban areas have two floors. Class IV buildings are assumed to have multiple floors in all areas. The buildings of class III and IV with multiple floors have a much greater footprint than the one assigned to the other classes. While buildings with smaller footprints are primarily single-family residential structures or within informal settlements, the buildings of the last two classes are mainly found in urban environments, with many of them being long apartment blocks with very large building footprints leading to a larger average footprint. The resulting building footprints for Ethiopia can be seen in Table 3.

To calculate the damage, we combine the new exposure and vulnerability data described above, with existing hazard maps derived from the GLOFRIS global flood risk model (WRI, 2018). These maps show inundation extent and depth at a horizontal resolution of 30′′×30′′ for different return periods for which per cell a Gumbel distribution was fitted to a time series of annual maximum flood volume extracted from simulated daily flood volumes (Ward et al., 2013). Details of the original model setup of GLOFRIS are described in Ward et al. (2013) and Winsemius et al. (2013). The maps used in this study are those developed for the current time period in Winsemius et al. (2015), which have been further benchmarked against observations and high-resolution local models in Ward et al. (2017). In doing so, we estimate damage for the return periods 2, 5, 10, 25, 50, 100, 250, 500 and 1000 years. The inundation associated with each return period is assumed to occur everywhere simultaneously. Therefore the inundation maps are not presenting single events but country-wide probabilistic maps for the return periods. We expressed flood risk using the commonly used metric of expected annual damage (EAD). This is estimated as the integral of the flood damage curve over all exceedance probabilities (e.g. Ward et al., 2013). A source of uncertainty in flood risk assessment is the level of incorporated flood protection. Here, we use the modelled protection standard for Ethiopia taken from the FLOPROS database, a global database of flood protection standards developed by Scussolini et al. (2016), namely 2 years.

The results of our classification of ImageCat cells for Ethiopia into urban or rural are shown in Table 5, along with summaries of data from other data sources. For rural areas, our result (7.2 %) is similar to that of GHS-SMOD (6.4 %), which is the only other data source among the products that has a specific value for rural areas. The area in Ethiopia categorized as urban or built-up is relatively low in all data sources and is in accordance with Ethiopia being one of the least urbanized countries in Sub-Saharan Africa, with the share of urban population being according to Schmidt and Kedir (2009) only between 11 % and 16 %, or according to more recent data from the World Bank (2016) at about 20 %.

Modelled flood damage for the different return periods and risk for urban and rural areas are shown in Fig. 5. To calculate the overall risk in the country, these simulation are based on probabilistic maps for which inundation associated with 2, 5, 10, 25, 50, 100, 250, 500, or 1000-year return period respectively occurs simultaneously in all flood-affected cells. For 2-year return periods the damage is always zero as it is assumed that these floods would not cause overbank flooding. As can be expected, the damage in urban areas is higher, as it is a more densely concentrated built-up environment and the value of the buildings is higher. On the other hand, the majority of exposed buildings are in rural areas. To illustrate, about 88 000 buildings in urban areas of Ethiopia are exposed to a flood of a 100-year return period, compared to more than 4 times as many rural buildings. Furthermore, we can see that a large amount of damage already occurs for higher-probability flooding; for example for the 25-year return period country-wide flooding, rural damage already amounts to over USD 200 million, and the damage amounts to over USD 700 million in urban areas.

Table 7 shows the EAD for the different vulnerability classes in urban and rural areas. These results show that most of the damage in rural areas results from damage to buildings of class I, which are buildings with the highest vulnerability. In urban areas, the largest share of the damage results from damage to buildings of class IV; these are the buildings with the highest exposed values. In addition, this class also makes up a large share of the exposed urban buildings, about 57 000 for a flood of a 100-year return period, which is more than twice as many buildings of class III. In total more than 464 000 buildings are simulated to be affected for flooding with this return period, but most are in rural areas with the majority belonging to class I (58.3 %) (class II 14.6 %, class III 8.1 %).

The overall flood risk in Ethiopia (i.e. expected annual damage, EAD) is about USD 213.2 million per year; 78 % of the total EAD is in urban areas. Whilst the rural EAD is below the EAD in urban areas, it is still high in absolute terms (USD 46.7 million per year). This demonstrates that neglecting damage to rural buildings in large-scale assessments may lead to a severe underestimation of total damage values. Furthermore, the flood damage in urban and rural areas has to be considered in the context of the coping capacity of the population in the respective areas. The flood vulnerability of people below the poverty line is higher, as a larger proportion of their wealth could be affected during a flood event (Winsemius et al., 2018). While this is also true for the urban poor, the livelihoods of rural people are more susceptible where services and infrastructure are limited (Komi et al., 2016).

Compared to a traditional land-use-based model, the total simulated damage in our approach is somewhat higher but similar in magnitude. For example, the new version of the GLOFRIS model used for the Aqueduct Global Flood Analyzer tool (WRI, 2018) applies the same inundation data as used in this study but follows the common approach of using land-use-based exposure and vulnerability data, resulting in EAD for Ethiopia of USD 182 million per year. The results from our approach contain much more detail on the exposed elements and their vulnerability and allow us to examine damage in urban and rural areas. Damage in urban and rural areas cannot be distinguished in GLOFRIS as it uses HYDE data (Klein Goldewijk et al., 2011) to represent exposure, which represents the urban built-up fraction per grid cell. Moreover, Fig. 6 compares the land-use exposure map using classified ImageCat data and HYDE for the example of Addis Ababa. As for the rest of the country, it demonstrates that datasets like the ImageCat exposure data can provide more spatial detail than the commonly used exposure maps such as HYDE used in land-use-based flood risk models. Settlement extent and outlines are more distinctive, resulting in an overall better representation of affected settlement areas in the risk assessment of our approach.

Further risk comparison as well as flood protection influence can be found in Sect. S2.

Given the uncertainty in the input datasets and methods used in our approach, we perform a one-at-a-time sensitivity analysis to assess how the simulated EAD is affected by our assumptions on the (a) structural maximum damage values, (b) threshold used in the urban/rural classification, (c) object area, and (d) stage-damage curves.

To assess the sensitivity of the results to the assumed values for maximum damage, we used the 90 % confidence interval of estimated construction costs for residential buildings reported by Huizinga et al. (2017). These state that construction costs can be between 28 % lower and 53 % higher than the estimates used in this paper. For sensitivity to the threshold used in the urban/rural classification, we used thresholds of 20 % and 80 % for classifying urban areas, instead of the 50 % used in the earlier analysis. Object areas can be very diverse between and within countries and depend on the characteristics of the housing market. For example, the Centre for Affordable Housing Finance in Africa's yearbooks include some indication on the average house size and price per country. However, the sample sizes used for example are very small, and the average value covers only the minimum size that formal developers in urban areas are prepared to build, therefore neglecting self-built houses. Furthermore, no differentiation between building types or constructions is given (CAHF, 2017). For the sensitivity analysis, instead of calculating the footprint areas from average floor areas across the construction types per vulnerability class, we used the most frequent floor area size per type in the ImageCat data. The building footprint sizes most affected by this are those for classes II and III (see Table S5), as the size decreased by 5 to 11 m2. The stage-damage curves in this study show a wide range of vulnerability (see Fig. 2). Nonetheless, this as well as a comparable shape can also be found in the identified residential curves for different continents by Huizinga et al. (2017) as for example their damage degrees at 1 m range between 38 % to 71 %. While our vulnerability functions show high degrees of damage particularly for class I and II (mud/adobe and wooden buildings), other functions that consider building structure such as in the CAPRA project (CAPRA, 2012; Wright, 2016) display similar behaviour for these types of buildings. The sensitivity regarding the vulnerability curves is analysed by applying like most traditional flood risk models only one vulnerability curve, thus neglecting the differentiation our model makes toward material-based vulnerability. To this end, we selected the residential stage-damage curve used in GLOFRIS, for which the degree of damage progresses slightly below the class III one-floor curve.

Results of the sensitivity analysis are summarized in Table 8. Clearly, the flood risk estimate is very sensitive to the applied maximum damage values, as the EAD scales linearly with maximum damage changes. The results also show the EAD to be sensitive to the applied vulnerability curve. Using the single curve from GLOFRIS leads to a higher total estimate of risk by 41 %. Therefore, the estimation of maximum damage values and improved representation of vulnerability are important considerations for large-scale flood risk modelling. Our approach improves the incorporation of vulnerability in the risk assessment by differentiating a built environment into classes that characterize the vulnerability of a building stock even on large scales. The EAD is very insensitive to the threshold used in the urban/rural classification. Even with the wide range of thresholds used in the sensitivity analysis, influence on the urban–rural distribution is minimal, confirming that the urban and rural built environment in Ethiopia is very distinct in terms of what materials and construction types are applied. Nonetheless, as previously discussed in Sect. 3.1, exposure of an area can vary depending on the applied dataset. Using ImageCat data, over half of the construction types in Ethiopia belong to class I, and about 14 % to each of the other classes (see Table 9). However, according to data from the last census in Ethiopia from 2007, 73.9 % of all housing units in Ethiopia have been assigned the wood and mud wall material, with 80 % of the urban units and 72.5 % of rural units, whereas a large share of rural units were built with wood (and thatch) walls (15.5 %). Compared to the ImageCat data, the Ethiopian building stock appears to be less diverse and shows a different distribution of urban and rural constructions, which is also affected by the applied definition of urban in the census. Since the 2007 census, Ethiopia has experienced considerable economic growth that appears to coincide with growth in the Ethiopian construction industry (World Bank, 2019). Furthermore, census data are aggregated to administrative levels and thus cannot be applied in the approach developed in this paper, for which an object-based dataset is required that is comparable between countries, such as the ImageCat data. With different methodologies in exposure datasets, future research should explore how flood risk assessments that are based on building-material-based vulnerability are affected by the applied building stock dataset and their different scales. In our sensitivity analysis, the assumptions made on the object areas have little influence on the EAD, with overall slightly lower EAD when using alternative footprint sizes. Even though the effect of the object areas is small, it must be noted that these are estimated sizes and in reality building layouts are very diverse.