For most parts of the world, accurate and reliable data on local topography are hard to acquire without significant financial efforts. Data from high-resolution light detection and ranging (lidar) are freely available only for the coastal USA, coastal Australia and parts of Europe but not for the majority of developing countries or emerging economies like Vietnam (Meesuk et al., 2015). This is particularly problematic when setting up urban surface runoff models, which heavily depend on terrain elevation. For the rest of the world, the only alternative to self-conducted measurements or unvalidated commercial digital elevation models (DEMs) (Planet Observer, 2017; Takaku and Tadono, 2017; Intermap, 2018), both of which are prohibitively costly (Hawker et al., 2018), is using open-access satellite-based DEMs. An example of such open-access DEMs is the highly popular Shuttle Radar Topography Mission (SRTM) (Hu et al., 2017; Sampson et al., 2016; Jarihani et al., 2015; Rexer and Hirt, 2014), which was acquired in 2000 and covers around 99.7 % of the global populated areas (Bright et al., 2011). However, these models have substantial vertical errors and relatively coarse resolutions. Accordingly, they cannot reflect micro-topographic features or infrastructure developments in relatively flat terrain (Gallien et al., 2011; Chu and Lindenschmidt, 2017). This is particularly evident for urban settings with a significant positive bias created by the backscatter of buildings and vegetation (Becek, 2014; Shortridge and Messina, 2011; Tighe and Chamberlain, 2009; LaLonde et al., 2010), making them unsuitable to resolve terrain features that actually control flood extents and dynamics (Schumann et al., 2014). In fact, the mean error in SRTM can reach up to 3.7 m when compared to lidar (Kulp and Strauss, 2019), significantly distorting simulated flood extents for coastal areas under considerable tidal influences. Furthermore, considerable problems may arise due to differences in geodetic referencing for various DEMs, which can lead to false absolute surface elevations (Minderhoud et al., 2019). An attempt to rectify these errors was undertaken by Kulp and Strauss (2018), who developed the novel CoastalDEM by using a neural network to perform a nonlinear, non-parametric regression analysis of SRTM errors, suggesting better performance and adequacy in urban environments. Another attempt at correcting a satellite-based DEM was done by Hawker et al. (2022), who created FABDEM (Forest And Buildings removed Copernicus DEM) by removing forests and buildings from Copernicus DEM (2019) through the use of machine learning. Although CoastalDEM and FABDEM have the ability to provide better elevation accuracy in urban settings, its plausibility still needs to be checked for each individual study area. This can be done through the inspection of terrain elevation at key locations, which can be either structures (canal banks, dikes, flood protection structures) or locations where flooding is frequently reported (hotspots), all the while taking the elevation data of other satellite DEMs like those of ALOS (2016; ALOS denotes Advanced Land Observing Satellite), ASTER (Advanced Spaceborne Thermal Emission and Reflection Radiometer), SRTM and Copernicus into account. Another issue with the freely available version of CoastalDEM is its resolution of 3 arcsec, whereas other open-access satellite-based DEMs are available in a 1 arcsec resolution. A list of available DEM data sets, their resolution and providing agencies is given in Table S1 of the Supplement to this article. To utilize an open-access satellite-based DEM in reliable flood simulations, several processing steps are necessary, which, for the case of HCMC, are summarized in Fig. S2. One solution to circumvent the limitation of vertical errors can be a height correction of SRTM based on CoastalDEM. To that end, an offset map representing the difference between SRTM and CoastalDEM is created and downscaled using a surface spline interpolation. This offset map is then added to SRTM, which results in a height-corrected, higher-resolution elevation model. Depending on the use case, the resulting elevation model can be further processed through the use of a 2D median filter to smooth out the surface and reduce noise (Ansari and Buddhiraju, 2018). Furthermore, filling algorithms can be used to counteract artifactual sinks and holes with no physical meaning that typically arise in remote sensing. These sinks and holes can be closed by a variety of methods. A comprehensive list of filling algorithms can be found in the works of Lindsay (2016). It is recommended to only use these after incorporating bathymetric data (Sect. 2.1.2) into the DEM to guarantee proper water routing (i.e., from higher-lying to lower-lying cells).

In the case of HCMC, the adequacy of these five elevation models was assessed by considering their terrain elevation at the inner-city canal banks that are well-known inundation hotspots. Only CoastalDEM delivered a plausible average terrain elevation of 0 m above mean sea level (a.m.s.l.) at this location, while all others returned average terrain elevations of +6 m and higher. As this level is far above storm surge peak water heights (FIM, 2013), the comparison suggests the best accuracy for CoastalDEM. An adequate representation of the canal bank elevations is especially important for flood modeling, since riparian areas are highly exposed to flooding through storm surges and because such events cause significant backwater effects that have a crucial impact on water drainage.

To evaluate the accuracy of the end result, a statistical comparison using the mean absolute error (MAE), the mean error (ME), the root mean square error (RMSE) and the standard deviation (SD) was made between SRTM, CoastalDEM v1 and the generated DEM, on the one hand, and lidar data from 2020 at three locations across HCMC on the other (Table 1). These locations, their extents and their corresponding lidar characteristics can be found in Sect. S3 to this article. The generated DEM shows a reduced error when compared to SRTM and CoastalDEM v1 vs. the lidar data set across all three areas. Specifically, the positive bias of SRTM is eliminated, all the while halving the negative bias of CoastalDEM v1 across all presented metrics. Although the ME of the generated DEM was calculated to be -0.45 m, it still offers a substantial improvement not only over SRTM (mean error of 1.22 m) and CoastalDEM v1 (mean error of -0.91 m) but also over all other DEMs presented in Table 1. The same applies for the absolute mean error, the RMSE and the SD of the error. A detailed comparison of all DEMs in Table 1 is provided in Sect. S4.

An intrinsic drawback of satellite-based DEMs is the inability of the synthetic-aperture sensor (SAR) to determine the geometry of river beds (Farr et al., 2007). Additionally, the generated pixels include surrounding regions, resulting in greatly overestimated channel depths (Yan et al., 2015b). Therefore, bathymetric data from other sources have to be incorporated into any satellite-based DEM. The availability of reliable open-access bathymetric data, with a resolution sufficient for use in flood modeling, greatly differs between countries and is generally more difficult to acquire. In fact, the availability of such data is restricted even in many developed countries (Moramarco et al., 2019), oftentimes requiring expensive surveys that are limited to the local scale (Guan et al., 2023). To circumvent this problem, more extensive research for bathymetric data into peer-reviewed articles as well as engineering reports (grey literature) is recommended. Where such literature does not exist, river width and depth can be either approximated (Patro et al., 2009; Neal et al., 2012; Yan et al., 2015a), obtained from calculated global river width and depth databases (Yamazaki et al., 2014; Andreadis et al., 2013), or surveyed in waterways with unknown navigational depths.

In the example of HCMC, the hydrological situation is defined by two major streams (cf. Fig. S5), namely the Dong Nai River, which passes the urban districts at the eastern city boundary, and the Saigon River, which enters the urban area in the central north and flows into the larger Dong Nai in the central south. These waterbodies are fed by a complex network of artificial canals that drain the inner city. Both the natural and humanmade waterways have to be incorporated into the DEM. To that end, the bathymetry of the Dong Nai River can be approximated from a research article by Gugliotta et al. (2020), who digitized bathymetric maps originally prepared by the U.S. Army Corps of Engineers (USACE) in 1965. No open-access data exist for the Saigon River, thus requiring an assumption based on official navigation depths at different shipping terminals along the river. The Saigon bed elevation was approximated through interpolation between locations with known navigation depths (10.5 m b.m.s.l. (below m.s.l.) at Ben Nghe port, 8.5 m b.m.s.l. at Tan Thuan port, 6.5 m b.m.s.l. at Truong Tho port) (Ben Nhge Port Company Ltd., 2014; Trameco, 2014; Saigon Port Joint Stock Company, 2019) and extrapolation beyond the most upstream value with a slope of 0.1 %. This slope represents the average of the Saigon at its midsection (IGES, 2007) and was extended until the northern boundary of the model.

The results of a sensitivity analysis to quantify the impact of this assumption on the simulation results is presented in Sect. 3.2. For the inner-city canals, a survey conducted by the Japan International Cooperation Agency (JICA, 2001) determined the average depth of these canals to range between 1.82 and 3.82 m b.m.s.l. Given that neither detailed cross-sections nor profiles were available, all identified canals and channels were set to a depth of 3 m b.m.s.l. For the specific case of HCMC, the aforementioned processing steps lead to the final elevation model: a height-corrected, 2D median-filtered and filled SRTM topography with a 1 arcsec resolution that incorporates bathymetric data for all relevant waterbodies (cf. Fig. S2). Based on this model, various local flow catchments can be defined of which, however, not all contribute to pluvial flooding in the metropolitan area. Therefore, the perimeter of the flood model is set to include the 18 major urban catchments which contribute to flooding inside HCMC (Fig. 3). This allows for limiting simulations to the area of interest and hence decreasing computation times without affecting simulated flood depths. Although based on several case-specific simplifications, this methodology illustrates how free satellite-derived DEMs can readily be combined with public information on river bathymetries and finally produce a terrain model that can be used for hydro-numerical simulations.

Due to the 1 arcsec resolution, buildings and extensive vegetation that significantly reduce the available cross-section for water routing are not represented as no-flow areas in the final DEM. Instead, an equivalent Manning friction coefficient was considered in the simulated hydraulic roughness, representing an additional macro-roughness effect that would be neglected if set to the value of, for example, concrete (Chen et al., 2012; Taubenböck et al., 2009; Vojinovic and Tutulic, 2009). HCMC, for instance, is a densely built urban city, whose surface is mostly composed of asphalt or concrete with very low roughness. To allow for this effect, a roughness coefficient range of 0.05 to 0.105 s m-1/3 for urban environments has been proposed (Hejl, 1977), whereby specific values depend on the ratio of built-up to non-built-up areas. In order to determine the optimal Manning friction coefficient for the presented model (uniformly applied across the whole modeling domain), a calibration was undertaken using inundation depths and locations across HCMC provided by local partners for three severe rain events. The simulated flood depths for the respective boundary conditions (precipitation depth, P; high-water level, HWL) for inundation events on 1 July 2010, 9 July 2012 and 1 October 2012, respectively, are then compared at the observation points using the RMSE, the Nash–Sutcliffe efficiency (NSE) and the percentage bias (PBIAS) to assess the quality of the results (Table 2). Following this approach, the best results for the RMSE, NSE and PBIAS are obtained for a Manning friction coefficient of 0.10 s m-1/3, which corresponds to the higher bound of the proposed range for mimicking urban settings (Schlurmann et al., 2010). The achieved NSE values of 0.50 to 0.64 are particularly encouraging when compared to the calibration of the flood model by Le Binh et al. (2019) that achieved values of 0.51 to 0.89 using 2 m resolution lidar data. The presented model was validated, subsequently, for a Manning friction coefficient of 0.10 s m-1/3 using a fourth, independent rain event. Detailed results of this validation are presented in Sect. 3.1.

Discharge data are typically readily available, especially in the presence of reservoirs along a river. For the Saigon and the Dong Nai rivers, however, no open-access discharge data exist following the FAIR (findability, accessibility, interoperability, reuse) principles in data policy and stewardship (GO FAIR, 2016; Wilkinson et al., 2016; Mons et al., 2017), although both are regulated by upstream reservoirs. Nevertheless, singular extreme discharge rates and their respective return periods can be found in the additional material of a research article by Scussolini et al. (2017). Furthermore, long-term mean river discharges of 54 m3 s-1 for the Saigon and 890 m3 s-1 for the Dong Nai, respectively, were reported by Tran Ngoc et al. (2016), with the long-term mean river discharge of the Saigon River corresponding well to the net discharge of 30 and 65 m3 s-1 for 2017 and 2018 calculated by Camenen et al. (2021). Extreme values can be used to investigate fluvial flooding, while the average values are of use when investigating the influence of other flood drivers in isolation. Notwithstanding the indisputable temporal variability in river discharge in nature, stationary flow conditions can be assumed for the upstream boundaries of many flood models. Specifically, this holds for all settings in which other flood drivers with significantly higher rates of change exist, such as in coastal storm surge or rainfall runoff models (Sandbach et al., 2018). For the case of HCMC, it is assumed that both the lowland location of the model domain and officially operated reservoirs upstream of the Saigon and Dong Nai rivers justify this simplification.

Although an official gauge station exists at Nha Be (see location in Fig. 3), directly at the southern boundary of the HCMC model domain, the corresponding tidal time series are not publicly available. Nevertheless, data from about 300 tide gauge stations are obtainable from the public repository of the University of Hawaii Sea Level Center including a station in Vung Tau (Caldwell et al., 2015). This gauge is located around 70 km downstream of Nha Be at the South China Sea and documents the periods of 1986–2002 and 2007–2021 almost consistently. To extrapolate that time series to the southern boundary of the model, a linear increase in the water levels can be assumed: as Gugliotta et al. (2020) report, high and low water levels steadily increase with a scaling factor of 1.05 between Vung Tau and Nha Be. In order to validate this approach, official Nha Be tidal time series were compared to the publicly available Vung Tau tidal time series for the year 2016. In fact, after adjusting for a temporal phase shift of 1.8 h and adjusting the water levels by a factor of 1.05, a linear regression returns a coefficient of determination of R2=0.964 and an RMSE of 0.157 m with a p value of p<0.001. Extrapolated and observed tidal time series from Nha Be are juxtaposed in Fig. S6 in the Supplement. Especially the depicted quality estimates corroborate the findings of Gugliotta et al. (2020) in regards to the water level relation between Vung Tau and Nha Be all the while validating the proposed approach for water level extrapolation. A drawback of this approach is the inability to calculate the temporal phase shift in water stages and discharges between Vung Tau and Nha Be. The reconstructed tidal data can be analyzed probabilistically for the determination of extreme tidal water levels if needed. In the present study case, an 8 d time series representing mean tidal conditions is used as the southern boundary of the hydro-numerical model. The 8 d time frame was chosen for two purposes: first, to ensure a so-called spin-up time needed for the numerical stabilization of water levels, and, second, to allow for physically realistic routing and concentration of rainfall runoff within the model domain.

In the example of HCMC, precipitation depths with return periods of 5 years and less vary greatly in the existing literature (Khiem et al., 2017; Quân et al., 2017; Loc et al., 2015; FIM, 2013; Nhat et al., 2006). In particular, the values for a 3 h duration, 2-year return period storm range from 28 to 45 mm h-1, requiring an independent statistical analysis. Daily precipitation time series for the Tan Son Hoa weather station in central HCMC spanning from 1960 to 2012 can be obtained from the repository of the National Oceanic and Atmospheric Administration (NOAA), which publishes quality-checked precipitation data for several weather stations across the globe (NOAA, 2022). To determine the daily extreme precipitation depth for return periods of 2 years and greater, the data are fitted to a Gumbel distribution where the mean y¯n and standard deviation σn of the Gumbel variate are taken as a function of the record length, which is equal to the number of years (n=28): 1P24h,T=P‾+-loglogT/T-1-yn‾σnσ, where y‾n is 0.5343 and σn is 1.1047 for n=28 (Selaman et al., 2007). Using the Cramér–von Mises criterion, an nω2 of 0.2831 is calculated, which satisfies testing for α=0.1 (Dyck, 1980). In contrast, the probability of occurrence for return periods of 2 years and less can be calculated by ranking the precipitation depth of the raw data using (2i-1)/2m, where i is the rank of the data point and m is the total number of data points. Given the 24 h temporal resolution of the raw data, a scaling function is applied to determine the intensities for lower durations (Menabde et al., 1999): 2id,T=PD,TDdD-β, where id,T is the intensity for duration d and return period T, PD,T is the precipitation depth to be scaled, and β is the scaling factor. Based on the literature average for HCMC, β is assumed to equal 0.854 (Khiem et al., 2017; Nhat et al., 2006). The ensuing intensity–duration–frequency (IDF) curves, which reflect the precipitation depth as a function of storm return period and duration, are presented in Fig. 4.

Using official hourly precipitation data for the Tan Son Hoa weather station over the same period, the performance of the NOAA time series as well as the adequacy of the temporal scaling factor β was evaluated (Table 3). The mean value of the daily yearly maximum precipitation is 94.7 and 104.3 mm, while the standard deviation is 69.13 and 40.64 mm for the NOAA and the official hourly precipitation data, respectively. The similarities and differences between the statistical results of both time series will be further discussed in Sect. 4.

As for the creation of an adequate hyetograph, i.e., the development and representation of precipitation depth over time, numerous algorithms for the creation of a design storm are available (Balbastre-Soldevila et al., 2019). For rain events in HCMC, the linear–exponential synthetic storm of Watt et al. (1986) has been taken to create the hyetograph of a 3 h duration, 1-year return period (3h1y) rain event, since it matches the hyetograph according to decision 752/QD-TTg by the HCMC government. The simple example of deducing the river discharge, tidal water levels and precipitation hyetograph for HCMC illustrates how open data, even if not in the form of time series, can be utilized to define reasonable boundary conditions for an urban flood model.

Ultimately, the presented methodology allows for setting up a hydro-numerical flood model that simulates surface runoff in a setting where urban features cannot be fully represented, e.g., exclusion of small-scale topographic elements like flood protection structures (artificial bank elevation, flood protection walls, etc.) or underground systems like technical details of a local stormwater drainage system. Given the regional scale of many models, however, it is assumed that the absence of the latter is compensated by the hydraulic efficiency of a smoothed and filled DEM, which guarantees that water always flows towards the lowest elevations driven by gravity, effectively mirroring the functions of a stormwater drainage system. Furthermore, there is significant evidence for the ineffectiveness of the stormwater drainage system in the particular case of HCMC (Le Dung et al., 2021; Nguyen, 2016). The local drainage system is not well maintained and has limited functionality (Nguyen et al., 2019). Drainage capacity is therefore strongly hampered in the case of storm events, which justifies its exclusion from the model representing a conservative approach.

In contrast, the absence of flood protection structures in the model has a significant impact on the runoff dynamics, whereby flooding can even occur in places where no inundation is plausible under normal conditions, i.e., no rain, mean tide and mean river flow. To counteract this effect, simulated water levels are corrected by taking the results of the regular conditions as a reference. This reference was defined based on flooding threshold values determined with local partners and information from grey literature like the JICA reports (JICA, 2001) as well as different media articles, whose URLs can be found in Sect. S7 of the Supplement. Accordingly, only the additional flooding (above regular inundations) is considered the actual level of flooding when simulating events with more intense conditions. In order to isolate the impacts of additional flooding, the results of the simulation under normal conditions are then subtracted from the results of simulations under more intense conditions occurring either in combination or in isolation.

In the HCMC example, the 3 h duration, 1-year return period rain event is taken for a detailed investigation. The reason for this choice is that these yearly recurring events are not usually put into focus when conducting flood simulations, although they bring about major economic losses that are comparable to and sometimes even greater than those from extreme flood events (ADB, 2010). In turn, the results of the simulation under long-term average tidal and riverine conditions are subtracted from the results of the simulation for a 3h1y rain event with mean tide and mean river discharge. These difference plots finally reflect the extents and dynamics of typical inundations induced by the isolated 3h1y rain event. This methodological approach can be easily applied to a variety of scenarios and corresponding simulations.

In urban flood modeling, the intensity of flooding in a predefined area is typically expressed in terms of maximum simulated flood depths. Although this is a good indicator for the exposure and scale of affected people during extreme events, it fails to provide an accurate estimate of projected damages or losses. This is especially important when taking into consideration that, particularly in coastal cities, certain flood depths can persist for a much longer time than others due to tidally induced backwater effects (Andimuthu et al., 2019). This flood duration, on the other hand, is very important when events of marginal intensity, i.e., high probability of occurrence, are investigated, since it can be an indicator for the persistence of economic and social disruption (Debusscher et al., 2020; Ismail et al., 2020; Feng et al., 2017; Wagenaar et al., 2016, 2017; Shrestha et al., 2016; Koks et al., 2015; Molinari et al., 2014; Thieken et al., 2005) in residential and industrial areas (Tang et al., 1992), as well as in an agricultural context (O'Hara et al., 2019). This effect can best be expressed through the creation of a “duration over threshold” map, which depicts how long a certain flood depth is exceeded. This threshold value can be adjusted according to the local constraints. In the case of HCMC, the threshold depth was set to 0.10 m, given that this value corresponds to the minimum reported flood depth provided by local partners.

In an attempt to combine the perspectives of flood intensity and duration, a simple two-parametric but more integrative proxy, namely the “normalized flood severity index (INFS)”, is defined and tested in this study. This proxy helps to identify areas where the combination of both time-independent maximum flood depth and the duration over threshold is at its maximum and where the largest flood impacts and, accordingly, the most severe damage potential can be expected. This is particularly useful when considering the high economic damage caused by less severe but more frequent urban floods that HCMC regularly suffers from (ADB, 2010). In order to increase the robustness of the dimensionless INFS against numerical divergence and artifacts, the normalization is based on the 95th (spatial) percentile of flood depth and duration. Depending on the specific case, however, this reference for normalization may be adjusted. The INFS at each grid cell (x,y) can be expressed as follows: 3INFS(x,y)(%)=dmax(x,y)⋅Td>10cm(x,y)dmax,95%(x,y)⋅Td>10cm,95%⋅100, where dmax(x,y) refers to the maximum (temporal) simulated flood depth at the local cell with coordinates x and y and Td>10cm(x,y) referring to the scenario-based flood duration over the predefined threshold of 0.10 m.

Due to its normalization, the application of the INFS is not restricted to singular analyses but can also be considered an indicator to express changes in flood severity due to changing boundary conditions. For example, when taking climate change scenarios into account, the INFS can be computed for a particular case and then normalized according to the base case without climate change effects.