In order to build a 1-D–2-D inundation model, field measurements (land level surveys, observed water levels, canal alignments and cross sections of the river and canals) and information from remote sensing (satellite imagery) were gathered (Fig. 3). The Institute of Water Modelling (IWM) of Bangladesh collected hydraulic, hydrologic and land-level data of the study area (along with other polders) in the framework of the feasibility study of the Coastal Embankment Improvement Project (CEIP). The IWM has kindly provided the measurement data for the study area.

The digital elevation model (DEM) was generated by combining the land-level surveys conducted by the IWM and FINNMAP. The land-level survey by the IWM (conducted in 2012) did not cover the whole study area. FINNMAP conducted a topographic survey of the study area in 1988 (MIWF, 1993). The differences in elevation between land surveys by IWM and FINNMAP indicated the land subsidence. An average subsidence was computed, which was used to update the elevations of the FINNMAP survey for the areas within Polder 48 for which survey data from the IWM were not available. The combined DEM has a resolution of 50 m. The same DEM was used for the simulations of the year 2100 without any corrections for further subsidence. Subsidence of the coast in the past has been reported by Brown and Nicholls (2015) and was verified with the survey data from the IWM and FINNMAP. Subsidence may continue in the future, but in the absence of scientific studies it was not considered for the future scenarios in this research. It is noteworthy that if subsidence continues, then the effect of the SLR may be increased, and the results reported in this research should be treated to some extent as underestimated values.

The bathymetry of the sea near the coast was collected from the Global Bathymetric Chart Of the Oceans (GEBCO) (Smith and Sandwell, 1997). The land use data were collected from the Ministry of Land of Bangladesh. MODIS reflectance data were used for the analysis of previous flood events. The methodology and equations suggested by Hoque et al. (2015) were used to analyse the MODIS reflectance data to determine flood extents during previous flood events. The intention was to utilize the flood extent generated from MODIS reflectance for calibration of the hydraulic model. However, no flood images from MODIS were available during the simulation period.

The river analysis tool HEC-RAS (version 5.0) from the US Army Corps of Engineers was used to develop the 1-D–2-D coupled inundation model. The flow in the river was modelled in 1-D, whereas the flow over the floodplain was modelled in 2-D. HEC-RAS 5.0 is a free tool which can simulate 1-D, 2-D and 1-D–2-D coupled models for steady and unsteady flow. The 2-D module of HEC-RAS provides the option to simulate flow of water either with the diffusion wave equation or with the full shallow water equation (St. Venant equation). The availability of irregular flexible mesh in HEC-RAS and the option for faster simulations led to the selection of HEC-RAS 5.0 as the modelling tool. Data utilized for developing the model and their sources are presented in Table 1.

The 1-D section of the model was developed and calibrated using the information shared by the IWM. The 1-D part of the developed model was calibrated for non-flood conditions as measured discharge and water level data during a cyclone event were unavailable. The model was simulated using discharge as the west boundary and water level as the east boundary conditions (Fig. 3). The calibrated 1-D model was then coupled with the 2-D model of flow over the floodplain using the DEM of the study area.

For the 1-D–2-D inundation model, a computational mesh with a flexible shape, was developed in HEC-RAS (Fig. 3). HEC-RAS generates meshes with irregular shapes. The rectangular cells of the developed 2-D mesh had a resolution of 25 m, and the non-rectangular cells had areas ranging from 625 to 1282 m2. The roughness coefficient (Manning's n varying from 0.025 to 0.05) was provided according to the land use of each cell. A sensitivity analysis as suggested by Hall et al. (2005) was carried out by varying Manning's roughness coefficient n before the calibration of the 2-D inundation model.

Building and calibrating the 1-D model was the preliminary step for developing the 1-D–2-D coupled model. The water bodies surrounding the study area were included in the 1-D model. The study area has Khaprabhanga River on the northern side and the sea on the southern side (Fig. 3). The connection of Khaprabhanga River with other rivers was not considered in the model. This was due to the fact that storm surges are observed during the pre- or post-monsoon periods, whereas fluvial floods are observed during the monsoon. Flow through rivers did not play a major role during the previous cyclones. The western and eastern side of the embankment have mangrove forests between the rivers and the embankment (Fig. 3).

For the river, the surveyed cross sections were used in the 1-D model (Fig. 4). The storm surge on the sea was conceptualized as a water surface profile in a 1-D channel on the southern side of the study area (Fig. 3). The GEBCO bathymetry (Fig. 5) was used for the channel. An alternative was to develop a 2-D model for the coastal hydrodynamics. However, as the coast of Bangladesh is flat and shallow a large area of the sea would have been included in the model. As the focus was on studying the inundation of Polder 48 and not the coast, we followed a simpler representation of the storm surges using a 1-D model. The synthetic water level data for boundaries of the model were generated by following the tidal water level pattern and the storm surge height considered for all the scenarios (Table 2). The water surface profile corresponding to each scenario (Table 2, discussed in Sect. 3.2) was considered as the profile in the 1-D model of the seaside (Fig. 6).

The dense canal network of 122 km, inside the study area, is connected with the Khaprabhanga River, which regulates the in- and outflow into the river network through a system of 13 control structures. The regulators remain closed during cyclones, making the canal network isolated. Therefore, the canal network inside the polder was not included in the 1-D model. However, the simulation of the overland flow consequent on breaching of the dike will be affected by the canal geometry, and therefore, the wider and larger canals were included in the DEM.

The geometry and propagation of the breach of the dike depend primarily on the storm surge height, the angle of landfall, soil properties and wave action. The coastal embankments of Bangladesh are usually earthen. The geometrical properties of the breaching of the dike and the time required for breaching were calculated following the instructions of the US Bureau of Reclamation. An S curve was used for breach propagation with time (Oumeraci, 2006). As the geometry of the breach is not independent, it was not considered as a parameter for scenario development.

In order to ensure model stability, a maximum spacing between the computational points was imposed and computed using Samuels' formula (1989), presented in Eq. (1): Δx≤0.15×D/S0, where Δx is the spacing between the computational points, D is the average bank full depth of the channel and S0 is the average slope of the channel. The maximum spacing between cross sections was calculated to be 300 m. The river had a steeper bed slope than the long shore slope of the sea bathymetry, requiring smaller Δx to ensure stability, and the same Δx will reduce instability of the foreshore as well.

As suggested by Fromm (1961), the Courant number was kept less than or equal to 1.0 to maintain the stability of the numerical model by controlling the time step. The Courant number was calculated using the following Eq. (2): Cr=V×Δt/Δx, where Cr is the Courant number, V is velocity, Δt is the time step and Δx is the spacing between the cross sections.

Different scenarios were developed considering the probability of the occurrence of cyclones, the angle of landfall, SLR due to climate change, diurnal, semi-diurnal and seasonal variation of tides, locations of breaching of the dike and geometrical properties of the breach.

Frequency of the cyclone. A cyclone with a 1-in-25-year return period was considered for all the scenarios as this is used as the design criteria for the dikes (BWDB, 2013). A total of 19 previous cyclones for different tidal conditions were simulated by the IWM using a 2-D model for the Bay of Bengal. A statistical analysis was conducted using these model results to generate the storm surge height corresponding to a cyclone with a 25-year return period (Islam et al., 2013). Due to a lack of data, change in the probability of the occurrence of cyclones in the future was not considered.

To identify the critical locations of breaching, results of the scenarios simulated with HEC-RAS corresponding to the three worst-case scenarios S1, S2 and S3 were compared based on the total area flooded and estimated damage due to flooding. Using the calculated damage and probability of occurrence of the event, a risk map was generated for the critical locations of the sea-facing dike. A probabilistic flood map (PFM) was generated from the flood maps of the 72 scenarios (Table 2; Output 2 in Fig. 2). As the storm surge height suggested by Islam et al. (2013) corresponds to an event with a 25-year return period, the PFM generated in this study corresponds to a 1-in-25-year return period.

A comprehensive damage calculation should involve both direct and indirect damage due to floods (Büchele et al., 2006). Direct damage is caused by physical contact of properties and human beings with floodwater. Indirect damage is caused by interruption of services, production and transportation and degradation of health due to floods. Due to a lack of data, only the direct damages to properties were calculated for the study area. The damage was considered a function of flood depth. The land use of the study area was classified by the Ministry of Land of Bangladesh as settlements, rice fields, shrimp ponds and water bodies (rivers/canals). Only the tangible damage was considered, and no environmental damage was calculated. Damage to the canal network was not considered. The damage in a flood event was calculated using Eq. (3). D=∑i=0nxi×f(xi)×Ai, where D is the total direct tangible damage in a flood event, n is the total number of computational cells within the flooded area, xi is the flood depth of cell i, f (xi) is the damage function for the land use of the flooded cell i and Ai is the area of cell i.

Depth–damage curves for different land classes for the study area were developed by adapting depth–damage curves found in the literature (Fig. 7). Reese et al. (2010) calculated flood damage as a percentage of the property value of buildings categorized based on the construction material. The buildings of the study area are primarily built of timber due to its low cost and easy availability. The depth–damage curve suggested by Reese et al. (2010) for buildings made of timber was used as a basis for generating the depth–damage curve for the settlements (residential area). Simple Action for the Environment (SAFE) carried out research on the average value of properties in rural areas of Bangladesh (SAFE, 2011). These property values were used to update the damage values used by Reese et al. (2010). Muktadir and Hasan (1985) reported that rural houses of Bangladesh are built with a large courtyard, and, as a result, houses have a lot of open and unoccupied space around buildings. The damage curve considered for the residential area was used for the damage to the buildings and not for the courtyard. Moreover, the satellite image of the area also indicated that about half of the settlement was without buildings. A satellite image from Google Earth was used for analysis. The satellite image of the area was downloaded and georeferenced. Then, the areas for buildings and open areas for households were manually calculated using ArcGIS. Therefore, 50 % of the settlement area was considered to have no damage.

The cultivation of rice involves flooding the rice field with water up to a few centimetres. However, if the height of water increases and the rice plant goes under water, then the productivity decreases. The damage to rice plants also depends upon the flood duration. If the rice plant is continuously under water for more than 2–3 days, then the damage can be up to 80 % (Chau et al., 2014). The simplified (with regards to flow velocity and flood duration) depth–damage curve for rice fields suggested by Chau et al. (2014) was used in this study (Fig. 7).

Shrimp ponds are surrounded by embankments so that there is no damage to shrimp ponds till the flood level crosses the embankment level. However, when the flood level is higher than the embankment level, shrimps escape causing a loss of the total investment. To take this into account, the investment made by farmers was assessed using a study conducted by Fatema et al. (2011). According to the study the investment for shrimp pond in the study area was about EUR 0.09 m-2. Based on the practices in the study area, the banks of the shrimp ponds were considered to be 2 m above the adjacent land, and the depth–damage curve (Fig. 7) was modified accordingly.

The damage calculations were carried out using ArcGIS. The simulated flood depth and land use for each grid cell were used as input, and the damage in each grid cell was computed using the depth–damage curve corresponding to that land use. The damage for each scenario was estimated using this procedure.

Flood risk assessment is an essential part of risk management. Spatial distribution of risk and areas requiring mitigation measures can be identified from flood risk maps. To examine the spatial variation of risk, flood risk analysis was carried out and a risk map was generated considering dike breaching at the critical locations. Van Manen and Brinkhuis (2005) and Klijn (2009), as part of the FLOODsite project, carried out research to quantify the flood risk for the polders in the Netherlands for dike failure defining the risk as a product of the probability of occurrence of the event and the consequences which was defined by Helm (1996). Equation (4) was used to calculate the risk due to flooding: R=PF×S, where R is risk, PF the probability of occurrence of the flood hazard and S the consequences.

The exceedance probability (return period) of the cyclone-induced storm surge was used as the probability of occurrence of the hazard. The probability of flooding within a protected area is not the same as the probability of the hazard and depends also upon the probability of failure of the dike. It is a difficult probability to compute as the probability of dike failure also depends upon the dike maintenance, about which information was not available. Here we have assumed that the probability of occurrence of the hazard and the probability of failure of dike are the same.

Purvis et al. (2008) stated that the risk assessment for the most probable scenario cannot take into account the impact of the scenario of low probability, stressing the necessity of a probabilistic risk analysis. The equation suggested by Purvis et al. (2008) for probabilistic risk analysis was adjusted and used for this research to calculate the probability of flooding of each cell and is presented below in Eq. (5): Pi(i=1toN)=∑j=1MFij×Pfj∑j=1MPfjandFij=1,if flooded0,if dry, where Pi is the probability of flooding at cell i; Pfj is the probability of reaching a certain storm surge level in simulation number j; Fij is the binary value indicating if the cell i is flooded or not in simulation j; and j=1,2,3,…,M, where M is the number of scenarios considered (=72) and i=1,2,3,…,N are the computational grid cells on the polder area and N is the number of cells.

Equation (5) was used in this study to calculate the probability of flooding in each cell. The probabilistic flood map (PFM) was calculated using the results of all the scenarios.

Among the simulated scenarios, the results of three worst-case scenarios (Scenario S1, S2 and S3) were compared to identify the critical location of breaching. The corresponding flood maps for the worst-case scenarios are presented in Fig. 8.

Flood extents corresponding to all different scenarios presented in Table 1 were compared to understand the effect of SLR, diurnal and seasonal tidal variation and the angle of cyclone at landfall. The flood extents of different scenarios considering the breaching in the central part of the sea-facing dike are presented in Fig. 9.

Moreover different land classes were considered while computing the flood extent for the three worst-case scenarios (Table 3). The analysis of the flood extent for different flood depths, based on the considered land uses, is presented in Fig. 10. The highest storm surge height among all the developed scenarios was 7.2 m PWD (Table 2). This storm surge height with breaching at the western, central and eastern parts of the dike was considered as the worst-case scenario and was denoted as Scenario S1, S2 and S3 respectively.

The damage due to flooding was calculated using the depth–damage curves for different land classes. The calculated damage for different land classes and damage for different flood depths corresponding to the three worst-case scenarios are presented in Table 4 and Fig. 11.

Figures 10 and 11 correspond to the flooded area and damage due to different ranges of inundation respectively. The flood area and damage were highest for inundation depths of 0.5 to 1.0 m.

The flood risk map for the scenario with the critical locations of dike breaching is presented in Fig. 12. The risk map presents the assessed risk of flooding due to breaching at critical locations of the dike. Comparison of the flooded area and damage due to flooding for the three worst-case scenarios led to the identification of Scenario S1 as the critical location of breaching. The identification of the critical location of breaching is described in Sect. 4.5.

Although the inundation maps are widely used for spatial planning and flood mitigation measures, the uncertainty of mathematical modelling affects the output of inundation maps (Alfonso et al., 2016). In order to account for uncertainty, probabilistic flood maps are suggested to be used (Domeneghetti et al., 2013). The probabilistic flood map was calculated from the inundation maps corresponding to the 72 scenarios considered in the study. Probabilistic flood maps were calculated for a threshold of flood depth greater than 0.5 m. The developed damage curves suggest that the damage for flood depth below 0.5 m is minimal. Moreover, considering the widely accepted “living with floods” philosophy in Bangladesh, a threshold of 0.5 m was adopted. This threshold was used in developing the PFMs. This threshold was not considered while the estimation of damage due to flooding was conducted. The calculated probabilistic flood map is presented in Fig. 13. The probabilistic flood map indicates the likelihood of being flooded. This will assist the planning for future land use zoning, which can be used to restrict further developments in the floodplains.

The flood extent for the simulated result of 72 scenarios was compared. Flood extent varies for different scenarios with different conditions such as the daily (high and low tide) and biweekly (spring and neap tide) tidal variation, sea level rise and the angle of landfall (Fig. 9).

Three worst-case scenarios (Scenario S1, S2 and S3) were compared by generating flood maps and calculating total flooded areas and total damages. The flood maps for Scenario S1, S2 and S3 (Fig. 8) demonstrated that a large area was flooded for all the breach locations. At least 25 % of the total area of Polder 48 was inundated for the three scenarios (Table 3). In the case of all three scenarios considered, the inundation area with flood depths from 0.5 to 1.0 m was larger than the inundation areas with other flood depths (Fig. 10). The inundation area with flood depths more than 1 m was largest for Scenario S3, due to the depressions close to the dikes (Fig. 10). The rice fields were flooded most, while the shrimp ponds were flooded least in all the scenarios (Table 3).

Flood risk was quantified with damage due to floods (negative consequences) and the probability of occurrence. The total estimated damages due to flooding for Scenario S1, S2 and S3 were EUR 10.7, 10.6 and 8.6 million, respectively (Table 4). For all the scenarios, a 1-in-25-year cyclone event was considered. The damages in the settlements were greater than other land classes for all the scenarios (Table 4). Rice fields were flooded most but they did not experience the highest damage compared to other land use classes (Tables 3 and 4). This can be explained by the high damages in settlements compared to rice fields (Table 4). The damage to crops depends on the flood depth, duration and overland flow velocity. For simplification, only the damage related to flood depth was used. As the probability of cyclones was considered the same for all the scenarios, the calculated damage governed the estimated flood risk; i.e., higher damage to the settlements translated as a higher risk of flooding. The primary economic activity of the inhabitants of the study area is farming (BBS, 2011), and most of the inhabitants are poor (with a poverty rate of 0.628) (Alamgir et al., 2018). Even though the estimated damage and risk of flooding to crops were much less compared to areas with other land uses, it will affect the people living in the study area most as they depend on the farming of rice for their livelihood (Nasreen et al., 2013). Hasan et al. (2004) found out that the dependence on fishing (in the sea) by the inhabitants of Polder 48 is increasing due to loss of crops by flood, loss of productivity, lack of jobs and poverty. Fishing in the coastal region of Bangladesh yields lower economic returns, leading to enhanced poverty (Hasan et al., 2004).

The damage was maximum for flood depths of 0.1 to 0.5 m for all the scenarios (Fig. 11). The damage due to inundation less than 0.1 m was small and insignificant. Damage is a function of flood depth, but the unit is per unit area (per m2). Therefore, if the flood extent for higher depths is lower, the damage due to flooding might be lower even though the flood damage increases significantly for inundation more than 0.5 m according to the depth–damage curves developed (Fig. 7).

Generated the PFM indicated that the areas adjacent to the dike facing the seaside have a higher probability of flooding and the rice fields are more prone to flooding (Fig. 13). Moreover, the areas protected by mangrove forest might also be flooded if the unprotected location of the dike is breached (Fig. 13), stressing the importance of proper maintenance of the dike everywhere.

The damage due to flooding was maximum for Scenario S1, which results in a higher risk of flooding for Scenario S1. The total flooded area for settlements of Scenario S1 was lower than Scenario S2 (Table 3), but the estimated damage for settlements of Scenario S1 was more than Scenario S2 (Table 4). This indicates that the settlements in Scenario S1 were exposed to greater flood depth and a higher risk of flooding than Scenario S2. Furthermore, Scenario S1 had similar total damage due to flooding, with a lower flood extent than Scenario S2 (Tables 3 and 4). Considering these facts, Scenario S1 was selected as the worst-case scenario, and breaching in the western part of the sea-facing dike was identified as the critical location for breaching during cyclones.

The scenarios with the effect of climate change (sea level rise) had more damage compared to the scenarios without climate change. Scenarios S1, S2 and S3 were associated with the highest storm surge height. With the same set of conditions without climate change (sea level rise), the storm surge height was 6.52 m PWD (Table 2). The damage corresponding to breaching of eastern, central and western locations of the dike due to the storm surge without climate change impact was 23.3 %, 20.5 % and 21.7 % lower than the damage with the climate change impact respectively. The corresponding values for the flood extent were 30.1 %, 21.67 % and 27.21 % lower than the flood extent areas with the climate change impact respectively.

The probability of occurrence of the storm surge and damage caused by inundation were taken into consideration for the risk calculation. In the case of breaching of the dike, the probability of flooding was considered the same as the probability of occurrence of storm surges. The depicted risk map (Fig. 12) shows the areas adjacent to the dike breach are at higher risk, and the risk reduces as the flood propagates towards the east.

Canals are used as a mode of transportation by the inhabitants of the area. Most of the economic activities and residential areas are near the canals. The risk analysis show that the areas at highest risk are the settlements by the canals (Fig. 12). Therefore, although canals play a crucial role in the economy and social life of the area, they also increase the risk of flooding and probability of higher damage to the adjacent areas.

Land use planning plays an important role in the reduction of vulnerability to disasters (Burby, 1998). Probabilistic flood maps (PFMs) can be used for land use planning (Alfonso et al., 2016). For better understanding of the area at risk of flooding due to the breaching of dikes, PFMs were generated for the study area (Figs. 12, 13). The results of 72 scenarios from the scenario matrix were used for the calculation of PFM. The areas adjacent to the sea dikes had a higher probability of flooding due to the breaching of dikes for both PFMs. The areas inland had a lower probability of flooding. Existing land use indicates that the areas with a lower probability of flooding are mostly rice fields (Figs. 12, 13). Land use zoning and management using the PFM can reduce the vulnerability.