A Novel Framework for Urban Flood damage Assessment

In the current study, a novel method is proposed to analyze the simultaneous impacts of non-stationarity in hydrological time series and land-use changes in urban areas to predict future floods and probable damage. For this purpose, rainfall frequency and land-use changes analyses were conducted for two time periods (first: 1979–2009 and second: 1979–2019), and the results were compared. Then, hydrologic modeling of the catchment was carried out using the HEC-HMS model, and obtained hydrographs were fed to the HEC-RAS2D model for estimating flood inundation areas. Using the financial information of assets and their damage functions, flood damages related to these two periods were evaluated through the HEC-FIA model. The results indicated that in the low return periods (e.g., 2-year flood), the damage in the second period was decreased with respect to the first one but increased for the return periods of 5 to 100 years. In the surface runoff, a 4.65% increase due to land-use change and a 12% increase due to rainfall non-stationarity signed the important role the hydrologic condition plays compared to land-use changes in flood modeling. Moreover, flood damage showed a 136% increase on average, and among the two studied factors, the non-stationarity of rainfalls is considerably more effective on flood intensification. All the points show that the studied socio-hydrological system is completely dynamic.


Introduction
Flood is one of the natural disasters that causes a lot of damage to human societies every year. Meanwhile, cities have the highest risk and probability of flood damage (Hallegatte et al., 2013;Zhang et al., 2019;Nourani et al., 2019;Wojnowska-Heciak et al., 2020;Hidayah et al., 2021;Han and Mozumder, 2022). Urbanization is a global trend and is not limited to some countries. At the beginning of the 21st century, the world's urban population has reached 50% of the world's population and is projected to exceed 61% by 2025 (Molajou et 1 3 al., 2021a). That is why studies related to urban floods are becoming more and more important, and many researchers from all over the world are focusing on it (Mark et al., 2004;Maksimović et al., 2009;Seyoum et al., 2012;Henonin et al., 2013;Moftakhari et al., 2017;Jamali et al., 2018;Tang et al., 2020;Wu and Guo, 2021).
Structural flood control measures have been one of the dominant methods of flood management for many years. However, this traditional method has been seriously questioned in recent years due to high uncertainty in determining the design flood due to various reasons such as climate change and changing rainfall patterns (Song and Chung, 2016;Arrighi and-Campo, 2019). In contrast, new methods have been introduced and developed to emphasize non-structural control measures. The most important achievement in this field has been the change of policies from crisis management to flood risk management (Söderholm et al., 2018;Uddin et al., 2020).
In recent decades, many studies have been conducted on flood risk reduction programs, especially in urban areas (Ten Veldhuis, 2011;Tsakiris, 2014;Park and Lee, 2019;Nofal et al., 2020, Singh et al., 2020Mubeen et al., 2021). It is obvious that the proper and effective planning and implementation of various programs to reduce the destructive effects of floods and preparedness against them requires evaluating the effects of this event and accurately estimating the amount of damage to different sections of society (Dutta et al., 2003;Merz et al., 2010;Hammond et al., 2015;Wedawatta et al., 2014;Chen et al., 2016;Martins et al., 2018;Jiménez-Jiménez et al., 2020). As a result, numerous flood studies focus on flood damage assessment and examine its various aspects (Freni et al., 2010;Tate et al., 2015;Tripathi et al., 2020;Wu et al., 2021).
Previous studies have shown that various parameters should be considered in urban flood modeling. One of the most important parameters, which has been emphasized in previous studies, is the non-stationarity in rainfall. The non-stationary rainfall means the probability distribution alters with alterations in time (Salas and Obeysekera, 2014;Vasiliades et al., 2015;Sharghi et al., 2018;Yang et al., 2020). The uncertainties in flood damage assessments are decreased via the interrelated factors, such as the rates of climate change and urbanization in urban flood simulations. In other words, the alternations in flood frequency could result from the combined effects of climate changes and human activities. Consequently, by considering the effects of non-stationarity in rainfalls leading to extreme urban floods, hydrological modelling would help the future hydraulic urban flood map simulations and urban flood damage assessments to have higher accuracy.
Another critical parameter in urban flood damage modeling is an urban development that should be considered in urban flood modeling and flood losses (Vogel et al., 2011, Kaspersen et al., 2017Zhou et al., 2019;Hodgkins et al., 2019). To be more specific, since land-use changes as the result of the numerous buildings and streets have altered the pattern of green spaces in urban areas and have diminished permeable surfaces, the imbalance in the natural water cycle has increased. Therefore, the time that runoff reaches the peak has decreased, in contrast to the flood volume and flood peak discharge (Lorup et al., 1998, Ranzi et al., 2002Liu et al., 2005;Nirupama and Simonovic, 2007;Saghafian et al., 2008;Suriya and Mudgal, 2012;Miller et al., 2014;Cutter et al., 2018).
According to the previous authors' studies, there has been no focus on how the combination of the factors of urban development and non-stationarity in rainfalls affects urban flood damages modeling. As a novel strategy, in the current study, it was tried to fill this gap, and the authors assessed the rate of each of these factors' effects and also both of them simultaneously on hydrological and hydraulic urban flood simulations, and economic damages of the future forecasted floods having various return periods. Besides, rainfall non-stationary conditions have been previously studied mostly using statistical analysis in the literature. It should be mentioned that the simultaneous use of statistical methods and hydrological/ hydraulic modeling has been considered in the present study. Fig. 1 The thematic of the study process.

Proposed method
The main steps of the proposed method in the present study are shown in Fig. 1.
According to Fig. 1, as the first step, the mentioned required data, such as rainfall and runoff time series, sub-basins information, and land-use maps, were collected. In the second part, the rainfall-runoff modeling was done using the HEC-HMS model, the maximum discharges were calculated, and also calibration and verification were done. In the following, the outcomes of hydrographs were applied in HEC-RAS2D, and flood maps for the target return periods were obtained. After that, as a fourth step, the flood maps obtained before were applied in HEC-FIA to serve the flood damage assessments. It should be noted that, as the final step, the results of the considered periods were compared to appraise the effects of rainfall non-stationary conditions and urban development. Furthermore, the models were selected since they could be linked with each other, helping the accuracy and the speed of modeling with high efficiency.

Study Area
The West-Main Channel catchment is located in the west and northwest of Tehran and is one of the main components of the drainage system in Tehran city (Fig. 2). It drains most of the floods in the northern, northwest, and west of Tehran. The catchment area is 433 km 2 , from which 283 km 2 is non-urban, and 150 km 2 areas are urbanized. The details of the sub-catchments, such as types of areas and time of concentration (Tc), are listed in Table 1.
The maximum and minimum altimetry in the catchment is 1420 m and 1125 m, respectively. The average annual rainfall in Tehran is about 320 mm. Streams in the north, i.e., in non-urban sub-catchments, are mainly mountainous rivers with flash flood regimes, and inside the city, they are converted to man-made concrete channels. In Fig. 2, the boundary of urban and mountainous areas is shown by a red line. The boundary of the studied catch-

Required data for the hydrological modeling
For hydrological modeling, rainfall data with one-minute time steps from 1979 to 2019 at Niavaran rainfall station (X = 543,001, Y = 3,963,312, WGS 1984 UTM Zone 39) were first collected. It is noticeable that among the existing meteorological stations in Tehran, Niavaran Station had the longest period of recorded continuous rainfalls. It should be noted that for studying the non-stationary effects, two statistical periods of 1979-2009 and 1979-2019 were considered.
For reliable estimation of rainfall quantiles, the length of the maximum annual time series should be long enough; thus, we defined only two periods over the available time period of data. Also, the land use map in 2009 was used for the first period and 2019 for the second period (i.e., the last year in each period was selected). Land use maps for the two mentioned periods accompanied with the service area of each urban channel and the map of soil hydrological groups of the region were prepared. The hydrologic model of the urban catchment was prepared based on this information.

Required data for hydraulic modeling and preparation of the flood inundation map
Required data for the hydraulic analysis includes geometric data of the channels, including the slope and shape of the channel's section in order to define reaches and channels; topographic data of streets, walkways, and urban features; Manning roughness coefficients and data associated with the existing inline structures along the main channel in the study area (USACE, 2016). A digital elevation model (DEM) with a resolution of 1 m² was prepared using Pleiades1Tri-Stereo. The hydrographs of sub-catchments for the considered floods were calculated using the calibrated HEC-HMS hydrologic model and entered into the hydraulic model along the main channel (see Fig. 2) at specific boundaries. In the pres- ent study, one input boundary at the beginning, four input boundaries along the channel, and one output boundary at the end of the channel were defined. The HEC-RAS2D hydraulic model was used in this study.

Required data to evaluate the flood damage
In order to evaluate the economic damage of floods, the HEC-FIA model was used (US Army Corps of Engineers, 2012). The digital elevation model (DEM), depth-damage curves of different land uses, the map of flood inundation depth (which is the output of the HEC-RAS2D hydraulic model), building occupancy (residential, industrial, administrative, and commercial), was introduced into the HEC-FIA model. For flood damage analysis, depthdamage curves of the buildings considering their occupancy as well as the depth-damage curves of their contents were used in this model (HEC-FIA User's Manual, 2012). The residential, commercial, administrative, and industrial occupancies were considered.

Hydrologic modeling
The HEC-HMS model was selected for hydrologic modeling, in which the Natural Resources Conservation Service (NRCS) method was used to estimate rainfall loss and excess rainfall. In this method, the physical properties of the land use are considered based on a number called curve number (CN) considering the soil characteristics as well as its moisture during rainfall, which its value can be derived from standard tables. The overall CN of a sub-catchment is obtained by averaging the curve numbers of different land uses and weighting based on the area of each land use (Chow et al., 1962). In the next step, the NRCS unit hydrograph method was used to convert excess rainfall to surface runoff. The reason was that the CN method is one of the most widely used within hydrological models because of its simplicity. Muskingum method was used to route surface hydrographs of subcatchments in the channel/rivers of the catchment (Chow et al., 1962). In order to do rainfall frequency analysis and extraction of rainfalls with different return periods, the following procedure is used for two different statistical periods : 1979-2009 and 1979-2019. Using the rainfall data of Niavaran station with one-minute time steps, the maximum annual rainfalls with a duration equal to the time of concentration of the catchment was first derived, according to recorded rainfalls between 1979 and 2019. Then, the best probabilistic distribution function was fitted to the maximum annual time series. The lognormal distribution was recognized as the appropriate function. Using the fitted distribution, floods with return periods of 2, 5, 10, 20, 25, 50, and 100 years were estimated separately for each statistical period. Finally, using the short rainfalls temporal pattern proposed by the World Meteorological Organization (World Meteorological Organization, 1969) and selection of a 5-minute time step, the rainfall depths with different return periods were distributed during the duration time, which is equal to the time of concentration of catchment, and the obtained rainfall hyetographs were introduced to the HEC-HMS model.

Flood zoning
HEC-RAS2D numerical model (USACE, 2016;) was used to provide flood zoning maps. The topographic information, including the channel cross-sections and the urban environment data as the digital elevation model (DEM), was introduced to the Land-Cover Manning friction coefficients Vegetated Open Space 0.05 Concrete Surfaces 0.018 Buildings 0.3 Roads 0.013 Table 2 Manning friction Coefficients Fig. 3 The depth-damage curve of the (a) structure (b) building contents (USACE, 2003) model. Then, the study area meshed considering the appropriate mesh dimensions (5 * 5 m 2 which was determined after sensitivity analysis). In the following, the boundary conditions of the Main Flood Channel, including the upstream, downstream, and intermediate boundary conditions along the channel, were defined. To define the Manning coefficient map, the concrete channel and flood plain were defined separately (Table 2). Eleven inline structures along the channel were also modeled. Finally, considering the unsteady flow simulation, the parameters of numerical solving were adjusted.

Estimation of the economic damage
In order to estimate the economic damage, the HEC-FIA model was employed. Data including DEM, the flood zoning maps of different floods obtained by the HEC-RAS2D model, the depth-damage curves for the main land use in the area including the residential, administrative, commercial, and industrial buildings, as well as the economic information related to the structures type and their contents in the mentioned occupancies were collected and used in modeling. The land uses located in flood inundation zone are predominantly included commercial, administrative and residential buildings. The economic values of different land uses were obtained by extensive field studies. Unfortunately, there is no depth damage available for the urban assets in Tehran at present. In the guideline of "Flood Damage Consideration" in Iran, the flood depth-damage curves of different land use in the USA (proposed by USACE, 2003) were presented and suggested for areas without information (Ministry of Energy, 2016), and here these relative curves were used. Figure 3 shows the depth-damage curves used for structures and their contents.

Calibration and Verification of the Hydrological Model
The simulated hydrographs of the HEC-HMS model were compared with the observed hydrographs in the calibration and verification stages. In order to calibrate, the parameters, including the K Muskingum parameter in the Muskingum method, the lag time, and the initial losses in the NRCS method, were considered (Table 3). The present study used statistical criteria, including the correlation coefficient (R 2 ) and the root mean squared error (RMSE), to assess modeling results.
The correlation coefficient has a range of changes between − 1 to + 1. A value of zero for this coefficient indicates that there is no relationship between observational and computational data. The closer it is to -1 or + 1, the greater the correlation between the mentioned data. The range of RMSE is (0, +∞), and the closer the values of the RMSE are to zero, the better the model's predictions fit the observations (Nourani et al., 2020;Molajou et al., 2021b).

Name of Parameter
Initial range  Table 3 The main calibrated parameters in HEC-HMS Where n is the number of data, Q 0 (i)is computed value, Q f (i) is observed data, Q 0 is the average of computed data and Q f is the average of observed data.
To calibrate and validate the model, rainfall data of five synoptic stations in Tehran for the considered events is served to the hydrological model, and the related hydrographs were extracted. Then, these hydrographs were compared with the observed ones at Jahan-Abad hydrometric station. According to the level of errors, the model parameters were calibrated to achieve the best agreement between the model hydrographs with observed ones. For the calibration of parameters, the event 8/29/2011 and for the verification, the event on 3/31/2009 were used ( Table 4).
Based on Table 4, by comparing the values of R 2 and RMSE with the results of previous studies, it can be claimed that simulations in the calibration and verification stages are in the acceptable level (Hawkins, 1993 Table 4 The statistical indices of the calibration and validation error

Estimation of rainfalls with different return periods, considering nonstationary conditions
Using the log-normal probability distribution, changes in extreme rainfalls for the 30-year period of 1979-2009 and the 40-year period of 1979-2019 were studied. The probabilistic characteristics of rainfalls in two periods were calculated and presented in Table 5. Then, the maximum rainfalls with different return periods of 2, 5, 10, 20, 25, 50, and 100 years were obtained through using the function of the log-normal distribution (see Table 6). According to Table 6, there was a decrease of 0.94% in the 2-year rainfall in the second period in comparison with the first one. It is attributable to the change in the maximum  annual rainfalls, which partly concentrated around the mean value of the time series. It has altered the frequency of maximum annual rainfalls and related probability distribution functions. For higher return periods, however, extreme data, the obtained probability distribution had higher skewness because of the longer the range of annual. Therefore, the quantiles of rainfalls and related surface runoff have increased. That is to say, by increasing the return period, the changes in the rainfall depth also increased.

Calculation of CN for sub-catchments and investigating the urban development conditions
CN for each of the sub-catchments can be calculated considering the land use types (Fig. 6). The spatial distribution of the urban development and land-use changes in terms of CN is shown in Fig. 7a (in 2009) and Fig. 7b (in 2019), comparing the land-use changes between two time periods for different sub-catchments. According to Figs. 6 and 7, CN has increased in most of the sub-catchments, due to the expansion of the impervious surface areas, as a result of urban development. It is obvious that the runoff has been increased. As can be seen in Figs. 6 and 7, sub-catchments no. w16, w17, and w20, with an average increase of about 8% in CN, showed the locations affected noticeably due to urban development.

Estimation of runoff regarding both effects of urban development and nonstationary rainfall
In order to investigate the effects of rainfall non-stationary conditions and urban development on the runoff volume, the maximum discharge at the outlet of the catchment was first  Table 7.
As it can be seen in Table 7, for floods with return periods of 5, 10, 20, 25, 50, and 100 years, considering just urban development, the maximum runoff discharge is increased by 2.4, 10.8, 3.8, 4, 4.4 and 4.7%, respectively. For the same return periods, when only the non-stationary condition is considered, the maximum runoff discharge will be increased by 6, 3.4, 15.1, 16.3, 20.2, and 23.8%, respectively. Analysis of the results shows that for a flood with a 2-year return period, consideration of rainfall non-stationarity decreases the maximum flood discharge and reduces the effect of urban development. For the rest of the return periods, the combination of these two factors enhances flood magnitudes. Moreover, the results indicate that certain change in rainfall depth leads to more amount of change in the runoff; for example, around 24% change in rainfall leads to nearly 30.5% change in the runoff for a 100-year flood. According to the outcomes shown in Table 7, for most of the return periods, non-stationarity of rainfalls is more effective than the urban development in the increase of flood maximum discharge, and both effects together implying they slightly strengthen each other on flood generation. It should be noted that the cumulative effects are expected to be more severe for fully mountainous catchments with steep rivers and the potential of creating floods, causing the importance of Table 7 The magnitude of floods with different return periods, considering the rainfall non-stationary conditions, and urban development flood forecasting and flood risk management in these areas. In the following, the outflow hydrographs of the catchment in two considered statistical periods are shown in Fig. 8. As it can be seen in Fig. 8, comparing the hydrographs indicates that by extending the return period, the difference between the maximum discharges of two periods has increased. Particularly, 100-year flood obtained by 30-year data is less than 50-year flood obtained by 40-year data period or 25-year flood in the latter is larger than 50-year in the former. This point accentuates the necessity of considering non-stationarity in rainfall time series in flood studies, such as the design of levees and the acceptable levels of related risks. For the study area, the West Main Channel (Fig. 2) was designed around 50 years ago based on a 25-year flood with a 4% risk of failure (Heydari Mofrad and Yazdi, 2022).

Flood zoning results using HEC-RAS-2D hydraulic model
In order to obtain a flood zoning map, hydrographs derived from the HEC-HMS model for each rainfall scenario were imported to the hydraulic model as boundary conditions, and the hydraulic model was performed. Flood maps are generated based on the hydrological analysis of two statistical periods, demonstrated in previous sections. The metrics of flood zones obtained by hydraulic simulation results are presented in Table 8.
The evaluation of the results of two periods in Table 8, flood zones indicates that flood zoning has been increased, and the inundation area has become wider. According to Table 8, the difference between the area of inundation zones for the return periods of 2 and 5 years in two statistical periods is small, which is attributed to the small difference between the maximum discharges in the mentioned periods.
For flood with a 10-year return period, a significant difference was observed between the inundation zones of two periods because of the change in land uses and their maximum discharge; as the result of the extension in the impervious surfaces in the second period, more runoff was generated. A similar trend was observed for the floods with return periods of 20 and 25 years, and a significant increase in the inundation zones was observed. For the floods of 50 and 100-year, in addition to the end of the channel, there was also a significant difference in the flood inundation area at the beginning of the channel between the second and first periods. Moreover, the results show that certain change in rainfall and impervious surface leads to a higher order of change in flood inundation areas. For example, in the case of a 100-year scenario, around a 15% increase in rainfall depth accompanied with the increase of impervious surface in the catchment lead to a 35% increase in a peak discharge of surface runoff which ultimately extends the flood inundation zone more than 50%. The flood inundation zone of the 100-year flood for the first and second periods is shown in Fig. 9. (a) 1979-2009 period, and (b) 1979-2019 period. According to the inundation maps for floods with various return periods, such as what is shown in Fig. 9, the difference between flood depths is fewer than what occurred in the areas of flooding. Therefore, this point should be paid attention that the flood inundation areas and their impacts on the urban environment would decrease by designing suitable inline structures playing as critical points in order to convey the volume of water in the channel in the right path.

The evaluation of economic impacts
For the evaluation of economic impacts, damage to different properties and their contents were considered. Damages of floods with different return periods for two considered periods are separately analyzed and compared (see Table 9).
As it can be seen in Table 9, the flood damage was decreased by 0.1% despite the flood inundation area was increased for the 2-year flood in the second period, showing that the effects of economic value of land use conditions plays a considerable role in flood damage assessments. For the 5-year flood, damage of the second period was increased by 9% compared to the first one due to the extension in residential areas located in the flood zone. For the 10-year flood, the damage was increased by eight times due to the significant difference between the flood inundation zones of two study periods and land uses in the area.
Furthermore, the results in Table 9 provide an insight to the authorities in Tehran city about the potential damages of floods threating the area and a basis for the assessment of various flood mitigation measures and their priorities. Tehran municipality has studied various flood mitigation measures, including enlargement of channels, bottleneck modifications, construction of additional channels, and detention ponds in various parts of the city which the study area here was also included. The analyses in this research can help to priori- tize the measures from the economical aspect and determine the cost-effective measures by the same modeling approach developed here. From the academic point of view, the results of this paper demonstrate how much the non-stationarity of rainfall and urbanization could influence on the flood regime and its consequences in a dense semi-urban area. The result indicates that the socio-hydrological system in the catchment is completely chaotic, where a 15% change in rainfall depth and less than 2% in surface land cover (in terms of CN numbers) could result in more than 50% change in flood zones and more than 100% change in flood damages.

Conclusions
The study of non-stationary effects of hydrological time series and land-use changes in urban areas is essential to predict future floods and probable damage. In this research, results showed that the non-stationarity of rainfalls led to the decrease of extreme rainfalls with low return periods and the increase of medium and high return periods. By increasing the return period of floods, the two factors of non-stationary rainfall and urban development become more important. Nevertheless, the effect of the non-stationarity of rainfalls on increasing the surface runoff was nearly three times more significant than the urban development for a mountainous-urbanized catchment. It is also worth mentioning that the studied sociohydrological system is completely dynamic. When non-stationary rainfall and urbanization are considered separately, they resulted in nearly 12% and 5% increase of surface runoff, respectively, but together they led to 18% increase in surface runoff, 38% increase of inundation areas, and 136% increase in flood damages, in average. Related to the estimated damages, in addition to inundation area, the type of land uses extended during the urban development process also affected the amount of damage such that in the case of a 10-year flood, the effect of the land use type on damage was more than the extent of the flood inundation area. Furthermore, the flooding area was more important than the flooding depth on damage values.
Funding None.
Availability of data and material Not applicable.