Development of a 2D hydrodynamic model for flood assessment for the lower Narmada basin, Gujarat (India)

Excess precipitation and climate change activities cause natural calamities like floods and other conditions (Sarker 2022a). Natural disasters cause innumerable damage that are vulnerable to human existence and their survival on earth (Neumayer & Plümper 2007). Floods are prominently indicated as the most severe natural calamities (Stefanidis & Stathis 2013). Natural calamities in semi-arid and arid regions cause significant injuries and pose prediction challenges due to their rapid and severe nature (Amarasinghe et al. 2020; Band et al. 2020). Every year, several parts of India are affected by floods during the monsoon.

Flood mitigation techniques such as flood forecasting and inundation modeling (Vojtek et al. 2019; Komolafe 2022), flood hazard, and risk mapping of flood-prone areas (Nghia et al. 2022; Puno et al. 2022) are required to minimize the adverse effects of floods and economic losses (Tamiru & Wagari 2022). The identification of flood-prone areas and their risk management with mitigation plans have the most effective solutions like developing flood inundation modeling (FIM) (Jacob et al. 2020; Nkwunonwo et al. 2020). FIMs are developed as a helping hand to policymakers and bureaucrats to understand better, analyze, and anticipate floods and their adverse effects. Flood early warning systems, emergency response planning, infrastructure reinforcement, and community-based disaster risk reduction strategies are crucial for flood preparedness and resilience. Governments, NGOs, and communities must work together to implement comprehensive flood management measures to protect lives, livelihoods, and property. Investing in climate change adaptation and nature-based solutions can also play a pivotal role in mitigating flood risks in the long term.

Hydrodynamic models mimic fluid movement and characterize water movement through the resolution of formulas created by physics rules (Sarker 2023). Flood models (FMs) were developed for inundation mapping, which depends on floods' spatial extent, dimensionality, and mathematical complexities (Kadam & Sen 2012). Several numerical models, such as HEC-RAS, HEC-HMS, MIKE Hydro, TUFLOW 1D, SOBEK 1D, and ISIS 1D, are used for one-dimensional (1D) flood simulation; due to some limitations, models failed to provide information on the flow field and such other important features throughout the simulation (Villazón et al. 2013). Various hydraulic models, such as HEC-RAS, FESWMS-2DH for two-dimensional (2D) surface water flow, FaSTMECH for flow and sediment movement, MIKE FLOOD, SOBEK, BreZo/HiResFlood, FLDWAV, and LISFLOOD-FP, are available for simulating water flow and flood dynamics (Praskievicz et al. 2020). These models can operate in either 1D or 2D modes. Although such models are precise and meet engineering standards by solving complex flow equations, they require extensive input, including detailed cross-sectional and topographic data, surface roughness values, and specifications for hydraulic structures.

Nowadays, HEC-RAS 2D, ISIS 2D, MIKE 21, TELECMAC 2D, and DIVAST have more attention from researchers who associated with FIMs and 2D flow simulations (Samaras et al. 2013; Ahn et al. 2019) which provides better comparative results with merits and demerits. FIMs were involved with uncertainty due to the complex and unpredictable character of floods, which marks a challenge for hydrologic and hydraulic studies at high spatiotemporal resolutions (Bales & Wagner 2009; Sarker 2022b; Sarker et al. 2023). Uncertainty, while model input parameters such as the digital elevation model (DEM), river bathymetry, Manning's roughness parameters, cross-sections, structures, predictions of discharge, and selection of the model and their conditions (El Bilali et al. 2021; AL-Hussein et al. 2022; Athira et al. 2023). DEM profiles also play a crucial role in modeling according to their temporal variation and availability as open-source data (Mangukiya & Andharia 2024). During the accurate creation of 2D FMs, land cover and land use maps play a vital role (Yalcin 2020; Puno et al. 2022), as important as determining the Manning's roughness coefficient for calibrating the model. Inaccuracies in LULC datasets and coarse-resolution DEMs, such as those from remote sensing, significantly impact hydrological parameters and flood extent predictions due to factors such as spectral confusion and elevation errors (Dube et al. 2023). These inaccuracies hinder accurate flood modeling in tools like HEC-RAS. This study is mainly associated with 2D hydrodynamic modeling for flood inundation mapping with HEC-RAS New Version 6 software developed by the Hydrologic Engineering Center's River Analysis System. Several prior studies are available on the New Versions of the HEC-RAS (Costabile et al. 2020; Mustafa & Szydłowski 2021) and their successful implementation for modeling.

The necessity for conducting 2D hydrodynamic modeling of the lower Narmada basin arises from the pressing need to mitigate recurring and devastating flood events in this region (Ilich & Manglik 2022; Mangukiya et al. 2022; Lalwani & Suryanarayana 2023; Bhargav et al. 2024). With climate change intensifying the frequency and severity of flooding, traditional flood management strategies have proven insufficient. The basin, characterized by its population, extensive agricultural areas, and complex flat topography with several meanderings, endures substantial economic losses and threats to human life during such events. Previous studies have failed to integrate high-resolution data and advanced modeling techniques necessary for precise flood risk prediction and management (Goyal et al. 2022; Gupta et al. 2023). This research bridges this gap by employing sophisticated tools for flood hazard assessment and inundation mapping, enabling the development of effective early warning systems and targeted mitigation strategies. Focusing on the adjoining tributaries of the Narmada River downstream of the Sardar Sarovar Dam at Ekta Nagar (Kevadiya), Gujarat, this study evaluates their contributions to flood inundation after 2019, following the dam's completion at its final constructional height of 138.68 m. By generating detailed depth maps, velocity distributions, and water arrival time predictions, the study provides critical, location-specific insights into flood dynamics. Ultimately, this work enhances the resilience of communities in the lower Narmada basin and offers a robust framework for flood risk management in similar vulnerable regions globally (Ilich & Manglik 2022; Mangukiya et al. 2022; Lalwani & Suryanarayana 2023; Bhargav et al. 2024).

The lower Narmada basin has seen multiple floods, especially in 1970, 1973, 1984, 1990, 1994, 2006, and 2013. Despite being in a semi-arid region, the upper mountainous parts receive significant annual precipitation (1,400–1,650 mm), resulting in downstream floods. This river's sinuosity index ranges from 1.60 to 1.69, indicating a meandering pattern with uneven changes over the year, which impacts the basin's behavior and river pattern systems (Lalwani & Suryanarayana 2023). The temperature in the bottom section of the basin varies from 10 to 40 °C depending on the season and is influenced by the neighboring sea. Agriculture cropland is the most common land use and land cover type (60%), next to barren land (11.5%) and urban areas (3%) (Thakur et al. 2021).

The data utilized for hydrodynamic models were retrieved from the open access websites and administrative departments. The SRTM (Shuttle Radar Topography Mission) DEM was acquired from the USGS portal (https://earthexplorer.usgs.gov/), with a 30-m spatial resolution. The research area and Google Maps view analysis to demonstrate the floods' significant impact in the lower Narmada region. The site visit was to check ground features while investigating using a bank discharge survey. It is one of the leading causes of the river having sufficient water beyond the validation point to flood the surrounding area. The Sardar Sarovar Narmada Nigam Limited (SSNNL) provided stage-discharge information for the Garudeshwar weir location. The past flood data for the research area was compiled from many official publications produced by the South Asian Networks on Dams, Rivers and People (SANDRP), Central Water Commission of India (CWC), and SSNNL authorities in Gandhinagar.

The data for the statistical evaluation were acquired using an integrated approach that included field surveys, prior publications, satellite imagery, digitized vector imagery, and information from administrative agencies. Table 1 summarizes the relevant facts and data needed for the analysis. Since the existing cross-sections from the field survey were limited for effective hydraulic modeling, additional cross-sections have been retrieved from an SRTM DEM. These were merged with the observed cross-sections to create connected river reaches for a hydrodynamic model. The DEM was accessible for free on the US Geological Survey's (USGS) website. The final extraction produced cross-sections of the Orsang, Karjan, and Narmada rivers, which may be modeled using the new HEC-RAS v 6.0. Flow data for catastrophic events were gathered from the SSNNL and CWC river gauge stations and used as unsteady flow parameters in the new HEC-RAS v6.0. Data on discharge and water levels were gathered from four gauges at Chanwada, Rajpipla, Garudeshwar, and Bharuch for 2020. To alleviate data scarcity, insufficient information from matching eras was created using correlation. Additional information, such as actual flood level observations, inundated zones, and damage losses, was obtained from disaster reports and related studies (Mangukiya et al. 2022). A land use and land cover map was obtained with Google Earth Engine, and the code for sentinel 1-A was developed for the respective year (Thakur et al. 2021; Pal et al. 2022; Shinde et al. 2023; Trambadia et al. 2023). Land class is classified and obtained as Waterbody, Trees, Flooded Vegetation, Agricultural Land, Built-up Area, Bare Land, Range land.

Developing a 2D hydrodynamic model for inundation and hazard mapping represents a significant advancement in flood simulation techniques. This approach builds upon the foundation of 1D HEC-RAS modeling for unsteady flow simulation, extending it to a more comprehensive 2D framework capable of detailed depth and velocity mapping across complex topographies. The HEC-RAS model, particularly in its version 6.0, employs the full momentum equation also known as the Saint Venant equation or the diffusive wave equation to describe water motion regarding flow depth and velocity. This sophisticated modeling approach also enables the generation of critical flood characteristics such as water arrival times and inundation percentages for the study area.

A key aspect of the 2D hydrodynamic model's implementation is the careful consideration of boundary conditions and computational parameters. In the case study presented, the Karjan Dam defined upstream boundary conditions, Garudeshwar weir, and Sukhi Dam, while the Golden Bridge served as the downstream boundary condition. The selection of appropriate cell sizes and corresponding time steps is crucial for accurate model simulation within the 2D flow area. To ensure model stability and accuracy, time steps were calculated according to the Courant–Friedrichs–Lewy condition (Costabile et al. 2020), adhering to HEC-RAS guidelines for computational time step determination. This methodological approach allows for a robust simulation of flood dynamics, providing high-resolution spatial and temporal data on inundation patterns, flow velocities, and flood wave propagation. Such detailed outputs are invaluable for comprehensive flood risk assessment, hydraulic structure design, and the development of effective water resource management strategies in flood-prone regions.

The findings from the 1D hydrodynamic model are crucial for informing the development of the 2D hydrodynamic model, especially regarding inundation boundaries and hydraulic characteristics. Inundation levels at cross-sections were determined using 1D models, while the extent of water coverage was assessed through 2D flow areas in the 2D models. This study aims to investigate ground conditions where tributaries meet the Narmada River, assessing the impact on inundation, time to flood, and establishing an early warning system to protect communities.

Using the 2D model, maximum water depth, velocity, current inundation status, and arrival time maps were generated based on simulation results. The simulation parameters were tailored to the 2020 event.

As with the calibration period, there were spatial variations in the performance metrics across different stations, likely due to site-specific factors influencing the model's sensitivity and accuracy.

Overall, the model's performance during both the calibration and validation periods was acceptable, with generally good to excellent NSE, R², and RMSE values across most stations. It is noteworthy that variations in the performance metrics were observed across different stations during both the validation and calibration periods. These spatial variations in model sensitivity and accuracy may be attributed to site-specific factors, such as local topography, land use characteristics, or other factors influencing the model's ability to simulate the observed data accurately.

The results of the water depth study at Golden Bridge, Bharuch, a model validation point reveal important insights into flood modeling and inundation patterns in the lower Narmada basin (see Figure 8). A graphical comparison (Figure 7 and Table 4) of modeled versus observed water surface elevation (WSE) over 6 days in August–September 2020 demonstrates the model's ability to capture general trends. Statistical analysis further supports the model's strong performance, with R² values of 0.92 for calibration and 0.77 for validation, demonstrating a high degree of correlation between modeled and observed data at the validation point (Table 5).

After the Karjan Dam releases water, the simulation indicates that water emerges near Nava Rundh in Rajpipla after 87 h, with flooding lasting between 55 and 90 h. This provides an 8-h window to alert people in the region of the Sardar Sarovar Narmada Dam's maximum or overflow dam conditions. The Narmada River takes 126 h to reach Kabirvad village and 361 h to reach Bharuch before reaching the Arabian Sea. Due to the higher coastline, transporting water to the sea takes longer in Narmada Maiya.

Water dispersed over the Kabirvad region takes 55–90 h, while the Orsang tributary takes 112 h to reach the estuary. On average, water covers 126.35 km² of the total 3,785.47 km² agricultural area under study. This map is also evaluated about evacuation time for local community with a span of 110 h in case of discharge release from the inflow point. Early warnings to local communities allow people to evacuate fields and reach safer areas, as most villages have elevated ground. The timing of water arrival from the input point is detailed in Table 7 for villages and other key locations in the study region.

The 2D hydrodynamic model simulation of the lower Narmada basin using HEC-RAS provides valuable insights into flood behavior, inundation patterns, and water arrival times. The depth map, velocity map, and water arrival map generated from the model offer critical information for decision-makers and emergency response authorities to develop effective flood mitigation strategies and early warning systems, as recommended by the World Meteorological Organization (WMO 2011) for integrated flood management. The developed model was calibrated and validated considering various locations to understand the flood behavior in the lower Narmada basin, allowing to simulate the critical details such as water depth, velocity, and arrival times, which are essential for effective flood management. Validation is performed at six key locations, namely, Sherav, Sinor, Orsang, Karjan, Kabirvad, and Narmada Maiya showed a strong correlation between observed and simulated water depths, with R² values between 0.83 and 0.99, matching or exceeding accuracy levels reported in similar studies (Pathan 2019; Yan et al. 2021; Gao et al. 2022; Mangukiya & Sharma 2022; Gangani et al. 2023; Mangukiya et al. 2024; Singhal et al. 2024). The depth map generated from the model reveals that a significant portion of the basin, approximately 326.45 km², is severely inundated, with agricultural lands being the most affected land cover class (Table 6). This finding aligns with the study by WCED (1987), Timbadiya et al. (2015), Islam et al. (2019), and Pathan et al. (2021), which highlighted the vulnerability of agricultural lands to flooding in the region. The low-lying areas of the basin, particularly regions such as Bharuch, Kabirvad, and Sinor, are prone to higher inundation levels, as evidenced by the depth map (Figure 7) and corroborated by the findings of Zischg et al. (2018), Mangukiya & Sharma (2022), and Chandole et al. (2024).

The maximum velocity map (Figure 10) indicates that the highest velocities occur near the model's inflow point, close to the Garudeshwar weir, which is consistent with the hydraulic principles of flow dynamics. However, within the Narmada region, the focus area of the study, the velocity range is relatively low, ranging from 0 to 11.75 m/s. While velocity may not be a significant constraint in this region, the potential for erosion should still be assessed and monitored, as suggested by Zhang et al. (2022) and Timbadiya & Krishnamraju 2023) in flood risk management studies. The water arrival map (Figure 11), a crucial component for developing an early warning system, provides valuable information on the time it takes for water to reach different parts of the study area. This information can aid decision-makers in assessing the effectiveness of the early warning system and facilitating the timely evacuation of communities in high-risk areas, as emphasized by Mitsopoulos et al. (2022), Šakić Trogrlić et al. (2022), and Trambadia et al. (2023). For instance, the simulation indicates that water takes approximately 126 h to reach Kabirvad village and 361 h to reach Bharuch before reaching the Arabian Sea (Table 7).

The study also highlights the importance of considering the timing of water arrival from different input points, such as dams and tributaries, as recommended by Ilich & Manglik (2022) and Yan et al. (2024) for effective flood management. For example, after the Karjan Dam releases water, it takes 87 h for the water to emerge near Nava Rundh in Rajpipla, providing an 8-h window to alert people in the region of the Sardar Sarovar Narmada Dam's maximum or overflow conditions.

Furthermore, the study reveals that water dispersal over the Kabirvad region takes 55–90 h, while the Orsang tributary takes 112 h to reach the estuary (Table 7). The study highlights the vulnerability of low-lying areas and agricultural lands to severe inundation, emphasizing the need for targeted flood management measures in these regions, as suggested by Abed-Elmdoust et al. (2016), Sarker et al. (2019), Mangukiya et al. (2024), and Yamagami & Kawasaki (2024) in their study on flood risk management in developing countries. The water arrival map provides crucial information for developing timely evacuation plans and prioritizing resources for affected communities based on the expected arrival times of floodwaters, aligning with the guidelines of the National Disaster Management Authority (NDMA 2017) for effective disaster response. This information is crucial for developing targeted evacuation strategies and prioritizing resources for affected communities, as Tang et al. (2024) highlighted in their study on flood preparedness and response.

The research contributes significantly to the global discourse on integrated flood management, as recommended by the WMO (2011). The findings support the development of evidence-based policies and strategies for flood risk reduction, which are particularly relevant for regions with similar hydrological characteristics. The study's approach to analyzing water arrival times and inundation patterns provides a replicable methodology for other river basins worldwide, supporting the United Nations Environment Programme's objectives for sustainable flood risk management.

In the context of global environmental protection, the study's findings on flood behavior and inundation patterns (Zischg et al. 2018; Mangukiya & Sharma 2022; Chandole et al. 2024) contribute to understanding how climate change affects river basin dynamics. This knowledge is crucial for developing adaptive management strategies that balance environmental protection with human development needs, particularly in regions experiencing rapid urbanization and climate change impacts. The study's emphasis on early warning systems and community preparedness aligns with international best practices for disaster risk reduction (Ilich & Manglik 2022; Yan et al. 2024), offering valuable insights for similar river basin management projects globally.

The integration of these findings with existing flood management frameworks, as guided by national authorities like NDMA (2017), demonstrates the study's practical applicability in enhancing flood resilience. This comprehensive approach to flood risk assessment and management provides a model for other regions facing similar challenges, particularly in the context of increasing climate variability and environmental change (IPCC 2023; Trambadia et al. 2023).

The 2D hydrodynamic model developed for the lower Narmada basin provides comprehensive insights into flood behavior, inundation patterns, and water propagation times. The study reveals significant flood risks, particularly to agricultural lands and low-lying areas such as Bharuch, Kabirvad, and Sinor. The model's outputs, including depth maps showing maximum inundation depths, velocity maps indicating flow dynamics, and water arrival time maps, offer critical information for flood management and early warning systems. Key results such as the 126-h travel time to Kabirvad village and the 361-h journey to Bharuch underscore the importance of timely alerts and targeted evacuation strategies. The model's depth, velocity, and water arrival time maps offer critical data for flood management and early warning systems, showing that approximately 326.45 km² of the basin faces severe inundation during major events. These findings underscore the importance of timely alerts and targeted evacuation strategies.

This research not only enhances our understanding of flood dynamics in the lower Narmada basin but also provides a robust foundation for developing comprehensive flood management plans in the context of changing climate patterns. The increasing variability in rainfall intensity and distribution, likely influenced by climate change, underscores the need for adaptive flood management strategies. By integrating climate projections and potential shifts in precipitation patterns, this model can be further refined to anticipate future flood scenarios, thereby improving long-term flood resilience in the region. The study's findings and methodologies can be valuable for similar flood-prone regions, contributing to broader efforts in flood risk reduction and climate change adaptation. The methodology demonstrated here can be valuable for similar flood-prone regions, contributing to broader efforts in flood risk reduction and climate change adaptation.

The author acknowledges the support and guidance provided by the SSNNL, CWC Tapi Circle, and all the rural people on the side of a river valley. The authors are thankful to the SSNNL and CWC for providing data related to stream discharge and water level stages at various locations along the lower Narmada basin, Gujarat (India).

All authors have read, understood, and have complied as applicable with the statement on "Ethical responsibilities of Authors" as found in the Instructions for Authors.

The corresponding author states that there is no funding for the present research on behalf of all authors.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.