Enhancing climate-resilient urban river restoration: predictive modeling of geomorphic changes

Predicting the stable cross-section of natural rivers has been the point of interest of many researchers for a long time (Francalanci et al. 2020). Rivers change their hydraulic geometry to remain stable against flow rates and sediments of the inlet and outlet. Thus, understanding hydraulic geometry is a primary engineering task for managing and organizing rivers. The hydraulic geometry of the river expresses the relationships between the channel geometry of width, average depth, velocity, longitudinal slope of the bed, and flow rate in a transverse section (local hydraulic geometry) or over an interval (intermittent hydraulic geometry) (Singh 2003; Eaton & Davidson 2013). Although river cross-sections are subjected to a wide range of flows, the shape and their geometry are generally regulated by a dominant discharge at a specified return period (Sharifi et al. 2021). The dominant discharge is used to describe the flow which itself has the main responsibility for governing the channel shape and form and is usually approximated by the discharge at bankfull or the effective discharge. Q_e is the flow that transports the maximum amount of sediment over time. Knowing the frequency of design discharges in rivers is crucial for river restoration. Changes in the river flow regime caused by climate change will alter the frequency of floods and bankfull discharge, and consequently affect the morphological and ecological functions of the river system (Eslamian 2014). Discharge indicators such as effective discharge and bankfull discharge enable hydrologists to better understand the geomorphology of rivers and the relationship between flow and sediment transport. Therefore, the most important thing for river restoration is determining the design discharge and consequently hydraulic geometry of the river (Gupta & Mesa 2014). The regime theory is used to estimate the stable geometry of river channels (Lacey 1930, 1934, 1946; Blench 1952, 1969, 1970; Lacey et al. 1958; Simons & Albertson 1960), as well as hydraulic geometry for stable river channels (Leopold & Maddock 1953; Parker 1979; Huang & Warner 1995; Huang & Nanson 1998).

In particular, Leopold & Maddock (1953) declared that the channel width, the average flow depth, and the average flow velocity are functions of the annually averaged flow discharge.

The process of widening straight channels in order to attain a stable cross-section has been simulated numerically by Pizzuto (1990), to derive the cross-sectional distribution of bed shear stresses. The channel bed topography was then derived according to the sediment flux balance equation and a heuristic bank failure law, based on exceeding the sediment repose angle. Kovacs & Parker (1994) continuously simulated the widening of a channel up to the equilibrium, without introducing any empirical bank collapse law.

Hydraulic modeling and the understanding of river processes stand as fundamental aspects of river management and restoration studies. Researchers have made significant strides in exploring various facets of river dynamics, including the pivotal impact of climate change on river systems.

Notably, Mann & Gupta (2022) conducted an insightful study titled ‘Temporal Trends of Rainfall and Temperature over Two Sub-Divisions of Western Ghats’. This research delved into the temporal trends of rainfall and temperature, providing invaluable insights into evolving climate patterns within specific regions. While their primary focus was not exclusively on rivers, such investigations contribute essential climate data that can illuminate and inform river management strategies in the face of changing environmental conditions.

In a distinct yet relevant context, Chomba et al. (2022) made significant contributions through their work on ‘Integrated Hydrologic-Hydrodynamic Inundation Modeling in a Groundwater Dependent Tropical Floodplain’. Their research underscored the intricate interplay between hydrological and hydraulic processes, emphasizing the complexity of floodplain dynamics. Such studies broaden our understanding of how rivers interact with their surrounding landscapes, particularly in flood-prone areas, and can have profound implications for effective river management and restoration practices.

Furthermore, Faye (2022) enriched the body of literature with the study titled ‘Comparative Analysis of Meteorological Drought based on the SPI and SPEI Indices’. While meteorological drought and river flow represent distinct phenomena, the comparative analysis of drought indices offers valuable perspectives on how shifting precipitation patterns might reverberate through river ecosystems and influence water availability. This holistic view is instrumental in comprehending the multifaceted impacts of climate change on river systems.

These aforementioned articles, in conjunction with existing research, underscore the multidisciplinary nature of river management and restoration. They emphasize the critical significance of considering climatic factors, hydrological processes, and hydraulic dynamics in comprehensive river restoration endeavors. These contributions collectively contribute to our broader understanding of the intricate and evolving relationship between climate change and river systems, which is of paramount importance in contemporary river management practices.

Many approaches have been proposed in the literature but still, a framework capable of explaining the stable width of urban rivers under climate change is rare. In this paper, we try to fill this gap by developing a method that predicts the stable bankfull width of urban rivers with cohesive erodible banks. In fact, one way of reducing the cost of river maintenance (dredging) and optimal use of floodplains in cities is to identify the river morphologically. This could only be achieved by understanding the river's adjustment to climate changes (Sharifi et al. 2021). Global climate change leads to alterations in rainfall patterns, especially the intensity and frequency of heavy rainfall (Steensen et al. 2022), and urban areas are now considered a vital part of the global response to climate change (World-Bank 2010; UN-Habitat 2011). Farahzad River, in Iran, is one of the urban rivers that could be used to test the theory. This article tries to find the river forming discharge and the stable design by studying the bankfull and effective discharge under climate change.

In addition, the findings of the current study indicate that the rainfall intensity under climate change is drastically increasing. Using intensity–duration–frequency (IDF) curves based on historic rainfall data may lead us to an underestimation of the stable channel geometry. Especially in cities, the highly modified environment and the lack of open spaces make it harder to apply the concept of river stable channel geometry, and it is even more difficult to apply, especially in cities that have highly modified environments with almost no open spaces. It raises doubts about the feasibility of adopting restoration approaches for urban rivers.

According to the research conducted by the authors, the need to consider climate changes in urban rivers for design purposes has been emphasized, but no practical solution to consider changes in cross-section due to climate change has been presented in the past articles, in which this research, the issue has been presented. The structure of the article is in such a way that in order to implement the presented method, a case sample of Tehran's urban river in Iran, which is located in the unmeasured basin, has been selected. Then, the runoff due to current and future rainfall is calculated and, after modeling in HEC-RAS and using geometric hydraulic methods, the average changes of cross-section in depth, and width are predicted in the future.

Estimation of design peak discharge, which has always been of paramount importance in hydrology, has been used as an indicator for water-related plans. Due to the lack of sufficient statistical data about flow type and its quantity, researchers proposed various empirical methods to determine the maximum discharge. A Fuller empirical formula, developed in the east USA, is one of them. It was developed by analyzing hundreds of flood peaks and has been used all around the world. Their coefficients are calibrated for many regions (Fuller 1914), and another method was developed for smaller basins by the US Soil Conservation Service (SCS) in 1957 which uses the daily precipitation values to calculate the peak flow rate (Gulbahar 2016).

Effective discharge plays a significant role in sediment and nutrient transport, landscape modification, and river restoration (Pradhan et al. 2021). It is the amount of flow that carries the highest sediment load over a period of 1 year (Figure 3). Therefore, by plotting a flow discharge–sediment discharge curve and frequency histogram of daily discharges with a specified class and multiplying the widths of the two curves, we get another curve representing the amount of sediment transported by each discharge. Here, the discharge matching to the maximum sediment is defined as the effective discharge (Sharifi et al. 2021).

Q_s represents the sediment transport in ton/day and Q represents the river discharge in m³/s. The coefficients a and b are constants.

The coefficients and exponents are specified for a given cross-section of a river. While these regime relationships are a response to a set of interacting factors associated with the amount of water and sediment in transport and many other factors like local vegetation, sediment texture, and regional gradient, they can simply be approximated in the form of river channels (Leopold & Maddock 1953; Parker 1979; Huang & Warner 1995; Huang & Nanson 1998). They can be demonstrated experimentally and they can be represented as b = 0.5, m = 0.2, and f = 0.3 (Schumm 1960; Ferguson 1986; Huang & Nanson 2000).

The hydrologic result of the study is the effect of climate change on peak floods for the return period. It applied to the rainfall data series under climate change conditions (Figures 4–6). Extreme events happen when we have high-intensity rainfall caused by climate change which leads to a growth in precipitation and consequently in the peak discharge.

The assessment of bankfull discharge is pivotal for understanding the river morphology and stability. The study entails cross-sectional bed shear stress plotted against increasing discharge for various reaches of the Farahzad River (Figure 7). Within this graphical representation, the maximum shear stress value signifies the reach-averaged bankfull discharge (Q^bf).

Effectively managing river ecosystems demands a thorough examination of the concept of effective discharge. To achieve this, daily discharges and sediments were meticulously aligned in an Excel dataset, with sediments on the y-axis and discharges on the x-axis. Employing regression analysis, a line was fitted to the data, yielding the equation Q_s = a·Q^b, accompanied by the calculation of the coefficients ‘a’ and ‘b’. The derived equation, Q_s = 32.613Q^2.33, offers critical insights into the relationship between sediment transport and discharge dynamics within the river (Figure 8).

A noteworthy revelation in this study is the discernible disparity between bankfull and effective discharge. In comparison to the effective discharge, bankfull discharge is found to be 28% higher in the upstream section and 22% lower in the downstream section (Figure 9). This discrepancy has been corroborated by previous research, including Goodwin (2004), who posits that such variations can provide valuable indicators of the river channel's dynamics. When the effective discharge can be comfortably contained within the active banks, it suggests the potential for river incision. Conversely, when the effective discharge surpasses the capacity of the active channel, it signifies a propensity for general deposition, marking a transformative phase in river morphology.

In line with the dynamic nature of rivers, particularly in urban settings, this study illuminates a critical facet of river behavior hydraulic geometry. Rivers, as observed, adapt by widening and increasing in velocity downstream while simultaneously reducing their depth in their quest for a stable configuration. What sets this study apart is its innovative approach, where hydraulic modeling is seamlessly integrated with climate change projections and hydrological analysis.

This integration allows us to predict the stable bankfull width of urban rivers with cohesive erodible banks under climate change scenarios as pioneering methodological innovation. The results unequivocally show a 35% increase in the width of the urban river as a consequence of the annual peak discharge (Figure 10). This finding revolutionizes our understanding of how climate change influences urban river morphology and, in turn, offers practical tools for sustainable river management.

In summary, this study not only advances our comprehension of climate change impacts on urban river systems but also introduces a groundbreaking methodological innovation for predicting river behavior under changing environmental conditions. These results are essential for river managers, urban planners, and policymakers seeking effective strategies to protect and manage urban rivers in an era of climate uncertainty.

This research has undertaken a comprehensive exploration to unravel the profound impact of climate change on the stable dimensions of urban rivers. Through meticulous analysis, including the comparison of effective and bankfull discharges and an exhaustive examination of hydraulic channel geometry, a multitude of significant findings and implications has surfaced.

Revealing climate-channel synergy: This study makes a substantial contribution by uncovering the intricate dynamics at the intersection of climate change and urban river morphology. By quantifying the effects of climate-induced perturbations, notably the intensification of high-intensity rainfall events, it introduces a groundbreaking perspective that bridges the realms of climate science and river geomorphology.

Innovative predictive methodology: A pivotal innovation presented in this research is the development of a predictive methodology to discern stable channel dimensions under climate change scenarios. This innovative approach not only enriches the scientific discourse but also equips river managers, researchers, and policymakers with a practical tool to assess and manage urban rivers in an era of climate variability and change.

Enhancing urban river restoration: The findings of this research hold immediate and far-reaching implications for urban river restoration projects. By recognizing the profound imprint of climate change on river stability parameters, such as width and depth, stakeholders can recalibrate their restoration strategies to align with evolving environmental conditions. This adaptability is pivotal for preserving and enhancing urban river ecosystems.

Ensuring resilience in a changing climate: In an era where climate change is reshaping the landscapes of natural resource management, this research underscores the importance of recalibrating historical reference conditions. By acknowledging climate-induced alterations, practitioners can design more resilient and adaptive restoration strategies, ensuring the long-term sustainability of urban rivers.

It is imperative to acknowledge certain inherent limitations within this research. The reliance on climate change projections introduces inherent uncertainties, necessitating ongoing refinement and validation of these projections against empirical data. Furthermore, the study's focus on a specific urban river, the Farahzad River, while insightful, may not capture the full spectrum of urban river dynamics. Expanding the study's scope to encompass a broader range of urban river systems could offer a more comprehensive perspective.

The journey of comprehending urban river response to climate change is an ever-evolving quest. To further enrich this field, future research endeavors may explore:

Ecological impacts: Delving into the ecological ramifications of changing river morphology and discharge dynamics under climate change scenarios can provide a deeper understanding of how urban river ecosystems adapt to evolving conditions.

Scenario-based analyses: Expanding the analysis to encompass various climate change scenarios and assessing their impacts on different urban river typologies can yield nuanced insights into the intricate interplay between climate, hydrology, and river morphology.

Interdisciplinary investigations: Collaborative research efforts that span climate science, hydrology, geomorphology, and ecology can provide a holistic perspective on urban river systems and their response to the multifaceted challenges posed by climate change.

This research stands as a pioneering endeavor by introducing an innovative predictive methodology that integrates climate change projections, hydrology, and river morphology. This methodological innovation not only advances scientific understanding but also empowers stakeholders with a practical instrument for informed urban river management in an era of climate uncertainty.

In conclusion, this research offers substantial contributions to climate change impact assessment, urban river management, and restoration practices. By quantifying the influence of climate change on river stability and providing a predictive tool, it empowers stakeholders to make informed decisions amid the complex and dynamic landscape of urban river management. Acknowledging its limitations and charting the course for future research, we anticipate that these findings will serve as a cornerstone for enhancing the sustainable management of urban rivers on a global scale.

The authors received no funding for this study.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.