A Comprehensive Review on Sediment Transport, Flow Dynamics, and Hazards in Steep Channels

Ajaz Ahmad Mir; Mahesh Patel

doi:https://doi.org/10.14796/JWMM.C517

A Comprehensive Review on Sediment Transport, Flow Dynamics, and Hazards in Steep Channels

Ajaz Ahmad Mir and Mahesh Patel

(2024)

Dr BR Ambedkar National Institute of Technology Jalandhar, India

DOI: https://doi.org/10.14796/JWMM.C517

Comments

Abstract

The hydrological channel networks of the steep mountains are extensively designated and organized geographic systems and are very complicated. They are composed of granular beds that are uneven and are subjected to fluid forces that fluctuate spatially and temporally. The flow and movement of sediment in these streams are significantly shaped by large rocks such as boulders. However, it is difficult to comprehend these mountain streams because significant information is unavailable regarding these channels as compared to plane bed streams. To address this issue, a critical review of the numerical, computational fluid dynamics, and machine learning mechanisms underlying sediment transport across different flow conditions in steep channels is presented while considering the current and foreseeable conditions for various sediment transport phenomena. Further analysis on these steep channels using advanced available techniques was used to get an insight into the morphology of these channels. Furthermore, the hazards associated with steep mountain channels are reviewed as they have a significant impact on infrastructure and habitation in mountainous regions.

1 Introduction

1.1 Background

Mountain channels are responsible for the development of the world landscape by redistributing mass throughout the surface of the earth. A steep channel is defined as one which is in a mountainous region and has an average elevation of more than one thousand metres. The bed morphology, hydrodynamics, and sediment transport regimes significantly different from gravel/alluvial channel sections on a mild slope. These streams transport water, sediments, and dissolved materials from higher elevations to lower regions. Furthermore, steep channels influence the rate of erosion, transportation, deposition, and weathering aspects that deteriorate the landscape. These aspects are crucial for determining the morphology of steep channels, encompassing the hydrological regime, channel slope, grain size distribution, sediment transport dynamics, and various types of bedforms.

Steep channels are primarily characterized by the step-like bed morphology, indicating an irregular longitudinal profile with varying slopes formed by vertical drops, scour holes, and mild slopes (Johnson et al. 2009; Piton and Recking 2017). Moreover, most river channels have significant longitudinal gradients, unlike the lowland river reaches (Corenblit et al. 2015) and the longitudinal slope of the steep channels varies between 4 to 5 percent (Comiti and Mao 2012). In addition to this, these channels are comprised of widespread occurrence of cobbles, micro-roughness elements, vegetation, and bedrock formations about the width of the channel (Haubrock et al. 2009). These characteristic profiles set them apart from lower-gradient streams (Mudd et al. 2014), and these channels often consist of bedrock with limited sediment availability, resulting in turbulent and unsteady flows (Curran and Wohl 2003; MacFarlane and Wohl 2003). The non-uniform profile induces a turbulent flow regime, which can be observed during periods of low to moderate flow rates (Comiti and Mao 2012). Consequently, rough bed surfaces alter velocity profiles which can increase flow resistance (Lamb et al. 2017; Cui et al. 2010; Wiele et al. 2007). However, the accurate flow observations are crucial for understanding sediment transport phenomenon in steep river systems.

In previous studies, various factors such as underlying bedrock structure, tectonic activity, glacial movements, beaver dams, wood debris accumulation, silt from hillslopes, and mass movements from tributaries have been identified as significant features that cause alterations to the longitudinal profile by redistribution of mass and sediment flux (Comiti et al. 2005; Ferguson 2007; Graham et al. 2005; Wohl et al. 2004). In addition to this, steep channels are typically characterized by a smaller width than the entire length (usually exceeding the average channel width by at least ten times). Although, these channels maintain a consistent morphology throughout length of the stream (Baker and Walford 2010). However, the mobile sediments within steep regions continuously remain in motion, leading to the development of diverse features.

The sediments in mountain streams have varied physical formations that depend on various parameters such as sediment flux, slope of the channel, and size of the channel (Brenna et al. 2020). Therefore, the unique channel morphology is formed as a result of complex interactions between flow dynamics, sediment transport processes, and various environmental factors. Steep mountain channels have unique features and characteristics. These require specific modeling approaches, effective management strategies, and conservation efforts in dynamic and challenging terrains. However, these processes have been studied experimentally and analytically (Bombar et al. 2011; MoayeriKashani et al. 2017; Singh and Ahmad 2019). Bombar et al. (2011) conducted experiments on unsteady sediment transport in a laboratory flume by introducing sedimentograph feedings to the setup. The experimental results showed that bedload transport rates matched triangular hydrographs with an average delay of 11 seconds. Similarly, the trapezoidal hydrographs aligned with bedload transport rates, exhibited an average delay of 30 seconds. Moreover, qualitative investigations were also conducted using unsteady-flow parameters and the total flow work index.

MoayeriKashani et al. (2017) carried out an experimental study by investigating fine sediments through particle image velocimetry. They demonstrated that gravitational forces on the sediments increases by over 50 percent at the greater depths and the optimal sediment collection efficiency at the water surface was observed to be approximately 80 percent. Additionally, a direct correlation was observed between flow rate and sediment size. However, Singh and Ahmad (2019) conducted experiments for the computation of suspended and bedload transport rates utilizing a cohesive mixture of clay, silt, and gravel with varied percentages of clay from 10 percent to 50 percent by weight. They observed that the sediment transport rate decreased with an increase in clay content, whereas it increased with excess shear stress. Bed degradation was higher in the upstream section compared to the downstream section. The clay content affected the bed degradation profile and equilibrium time.

In addition to this, Singh and Tayfur (2008) used a numerical approach by using St. Venant equations and mass conservations of mobile bed and sediments. It was hypothesized that the motion of bed sediments in streams can be characterized as a kinematic wave. Whereas Tayfur and Singh (2012) employed various dominant variables (discharge, stream power, velocity slope, and shear stress) in the sediment transport capacity expression and several numerical experiments were conducted to analyse unsteady and non-equilibrium sediment transport phenomena. The results obtained align with theoretical observations for hypothetical scenarios. Also, the model underwent calibration and validation processes using diverse sets of experimental data.

Besides these finite difference methods, various studies were carried out based on finite element methods (Fiengo Pérez et al. 2017; Chalov et al. 2015). Fiengo Pérez et al. (2017) used a mathematical model that relied on the van Rijin suspended load formula and the advection-diffusion equation. They further incorporated a source/sink to represent erosion/deposition fluxes. They suggested that the sediment transport model produced realistic outcomes as it achieved a Nash-Sutcliffe model efficiency of 0.6 when matched against measurements, and an efficiency of 0.96 when compared to non-cohesive sediment transport module (NST) MIKE 11 simulations. The outcome of the study implied that the model is both practical and efficient. However, Chalov et al. (2015) addressed key challenges in quantifying sediment loads, erosion-deposition patterns, and particulate matter composition in the context of Asian rivers. They focused on the Selenga River and its basin, an undisturbed system in Russia and Mongolia contributing 50 percent of Lake Baikal's inflow. It was concluded that peak flow events in spring and summer determine 70 to 80 percent of annual sediment and pollution loads, predominantly consisting of silt and sand.

Furthermore, Qian et al. (2015) presented a one-dimensional and well-balanced model for simulating non-uniform sediment transport in alluvial rivers. The model used the Slope Limiter Centred scheme with an active layer formulation and a surface gradient method. The model was tested against scenarios with irregular topography, and it revealed enhanced performance as compared to non-well-balanced models. The approach utilized holds potential for modeling non-uniform sediment transport in alluvial rivers, especially in mountainous regions with irregular bed topography. In another study by Zhao et al. (2019) they incorporated a finite volume method (Harten, Lax, and van Leer Riemann solver) to improve the accuracy and stability in predicting sediment transport. They introduced a suspended load ratio to differentiate between the movement of suspended load and water. The model was used for both fixed and movable beds. In addition to this, the model was tested in different scenarios, showing strong agreement with measurements, except in cases that were dominated by local three-dimensional effects.

The studies discussed above by Bombar et al. (2011), MoayeriKashani et al. (2017), Singh and Ahmad (2019), Singh and Tayfur (2008), Tayfur and Singh (2012), Fiengo Pérez et al. (2017), Chalov et al. (2015), Qian et al. (2015), and Zhao et al. (2019), have significantly advanced our understanding of sediment transport in mountain streams. However, it is crucial to acknowledge certain limitations and drawbacks in these investigations. Chalov et al. (2015) focused on specific regions, such as the Selenga River in Russia and Mongolia which may limit the generalizability of the findings. Laboratory experiments, despite the controlled conditions, may not fully capture the scale and complexity of natural mountain stream systems, raising concerns about their applicability to real-world scenarios. Additionally, the simplification of environmental conditions in both experimental and numerical studies might overlook the intricate interactions between various factors influencing sediment transport. The calibration challenges in numerical models, as observed in study by Fiengo Pérez et al. (2017), emphasize the need for careful consideration of model applicability to diverse scenarios. Future research should aim to address these limitations by adopting interdisciplinary approaches, considering long-term perspectives, and considerations for a more comprehensive understanding of sediment transport in mountain streams. In addition, a comprehensive review of previous studies has been carried out with outcomes explained in Table 1.

Table 1 Summary of previous experimental studies conducted in steep mountain channels.

Source	Approach utilized	Outcome of the study	Parameters investigated
Li et al. (2023)	Experimental and DEM	Keystones have a minor control on bed surface grain-size distribution, spatial distribution of keystones naturally evolve towards random distribution with increasing flow rates. Sediment transport has higher correlation with proportion of dislodged keystones than with flow discharge.	Density and spatial distribution of keystones
Hassan et al. (2023)	Previous experimental data	Step-pool streams are a common morphological feature in gravel-bed streams with gradients between 3% and 30%. The authors used an 18-year dataset of field observations to investigate the sediment dynamics and bed stability of step-pool streams.	Sediment entrainment, sediment transport, flow resistance, sediment supply
Wang et al. (2022b)	Experimental	Deflection walls at stream confluences can effectively mitigate debris flow hazards by modifying the confluence angle and reducing blockage in the main channel.	Mitigation effects of deflection walls on debris flow hazards at the confluence of tributary and main river.
Wang et al. (2021)	Experimental	Episodic sediment supply alters step-pool channels, impacting bedload transport, aggradation, and step formation. Sediment pulse magnitude and frequency influence channel stability, with high-magnitude pulses forming steps and low-frequency pulses promoting stabilization.	Examining factors such as sediment feed, width variations, bedload transport, and channel stability in the context of step formation and collapse.
Wang et al. (2022a)	Experimental	In a step-pool channel, the sequencing of events does not significantly influence channel evolution. Flow characteristics, bedload transport, sediment storage, and step evolution exhibit consistent trends, irrespective of sediment pulse sequencing. Short-term channel adjustment and stability primarily depend on the magnitude and frequency of sediment pulses.	Event sequencing of sediment pulses, grain size of sediment input, flow characteristics, bedload transport, sediment storage, step evolution, and step frequency, etc.
Saletti and Hassan (2020a)	Experimental	Width variations enhance the formation of steps in steep streams. Steps are more common, stable, and occupy a larger portion of the channel width in narrow/narrowing areas.	Impact of width variations on the development of grain structuring in steep step-pool dominated streams
Saletti and Hassan (2020b)	Experimental	Steps form in segments where the channel width narrows due to particle jamming and are more stable.	Sediment supply and its influence on step formation, step location, and step stability.
Palucis et al. (2018a)	Experimental	A new mode of sediment transport in steep streams called sheetflow. Sheetflow is a dense granular slurry that is a hybrid between traditional river transport and debris flows. It occurs on lower gradient sandy beds under high shear stresses but has not been previously documented in steep mountain streams.	Sheetflow characteristics, such as thickness and particle velocities, and shear stress are influenced by bed slope and grain size.
Palucis and Lamb (2017)	Field and modeling	The channel form of steep mountain streams is controlled by a variety of factors, such as bed slope, sediment supply, flow discharge, and the presence of bedrock outcrops.	Bed slope, sediment supply, flow discharge, presence of bedrock outcrops
Elgueta-Astaburuaga et al. (2017)	Experimental	The temporal variation of bed load transport was strongly influenced by the magnitude and frequency of the sediment pulses. High-magnitude pulses caused an increase in bedload transport, while low-frequency pulses caused a decrease in bedload transport. The step-pool morphology also influenced the temporal variation of bed load transport.	Sediment feed magnitude, sediment feed frequency, step-pool morphology, bed load transport rates
Saletti et al. (2015)	Experimental	Sediment transport was highly variable, both in time and space. The variability was caused by several factors, such as the magnitude and frequency of the flow, the grain size of the sediment, and the morphology of the channel.	Flow magnitude, flow frequency, grain size, channel morphology, sediment transport rates
Ghilardi et al. (2014a)	Field and experimental	Bed load transport in steep channels is characterized by significant fluctuations over time. The fluctuations are periodic, with a period of about 10 minutes. The fluctuations are correlated with the flow velocity.	Bed slope, flow velocity, shear stress, sediment size
Turcotte et al. (2013)	Numerical modeling	The freeze-up process was influenced by the channel morphology, the water temperature, and the wind speed. The freeze-up process could be divided into three stages: the initial freezing stage, the ice growth stage, and the ice breakup stage.	Channel morphology, water temperature, wind speed
Comiti and Mao (2012)	-	Steep channels are characterized by high gradients and narrow widths. They are typically found in mountainous regions and are fed by small, high-gradient streams.	Turbulence, climate change, human activities
Chiari et al. (2011)	Modeling	The authors developed a numerical model to simulate bedload transport in steep channels. They used the model to back-calculate the bedload transport during six extreme flood events in the Alps.	Sediment availability, armouring, macro-roughness, flow resistance, relative flow depth
Johnson et al. (2009)	Field	The authors investigated the relationship between transport slopes, sediment cover, and bedrock channel incision in the Henry Mountains of Utah. They found that channels with more sediment cover incised at lower transport slopes than channels with less sediment cover.	Transport slope, sediment cover, bedrock channel incision
Lamb et al. (2008)	Experimental and modeling	The critical Shields stress increases with channel-bed slope. The study also found that the critical Shields stress is higher for coarser sediment particles than for finer sediment particles.	Channel-bed slope, sediment grain size
Weichert et al. (2008)	Experimental	The authors conducted a series of flume experiments to study the formation and evolution of step-pool channels. They found that the steps are formed by the entrainment and transport of large clasts by the flow.	Grain size distribution, slope of the channel, flow discharge
Church and Zimmermann (2007)	-	Step-pool channels are a common morphological feature in steep, sediment-filled channels. Step-pool channels are thought to be self-organizing systems that are controlled by a balance between the entrainment and transport of sediment and the flow resistance of the steps.	Sediment entrainment, sediment transport, flow resistance, bedrock geology, sediment supply, discharge, channel width, channel slope
Lamarre and Roy (2008)	Field experiments	The authors conducted a field experiment to study the development of sedimentary structures in a gravel-bed river. The authors also found that the development of sedimentary structures was influenced by the flow regime, with more complex structures forming in areas with higher flow velocities.	Flow regime, sediment type, grain size, bed slope
Yager et al. (2007)	Numerical modeling	Conventional bed load transport equations often overpredict the sediment flux in steep, boulder-bed channels because they do not account for the following factors: The stress borne by rarely mobile grains. The limited availability of mobile sediment. The results of their experiments show that the modified bed load transport equation predicts sediment fluxes to within an order of magnitude of the measured values.	The stress borne by rarely mobile grains, the differentiation between highly and rarely mobile sediment, the limited availability of mobile sediment

Moreover, in the present review, work a comprehensive bibliographic analysis was conducted examining previously available literature in steep channels and sediment transport domain. The main aim was to uncover overarching trends within this research domain, collective knowledge, and advancements in understanding steep channel dynamics and sediment transport processes. Bibliometric analysis provides a dependable overview of the current research landscape pertaining to the interaction among sediment transport, steep channels, and bed morphology. The bibliographic analysis based on keywords and authors is depicted in Figure 1 and Figure 2, respectively.

Figure 1 Bibliometric analysis based on previously available literation utilized by various authors in this domain.

Figure 2 Bibliometric analysis based on keywords utilized by various authors in this domain.

In a previous study by Kondolf et al. (2016), geomorphological structures called channel units were identified, which had dimensions like the channel width. However, Montgomery and Buffington (1997) had previously categorized steep streams at the channel reach scale, with individual reaches measuring about 10–20 channel widths. The terminology used in both scales was unclear. To address this confusion, the term "step-pool reach" was introduced to describe these sections, acknowledging that not all sections exclusively consisted of step pools. Church (2002, 2006) proposed a classification system based on bed mobility in steep streams, considering factors like channel stability, sediment transport, and sediment type. Bed mobility was assessed using shield stress, indicating the mobility of median-sized bed material in steep channels (Kaufmann et al. 2009). The classification system outlined six types of steep channels based on bed material. Buffington and Montgomery (2013) found similarities between Church's (2002) classification and primary reach scale morphologies suggested by Rosgen (1994). Additionally, there are other channel types commonly observed in steep mountain regions. This classification system outlined six types of steep channels based on the type of bed material, as presented in Table 2.

Table 2 Classification of steep channels according to Church (2002).

Bed material	Type of steep channel	Shields stress
Cobble-boulder	Jammed channels	0.04
Cobble-gravel	Threshold channels	0.04
Sandy-gravel	Transitional channels	0.15
Sand to gravel	Transitional channels	0.15 to 1.0
Sand or fine sand	Labile channels	>1
Silt to clay	Labile channels	up to 10

The other type of steep channels that are often characterised by high gradients and rapid flow include cascade channels. These channels possess plenty of energy dissipated around and over individual large stone clasts by tumbling and jet-and-wave interactions (Church and Zimmermann 2007). These interactions contribute to the unique flow dynamics and the energy of the flowing water is notably dispersed, affecting both channel hydrodynamics and sediment transport. In addition, the bed material in these channels generally comprises of boulders (diameter greater than 250 mm) and cobbles (diameter between 60 and 250 mm). Due to the large particle size, the bed material is immobile and has a low periodic return flow. The other type of steep channel is step-pool, where the rocks are arranged in steps that go across the stream, and these steps are separated by pools of smaller stones that are about one to four times the width of the channel. The plane bed and pool riffle channels are generally classified as low-gradient streams and observed in plane regions. The widely regarded channel morphologies that are developed in the steep areas are depicted in Figure 3.

Figure 3 Channel morphologies typically found in steep mountain streams, modified from (Montgomery and Buffington 1997).

Among the continents of the world, Asia has the most extensive mountain range. In addition to this, Asian countries, particularly India, have a wide range of Himalayan Mountain ranges, as depicted in Figure 4. The steep channel morphology is studied along the reach scale, which is different in many stream sections along the length of the channel (Buffington and Montgomery 1997; Montgomery and Buffington 1998). Based on the bed material, the steep channels are categorised as bedrock, colluvial and alluvial, respectively (Church 2006; Hassan et al. 2020). The colluvial reaches are channels that receive sediment and wood debris from adjacent hill slopes, and this material accumulates in the channel bed (Church 2010). However, colluvial channels tend to have sediment deposits that persist for longer periods of time. Furthermore, among headwater streams, steep channels are the most prevalent, however limited attention has been given to understanding the dynamics and morphology of these channels (Church 2010). In contrast to this, the channels with the bedrock reach lack continuous alluvial deposition (Dos Santos et al. 2022).

Figure 4 World mountain coverage, with Asia having the highest percentage.

The predominant flow and sediment transport capacity affects the abrasion of channel bed, bedrock resistance, and weathering processes (Lamb et al. 2015). As a result, the morphology of the bedrock alters the erosion frequency and direction. The high amount of sediment transport and wood debris supply from upper reaches can also cause modifications to the bedrock reach (Wasklewicz and Hattanji 2009). Furthermore, various systems of classification for the bedrock reaches based on the morphological features were proposed based on the morphology of the steep channel (Kondolf et al. 2016). In addition to this, there has been a significant focus on alluvial reaches over the past few decades (Brakenhoff et al. 2020; K. Hu et al. 2009). The main difference between these channels is that the beds consist of sediment carried away by the flood flows (Surian and Cisotto 2007). However, steep channels are often classified as transport-limited channels, as sediment supply exceeds the amount of sediment transport.

In mountain channels, the depth of the water is shallow as compared to roughness factors such as substantial solitary gravels (Swanson and Meyer 2014). Macro roughness elements are large as compared to alluvial plane bed channels. The immobile boulders that are considered to have a relative roughness exceeding the unit value (Ghilardi et al. 2014a). In steep channels with coarse beds, it is observed that the grain size distribution of the bedload is same as that of the bed material when the flow rate is very high (Chatanantavet et al. 2013; Ferguson 2012; Mueller et al. 2005; Nelson et al. 2009). Furthermore, in various previous studies carried out on steep channels, it was observed that the flow resistance is caused by large immobile boulders that account for more than half of the total flow resistance (Canovaro et al. 2007; Chiari et al. 2010; Church and Zimmermann 2007; Nitsche et al. 2011). By following that, the boulders are also called macro roughness components and are rarely studied in experimental bedload transfer rate investigations. A study demonstrated that flow resistance increases when a rough bed changes the velocity profile (Lamb et al. 2017). Moreover, the effect of boulders on the bed morphology and flow hydrodynamics has been missing and is not discussed in previous studies. This illustrates a need for a systematic investigation of boulder influence in a channel reach, bed morphology, and roughness.

This review paper explores a comprehensive investigation of the intricacies associated with steep mountain channels. In the following subsequent sections, the specific aspects that are critical to the understanding of the dynamic systems of steep channels are addressed. In Section 1.2, the phenomenon of energy dissipation and the effects of turbulent flows within steep mountain channels is highlighted. Section 1.3 highlights the concept of flow resistance, which is a fundamental attribute in shaping the hydrodynamics of steep channels. Bed shear stress and its implications for sediment transport are discussed in Section 1.4. Section 1.5 discusses the complex phenomenon of sediment transport in steep mountain channels, and the interactions between flow, sediment, and channel morphology. In Section 1.6, the effective discharge for sediment transport in steep channels is provided. In addition to this, the current review then investigates various experimental approaches in Section 1.7, and modeling approaches utilizing CFD in Section 1.8, respectively, which provide insights into the methods used to simulate and analyse the behaviour of the steep channels. Beyond traditional modeling approaches, Section 1.9 explores the applications of machine learning (ML) algorithms in understanding and predicting the behaviour of steep mountain channels. In Section 1.10, the paper focuses on the inherent hazards posed by these channels, highlighting the deep implications for the surrounding environment and human settlements. Furthermore, Section 2 and Section 3 focus on the exploration and engaging in discussions and presenting future perspectives that are essential for comprehending the risks associated with steep mountain channels, mitigating several hazards, and implementing ever-advancing technologies that hold the potential of developing the understanding of these natural phenomena.

1.2 Energy dissipation

The movement of water is observed to be over the bank irregularities of a channel as it interacts with the channel boundaries, leading to energy dissipation, flow resistance, and energy loss over a particular stretch of the channel (Comiti et al. 2010; David et al. 2010, 2011; Ferguson 2010). Skin friction and form drag are developed due to differential pressure around macroroughness elements such as boulders (Davidson-Arnott 2005), creating shear stresses (Nikora et al. 2001) because spatial and temporal loss of energy in a channel is influenced by various factors, for instance the fluctuations in the turbulent flow field and the diverse nature of the channel bed. Most of the steep channels depict significant roughness that obstructs flow, including boulders, boulder clusters (steps), and wooden debris. When the flow is forced to deviate around these obstructions, a drag force is experienced. Flow momentum is diminished in specific regions, and the velocity distribution shifts (Marion et al. 2006). The boulders in the downstream and hydraulic jumps with breaking waves can be observed, and low energy is rapidly dissipated (Curran and Wohl 2003). However, the formation of hydraulic jumps is one of the critical aspects of the steep mountain channels, as it results in a significant amount of energy dissipation downstream of boulders, which is proportional to the drop height. This phenomenon significantly impacts sediment transport, as hydraulic jumps play a crucial role in energy dissipation.

1.3 Flow resistance

The various methods of energy loss are typically combined into a single resistance coefficient, which is commonly called the Darcy-Weisbach coefficient (f) as represented in Equation 1.

fraction numerator U over denominator u space asterisk times end fraction equal fraction numerator U over denominator square root of g R subscript h S end root end fraction equal open parentheses 8 over f close parentheses to the power of 1 divided by 2 end exponent

(1)

Where:

U	=	flow velocity,
u*	=	the shear,
g	=	gravity acceleration,
R_h	=	hydraulic radius, and
S	=	slope of the river.

Another familiar formula that is used for calculating (f) is provided in Equation 2.

open parentheses 8 over f close parentheses to the power of 1 divided by 2 end exponent equal fraction numerator U over denominator u space asterisk times end fraction equal fraction numerator 2.3 over denominator italic kappa end fraction italic log open parentheses fraction numerator 12.2 R subscript h over denominator k subscript s end fraction close parentheses

(2)

Where:

κ = 0.4	=	von Karman coefficient, and
k_s	=	Nikuradse's equivalent grain roughness.

The inability to accurately predict flow resistance poses a significant challenge when replicating the interconnection between flow and sediment transport in steep channels (Papanicolaou et al. 2010). The challenge of resistance to flow in rivers lies in determining flow velocity while considering the resistive features of mountainous streams (Ward et al. 2012). However, accurately predicting the forces that stabilize sediments in a river is challenging without reliable estimates of flow velocity and depth (Yager et al. 2007). However, previous studies on this aspect have relied on flows characterized by small-scale roughness, where the sediment size is relatively small in comparison to the depth of flow (Coscarella et al. 2020; Li et al. 2023; Powell 2014). In such scenarios, the conventional approaches are used to estimate flow resistance, which may not be adequate. These methods typically emphasize the skin resistance of grains and tend to overlook the influence of form drag and the scattering effect of turbulence in the bottom layer of the flow (Papanicolaou et al. 2010). When the relative roughness exceeds the value of 0.3, the roughness can no longer be on a smaller scale. The logarithmic resistance equation for small-scale roughness may not completely address the flow resistance in certain situations, where the actual effects on flow resistance can be more significant. It is because the logarithmic resistance equation considers only larger-scale roughness, while other factors, such as smaller-scale roughness, can also play a role in influencing the flow resistance (Schleiss 2010).

Moreover, the irregularities in the riverbed can disturb the self-similarity of the flow within the troughs and crests, disrupting the vertical scale separation. Consequently, the flow patterns may no longer exhibit the same characteristics and behaviour at different scales of observation (Ferreira et al. 2010, 2012). The analysis of rivers characterized by high relative roughness resulting from the topography should begin with the consideration of drag resistance, which is a crucial aspect representing one of the form-induced moment sinks in turbulent flows. Although, drag resistance occurs due to localized flow separation, which creates a pressure difference around the obstacle (Yager et al. 2007). However, when the relative roughness exceeds unit value, the roughness elements are considered to be of a large scale. There exists a transitional flow regime when the value of relative roughness lies in between 0.3 and 1 (Schultz and Flack 2007).

The roughness elements on a channel bed can obstruct the flow and generate drag forces that decrease flow momentum and alter the velocity distribution (Powell 2014). When the number of macro-roughness elements is high, the assumption of a logarithmic velocity profile may be invalid. In such cases, roughness elements can significantly alter flow behaviour, deviating from the expected characteristics of a logarithmic profile (Kadivar et al. 2021). In scenarios where the roughness elements on the bed surface do not behave as a single surface, the conventional flow resistance formulas may not be applicable. In addition to this, the frictional shear on the flow cannot be accurately determined due to multiple roughness elements that can interact with the flow in complex ways. As a result, the classical expression of flow resistance formulae may not provide accurate predictions of flow behaviour in such situations (Bates et al. 2010). In addition to this, when the water depth is less than the height of the roughness components on the bed, the mean flow velocity is generally expected to remain constant. However, when the water flows over the top of these components, even a slight increase in the water depth can cause a significant increase in the flow velocity (Folkard 2005). This is because the roughness elements can act as obstacles to the flow and create a zone of higher velocity flow above them, which can enhance the overall flow velocity in the channel (Schleiss 2010).

Several studies have proposed that resistance equations should account for various factors such as channel slope, Froude number, Reynolds number, sediment mobility, channel shape, and aeration to estimate flow resistance in natural channels accurately (Church 2006; Church and Zimmermann 2007; Ghilardi et al. 2014b; Hassan and Reid 1990; Zimmermann 2010). These studies have indicated that the velocity profile and flow resistance in the presence of macro-scale roughness may not completely depend on the relative submergence of the roughness elements. Although, other parameters that describe the geometry of the roughness, such as spatial density and arrangement of macro-roughness elements, may also play an important role in determining flow behaviour (Jiang and Liu 2018; Juez et al. 2018). The complex interaction between the flow and roughness elements can affect the velocity and shear stress distribution across the channel, which can vary depending on the geometry and spatial arrangement of the roughness elements. As a result, these parameters can significantly impact the flow resistance and velocity profile in channels with macro-scale roughness. Previous research suggests that analyzing resistance elements individually may not be accurate. This is because combining them to determine overall channel resistance can be affected by the interaction among roughness elements (Canovaro and Solari 2007; Yager et al. 2007). It is because the different resistance components, such as skin friction, form drag, and turbulence dispersion, interact with each other in complex ways, and the presence of one can affect the behaviour of the others. For instance, the presence of roughness elements on the channel bed can generate form drag, which can interfere with the skin friction and the turbulence dispersion in the flow. Therefore, it is necessary to consider the interactive effects of different resistance components when analyzing the overall flow resistance in a channel (Gao and Abrahams 2004; Hu and Abrahams 2004; Wilcox et al. 2006). Determining the relative influence of different sources of friction is very complex due to the occurrence of wakes, jets, and standing waves generated by roughness features in themountainous channel (Powell 2014). This additional complexity makes the task more challenging and requires adequate intervention.

1.4 Bed shear stress

Bed shear stress is a measure of the force per unit area acting on the riverbed due to the water flow. It is commonly utilized to characterize the conditions under which sediment movement occurs, as sediment transport is closely related to the level of bed shear stress (Boyer et al. 2006). Bed shear stress is measured directly on the riverbed using sensors or estimated using flow velocity measurements and models. In turbulent flow conditions, the bed shear stress is balanced by the mass or gravity force acting on the sediment particles. When the bed shear stress exceeds a critical threshold value, the sediment particles start to move and get transported downstream (Nafchi et al. 2021). The critical threshold value of bed shear stress required for sediment movement depends on the size, shape, density of the sediment particles, the water temperature, and the chemical composition of the water (Grabowski et al. 2011).

Bed shear stress can be affected by various factors, such as changes in flow velocity, water depth, and bed roughness. In steep mountain channels, bed shear stress can be particularly higher due to the steep slope of the channel and the presence of large boulders and rocks on the bed (Johnson and Cowen 2017; Mathis et al. 2014). However, understanding the dynamics of bed shear stress in steep mountain channels is important for predicting sediment transport rates and erosion processes in these environments is very crucial. Equation 3 is used to calculate the bed shear stress.

italic tau subscript o equal italic rho open parentheses u asterisk times close parentheses to the power of 2 equal italic rho g R subscript h S

(3)

Where:

$italic rho$

the density of water.

When utilizing an upscaling technique for large-scale river reaches, it is commonly assumed that the uniform flow approximation remains valid; although constant flow approximation is extremely rare in steep mountain rivers (Ferreira 2015; Vergeynst et al. 2017). Therefore, Equation 3 may be utilized to depict the actual action that is being performed on the bed (Kabiri et al. 2017; Larrarte et al. 2020). In addition, this approximation is often implemented in various field research and practical applications. Equation 4 may be used to get the related dimensionless version of the bed shear stress, typically used to find sediment transport.

italic tau subscript o to the power of asterisk times equal fraction numerator italic tau subscript o over denominator open parentheses italic rho subscript s minus italic rho close parentheses g d subscript 50 end fraction

(4)

Where:

$italic tau subscript o asterisk times$	=	critical shear stress for sediment movement,
$italic tau subscript o$	=	shear stress,
$italic rho subscript s$	=	density of sediment particles, and
$d subscript 50$	=	median grain size of a sediment sample.

The momentum balance equations directly consider the bed shear stress as a contact force term, affecting the amount of energy the flow dissipates. Therefore, there exists a direct correlation between the total bed shear stress and flow resistance, expressed as shown in Equation 5.

open parentheses 8 over f close parentheses to the power of 1 divided by 2 end exponent equal fraction numerator U over denominator u space asterisk times end fraction equal fraction numerator U over denominator square root of italic tau subscript o divided by italic rho end root end fraction

(5)

The significant spatio-temporal diversity of hydrodynamic properties of steep channels is the primary source of the problem that arises when determining bed shear stress. The potential differences in velocity and shear stress can be observed throughout a cross-section or along a reach due to the spatial diversity of the bed, which is brought about by different-sized sediments and bedforms (Wohl 2013). However, in rivers characterized by steep gradients, substantial boulders can undertake a significant proportion of the total shear stress. Consequently, the available force for transporting smaller sediments between these boulders is reduced. Moreover, the interference with the flow is caused by roughness components that protrude from the channel bed. The drag resistance results in a loss in the momentum of flow, which consequently modifies the velocity distribution (Yager et al. 2007). This drag is a sink for momentum in the flow, representing drag shear stress. However, in previous studies, skin friction was attained by the frictional elements and the bed material (Bathurst 1985; Yager et al. 2007). Furthermore, when multiple obstacles such as large roughness boulders are present in the flow and have similar drag coefficients, the shear stress on the riverbed increases.

The broad spectrum of grain sizes in mountain rivers presents various challenges, as the interactions between particles of different sizes can lead to phenomena such as concealing and protrusion effects. These effects, in turn, affects the initiation of motion in the steep channels (Lenzi 2001). Moreover, studies have explored the transport characteristics of particles in riverbeds, investigating whether size-selective transport or equimobility prevails (Scheingross et al. 2013; Yager et al. 2007). The sediment particles are entrained at the same shear stress value as they would be in a well-sorted bed because the shear stress is proportional to the particle size. By following that, each particle has the same dimensionless critical shear stress value. Conversely, in the case of equimobility, the relative size effects are so significant that all particle sizes have the same dimensional shear stress value. It indicates that the dimensionless critical shear stress is higher for finer particles due to hiding effects and for coarser sediments due to protrusion. Generally, bedload transfer situations fall between size-selective transport and equimobility extremes. Whereas, in steep channels, some studies showed a phenomenon called partial transport, where a component of the particle size distribution remains immobile (Heyman et al. 2013; Lenzi 2001; Yager et al. 2007).

1.5 Sediment transport in steep mountain channels

The bedload is the portion of the total sediment load moving slightly above the bed surface, and it is transported by fluid turbulence and intergranular collisions between the sediment particles. The steepness of the channel causes the particles to roll, slide, and travel in the downstream direction (Cohen et al. 2022; Recking et al. 2012; Zimmermann et al. 2010). However, considering the coarse grain size distribution, bedload transport is the dominant mode of sediment transfer in mountain rivers. Sediment movement in steep rivers is poorly understood and is a highly unpredictable process despite its crucial role in the development of mountain landscapes. In steep flume laboratory tests, most sediment transport formulas significantly overestimate the actual sediment movement (Heyman et al. 2013; Kammerlander et al. 2017; Yager et al. 2007). Additionally, the presence of graded sediments causes bedload oscillations, even when water and sediment feed rates are constant. Several researchers have noticed this phenomenon, which appears to be driven by longitudinal and vertical grain sorting, bedform migration, and development of bedforms (Frey and Church 2009; Heyman et al. 2013; Iseya and Ikeda 2017; Recking 2009).

Furthermore, various researchers conducted field studies on sediment transport (Khan et al. 2019; Papangelakis et al. 2019; Chalov et al. 2015). However, these studies have provided insights into various aspects of sediment transport, incipient motion, particle velocity, and flow conditions, particularly under steady and uniform flow conditions. In addition, the investigations have resulted in the formulation of numerous empirical equations. Therefore, it is important to note that these equations often exhibit variations when applied to predict observed data, even under identical flow conditions. The variability arises due to fact that each empirical equation is derived from specific experiments and may not possess universal applicability across diverse scenarios.

In another previous study, when a sediment supply pulse was introduced into an experimentally aggrading channel, it was observed that the sediment yields significantly increased (Jobe et al. 2015). However, the impact did not last for a very long time. When the flume was started for the first time without any sediment being injected into it, the bed surface immediately began to become more uneven (Sklar et al. 2009). The median grain size and armour ratio showed that the bed grain size distribution did not change significantly after this initial modification. The bed topography was statistically evaluated in each feed pulse and found to be expanding, flattening, and becoming less complex. The texture of the bed remained almost same throughout the experiment, but new stone structures were observed which eventually destroyed. After each pulse, new forms would appear and the previously formed would be destroyed. The stabilizing effect of bed structures was enhanced during the pulses (Marant and Cossu 2018). It was observed that different metrics and measurements of bed surface topography, such as grain size, number and size of the structure, and surface roughness statistics in both vertical and horizontal directions, appear to fluctuate independently (Sklar et al. 2009). In the experiments, the response of the bed to a constant sediment supply rate and sediment pulses varies, showing a significant impact on the existing topography and bed surface condition. This adjustment affects the bed structure and topography in response to changes in sediment supply. Although there are no apparent connections between the variables, this information is necessary for analyzing and documenting the responses of the bed to changes in the boundary conditions (Hassan et al. 2020).

Despite sediment-transporting floods, most alluvial stream channels undergo minimal changes over years or decades, as these channels inherently seek stability. The morphology that remains is the most stable in the face of forced fluxes. Stability is acquired when the stream's energy can be dispersed without considerable channel-deforming effort, even if sediment transfer may still occur. Channel patterns such as pool and riffle, and sedimentary bed types have energy-dissipating features. The granular border materials, the potentially mobile sediments, provide the highest stability in gravel-bed channels. The hydrodynamic forces overcome particle inertia to entrain grains in stream channels (Shields 1936). However, researchers have considered various factors, such as sheltering effect of large particles (Einstein 1950), particle protrusion (Fenton and Abbott 1977), the pivot moment needed to move a particle past its downstream neighbor (Komar and Li 1988), and the influences of particle size grading (Wilcock and Southard 1989) and particle shape (Gomez 1993).

To determine debris flow transport mechanisms, it is necessary to collect data on flow resistance and sediment flux at steep slopes (S ≥ 10 percent) that are subjected to significant bed stresses (Schneider et al. 2015). In addition, the most widely employed flow resistance models should be evaluated (Recking 2009), and sediment transport models have a wide range of applications, including steep channels. In addition to this, some of the findings from the experiments mainly focused on the advancement of sheetflow at higher Shields stresses. Also, the structure of particle velocities within sheetflows and the occurrence of sheetflow in high-gradient steep channels differs from sheetflow occurring in low-gradient systems (Palucis et al. 2018b). In this study, new data on the development of bedforms, flow resistance, and sediment transport across the bedload-to-sheet flow transition requires adequate attention. These are all aspects of the transition from bedload to sheetflow.

Sediment transport measurement is challenging, especially in gravel-bed rivers and channels with mild gradients. High-gradient streams pose a unique set of challenges for sediment transport prediction due to their complicated hydrodynamics, morphological dynamics, and sedimentological processes. Since bedload transport is directly connected to channel shape and flow resistance, in future, the focus must be on these aspects and not on non-Newtonian flows or suspended transport.

1.6 Effective discharge for sediment transport

Effective discharge plays a crucial role in the context of sediment transport in steep mountain channels. It is an important parameter that characterizes the flow conditions, and it is necessary to mobilize smaller and larger sizes of sediments within a mountain stream. It represents the specific flow rate or discharge at which the sediment transport is most efficient, and it varies depending on factors such as steep channel geometry, sediment size distribution, and channel hydraulics. Understanding and computing the effective discharge is essential for predicting sediment transport in the complex steep regions. In this regard, several studies have been conducted to formulate methods for calculating effective discharge in steep mountain channels, considering the distinct characteristics (Hassan et al. 2014; Lenzi et al. 2006; Zakwan et al. 2018, 2021).

Lenzi et al. (2006) explored the high-gradient, boulder-bed streams such as Rio Cordon in the Italian Alps and observed that several key flow parameters were essential. The investigation of the study emphasized the impact of variables such as flow classes and sediment fraction on effective discharge. Also, when long-term sediment load data was considered, the effective discharge was used to calculate bedload transport, which was more effective than the counterpart related to suspended sediment load in explaining channel formation and maintenance. The findings suggest the need for two dominant discharge ranges in steep mountain rivers: a frequent flow range for sustaining channel form and a less frequent high flow range for macro-scale channel shaping.

Furthermore, Hassan et al. (2014) examined small mountain streams with irregular sediment supply and observed that the effective discharge varied significantly. Moreover, low-magnitude and high-frequency events were responsible for sediment transport in these channels. By following that, sediment transport models and discharges were recorded. Three stream types emerged: Frequently Mobile Gravel (FMG), Infrequently Mobile Gravel (IMG), and Sand over Immobile Gravel (SG). The IMG streams had infrequent, substantial effective discharges approximating bankfull discharge. In contrast, FMG and SG streams experience more frequent, smaller effective discharges for channel maintenance. This suggests that effective discharge alone cannot serve as a representation for channel-forming discharge in mountain stream channel design and management.

However, another investigation by Zakwan et al. (2018) evaluated effective discharge for suspended sediment transport at 15 Ganga River stations. They noted that moderate-magnitude and moderate-frequency discharges were primarily responsible for sediment transport, with over 90 percent of sediment carried by discharges recurring within three years. In addition to this, bankfull discharge considerably exceeded effective discharge at most of the stations, and the ratio of bankfull to effective discharge varied extensively, although it correlated strongly with a discharge of a 1.5-year return interval. It was also inferred from this study that utilization of the rating curve approach can lead to overestimation of effective discharge and the frequency of data collection affected effective discharge for large rivers with a 0.5 percent error.

However, Zakwan et al. (2021) observed that sediment transport frequency is essential for understanding river sediment characteristics, particularly in hydroelectrically developed regions such as the Drava River basin. The study conducted at the Botovo and Donji Miholjac gauging stations highlighted the significant role of discharges around daily averages in sediment transport. Furthermore, it was observed that the discharge with a 1-year return interval in the annual maximum discharge series is responsible for carrying 90 percent of the total sediment load in the lower Drava River.

In the context of effective discharge for sediment transport, Zakwan et al. (2022) studied the role of sediment transport in river systems, particularly in the context of water resource projects. The main aim of the study was to determine the impact of high-magnitude discharge events in shaping river channels. They focused on using the effective discharge concept in the Godavari River, India. It was confirmed that most sediment movement was observed during moderately frequent discharges, with rare high-magnitude flows contributing less. Besides this, other studies contributed to the field of magnitude frequency analysis of sediment transport and effective discharge (Henck et al. 2010; López-Tarazón and Batalla 2014; Ma et al. 2010; Sun et al. 2023).

Furthermore, the studies on effective discharge in sediment transport within steep mountain channels, conducted by various authors such as Hassan et al. (2014), Lenzi et al. (2006), Zakwan et al. (2018, 2021), Singh and Ahmad (2019), Zakwan et al. (2021), and Zakwan et al. (2022), have significantly advanced our understanding of channel-forming conditions. However, future research should address certain drawbacks and explore new perspectives to enhance our comprehension. In addition, limitation lies in the regional focus of some studies, such as the one on the Ganga River and the Godavari River (Zakwan et al. 2018; Zakwan et al. 2022), which may limit the generalizability of findings to other mountainous regions. Additionally, the reliance on specific methodologies for calculating effective discharge, as observed in studies by Zakwan et al. (2018), raises questions about the universality of these approaches. Future studies should aim for more comprehensive approaches, considering diverse environmental conditions, adopting interdisciplinary perspectives, and incorporating long-term considerations. In discussing these studies, it is evident that while effective discharge is a crucial parameter, its applicability varies in different contexts. A study by Hassan et al. (2014) highlights the significance of sediment transport models in capturing the complexities of small mountain streams. The observed variation in effective discharge across different stream categories emphasizes the need for a refined approach in channel design and management. Moreover, Zakwan et al. (2022) sheds light on the changing sediment transport pattern in the Godavari River, highlighting the dynamic nature of these systems. However, the reliance on discharge intervals, as observed in Zakwan et al. (2021), may oversimplify the intricate sediment transport processes in hydroelectrically developed regions. Therefore, a more holistic understanding, considering the interplay of various factors, is crucial for effective river management in mountainous terrains.

The concept of effective discharge for sediment transport is a significant aspect of understanding steep river systems and carries several intrinsic limitations. The variability in effective discharge values across these systems is driven by several attributes, such as channel geometry, sediment characteristics, and hydraulic conditions, that make it challenging to establish a universally applicable function. The data availability can be a significant limitation, as the calculations often rely on historical or long-term data, which can be unreliable in some complex steep regions. The temporal and spatial variations, influenced by natural events, can further complicate the determination of effective discharge values. Although, measurement challenges, particularly in steep mountain channels, introduce errors and uncertainties in different measurements. However, the complexity of mountain river systems with multiple sediment types and flow interactions cannot be entirely captured by a single effective discharge value. The application of effective discharge observations to river management can be intricate, as real-world decisions may require additional considerations beyond effective discharge. Furthermore, modeling assumptions and the impact of human activities on river systems can affect the accuracy and applicability of effective discharge. Monitoring challenges and the logistics of continuous data collection pose additional limitations in some mountain ranges. However, addressing these limitations is crucial for a comprehensive understanding of effective discharge and its role in sediment transport for controlling future research and river management efforts.

1.7 Experimental modeling

In previous studies, different models were developed to provide information on bed erosion and water quality processes (Gamvroudis et al. 2015; Kiat et al. 2005, 2008). A study by Gamvroudis et al. (2015) focused on analyzing runoff and sediment transport in the Evrotas River Basin, a vast Mediterranean watershed. They employed the Soil and Water Assessment Tool (SWAT) model, which was calibrated and validated using extensive discharge and sediment data. The model demonstrated robust performance by effectively simulating hydrology and sediment transport, depicting strong agreement with field observations across various metrics. A significant variation in sediment yield, with the highest annual sediment load at 3.5 tons per hectare per year was observed in the western part of the watershed; whereas Kiat et al. (2008) studied the Kulim River catchment in Malaysia using a FLUVIAL-12 model. They predicted the impact of existing and future developments on river channel stability. Moreover, the Engelund-Hansen formula was utilized to accurately predict sediment transport with a roughness coefficient of 0.030. The significant changes in the Kulim River from 2006 to 2016 were also observed; however, overall stability was expected at most locations during this period.

Sinnakaudan et al. (2003, 2006) used ArcView geographic information system (GIS) that is integrated for efficient flood risk analysis for the Pari River (Farnce). These studies demonstrated GIS as an effective tool for analyzing and mapping flood risks within boundaries. Whereas Kiat et al. (2005) analyzed 122 sediment datasets collected between May 2000 and October 2002 in the Kinta River Catchment, focusing on suspended load, bed load, bed material, and flow discharge at six study sites. However, these models are inappropriate for providing various parameters, such as catchment scale and sediment transport predictions. In addition to this, there exist certain difficulties such as over-parameterization, unsuitability of model assumptions based on local conditions, and non-availability of documentation regarding model testing and observation performance (Lobera et al. 2016).

The discussed studies that employed models such as SWAT, FLUVIAL-12, and ArcView GIS, have significantly contributed to understanding hydrological and sediment transport processes in diverse river basins. For instance, Gamvroudis et al. (2015) demonstrated the robustness of the SWAT model in simulating hydrology and sediment transport in the Evrotas River Basin, revealing spatial variations in sediment dynamics. Kiat et al. (2008) utilized the FLUVIAL-12 model to assess the impact of development on river channel stability in the Kulim River catchment, depicting the versatility of modeling tools in addressing regional challenges. Sinnakaudan et al. (2003, 2006) and Kiat et al. (2005) illustrated the efficiency of ArcView GIS in flood risk analysis and sediment dataset analysis, respectively. Despite these advancements, limitations such as over-parameterization, model assumptions based on local conditions, and insufficient documentation pose challenges. Future perspectives should focus on refining models, incorporating accurate local conditions, and enhancing documentation for improved transparency and reliability with proper model calibration.

However, the various models that can be used in predicting erosion and sediment transport are shown in Table 3. These depict the approaches that have been used to represent sediment transport and the movement through the different landscapes. The models can vary significantly in the processes they exhibit, considering both spatial and temporal scales. Although, there is a lot of scope for these models to be used in the scaled catchments. Along the catchment, a sediment-associated water module requires a rainfall-runoff module, a surface erosion module, and an instream module. Considering these models, data regarding the steep channels have been obtained from Himalayan steep rivers to be modeled in the laboratory experimental flume. To assess the impacts on sediment transport, various systematic experiments would be carried out on the tilting flume. The flume slope, mean sediment size, and flow depth would be tested for multiple combinations of discharge and sediment feeds.

Table 3 Description of various sediment transport models.

Models	Type	Scale	Input data	Output	Reference
GUEST	Physical	Plot	Hydrological, sediment	Runoff, sediment yield	(Yu et al. 1997)
LISEM	Physical	Small catchment	GIS maps, rainfall data, catchment morphology	Runoff, sediment yield	(Takken et al. 1999)
PERFECT	Physical	Field	Daily climate data, soil parameters	Water balance, erosion	(Littleboy et al. 1992)
SEDNET	Empirical/ conceptual	Catchment	Channel bank dimensions and vegetation	Sediment transport, bank depositions	(Prosser et al. 2001)
TOPOG	Physical	Hillslope	Topography, soil climate and vegetation	Water fluxes, sediments	(McVicar et al. 2000)
USLE	Empirical	Hillslope	Annual rainfall data, land cover information, topography	Estimates annual soil erosion from hillslopes	(Wischmeier and Smith 1978)
WEPP	Physical	Hillslope/ catchment	Plant growth and residue component	Runoff and erosion summary	(Laflen et al. 1991)
MIKE-11	Physical	Catchment	River network, land use soil type, groundwater depth	Sediment transport in rivers and in other inland water bodies	(Hanley et al. 1998)
FLUVIAL-12	Empirical	Catchment	Geometry, hydrology, sediment	Sediment transport, simulated water surface level, etc.	(Chang 1982)

1.8 Modeling approaches using Computational Fluid Dynamics

Computational Fluid Dynamics (CFD) modeling is a numerical approach used to simulate and analyze fluid flow phenomena. It involves solving the Navier-Stokes equations, which describe the conservation of mass, momentum, and energy in a fluid. The CFD modeling is widely used in various fields such as aerospace, automotive, chemical, and environmental engineering. However, in the context of rivers and channels, CFD can be used to simulate flow conditions such as velocity profiles, turbulence intensity, and bed shear stress. In recent years, advancements in algorithms and computational dynamics have allowed for highly accurate simulations of sediment transport using the Computational Fluid Dynamics–Discrete Element Method (CFD–DEM) (Ahadi et al. 2020; Heydari-Beni et al. 2021; Ma et al. 2022; Sun et al. 2017).

In the context of CFD, Sun et al. (2017) introduced an efficient CFD–DEM approach using bonded spheres to simulate irregular sediment grain shapes, overcoming limitations in existing methods. However, numerical simulations demonstrate improved efficiency, flexibility, and accuracy in predicting sediment transport characteristics, making it promising for realistic simulations of natural sediment dynamics. In this regard, Ahadi et al. (2020) conducted an extensive review on CFD in modeling by considering two-phase flow of water and sediment in stormwater retention ponds. They emphasized recent advancements in computational sediment transport modeling. However, Heydari-Beni et al. (2021) revealed that negative wake occurred at a Weissenberg number (value equal to 2.45) for various blockage ratios (e.g., 0.390, 0.464, and 0.538). A linear relationship was observed between overshoot/steady-state velocity and blockage ratio due to shear-thinning effects. Additionally, the sphere velocity oscillations disappeared at the highest blockage ratio, except at specific cases such as 0.464 and 1. At higher blockage ratios, the viscoelastic fluid velocity showed oscillations, becoming more damped due to the dominance of shear-thinning and wall effects. The approach improved efficiency in simulating the sediment transport dynamics in steep mountain channels. Furthermore, these approaches can also be used to assess the hydraulic characteristics of steep channels to predict the effects of changes in channel geometry and evaluate the performance of hydraulic structures. Whereas Ma et al. (2022) conducted a review of the development of CFD-DEM studies regarding non-spherical particles, encompassing theoretical models to practical applications. Some examples of CFD models such as Fluent, Ansys CFX, OpenFOAM, Delft3D, respectively, can be utilized for river and channel applications.

In previous studies, the effect of sediment transport on flow characteristics in a non-prismatic compound channel was observed (Nazari-Giglou et al. 2016; Sakib et al. 2022; Selim et al. 2022). These studies employed CFD software to investigate sediment transport in non-prismatic compound channels, considering both primary (water) and secondary (sediment) phases. The various sediment sizes and mass discharges were examined, revealing that stream-wise flow velocity decreased for small sediment sizes and increased sediment mass discharge (Selim et al. 2022). Turbulence decreased in the presence of sediments, particularly near the free channel surface. However, incorporating sediment transport analysis in the CFD simulations with Fluent can provide a better understanding of the complex interactions between fluid flow and sediment transport, and develop more effective strategies for managing and optimizing steep channel systems.

Another tool in CFD is ANSYS-CFX, which uses numerical methods to solve the governing equations of fluid flow and sediment transport, and can provide detailed information on sediment transport rates, bed morphology, and sediment concentrations. In this regard, a study assessed the hydraulic characteristics and sediment transport capacity in circular cross-section channels with different bed slopes using 3D numerical simulations with ANSYS-CFX software (Bonakdari et al. 2015). The study examined flow through circular channels under two or three-phase conditions and validated the results using laboratory data (Ahadi 2021). In another study, modeling of flow and sediment transport in a novel vortex-style stormwater retention pond was carried out by utilizing computational and physical approaches (Ahadi et al. 2020). Kadia et al. (2020) studied numerical modeling considering high sediment content in a hydraulic turbine in two-phase flow, and wear prediction was also carried out. However, Jodeau et al. (2018) carried out a numerical simulation based on turbidity currents using ANSYS CFX and Telemac 3D. They noticed that ANSYS CFX provided advanced tools for mesh generation and post-processing, allowing users to create detailed models for the channel geometry, and analyzed the results of the simulations. Therefore, by integrating sediment transport analysis into the CFD simulations with ANSYS CFX, engineers and researchers can achieve a better understanding of the complex interactions between fluid flow and sediment transport and can develop more effective strategies for managing and optimizing steep channel systems.

In addition to this, many studies have been carried out utilizing OpenFOAM software (Higuera et al. 2013; Karagiannis et al. 2020; Kazakis and Karambas 2023). Higuera et al. (2013) introduced OpenFOAM for coastal engineering by emphasizing its utility in solving 3D domains and handling two-phase flow. The simulations and results presented were theoretical, showcasing the effectiveness of implemented methods across different theories (2D, Quasi-3D, and 3D).

Shim et al. (2016) employed OpenFOAM software to investigate sediment particle movement around a bridge pier and scour hole formation processes. In addition to this, experimental flume tests and high-speed camera data were used to verify the simulated results, providing insights into sediment dynamics at the particle scale. In addition to this, OpenFOAM also provides advanced tools for mesh generation and post-processing, allowing users to create detailed models of the channel geometry and analyze the results of their simulations. Furthermore, the particle-laden flow with a focus on sediment transport was studied using computational fluid dynamics coupled with the discrete element method (Sun and Xiao 2016). Because it is open-source, users have access to the source code and can modify the software to meet their specific needs, making it a flexible and customizable tool for modeling fluid systems. However, by integrating sediment transport analysis into their CFD simulations with OpenFOAM, engineers and researchers can gain a better understanding of the complex interactions between fluid flow and sediment transport and develop more effective strategies for managing and optimizing steep channel systems. A hydrodynamic and sediment transport model was applied in both 2D and 3D dimensions to the Yangtze Estuary in China (Hu et al. 2009), in the Arabian Gulf (Elhakeem et al. 2015), and the Song Hau channel in Mekong Delta (Xing et al. 2017), respectively. In addition to this, the impact of scaling factors in sediment transport on cross-shore beach profiles utilizing Deflt3D was carried out by Yang and Son (2019).

Another modeling software, Delft3D, provides advanced tools for mesh generation and post-processing, allowing users to create detailed models of the channel geometry and analyze the results of the simulations. In the context of steep channels and sediment transport, Delft3D can be used to simulate the morphological changes in steep channels, and the development of bedforms and the erosion and deposition of sediment. The influence of bedform-related roughness on hydrodynamics and sediment transport patterns, from ripples to large-scale sand transport in Delft3D (Brakenhoff et al. 2020). Furthermore, the software is capable of modeling complex systems, including the effects of waves, tides, and river flow on sediment transport in steep channels. Moreover, Delft3D is a valuable tool for engineers and researchers working on projects related to sediment transport and management in steep channels.

CFD models such as Fluent, ANSYS CFX, OpenFOAM, and Delft3D have significantly advanced our understanding of sediment transport in river channels, particularly in steep mountain terrains. Studies utilizing CFD–Discrete Element Method (CFD–DEM) by Ahadi et al. (2020), Heydari-Beni et al. (2021), Ma et al. (2022), and Sun et al. (2017) demonstrated the capability of these models in simulating sediment transport dynamics with high accuracy. ANSYS CFX, as shown in the studies by Bonakdari et al. (2015) and Ahadi (2021), provides detailed information on sediment transport rates, bed morphology, and sediment concentrations. Moreover, OpenFOAM, employed in studies by Higuera et al. (2013), Karagiannis et al. (2020), and Kazakis and Karambas (2023), stands out for its open-source nature, offering flexibility and customization. Delft3D, utilized in studies such as Brakenhoff et al. (2020), outperforms in simulating morphological changes and complex interactions. However, these models have limitations, including regional specificity, potential oversimplification of natural systems, and calibration challenges. The focus on numerical methods might overlook real-world complexities and the role of unforeseen factors. Future perspectives should address these limitations, incorporating interdisciplinary approaches, considering long-term effects, and developing more robust models to advance comprehension of sediment transport in steep channels.

1.9 Machine learning algorithms

ML and artificial intelligence (AI) algorithms can be trained using existing data sets to predict bed shear stress in mountain channels based on input parameters such as flow velocity, channel slope, and bed roughness. This approach has the potential to provide accurate predictions of bed shear stress in complex environments where traditional methods may be unreliable or impractical. To manage the complex river systems, it is crucial to accurately predict both instream discharges and sediment transport in an intricate network of channels, tributaries, and frequent flood occurrences. In this regard, there have been a few studies conducted to predict the sediment transport based on data-driven models for prediction based on ML (Adib and Mahmoodi 2017; Bouguerra et al. 2019; Cigizoglu 2004; Cigizoglu and Alp 2006; Gupta et al. 2021). A study by Adib and Mahmoodi (2017) investigated suspended sediment load changes in the Marun River, Iran, over 42 years due to urban development, deforestation, and population growth. Using a perceptron artificial neural network (ANN) optimized by the Genetic Algorithm, the study predicted a suspended sediment load from 400,000 to 800,000 tons per day in future flood conditions (Sirdari et al. 2014). Also, Bouguerra et al. (2019) utilized ANN to predict suspended sediment discharges during floods in two Algerian catchments, Ressoul and Mellah, over 31 and 28 years, respectively. Two training algorithms, Levenberg–Marquardt (LM) and Quasi-Newton (QN) were compared, with QN demonstrating superior performance. The Quasi-Newton method consistently outperformed LM. In another study Al-Mukhtar (2019) used random forest, support vector machine, and neural networks models for analysing the suspended sediment in the Tigris River in the Baghdad region, whereas Nivesh et al. (2022) focussed on river discharge in the Kesinga sub-catchment of the Mahanadi Basin, respectively.

In addition to this, ensemble models were employed for developing daily sediment rating curves to predict sediment transport rates (Niazkar and Zakwan 2021). They utilized Multigene Genetic Programming (MGGP), an emerging ML method, to develop daily sediment rating models for two river gauging sites. In which the comparison has been made based on the performance of MGGP with an empirical model and Artificial Neural Network (ANN). The results showed the dominance of the MGGP model in estimating sediment loads. Moreover, another study primarily utilized monthly sediment rating curves to analyze sediment and discharge characteristics in 15 gauging stations along the Ganga River. In this regard, a novel monthly index number is introduced to address scatter in sediment-discharge relationships, and its parameters are estimated using a generalized reduced gradient solver. The approach enhanced the understanding of spatiotemporal variations and the inverse correlation between sediment rating parameters, particularly during the monsoon season (Zakwan and Ahmad 2021). Recently, Hanoon et al. (2022) assessed the performance of different ML approaches in predicting suspended sediment loads in river systems in Malaysia. Apart from that, several ML techniques, which were used for predicting bed shear stress and sediment transport in mountain channels, are documented below.

Artificial Neural Networks (ANN)

ANN is a type of machine ML that is commonly used for predicting complex nonlinear relationships between input and output variables. The ANN model can be trained on existing datasets of flow and bed shear stress measurements to develop a predictive tool that can anticipate sediment transport patterns and sediment load estimates. Earlier, Tayfur et al. (2013) employed principal component analysis (PCA) along with ANNs and genetic algorithms (GAs) to predict sediment loads from laboratory to field scale. They identified five key dimensionless parameters using PCA, then incorporated them into ANN input vectors for total sediment load prediction. In addition, nonlinear equations based on the same parameters are constructed and optimized using GA. The results demonstrated the transferability of models (ANN and GA) for predicting total sediment load from laboratory to field, while showing limitations for suspended load, potentially due to insufficient laboratory data. However, these methods effectively predict suspended load in the field when trained with relevant field data.

In a recent study, Niazkar and Zakwan (2023) explored methods to enhance the accuracy of sediment load estimations for water resource projects. They introduced a four-parameter equation and employed ensemble ML and ensemble empirical models, including ANN and MGGP. The comparative analysis revealed that ML-based simple average ensemble models and empirical-based nonlinear ensemble models achieve improved accuracy for sediment load estimations across different time scales. In addition to this, the ensemble-based models demonstrate enhanced performance in estimating sediment loads at daily, 10-daily, and monthly intervals.

The ANN model has been utilized in previous studies to address intricate hydrological processes (Niazkar and Zakwan 2023; Sharma et al. 2022; Yitian and Gu 2003). However, the emergence of ML techniques has offered a useful approach for tackling the complexities of sediment transport. In this regard, various studies employed the ANN model to estimate sediment loads and confirmed the reliability of ANN-based predictions (Adib and Mahmoodi 2017; Gupta et al. 2021).

Support Vector Regression (SVR)

An SVR model is a type of ML algorithm that can be used for regression analysis, which involves predicting a continuous output variable based on input variables. It can be trained on existing datasets of flow and bed shear stress measurements for prediction. A study by Al-Mukhtar (2019) employed extreme ML and twin support vector regression in conjunction with wavelet analysis to model suspended sediment load in a river. The wavelet-based models exhibited favourable performance according to five evaluation techniques: root mean square error, mean absolute error, ratio between sum of squares error and total sum of squares, symmetric mean absolute percentage error, and mean absolute scaled error. The results suggest that the hybrid models based on the wavelet enhance sediment load estimation performance (Hazarika et al. 2020).

Random Forest (RF)

The model RF is a type of ML algorithm that is commonly used for classification and regression analysis. It can be trained on existing datasets of flow and bed shear stress measurements to develop a model that could be used for prediction purposes. Recently, Bassi et al. (2023) studied the challenge of predicting the friction factor in movable bed channels by employing eight ML techniques with various input features. The traditional methods face limitations in predictability due to their subjective nature and assumptions. The models were assessed using different error metrics, and results were visualized through heatmap data, Taylor diagram, sensitivity analysis, and parametric analysis. The models such as K Star, M5 Prime, and Random Forest emerged as the top-performing ML models, providing superior predictions for friction factor with minimal errors across different input scenarios. A study compared sediment yield estimation methods for suspended sediment concentration in the Central Spanish Pyrenees. It was observed that traditional sediment rating curves were inadequate for highly variable data, while RF and Quantile Regression Forests offered robust and accurate modeling, with QRF providing uncertainty assessments (Francke et al. 2008).

Gradient Boosting Machines (GBM)

The GBM model is a type of ML algorithm that can be used for regression analysis. The model can be trained on existing data sets of flow and bed shear stress measurements to develop a predictive model. Shadkani et al. (2021) estimated sediment load at the St. Louis and Chester stations of the Mississippi River using an ML model for sediment transport prediction. They employed three ML models such as multi-layer perceptron, multi-layer perceptron-stochastic gradient descent, and gradient boosted tree to estimate suspended sediment load at the Mississippi River stations. The evaluation criteria included correlation coefficient, Nash Sutcliffe Efficiency, scatter index, and Willmott's Index (WI). Sensitivity analysis depicted day discharge as crucial, but in its absence, a combination of other parameters is effective.

Convolutional Neural Networks (CNN)

The CNN model is a type of ML algorithm that is commonly used for image and signal processing applications. It can be used for predicting bed shear stress in mountain channels by processing high-resolution topographic data generated by remote sensing techniques. These are just a few examples of ML techniques that can be applied to predict bed shear stress in mountain channels to debris flow (Pham and Kim 2022). The choice of a specific technique depends on the nature of the data and the complexity of the relationships between input and output variables. In this regard, a study emphasized the importance of managing coastal and estuarine areas for sustainable use. It introduced a convolutional neural network to efficiently emulate complex numerical models, accurately forecasting morphological changes in estuaries in seconds, optimizing computational resources, and enhancing operational forecast platforms (de Melo et al. 2022).

The limitations of current sediment transport studies utilizing ML and AI approaches include challenges related to data quality and availability. However, the comprehensive datasets necessary for training ML models may be limited, impacting the accuracy of these models. Additionally, the sensitivity of ML models to input parameters requires careful validation, and the generalization of models across diverse river systems poses a considerable challenge. On the positive side, recent studies demonstrated significant progress in the field. For instance, advancements in ensemble ML models were observed in a study by Niazkar and Zakwan (2023), determining improved predictive capabilities. The emergence of novel approaches, such as the MGGP model illustrated in Niazkar and Zakwan (2021), signifies promising developments in sediment rating curve development. These advancements contribute to a better understanding of sediment transport dynamics, despite the existing challenges.

1.10 Hazards of steep mountain channels

Steep mountain channels can pose several hazards, and it is important to take steps to mitigate these risks. They can include measures such as building protective structures, monitoring weather conditions, and implementing early warning systems to alert people to potential hazards.

Landslides and flash floods

Steep channels can be prone to landslides, which can be triggered by heavy rainfall, seismic activity, or other factors. These landslides can result in significant damage to infrastructure, homes, and other buildings and can even lead to loss of life. Steep channels are also susceptible to flash floods, which can occur when heavy rain falls in a short period of time. These floods can be hazardous, as they can carry large boulders, logs, and other debris downstream, potentially causing damage to bridges, roads, and other structures. Ávila et al. (2016) observed the changing precipitation patterns in southeastern Brazil and their relationship with the increasing occurrence of flash floods and landslides. It was determined that the rainfall data from 1978 to 2014 which focused on Rio de Janeiro and the Santa regions, showed a drastic change in the rainfall pattern. Moreover, the findings revealed the trends in annual and seasonal precipitation, particularly in extreme precipitation events, and established significant correlations between landslide/flash floods and consecutive rainfall.

Pham et al. (2019) examined farmers’ decision-making processes in adapting to flash floods and landslides in the steep northern regions of Vietnam. They surveyed rural households' decision-making in adapting to flash floods and landslides (FFandLS) in Yen Bai province, Vietnam. Through a household survey of 405 selected households, primary adaptation measures include changing cropping patterns, crop variegation, and crop protection. Key constraints include financial limitations, inadequate government support, machinery shortage, and insufficient knowledge about FFandLS. Multivariate Probit models reveal that farmers' decisions are influenced by perceptions, socio-economic factors, farming characteristics, and institutional conditions, emphasizing the need for tailored policies addressing these factors.

Rockfalls, debris flows, and avalanches

Steep channels can also be prone to rockfall, which occurs when rocks or boulders detach from the surrounding slopes and roll or slide down into the channel. It can pose a significant risk to anyone in the area and can also cause damage to infrastructure and buildings. Debris flows are a type of fast-moving landslide that can occur in steep channels. They typically involve a mix of soil, rock, and water and can be extremely dangerous due to their speed and the large quantity of debris they carry. In areas with heavy snowfall, steep channels can be prone to avalanches, which can be triggered by several factors, including wind, temperature changes, and human activity. Avalanches can be extremely dangerous, as they can bury people and structures in a matter of seconds. A study by Luckman (2017) observed that snow avalanche landforms and debris flow in Lairig Ghru, Cairngorm Mountains, Scotland. The study highlighted the reworking of debris flow deposits by avalanches and suggested that the snow avalanches are significant geomorphic agents in the region, although the morphological evidence may be obscured by debris flow from similar sources. In addition, the research analyzed seismographs from rockfalls and avalanches at Mount St. Helens, Mount Adams, and Mount Rainer in Washington’s Cascade Range. It was observed the factors such as source volume, materials, failure modes, and track materials impact the avalanche seismicity.

Compound and cascade hazards

Compound and cascade hazards are types of hazards that occur when multiple hazards combine or interact with each other, leading to increased risk and complexity. Compound hazards refer to the combination of two or more different types of hazards, while cascade hazards refer to the sequential occurrence of multiple hazards over time. Examples of compound hazards include landslides that trigger flash floods, earthquakes that trigger landslides, and wildfires that lead to debris flows. These hazards can be particularly dangerous because they combine the effects of multiple hazards, leading to increased damage and complexity (Alfieri et al. 2017; Ward et al. 2020). Cascade hazards, on the other hand, occur when multiple hazards occur in sequence, leading to a cascading effect. For example, in previous studies, a landslide can block a river, leading to the formation of a lake behind the dam. If the dam fails, it can trigger a flood downstream, which can then lead to a secondary hazard such as erosion or further landslides (Cui et al. 2013; Fan et al. 2020; Korup and Tweed 2007).

The interconnection between geomorphic hazards and climate change

Geomorphic hazards are hazards that are related to the natural processes of the earth, such as landslides, floods and erosion (Chelli et al. 2021; Keller and DeVecchio 2019). These hazards are influenced by a range of factors, including climate, geology, topography, and land use. Climate change is one of the factors that can significantly influence the occurrence and severity of geomorphic hazards. As global temperatures continue to rise, climate change is leading to changes in precipitation patterns, which can increase the frequency and severity of floods and landslides. In addition to changes in precipitation patterns, climate change is also leading to changes in the intensity and frequency of extreme weather events, such as hurricanes, cyclones, and typhoons (Zwiers et al. 2013). These events can lead to compound and cascade hazards, as multiple hazards combine or occur in sequence, leading to increased damage and complexity.

Moreover, climate change can also affect the stability of slopes and the behaviour of water and sediment, which can increase the risk of landslides and erosion (Crozier 2010; Jakob 2022; Stoffel et al. 2014). For example, melting permafrost in high-altitude regions can lead to destabilization of slopes and rockfalls, while increased rainfall intensity can lead to soil erosion and landslides. In addition to this, the connection between geomorphic hazards and climate change is complex and multifaceted (Gorelick and Zheng 2015). While climate change is not the sole cause of these hazards, it can significantly increase their frequency and severity, leading to increased risk and vulnerability for people and infrastructure (Hallegatte and Corfee-Morlot 2011). Addressing the impacts of climate change on geomorphic hazards will require a range of measures, including early warning systems, hazard mapping, risk assessment, and adaptation strategies that incorporate the latest scientific understanding of these hazards. Preventing hazards in steep mountain channels can be a challenging task, but there are several strategies that can be used to reduce the risks and ensure the safety of people and infrastructure. Here are some measures that can be taken to prevent hazards in steep mountain channels.

Hazard mapping, risk assessment, and structural measures

Conducting hazard mapping and risk assessment is an important first step in identifying potential hazards in steep mountain channels. It involves identifying areas that are susceptible to landslides, flash floods, rockfall, debris flows, and other hazards, and assessing the potential risks to people and infrastructure (Santi et al. 2011). Moreover, Zou et al. (2019) focused on regional risk assessment of debris flow in the Longxi River Basin, China, using a hydrological response unit approach. The method considered 11 disaster factors and establishes a hazard integrated model to evaluate debris flow and hazard levels. The study incorporated exposure and vulnerability analysis for different elements at risk. The approach was validated with field studies, resulting in a debris-flow risk map that aligned with the actual disaster situation. The findings emphasized the correlation between high-risk zones and topographic and socioeconomic characteristics, offering scientific support for planning measures to prevent or reduce debris flow hazards in the region. Implementing structural measures such as retaining walls, gabions, and concrete barriers can help to stabilize slopes and prevent landslides and rockfall. Similarly, constructing flood control measures such as dams and levees can help to control the flow of water and prevent flash floods.

Vegetation management and early warning systems

Vegetation can play an important role in stabilizing slopes and reducing the risk of landslides and rockfalls. Maintaining a healthy vegetation cover, including trees, shrubs, and ground cover, can help to stabilize slopes and reduce the risk of erosion (Löbmann et al. 2020; Morgan and Rickson 2003). Developing and implementing early warning systems can help alert people to potential hazards, giving them time to take action to protect themselves and their property (Kelman and Glantz 2014; Leonard et al. 2008). Early warning systems can include flood gauges, rain sensors, and seismic sensors, etc.

Land-use planning and awareness

Proper land-use planning can help to prevent hazards in steep mountain channels. This involves regulating the types of activities that are allowed in these areas, such as construction, mining, and logging, to prevent damage to slopes and minimize the risk of hazards (Jakob and Hungr 2005; Jakob et al. 2022). The awareness among people about the potential hazards in steep mountain channels and to stay safe can help to prevent accidents and minimize the risks. It can also involve providing information about evacuation routes, emergency procedures, and hazard mitigation measures.

The hazards associated with steep mountain channels such as landslides, flash floods, rockfalls, debris flows, and avalanches, pose significant risks to both humans and infrastructure, as discussed by Ávila et al. (2016), Pham et al. (2019), Luckman (2017), Alfieri et al. (2017), and Ward et al. (2020). However, implementing mitigation measures, such as hazard mapping, risk assessment, and structural interventions including retaining walls and flood control measures can help reduce these risks as mentioned by Santi et al. (2011), and Zou et al. (2019). In addition to this, Löbmann et al. (2020), Morgan and Rickson (2003), Kelman and Glantz (2014) studied vegetation management and early warning systems that contribute to slope stabilization and timely alerts, while proper land-use planning ensures sustainable development in mountainous regions. However, Jakob and Hungr (2005) and Jakob et al. (2022) addressed these strategies and challenges, including financial constraints, inadequate government support, and insufficient knowledge among affected communities. Based on these studies, future perspectives should focus on improving the effectiveness of early warning systems, enhancing climate change resilience, and promoting sustainable land-use practices. Additionally, studies need to address the complex interplay between geomorphic hazards and climate change and consider the multifaceted factors influencing these phenomena. Future studies should be carried out to overcome these limitations for more comprehensive risk management strategies in steep mountain regions.

2 Discussions and future perspectives

Research on the sediment transport and the morphology of the steep channels is necessary to enable optimum land and water usage in the mountainous region. Based on the literature reviewed in the current study, it is evident that there is a significant gap in understanding the hydrodynamics and morphological processes in steep mountain streams. Some of the potential discussions and future perspectives are stated as follows:

2.1 Effective discharge, flow dynamics, and challenges in sediment transport in steep channels

The concept of effective discharge for sediment transport in steep mountain channels is essential but complex. The variability observed in steep channels is influenced by factors such as channel geometry and sediment characteristics which poses challenges in establishing a universally applicable function. In the context of river management, applying effective discharge necessitates careful consideration of real-world complexities and modeling assumptions, emphasizing the importance of addressing these limitations for comprehensive insights. In addition to this, understanding the complex flow dynamics and sediment transport in steep mountain channels is essential for optimizing land and water usage in these regions. The primary focus should be on analyzing the flow characteristics, such as steep hydrographs, non-uniform geometry, and lateral inflow that change with time. The phenomenon of sediment transport is not only governed by discharge, but the grain size distribution, spatio-temporal variations of hydrographs, and sediment supply play a significant role. Furthermore, understanding the non-uniformity of sediment transport under fluctuating flow conditions is crucial. In addition to this, accurate predictions of sediment transport and water supply in steep mountain streams pose significant challenges. Future research should focus on improving prediction models that consider the variations in flood hydrographs, hydrologic processes, and meteorological conditions.

2.2 Impact of non-uniform geometry, macro roughness elements, and flow turbulence

Investigating the effect of non-uniform geometry at different stages of steep channels on sediment transport and bed morphology is crucial. It involves understanding the transitions in flow regimes, the influence of sediment transport, and bed stability. Moreover, the presence of macro roughness elements in mountain streams can lead to changes in flow patterns, such as the formation of drag waves, cross waves, and hydraulic jumps. Future studies should focus on the impact of these roughness elements on flow turbulence and its consequences.

2.3 Subsurface flow in permeable beds

The investigation of subsurface flow within permeable riverbeds in mountain streams is a critical area of investigation. However, to gain a deeper understanding of flow dynamics and sediment transport in these unique environments, comprehensive research is required to focus on several key aspects. Firstly, there is a need to develop robust measurement techniques that can accurately quantify subsurface flow. The understanding of different pathways and dynamics of water movement beneath the riverbed is essential for comprehending the entire flow structure. Secondly, future research should investigate the influence of subsurface flow and the behaviour of mobile sediments in mountain streams. The interactions between subsurface flow and sediment transport are pivotal for making accurate predictions and for implementing strategies to manage sediment movement and potential hazards in these regions. However, validating measurements and studying these intricate relationships can improve overall knowledge of flow processes and enhance our ability to address the challenges associated with steep mountain channels.

2.4 Morphological stability in mountain river reaches and geomorphic hazards

The morphological stability of mountain river reaches varies over time, influenced by changing flow conditions and sediment input. Researchers should investigate the effects of sediment composition, rate of sediment input, and the presence of sediment control structures on river morphology. Furthermore, geomorphic hazards in steep mountain channels are intensified by climate change. Future research should focus on the specific ways in which climate change impacts these hazards and explore effective strategies for adaptation and mitigation.

2.5 Advanced modeling approaches for fluid flow in steep channels

The utilization of various modeling approaches, such as CFD, OpenFOAM, and other approaches to simulate fluid flow in steep channels presents a promising avenue for research. By following advances in numerical methods and the accessibility of high-performance computing systems, these tools can accurately model complex geometries. Furthermore, combining CFD with experimental modeling enhances understanding of flow dynamics in steep terrains The approaches help in exploring the capabilities of these technologies to improve model accuracy and reliability, which is crucial in gaining a substantial comprehension of complex processes in mountainous regions. By integration of CFD, experimental modeling, and advanced data collection techniques, the research community can venture on a multidisciplinary journey to tackle the intricacies of steep mountain channels.

2.6 Future scope using ML and AI

The integration of ML and AI into predictive models for sediment transport and flow dynamics in steep channels offers substantial potential. The future scope in sediment transport studies using ML and AI approaches holds promising future advancements. The efforts can be directed towards addressing the existing limitations by enhancing data collection methods and promoting collaboration for the development of more comprehensive datasets. Future research can focus on refining ML models, such as CNNs and recurrent neural networks (RNNs), to improve the robustness and applicability across a broader range of river systems. Additionally, exploring innovative approaches such as fuzzy logic systems can contribute to a deeper understanding of sediment transport dynamics. The incorporation of advanced techniques, including ensemble modeling and emerging methodologies can further enhance the accuracy of predictions. Collaborative interdisciplinary research efforts, combining expertise in hydrology, geology, and data science, could play a crucial role in unlocking the full potential of modeling and AI-based approaches in advancing the understanding and predictive capabilities in sediment transport studies. The studies reviewed in the present work encompass the role of ML and AI in improving predictive models, understanding sediment transport and flow dynamics in steep channels, thus further emphasizing the importance of these technologies in the field.

3 Conclusion

Based on this extensive literature evaluation, the present understanding of the mechanisms governing flow dynamics, sediment transport, effective discharge and morphological evolution in steep channels is still restricted. It is because of the complexities of boulder-bed channels, deterministic prediction models are unlikely to forecast the actual behaviour effectively. Probabilistic approaches, on the other hand, are more suited for this purpose. Despite significant progress over the last decade, fundamental aspects remain unknown, particularly the flow and sediment fluxes during numerous flood events, which frequently cause significant changes in channel morphology and sediment availability at both river network and basin scales. As a result, the creation of experimental monitoring stations becomes critical for gaining insights into hydrodynamics and sediment transport, which would otherwise require depending primarily on laboratory trials.

The importance of researching these properties cannot be emphasized if such models effectively reflect the complicated and stochastic interactions between flow, bed, and bank within steep channels. Furthermore, repeated testing and a greater emphasis on investigating the impact of channel width and bank roughness in determining bed stability within flume investigations are recommended. Furthermore, experts from diverse disciplines like geomorphology, engineering, and physics should collaborate to create cutting-edge technologies for monitoring water and sediment flows throughout distinct flow phases. Because the long-term stability of steep channels demands significant monitoring efforts to solve shorter-term concerns, these instruments should be included in long-term activities. Estimating bed erosion or aggradation, flow velocity, and bedload transit volumes is critical for effectively addressing flood hazards and managing environmental problems. Significant efforts are necessary to improve data quality and monitoring to improve erosion and sediment transport models. Furthermore, due to its developing capabilities, mathematical modeling, hydrodynamic models, and ML has emerged as a significant technique. Finally, the predictions of these models are based on adequately collected data, which should be obtained with accuracy to maximize the model's utility and performance. Therefore, it is crucial to engage in thorough discussions and progress towards future perspectives concerning steep mountain channels and the consequent hazards. In addition to this, it illustrates the mitigation of risks associated with natural features and for the development of a sensitive understanding of the complex interplay between natural processes and human activities in mountainous regions.

Acknowledgements

The authors would like to thank their fellow researchers for their insightful comments, which helped to significantly enhance the overall quality of the work.

Role of funding sources

The authors gratefully acknowledge the financial support received from the Core Research Grant, SERB Government of India (CRG/2021/002119), to carry out the review work presented in this paper.

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CHI ref #:	C517 191419
Volume:	32
DOI:	https://doi.org/10.14796/JWMM.C517
Cite as:	JWMM 32: C517

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Received:	June 23, 2023
First decision:	August 25, 2023
Accepted:	January 29, 2024
Published:	May 28, 2024

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# reviewers:	2
Version:	Final published

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© Mir and Patel 2024 Some rights reserved.

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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A Comprehensive Review on Sediment Transport, Flow Dynamics, and Hazards in Steep Channels

Abstract

1 Introduction

1.1 Background

1.2 Energy dissipation

1.3 Flow resistance

1.4 Bed shear stress

1.5 Sediment transport in steep mountain channels

1.6 Effective discharge for sediment transport

1.7 Experimental modeling

1.8 Modeling approaches using Computational Fluid Dynamics

1.9 Machine learning algorithms

Artificial Neural Networks (ANN)

Support Vector Regression (SVR)

Random Forest (RF)

Gradient Boosting Machines (GBM)

Convolutional Neural Networks (CNN)

1.10 Hazards of steep mountain channels

Landslides and flash floods

Rockfalls, debris flows, and avalanches

Compound and cascade hazards

The interconnection between geomorphic hazards and climate change

Hazard mapping, risk assessment, and structural measures

Vegetation management and early warning systems

Land-use planning and awareness

2 Discussions and future perspectives

2.1 Effective discharge, flow dynamics, and challenges in sediment transport in steep channels

2.2 Impact of non-uniform geometry, macro roughness elements, and flow turbulence

2.3 Subsurface flow in permeable beds

2.4 Morphological stability in mountain river reaches and geomorphic hazards

2.5 Advanced modeling approaches for fluid flow in steep channels

2.6 Future scope using ML and AI

3 Conclusion

Acknowledgements

Role of funding sources

References

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Ajaz Ahmad Mir

Mahesh Patel

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