Introduction

Alluvial rivers flowing through floodplains exhibit complex patterns of morphological evolution, influenced by spatial variability in channel geometry, hydrodynamic conditions, and sediment transport dynamics. Based on their planform characteristics, alluvial channels are typically classified into four distinct morphological types: straight, meandering, braided, and anabranching systems. Among these, wandering rivers are particularly notable for their distinctive geomorphological features, which are characterized by heightened morphological complexity and dynamic instability1,2,3. Extensive research has demonstrated that alluvial river systems have experienced significant morphological transformations in recent decades, primarily driven by the combined effects of anthropogenic interventions and natural processes. The spatial and temporal heterogeneity of fluvial erosion-deposition patterns has become increasingly pronounced, with land use and land cover changes emerging as critical factors influencing riverine dynamics. Understanding these complex sediment transport processes is crucial for elucidating fluvial system behavior and developing sustainable river management strategies in response to changing environmental conditions4,5,6.

Current research indicates that fluvial processes in wandering rivers exhibit heightened sensitivity to variations in water discharge and sediment flux. Alterations in upstream hydrological and sedimentological conditions can significantly disrupt the equilibrium state of channel morphology, with these parameters emerging as primary controlling factors governing thalweg migration patterns. The thalweg trajectory serves as a reliable indicator of main channel dynamics, providing critical insights into the spatial and temporal evolution of the dominant flow path within the river system7,8,9,10. Furthermore, the dynamics of water-sediment regimes are intrinsically linked to multiple environmental factors, including meteorological patterns, geological characteristics, and anthropogenic modifications such as upstream reservoir construction, which collectively influence the fluvial system’s hydrological behavior11,12,13. Previous investigations, primarily focusing on interannual comparisons during flood seasons14, have consistently demonstrated the significant influence of hydrological and sedimentological variations on fluvial morphological adjustments, despite variations in temporal scales across different studies.

Bank stabilization engineering measures have been demonstrated to effectively enhance channel morphology by reducing channel braiding intensity, constraining lateral migration, and promoting flow concentration. These interventions contribute to improved main channel stability, enhanced flood control capacity, and reduced embankment vulnerability, thereby mitigating flood risk and ensuring river management objectives15,16,17. The effectiveness of bank protection structures is significantly influenced by channel geometry parameters, particularly curvature radius and bend configuration. Differential implementation of revetment schemes induces distinct patterns of erosion and deposition in meander bends, consequently altering thalweg alignment and exerting substantial control on channel morphological evolution processes18,19. Currently, with the continuous advancement of the river training project, the river is increasingly influenced by the effects of artificial control, the existing river boundary has gradually become a constrained boundary of limited control from the natural river, and the river boundary has been transformed into a weak impact resistance of the natural soil boundaries and impact resistance of the engineering boundaries of the strong common composition20. With the increase of the density of the regulation project, the plane shape of the wide, shallow and scattered river channel has been significantly improved, and the blank section of flood control has been reduced.

Tarim River is the first largest inland river in China, Tarim River its upper reaches for a typical wandering river21, the majority of the high beaches on both sides have been reclaimed for farmland. In the static context, the river channel exhibits a progressive widening, accompanied by an increase in the formation of sandbars and beaches. Dynamically, the absence of riparian vegetation, coupled with the presence of fine sand characterized by low clay content, renders the riverbanks highly susceptible to erosion22. Consequently, the processes of flow and sediment transport become highly concentrated and undergo significant fluctuations, leading to alternating patterns of riverbed erosion and siltation. This dynamic environment results in the frequent interchange of main river branches and continual alterations in the flow path23. The erosion and deposition dynamics of the riverbed in the upper reaches of the Tarim River are influenced by two primary factors: the water and sediment processes originating from the three upstream tributaries, and the inherent stability of the riverbed itself24. Due to the fine and silty sand composition of the upper reaches of the Tarim River, the riverbed exhibits poor anti-scourability. As a result, significant vertical erosion and deposition changes, as well as lateral swings, frequently occur during the flood season25,26. Consequently, the riverbed is generally characterized by siltation and uplift, while the average river width demonstrates a decreasing trend24,27. When analyzing the driving factors behind river morphology evolution, two primary control variables—water flow and sediment—are typically considered. This is primarily because changes in water flow directly influence sediment transport processes, which in turn drive morphological alterations in the river system28. In the early stage of our research, our team proposed a calculation method for the deviation degree of the planar shape parameters of the Tarim River channel29. Furthermore, we demonstrated that the positive deviation deformation pattern of the river channel is strongly correlated with annual runoff, annual sediment transport, and bankfull discharge. Simultaneously, the evolution processes of water and sediment exhibit complex nonlinear characteristics, including both abrupt changes and trend patterns30,31. Additionally, the intensity of flow erosion during the flood season undergoes significant variations. The wandering river section in the upstream exhibits the most pronounced erosion and deposition dynamics. A strong correlation exists between the width of the flat beach, the water depth of the flat beach, and the erosion intensity during the flood season. Moreover, the adjustment of the flat beach channel morphology effectively responds to changes in water and sediment conditions26.

In recent years, remote sensing technology and geographic information systems (GIS) have been extensively applied in river morphology studies, particularly for monitoring river migration, erosion, and deposition processes32,34. However, limited research has been conducted on analyzing river channel adjustment and evolution under the combined effects of water-sediment dynamics and boundary conditions using remote sensing technology and geographic information systems (GIS). Most existing studies have focused on the evolution of river morphology and the characteristics and patterns of the overall centerline migration. However, there is limited research on the quantitative analysis of planar morphological changes. Additionally, the adjustment and variation of local river segments under fixed boundary conditions have been largely overlooked, and there is a lack of quantitative analysis of thalweg dynamics in continuous bends within local river segments. Therefore, this study focuses on the wandering section of the upper Tarim River as the research area. Utilizing Landsat-8 and Landsat-9 satellite images from 2013 to 2023, the river boundaries and planar morphological parameters of the study section were extracted. Combined with hydrological station data, the study aims to achieve the following objectives: (1) Quantitatively analyze the planar morphological characteristics of the river under fixed boundary conditions, revealing the driving mechanisms behind river morphological changes; (2) Investigate the relationship between thalweg migration width in local continuous bends and influencing factors such as water-sediment dynamics and fixed boundaries, exploring the thalweg migration mechanisms under the synergistic effects of multiple factors; and (3) Establish an empirical formula for the migration width of thalwegs in continuous multi-bend sections. The findings of this study are expected to provide critical insights for river management, flood control, disaster mitigation, and ecological restoration projects, offering significant practical implications.

Materials and methods

Study area

The mainstream of the Tarim River, situated in the hinterland of the Tarim Basin, spans a total length of 1,321 km from Sanyuankou to Taitema Lake. It is characterized as a plains-type river and is divided into three segments: the upstream section (from Sanyuankou to Yingbazha) covering 495 km, the middle reaches (from Yingbazha to Qiala) spanning 398 km, and the lower reaches (from Qiala to Taitema Lake) extending over 428 km. Due to the diverse environmental conditions across these segments, significant variations exist in river characteristics and ecological environments23,24,35.

The wandering reaches of the Tarim River cover an extensive geographical area. However, due to constraints such as limited funding, protective measures have not yet been implemented in some sections. To safeguard critical areas of the river section, the First Division of the Tarim River has primarily implemented a renovation project along the river section near Alar City since 2013. This initiative aims to achieve preliminary stabilization of the river regime, enhance flood control, and mitigate disaster risks. The study area spans a 65 km stretch of the Tarim River, extending from Sanyuankou in the upper reaches of the main stream to the vicinity of the Third Bridge in the First Division. The basin is geographically located between 80°94′E to 81°48′E and 40°48′N to 40°70′N. Most administrative units within the jurisdiction of Alar City are situated near the river. The basin exhibits unique natural conditions, characterized by high mountains surrounding the area and a desert in the central region. It falls under the warm temperate extreme continental arid desert climate, featuring low precipitation, high evaporation, and significant diurnal temperature variations. The annual average temperature is 11 °C, with an average annual rainfall of 53.3 mm. The river section is wide and shallow, with an average width ranging from 0.6 to 1.2 km. The average longitudinal slope of the riverbed in the upper reaches is 0.2‰, while the longitudinal stability coefficient (φ = d/J) is 3.64, and the lateral stability coefficient (ψ = b/B) is 0.16. The river exhibits characteristics typical of a wandering river section. The spatial location of the study area is shown in (Fig. 1a). During the flood season, the mainstream undergoes lateral migration, causing strong currents to erode the riverbanks. To safeguard the lives and property of residents on both sides, the existing riverbanks have been reinforced. Specifically, revetment projects spanning 29.92 km on the left bank and 37.07 km on the right bank have been constructed. The majority of these revetments utilize rough slope protection and riprap foot protection, as illustrated in (Fig. 1b, c). The study section is depicted in (Fig. 1d).

Fig. 1
figure 1

Study the geographical location and revetment of the area. (a) The spatial location of the study area. (b) and (c) River bank protection type. (d) The specific river section of the study area. The local spatial location map of China was generated using the China map in ArcGIS software (version 10.8, available at https://desktop.arcgis.com/zh-cn/arcmap/index.html) and ArcMap software. The location map of the study area was created using Bigemap GIS Office software (version 2.1.8, available at http://www.bigemap.com/).

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Data sources

Remote sensing image data were adopted from the Landsat series provided by the Geospatial Data Cloud Platform of the Computer Network Center of the Chinese Academy of Sciences (https://www.gscloud.cn/). During the abundant water period (July-August), the high incoming flow causes the water level in the upstream wandering section to rise, and the water flow cuts through large sandbars or submerges smaller ones. This results in an increase or decrease of the number of sandbar units. Therefore, remote sensing images taken during this period are selected to reflect the geomorphological characteristics of the river for the year. The increase of flow in the wet season causes the mainstream of the wandering section to oscillate unpredictably, and the river regime changes sharply. Moreover, the thalweg of the river channel often changes sharply after the wet season. The swing of the thalweg reflects the change in the width of the river channel36 and reflects the change in the mainstream of the river channel to a certain extent. The flow of the Tarim River is minimal during the dry period, resulting in little change to the thalweg. To reflect the changes in the thalweg during the abundant water period, the centerline of the river channel during the dry period is selected based on remote sensing images to represent the thalweg of the river channel. Due to cloud cover in the remote sensing images, the river channel is obscured, which hinders accurate water body extraction. Consequently, October was selected for certain years, while the remaining images were primarily acquired close to December. Although a one-month interval may result in minor changes in surface morphology, the surface characteristics of the study area are relatively stable, making significant changes during the dry season unlikely. While this temporal difference has a limited impact on the overall results, selecting remote sensing images with closer acquisition dates would enhance comparative consistency. Consequently, after screening the remote sensing images, the study data were categorized into two groups based on the acquisition period: Group 1 comprises Landsat-8 images without cloud cover during the high-water period (2013–2023), and Group 2 consists of Landsat-8 images without cloud cover during the low-water period (2013–2023). The spatial resolution of the Landsat-8 and Landsat-9 data in both groups is 30 m, as detailed in Table 1.

Table 1 Remote sensing image data sources.
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The runoff of the Tarim River is primarily supplied by its three major tributaries: the Yarkant River, the Hotan River, and the Aksu River. Additionally, during flood events, when a major flood occurs at the Alar station, the Aksu River typically experiences a corresponding large flood, whereas the Hotan River and the Yarkant River do not necessarily exhibit similar flood magnitudes. This indicates that the Aksu River is the primary source of floods in the mainstream of the Tarim River. The average discharge of the Aksu River during the flood season is 195 m³/s. The Alar hydrological station, located near the study section, serves as the primary control station for the upper reaches of the Tarim River. Given the limited number of hydrological stations and their spatial distribution, the Alar station provides the most representative data for this study. Considering the proximity of the study section to the Alar station and the minimal flow loss along the river section, we assume that flow variations within the study section are negligible. The average annual runoff and annual sediment yield of Alar station (2013–2023) were 5.210 billion m3 and 148.270 billion t, respectively. 70.9% of the annual runoff and 95% of the sediment discharge are mainly concentrated in July-September. The maximum channel forming discharge is 960.21 m3/s, which occurs in 2022, and is illustrated in Fig. 2.

Fig. 2
figure 2

The annual runoff, annual sediment yield and channel forming discharge of Alar hydrological station from 2013 to 2023 were analyzed.

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Methods

Image processing method

The modified normalized difference water index (MNDWI) enhances the extraction of water body information across different spectral bands. By analyzing the spectral characteristics of various land types, this method effectively distinguishes water bodies from shadows and accurately extracts water body information37. The calculation formula is presented in Eq. (1). Landsat 8-OLI and Landsat 9-OLI satellite remote sensing data were synthesized using bands B5, B4, and B6 to extract river water information during the wet season from 2013 to 2023. The entire river boundary, as well as the boundaries of beaches and sandbars for each year, were delineated. Based on the entire river boundary, the river centerline was extracted using the ArcGIS vectorization tool, ArcScan. In order to systematically analyze the river dynamics, we used the ArcScan tool to divide the study reach ( 65 km ) into 26 sub-reaches at an equidistant interval of 2.5 km. Each sub-reach is further equidistantly divided into 10 small reaches, a total of 260 small reaches. Following the extraction of water bodies from the river during the dry season, the river centerline was derived using the vectorization tool ArcScan, serving as the primary analysis target for the river thalweg in this study.

To assess the potential impact of clouds and shadows on remote sensing images, we employed a confusion matrix and the Kappa coefficient to evaluate classification accuracy. The MNDWI threshold was adjusted through sensitivity analysis to optimize the classification results. The results indicate that a threshold of 0.2 yields the maximum Kappa coefficient of 0.80, which was therefore selected as the optimal threshold. Detailed values are presented in Table 2.

Table 2 Image sensitivity analysis.
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$$MNDWI = \frac{{p(Green) - p(MIR)}}{{p(Green) + p(MIR)}}$$
(1)
$$k = \frac{{{P_o} - {P_e}}}{{1 - {P_e}}}$$
(2)
$${P_o} = \frac{{\sum\nolimits_{i = 1}^k {T{P_i}} }}{N}$$
(3)
$${P_{\rm{e}}} = \frac{{\sum\nolimits_{i = 1}^k {\left( {Ro{w_i} \times Colum{n_i}} \right)} }}{{{N^2}}}$$
(4)

Here, Green denotes the green band, MIR represents the mid-infrared band, and for Landsat 8-OLI and Landsat 9-OLI, these correspond to Band 3 and Band 6, respectively. k is the number of categories, Po represents the observation accuracy, Pe denotes the expected accuracy, TPi is the number of correctly classified samples for class ii, N is the total number of samples, Rowi is the sum of row i in the confusion matrix, and Columni is the sum of column i in the confusion matrix.

Density analysis of river regulation project

Bank protection construction in the wandering reach of the upper Tarim River commenced in 2013. To evaluate the constraining effect of the bank protection project on the river regime, data on river regulation construction within the study area (a 65 km stretch from Sanyuankou to the Third Bridge of the Tarim River in the First Division) from 2013 to 2023 were collected. To reflect the constraint effect of the wandering river revetment project on the river regime, the construction of the river regulation project in the study area (65 km from Sanyuankou to the First Division Tarim River Third Bridge) from 2013 to 2022 was collected. To facilitate the analysis and comparison of the distribution of revetment projects in different river sections, the ratio of the total length of the river regulation projects to the total length of the river channel is defined as the density of the river regulation projects. This index, spanning from 2013 to 2022, is illustrated in Fig. 3. The study section is a control project that limits the river regime. It can be seen from Fig. 3 that the density of revetment works in this river section is increasing year by year, and the left bank (2013–2016, 2017–2018, 2019–2023) and the right bank (2013–2015, 2016–2018, 2019–2023) of this river section can be divided into three periods. Among them, 2013 to 2015 is the period with the largest number of right bank treatment projects, with an increase of about 37.61%. In the last two periods, the density of revetment projects increased slightly, about 2.41% and 12.83%; The most intensive period of the left bank treatment project is from 2017 to 2018, with an increase of about 27.02%, while the other two periods have a small increase. Since 2018, large-scale revetment projects have rarely been built on the left bank and right bank of this study section. Generally, existing projects are reinforced or partially expanded. Therefore, after 2018, the density of revetment works on the left and right banks of the upstream wandering section has not changed much.

Fig. 3
figure 3

Density of river bank protection works in the study section 2013-2022.

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River shape parameter calculation and data analysis method

Based on the remote sensing image, the plane shape parameters of the wandering river channel are calculated: sandbar index \(BI_B^*\), thalweg swing amplitude TS. The sandbar index \(BI_B^*\) is widely used to characterize the branching intensity of the planar morphology of the wandering channel38. The thalweg swing amplitude TS is expressed by the absolute value of the difference between the abscissa distance and the abscissa distance corresponding to the same section of the main streamline in the dry season of the river in the adjacent years. The calculation method for each morphological parameter is:

$$\varphi = \frac{d}{J}$$
(5)
$$\Psi = \frac{b}{B}$$
(6)
$$BI_B^* = 2\frac{{\sum {L_b} }}{{L_r}} + \frac{{N_b}}{{L_r}}$$
(7)
$$TS = {S_a} - {S_b}$$
(8)

Here, d represents the median diameter of the bed sediment (m); J demonstrates the river slope (‰); b illustrates the width of the river channel during the dry season (m); and B indicates the width of the river at bankfull stage (m); Lb represents the length of each sandbar; Lr indicates the length of the river segment; and Nb illustrates the number of sandbars; Sa shows the abscissa value corresponding to the main stream line in the dry season of the new year; Sb demonstrates the abscissa value corresponding to the main stream line in the dry season last year.

The curved section, slightly curved section, straight section and relatively straight section of the wandering river were selected to analyze and compare the changes of the whole sandbar and thalweg in the wet season (July-September) and the dry season (October-April). Data on flow, water depth, and sediment particle size from 2013 to 2023 were obtained from hydrological stations and field surveys (available at: http://www.mwr.gov.cn/sj/tjgb/zghlnsgb/). The relationship between the finite control boundary and the continuous curve thalweg of the wandering section is established, and the quantitative relationship between the swing width of the continuous curve thalweg and the water and sediment conditions is quantified. The main research framework is illustrated in Fig. 4.

Fig. 4
figure 4

The research methods of riverbed morphology analysis and thalweg empirical formula establishment are summarized.

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Results and analysis

Analysis of sandbar dynamics under fixed boundary conditions

Under varying discharge conditions in the wandering reach of the upper Tarim River, significant changes occur in riverbed sandbars and bars. Consequently, the main branches of the river channel frequently shift due to these morphological alterations. With the progressive implementation of river regulation projects in the upper Tarim River, the morphology of the bank slope has undergone significant changes. Consequently, under fixed boundary conditions, the number of sandbars in the river has markedly decreased. On one hand, the alteration of sandbars leads to shifts in the mainstream flow path; on the other hand, the flow erodes or submerges sandbars, transporting sediment downstream.

Figure 5 indicates the results of the change in the sandbar index of the river segments, there are some fluctuations in the sandbar index \(BI_B^*\) on the condition that the revetment density is different, with 2018 as the cut-off point, the 26 river segments sandbar index\(BI_B^* \in \left[ {{\rm{0\sim11}}{\rm{.70}}} \right]\)in 2013–2017 (refer to Fig. 5a), the average value of 4.31, and the 26 river segments in 2018–2022 (refer to Fig. 5b) Sandbar Index\(BI_B^* \in \left[ {{\rm{0\sim8}}{\rm{.71}}} \right]\), with a mean value of 2.80. Following 2018, the overall sandbar index \(BI_B^*\) of the left and right banks of the river with a riparian density of 40% or more decreased substantially compared to that of the overall sandbar index \(BI_B^*\)with a riparian density of less than 40%, which was due to the fact that the riparian project constrained the erosion of the water flow on the boundary, resulting in a more concentrated water flow, causing the sandbars within an average river width of 0.5 km to be easily submerged or eroded by the current. Despite the fact that the number of sandbars increases following cutting, the length of the corresponding sandbars decreases accordingly, resulting in a decrease in the sandbar index of the whole river section.

Fig. 5
figure 5

Changes in beach sandbar index \(BI_B^*\) from 2013 to 2022.

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To compare the effect of the morphology of continuous curved sections and straight sections of wandering channels on the sandbar index, two groups of river sections with different riparian densities for the year and similar flows during the high water period (average flow in July, August, and September) were selected for comparison, 2013 (Q = 488m3/s), 2018 (Q = 443m3/s) and 2015 (Q = 535m3/s), 2021 (Q = 487m3/s). Analysis of the results indicates that in 2013 and 2018, the average \(BI_B^*\) of the first section of the more straight stream was 6.98 and 2.84, respectively, the average \(BI_B^*\) of the second section of the more straight stream was 5.90 and 4.60, respectively, the average \(BI_B^*\) of the continuous bend section was 3.11 and 2.04, respectively, and the average \(BI_B^*\) of the more continuously curved section was 3.37 and 3.33, respectively, whereas in 2015 and 2021, the average \(BI_B^*\) of the first section of the more straight stream was were 3.66 and 3.53, respectively, and the average \(BI_B^*\) for the second smoother stream segment was 6.79 and 3.95, respectively, while the average \(BI_B^*\) for the continuous bend segment was 3.55 and 1.40, respectively, and the average \(BI_B^*\) for the more continuous bend segment was 4.91 and 1.95, respectively, as indicated in Fig. 6 below. Through the two groups of rivers, comparison found that, regardless of whether the river bank density is larger or smaller, the overall river section of the continuous bend the \(BI_B^*\) compared to the straight river \(BI_B^*\) is smaller, this is due to the fact that the curved river and straight river in comparison to the curved river by the impact of inertia and centrifugal force of the current, the impact of the water flow on the riverbanks leads to the pooling of water. When the length of the bend is not extensive, the current quickly enters the next bend, allowing the water flow to concentrate on submerging small sandbars or eroding portions of larger sandbars, so that \(BI_B^*\) is reduced. When a certain flow, part of the straight section of the river along the course of the construction of the bank protection project, and yet the river width is too large, wide and shallow channel is prone to water flow cut beach, so that some sections of the river sandbar increase in number. The analysis shows that the bending coefficient of the bend also has a significant influence on the sandbar index. The continuous bend with an average bending coefficient of 1.59 is relatively smaller than the continuous bend sandbar index \(BI_B^*\) with a bending coefficient of 1.32. Furthermore, the change of continuous bend \(BI_B^*\) under the action of revetment is more obvious.

Fig. 6
figure 6

Comparison of River Sandbar Index \(BI_B^*\).

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Analysis of Thalweg dynamics under fixed boundary conditions

The upper reaches of the Tarim River comprise the wandering section. Due to the similar sediment composition of the banks on both sides of the river and the center of the trough23, the poor bank constraints and the shallow width of the river are conducive to the oscillation of the river, as well as the thalweg of the river oscillates drastically under distinct time series. On the condition that the density of the left and right bank protection of the river channel was not uniform, the width of the thalweg oscillation between distinct sections of the river channel varied greatly, and the overall degree of oscillation of the thalweg slowed down as the density of the bank protection increased. As shown in Fig. 7, when the density of the left berm of the channel increased from 9.2 to 28.11% and the right berm from 0 to 40.02%, the average swing width of the thalweg was 0.33 km towards the left bank and 0.32 km towards the right bank. When the river’s left and right bank protection density increased from 28.11 to 41.48% and 40.02–52.85%, respectively, the average swing width of the thalweg was 0.21 km towards the left bank and 0.18 km towards the right bank, reducing the average swing width by 0.12 km towards the left bank and 0.14 km towards the right bank compared to before the increase in bank protection density. As the Tarim River suffered the largest flood peak (Q = 1830m3/s) in the last 10 years in 2022, thus the maximum swing to the left bank and the right bank both occurred in 2021–2022 and the swing width of the Thalweg was 1.94 km and 1.63 km, respectively. The greater the density of bank protection is, the greater the influence on the amplitude of the river’s thalweg oscillation is. On the contrary, the lower, the less, when in a certain density of bank protection, the influence of higher flow on the amplitude of the thalweg oscillation also increases. In Fig. 7, it is evident that the typical continuous multi-bend river section of the thalweg (about 18 km from the Sanyuankou-30.3 km from the Sanyuankou) has a small oscillation amplitude relative to the thalweg in the straight river section, and the density of river bank protection is less than 40%, the average oscillation amplitude of the straight river section is -0.37 km ~ 0.36 km and the average oscillation amplitude of the typical continuous multi-bend river section is -0.12 km ~ 0.15 km; when the riparian protection density exceeds 40%, the average oscillation amplitude ranges from − 0.23 km to 0.21 km in the straight river section, and from − 0.06 km to 0.05 km in the typical continuous multi-bend river section. Variance analysis was conducted on the thalweg of the river across four distinct periods, as illustrated in Fig. 8. The standard deviations of thalweg swing in the initial section for these periods were measured at 0.40, 0.20, 0.60, and 0.22, respectively. Correspondingly, the standard deviations for the second section were recorded as 0.66, 0.47, 0.61, and 0.40. In the continuous curved river sections, the standard deviations were observed to be 0.20, 0.12, 0.26, and 0.09, respectively, while another set of continuous curved sections exhibited standard deviations of 0.45, 0.29, 0.46, and 0.26. Notably, the standard deviation of the thalweg in straight river sections was found to be significantly larger than that in curved sections, with marked differences observed across various river segments. Compared with the straight river, the lateral gradient and spiral flow in the continuous bend are much larger than those in the straight river due to the fact that the movement of the water flow along the bend is affected by the acceleration of centrifugal force, resulting in the water flow scouring the concave side of the riverbed. Before the construction of the revetment, the water flow scours the riverbank, causing continuous changes in the thalweg. After the construction of the revetment, the concave bank of the continuous curve forms a relatively stable curved thalweg, with changes mainly occurring in the discontinuous area between the gradient from the previous curve to the latter curve.

Fig. 7
figure 7

Oscillating difference in width of the thalweg from 2013 to 2022.“+” indicates that the thalweg is shifted to the right bank; “-” represents that the thalweg is shifted to the left bank.

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Fig. 8
figure 8

Significance analysis of thalweg migration width variability.

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Derivation of an empirical formula for Thalweg migration in continuous multi-bend channels under fixed boundary conditions

Due to the revetment’s influence, the swing amplitude of the river thalweg in the typical continuous multi-bend section is most pronounced, with an average swing amplitude ranging between − 0.26 km and 0.22 km. Due to the staggered construction of continuous bend bank protection from 2013 to 2018, the overall construction was completed merely in 2018, to study the change process of the thalweg of the continuous bend of the river, consequently, the research focused on Sects. 68–112 of the continuous bend section from 2018 to 2021, employing the multiple regression analysis method to quantitatively analyze the relationship between the thalweg oscillation width and water-sand factors and boundary conditions. An empirical formula and a functional formula were established to predict the future changes in the thalweg in this section of the continuous bend river.

Determination of the length of the Thalweg outbound straight line

The water flow in the river channel undergoes a curvilinear motion in continuous bends, forming lateral circulation due to centrifugal force, which results in erosion on the concave bank and deposition on the convex bank, contributing to deeper erosion near the concave bank, following the construction of revetment works on the concave bank, the thalweg of the river channel developed close to the concave bank. From Fig. 9, it is apparent that the swing of the thalweg near the concave bank is minimal. Once the water flow exits the bank protection project, it ceases to follow a curved path, resulting in reduced centrifugal force and increased oscillation activity of the thalweg. Consequently, emphasis should be placed on studying the width of the swing of the thalweg upon leaving the bank. For the purpose of better analyzing the fluctuation process of river channel thalweg under distinct years, a bend coordinate system is established with the midpoint of each bend protection project length as the origin O, as demonstrated in Fig. 10.

Fig. 9
figure 9

The process of oscillating the thalweg of the river from 2018 to 2021.

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Fig. 10
figure 10

Schematic diagram of analysis for the Swing of the thalweg. The local map of the study area was generated using Bigemap GIS Office software (Version 2.1.8, available at http://www.bigemap.com/).

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The three-bend revetment engineering in the research area have bending radii of 1.855 km, 2.441 km, and 2.028 km respectively, belonging to the micro-bend type improvement project. Thus, the length of the straight line fitted through the three curved thalwegs closely matches the distance of the river regulation project. Moreover, the distance of the river regulation project is mainly related to the flow intensity, the river bend parameters, the soil composition of the river bed, the sediment concentration of the water flow, the sediment gradation, as well as the river gradient39. When integrating the current water and sediment conditions, boundary conditions, and individual bend indices of the Tarim River, refer to Table 3. Due to the complex evolution of the river, statistical analysis and multiple regression methods are employed to fit the relationship between the length of the outbound straight line, namely, Eq. (9). Detailed information regarding the approximate shoreline length of the thalweg and the initial shoreline length is provided in Supplementary Information S1.

$${L_e} = - 0.0026{\rm{\;}}W + 0.00005{Q_s} - 0.8305R - 0.7435{L_c} + 6.613\quad {R^2} = 0.88$$
(9)

Here, Le indicates the straight-line length of the thalweg out of the bank; W demonstrates the annual runoff volume; Qs shows the annual sand transport volume; R illustrates the bending radius of the revetment project; Lc represents the approximate length of the thalweg against the bank.

Table 3 Impact indicator for straight-line length of out of the bank.
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Determination of swing width of continuous curved Thalweg

To further analyze the oscillation width of the thalweg along the continuous curve from 2018 to 2021, the length of the thalweg outbound straight line is used as the abscissa. This length is divided into 20 segments each year. According to the 20 points divided by the average length of the straight line out of the shore, the longitudinal values of the swing of the three bends are measured in turn. Following processing, it is determined that the longitudinal value of the thalweg swing in No.1 bend is undulating every year, and the maximum longitudinal value occurs in the second half of the straight line. The maximum and minimum longitudinal extents between the second half of 2018 and 2021 are 0.547 km and 0.219 km, respectively. The longitudinal values of No.2 bend and No.3 bend are typically increasing. Besides, the thalweg of No.2 bend is located below the length of the thalweg outbound straight line, and the maximum longitudinal value also occurs in the second half of the straight line. The maximum and minimum longitudinal values are − 0.00071 km and − 0.037 km, respectively. At the No.3 bend, the maximum longitudinal value occurs at the endpoint, with values ranging from 0.809 km to 1.036 km. The initial longitudinal average values of the three bends are quite different, that is, the ratio of the average flow erosion intensity to the relative mobility of the composition in the first four years is defined to reflect the change of the initial longitudinal average value of the thalweg, as illustrated in Table 4 below. When the\(\overline {{F_n}} /M\)ratio is larger, the change of the initial 5-point longitudinal mean of the first 5 points is correspondingly larger, and thus the thalweg oscillates to a large extent upon disembarkation, and the thalweg oscillates above the straight line of leaving the shore on the condition that the \(\overline {{F_n}} /M\)is larger, conversely, in 2020, the\(\overline {{F_n}} /M\)ratio is 1.069, the initial 5-point longitudinal means of the first 5 points of the three bends are 110.44, -300.73, and 39.50, respectively, while\(\overline {{F_n}} /M\)is the smallest in 2021, and the initial longitudinal mean values of -11.03, -154.04, and − 44.84, respectively.

Table 4 Initial longitudinal mean of the first 5 points.
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As illustrated in Fig. 11, Bend No. 1 exhibits a multi-fluctuation trend, while Bends No. 2 and No. 3 display a gradual upward trend. The thalweg migration interval for Bend No. 1 is 0.542 km, whereas those for Bends No. 2 and No. 3 are 0.162 km and 0.42 km, respectively. Consequently, Bend No. 1 is classified as Category I, and Bends No. 2 and No. 3 are classified as Category II. Since the thalweg of Bend No. 2 lies below the straight-line length, the first 10 points of the thalweg are elevated by 0.2 km annually, points 11 to 15 by 0.4 km, and the last 5 points by 0.6 km to facilitate alignment with the thalweg of Bend No. 3. After calculation, each point is adjusted by subtracting the corresponding value. Based on the 20 horizontal values for each year from 2018 to 2021, the two types of thalweg curves are fitted, as shown in Eqs. (10) and (11). The discrepancy between the fitting line trend and the observed data for Curve No. 1 is discussed in Sect. 4.2.

$$y=181.727\sin \left[ {\pi (\frac{{x - 977.758}}{{144{\text{4}}0.130}})} \right]+{\text{215}}{\text{0.336}}\quad {R^2}=0.52$$
(10)
$$y=0.0174{x^{1.348}} - 130.627\quad {R^2}=0.{\text{85}}$$
(11)
Fig. 11
figure 11

The relationship between the swing width of the thalweg and the length of the straight line from 2018 to 2021.

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To validate the relationship between the migration width of the two thalweg types and the length of the shoreline straight line, data points from the shoreline straight line in 2022 and 2023 were used for verification. The thalweg positions were calculated as illustrated in Fig. 12. It is demonstrated that the two fitting formulas are related to the average number of division points along the shoreline straight line. A higher number of average division points leads to more accurate fitting and calculation results, which better align with the actual conditions and more effectively reflect the thalweg migration in continuous river bends.As illustrated in Fig. 13, statistical analysis reveals that the absolute errors between the calculated and observed values for the three bends in 2022–2023 are ≤0.05 km, ≤0.08 km, and ≤0.11 km, accounting for 68%, 84%, and 97% of the total cases, respectively. The predicted values exhibit a high degree of consistency with the observed values (Fig. 13a and b).From 2018 to 2023, the absolute errors between the calculated and observed values for Bend No. 1 are ≤0.05 km, ≤0.1 km, and ≤0.15 km, accounting for 48%, 50%, and 93% of the total cases, respectively (Fig. 13c). During the same period, the corresponding proportions for Bends No. 2 and No. 3 are 58.3%, 86.7%, and 97.1% (Fig. 13d).The mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE) of the thalweg migration width from 2018 to 2023 are presented in Table 5. During this period, the mean values of MAE, RMSE, and MAPE for the thalweg migration width in Bends 1, 2, and 3 are 2.89, 16.50, and 4.57%, respectively.The predicted values closely align with the observed values. Although significant discrepancies exist in localized areas, the results effectively capture the thalweg migration trends in the continuous bends of the Tarim River under the influence of revetment structures.Specifically, the first type of formula can be applied to simulate similar rivers with continuous bends where the thalweg oscillates widely, ranging between 0.5 km and 0.6 km. On the other hand, the second type of formula is suitable for simulating thalweg oscillation patterns characterized by gradual increases within a range of 0.15 km to 0.5 km.

Fig. 12
figure 12

Comparison of calculated and measured values of the thalweg in multiple consecutive bends from 2022 to 2023.

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Fig. 13
figure 13

Absolute error distribution.

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Table 5 Error analysis of observed and predicted values from 2018 to 2023.
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Discussions

The impact of river regulation project density on channel morphology

It is observed that under conditions of high flow rates or inconsistent water level differences between two or multiple branches, the overall sandbar is more susceptible to oblique flow erosion, leading to the formation of irregular sub-sandbars. These findings are consistent with previous studies40,41. The intensification of oblique erosion may be attributed to enhanced flow dynamics, particularly under high-flow conditions, where the erosive capacity of the flow increases, leading to the division of sandbars into multiple sub-sandbars. With the increasing density of revetment projects, these structures stabilize riverbanks and regulate the river regime, thereby limiting lateral erosion by the water flow. As a result, local river bends develop into inclined asymmetric bends or non-oblique symmetric bends, which subsequently influence the sandbar index and the overall morphology of the sandbars. Particularly in the continuous bend sections, the revetment projects mitigate erosion of the concave bank by the water flow, regulate the river width, and restrict the development of sandbars. In alluvial rivers, the composition of the riverbed plays a critical role in shaping river morphology. When the riverbed consists of fine sediment, significant channel changes occur during the flood season, including frequent main channel shifts and pronounced thalweg migration42,43,44. Prior to the construction of the revetment project, the flow in the curved river section was highly unstable due to centrifugal forces, resulting in pronounced thalweg migration. However, following the implementation of the revetment project, the river regime stabilized, and the amplitude of thalweg migration was significantly reduced.

The trend of the curve-fitting line does not align with the observed phenomenon

With changes in upstream water and sediment conditions, the river regime of local sections undergoes adjustments. The shifting of the main flow line alters the apex of the bend flow, which, under certain conditions, leads to the formation of skimming bends45,46. Flow scouring intensity is commonly used to characterize incoming water and sediment conditions. When the scouring intensity is low, significant siltation occurs on the convex bank of Bend No. 1. As the scouring intensity increases, the siltation diminishes, leading to fluctuations in the thalweg of Bend No. 1 in response to variations in water and sediment conditions (siltation typically occurs between one-third and two-thirds of the straight-line length). The fluctuation of the thalweg in Bend No. 3 is minimal due to variations in flow erosion intensity. This phenomenon may be attributed to the large radius of the revetment project, which directs the flow along a specific trajectory. As a result, the main flow line straightens, the flow circulation weakens, and the erosive capacity of the riverbed diminishes, leading to a linear migration pattern of the thalweg (see Fig. 14; Table 1).

Fig. 14
figure 14

The local comparison of No.1 bend and No.3 bend in 2018 and 2022 is carried out. The local map of the study area was generated using Bigemap GIS Office software (Version 2.1.8, available at http://www.bigemap.com/).

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Impacts and limitations

The findings of this study align with previous research, further confirming the critical role of revetment engineering in river regulation. However, this study also reveals that the influence of revetment engineering on river morphology exhibits spatial heterogeneity. In the continuous bend sections, the revetment project significantly reduces the amplitude of thalweg migration. In contrast, its impact is relatively limited in wide and shallow straight river sections. This phenomenon may be attributed to variations in channel sinuosity (e.g., sinuosity index > 1.3) and width-to-depth ratio (e.g., > 40), suggesting that the potential effectiveness of bank protection measures could be pre-evaluated through geomorphic parameters in other rivers. Future river management strategies should comprehensively consider both the local effects and overall benefits of revetment projects to prevent new instabilities arising from excessive intervention. Based on the observations of this study, the design of bank protection structures should prioritize highly dynamic reaches (e.g., those with thalweg migration exceeding 15% of the channel width) while preserving natural adjustment space in low-impact zones (e.g., wide-shallow straight reaches), to balance engineering efficacy and ecological resilience. Additionally, the empirical formula for thalweg migration width established in this study (with key parameters including median bed material size, bend radius of bank protection, annual runoff, and annual sediment load) provides a novel methodology for quantitatively analyzing the impacts of bank protection engineering on channel morphology. However, the general applicability of this formula requires further validation across more river systems under diverse flow and sediment conditions. In particular, parameter recalibration is necessary when applying the formula to high-sediment-concentration rivers or those with gravel-bed channels. Future research should focus on comprehensively analyzing the impact of revetment projects on river ecosystems by integrating machine learning with long-term monitoring. Additionally, further investigation into the patterns of thalweg migration in rivers is essential.

Conclusions

Utilizing remote sensing imagery, this study analyzes the coupled effects of adjustments in meandering river channels, taking into account the constraints imposed by fixed boundary conditions and variations in water-sediment dynamics in the upper Tarim River. The planar morphological parameters of the riverbed are quantitatively calculated, and hydrological data are integrated to precisely assess the migration width of thalwegs in continuous bends under constrained boundary conditions. The key findings are summarized as follows:

  1. (i)

    When the revetment density on both banks exceeds 40% in 2018, the average sandbar index \(BI_B^*\) for the entire river section from 2018 to 2022 is 2.80, representing a decrease of 1.51 compared to the average value from 2013 to 2017. At revetment densities above 40%, the sandbar index \(BI_B^*\) for continuous bends is 1.20 lower than that for straight river sections. Furthermore, compared to revetment densities below 40%, the overall sandbar index \(BI_B^*\) decreases by 0.58.

  2. (ii)

    When the revetment density on both banks reaches 40% or higher, the average migration width of the thalweg toward the left and right banks decreases by 0.12 km and 0.14 km, respectively. The average migration amplitude in the straight river section ranges from − 0.23 km to 0.21 km, representing a reduction of 0.14–0.15 km compared to cases with revetment densities below 40%. Similarly, the average migration amplitude in the typical continuous multi-bend section ranges from − 0.06 km to 0.05 km, which is 0.06–0.1 km lower than that observed at revetment densities below 40%.

  3. (iii)

    Since 2018, the thalweg in continuous bends has gradually flattened, with the average migration amplitude decreasing by 0.14–0.31 km compared to the average absolute migration amplitude from 2013 to 2017. The mean values of MAE, RMSE, and MAPE were 2.89, 16.50, and 4.57%, respectively, indicating that the model effectively captures the oscillation trend of the thalweg.