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Article

Declining Bank Erosion Rate Driven by Hydrological Alterations of a Small Sub-Alpine River

by
Alexandra Pusztai-Eredics
1,2 and
Tímea Kiss
3,*
1
Department of Geography, ELTE Savaria University Centre, Károlyi Gáspár Sq. 4, 9700 Szombathely, Hungary
2
Doctoral School of Environmental Sciences, Faculty of Science, Eötvös Loránd University, Pázmány P. Str. 1/A, 1117 Budapest, Hungary
3
Independent Researcher, Horváth Gy. Str. 80, 6630 Mindszent, Hungary
*
Author to whom correspondence should be addressed.
Hydrology 2024, 11(8), 114; https://doi.org/10.3390/hydrology11080114
Submission received: 16 June 2024 / Revised: 25 July 2024 / Accepted: 30 July 2024 / Published: 31 July 2024
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Abstract

:
In the 21st century, climate change and its consequences are getting more serious. The changes in temperature and precipitation alter the run-off conditions, subsequently influencing the channel processes of rivers. The study aims to analyse the hydrological changes in a small, sub-alpine river (Rába/Raab River, Central Europe) and the bank erosional processes (1951–2024). The bank erosion was determined based on topographical maps, aerial photographs, and field (RTK–GPS) surveys. Short (2–3 days) floods were common between 1950 and 1980, and low stages occurred in 65–81% of a year. However, extreme regimes developed in the 21st century, as record-high, flash floods altered with long low stages (91–96% of a year). The bank erosion shows a cyclic temporal pattern, gradually increasing until it reaches a high value (4.1–4.9 m/y), followed by a limited erosional rate (2.2–2.8 m/y). However, the magnitude of the bank erosion is decreasing. This could be explained by (1) the lower transport capacity of the more common low stages and (2) the seasonal shift of the flood waves, which appear in the growing season when the riparian vegetation can more effectively protect the banks from erosion.

1. Introduction

In the 21st century, climate change and its impacts on the natural environment are becoming increasingly evident. Changes in temperature and precipitation patterns significantly influence all elements of the natural environment. Knox [1,2] suggested that annual changes in temperature of ±1–2 °C and precipitation of ±12–20% can already cause significant changes in the magnitude and frequency of floods. Increases in temperature result in an increase in evapotranspiration rates and an earlier snowmelt date, so they can indirectly influence water flow [3]. In turn, changes in the temporal pattern of precipitation alter the runoff and soil erosion, influencing the water and sediment transport of rivers [3,4,5,6,7], riverbed processes, and channel patterns [8,9,10]. The changes in frequency, magnitude, duration, sequence, and trend of low stages or flood waves can alter the channel and floodplain development, the rate of lateral displacement of river channels, the extent of the point-bar surfaces, and the size and shape of meanders [9,11,12].
The frequency of flash floods has increased in recent decades [13]. These extreme floods result in significant sediment transport, cause widening or incision of the channel [14], intense channel migration [15,16], rapid overbank aggradation, and sedimentation in channel segments [17]. The increasing frequency of small floods triggers opposite processes, as they can lead to channel narrowing and secondary loop formation on large meanders [18]. Smaller and narrower meanders impede the conveyance of large floods and thus lead to increased flood risk [18,19].
Heavier rains and longer dry periods can lead to more extreme flows [1]. However, while some rivers have experienced more frequent low flows and disappearing floods [9], in others, the magnitude and frequency of floods have increased [20,21]. Researchers differ in their opinions on which characteristic discharge plays the most important role in transforming channels and floodplains. Gilvear et al. [20] stressed the role of increasingly frequent extreme floods; others considered the changes in bankfull discharge as the key factor [22,23]. However, the role of increasingly frequent and persistent low stages in shaping the channel morphology is also not negligible [24].
The impact of climate change is not only reflected in changes in the regime of rivers. Climate change-driven changes in catchment vegetation and land cover can modify the spatial and temporal distribution of runoff and sediment discharge by controlling soil erosion and water retention [25,26], which ultimately change the parameters of the channel [27]. The altered intensity of soil erosion, altered denudation rates, and mass movements lead to the altered amount of sediment entering rivers [28,29]. The additional sediment decreases the transport capacity, causing sediment deposition and leading to the aggradation of the channel and floodplain [30]. The aggraded riverbed has a lower conveyance capacity; thus, it is less able to drain high flows, so overbank floods might become more frequent, leading to further rapid sediment accumulation in the floodplain [31]. As a result, the catchments become more vulnerable to extreme weather events [32].
The consequences of altered hydrology may differ between rivers [33] as the fluvial response to change may vary in space and time, even within the same river, depending on the current state of the system [20,33]. The main difficulties in analysing the effects of environmental change are the uncertainties of the initial state and the non-linearity of the processes involved [34,35]. Moreover, the effects of different processes can amplify or extinguish each other [30,31]. The nature of the consequences depends on the internal (in)stability of the river system and its capacity to adapt to change, i.e., the sensitivity of a given reach and its environment [36]. In this respect, the closeness of the hydro-morphological regime of the river to some threshold of equilibrium and the capacity of the system to regenerate are important [35].
In Central Europe, decreasing snow cover, warmer temperatures, and more frequent dry periods [37,38] could reduce flooding [6]. However, the Rába or Raab River, originating in the Eastern Alps, is under a double effect. A slight increase in flood discharge was indicated on its sub-alpine catchment; however, along its lowland reach, a decrease in floods was reported [6]. In the lowland Hungarian section, the prolonged low stages are altered by flash flood waves. As most of the meanders in the upstream reach of the Rába in Hungary are freely developing, they provide an excellent opportunity to analyse the effect of altering flow conditions on channel morphology. Therefore, the objectives of this research are (1) to analyse the hydrological changes in the Rába River since 1950, (2) to determine the extent of bank erosion, and finally (3) to analyse the relationship between the regime and bank erosion. Our ultimate goal is to evaluate the river’s morphological response to hydrological changes to support future flood prevention and river restoration measures.

2. Study Area

The Rába or Raab River (length: 287 km) is a small river shared by Austria and Hungary in Central Europe [39]. The river originates in the Eastern Alps, and it joins the Danube. Most of its catchment (10,113 km2) is mountainous and hilly, though the lowland reach crosses a plain in Hungary (Figure 1). Due to the great elevation changes (107–1750 m) of the catchment, the mean annual precipitation decreases from 1050 mm in the mountainous sub-catchments to 590–650 mm in the plain [40]. The mean annual precipitation was constant between 1979 and 2019; however, its seasonality has changed as the amount and intensity of summer rainfalls have increased [3].
The alpine catchment has a key influence on the regime. This is reflected by the fact that 85% of the total annual discharge of the Rába (1.12 km3/y) originated from the mountainous Austrian sub-catchments [41]. In its natural state, the river had three floods [42]. Snowmelt and rainfall initiated a flood in March, and heavy rainfalls caused flash flood waves in July. A third, smaller flood in October and November was related to Mediterranean cyclones. Flood waves usually quickly develop [39]. The maximum discharge (Qmax = 471 m3/s) measured at Szentgotthárd gauging station (Figure 1) is almost two hundred times larger than the minimum discharge (Qmin = 3 m3/s). Water withdrawal is limited, as only 1% of the total annual discharge is used for agricultural and domestic purposes [41].
The Upper Rába (from its source in Austria to Sárvár in Hungary) has been regulated only at some points; thus, it still meanders freely on its floodplain. The local regulation works aimed to protect settlements and transport infrastructure from lateral erosion and to provide flood safety [42]. In addition, several lock dams were built on the Upper Rába. Their total capacity is low (ca. 2 MW); therefore, they use only ≤28 m3/s discharge during their operation. They slightly impound the river during low stages, but the gates are open during flood waves to support flood conveyance [43]. On the other hand, the Lower Rába (between Sárvár and the Danubian confluence) is confined by artificial levees, and the channel is regulated by cut-offs and revetments to a large extent [43].
The downstream half of the Upper Rába River (length: 127 km) was selected as a study area (Figure 1). The local river engineering works were mostly performed between 1968 and 1977. Based on the extent of human influence and meander migration characteristics, 14 units were identified. Some units are free of direct human impact, so they reflect the natural state of the channel (U1, U3, U5–6, U8, U10, U12, and U13); in other units, the channel is slightly regulated by revetments at some points (U1, U8, U10, and U12). Other units (U2, U4, U7, U9, U11, and U14) have been intensively regulated (by revetments and cut-offs), and the floodplain is artificially confined. As the units free of engineering works are between modified units, they were also influenced by human impact, but indirectly. The artificial cut-offs or the revetments increase the slope and flow velocity and alter the sediment household, which propagates downstream, influencing the processes even in the intact channel segments.

3. Materials and Methods

The hydrology of the Rába River was analysed based on the daily stage data measured by the West-Transdanubian Water Directorate at Szentgotthárd gauging station (Figure 1). Water level (H) data are from 1950 to 2024, while discharge (Q) data are from 1970 to 2024. Based on the daily data, the maximum (Hmax, Qmax), average (Hmean, Qmean), and minimum (Hmin, Qmin) values were calculated for each year. Low stages were determined as stages below 0 cm. The bankfull level is reached by 250 cm-high stages; thus, above this level, the overbank floods enter the floodplain. A flood wave was considered when the water level rise was at least 50 cm. The recurrence interval (years) of the annual highest floods was determined by the Gringorten plotting position formula [44].
Preliminarily, distinctive periods were identified based on the characteristic changes in the annual stage and discharge values. The reliability of the identification was checked by applying a hierarchical divisive multiple change point analysis carried out on the principal components (Hmax, Hmean, Hmin, Qmax, Qmean, and Qmin) at a significance level of 0.05 using the ecp package [45]. All parameters were left as default values [46]. The minimum number of change points was selected to be two. Finally, the discharge values were analysed separately because no discharge measurements existed before 1970.
Maps (1951, 1955–1956, 1960–1961, 1983–1984, and 1996–1998) and aerial photographs (1967, 1972, 2000, 2005, 2008, 2012, 2015, 2018, 2021, and 2022) were used to analyse the horizontal displacement of the bankline (Table A1). The maps were processed using QGIS software (3.28/Firenze). The banklines were manually digitized on the maps and automatically determined on the aerial images by applying the image processing method Classification (plugin) within QGIS. It classified the pixels into “land” and “water” classes [47]. Therefore, the precision of the delineation of the banklines on the aerial photographs depended on the resolution (0.2–0.5 m) of the applied sources.
The vectorized bank polygons were overlapped in QGIS using the NNjoin module. The new polygon between two subsequent banklines in the direction of channel migration indicates the area affected by bank erosion. Perpendicular lines were constructed on the digitised bankline every 2 m all throughout the studied reach to determine the bank erosion rate (Figure 2A). Along these lines, the lateral channel shift was measured automatically within the QGIS NNjoin module [48], and the mean annual bank erosion rate (m/y) was calculated. To identify the maximum bank erosion, circles with a diameter of 500 m were placed along the centre line of the meander belt. The circles overlap by 90 m, equal to two channel widths (Figure 2B). The maximum bank erosion within the circles was determined by applying a moving average. Pearson correlation analysis between the long-term bank erosion rates and the main hydrological parameters was applied to evaluate their relationship.
Field measurements were performed along 20 intensively migrating free meanders to evaluate the actual bank erosion and to understand its seasonal variability. The bankline was surveyed seven times (every four months) between April 2022 and April 2024 along the outer curve of the bends using Hi-Target iRTK-4 (Real Time Kinematic) satellite geodetic GPS (horizontal precision: 0.1–3 cm). The bank erosion within the surveyed bends was calculated using the perpendicular line method mentioned above. The maximum bank erosion was measured using circles with a diameter (30 m) along the concave banks of single bends. The maximum displacement within the circles was determined by calculating a moving average. The bank erosion between the subsequent field surveys was expressed in m/4 months.

4. Results

4.1. Hydrological Changes in the Rába River (1950–2024)

Floods with a recurrence interval of 1.3–47 y were typical in the first period (1950–1980). The average stage of yearly highest water levels was 272 ± 74 cm (Figure 3A), and their mean discharge was 214.7 ± 71 m3/s in the 1970s (Figure 3B). A record-high, overbank flood (H: 408 cm) was recorded in 1965, 158 cm above the bankfull stage. The flood waves typically occurred in March, June, and July–August (Figure 4). Overbank floods typically covered the floodplains for 2–3 d/y, although in 1965, two summer floods lasted for eight days. The mean level of the annual lowest stages was −71 ± 12 cm (Qmean: 7.3 ± 2.6 m3/s). Low stages (≤0 cm) were common in 65–81% of the year (Figure 5).
Between 1981 and 2000, smaller floods (recurrence interval: 1.3–26.6 y) became common, so they rarely entered the floodplain (Figure 3, Figure 4 and Figure 5). Although floods in March persisted, the former summer floods shifted to August–October. Though the floods in 1987 and 1996 were not the highest, they had higher discharges (454–457 m3/s) than before. The average level of the annual highest stages decreased by 27 cm (Hmax: 226 ± 85 cm). The other characteristic water stages also decreased, as the mean annual stage decreased by 31 cm (Hmean: 69 ± 45 cm), and the mean annual lowest stage decreased by 18 cm (Hmin: −88 ± 7 cm). A new, record-low stage was measured (1983: −107 cm), which brought the record 11 cm deeper. Overall, low stages characterized 92–92% of the year. At the same time, the typical discharge values increased, although their deviation increased, referring to more extreme flow conditions (Qmax: 244 ± 111 m3/s, Qmean: 126 ± 56 m3/s and Qmin: 8.2 ± 2.1 m3/s).
The hydrology became even more extreme in the last period (2001–2024). The absolute water level differences between the annual minimum and maximum stages increased. While the absolute water level difference was 484 cm in the first period, it has now increased to 602 cm. The centurial flood in 2009 reached a new record height (491 cm) and discharge (471 m3/s). However, the mean annual highest stages (Hmax: 181 ± 132 cm) decreased further by 45 cm. The intra-annual pattern of flood waves has also changed, as the March flood waves disappeared, and the floods shifted to May–June and August–September. The low water level decreased moderately (Hmin: −96 ± 9 cm). A new, record low stage was measured (2012: −111 cm); thus, it decreased by 4 cm compared to the previous record. As a result of these processes, the frequency of low stages increased to 91–96%.
Regarding discharge, splitting this period in two is necessary (Figure 3B). Water flows decreased considerably and became more extreme between 2001 and 2015 than in previous periods (Qmax: 221 ± 140 m3/s; Qmean: 114 ± 71 m3/s; Qmin: 6.7 ± 3 m3/s). However, the annual discharges decreased even more markedly in the last decade (2016–2024) (Qmax: 182 ± 133 m3/s; Qmean: 95 ± 66 m3/s and Qmin: 6.6 ± 3 m3/s). The lowest discharge of the whole studied period was recorded in 2003 (2.6 m3/s).
From the point of view of channel dynamics, the changes in the discharge–stage relationship are important. The same stages were associated with increasingly higher discharges in the range of small and medium water levels. For example, the −50 cm water level in 1970 was associated with a 13.6 m3/s discharge and increased to 26.7 m3/s in 2021. Simultaneously, the 0 cm water level had a 24.0 m3/s discharge in 1970, which increased to 52.1 m3/s in 2020. These data indicate the incision of the channel. Similarly, the discharge values increased in the medium and high stage ranges, suggesting that the drainage capacity of the entire channel is increasing.

4.2. Hydrological Changes in the Rába River (2022–2024) during the Field Surveys

The water regime differed substantially between the four-monthly bankline surveys (Figure 6). Low stages were typical during Periods 1 and 2. Only three small flood waves occurred in late May and early June, but they were far below the bankfull level (H: 4, 55, and 68 cm); these waves developed rapidly, with a maximum rising velocity of 77 cm/day. The flood waves were followed by a prolonged period of low stages. Thus, only very low stages appeared in Period 2, interrupted by a few small water level rises (ΔHmax: 48 cm/day).
The dominant feature of Period 3 was that the small stages were interrupted by small flood waves in January (H: −65 to −13 cm) and mid-April (92 cm). During the latter flood wave, the water level rose (109 cm/day) and recessed (50 cm/day) quickly, but it was below the bankfull water level. The fourth survey was conducted one week after the flood wave.
Period 4 was very active from the hydrological point of view. Two of the eight flood waves exceeded the bankfull level, so they entered the floodplain. The first overbank flood wave (17 May 2023: 268 cm) had a rapid rise (ΔHmax: 261 cm/day) and falling limbs (ΔHmax: 190 cm/day). The second overbank flood was much higher (05 Aug 2023: 477 cm); it approached the previous largest stage on record (491 cm). During the rise, the water level changed faster than in previous periods (ΔHmax: 305 cm/day), but it receded much slower (ΔHmax: 60 cm/day) as the water drained back slowly to the channel from the floodplain.
Periods 5 and 6 were similar to the first period in hydrology: small flood waves appeared during a low-stage period. The largest of the waves was only 109 cm high. During these flood waves, the water level rose by 135–161 cm/day and recessed by 70–101 cm/day.

4.3. Bank Erosion of the Studied Reach of the Rába between 1951 and 2022

The mean lateral bank erosion of the studied Rába reach was high in three distinct periods: in the 1960s (6.9 m/y), in the late 1990s (4.6 m/y), and a third small erosional peak (3.3 m/y) occurred in 2012–2014 (Figure 7). The temporal trends in bank erosion reflect that it gradually increased until it reached a peak value. For example, from the 1950s to the 1960s, the mean bank erosion increased from 4.1 m/y to 6.9 m/y. Similarly, the 20th century started with a low bank erosion rate (mean: 2.0 m/y), gradually increasing until it reached a small peak in 2014 (mean: 3.3 m/y).
The bank erosion rate was diverse within the intensively eroding periods, as reflected by the box plots with many outliers and a wide range between extreme values. In some bends, the bank erosion was over 10 m/y, being very intensive in the late 1990s, when the bank erosion rate of some meanders was 24–27 m/y.
The periods of intensive bank erosion were always followed by periods with declined bank erosion. The mean bank erosion rate also has a decreasing trend: In 1972–1982, it was 4.1 m/y; in 2000–2004, it dropped to 2.0 m/y, and finally, in 2015–2022, to 1.6 m/y. The bank erosion rate had a low standard deviation in these periods, referring to uniform processes along all meanders.

4.4. Bank Erosion of the Selected Meanders of the Rába between 2022 and 2024

Short-term bank erosion was measured along 20 meanders for two years (from April 2022 to April 2024). The average bank erosion was 2.8 m/y, which is the same as the long-term average measured in the previous period (2015–2022). However, the multiple measurements within a year help to highlight the seasonal variations in bank erosion and the controlling hydrological processes.
In Periods 1–3 of the survey (April 2022–April 2023), the mean bank erosion (0.3–0.7 m) was similar in most of the meanders (Figure 8, Table 1). There was only one bend (G) in Period 3, where the mean bank erosion exceeded 1.0 m. The maximum bank erosion at some points reached 1.2–2.2 m in Periods 1 and 3. However, in Period 2, the maximum values were even and never higher than 0.6–0.8 m.
In Period 4 (April–Aug 2023), the mean bank erosion (2.8 m) increased significantly in all meanders. Only the most downstream meander (U) had a mean bank erosion of less than 1 m. The highest average value (6.9 m) was measured in Bend C. However, at certain points in some meanders, the bank eroded to an extreme extent. For example, at the most eroded point in Bend A, the bank eroded by 19.8 m.
Then, in Period 5 (Aug–Dec 2023), the average rate of bank erosion was reduced by two-thirds (1.0 m) in all bends. The bends showed considerable variations, as the mean bank erosion remained high (1.0–3.4 m) in almost a third. Maximum erosion in Bend A, previously marked by very fast bank erosion, was strongly reduced (0.9 m). New points of moderate erosion (1.5–4.6 m) appeared in Bends F–I.
In Period 6 (Dec 2023–April 2024), the mean bank erosion slowed further (0.4 m) to half of the previous period and reached the average values of the first periods. There was only one bend (H) where both mean (4.0 m) and maximum (1.9 m) erosion were significant, although here, the bank erosion was consistently high throughout the last year. The maximum erosion in the other bends was sharply reduced (0.3–1.0 m).
Bank erosion showed a characteristic downstream trend only in Period 4. At this time, the mean and maximum bank erosion rates decreased downstream, broken only at two locations (F–H and S–T) by more intensively forming meanders. In the other periods, however, this downstream trend was not obvious, and the bank erosion showed higher values at a few locations (C, G, and M) but without any spatial trend.
The locations of the highest bank erosion differed at the meanders (Figure 9). In most bends (e.g., C, D, G), the highest bank erosion was measured at the downstream third of the meander, and these meanders showed a classic expanding meander development pattern.
In other meanders (e.g., A, B, and J), a mid-channel bar or island pushes the thalweg against the bankline at different points of the bend, where extreme bank erosion values were measured. In the studied reach, there are also some confined meanders (A, B, and E) where the high banks hamper the lateral channel shift; thus, they decrease the rate of bank erosion. However, some complex meanders also exist (F, H, L, M, T, and U). They refer to the fragmentation of a previous, larger meander. Thus, in some places on the original convex bankline, the bank erosion became more intensive, forming smaller, secondary bends.

5. Discussion

5.1. Hydrological Alteration of the Rába River since 1950

Previously, Csoma [42] described two major and one minor flood (March, July, and November) per year on the Rába. Our data from the Szentgotthárd gauging station for the years 1950–1980 verified the existence of floods in March and June, and a late summer flood in August was identified instead of an autumn flood. After the 1980s, the hydrology of the river gradually changed. Thus, although the March flood persisted between 1981 and 2000, the early summer flood wave disappeared, and the late summer floods appeared in a longer period (August–October). In the 21st century, a completely different flood pattern has emerged, with the spring flood being replaced by a prolonged flood period in May–June and a marked peak in August–September. The strong inter-annual shift is probably due to climatic reasons [49], following the heavier and more frequent summer and early autumn rainfalls than in the past [3,40]. Meanwhile, the heights of annual highest flood waves show a declining trend, in good agreement with Blöschl et al. [6], who reported a 5–10% decrease in flood discharge along the Rába River. At the same time, the more intense summer floods could be explained by the slight increase in discharge in smaller catchments in the Eastern Alps [6] and by more frequent extreme rainfall events [13].
The length of the low stages has increased dramatically, from 65–81% of the year (1950–1980) to 91–96% (2001–1924). The dropping of low stages is partly related to the widening and incision of the channel, as the discharges at the same water levels have almost doubled. However, while the annual minimum discharge averaged 8.2 ± 2 m3/s in 1981–2000, it gradually decreased to 6.7 ± 3 m3/s (2001–2015) and further to 6.5 ± 1.9 m3/s (2016–2024). By the end of the 21st century (RCP4.5 and RCP8.5 scenarios), droughts are predicted to become more frequent in the area [37], increasing the length and frequency of low-stage periods. Similar, increasingly extreme flows have been observed in many rivers around the world [9,18,19,20,21,32,49,50].

5.2. The Relationship between Hydrology and Bank Erosion

Short-term field measurements of bank erosion have allowed us to analyse the relationship between hydrology and bank erosion at a better temporal resolution (every four months). Bank erosion is associated not only with flood waves at or above bankfull levels but also with any water level, just to different extents (Table A2). During low-stage periods, when flood waves with a 50–150 cm water level were conveyed in the Rába’s channel, the average rate of bank erosion was below 1 m/4 months. The annual duration of low stages has a very strong, negative correlation (r = −0.8) with bank erosion, as the river does not have enough stream power to effectively erode the collapsed material accumulated at the toe of the bank. However, the ongoing erosion during small and medium stages is related to their locally high slope and flow velocity related to channel forms (e.g., riffles, bars), which allows for slight sediment transport [24,51].
Successive and larger (200–400 cm) flood waves can cause significant bank erosion along the entire length of a reach. This is well reflected by the strong correlation (r = 0.7) between mean and minimum bank erosion and the annual duration of overbank floods (Table A2). The short-term surveys (2022–2024) revealed that the subsequent flood waves were associated with the highest bank erosion (on average: 2.8 m/4 months equals 8.4 m/y), while on some points of the bank, the erosion rates were as much as 10–19 m/4 months (i.e., 30–58 m/y). This could be explained by the favourable conditions for intensive bank erosion created by mostly bankfull levels or overbank floods [14,15,16,20,23,26]. It is related to the high specific stream power during flash floods, which can (1) remove formerly collapsed bank material from the feet of the banks and (2) directly erode the banks [12,19,51].
An important element of the hydrological changes is the seasonal change in floods [51,52]. In the case of the Rába River, the early spring floods became absent, but new floods appeared in summer and early autumn. Mainly, there are pastures and plough fields along the river, and the roots of the herbs can stabilise the banks just during the growing season [12,52]. However, this bank-stabilising effect cannot be achieved prior to their development. The seasonal shift in the flooding period is therefore important, since in the second half of the 20th century, during the early spring floods, the banks of the Rába were less stabilised by weak vegetation, and therefore, the bank erosion was greater than nowadays.
Regime changes also affect the spatiality of bank erosional processes. Our short-term study has shown that bank erosion shows a longitudinal trend only during major flood events. Then, with the gradual slope decrease, the bank erosion also gradually decreases. However, this downstream trend does not prevail during low stages, and bank erosion in all meanders becomes more uniform regardless of their longitudinal position.

5.3. Relationship between Hydrology and Bank Erosion: A Conceptual Model

During the first few decades of the study (1951–1971), the gradually increasing bank erosion was driven by stages at or above the bankfull level. These flood waves were frequent and occurred at regular intervals. In addition, a record-high flood occurred in 1965 and the level of the low stages increased. Therefore, the higher stream power facilitated bank erosion. According to our conceptual model (Figure 10), the bankfull water levels created suitable conditions for intense bank erosion [22,23].
As flood waves and low stages followed each other evenly in the second half of the 1950s, the river also experienced a strong lateral erosion, as the channel had to expand to convey the floods. Meanwhile, the low stages allowed the formation of mass movements (e.g., landslides, falls) of the banks. The elevated low water levels, the higher variability of stages, and the higher slope (65 cm/km) allowed for debris transport from the toe of the bank. However, in the last five years (1967–1971), the lower frequency and height of near-bankfull floods no longer justified the high bank erosion rate. This refers to the existence of a delay in the response of the river, as it takes several years for the morphological response of the system to floods or their absence to be completed [53]. Thus, it could be identified as the end of a longer erosional cycle, initially triggered by frequent flood waves at or above the bankfull level and the extreme flood of 1965. The erosional cycle was closed by a relaxation period (1972–1982) [18,53]. No intensive bank erosion could be detected during this period despite the successive regular bankfull stages. It can be partly explained by the bank stabilisation works carried out at this time (1968–1984), which aimed to mitigate the destruction of overbank floods such as the one in 1965. Alternatively, the reduction in bank erosion might be explained by the fact that during the erosional phase of the cycle, the channel had widened and reached the parameters required to convey large flows. In addition, by the end of the period, large flood waves became rare, and the duration of low stages with low stream power increased, also reducing bank erosion.
The bank erosional became increasingly intensive at the beginning of the next, second erosional cycle (1983–2004), reaching its maximum between 1996 and 1999. However, this erosional cycle had a smaller magnitude than the first cycle. The channel regulation of the Rába could explain the moderate bank erosion, as the revetments stopped lateral erosion of some meanders and sections. However, in the naturally developing units below them, the locally increased flow velocity might have intensified bank erosion, also facilitated by higher low and medium stages. This erosional cycle was also completed by a relaxation period of limited bank erosion (2000–2004) supported by the almost complete absence of bankfull flood waves.
The bank erosion increased slowly in the third bank erosional cycle (2005–2014) but was not as intense as in the previous cycles. This increased bank erosion might be related to the highest discharge on record in 2009 and the successive floods that typically were just below the bankfull level. These flood waves, similar to those experienced in 1951–1954 and 1996–1999, transported away the previous debris accumulated at the feet of the banks, deepened the channel, and thus increased the lateral channel migration. The mean bank erosion increased slightly, as the flood waves did not last long, and the long-lasting low stages did not support intensive bank erosion.
The last decade (2015–2024) could be evaluated as the end of the third erosional cycle (relaxation time) or the beginning of a new development phase. The bank erosional rate gradually decreased due to the missing or shortened flood waves and bankfull stages and the increasing frequency of low stages (91–96%). Low stages create good relief conditions for mass movements of the banks as the banks lose their support. However, the debris that accumulates at the toe of the bank is transported away slowly without flood waves. The slow change in meander shape justifies the new development phase. In some of the large, freely developing meanders, a slow fragmentation of the meander into smaller bends and the formation of secondary bends can be observed. These processes can be clearly explained by the increased frequency of low stages [18] as the flow circulation in the channel was altered [27,33]. Similar phenomena have been observed in sections below the construction of reservoirs, where secondary bends developed due to a decrease in discharge [18,54].

5.4. Spatiality of Bank Erosion

In most of the studied meanders, the largest bank erosion was downstream of the bend’s apex. This is consistent with the general course of meander evolution [27,55], as the centrifugal force pushes the flow against the bank just downstream of the axis due to the inertia of the water mass. Thus, the water mass can exert the greatest erosion here, resulting in a gradual downstream migration of the meanders.
However, there were also meanders where the most intensively eroded points were upstream of the axis. This is partly explained by the development of secondary meanders, which is based on the assumption that the more sinuous thalweg triggers bank erosion at new locations. Kiss and Blanka [18] identified a similar pattern of bank erosion on the Hernád River (Hungary) as an effect of water discharge reduction. In addition, the Rába River has repeatedly reworked the floodplain; thus, if some meanders develop in areas that have been reworked a few decades earlier, the bank erosion will accelerate, as loose, barely compacted sediments create favourable conditions for rapid meander migration. Furthermore, mid-channel bars or islands could also divert the thalweg, initiation bank erosion at new locations.
There is also a difference between the meanders in terms of their confinement. At some points, high banks (related to terraces) were reached by meanders. The erosion of the high banks is slower than that of normal banks as the river has to carry away much more material. Therefore, the shape of the meanders will be distorted. Similar distorted meanders have been described along Hungary’s high banks of the Dráva and Hernád Rivers [18,19].

6. Conclusions

The changing bank erosion and riverbed development of the studied reach of the Rába/Raab River provided a classic example of fluvial processes altered by hydrological changes. In our case, the water regime became more extreme with a drastically increased duration of low stages. The flood waves, which shift into summer and early autumn, rise rapidly as heavy rainfalls in the sub-alpine sub-catchments result in high run-off. At the same time, low stages have become increasingly dominant every year. Although bank erosion shows a cyclical temporal pattern, its amplitude is decreasing. This can be explained by the low stream power of the dominant low stages, the decreasing frequency of flood waves, and the increasing role of riparian vegetation.
The results of the study could support the work of, e.g., water managers, hydrologists, or ecologists. The stakeholders must be prepared for the altered temporal pattern in hydrology. The shift of floods to the summer and their increasing height can increase the damage to agriculture. On the other hand, the drastic increase in low stages (from 65–81% to 91–96% of the year) will intensify the drying of the riparian zone, endangering species, habitats, and traditional agriculture. These hydrological extremities must be considered in future restoration plans.
The summer floods could erode the banks less successfully than the early spring floods, as the strong and dense vegetation in the growing season could more effectively protect the banks than the dormant herbs. The dominance of low stages has a double effect on bank erosion. During low stages, the banks could collapse more easily without the support of the water column, and the dry cracks could also increase their erodibility. On the other hand, the debris at the toe of the bank could be transported away just slowly by low stages, supporting the decline of bank erosion. Thus, it is advised that if bank protection is needed, “design-with-nature” solutions should be considered, as they will be sufficient enough to protect a bank with a declining bank retreat.
Although bank erosion is still present, its moderate rate raises important questions about its effect on sediment dynamics and the habitat of birds using the banks (e.g., bank swallow and European bee-eater). Understanding these impacts is crucial for the work of environmental scientists, ecologists, and conservationists.

Author Contributions

Conceptualization, A.P.-E. and T.K.; methodology, A.P.-E.; formal analysis, A.P.-E.; data curation, A.P.-E.; writing—original draft preparation, A.P.-E.; writing—review and editing, A.P.-E. and T.K.; visualization, T.K. All authors have read and agreed to the published version of the manuscript.

Funding

The research was funded by the Sustainable Development and Technologies National Programme of the Hungarian Academy of Sciences (FFT NP FTA).

Data Availability Statement

The data presented in this study are available on request from the corresponding author.

Acknowledgments

The authors are grateful for the West-Transdanubian Water Directorate (NYUDUVIZIG) for providing the hydrological data, for the advices of G. Tóth, and for the methodological support of G. Kovács (ELTE Savaria University Centre). We are also grateful for K. Nardai for providing help during the field surveys.

Conflicts of Interest

The authors declare no conflicts of interest.

Appendix A

Table A1. Main characteristics of maps and orthophotos used to determine the bank erosion of the Rába River (Data sources: * [56], ** West-Transdanubian Water Directorate).
Table A1. Main characteristics of maps and orthophotos used to determine the bank erosion of the Rába River (Data sources: * [56], ** West-Transdanubian Water Directorate).
Source (Survey Date)ScaleResolution (m/px)Mean
Horizontal Error (m) *		Discharge (m3/s) **Water Level (cm) **
minmaxminmax
Topographical map (1951)1:25,000 0.8 ± 0.4no datano data−79296
Topographical map
(1955–1956)		1:25,000 0.8 ± 0.4no datano data−74287
Topographical map
(1960–1961)		1:10,000 negligibleno datano data−83200
Aerial photograph
(05–06 May 1967)		 0.20.4 ± 0.1no datano data−10−6
Aerial photograph
(20 Oct 1972)		 0.20.4 ± 0.115.718.8−28−22
Topographical map
(1983–1984)		1:25,000 negligible3.9165−107188
Topographical map (1996–1998)1:10,000 negligible9.2457−84390
Orthophoto
(07 Mar–02 Aug 2000)		 0.5negligible8.8135−87123
Orthophoto
(13 June–06 Sept 2005)		 0.5negligible7.6368−89376
Orthophoto
(02–11 Aug 2008)		 0.5negligible18.754−61−17
Orthophoto
(19–25 Aug 2012)		 0.4negligible12.815−85−80
Orthophoto
(08 May–10 July 2015)		 0.4negligible7.2132−94162
Orthophoto
(31 May–23 Aug 2018)		 0.4negligible12.9119−8279
Orthophoto
(06 July–15 Sept 2021)		 0.2negligible7.141−97−21
Orthophoto
(07 June–19 Aug 2022)		 0.2negligible5.387−10768

Appendix B

Table A2. Correlation matrix between the long-term (1951–2022) bank erosion rates and the duration of overbank flood waves and low stages.
Table A2. Correlation matrix between the long-term (1951–2022) bank erosion rates and the duration of overbank flood waves and low stages.
Max Bank Erosion RateMean Bank Erosion RateMin Bank Erosion RateNumber of Overbank Flood Waves Annual Duration of Overbank Flood WavesAnnual Duration of Low Stages
Max bank erosion rate1
Mean bank erosion rate0.7888481
Min bank erosion rate0.0936970.4732521
Number of overbank flood waves0.2522450.5244880.6642561
Annual duration of overbank flood waves0.4174480.7048610.7329550.9303181
Annual duration of low stages−0.60288−0.82471−0.56998−0.82297−0.884891

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Hydrology 11 00114 g001
Figure 1. The catchment of the Rába/Raab River is located in Central Europe (A). Its middle reach was studied in detail (B). The studied reach was divided into 14 units (U1–14) based on the degree of human impacts, and along some meanders (meander ID: A–U), the bank erosion was measured using an RTK–GPS (C).
Figure 1. The catchment of the Rába/Raab River is located in Central Europe (A). Its middle reach was studied in detail (B). The studied reach was divided into 14 units (U1–14) based on the degree of human impacts, and along some meanders (meander ID: A–U), the bank erosion was measured using an RTK–GPS (C).
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Figure 2. The mean bank erosion was calculated based on the length of lines perpendicular to a former bankline (A). The maximum bank erosion was calculated within circles (B).
Figure 2. The mean bank erosion was calculated based on the length of lines perpendicular to a former bankline (A). The maximum bank erosion was calculated within circles (B).
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Figure 3. Annual highest, mean, and minimum water stages (A) and annual highest, mean, and minimum discharges (B) measured at Szentgotthárd gauging station.
Figure 3. Annual highest, mean, and minimum water stages (A) and annual highest, mean, and minimum discharges (B) measured at Szentgotthárd gauging station.
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Figure 4. Monthly distribution (%) of overbank (H ≥ 250 cm) flood waves (A) and low stages (H ≤ 0 cm) measured at Szentgotthárd gauging station (B).
Figure 4. Monthly distribution (%) of overbank (H ≥ 250 cm) flood waves (A) and low stages (H ≤ 0 cm) measured at Szentgotthárd gauging station (B).
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Figure 5. Mean duration of low stages (≤0 cm) and overbank stages (≥250 cm) at Szentgotthárd.
Figure 5. Mean duration of low stages (≤0 cm) and overbank stages (≥250 cm) at Szentgotthárd.
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Figure 6. Daily water level (cm) and discharge (m3/s) changes in the Rába River measured at Szentgotthárd gauging station during the field survey.
Figure 6. Daily water level (cm) and discharge (m3/s) changes in the Rába River measured at Szentgotthárd gauging station during the field survey.
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Figure 7. Bank erosion rates of single bends of the studied reach of the Rába River (A) and the characteristic annual stages during the same time (B).
Figure 7. Bank erosion rates of single bends of the studied reach of the Rába River (A) and the characteristic annual stages during the same time (B).
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Figure 8. Mean bank erosion (A) and maximum bank erosion (B) of some meanders between the RTK–GPS surveys performed in every four months between April 2022 and April 2024.
Figure 8. Mean bank erosion (A) and maximum bank erosion (B) of some meanders between the RTK–GPS surveys performed in every four months between April 2022 and April 2024.
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Figure 9. Short- (2022–2024) and long-term (1951–2022) changes in the position of the bankline at selected meanders. Meander B represents a bend where the location of an island influences the bank erosion. Meander C shows a classical meander expansion. North of Meander E is a terrace rim; thus, the meander development is confined. On Meander H, secondary bends develop.
Figure 9. Short- (2022–2024) and long-term (1951–2022) changes in the position of the bankline at selected meanders. Meander B represents a bend where the location of an island influences the bank erosion. Meander C shows a classical meander expansion. North of Meander E is a terrace rim; thus, the meander development is confined. On Meander H, secondary bends develop.
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Figure 10. Conceptual model of declining bank erosion driven by hydrological changes.
Figure 10. Conceptual model of declining bank erosion driven by hydrological changes.
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Table 1. Bank erosion (m/4 months) in some meanders of the studied reach of the Rába based on RTK-GPS surveys of the bankline.
Table 1. Bank erosion (m/4 months) in some meanders of the studied reach of the Rába based on RTK-GPS surveys of the bankline.
Survey PeriodPeriod 1Period 2Period 3Period 4Period 5Period 6
Apr–Aug 2022Aug–Dec 2022Dec 2022–Apr 2023Apr–Aug 2023Aug–Dec 2023Dec 2023–Apr 2024
mean bank erosion0.5 ± 0.20.3 ± 0.10.7 ± 0.22.8 ± 1.61.0 ± 0.60.4 ± 0.4
greatest mean bank erosion (ID of meander)0.9 (G)0.5 (H)1.1 (G)6.9 (C)3.4 (H)1.9 (6)
maximum local bank erosion1.6 (G)0.8 (G)2.2 (G)19.8 (A)4.6 (H)4.0 (H)
number of bends with bank erosion higher than 0.8 m20520141
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Pusztai-Eredics, A.; Kiss, T. Declining Bank Erosion Rate Driven by Hydrological Alterations of a Small Sub-Alpine River. Hydrology 2024, 11, 114. https://doi.org/10.3390/hydrology11080114

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Pusztai-Eredics A, Kiss T. Declining Bank Erosion Rate Driven by Hydrological Alterations of a Small Sub-Alpine River. Hydrology. 2024; 11(8):114. https://doi.org/10.3390/hydrology11080114

Chicago/Turabian Style

Pusztai-Eredics, Alexandra, and Tímea Kiss. 2024. "Declining Bank Erosion Rate Driven by Hydrological Alterations of a Small Sub-Alpine River" Hydrology 11, no. 8: 114. https://doi.org/10.3390/hydrology11080114

APA Style

Pusztai-Eredics, A., & Kiss, T. (2024). Declining Bank Erosion Rate Driven by Hydrological Alterations of a Small Sub-Alpine River. Hydrology, 11(8), 114. https://doi.org/10.3390/hydrology11080114

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