Increased Riparian Vegetation Density and Its Effect on Flow Conditions

: The physical and biological structure of riparian vegetation fundamentally inﬂuences ﬂoodplain roughness, and thus the ﬂood velocity and ﬂood levels of a river. The study aims to provide detailed spatial data on the vegetation density of a ﬂoodplain, and to model the effect of the actual vegetation and various scenarios on ﬂow conditions. LiDAR data were applied to evaluate the density and roughness of the submerged understory vegetation over the densely vegetated ﬂoodplain of Lower Tisza, Hungary. Then, HEC–RAS 2D modelling was applied to analyse the effect of the actual vegetation on ﬂow conditions. Further scenarios were also created to predict the effect of (i) invasive plant control, (ii) no maintenance, and (iii) riparian vegetation restoration (meadows). According to the results, since the 19th Century, the increased vegetation density is responsible for a 17-cm ﬂood level increase, and if the vegetation grows even denser, a further 7 cm could be expected. As the vegetation density increases, the overbank ﬂow velocity decreases, and the crevasses and ﬂood conveyance zones gradually lose their function. Simultaneously, the ﬂow velocity increases in the channel (from 1 m/s to 1.4 m/s), resulting in an incision. Applying LiDAR-based 2D ﬂow modelling makes it possible to plan sustainable riparian vegetation maintenance (e.g., forestry, invasive species clearance) from both ecology and ﬂood control perspectives.


Introduction
Most of the rivers and their floodplains in densely populated areas are influenced by engineering works [1,2]. The channels are straightened and dredged [3,4] to support flood conveyance and shipping, their banks are revetted to stop lateral erosion and channel migration [5,6], and dams are built to create reservoirs for various purposes. At the same time, vast floodplains have been confined by artificial levees to provide flood-protected lands for agriculture and settlement development [7].
Due to these human interventions and climate change, the river channels and floodplains altered, and many of the fluvial processes accelerated [8][9][10][11][12][13][14]. In many rivers, the channel pattern changed from multithread or meandering to sinuous; the channel often incised and became narrower [15][16][17][18][19]. While channel processes are the focus of geomorphologists and engineers who deal with shipping or flood protection [20][21][22], floodplain processes are often neglected, though they are closely related to in-channel processes.
Ecologists have drawn attention to the changing riparian vegetation [23,24], which is rapidly altering as a consequence of extreme hydrological situations, such as recent droughts or long and high floods [25], plant invasions, and altered land use [26]. Over time, the confined floodplains have become ignored by society, traditional land uses (e.g., pasturing) have become neglected, and floodplains are no longer a priority of the nearby communities [27,28], especially in developed countries. On the other hand, the changing riparian vegetation has also influenced the fluvial processes. Along banks, vegetation can influence bank stability and channel morphology [29,30], whereas, on the The results of the study could be applied by hydrologists during the planning of flood control measures, by foresters and land owners who could manage the vegetation by controlling invasive species on the most crucial plots, and by ecologists who evaluate the dynamics of riparian vegetation.

Study Area
Along the Tisza River (catchment area: 157,200 km 2 ; length: 962 km) in Central Europe (Figure 1), the 5-10-km-wide natural floodplain was confined by artificial levees to 1-4 km in the mid-19th Century [34,77,78]. Ever since, the floodplain has been gradually altered by semi-natural processes. The original wetlands quickly disappeared after the river regulation works, as the channel incised by 3-4.6 m (max 45% increase), and the originally six-month-long floods shortened to 1-3 months [34,[76][77][78]. The wetlands were replaced by meadows and plough fields, but by the late 20th Century, even these traditional land uses were abandoned as intensive animal husbandry moved to the villages, and the increasing flood levels destroyed the crops; thus, the farmers ended the cultivation of their lands. In the 1970s and 80s, forest plantations became widespread; thus, today, poplar and riparian willow forests cover 76% of the floodplain [76,77]. Between 1998 and 2006, some extremely high and long floods supported the spread of invasive species (e.g., Amorpha fruticosa, Vitis vulpina, and Echinocystis lobata). These centurial vegetation changes resulted in a 2-4-fold increase in vegetation roughness [76,77] and changed the spatio-temporal pattern of overbank accumulation [34]. different management scenarios (e.g., with and without invasive plant control, replacement of forests by meadows and pastures). The results of the study could be applied by hydrologists during the planning of flood control measures, by foresters and land owners who could manage the vegetation by controlling invasive species on the most crucial plots, and by ecologists who evaluate the dynamics of riparian vegetation.

Study Area
Along the Tisza River (catchment area: 157,200 km 2 ; length: 962 km) in Central Europe (Figure 1), the 5-10-km-wide natural floodplain was confined by artificial levees to 1-4 km in the mid-19th Century [34,77,78]. Ever since, the floodplain has been gradually altered by semi-natural processes. The original wetlands quickly disappeared after the river regulation works, as the channel incised by 3-4.6 m (max 45% increase), and the originally six-month-long floods shortened to 1-3 months [34,[76][77][78]. The wetlands were replaced by meadows and plough fields, but by the late 20th Century, even these traditional land uses were abandoned as intensive animal husbandry moved to the villages, and the increasing flood levels destroyed the crops; thus, the farmers ended the cultivation of their lands. In the 1970s and 80s, forest plantations became widespread; thus, today, poplar and riparian willow forests cover 76% of the floodplain [76,77]. Between 1998 and 2006, some extremely high and long floods supported the spread of invasive species (e.g., Amorpha fruticosa, Vitis vulpina, and Echinocystis lobata). These centurial vegetation changes resulted in a 2-4-fold increase in vegetation roughness [76,77] and changed the spatiotemporal pattern of overbank accumulation [34].   The study was performed on a 5-km-long section (210-215 fluvial km) of the Lower Tisza, where the artificially confined floodplain is 0.7-1.5 km wide with a slope ≤2.9 cm/km ( Figure 1). Since the beginning of the 20th Century, along this section, the originally 160-220-m-wide channel became narrower (120-160 m), increasing the flood levels by 30-70 cm. The accelerated aggradation increased the food levels by a further 0.3-1.9 m [34].
Just upstream of the study area is a gauging station (Mindszent), where stage measurements were performed. From the start of the measurements (1900), the peak flood level increased by 220 cm. Thus, the highest flood on record in 2006 had already reached the top of the artificial levees. The declining flood conveyance of the channel and the floodplain was well presented by the fact that the increasing flood levels have contributed to the decreasing peak discharge [79]. Downstream of the study area, at Szeged (Figure 1), the peak flood level was 923 cm with 4346 m 3 /s discharge in 1932, but during the 1970s, the discharge dropped to 3820 m 3 /s (−12%), but the peak water level increased by 36 cm to 959 cm. The situation became even worse in 2006, when 3780 m 3 /s contributed to a 1009-cm peak flood level; thus, the peak stage increased by a further 50 cm [34,80]. The 2006 flood was exceptional, the highest flood on record, as the peak flood level reached the top of the artificial levees. Thus, in 2006 the flood protection costs were ca. 120 million USD (0.6% of the annual GDP of Hungary) [81]. Since then, only two small overbank floods have been recorded (2010 and 2013), and the last decade was flood free.
The vegetation is quite dense in the selected section of the Lower Tisza at Mindszent. According to our previous measurements [76][77][78], within a century, the meadows were replaced by planted (43%) and riparian forests (31%), and only 13% of the original meadows and plough fields remained. Moreover, as the study area is located very close to the town of Mindszent, fruit and vegetable gardens were on the floodplain but, due to their gradual abandonment, invasive plants colonised them. Thus, today, Amorpha thickets occupy 13% of the area.
The false indigo (Amorpha fruticosa L.) originated from North-East America and rapidly spread on the floodplain of the Tisza after World War II [82]. Its invasion was related to the end of traditional floodplain farming (grazing) and extensive forestation. The false indigo can seriously inhibit forest renewal, as it overgrows the native plants. Without clearance, it spreads very rapidly, and monodominant stands develop. Under the impenetrable false indigo thickets (height: 3-4 m), the native plant species cannot survive. The habitat becomes unsuitable for animals; thus, the fauna of homogenous false indigo stands is very poor, almost impassable for larger mammals, and unsuitable for nesting or hunting birds. Moreover, the false indigo weakens the artificial levees by its root system and blocks canals and crevasse channels.
Other invasive plants, including wild grape (Vitis vulpina L.) and wild cucumber (Echinocystis lobata Torr. et Gray), also originate from North America, and their invasions started in the first half of the 20th Century [82]. Both plants are lianas, climbing high (>8 m) in the canopy. Their disadvantageous effects include shading, pressing down the native vegetation, and decreasing the biodiversity of the habitats.

Methods
The vegetation density was determined by analysing the reflectance ratios using the NRD method [63]. The effect of vegetation density on water level and overbank flood velocity was modelled in HEC-RAS 2D for the highest flood on record (2006 First, the necessary steps for processing the LiDAR data (format conversion, data quality control) were performed. Then, the point-to-cloud reflectance ratios were calculated for the different height zones (1-2 m; 2-3 m up to 4-5 m) at a 15 × 15 m resolution (fitted to the largest canopy diameter) using the DensityMetrics function of the Fusion software. The input data were the elevation model and the LiDAR point cloud. The density calculation was based on the reflectance ratios of the different height zones applying the NRD method [63,73]. To calculate the vegetation density in a given height zone, the number of points reflected from the vegetation height zone under study was divided by the total number of points reflected from and below the given height zone. The calculations were performed for each vegetation height zone on a metered basis. However, only the zones between 1 and 5 m above the surface were analysed in detail, as a record-high overbank flood could submerge these vegetation zones. Thus, their vegetation density could influence the overbank flow velocities during a flood event.
The distribution analysis of the density data (NRD) was performed to determine the vegetation density categories. As a first step, the density values and their corresponding frequency values were plotted on a histogram. The histogram showed that the distribution has a highly skewed peak (towards values < 0.1). According to Francisci [84], such highly skewed distributions could be categorized using class boundaries following the geometric distribution. When defining class boundaries based on the geometric distribution, the class boundaries follow a geometric sequence that distributes the data as evenly as possible into a fixed number of categories. Based on the distribution curves and field observations, the class boundaries were generated at the maximum values of 1, 2, 4, and 16% of the data series, resulting in density classes shown in Table 1. The probability of inundation and the return period of floods submerging a given vegetation zone were also calculated. The Gringorten formula was used based on the time series (1901-2022) of water stages measured at the Mindszent gauge station, just at the upstream end of the study area ( Figure 1).
where T is the recurrence interval of floods, n is the total number of years of record, and m is the magnitude or rank of a given flood.

Hydrodynamic Modelling in HEC-RAS 2D
To model the effect of vegetation density on flow conditions (water levels and flow velocity), the HEC-RAS 2D model was used. The HEC-RAS software was developed at the Hydrologic Engineering Center (HEC), an Institute for Water Resources division, U.S. Army Corps of Engineers. HEC-RAS can perform two-dimensional (2D) hydrodynamic modelling under unsteady, supercritical, or subcritical flow conditions. Thus, detailed 2D channel and floodplain modelling could be performed [85]. The model was calibrated for the record-high 2006 flood. Water levels were validated with the second-largest flood wave in 2000, and at-site flow measurements validated water velocities during the 2006 flood [83].

Geometric Data of the Model
The model was built by integrating the geometry data (topography, roughness, and artificial structures), specifying the hydrological boundary conditions (water level and discharge), performing the calibration runs, and validating the model. The model geometry was based on a terrain model (spatial resolution: 1 × 1 m) that included the elevation of the floodplain and the channel. The resolution of the 2D computational grid mesh in the geometry structure is key to the stability of the model, and it influences the precision of the modelled hydrological processes. Thus, based on test runs, a 10 × 10 m computational grid mesh was defined for the study area.
Manning's roughness coefficient depends on different environmental factors [42], such as bed material, bed surface, vegetation, bed contour, quantity and quality of transported sediment, and built-in structures (e.g., bridges, embankments). The mean vegetation roughness value for each vegetation density class for the 1-5-m vegetation zone was assigned by applying values published by various authors [42,75,76,83,86]. Thus, the following roughness values were applied: channel n = 0.025, open surface n = 0.02, sparse vegetation n = 0.04, medium dense vegetation n = 0.08, dense vegetation n = 0.016, very dense = 0.2.

Model Scenarios
To evaluate the effects of various management methods of the riparian vegetation on flow conditions, four scenarios were created: 1.
The base scenario (S_base) corresponds to the actual state of the floodplain vegetation. It includes the spatially assigned roughness values based on the vegetation density classes calculated from the LiDAR data.

2.
The next scenario (S_maintained) represents a state when the actually dense (n = 0.16) and very dense (n = 0.2) understory vegetation patches dominated by invasive species are maintained by invasive plant control. Thus, the vegetation roughness in these patches is reduced to n = 0.08. This scenario represents the most reasonable compromise for the future, as it assumes that the very high areal proportion (ca. 80%) of invasive species is artificially reduced in the floodplain forests.

3.
In the least advantageous scenario (S_invasive), the vegetation conditions would deteriorate further, due to the further expansion of invasive species, abandonment of plough lands, and without proper management of planted forests. Thus, patches with very dense undergrowth (n = 0.2) would replace patches with dense (n = 0.16), medium (n = 0.08) and sparse (n = 0.04) undergrowth.

4.
The scenario with the lowest roughness (S_meadow) assumes that meadows with low grass cover the floodplain. Thus, over the entire floodplain, the roughness is 0.06. This scenario represents a significantly different state from the actual one; however, it represents 19th Century (pre-regulation) conditions, when marshes and grassy wetlands covered the study area according to the First Military Map (1763-1787).

Hydrological Boundary Conditions of the Model
The model covered the period from 5 April to 5 May 2006, when the floodplain was entirely inundated. During this flood, the highest water level on record reached almost the top of the artificial levees and covered the floodplain with up to 5-m-deep water. At the study area at Mindszent, no discharge data are available. Thus, water level data measured at Mindszent and discharge data were used from a model calibrated by the Middle Tisza Hydrological Directorate for the 2006 flood wave (±5 cm). The upper boundary condition was discharge, while the lower boundary condition was water level. Since the output data of the model were velocity conditions, the SW Momentum algorithm with the full equation SW Momentum was used, which is capable of modelling complex flow conditions with increased computational power. The calibration of the model was based on the water level measurements along the artificial levees at the peak of the 2006 flood. During the runs, the recorded water levels' elevation and the model's calculated ones were retrieved and used to generate a hydrograph ( Figure 2). The model adequately represents water levels, though deviations (−9 cm) in the upstream section of the modelled area exist due to the small model area, the extremely low slope (≤2.9 cm/km) of the river, the effect of the reduction of the grid resolution (10 m), and the uncertainties of the water level measurements. Therefore, the flow conditions were analysed in detail in the central part of the modelled area (Mindszent: 215-210 fluvial km), where the accuracy was within ca. 5 cm.
Tisza Hydrological Directorate for the 2006 flood wave (±5 cm). The upper boundary condition was discharge, while the lower boundary condition was water level. Since the output data of the model were velocity conditions, the SW Momentum algorithm with the full equation SW Momentum was used, which is capable of modelling complex flow conditions with increased computational power.

Calibration of the Model
The calibration of the model was based on the water level measurements along the artificial levees at the peak of the 2006 flood. During the runs, the recorded water levels' elevation and the model's calculated ones were retrieved and used to generate a hydrograph ( Figure 2). The model adequately represents water levels, though deviations (−9 cm) in the upstream section of the modelled area exist due to the small model area, the extremely low slope (≤2.9 cm/km) of the river, the effect of the reduction of the grid resolution (10 m), and the uncertainties of the water level measurements. Therefore, the flow conditions were analysed in detail in the central part of the modelled area (Mindszent: 215-210 fluvial km), where the accuracy was within ca. 5 cm. The calibration also included a sensitivity analysis of the different understory density categories. The initial value was determined based on Sándor [83], and the sensitivity tests were performed by increasing and decreasing the roughness values for each category by 20%.

Validation of the Model for Water Level
The calibrated model was validated using hydrological data at the peak of the 2000 flood. For the validation, the model data calibrated by the Central Tisza Region Water Directorate (KÖTIVIZIG) for the 2000 flood event were used as boundary conditions. Furthermore, the land-use data based on an orthophoto taken in 2000 (resolution: 10 cm) were applied. To verify the calculated results, water level measurements made in 2000 along the artificial levee during the flood peak were used.
Despite the close temporal proximity of the flood waves and the similar peak stages, the control fit (2000 flood water level recordings and modelled water levels at the peak of the 2000 flood) did not give a good match, as the differences exceeded 20 cm at several points ( Figure 3). It could be reasoned by (1) the difference in mean water depths during The calibration also included a sensitivity analysis of the different understory density categories. The initial value was determined based on Sándor [83], and the sensitivity tests were performed by increasing and decreasing the roughness values for each category by 20%.

Validation of the Model for Water Level
The calibrated model was validated using hydrological data at the peak of the 2000 flood. For the validation, the model data calibrated by the Central Tisza Region Water Directorate (KÖTIVIZIG) for the 2000 flood event were used as boundary conditions. Furthermore, the land-use data based on an orthophoto taken in 2000 (resolution: 10 cm) were applied. To verify the calculated results, water level measurements made in 2000 along the artificial levee during the flood peak were used.
Despite the close temporal proximity of the flood waves and the similar peak stages, the control fit (2000 flood water level recordings and modelled water levels at the peak of the 2000 flood) did not give a good match, as the differences exceeded 20 cm at several points ( Figure 3). It could be reasoned by (1) the difference in mean water depths during the studied flood waves and (2) the increase in vegetation density between 2000 and 2006. Since the energy loss caused by vegetation in the flow path is proportional to the surface area exposed to the flow, lower water depths are expected to result in lower energy loss; i.e., a lower roughness coefficient. Considering this, Manning's (n) roughness coefficient values determined for the forested areas during validation were uniformly reduced. After this adjustment, the measured and calculated water levels along the entire length of the studied section showed very good correspondence, with differences of less than 10 cm (root mean square error: 5.5 cm).
the studied flood waves and (2) the increase in vegetation density between 2000 and 2006. Since the energy loss caused by vegetation in the flow path is proportional to the surface area exposed to the flow, lower water depths are expected to result in lower energy loss; i.e., a lower roughness coefficient. Considering this, Manning's (n) roughness coefficient values determined for the forested areas during validation were uniformly reduced. After this adjustment, the measured and calculated water levels along the entire length of the studied section showed very good correspondence, with differences of less than 10 cm (root mean square error: 5.5 cm).

Validation of the Model for Flow Velocity
The model was validated not only for water level but also for flow velocity at 23 points in 90-cm depth. The flow velocity measurements were made on the eastern floodplain area of the study site by A. Sándor and T. Kiss during the peak of the 2006 flood [83]. The measurements were made with a calibrated GR-21 flow velocity meter, which accurately measures the velocity in the range of 0.14-2.86 m/s. The mean difference between the modelled and measured velocities was 0.1 m/s, which, considering the instrument's accuracy, was considered as good. The largest deviation was 0.3 m/s (modelled 0.42 m/s instead of measured 0.12 m/s), but there were 6 points where the differences were within ±0.01 m/s.

Vegetation Density of the Submerged Vegetation Zones
On the floodplains of low-gradient rivers, the overbank flow velocity is low; thus, the obstacles in the flow path can substantially alter flow conditions. Since the artificial levees along the confined floodplain of the Tisza have an average height of 5 m, the vegetation density of the 1-5-m height zone was the focus of our study, as during the highest floods (which reach the top of the levee) this vegetation zone is inundated.
Diverse vegetation patches with various density conditions were identified in the studied floodplain section (Figure 4). In the narrow, western floodplain section, the vegetation is dense or very dense; though, in some patches, the vegetation was cleared for young poplar plantations.
The wide eastern floodplain has spatially diverse riparian vegetation. In its upstream part, near the levee, sparse understorey poplar plantations occur, and riparian willow

Validation of the Model for Flow Velocity
The model was validated not only for water level but also for flow velocity at 23 points in 90-cm depth. The flow velocity measurements were made on the eastern floodplain area of the study site by A. Sándor and T. Kiss during the peak of the 2006 flood [83]. The measurements were made with a calibrated GR-21 flow velocity meter, which accurately measures the velocity in the range of 0.14-2.86 m/s. The mean difference between the modelled and measured velocities was 0.1 m/s, which, considering the instrument's accuracy, was considered as good. The largest deviation was 0.3 m/s (modelled 0.42 m/s instead of measured 0.12 m/s), but there were 6 points where the differences were within ±0.01 m/s.

Vegetation Density of the Submerged Vegetation Zones
On the floodplains of low-gradient rivers, the overbank flow velocity is low; thus, the obstacles in the flow path can substantially alter flow conditions. Since the artificial levees along the confined floodplain of the Tisza have an average height of 5 m, the vegetation density of the 1-5-m height zone was the focus of our study, as during the highest floods (which reach the top of the levee) this vegetation zone is inundated.
Diverse vegetation patches with various density conditions were identified in the studied floodplain section (Figure 4). In the narrow, western floodplain section, the vegetation is dense or very dense; though, in some patches, the vegetation was cleared for young poplar plantations.
The wide eastern floodplain has spatially diverse riparian vegetation. In its upstream part, near the levee, sparse understorey poplar plantations occur, and riparian willow patches with dense understorey appear towards the channel. In the middle part of the floodplain, poplar plantations were identified with very dense understorey invaded by Amorpha along the levee and with low to medium vegetation densities along the river bank. On the downstream part of the eastern floodplain, mostly abandoned gardens and agricultural fields with very dense Amorpha thickets were identified (rectangular pattern), and only some plough land mosaics and medium-density poplar plantations occur. Along the river, riparian willow forests with dense undergrowth are common. patches with dense understorey appear towards the channel. In the middle part of the floodplain, poplar plantations were identified with very dense understorey invaded by Amorpha along the levee and with low to medium vegetation densities along the river bank. On the downstream part of the eastern floodplain, mostly abandoned gardens and agricultural fields with very dense Amorpha thickets were identified (rectangular pattern), and only some plough land mosaics and medium-density poplar plantations occur. Along the river, riparian willow forests with dense undergrowth are common. Overbank flood waves submerge the vegetation of the 1-2-m height zone approximately every second year, when the water level at the Mindszent gauging station is 600-700 cm. In this height zone, dense (23%) and very dense (5%) understorey patches are common ( Figure 4, Table 2). The vegetation is especially dense in abandoned gardens, fallow agricultural fields, and unmanaged forests. In contrast, patches with very sparse (38%) and sparse (12%) undergrowth cover 50% of the area. Such patches are mainly found in the middle of the eastern floodplain, where crops are planted on some large plots and the poplar forests are managed by clearing the understorey bushes.
The 2-3-m height vegetation zone is inundated by 700-800 cm floods with a return period of ca. three years. In this zone, the proportion of dense (20%) and very dense (2%) undergrowth decreases by 6% compared to the 1-2-m zone, while the very sparse vegetation became more common (44%). Thus, in terms of overbank flow, this zone can convey floods more effectively than the lower, 1-2-m height zone.
The 3-4-m vegetation zone is flooded every 9 years by 800-900-cm high stages, whereas the uppermost, 4-5-m vegetation zone is rarely submerged (return period: 25 y) by record high floods (>900 cm). In these zones, the proportion of dense and very dense understorey patches is lower (3-4 m: 15%; 4-5 m: 10%), as they are replaced by low-density or vegetation-free cells. Overbank flood waves submerge the vegetation of the 1-2-m height zone approximately every second year, when the water level at the Mindszent gauging station is 600-700 cm. In this height zone, dense (23%) and very dense (5%) understorey patches are common (Figure 4, Table 2). The vegetation is especially dense in abandoned gardens, fallow agricultural fields, and unmanaged forests. In contrast, patches with very sparse (38%) and sparse (12%) undergrowth cover 50% of the area. Such patches are mainly found in the middle of the eastern floodplain, where crops are planted on some large plots and the poplar forests are managed by clearing the understorey bushes. Table 2. Spatial distribution (%) of the vegetation density classes at the various height zones; the return period and exceedance probability of flood waves inundating a given vegetation zone based on the Gringorten formula.

Vegetation Density Class
Areal Distribution (%) The 2-3-m height vegetation zone is inundated by 700-800 cm floods with a return period of ca. three years. In this zone, the proportion of dense (20%) and very dense (2%) undergrowth decreases by 6% compared to the 1-2-m zone, while the very sparse vegetation became more common (44%). Thus, in terms of overbank flow, this zone can convey floods more effectively than the lower, 1-2-m height zone.
The 3-4-m vegetation zone is flooded every 9 years by 800-900-cm high stages, whereas the uppermost, 4-5-m vegetation zone is rarely submerged (return period: 25 y) by record high floods (>900 cm). In these zones, the proportion of dense and very dense understorey patches is lower (3-4 m: 15%; 4-5 m: 10%), as they are replaced by low-density or vegetation-free cells.

Spatial Distribution of Flow Velocity Fields in Different Scenarios
Based on the vegetation density map, a vegetation roughness map was created by applying the vegetation roughness values determined by Chow [42], Sándor [83], and Nagy et al. [76]. The created vegetation roughness map was input data of the 2D hydrodynamic model; thus, the effect of vegetation on flood flow conditions could be quantified ( Figure 5).

Spatial Distribution of Flow Velocity Fields in Different Scenarios
Based on the vegetation density map, a vegetation roughness map was created by applying the vegetation roughness values determined by Chow [42], Sándor [83], and Nagy et al. [76]. The created vegetation roughness map was input data of the 2D hydrodynamic model; thus, the effect of vegetation on flood flow conditions could be quantified ( Figure 5). The S_base scenario represents the actual vegetation and flow conditions. Along the banks, in the vegetation with dense understorey, the flow velocity of the overbank flood is below 0.1-0.2 m/s, even during the peak of the flood. This zone with high vegetation roughness forces the flow towards the eastern artificial levee. Thus, in between them, in the sparse poplar plantations and especially in its low-lying areas, the flow accelerates to In the S_maintained scenario, the management of the undergrowth vegetation (e.g., clearance of invasive species) improves the vegetation roughness, especially in the nearbank zone. Therefore, the flow velocity increases to 0.2-0.4 m/s along the bankline and decreases to 0.3-0.5 m/s along the artificial levee. The crevasses merge to form a wider strip where the overbank flow velocity reaches 0.5-0.6 m/s. In this scenario, the in-channel flow velocity decreases to 0.8-1 m/s.
As the dense undergrowth with invasive species spreads over the floodplain (S_invasive), the flow velocity decreases to ≤0.1 m/s on the entire floodplain. The overbank flow is almost uniformly stagnant all over the study area. Thus, no distinct conveyance zone is formed, and the activity of crevasses is very limited. On the contrary, the flow velocities in the channel increase to 1.2-1.3 m/s, and areas of pronounced high velocity (1.4 m/s) develop in the northern meander ( Figure 5).
The S_meadow scenario represents a much lower vegetation density and roughness than the current conditions. In this scenario, the overbank flow enters the floodplain through crevasses (e.g., in the lower third of the upstream meander). Thus, high flow velocities (0.5-0.7 m/s) evolve over the entire floodplain. Since vegetation does not block the crevasses, they merge, creating a wide flood conveyance zone. This conveyance zone extends to the artificial levee, and in its widening section, the maximum flow velocity reaches 0.8 m/s. In the low-lying areas of the floodplain, the flow velocity also accelerates (0.5-0.6 m/s). Meanwhile, in the channel, the lowest water velocities of all scenarios prevail (0.6-0.8 m/s).
On the downstream part of the western floodplain, low flow velocity fields form in all scenarios. Its development is influenced by the remnants of a 19th Century artificial levee running perpendicular to the channel. It effectively blocks the overbank flow; therefore, in all scenarios, the flow velocities are ≤0.1 m/s. In the actual situation (S_base), on the first day of the modelled period, the floodplain was already covered by a 2-m deep water column, and the mean overbank flow velocity was 0.09 m/s. During the rising limb, the flow velocities increased, as the 0-0.3 m/s velocity field covered 81% of the study area. During the peak of the flood, the mean inundation depth was ca. 5 m, the mean overbank flow velocity increased by 2.6 times to 0.24 m/s, and the maximum flow velocity was 1.3 m/s. Even during the peak, the overbank flow was relatively slow on the floodplain, as flow velocities ≤ 0.3 m/s appeared on two-thirds of the study area. During the falling limb, the drop of stages was slow; thus, the changes in average floodplain velocities were also moderate: in two weeks the average velocity (0.21 m/s) only decreased by 13%. The proportion of areas with low flow velocities (0-0.3 m/s) increased to 69%, while the proportion of areas with higher water velocities gradually decreased (Table 3).

Temporal Changes in Overbank Flow Velocities in Different Scenarios
In the case of invasive plant management (S_maintained), the flow velocities only differ by 1-2% from the base situation. At the peak of the flood, the mean flow velocity increases to 0.28 m/s, thus, by 16% compared to the S_base situation. The maximum flow velocity (1.1 m/s) on the day of the peak is slightly less than for the base scenario (1.3 m/s). However, the proportion of medium (0.3-0.6 m/s) and high (>0.6 m/s) flow velocity fields significantly increases during the peak. During the falling limb, the water level decrease remains slow due to the nature of the flood wave (impoundment by the Danube). However, on the last day of the modelled period, the average velocity is still 17% higher than in the base scenario. Thus, vegetation maintenance reduced the proportion of low flow velocity fields during the peak and the falling limb of the flood wave and increased the proportion of higher water velocities (≥0.3 m/s). The worst flood conveyance conditions develop in the absence of vegetation management, when the forest understorey is dense, and the fallow lands are invaded by invasive species (S_invasive). In this case, at the beginning of the flood, the mean overbank flow velocity decreases to 0.06 m/s, being one-third lower than in the S_base. In the rising limb, there is only a 1-2% difference between the S_invasive and S_base scenarios. At the peak of the flood, there is a 30% velocity drop due to dense vegetation. This velocity difference also remains in the falling limb when the mean floodplain velocity drops to 0.15 m/s, being lower than the S_base by 28%. This implies that the extent of low flow velocity (<0.3 m/s) fields during the peak and the falling limb significantly increases, and higher velocities only appear in small patches.
In the case of floodplain restoration, when the study area is completely covered by meadows and open surfaces (S_meadow), the mean flow velocity could be 0.16 m/s on the first day of the flood; thus, it is doubled compared to the S_base. In this scenario, the proportion of medium and high flow velocity fields increases by 3-4%, and a zone with high overbank flow velocity also evolves. At the peak of the flood, the mean flow velocity over the floodplain increases to 0.41 m/s, which is higher than the velocity conditions of the S_base by 70%. The area of the low-flow velocity fields significantly decreases, while the medium-and high-velocity flow fields become dominant. However, the maximum velocity decreases, and it reaches its lowest value (1 m/s). During the falling limb of the flood wave, the mean overbank flow velocity decreases from 0.41 m/s to 0.38 m/s in two weeks, which is 80% higher than the value of the reference scenario.

Temporal Changes in In-Channel Flow Velocities in Different Scenarios
The flow velocity in the channel is closely related to the flow velocity in the floodplain, as models reflect their complementary character: as the overbank flow velocity in the floodplain increases, it decreases in the channel.
The temporal connection between the mean overbank and in-channel flow velocities could be described by a loop-like curve ( Figure 6). During the first part of the loop floodplain and slowly reaches its peak (11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22) April; H: 873-1062 cm), the in-channel flow velocity increases more and more intensively as a function of vegetation roughness. The greater the vegetation roughness of the floodplain, the more intensive the velocity increase rate in the channel, causing the loop curves to rotate counter-clockwise. For example, in the S_meadow scenario, the flow velocity in the channel decreases as the flood progresses. After reaching the peak in the third period (23-28 April; H: 1060-1036 cm), the falling limb slowly starts. At this time, both the in-channel and overbank flow velocities are reduced, and the curve inverts. In the last part of the flood wave (after 29th April; H: <1028 cm), the flood conveyance in the channel becomes more intensive as the impoundment by the Danube ceases. Thus, in-channel flow velocities start to increase, while overbank flow velocities slowly decrease.

Changes in Water Levels in Different Scenarios
Based on the modelled data, the differences in water levels were analysed for a transect in the middle of the study area (213.4 fluvial km; Figures 1 and 7). In the case of managed understorey vegetation (S_maintained), the water levels are lower by 7 cm than in the case of S_base at the beginning of the flood wave. However, as the flood rises, their difference steadily increases, reaching a 10-cm difference during the peak of the flood. It indicates that forest maintenance could achieve a 10-cm decrease in peak water levels. During the falling limb of the flood, this difference remained at 9 cm.

Changes in Water Levels in Different Scenarios
Based on the modelled data, the differences in water levels were analysed for a transect in the middle of the study area (213.4 fluvial km; Figures 1 and 7). In the case of managed understorey vegetation (S_maintained), the water levels are lower by 7 cm than in the case of S_base at the beginning of the flood wave. However, as the flood rises, their difference steadily increases, reaching a 10-cm difference during the peak of the flood. It indicates that forest maintenance could achieve a 10-cm decrease in peak water levels. During the falling limb of the flood, this difference remained at 9 cm. Due to the extremely dense vegetation (S_invasive), the water levels only exceed the S_base stages by 2 cm at the beginning of the rising limb. However, during the peak, their difference increases to 7 cm, however, and it remains at 6 cm during the falling limb.
Thus, the comparison of the above-presented scenarios (S_maintained and S_invasive) shows that the further spread of invasive species could increase the flood stages by just 2-7 cm, while the maintenance of vegetation could reduce water levels by 7-10 cm compared to the actual situation.
On the contrary, if pastures and meadows could be restored in the floodplain Due to the extremely dense vegetation (S_invasive), the water levels only exceed the S_base stages by 2 cm at the beginning of the rising limb. However, during the peak, their difference increases to 7 cm, however, and it remains at 6 cm during the falling limb.
Thus, the comparison of the above-presented scenarios (S_maintained and S_invasive) shows that the further spread of invasive species could increase the flood stages by just 2-7 cm, while the maintenance of vegetation could reduce water levels by 7-10 cm compared to the actual situation.
On the contrary, if pastures and meadows could be restored in the floodplain (S_meadow), even at the beginning of the flood the water levels could decrease by 11 cm compared to the S_base. At the peak of the flood, the water level difference is already 17 cm, and it slightly decreases to 16 cm during the falling limb (Figure 7).

Discussion
From the point of view of hazard management, the primary function of the lowgradient, lowland rivers is to support the propagation of flood waves and to provide fast and safe flood conveyance without levee breaching or overtopping. According to our hypothesis, the submerged vegetation's spatial dimensions (vertical and horizontal) fundamentally influence the flow conditions (e.g., velocity, directions) and height of flood waves.

Riparian Vegetation Density with Special Respect to the Submerged Vegetation Zones
Due to the centurial changes in riparian vegetation cover along the Tisza River [76], today, the mean vegetation density is quite high (NRD median : 0.007-0.051) in the area, especially in the lowest inundation zone, in the Amorpha thickets [78]. Our NRD results provided very similar data to the results of point-like density measurements performed by Sándor [83] and Delai et al. [75] in the same area. However, applying the LiDAR dataset as a source and the NRD as a method, the vegetation density of the entire study area could be evaluated, thus spatially detailed roughness data for the 2D modelling could be provided.
In the study area, the vegetation is the densest in the lowest (1-2 m) flooded zone, and upward in the higher zones it becomes thinner [78]. Thus, in the 1-2-m zone, the proportion of very dense and dense vegetation is 28%, but it decreases to 10% in the uppermost (4-5 m) zone. Simultaneously, sparse or very sparse vegetation occupies 50% of the territory in the lower zone, but their proportion increases to 78% in the uppermost zone [78]. Thus, the propagation of smaller flood waves (H: <800 cm, return period: ≤3 y) or the rising stages of the larger flood waves are more influenced by the dense vegetation than the peak periods of the extreme high floods.
Comparing the spatial distribution of vegetation density classes to vegetation types of the floodplain [78], it should be noted that the dense and very dense patches are common under the natural willow forests and in the Amorpha thickets. As the willow forests are along the banks, where the channel narrowing created new areas [79] to be colonised by natural riparian forest, the near-bank zone has high vegetation density, thus high vegetation roughness, unfavourably influencing the flood conveyance. Moreover, the canopy structure and the relatively short lifetime of the Salix species [87] provide good light conditions for the growth and spread of invasive plants, such as Amorpha, which further deteriorate the flood conveyance of these patches. Along the sharp southern bend, fallow agricultural parcels and abandoned gardens occur, and dense Amorpha thickets occupy them. As these plants are usually 3-4 m high, they increase the vegetation density in the lower zones, effectively blocking the overbank flow in the chute of the meander.

Hydrological Consequences of Vegetation Changes
The submerged Amorpha thickets effectively impede overbank flood flow. It was also supported by our former, point-like velocity measurements [79] during the peak of the 2006 flood: within the thickets, the flow velocity was 0 m/s, but above them, it was 0.13 m/s. However, our modelling proved that the spread of invasive plants is especially problematic along the banks where the flood enters the floodplain and along flood conveyance zones in the distal, deep-lying areas. The situation is especially critical along the southern, sharp meander. Here, on the eastern part of the floodplain, the very dense vegetation effectively delays the flow. In contrast, on the western side, the remnants of a 19th-Century artificial levee (perpendicular to the flow) block the overbank flood. Moreover, the sharp meander also slows down the flood wave. Thus, here, the increase in flood levels due to local reasons is expected.
The four modelled scenarios reflect gradual vegetation changes in the floodplain and its hydrological consequences. Thus, the subsequent scenarios could be used to interpret the historical changes in flood conveyance: The S_meadow scenario reflects the vegetation conditions before the 19th-Century regulation works when only meadows and wetlands covered the floodplain. Then, the S_maintained represents the stage in the mid-20th Century when invasive species have not been on the floodplain yet, but already forests have become widespread due to extensive plantations. The S_base reflects the actual situation, and the S_invasive predicts the changes if everything goes on as usual, so no invasive plant control will be made.
In the scenario reflecting 19th-Century conditions (S_meadow), channel morphology, relief, and floodplain width were the most important factors influencing the overbank flood flow velocity and directions, as the vegetation was spare and mainly herbaceous. Upstream of the meander's axes, the flood could easily enter the floodplain in a wide (crevasse) zone, and the flood conveyed in the chute of the meanders. However, as the vegetation became denser on the floodplain in the 20th Century (S_maintained and S_base), it could effectively obstruct the flood flow entering the floodplain. Thus, the crevasse zone became gradually narrower and the overbank flood velocity became slower. In the future, when the invasive species (S_invasive) are likely to invade the floodplain more than today [88], these crevasses will almost stop functioning. As the vegetation grows denser, the flow velocity in the thickets of the floodplain will be almost zero. Thus, most of the water will be conveyed within the channel, and if the flood is high enough, water movement will be detectable just above the densest vegetation zone (1-3 m).
Increased vegetation density and the spread of invasive plants have already affected flood levels and safety. Since the beginning of the 20th Century, the peak flood levels have considerably increased (by 220 cm), which means that the artificial levees have had to be heightened to provide flood safety. According to our results, since the 19th Century, the increased vegetation density is responsible for a 17-cm flood level increase. If the vegetation grows even denser, a further 7 cm could be expected. As the 2006 flood reached the top of the levees at some locations, it is urgent to develop an action plan to control invasive plants or re-plan the vegetation patches to support overbank flood conveyance.
On the other hand, the result of the 2D modelling is quite contradicting, as our previous 1D modelling indicated a 42-139-cm flood level increase due to the dense vegetation [34,77,80]. The difference probably originates from the different study area sizes (1D: 350 km; 2D: 6 km) of the models. Suppose a modelled area managed by invasive plant control is embedded into a larger floodplain area with dense riparian vegetation. In that case, there is a considerable drop in stages, increased velocity at the upstream end of a managed area, and significant impoundment at the downstream part (1-2 km) as the flow enters the next impenetrable vegetation [77]. If the modelled (managed) area is long enough, these upstream and downstream effects become negligible (like in our 1D modelling); however, in the case of short sections, the effects overlap.
The decreased overbank velocities influence the overbank aggradation rate. As the Tisza transports a large amount of suspended sediment [89], the gradually declining flow velocities could support increasing aggradation. The role of vegetation in overbank aggradation has been emphasized by several researchers [34,78,80,83,90]. It must also be noted that the increased sedimentation will further contribute to flood level increase [34,80]. Thus, the vegetation indirectly further decreases the flood conveyance of the confined floodplain.
The modelling also supported that the maximum in-channel flow velocity increased from 1.0 m/s (S_meadow) to 1.3 m/s (S_base), and in the future, it will likely further increase to 1.4 m/s (S_invasive). The increased velocity increases the shear stress on the channel. On the other hand, the dense vegetation blocks lateral erosion and channel widening. Thus, the Tisza is already incised, and the process will likely continue. As a result of the ongoing incision, the point bars have already disappeared [91], and the level of the lowest discharges has dropped [80], triggering the drop in groundwater level, which generated the aridification of the nearby areas [88,92]. As the floodplain becomes drier, the spread of invasive species will be further supported, whereas the hygrophilous native plants disappear. Thus, in the future, further channel incisions could be predicted. However, the incision will probably not reduce the overbank flow as it has been reported on other rivers [93] because the incision of the Tisza is surpassed by considerable channel narrowing and cross-sectional area decrease [79,80].
The hydrological model also highlighted another zone where the flow velocity increases: along the artificial levees. Low vegetation density grassland is maintained in a ca. 10-m-wide zone by the feet of the levees. In this zone, the flow velocity is high (S_base: 0.4-0.7 m/s), which endangers the stability of the levees built of silt and clay [94], thus they could be eroded by the flow.
All these direct and indirect hydro-morphological processes increase the flood levels and decrease flood safety [34]. They also support the further spread of invasive plant species and the appearance of new ones. The extremely dense, already impenetrable riparian vegetation increases other hazards as well, including fire hazard [69], aggradation of microplastics and other pollutants in the sediments, and the trapping of macroplastics in the riparian vegetation [95].

Suggestions for Sustainable Flood and Riparian Vegetation Management
Proper riparian vegetation management could mitigate the unfavourable hydromorphological changes related to vegetation density. The vegetation density should be decreased by removing invasive species and replacing forests with meadows at some key locations. These measures would also be favourable from the perspective of biodiversity. The invasive species widespread on the Tisza floodplain are bushes or lianas shading the original habitats and suppressing shorter plants. Moreover, the Amorpha impedes the germination of other seeds and causes serious problems in the renewal of riparian forests [82]. Therefore, the clearance of these invasive species would be necessary, both from hydrological and ecological points of view. Furthermore, the re-created open riparian habitats (e.g., meadows and pastures) could support diverse flora and fauna [88].
The modelled scenarios highlighted those areas where the management should be the most important: along banks where the flood enters the floodplain and in flood conveyance zones (deep-lying areas) of the floodplain. Therefore, it is suggested to perform similar 2D modelling, especially in areas where the local flood level increase is the greatest, and to highlight those zones which should be managed. Moreover, the maintenance of the riparian vegetation could support not just floodplain management, but also help to stop channel incision and groundwater lowering.
The presented case study was performed on the low-gradient Lower Tisza River (slope: 2.9 cm/km), but the method should be tested on rivers with greater slopes. Our previous HEC-RAS 1D modelling on the Middle Tisza (slope: 3.7 cm/km) and on the Maros (slope: 5 cm/km) proved that as the slope of the floodplain increases, the blocking effect of the vegetation decreases [77].
A pilot project within the frame of the Danube Floodplain Project [40,96] aimed to manage the riparian vegetation at some sites of the Middle Tisza. However, their success is questionable, as here only small patches were managed by grazing, and according to our 1D and 2D modelling, longer (several km long) floodplain sections should be managed, otherwise, it has no hydrological effect. Moreover, these pilot projects were not continued after the end of their financed period, thus, with the lack of financial support, the grazing and the invasive plant control were terminated, and even denser invasive vegetation developed. Therefore, we suggest creating legislation, similar to the control of common ragweed (Ambrosia elatior), which is also densely spread in Hungary. According to the Hungarian Government decree [221/2008. (VIII. 30.)], every landowner must clear it before flowering unless a considerable fine is paid. Similar legal regulations should also be implemented on the invasive species of the floodplains, which could encourage landowners to reduce vegetation density. Furthermore, educational programs could help local stakeholders to understand the problem and to accordingly act. Continuous maintenance would be especially important, as the invasive species, including Amorpha, have large seed and propagulum production and long seed lifetime (ca. 40 years) [82,87].
It also has to be emphasised that though local initiatives are important, only large-scale vegetation management could result in proper flood conveyance zones on the floodplain and decrease flood levels. If the vegetation will not be managed, other engineering solutions (e.g., heightening artificial levees, channel widening) will be needed to support flood safety.
Another aspect of proper management is up-to-date monitoring. Our study proved that the analysis of a LiDAR survey could provide accurate data on the spatiality of vegetation density of the potentially submerged understorey vegetation. It is a good tool for estimating vegetation density in areas with impenetrable shrubbery. Thus, the critical vegetation patches could be identified by regular monitoring using a LiDAR survey; thus, the areas where maintenance is needed could be identified, and the effect of the maintenance could be evaluated. Only one LiDAR survey was made along the Tisza; thus, no information on the temporal changes in the vegetation density could be provided.

Conclusions
The riparian vegetation along rivers is highly affected by climate-change-driven environmental processes (e.g., flash floods, droughts, fires) and various human impacts (e.g., river engineering, forestry). Thus, the vegetation type and composition of the riparian zone gradually change, which alters the hydrological processes. Some regions are especially prone to floristic changes: for example, the floodplains of Central European rivers are highly invaded by invasive plants, which displace the native vegetation. Thus, along the Tisza, almost impenetrable shrubbery has developed, replacing the native meadows and invading the understorey of native and planted forests and fallow lands.
The drastic change in vegetation altered the fluvial processes, as was proven by our 2D modelling. Flow velocities gradually drop, and if the invasive plants are not controlled, and the planted forests further gain space, the floodplain will limitedly convey overbank floods in the future. Therefore, it will act rather like a sponge with stagnant water. As the main hydrological function of the floodplains is to convey floods, these processes are very unfavourable from the point of view of flood hazard management. In our case, the modelled 2006 flood already reached the top of the artificial levees, and ever since, the riparian vegetation has become even denser. Therefore, in the future, a flood with a similar discharge will have higher stages; thus, the levees will be overtopped. It endangers those millions who live along the river and exposes the infrastructure to damage.
Thus, the maintenance plans for the floodplain should be created as soon as possible, considering and fitting the needs of hydrology, ecology, forestry, and land owners.
The 2D model was developed for a low-slope floodplain with impenetrable vegetation invaded by invasive plants. Climate change, fires, acidification, and extreme floods also support the spread of invasive species in other regions. However, to understand their effect on hydrology, the modelling should be performed on floodplains with various slopes, widths, and hydrology.