Blockage effect of emergent riparian vegetation patches on river flow

Woody riparian vegetation typically clusters in patch form and increases flow resistance more significantly than individual plants. In this study, we examined the patchiness effects in non-submerged (emergent) conditions on the reach-scale flow resistance in field-scale experiments involving nature-like artificial willow patches. The patchiness characteristics of woody vegetation were systematically defined and classified using the canopy density, patch geometry described by cross-sectional and planar blockage areas, cross-sectional and volumetric blockage factors of the patches, and patch location in the cross-section. We developed quantitative relationships as empirical equations for estimating the vegetative flow resistance using blockage factors, that is, the area or volume fraction of canopy occupation. The results revealed that flow resistance due to emergent willow patches under relatively densely foliated and low volumetric blockage conditions was mostly explained by the blockage parameters and to a lower degree by the canopy density. In addition, it reveals the effects of the spatial distribution of flow and velocity by the relative position of patches, i.e., the flow resistance varies with different tendencies according to hydraulic conditions as the patch shifts from the channel centerline toward the bankside. This study provides reliable and practical relationships for estimating the flow resistance induced by riparian vegetation patches under reach-scale field conditions.


Introduction
Riparian vegetation growing on river edges, banks, and sandbars benefits fluvial systems in various ways (Riis et al., 2020).For example, it provides habitats, shades river channels, reduces sediment and toxic particles, sequesters carbon, and stabilizes stream channels (Beck et al., 2001;Feld et al., 2018;Naiman et al., 2010;Sutfin et al., 2016).However, changes in water flow regimes due to climate change and increasing urban construction and agricultural activities in watersheds often lead to the excessive growth and settlement of riparian vegetation (Choi et al., 2005;Lee et al., 2019Lee et al., , 2023;;Sankey et al., 2015;Singh et al., 2021).Excessive riparian vegetation is targeted for removal from a river management perspective because it increases flood risk by inducing drag forces on the flow and causing energy loss through turbulence (Lee et al., 2021;Nepf, 2012;Yen, 2002;Yokojima et al., 2015).The accumulation of large woody debris from riparian vegetation can induce a severe hazard to the bridge piers and is directly linked to bridge failures (Benn, 2013;Diehl, 1997;Panici and Kripakaran, 2023).Therefore, accurate prediction of the hydraulic resistance with consideration of the physical properties of riparian vegetation is needed to maintain a tradeoff between the ecological benefits and flooding risks of riparian vegetation.
Riparian vegetation is characterized by a diversity of species and types, including trees, shrubs, grasses, and vines, and is often combined as a complex structure of the canopy and understory (Singh et al., 2021).Woody vegetation consists of heterogeneous structural components such as stems, branches, twigs, and leaves and typically clusters in a patch form.Therefore, it is difficult to parameterize the different physical and morphological characteristics according to the species, growth, and geometry of the patches and apply them to estimate vegetative resistance to the flow.However, considering the physical properties of a plant (e.g., leaf and stem densities, stem rigidity, and plant morphology) and patchiness (e.g., canopy density, blockage area and volume, and patch geometry) is necessary to increase the evaluation accuracy for the flow resistance induced by woody vegetation patches (Carollo et al., 2005;Nikora et al., 2008;Shields et al., 2017).
Canopy density, which is generally defined as the frontal area of each plant element per canopy volume, is a significant factor affecting flow resistance (e.g., Cheng et al., 2019;Chiaradia et al., 2019).The canopy density of foliated and branched vegetation patches can be determined by measuring the areas of leaves and woody plant parts.Notably, the foliage area can be considered alone for dense leafy vegetation because the leaf-induced drag accounts for most of the total drag (Västilä et al., 2011).Therefore, the leaf area index (LAI), which conventionally refers to the canopy density of trees or shrubs, has been a representative factor in analyzing the flow resistance due to woody riparian vegetation (e.g., Box et al., 2022;Fathi-Maghadam and Kouwen, 1997;Jalonen et al., 2013;Järvelä, 2004;Kouwen and Fathi-Moghadam, 2000;Västilä and Järvelä, 2014).Analytical and theoretical models using the LAI as a density parameter have been experimentally demonstrated to be suitable for estimating flow resistance due to foliated woody patches under natural conditions (Ji et al., 2023).However, the relative importance between density and other patchiness characteristics on the flow resistance has not been investigated because of limited experimental data for flows with patchy woody vegetation.
The blockage factor, which denotes the area or volume fraction of canopy occupation in the water, depends on the geometry of the vegetation patches.Nikora et al. (2008) suggested that the blockage factor is the most useful predictor of the flow resistance induced by macrophytes, regardless of species-specific characteristics.It was also identified that the blockage factor for the riparian zone can be a primary parameter controlling the flow resistance due to grass and leafy woody patches (Ji et al., 2023;Phillips and Ingersoll, 1998;Västilä et al., 2016).However, Västilä et al. (2016) showed that the dependence of the flow resistance due to woody vegetation on the blockage factor can significantly diminish under sparsely foliated conditions, and the drag parameter C D a, which is the product of the drag coefficient C D and the volumetric frontal area density a, has a more substantial effect on the flow resistance in this case.Moreover, Savio et al. (2023) emphasized that patchiness characteristics such as the spatial distribution of patches and vegetation coverage in the channel reach affect the flow resistance in the case of submerged aquatic vegetation patches.For woody riparian vegetation, the patchiness characteristics, which can impact the reachscale flow resistance, can be characterized by three dominant factors: the canopy density, blockage factors, and spatial distribution which influences the approach flow velocity and thus the drag forces of the patches; therefore, these components should be utilized together to quantitatively analyze the patchiness effects.
The primary objectives of this study were to define and specify the patchiness characteristics of woody riparian vegetation and to quantify the blockage effects of emergent woody riparian vegetation patches on reach-scale flow resistance based on a dataset from large-scale experiments.The patchiness of woody riparian vegetation was characterized by the canopy density, cross-sectional and volumetric blockage factors, and patch location in the cross-section.Two types of nature-like artificial willows with different canopy densities were adopted to determine the effects of canopy density differences on the flow resistance under similar blockage factors and patch layouts.Large-scale experiments with a dense canopy were performed in this study, and a set of experimental data from Ji et al. (2023) and Bae (2024) for sparser canopy cases was adopted for a combined analysis.The effects of blockage factors of vegetation patches on the bulk and vegetative flow resistance were evaluated with 27 experimental datasets from four cases of vegetation patch layouts involving two types of willows under various hydraulic conditions and from six baseline tests without vegetation.The full-scale artificial willow, with similar structural and mechanical properties to woody riparian vegetation, was used to mimic natural willows.

Woody riparian vegetation patches
Rivers form a dynamic topography owing to their spatial and temporal variability in hydraulic conditions.Stream bars are dynamically formed in channels near banks and floodplains through erosion, transportation, and sedimentation.If the stream bars are flooded, the topography changes, and the environment is rearranged (Arscott et al., 2002;Seok et al., 2023).Owing to the variability in the flow regime and flooding intervals, vegetation settles in stream bars, stabilizes, and grows, keeping them relatively long and functioning as habitat or landscape elements (Kollmann et al., 1999;Lee et al., 2009;Tsujimoto, 1999;Woo, 2004Woo, , 2010)).These processes induce the spatial zonation of riparian vegetation, with the formation of vegetation patches mainly according to the frequency and intensity of flooding (Naiman et al., 2005;Nilsson and Svedmark, 2002;Seok et al., 2023;Yarnell et al., 2015).Once formed in a channel, woody riparian vegetation patches are not easily removed by flooding and become a significant resistance factor to river flow (Fig. 1).Therefore, the geometrical characteristics of woody riparian vegetation patches in the channel reach are useful physical parameters for quantifying its effects on hydraulic resistance.Woody riparian vegetation patches are typically elongated in a rhombus-like shape (e.g., Forio et al., 2020;Ji et al., 2023;Västilä et al., 2022).Patches typically exist in a single form or group (Fig. 2).A group patch can be considered as one cluster if two or more patches overlap in the streamwise and lateral directions.Otherwise, a dominant flow may form between the patches, in which case they can be considered as two independent patches.In this study, the longitudinal-overlapping ratio of L OR (=L p ′/L p ) and the lateral overlapping ratio of W OR (=W p ′/W p ) were used to differentiate the group and single patches (Fig. 2b).The overlapping patches in the longitudinal and lateral directions (i.e., L OR < 1 and W OR < 1) were regarded as a single obstruction of the group patch in the channel.Therefore, L and W affect the blockage parameters representing the patch geometry, which is addressed later in this section.The L OR and W OR of the group patch tested in this study were approximately 0.5 and 0.6, respectively, and the aspect ratio of the patch (L p /W p ) was approximately 3 for a single patch of natural willows along the Naesungcheon Stream in South Korea (Västilä et al., 2022).
The patch geometry of woody riparian vegetation can be considered using two representative dimensionless parameters, which can be considered as a type of relative roughness: the cross-sectional and volumetric blockage factors B X and B V , respectively (Ji et al., 2023).B X represents the fraction of the channel cross-section blocked by the patch (i.e., B X = B A /A, where B A represents the cross-sectional blockage area of the patch, and A represents the cross-sectional flow area).In this study, B A represents the projection area of the patch in the flow direction (Fig. 2c), and B V represents the volume fraction of the patch and the flow in the channel reach (i.e., B V = V p /V w , where V p represents the submerged patch volume and V w represents the water volume).V p and V w were calculated as V p = A b,p h and V w = AL r , respectively, where A b,p represents the horizontal canopy projection area (i.e., planform area) of the patch, h represents the water depth, and L r represents the reach length.In this study, the parameters related to patchiness characteristics were defined and specified by comparing them with those of a single plant, as shown in Table 1.The various patch canopy densities and geometry defined in Table 1 were parameterized to evaluate the changes in flow resistance due to woody vegetation patches.

Characteristics of nature-like foliated and branched woody vegetation
Two types of artificial willow trees with different quantities of leaves but nearly identical configurations and areas for woody parts were employed for the large-scale experiments in this study (Fig. 3).A sparsely foliated tree was used in the experiments of Ji et al. (2023), and another tree with denser leaves was created specifically for the present study.Ji et al. (2023) changed the canopy density of a patch using only the number of plants per patch N.However, changing the canopy density of individual trees can alter that of the patch.The physical properties of the foliated and branched woody plants adopted in the present study, including the drag force induced by each tree as measured via towing tests, were investigated to characterize and fully account for the irregularity and naturality of nature-like artificial woody vegetation.
For the two types of trees, the leaf area was quantified as the onesided leaf area A L , which was measured through image analysis involving a scanner and manual counting of leaves.The frontal stem area A S (including branches and twigs) was determined by multiplying the length and diameter of each stem segment.The A L /A S ratios for sparse and dense vegetation were approximately 9.0 and 15.6, respectively, indicating leaf area dominance under both conditions.For simplicity, for sparsely foliated trees, the vertical distributions of A L and A S were assumed to be uniform across the vegetation height in the study of Ji et al. (2023).In the present study, the vertical distributions of A L and A S for both types of trees were manually surveyed at 10-cm intervals (Figs.4a and 4b) to accurately compute the area contributing to hydraulic resistance under water levels.As shown in Fig. 5, the distribution of the total frontal area A t (=A L + A S ) roughly fell within the range of natural riparian woody species (Alnus glutinosa and Salix caprea) surveyed by Jalonen et al. (2015) via terrestrial laser scanning (TLS).
The LAI (=A L /A b , where A b represents the unit ground area) was used to characterize the canopy density, considering only the leaves of the plants.The total LAI was approximately 1.7 for sparse and 3.1 for dense plants.However, the LAI, which affects vegetative resistance, varies with respect to the submerged depth under emergent conditions.The submerged LAI was computed by applying the vertical distribution of A L (Fig. 4c).
The drag force F D exerted by each plant in response to flow velocity changes within the range of 0.1-1.5 m/s was measured using a load cell (SP8; HBM, Darmstadt, Germany) in a controllable towing tank (40 m long, 40 m wide, and 2.8 m deep) located at Ice Tank of Aalto University in Finland (refer to Jalonen and Järvelä, 2014;Ji et al., 2023 for measurement details).The drag force was measured under leafy and leafless conditions to separate the force contributions from different parts of the plant.The total drag force F tot can be divided into foliage and stem drag (F tot = F F + F S ).Here, "stem" refers to all woody parts of the tree (main Note: Parameters affected by changes in the water depth should consider the submerged height of a single plant or vegetation patch. stem, branches, and twigs).F S was measured using a leafless tree, and the foliage-induced drag was calculated as F F = F tot -F S .

Reach-scale experimentation
The large-scale outdoor flume of the River Experimental Center (REC-KICT; Korea Institute of Civil Engineering and Building Technology, South Korea) was used for experiments with eight full-scale artificial willow patches (Fig. 6a).The experiment conducted in this study was part of the same experimental campaign as that conducted by Västilä et al. (2022).The experimental section was a straight channel with a length of 69.8 m and bottom slope of 1/800.The cross-section was trapezoidal, with bottom and top widths of approximately 3 and 11 m, respectively, and a bank slope of 1:2 (V:H).The channel bottom was composed of movable sand (median particle size of 1.06 mm), and the banks were bare soil with low grass.The main geomorphic change to the channel bed occurred until the equilibrium bedforms were generated at the hydraulic conditions studied.In this study, bedforms at a given flow condition were all observed as dunes.
Four hydraulic conditions were induced according to the flow discharge Q and water level H by controlling the upstream discharge supply and downstream gate (Table 2).The flow discharge was adjusted in three steps, i.e., high, medium, and low (range of 1.4-2.6 m 3 /s), with the fixed downstream gate closed by 50 %; accordingly, the discharge with the fixed downstream gate determined the water level for each case (see Fig. 6c).Additionally, a different downstream boundary condition was applied to the low flow discharge cases by closing the downstream gate by 75 %.Q was controlled by upstream pumps and measured using an acoustic Doppler current profiler (ADCP; RiverSurveyor M9, SonTek, San Diego, CA) at a cross-section located 3.3-m upstream from the first patch.ADCP measurements were performed using the moving boat method (Mueller et al., 2013) in a transect, from one bank to another.To obtain reliable discharge values, the ADCP measurements were repeated more than eight times for each run and averaged.The topography of the channel was surveyed using a total station.The site-averaged h, A, and hydraulic radius R for transects A and B were computed using the topographic data with the water levels measured by pressure sensors (Table 2), which is addressed later in this section.Subsequently, the siteaveraged cross-sectional mean velocity U m was determined using a continuity equation.
Patch layouts were designed to consider the representative geometrical characteristics of woody riparian patches, which include the patch formation (single or group) and the patch location in the cross-section (centerline or bankside) (Fig. 6).In each layout, eight artificial willow patches with the same dimensions as the densely foliated trees shown in Fig. 3b were placed on the channel bed at equal intervals (8.6 m) in the streamwise direction.To analyze the effect of the canopy density on the flow resistance by comparing datasets with similar patch layouts but different canopy densities, all datasets with sparse canopy density were adopted from the experiments of Ji et al. (2023).Furthermore, to examine the effect of patch locations in the cross-section on the reachscale flow resistance, we shifted the single-patch layout toward the left bankside from the channel centerline in the S[HL] cases.In addition, the bare channel condition without vegetation was tested to separate the flow resistance due to vegetation patches from the bulk flow resistance, including the boundary friction of the channel.
Accurate measurement of the water surface slope S w ensures high accuracy in calculating the reach-scale flow resistance according to the friction slope S f .The representative S w for the channel reach was determined using the water-level difference between transects A and B. The water-level difference was measured using pressure sensors, and the accuracy and consistency of the measurements were verified through repeated tests by Ji et al. (2023).Seven pressure sensors (Orpheus Mini;  OTT HydroMet GmbH, Kempten, Germany) were used to measure the water level in the channel reach (Fig. 6a).The S f between transects A and B was determined using the following energy equation: where l represents the distance between transects A and B, and A A and A B represent the cross-sectional flow areas of transects A and B, respectively.
The reach-scale flow resistance was evaluated as the Darcy-Weisbach friction factor f, which was calculated using the conventional definition f = 8gRS f /U m 2 , where g represents the gravitational acceleration.The bulk friction factor f of the vegetated channel can be decomposed into the friction factor of the channel boundary f′ and the vegetative friction factor f″ according to the linear superposition principle as f = f′ + f″ (Ji et al., 2023;Yen, 2002).f′ was determined as f measured for the non-vegetated cases under corresponding boundary conditions.The boundary friction f″ was determined independently without vegetation for each hydraulic condition to consider the bed material and bedform induced resistance under different experimentation conditions.Consequently, the vegetative friction factor f″ was evaluated by subtracting the non-vegetated friction factor from the bulk friction factor (f″ = f − f′).
All the vegetation cases in this study were analyzed under emergent conditions.The cross-sectional blockage area B A and horizontal canopy projection area A b,p of the patch should be calculated by considering the submerged water depth corresponding to the water levels.Therefore, B A and A b,p were computed for the submerged part of the patch by processing the point-cloud data collected via TLS based on the site-averaged water level of the channel reach (Table 3).A three-dimensional laser scanner (RTC360, Leica Geosystems AG, Heerbrugg, Switzerland) was used to collect the point-cloud data, which had a point accuracy of 1.9 mm at a distance of 10 m and a scanning resolution of 3 mm (i.e., 3 mm of space between points at a distance of 10 m).Subsequently, the crosssectional blockage factor B X and volumetric blockage factor B V corresponding to each area were calculated (see Section 2.1, Table 3).The point-cloud data were processed using the workflows presented by Ji et al. (2023).
The canopy densities of the emergent patches were determined according to the submerged A L and A S of a single plant, which were computed using the vertical submerged distribution corresponding to the site-averaged water depth (Table 3; refer to Section 2.2).The submerged LAI of the patch was computed as NA L /A b,p and the volumetric leaf and stem area densities were a L = NA L /A b,p h and a S = NA S /A b,p h, respectively (see Fig. 2).
The relationships between the vegetative friction factors and patchiness characteristics were quantified using the variables LAI, a L , B A , A b,p , B X , and B V , which reflect the quantitative changes in all the features of the canopy density and patch geometry affected by the water depth variation due to the emergent conditions.Regarding canopy density, the LAI is a function of the water depth in emergent conditions, whereas the volumetric leaf area density a L is relatively uniform at varying water depths.Therefore, the vegetative friction factor f″ can be normalized as f″/LAI.

Drag characteristics of single woody plant
Fig. 7a shows the drag force generated by two single plants with different canopy densities.The total drag force F tot induced by the densely foliated plants was approximately 1.7 times larger than that induced by the sparsely foliated plants across the entire velocity range (Fig. 7a).Additionally, the foliage drag force F F was dominant (70-80 % of total drag force) within the relatively low-velocity range for both types of plants.However, the contribution of F F to the total drag force decreased due to the reconfiguration of the leaf area as the flow velocity increased.The values of the characteristic drag coefficient C D A p from the drag-force equation 2 are compared in Fig. 7b, where ρ represents the water density, C D is the drag coefficient, A p represents the frontal-projected area of the object, and U c represents the characteristic approach velocity.With an increase in the velocity, the characteristic drag coefficient C D A p for the foliated tree decreased significantly, whereas the C D A p for the leafless plant remained relatively constant.This trend indicated that the experimental trees had similar characteristics to natural vegetation (Armanini et al., 2005;Wilson et al., 2008).

Reach-scale flow resistance due to woody patches
The water surface slope S w in the channel reach calculated using water levels measured at each point are shown in Table 2.The friction slope S f was calculated using S w based on Eq. (1).The S f for the nonvegetated channel ranged from 0.0001 to 0.00029, according to the flow discharge and downstream gate conditions.The S f for the vegetated channel was increased by a factor of about six for group patches and four for single patches compared with the non-vegetated conditions.The bulk friction factor f, i.e., the reach-scale flow resistance affected by both the vegetation patch and boundary friction of the channel, ranged from 0.082 to 0.203 for the densely foliated willow cases and had a similar overall range to the cases examined by Ji et al. (2023) with sparsely foliated willows (0.068 to 0.213).The boundary friction factor of the channel f′ had values of 0.025-0.049.Hence, the vegetative friction factor f″ was estimated as 0.036-0.154for densely foliated patches according to the linear superposition principle, i.e,.f = f′+f″.

Dependence of flow resistance on canopy density and blockage factors
The dependence of the bulk friction factor f on the blockage parameters (B A , A b,p , B X , and B V ), which are related to the patch geometry, is shown in Fig. 8. Overall, the bulk friction factor f was strongly correlated with the blockage parameters (R 2 ≥ 0.86), which is consistent with previous experimental studies on woody riparian vegetation conducted by Ji et al. (2023) and field studies on the roughness of aquatic vegetation conducted by Champion and Tanner (2000) and Nikora et al. (2008).The exponential formulation is a proper type for including the boundary friction factor in the bulk friction factor equation on the blockage parameter.Therefore, the bulk friction factor f was exponentially fitted with B A and B X as f = f′ exp(γB A ) and f = f′ exp(γB X ) (R 2 = 0.90 and 0.88; Figs.8a and 8c) as follows, where f′ represents the boundary friction factor when B A → 0 and B X → 0, and γ is a coefficient. (2) Despite the considerable differences in canopy density, f strongly correlates with B A (R 2 = 0.9) regardless of differences between the sparsely and densely foliated patches (Fig. 8a).Similarly, B X had an exponential relationship with f (R 2 = 0.88; Fig. 8c).However, the f within each single and group layout was inversely proportional to B X locally for the same patch layout.Because B A and A are linked to the water depth changes in emergent conditions, B X can be decreased as h increases due to the trapezoidal cross-section affecting the channel width and cross-sectional flow area according to h.If the patch width is relatively uniform, even if the water depth of the trapezoidal crosssection increases, B X can decrease because the increase rate of B A and A are not the same (i.e., B X = B A /A ∝ h).
The bulk friction factor f was also exponentially fitted with A b,p and B V , as f = f′ exp(γA b,p ) and f = f′ exp(γB V ) (R 2 = 0.88 and 0.86; Fig. 8b and  8d) as follows:

Table 3
Vegetative properties of the artificial willow patch for each test case.
Case A L (m 2 ) Notes: A L , A S , a L , a S , and LAI for the patch considering nonlinear vertical distribution examined in this study differ slightly from the values reported by Ji et al. (2023) and Västilä et al., (2022), which assumed a linear vertical distribution in each area of the plant.In the case names, the first letter-G or S-denotes group or single patch, respectively; the second and third letters-[HL] or [LL]-denote dense or sparse leaves, respectively; the fourth letter-H, M, or L-denotes high, medium, or low flow discharge, respectively; the number-75 or 50-represents the closure percentage of the downstream weir; and the subsequent letter-B, C or S-denotes the experimental case with single patches located on the bankside, channel centerline or that with sparse plants, i.e., fewer trees, respectively (refer to Fig. 6c for details).a Experimental cases presented by Ji et al. (2023).b Original case names used by Ji et al. (2023).
The relationships of f with A b,p and B V for densely foliated patches differed slightly from that under sparse conditions (Figs. 8b and 8d); however, this was due to the discrepancy in A b,p quantified for the same patch layout cases of the two canopy densities.The difference in leaf abundance can cause a difference in A b,p , which is an uncertainty factor,  under field conditions.In addition, A b,p and B V were relatively uniform for changes in h in the same patch layout, in contrast to B A , which increased proportionally with h (Table 3).Despite the computational sensitivity of the A b,p and B V for h changes with varied discharge, the overall trend indicates the strong dependence of f.The stream-scale experimental results exhibited a similar range of f values induced by the same patch layout with different canopy densities.It suggests that the blockage factors B X and B V , which are the dimensionless measures of the blockage parameters, can be used as representative parameters to estimate the reach-scale flow resistance.The exponential dependence of f on the blockage parameter is in agreement with that of aquatic vegetation patches, reported in Nikora et al. (2008).
The vegetative friction factor f″ was fitted by a power function with the blockage parameters (B A , A b,p , B X , and B V ) with R 2 in the range 0.75-0.80(Fig. 9).
Because the vegetative friction f″ is zero with the non-vegetated condition, the power function is more appropriate to explain the dependence of the vegetative flow resistance on the blockage parameters rather than the exponential function.Overall, the result implies that the reach-scale vegetative flow resistance due to the leafy woody patches depended more on the patch geometry represented by the blockage parameters (B A , A b,p , B X , and B V ) than on the canopy density under these experimental conditions (2.6<a L <6.6).
By using f″/LAI instead of f″ for the relationships with the blockage parameters (B A , A b,p , B X , and B V ), the influence of canopy density (LAI) can be added to the analysis because the LAI is a function of the water depth in emergent conditions.To normalize the relations between the vegetative friction factors and patchiness characteristics, B X and B V were adopted because B X is a dimensionless variable considering B A , which has the most significant influence on the flow resistance of the vegetation patch (Fig. 8a), and B V is a non-dimensional parameter that can consider the variation in longitudinal length according to the A b,p of the vegetation patch.Fig. 10 shows that the relationship between f″/LAI and the blockage factors (B X and B V ) can be approximated by power functions for each canopy density condition as follows: The relationships of f″/LAI with B X and B V for the sparsely foliated patch (2.6<a L <3.1) exhibited strong correlations with high R 2 = 0.96 and 0.95, respectively; for the densely foliated condition (5.0≤a L <6.6), R 2 was 0.86 and 0.78.Mainly because of the partial deviation of f″ due to the bankside patches (e.g., S[HL]L75-B; see Section 3.4), the relationships for the densely foliated patches produced slightly weaker correlations than those for the sparsely foliated patches.

Vegetative flow resistance of bankside patches
Fig. 11 shows the differences in flow resistance between bankside and centerline patches under comparable water depth and mean velocity conditions.Note that it is not the absolute position relative to a channel centerline but the distribution of depth and velocity across a cross-section that influences the hydraulic resistance of vegetation patches.There appears to be a trend that f″ ratio between the bankside patches and centerline patches decreases as the flow velocity decreases.In particular, the bankside patches generated a notably lower flow resistance than centerline patches under the lowest examined flow velocity condition (comparison of S[HL]L75-C and S[HL]L75-B; see Fig. 11a).In this case, the single patches located on the channel centerline resulted in the maximum f (=0.128) and f″ (=0.078) due to the relatively low flow velocity (S[HL]L75-C).However, bankside patches with the same hydraulic conditions (S[HL]L75-B) generated considerably lower f (=0.085) and f″ (=0.036) values, despite having the highest water depth h (=0.84 m) and B A (=1.33 m 2 ).
The f″ generated by the bankside patches in the low flow velocity condition decreased to below half of that induced by the centerline distribution.As a result, the contribution of the vegetative flow resistance was less than the boundary friction of the channel, as f″/f was 42 % (see Fig. 11b).The reduced f″ due to the bankside patches is similar to that of single centerline patches having almost half the B V (see Fig. 9d).This is consistent with the study of Errico et al. (2018), who showed that the vegetation buffer on one bankside of the channel had less impact on the flow resistance.However, our results indicate that the distribution effect of bankside patches depends on hydraulic conditions.The largest impact of bankside patches was observed in the case of a high-water surface level with low flow discharge (S[HL]L75) (Fig. 11a).It can be inferred that the impact of the spatial distribution depends on the water depth and approach flow velocity; however, more data with various emergent conditions and distribution scenarios should be acquired under field conditions to assess this implication quantitatively.

Patchiness effects on flow resistance of emergent woody riparian vegetation
The towing test of the drag force F D induced by each type of tree with different canopy densities (e.g., a L and LAI) revealed that the canopy density was a significant factor affecting the flow resistance at the plant scale (see Section 2.2), which is consistent with previous studies (e.g., Armanini et al., 2005;Whittaker et al., 2013;Wilson et al., 2008).However, for the reach-scale flow resistance due to foliated woody vegetation patches under emergent conditions at a L >2.6 and relatively low volumetric blockages (up to 10 %), we confirmed that the patch geometry was more dominant than the canopy density (Figs. 8 and 9).All the blockage parameters (B A , A b,p , B X , and B V ) exhibited strong correlations with bulk and vegetative friction factors.Although the reach-scale flow resistance decreased with a decrease in number of plants per unit ground area, i.e., N/A b,p , it was not independent of the patch geometry (S[LL] cases).
The finding of the dominant dependence of reach-scale flow resistance on the blockage parameters parallels the results for aquatic vegetation and riparian grasses, which are known for their resistance to the flow being primarily correlated with the blockage factors (Bakry et al., 1992;Champion and Tanner, 2000;Green, 2005a;Nikora et al., 2008;Savio et al., 2023;Västilä et al., 2016).Green (2005b) claimed that flow resistance of partially vegetated channels can be considered to operate at the plant stand scale rather than at the leaf and stem scales.A plant stand is a group of trees, and this term has the same meaning as "vegetation patch" as defined in this study.The stream-scale experiment results demonstrated that the reach-scale flow resistance due to the riparian woody patches is dominated by the patch-scale processes.In comparison, most of the energy of the flow is directly dissipated by the complex interference with individual leaves and branches at the leaf/ stem scale if the canopy density is sparse enough to allow a relatively large flow rate into the patch (e.g., Västilä et al., 2016).
Our results support the straightforward robust reach-scale estimation of the flow resistance for relatively densely foliated woody patches (a L >2.6) by blockage factors, which is beneficial particularly for small vegetated channels and other cases where two-dimensional hydraulic modeling with spatial discretization of the vegetation properties is not feasible.Since the vegetative flow resistance depended less on plantscale properties, differences in plant species may not significantly alter the flow resistance for relatively densely foliated conditions, at least under the examined low blockages.In addition, woody riparian species have an optimal canopy density for forming a patch shape, which is determined by their biological characteristics, physical disturbance, and environmental stress (Shafroth et al., 2002).If blockage factors can be derived using remotely sensed vegetation characteristics such as patch boundaries, canopy height, and patch density, the remote sensing data are suited for estimating vegetative friction factors (e.g., Chaulagain et al., 2022;Prior et al., 2021;Straatsma and Baptist, 2008;Wang and Zhang, 2019).
Fig. 12 shows a comparison of Eq. ( 5) presented in this study to the regression equation suggested by Nikora et al. (2008).Nikora et al. (2008) suggested a quantitative relationship between the site-averaged relative roughness of a submerged aquatic vegetation patch and the bulk friction factor f based on their field observations: f = 0.065exp[6.4(h c W c L c /hW r L r )], where h c represents the patch-averaged height of the vegetation canopy, W c represents the mean width of the vegetation patches in the cross-section, L c represents the longitudinal length of the vegetated section, W r represents the channel width, and L r represents the reach length.The site-averaged relative roughness (=h c W c L c /hW r L r ) has the same physical meaning as B V defined in this study for emergent conditions.Although the presently examined range of B V was limited 0.04-0.1, the comparison shows that the f induced by woody vegetation was far larger than that of aquatic vegetation.The difference found here implies that the blockage dependence of vegetation patches can significantly vary according to the physical properties of the plants, such as rigidity.This suggests that the different physical properties of riparian and aquatic vegetation, can result in differences in vegetative resistance, despite similar blockage effects.Submerged aquatic vegetation typically reconfigures closer to the riverbed where velocities are lower.In contrast, emergent riparian vegetation is impacted by higher velocity and has higher drag forces for the same blockage.

Normalization of vegetative flow resistance based on patchiness characteristics of emergent woody riparian vegetation
While flow resistance of leafy woody patches was mostly explained by the blockage factors, using LAI as additional explanatory variable enhanced the predictive power (Fig. 10), indicating that flow resistance is generated also at the leaf/stem scale.As the canopy density decreases, allowing more flow within the patch, the flow resistance is increasingly produced at the leaf/stem scale (Green, 2005b).Estimating the flow resistance is more complex in such cases because the flow resistance operates simultaneously at both the leaf/stem and patch scales (e.g., Västilä et al., 2016), and the reconfiguration of the vegetation interacting with flow inside the patch may not be negligible (e.g., Järvelä et al., 2016;Nicosia et al., 2021).Ji et al. (2023) demonstrated that the flow resistance of the sparsely foliated woody patches (2.6<a L <3.1) could be estimated using momentum-based models (e.g., Järvelä, 2004;Västilä and Järvelä, 2014) that consider the canopy density as LAI and A S /A b with species-specific reconfiguration characteristics.Once data over larger ranges of conditions become available, those models could likely be further developed to allow predictions of flow resistance under seasonally variable physical properties, such as differing foliation conditions, including leafless seasons, and for diverse species (e.g., Camporeale and Ridolfi, 2006;Champion and Tanner, 2000;Magdaleno et al., 2014).

Vegetative flow resistance changes of bankside patches
The reach-scale experiments showed that the influence of patch location in the cross-section varies mainly as a function of the mean flow velocity.Specifically, patches located at the bankside can induce less flow resistance under the low flow velocity condition than that of centerline patches (S[HL]L75-B; see Section 3.4).This is consistent with a previous study by Bal et al. (2011), in which different spatial distributions of the same biomass resulted in significantly different flow resistances in a laboratory-scale experiment.Yokojima et al. (2015) found through large-eddy simulation that the flow resistance can be reduced by shifting vegetation patches toward a channel bank, regardless of the spatial configuration of patches, and that this effect could result from the lower drag force proportionally decreasing with the relatively low flow velocity near the sidewall.Fig. 5 of Västilä et al. (2022) presented the velocity distributions in the cross-sections for the low flow case of this study (S[HL]L75-C → CD-LQ and S[HL]L75-B → BD-LQ).Velocities in the non-vegetated configuration were somewhat lower at the location of the bankside patch compared to the centerline patch, resulting in lower drag forces for the bankside patch.The comparable results for the low flow velocity condition of this study support the idea that the bankside distribution of patches impacts the reach-scale flow resistance, that is a woody riparian vegetation patch located on the bankside has a lower flow resistance than a patch located at the center.However, this result could not be consistent at other sites where morphodynamic change during floods causes significant heterogeneity in water depths and velocities throughout a river.Particularly, the findings from this study based on the relatively straight and trapezoidal channel may not apply to meandering rivers and braided gravel-bed channels.
On the contrary, S[HL]M50-B results indicate that the bankside patches can lead to more flow resistance than the centerline patches (Fig. 11a).The lower flow resistance can result from the inverse relationship with the flow velocity (i.e., f = 8gRS f /U m ), although the drag force induced by the centerline patches is expected to increase with higher velocity.Also, the morphological change differences between centerline-and bankside-located patches could alter the spatial distribution of water depth and velocity, contributing to form drag and total resistance.Therefore, the flow resistance induced by bankside patches can exceed that induced by the centerline, even for the same vegetation patch.

Conclusions
In this study, we identified the patchiness effects of emergent riparian vegetation on reach-scale flow resistance, through a field-scale experiment involving nature-like artificial willows.We defined the patchiness characteristics of woody vegetation using the canopy density, patch geometry described by cross-sectional and planar blockage areas (B A and A b,p ), cross-sectional and volumetric blockage factors (B X and B V ) of the patches, and patch location in the cross-section (center or bankside).The experimental datasets produced quantitative relationships for estimating vegetative flow resistance by considering the patch geometry.The induced bulk friction factor f for all experimental conditions collapsed around a single curve as exponential functions (Eqs. (2)−( 5)) for the blockage parameters (B A , A b,p , B X , and B V ), with compelling explanatory power.It was concluded that the reach-scale flow resistance induced by emergent and woody riparian patches primarily depends on the patch geometry and depends less on the canopy density for the investigated relatively densely foliated conditions (i.e., a L >2.6) and relatively low volumetric blockages (up to 10 %).Therefore, B X and B V , i.e., the dimensionless blockage factors for the patch geometry, can be reliable parameters for estimating the reach-scale flow resistance induced by foliated and branched vegetation patches.Also, the suggested empirical equations for the vegetative friction factor f″ approximated by power functions with the blockage parameters (Eqs.( 6)−( 9)) allow the prediction of independent flow resistance due to the woody riparian patches.To normalize the relations between the vegetative friction factors and patchiness characteristics, f″/LAI instead of f″ was approximated by power functions with the blockage factors (B X and B V ) (Eqs. ( 10)-( 13)) for each canopy density condition.Furthermore, the experimental data indicated that the distribution of flow and velocity by the relative position of patches has an influence on the reach-scale flow resistance.The patches located at the bankside rather than the channel centerline generated significantly lower flow resistance in a relatively low flow velocity condition; however, higher flow resistance than the centerline patches was also generated by the bankside patches in higher velocity conditions.It implies the effects of patch distribution on the reach-scale flow resistance could depend on the hydraulic condition.Additional experimental cases with various configurations of woody riparian patches and hydraulic conditions would be beneficial for extending the relationship beyond the range of the present experimental conditions.Nonetheless, the findings of this study provide evidence that patchiness characteristics have a dominant impact on flow resistance in channels with woody riparian patches.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Fig. 1 .
Fig. 1.Field observation of a woody riparian vegetation patch about 265 m long and 80 m wide in the Naeseong-cheon Stream, South Korea (white arrow: flow direction).

Fig. 2 .
Fig. 2. Conceptual diagram of the shape, configuration, and blockage area of the woody riparian vegetation patch.

Fig. 3 .
Fig. 3. Schematic of sparse and dense artificial willows and the average values of eight sample willows for the physical properties of each type of tree.

Fig. 4 .
Fig. 4. Vertical distribution of the characteristic area and cumulative LAI along the relative vegetation height for the representative trees of sparse and dense artificial willows: (a) one-sided leaf area (b) frontal stem area (c) LAI.

Fig. 5 .
Fig. 5. Vertical distribution for the cumulative total frontal area of the artificial willows of this study and natural riparian woody plants investigated by Jalonen et al. (2015) via TLS.Average distributions are shown for the data of Jalonen et al. (2015) (three specimens for each type of plant).

Fig. 6 .
Fig. 6.Design of the experimental channel, patch layouts, and hydraulic conditions: (a) plan view of the experimental section with the pressure sensors and the willow patches (b) details of the group centerline patch, single centerline patch, and single bankside patch layouts (c) experimental conditions and case descriptions.

Notes:
In the case names, the first letter-G or S-denotes group or single patch, respectively; the second and third letters-[HL] or [LL]-denote dense or sparse leaves, respectively; the fourth letter-H, M, or L-denotes high, medium, or low flow discharge, respectively; the number-75 or 50-represents the closure percentage of the downstream weir and the subsequent letter-B, C, or S-denotes the experimental case with single patches located on the bankside, channel centerline or that with sparse plants, i.e., fewer trees, respectively (refer to Fig.6cfor details).aExperimental cases presented byJi et al. (2023).b Original case name used byJi et al. (2023).

Fig. 7 .
Fig. 7. Variations in the drag force and parameter C D A p with respect to the velocity for artificial willows: (a) drag force for leafy and leafless plants and foliage (b) C D A p for leafy and leafless trees.

Fig. 8 .
Fig. 8. Bulk friction factors f according to the blockage factors of the woody vegetation patch: (a) the cross-sectional blockage factor B X (b) the volumetric blockage factor B V .

Fig. 9 .
Fig. 9. Vegetative friction factors f″ with respect to the blockage parameters related to the patch geometry of woody vegetation: (a) cross-sectional blockage area B A (b) horizontal canopy projection area A b,p (c) cross-sectional blockage factor B X (d) volumetric blockage factor B V .

Fig. 10 .
Fig. 10.f″/LAI according to the blockage factors of the woody vegetation patch: (a) cross-sectional blockage factor B X (b) volumetric blockage factor B V .

Fig. 11 .
Fig. 11.Variations in friction factors induced by single patches located on the channel centerline (S[HL]-C cases) and bankside (S[HL]-B cases) according to hydraulic condition: (a) changes in vegetative friction factor f″ (b) contribution of each component (vegetative and boundary friction factors f′ and f″) of bulk friction factor, where H50, M50, L50, and L75 represent hydraulic conditions (refer to Table 2 and Fig. 6c for case details).

Fig. 12 .
Fig. 12. Dependence of the bulk friction factor f on the volumetric blockage factor B V : comparison of the riparian woody vegetation (present study) and aquatic vegetation (Nikora et al., 2008).

Table 1
Systematic definition and classification for the physical properties of woody riparian vegetation and patchiness characteristics.

Table 2
Hydraulic conditions of the experimental cases and the measurement and calculation results.