Flow Resistance in Lowland Rivers Impacted by Distributed Aquatic Vegetation

This study addressed a research concern that employing a fixed value for the bed roughness coefficient in lowland rivers (mostly sand-bed rivers) is deemed practically questionable in the presence of a mobile bed and time-dependent changes in vegetation patches. Accordingly, we set up 45 cross-sections in four lowland streams to investigate seasonal flow resistance values within a year. The results revealed that the significant sources of boundary resistance in lowland rivers with the lower regime flow were bed forms and aquatic vegetation. The study then used flow discharge as an influential variable reflecting the impacts of the above-mentioned sources of resistance to flow. The studied approach ended up with two new flow resistance predictors which simply connected the dimensionless unit discharge to flow resistance factors, Darcy-Weisbach (f) and Manning (n) coefficients. A comparison of the computed and measured flow resistance values also indicated that 87–89% of the data sets were within ± 20% error bands. The flow resistance predictors were also verified against large independent sets of field and flume data. The obtained predictions using the developed predictors might overestimate flow resistance factors by 40% for other lowland rivers. Based on a different view, according to the findings of this research, seasonal variation of vegetation abundance could show the augmentation in flow resistance values, both f and n, in low summer flows when vegetation covers river bed and side banks. The highest amount of flow resistance was observed during the summer period, during the July–August period.


Introduction
The responsibility for catchment management in lowland areas is of paramount importance since the freshwater environment receives vast development pressures. Aquatic vegetation constitutes a substantial component of many rivers in a lowland catchment.
They contribute significantly to the flow conditions and ecological function of the habitat structure (Cornacchia et al. 2020;Willemsen et al. 2022). Regarding flow conditions, vegetation patches on the river bed or the river bank often increase boundary roughness, decrease velocities and enhance the river depth and cross-sectional area (Sulaiman et al. 2017;Šoltész et al. 2021), resulting in the increased potential of overbank flow and flooding and decreased discharge capabilities (Thomas and Nisbet 2007;Kastridis et al. 2021). The extension of aquatic vegetation depends on many factors such as flow discharge and velocity (Riis and Biggs 2003;Cornacchia et al. 2020), nutrient and light accessibility (O'Hare et al. 2018), and material formation of the river bed (Green 2005). Among these parameters, Franklin et al. (2008) concluded that flow velocity had the most significant impact on the presence of vegetation. Therefore, it is vital to focus more on a better catchment management of lowland rivers.
Flow velocity can be measured by a current meter directly in natural streams or through the equation of continuity (u = Q/A) when both the flow discharge, Q, and the wetted crosssectional area, A, are known. Nevertheless, in many cases, such measurements are not feasible; instead, a flow resistance predictor must be employed. Several flow resistance equations are well-acknowledged and they do not need to be calibrated when the uniform flow is deemed for a river reach. The Chezy and Darcy-Weisbach expressions, as well as the Manning formula, are the most widely-used equations (Rickenmann and Recking 2011;Okhravi and Eslamian 2022).
Among effective parameters on flow resistance values, special attention has been given to the primary source of boundary resistance, bed forms, and grain sizes (Yang et al. 2005;Ferguson 2007;Okhravi and Gohari 2020). However, in rivers located in low-gradient areas, vegetation needs to be considered since it does alter roughness coefficients (Champion and Tanner 2000;Cai et al. 2020). In a recent study, Song et al. (2017) appraised the seasonal values of the Manning's roughness with the 1D hydraulic model in a German lowland vegetated river. According to their study, the model could predict water surface variations and flow velocities reasonably well after the seasonal roughness factor was adopted.
The analyses done by Ferguson (2010) through the extensive field data set reflected that the use of Manning equation with the fixed value of n was not preferable for mobile river beds (sand-bed rivers mostly in lowland areas) with relatively high submergences,R∕d 84 > 5 ( d 84 is 84% finer grain size and R is the hydraulic radius). The other performer types of resistance law after Manning expression are logarithmic law and power law approaches, using relative submergence scaled on a d 84 (Namaee et al. 2017). According to the data from lowland rivers, relative submergence is usually high, and sediment motion is only initiated with low shear stress. Hence, the effects of relative submergence on the sediment transport rate can be neglected (Sulaiman et al. 2017). Also, the grains forming the bed are well distributed in lowland rivers, and the median particle size ( d 50 ) is usually transported as the suspended loads. Therefore, for sand-bed rivers, the main sources of boundary roughness are the lower regime bed forms (ripples and dunes) and the aquatic vegetation occurrence. Hence, the resistance law using relative submergence is not often the safest choice since it does not account for the bed form roughness. Since flow discharge is the characteristic that shapes the channel and considers the irregular bed topography and water elevation variations, several authors have suggested nondimensional hydraulic geometry equations that connect the dimensionless mean flow velocity ( u * * ) and dimensionless unit discharge ( q * ) (Ferguson 2007;Rickenmann and Recking 2011). Hence, the flow discharge approach is an alternative to develop an equation for predicting flow resistance factors incorporating the primary sources of boundary resistance in lowland rivers with a lower regime flow. The application of this method in lowland rivers occupied by distributed aquatic vegetation has not, however, been examined; in particular, no study, to the best of our knowledge, has yielded the connection between u * * and q * . The predictor of u * * builds a bridge to predict the Darcy-Weisbach resistance factor in the lowland rivers for the improvement of the hydraulic model's performance, which is far lacking in the scientific literature.
Several field studies have investigated the effect of the behavior of overgrown streams on the roughness coefficient in terms of improving the developed flow resistance predictors (Champion and Tanner 2000;Green 2005;Cai et al. 2020) or optimizing the model's performance (Song et al. 2017). The present study, therefore, aimed to explore the seasonal variation of roughness coefficients in lowland streams with distributed vegetation. This research could contribute to providing empirical reference data to validate the hydraulic models in which aquatic vegetation is considered in the hydraulic modeling. Besides this, we tried to develop some new equations for flow resistance determination of seasonally overgrown lowland streams by using the collected field data. The developed flow resistance predictors take the impacts of bed form and vegetation occurrence by applying the dimensionless flow discharge as an input parameter. Finally, the accuracy and applicability of the developed roughness predictors have been evaluated and compared with large sets of independent field and laboratory data.

Methodology Framework
The formulation of well-known flow resistance relations applied to flow velocity prediction can be presented as follows.
Here, u is the mean flow velocity (LT -1 ), C is the Chezy coefficient (L 1/2 T −1 ), n is the Manning coefficient (L −1/3 T), f (dimensionless) is the Darcy-Weisbach friction factor, S is the energy slope, and g is the acceleration due to gravity (LT −2 ). The term (gRS) 1/2 in Eq. (1) has the dimension LT -1 , reflecting a velocity term usually named the shear velocity and denoted by u * . Since f is dimensionless (Eq. (2)), most proposed relations under the two mentioned approaches were derived for f. The logarithmic and power-law approaches connect f to the relative submergence, as shown in Eqs. (3) and (4).
where a 1 and a 2 (as well as a and ) are empirical constant coefficients, and h is the flow depth. In low-gradient narrow streams, it is recommended to use R instead of h (Ferguson 2007).
To develop regional resistance relationships for lowland streams, watersheds with the same physiographic region should be selected. The watersheds should be similar in flow regime, precipitation, land use, bed forms, and aquatic vegetation. As briefly described before, the flow discharge is the only characteristic that shapes the channel and postulates the bed forms and submerged vegetation occurrence. Hence, flow discharge measurements in lowland rivers are much more accurate than the relative submergence ones. Therefore, the relationships based on flow discharge have higher reliability than those which are according to relative submergence (Eqs. (3) and (4)). The general form and optimal parameterization of such relationships have been proposed by Rickenmann and Recking (2011): In Eq. (5), k and m are determined empirically, according to u * * = u∕u * = u∕(gRS) 0.5 and q * = q∕(gR 3 S) 0.5 ; q is the discharge per unit channel width ( q = Q∕B ) and B is the channel width. It is worth mentioning that the final developed equation is a contribution to this work. The process of regression analysis for producing the suitable fit between data and parameters was performed by applying an iterative least-squares fitting routine. The quantitative comparison of the predicted and measured values of u * * was performed by using determination coefficient (R 2 ) and error-measures such as root mean square error (RMSE), standard deviation (SD), scatter index (SI), and index of agreement (I a ). These parameters are described below.
where x m,i and x p,i are the measured and predicted values, respectively; x m,i and x p,i are the average values of the measured and predicted data, respectively. Also, N is the number of samples. It should be noted that the optimal values of RMSE were close to zero, thus indicating the best fit between the measured and predicted data (Moriasi et al. 2007). A similar method has been employed to extract the n flow resistance predictor in reference to q * .

Description of Field Measurements Localities
The selected lowland streams were located in the western part of Slovakia, the city of Bratislava (Fig. 1). The annual temperature range is from -0.4 (January) to 21 °C (July), and the average annual rainfall is about 565 mm, mainly in the spring-summer half year (from May to July). Bratislava is 134 m above the mean sea level (amsl). In this study, four streams with a gradient of < 2 m/km were selected ( Fig. 1). Besides the low slopes, the selected streams could be characterized by the low grain roughness of bed, well-sorted bed material configuration dominated by sand-sized particles, and the so-called sand bed streams with a uniform sediment size particle distribution .
Regarding climate conditions, extensive aquatic vegetation occurs mainly during the summer and autumn seasons, but with low dense biomass during winter and spring. The vegetation coverage around the side bank is generally grass and shrubs, while submerged or non-submerged aquatic plants are on the stream bed. The measured streams are surrounded by pasture and grassland or other agricultural lands (Sokáč et al. 2020). In this case, fertilizer increases the plant's growth due to nutrient availability in water. The corresponding effects may lead to a change in vegetation types growing in the streams and their surrounding area.
Four natural stream sites, namely, Malina (A), the Šúrsky channel (B), the Gabčíkovo-Topoľníky channel (C), and the Chotárny channel (D) were selected for this study (Fig. 1). A typical view of the selected streams is shown in Fig. 2. Overall, 45 stream cross-section profiles were used in this study. The cross-sections were not only placed almost evenly from each other, but also a steady uniform flow was maintained in each stream section. Field measurements along the streams were performed to collect the necessary hydraulic data like water surface elevation, channel width, water depth, flow discharge, and velocity profile (see Table 1). The field study was carried out from April to September at the Malina stream, and from February to August at the Šúrsky channel for the 2019-2020 period. Regarding Gabčíkovo Topoľníky and Chotárny channels, the field measurements were done only in June, 2020. The data, as listed in Table 1, were the measured values during a moderate water level period (June). The flow velocity measurements were taken by SonTek Fig. 1 The location of lowland streams in Western Slovakia and study points FlowTracker Handheld ADV and SonTek RiverSurveyor-M9, which have been proved to be accurate and applicable for the field survey (Schügerl et al. 2019).

Roughness Variations
The monthly variations of flow resistance in terms of the Darcy-Weisbach and Manning coefficients can be shown for Malina and Šúrsky streams. Figure 3 indicates the roughness condition for each of the measured cross-sections from April to September for Malina and Šúrsky streams. It reflects aquatic vegetation effects on the flow roughness increase in summer and early autumn, from June to September. The changing trends of f and n for the Malina stream were almost similar, showing August as a month with higher roughness for the study sites A1 and A2, and September for A3 and A4. However, a similar trend between f and n was not been obtained for the Šúrsky channel. The higher values of f for the study sites B2 and B4 were observed in June, while the corresponding n values showed higher roughness in August. This appears to be the case of calculation methods of flow roughness since a directly measured value of Q was used to calculate n; meanwhile, the measured velocity was used for the f estimation.
For the other two lowland streams, the Gabčíkovo-Topoľníky and Chotárny channels, similar measurements were performed one time in June (Table 1)  and 0.01-0.053 for Malina, Šúrsky, Gabčíkovo Topoľníky, and Chotárny streams, respectively. This, thus, shows that the sources of boundary resistance in the lowland streams can be highly variable along a stream. The seasonal changes in flow velocity and aquatic vegetation could alter the stream bed morphology. The velocity reduction during summer could enhance sedimentation within submerged vegetation. Later, high flows during winter remove much of the deposited sediment. These processes, along with river bank alterations, would display the changes in the river bed topography, resulting in different values of flow resistance. Table 1 shows that the roughness of the points C1 and C23 was the highest in the selected reach at the Gabčíkovo-Topoľníky channel, with a value of 0.084. The same for the Chotárny channel was observed at the points D5, D4and D8, with the variation being from 0.05 to 0.053. In general, for the study sites with low flow velocity and full coverage of vegetation patches at the bed and stream banks, the roughness reached near the peak values. During summer, submerged vegetation beds acted like semi-permeable dams, diminishing flow velocity, increasing flow depth, and wetting the cross-sectional area (Fig. 2). Also, the presence of vegetation beds causes the great variation range of flow velocity, resulting in habitat heterogeneity. These observations, thus, revealed that the abundance and diversity of aquatic vegetation were restricted at higher water velocities.

Development of New Equations
As mentioned before, the rate of flow resistance can vary along lowland streams. Its value mainly depends on the bed material formation and density of the aquatic vegetation. Its correct value is significant for practice, but determination of it is complex. By proposing a new relationship, we tried to contribute to solving this problem.
The new flow resistance equations have been developed based on field data at stable and alluvial stream cross-sections. As a design tool, the new predictor considers two influential aspects of flow resistance in lowland streams: bed and bank vegetation and bed forms. Hence, the new equation is not only valuable for predicting flow velocity and flow resistance in lowland streams, but also is helpful in the proper design of the stable channel geometry in similar physiographic areas.
To determine the mean flow velocity and thus, f, by using a new flow resistance predictor, the formula structure of Eq. (5) was applied to the field data for four natural streams in the lowland regions (see Fig. 1). By using a power function in the form of Eq. (5) and flow discharge as an input parameter, the following equation is proposed. The corresponding variables have already been described under Eq. (5). Figure 4a shows the relationship between u * * and q * , depending on flow discharge as a controlling factor. The determination coefficient (R 2 ) was calculated to be about 0.97, thus showing the perfect correlation made by the power equation. According to the results of error analysis, the new predictor indicated a good performance because of the high value of I a and the low values of RMSE and SI (Fig. 5a). It is known from Singh et al. (2005) that the value of RMSE can be considered low and acceptable for the model's performance evaluation when it is less than half of SD. According to the values of RMSE = 0.955 and SD = 5.74, RMSE was quite low and the measured and predicted values were in a very good agreement. Also, the low value of the normalized RMSE ( NRMSE =RMSE∕x m,i = 0.129) of the measured data confirmed the above-mentioned explanation. From another point of view, the value of u * * , as calculated by Eq. (10), gives an acceptable prediction for most cross-sections. The accuracy of the prediction of u * * values was assessed by counting the number of results lying between two asymmetric bounds (± 20% concerning the (10) u * * = 0.978q * 0.953 Fig. 4 Relationship of q * with u * * (a) and with n (b) perfect agreement line (45-degree line)), i.e., considering an overestimation of 20% and an underestimation of 20%, respectively. According to this method, more than 87% of the predicted values (64/73) were within the boundaries (Fig. 5a). The results, thus, provided the evidence of similarity in the streams and watershed characteristics in those streams used to develop Eq. (10) for predicting the flow velocity and friction factor since data scatter around the regression line was within reliable ± 20% errors. It is also worth noting that the new predictor not only takes flow discharge into account, but also considers hydraulic radius and surface variations of water.
The power equation also showed an appropriate fit for the n estimation in relation to q * ; so, the next predictor was extracted to estimate n as: Figure 4b shows the scattering between the values of n and q * . The statistical analysis showed that the low values for RMSE (RMSE = 0.013 < (SD/2 = 0.04)) and SI, along with high correlations (R 2 ) and I a , indicating good predictions for n, were obtained by Eq. (11). The low value of NRMSE = 0.176 for the measured data indicated the perfect performance of the n predictor. As can be seen in Fig. 5b, 89% of the predicted values (65/73) were surrounded by the same referred bounds (± 20%).

Seasonal Roughness in Similar Physiographic Regions
Flow velocity, hence flow discharge, has long been recognized as a major factor controlling the growth extension and distribution of aquatic vegetation in rivers (Franklin et al. 2008). Typically, aquatic vegetation growth is restricted at high flow velocities (Riis and (11) n = 0.32q * −0.978

Fig. 5
Comparison of u * * and n values predicted using Eqs. (10) and (11), respectively, and those calculated from measured data Biggs 2003). As the flow velocity in the summer season is less than that in other months of the year, the growth conditions are relatively stimulating for vegetation establishment. Since there is a positive relationship between the percentage of vegetation abundance and bottom roughness in lowland rivers, the values of n or f are higher in the summer period. According to this result, a similar trend was observed by Champion and Tanner (2000) and Song et al. (2017), thus showing that the flow resistance values were higher in summer and early autumn for lowland rivers in New Zealand and Northern Germany, respectively.
The field study in lowland streams near Bratislava, Slovakia, revealed that n values were raised from 0.016 to 0.373 with the increase of aquatic vegetation from 0 to 100%. The corresponding range for the field survey of Champion and Tanner (2000) was between 0.05 and 0.5. Also, O'Hare et al. (2010) reflected ± 50% variations of the Manning roughness coefficient value from the annual mean values for lowland river reaches in England and Scotland. The present study, thus, confirmed the findings of Ferguson (2010) regarding the variations of the Manning roughness coefficient for sand-bed rivers located in lowland areas due to great changes in bed forms and vegetation abundance. Hence, the calibrated seasonal roughness coefficient for the actual aquatic vegetation condition is highly recommended to better model flow resistance and calculate flow velocity.

Assessment of Flow Resistance Predictors
To verify the application of the developed equations for predicting flow resistance in the form of Manning (n) and Darcy-Weisbach (f) expressions, a series of data sets from the literature were used (Brownlie 1981;Song et al. 2014Song et al. , 2017. According to the field-measured data, Eq. (10) was developed to predict the Darcy-Weisbach friction factor in lowland streams with bed forms and submerged aquatic vegetation. To estimate the value of f by Eq. (10), the dimensionless value of q as q * must be first calculated. To predict the accuracy of Eq. (10), field data from a lowland river located at the Upper Stör catchment in Northern Germany were used (Song et al. 2014(Song et al. , 2017. According to the results brought above, the seasonal variations of roughness values presented in this study were similar to the German lowland catchment since they were both located in the same physiographic area. A comparison of the calculated f values by Eq. (2) with the predicted f by Eq. (10) is shown in Fig. 6. The results showed that most of the data were between the perfect agreement line and a band specified by + 40%. In fact, 92% of the predicted values (82/89) were included by the above-referred bounds. The good predictions by Eq. (10) could be due to the similarity of hydraulic and sediment characteristics of the selected German catchment and the resemblance of the distributed vegetation throughout a yearly field study.
Data scattering of the Manning roughness coefficient with q * showed the similar form of power equation presented in Eq. (11). To assess whether Eq. (11), developed on the collected field data from the lowland streams near Bratislava, could be applicable for other lowland rivers (sand-bed rivers), a database consisting of 420 flume and field data has been used. The data sets were extracted from a database compiled by Brownlie (1981). Each data set was selected based on similar hydraulic and sediment conditions and flow regimes with the lowland streams in the study area. The database contained comprehensive records of flow discharge, channel width, water depth, bed slope, median grain size of bottom material, sediment gradation, and specific sediment gravity. The hydraulic and sediment parameters of the selected data sets are listed in Table 2. To verify the validity of Eq. (11), the results were compared with the Manning roughness predictions obtained by Brownlie's Eq. (1981): The predictor of Brownlie (Eq. 12) for the Manning roughness coefficient is recommended for sand-bed streams, taking into account both aquatic vegetation and bed forms. Following the afore-mentioned results, Fig. 7 compares values of n computed by using the two methods (Eqs. (11) and (12)). The obtained results were bounded by two defined lines, -30% and + 50%. Investigation of the values of the Manning roughness coefficient using both equations showed that these two methods were in an acceptable agreement. A closer look revealed that most field data were within + 50% and the perfect agreement line. The consistency of data was reasonably good considering the usually large degree of uncertainties in field measurements. Part of the scatter in the data could be a result of the dissimilarity in rivers and catchment characteristics, abundance and density of submerged vegetation, land use, sediment load and gradation, and geographic areas. The presence and percentage of cohesive sediment in the bottom and/or aquatic vegetation on the bottom and bank could significantly affect the roughness values (Franklin et al. 2008;Horstman et al. 2018).
It should be mentioned that Eq. (11) takes non-uniformity in flow (sourcing by bed forms and vegetation) into account by using q * , with no need to have d 50 . The new predictor benefits from the calculation of flow discharge as the main characteristic, which considers the effects of the primary sources of boundary resistance in lowland streams (bed forms and vegetation). The results confirmed that Eq. (11) could be an excellent choice for predicting the Manning roughness coefficient for low flows through distributed aquatic vegetation.

Conclusion
In the present study, field data from 45 cross-section profiles of four streams were collected at Slovakian lowland areas near Bratislava during different seasons of the year. The study aimed to first explore the effects of submerged aquatic vegetation on flow resistance coefficient, Darcy-Weisbach and Manning; the other goal was to contribute to developing new simple flow resistance predictors in lowland streams. The main findings could be summarized here: • The primary sources of flow resistance in lowland rivers with lower flow regimes were bed form and aquatic vegetation. • Seasonal variations of flow resistance, both in f and n, showed the dominant impact of vegetation patches during summer months when stream discharge is low. Two roughness coefficients revealed similar trends during the year, leading to the maximum value in the second-half summer (July-August) and the minimum one in the first-half spring (March-April). • A new equation for flow resistance determination was then developed based on the recommended structure form of Rickenmann and Recking's study; this was done using flow discharge as the input to predict the mean flow velocity and hence, Darcy-Weisbach friction factor, f (Eq. (10)). The same structure was also applied to connect flow discharge with Manning roughness coefficient, n, leading to the generation of another flow resistance predictor (Eq. (11)). Both predictors showed a perfect fit with the data set of the present study in which 87-89% of all data was within ± 20% error bounds with respect to the perfect agreement line. • To verify the suitability and applicability of the above-referred flow resistance predictors, Eqs. (10) and (11) were evaluated by using another extensive field database from similar physiographic lowland areas (for Eq. (11), the flume database was also employed). The statistical analysis of the predicted values of f and n represented a reasonable agreement with the corresponding values obtained from a series of data sets. The results, thus, showed that both flow resistance predictors could be employed for lower flow regimes in lowland rivers.
The present study provided reference field data for validating hydraulic models in which the characteristics of lowland streams were considered. The improvement of the model's performance, by taking the composition of river beds and side banks into account, could be practical to better simulate flood events and reduce flood risks.