Estimation of drag forces caused by natural woody vegetation of different scales*

JALONEN Johanna, J?RVEL? Juha

Department of Civil and Environmental Engineering, Aalto University, Espoo, Finland, E-mail: johanna.jalonen@aalto.fi

Estimation of drag forces caused by natural woody vegetation of different scales*

JALONEN Johanna, J?RVEL? Juha

Department of Civil and Environmental Engineering, Aalto University, Espoo, Finland, E-mail: johanna.jalonen@aalto.fi

(Received March 5, 2014, Revised April 30, 2014)

To reliably estimate water levels and velocities in vegetated rivers and floodplains, flow resistance models based on physical plant properties are advantageous. The purpose of this study is (1) to assess the suitable parameterization of woody riparian vegetation in estimating the drag forces, (2) to address the effect of plant scale on the drag estimates and reconfiguration, and (3) to evaluate the applicability of three recently developed flow resistance models. Experiments on four tree species in a towing tank together with detailed characterization of tree properties were carried out to establish a novel dataset. Despite the variability in the tree height (0.9 m-3.4 m), the stem, leaf and total areas proved to be suitable characteristic dimensions for estimating the flow resistance at different scales. Evaluations with independent data revealed that the tested models produced reasonable results. The performance of the models was controlled by the parameter values used rather than the model structure or the plant scale.

drag force, flow resistance, woody vegetation, modelling

Introduction

Woody riparian vegetation is an important feature in river and wetland environments and it is used for river bank stabilization and in floodplains and channels to create shade and to increase biodiversity. Even though vegetation is essential for ecological functions, it significantly influences the hydraulics and may raise the water levels during a flood event. A reliable estimation of the flow resistance of trees is vital in flood protection, river restoration and modelling sediment processes. To improve the resistance estimation of complex vegetation, physically-based methods based on objective and measurable vegetation properties are desirable[1]. Therefore, the hydraulic resistance of vegetation has been investigated in flumes with living and artificial plants, both in arrays and as isolated plants[2-7]. The experiments on the resistance of woody vegetation are often restricted by the flume size, and thus conducted with parts of trees, twigs, or small trees. The flow resistance, the reconfiguration and the structural properties of trees of larger size are less explored. Only few studies for trees have been conducted in water[8,9], though useful knowledge is available for air flows from wind tunnel experiments[10].

Estimating the flow resistance of trees is complex due to the variability in tree morphology[1]. In addition, the flow characteristics and the vegetative resistance vary with the scales of leaf, plant or plant-stand[11]and for small patches which are affected by the momentum exchange at the patch boundaries[12]. The leaf drag depends on the leaf characteristics, such as the surface type, the roughness and the shape, and the flexural rigidity[13]. Leaves attached to the plants exert less drag than that measured for individual leaves due to shading and more efficient reconfiguration[13,14]. The force exerted by vegetation is usually expressed in the form of the classical drag force approach

where CDis the drag coefficient,ACis the reference area (commonly the frontal projected area,AP), and uCis the characteristic approach velocity (typically the mean velocity,um).

The methods for quantifying the resistance vary from one-dimensional approaches, such as Manning’s n or Darcy-Weisbach friction factorf, to three-dimensional approaches based on the drag force equation (Eq.(1)). The resistance is often expressed through a resistance coefficient, which combines all the factors related to the resistance, and is estimated from reference values in similar channels or calibrated as site-specific values. A simple way to estimate the vegetative resistance is to decompose the friction factor into the bed friction(f′)and the form resistance (f′′)through a linear relation of f=f′+f′′. The vegetative friction factor can be derived from the spatially averaged drag force per unit ground areaAB[1]by

J?rvel?[18]quantified the resistance from the one-sided leaf area per ground area AL/ABexpressed as leaf area index, LAI, the species-specificCDχ, and the reconfiguration parameterχ

To take into account the different properties and reconfiguration of the stem and leaves V?stil? and J?rvel?[7]reformulated the J?rvel?[18]model (Eq.(4)) by separating the foliage and stem friction factors by linear superposition as f=fF+fS, leading to

1. Methods

1.1 Modelling of drag force

In the present study, Eqs.(4) and (5) for the friction factors are reformulated in the form of a drag force. Similar to Eq.(5), the drag force (Eq.(1)) maybe divided in to foliage and stem drag

Cis equal to C/uand has a unit ofm-χ.D,bulkDχχ Fbulkis used here to distinguish the foliated bulk drag from Ftotaccording to the model presented in Eq.(8).

The performance of Eqs.(6), (8) and (9) is evaluated in Section 2.3. The models are evaluated by comparing with the direct drag force measurements of the present study (Section 1.2) and applying the species-specific drag and reconfiguration parameters of J?rvel?[18](Eq.(4) reformulated as Eq.(9)), V?stil? and J?rvel?[7](Eq.(5) reformulated as Eq.(8)) and Whittaker et al.[16](Eq.(6)). The extraction of the tree characteristics required for the models is described in Section 1.3.

1.2 Towing tank experiments

The measurement system attached to the carriage was towed empty to ensure that there was no disturbance to the force measurement at any point at the length of the towing tank.

The trees were mounted upside-down on the measurement system with an aluminum cylinder of 0.035 m in diameter. To adjust the trees of different diameters to the cylinder, polyurethane was used to fill the extra space in the cylinder. Before fixing the cylinder on the drag measurement system, the trees were rotated so that the natural curvature of the main stem was directed downstream, i.e., opposite to the towing direction. Two camera positions were used to collect underwater video recordings. The submerged side and rear view cameras were attached at a distance of 3 m and 5.5 m, respectively, from the plant.

The drag forces were directly measured both under foliated and defoliated conditions in the velocity range of 0.1 m/s-1.5 m/s and 0.1 m/s-2.5 m/s, respectively. Velocities higher than 1.5 m/s were not measured under foliated conditions for most specime- ns, as the forces were higher than those under defo- liated conditions, and it could be observed from the side view cameras that the specimens were already streamlined close to a maximum. The measurements were carried out by towing the specimens in one direction, and after each run the carriage was brought back to the starting position. The next experiment was started after there was no disturbance in the water from the previous run. Velocities of 0.1 m/s, 0.2 m/s, 0.3 m/s, 0.4 m/s and 0.5 m/s were measured in one run as also the velocities of 0.6 m/s and 0.8 m/s. Due to the length limitation of the tank, the velocities of 1.0 m/s, 1.25 m/s, 1.5 m/s, 1.75 m/s, 2 m/s, 2.25 m/s and 2.5 m/s were measured individually.

Only the values of the measured forces ten se-conds after reaching the measurement velocity were selected for the analyses, as with the acceleration there was a peak in the forces especially for velocities higher than 0.6 m/s. It took 1 s-10 s depending on the change of velocity for the specimens to reach a condition where the reconfiguration did not considerably change. This resulted in an effective measurement period of 35 s for velocities below 1.5 m/s. For the highest velocity of 2.5 m/s the effective measurement period was 10 s due to the tank length limitation. The force data for the effective measurement period were selected and the averages and coefficients of variation (standard deviation divided by the mean) were computed. The forces under the defoliated condition at the lowest velocity 0.1 m/s could not be measured for two specimens (AG6 and SC9, Table 1). These specimens were small, and the corresponding forces subjected to the individual load cells were below the measurement range. Subsequent statistical analyses were conducted in SPSS Statistics 21.

1.3 Experimented trees

The investigated species were the Common Alder (Alnus glutinosa), the Goat Willow (Salix caprea), the Silver Birch (Betula pendula) and the White Birch (Betula pubescens). The measurement period was scheduled in the beginning of June 2012 when the trees had reached full foliage. These trees were picked from a nearby wetland area in the mor- ning before the measurements.

For all specimens, the length, the height, the wet and dry biomasses, the projected area in still air under defoliated and foliated conditions, and the one-sided leaf area were determined (Table 1). The trees were photographed against white background from four directions in still air. A 3-D tree structure model of the leafless trees was established by digitizing the tree elements with a device based on the electromagnetic field (EMF, see detailed description in Ref.[20]). The one-sided stem area,AS, and the stem volume,VS, were obtained from the 3-D tree structure model. The method takes into account the whole main stem and branch area in contrast to the photographic analysis where parts of the branches are shaded. The stem area used is defined as the projected one-sided area of the main stem and the branches obtained from the 3-D model. The stem frontal projected area in still air was measured for ten specimens from photographs, and the difference between the photographs and the stem area from the 3-D tree structure model varied between -13%and+24%, and was on average 4% smaller for the photographs (3 alders, 4 birches and 3 willows). A leaf thickness of 0.00035 m was used to obtain the leaf volumes, and the total volume was obtained as the sum of the leaf volume and the stem volume. The underwater frontal projected area was obtained from the images of the video footage in Matlab by selecting the tree pixels.

After the towing tank measurements in foliated conditions, the specimens were left to dry so that the leaves could be plugged for determining the leaf wet (fresh) and dry masses. The lengths of the trees were then measured and the trees were divided into four length sections. The biomass was analyzed for the four length sections, separately. Due to the large size of the trees, the leaf area was measured only for the second section from the top. For this section, three samples were taken and for each of them, both the leaf areaALand the wet and dry masses were determined. The leaves were scanned with an office scanner to obtain the leaf area, andALwas obtained from the scan with the pixel counting in Matlab. The ratio of the leaf areaALto the dry mass was determined as LAR=AL/mL,d. Hence, the total leaf area was obtained by multiplying LAR with the total dry mass. The total area of the plants was defined as the sum of the leaf and stem areas,Atot=AL+AS. After taking the leaf samples the specimen was towed again under the leafless condition. Subsequently, the stem wet mass and dry mass of the defoliated specimens were measured for the four length sections.

The flexural rigidity in Eq.(6) was determined by placing a loadPto the mid-stem at a distance L50(half the tree height) from the base. EI50was derived from the measured displacementδas

2. Results

2.1 Relationship between drag force and physical tree properties

The towing tank experiments resulted in a large range of measured forces due to the differences in the tree size (Fig.2). For instance, at a velocity of 1.5 m/s the measured range of bulk drag forces was from 10 N to 110 N, and the range of the stem drag was from 5 N to 70 N.

The normalizations of the bulk drag, the foliage drag and the stem drag with the total area, the leaf area and the stem area, respectively, are shown in Fig.3. The species-averaged parameters required for the use of Eqs.(8) and (9) were obtained from the power law fitting in Fig.3 (see Table 2). The foliage drag forces showed an almost linear relationship with u, as χFwas on average -1.03 whereas the bulk drag showed a less efficient reconfiguration of the stem and leaves withχ≈-0.81.

The stem drag appeared to have a piece-wise relationship withu (Fig.3(c)). Thus, the three different CDandχparameters for FS/ASin Table 2 were derived from a power-law regression in the whole velocity range, for the velocities between 0.1 m/s-0.6 m/s (subscript “l(fā)ow” in Table 2) and for the velocities above 0.6 m/s (subscript “high”). By neglecting the velocities below 0.6 m/s, the fitting was close to a linear relationχ≈-1(Table 2,χS,high). The power law fitting for all velocities implied a non-linear relationship between the stem force and the velocity with an average χSof –0.64. For the velo- cities below 0.6 m/s the FS-urelationship was close to a squared relation with species-averagedχS,lowbetween -0.19 and -0.36.

The interspecies variation of the normalized drag forces was smaller forFbulk/Atotthan for FF/ALand FS/AS(Fig.4). The intraspecific variation for Fbulk/Atotwas 24% and 16% smaller than FS/ASand FF/AL, respectively. For Fbulk/Atotthe variation was the smallest for A. glutinosa and S. caprea. TheFbulk/Atotdataset consisted of six specimens of A. glutinosa and eight of S. caprea, but Fbulk/Atotwas available only for three specimens of B. pendula and B. pubescens. When Fbulkwas normalized with ALthe normalization was similar to Fbulk/Atotdue to the high share of foliage to the total area, and Fbulk/ Atotwas only 4%-9% smaller than Fbulk/AL(Fig.4(a)). The interspecies variability was similar for Fbulk/Atotand Fbulk/AL, but the intraspecific variation was on average 12% higher for Fbulk/AL.

The normalization of FFand Fbulkwith the wet mass showed a smaller overall intraspecific variationthan the normalization with the dry mass. The wet and dry masses showed a similar variation for FS(Fig.4(b)). The interspecies variations of FFand Fbulkwere on average 14% and 24% higher against the dry mass than against the wet mass, respectively.

When the stem drag was normalized with the volume, the smallest variation with the coefficient of variation cv=0.10 was observed for S. caprea (Fig.4(a)). The other species showed larger variations and the value ofcvwas on average 0.23. The interspecies variation of FS/ASwas 17% lower than that ofFS/mS,W, and 7% higher than that of FS/mS,D. The normalization with the stem and total volumes had the smallest variation for S. caprea and A. glutinosa.Ftot/Atothad a higher overall intraspecific variation (cv=0.32)than FS/VS.

2.2 Drag force and reconfiguration of trees under flow

The share of the foliage drag to the total drag as an average for all the species is shown in Fig.6(a). At a velocity of 0.1 m/s the foliage contributed 70%-80 % of the total drag. This share decreased to 40%-50% at u =0.6 m/s and higher. The FF/Fbulkshare of A. glutinosa was on average 15% higher than that of S. caprea. The change in the FF/Fbulkpattern (Fig.5(a)) at u=1.75 m/s for B. pubescens was due to the smaller sampling size, as only a few foliated specimens were towed with velocities higher than 1.5 m/s.

The frontal projected area in relation to the frontal area at zero velocity was around 70%-90% of that at 0.1 m/s (Fig.5(b)). Similar to the share of the leaf drag, the frontal projected area under water(APW) decreased rapidly to about 35% at 0.6 m/s (Fig.5(b)). At velocities above 0.6 m/s the frontal projected area continued to decrease at a lower rate of change.

The deflected height,Hd, of the leafy trees decreased almost linearly up to a velocity of 1.0 m/s, after which this decrease was slightly slower (Fig.6(a)). On the other hand, for the defoliated trees, the decrease in the deflected heights was more pronounced at 0.5 m/s-1.5 m/s than at lower velocities of 0.1 m/s-0.4 m/s (Fig.6(b)). In Fig.6(b) there was a rise in the average of the ratio of the deflected height to the height in still water,Hd,S/Hd,S,0, for S. caprea at 2 m/s due to the smaller sampling size for velocities higher than 1.75 m/s.

The differences in the leaf and stem areas for plants of different scales are shown in Fig.7(a). The AL/ASvalues fell close to each other for all specimens, but the smaller trees(＜1.5m)were characterized by a larger share of leaves compared to the stem. AL/ASshares of S. caprea were generally slightly lower compared to the other species.

The flexural rigidity of the main stem,EI50, increased with the increase of the tree length (Fig.7(b)). This increase in the rigidity was not linear, as the increase was more pronounced for tall treesH=2m-3m , than for short trees of H =1m-2m.

Theχvalues for the bulk, the foliage, and the stem drag were not dependent on the tree length (Fig.8). Hence, theχvalues for trees with AL/ASin the range between 9.6 and 27 did not deviate notably. Similarly, the dependency betweenχand EI50was not evident.

The values predicted by Eq.(6) were lower than the measured ones (Fig.9(c)). Eq.(6) requires theK parameter values, which correspond to some initial CDAPvalues.K refers to K50whenEIis measured at the half tree height. These values are derived from a linear relationship betweenK50and Vprovided in Ref.[16] for Salix alba. The F values could be estimated for three foliated specimens (SC1,SC2 and SC5), as the K50vs.Vtotrelationship is valid forVtot＞5×10-4m3. Under defoliated conditions, theKvs.Vrelation is valid for V＞0m3,

50SS and thus we could analyse six specimens. For defoliated specimens, the predicted values were on average 49 % smaller than the measuredFS. For foliated specimens, the predicted values were 18% lower than the measuredFbulk. The applicability of the three models at different flow velocities and tree scales is evaluated in detail in the discussion section below.

3. Discussions

3.1 Tree parameterization for resistance estimations with a view on scale

The normalized bulk and stem drag forces Fbulk/ Atotand FS/AShad both the smallest interspecies and intraspecific variations as compared to the normalizations with biomass and volume. The normalization of the bulk drag with the leaf area,Fbulk/AL, had a similar interspecies variation as Fbulk/Atot(Fig.4(a)), but was characterized by a larger intraspecific variation, which was most likely attributed to the different leaf to stem area ratio of the specimens. The foliage drag,FF, normalized with the dry and wet masses as well as the leaf area showed a greater variation than the corresponding normalizations forFbulkand FS. The intraspecific variation of FF/ALwas similar to FF/mL,W, but the interspecies varia- tion was lower forFF/AL.

3.2 Drag force models

The reconfiguration of the stem was more effective for the trees in our study than twigs in Ref.[7], as theχSvalues were two times larger in absolute value than those of the twigs[7]. The χSin an average for all the specimens, with velocity ranges of 0.1 m/s-0.6 m/s and 0.1 m/s-0.8 m/s, was -0.24 and -0.32, respectively, and thus very close to theχSof the twigs[7]with low velocities (u =0.2m/s-0.8m/s). For the case ofA . glutinosa χSwas similar to that of A. glutinosa in Ref.[16]. (χS=-0.57), but forS. caprea the stem reconfiguration was less efficient than those of S. alba (χS=-0.84)in Ref.[16]. However, the specimens in Ref.[16] were experimented at higher velocities of up to 3.5 m/s, which reduced the impact of the low velocities on the power-law fit. Although significant differences in the flexural rigidity of the specimens of the present study in comparison to other studies were shown (Fig.10(b)), the reconfiguration parametersχ and χSappeared to be more similar than EI50for trees of different sizes and habitats.

Similar to the studies of Whittaker et al.[16], a linear regression was found for K-V(R2=0.875)

50tot and K-V(R2=0.798), but with an error of 49%

50S for the measured FSvalues in this paper as compared with FSestimated by Eq.(6), most probably due to the difference in both K50and χS(23% difference for χS). The K50for the defoliated trees were three times larger for our data than derived from the linear fit in Ref.[16]. For the foliated trees theχwas similar to that in Ref.[16], but the K50was 36% higher from our data and the error in the predicted Fbulkwas 18% (Fig.9(c)). The K50values for the stem varied more than those for the foliated tree and they differed between low and high velocities due to the piece-wise form ofFS-u relationship. The K50vs.V relation was affected by EI50andH, which deviated for the specimens of Ref.[16] as compared to the present study (Fig.10(b)).K50appeared to correlate with the stem and total areas (Fig.12), which implied that K50could be replaced with a characteristic area multiplied with a constant, e.g. CDAC. This is in line with the definition of Ref.[16] that the K50corresponds to some initial value of CDAP. Eq.(6) is based on a modified Cauchy number CY=ρU2VH/EI. In comparison, Luhar and Nepf[12]usedbl3(whereb is the blade width andlis the blade length) for the flexible aquatic vegetation in predicting the drag based on the vegetation Cauchy number and buoyance. As in the present study, the total and stem areas were found to be better resistance predictors than the volume, the use ofACinstead of Vcould be investigated in further studies. For such investigations we propose formulating Eq.(6) to includeAH2as

C

4. Conclusions

Our experimental investigations with several alternative parameterizations of tree properties together with direct drag force measurements at different scales (0.9 m-3.4 m) provided a new dataset more extensive than those in the existing literature. The comprehensive tree property and force data allowed us to compare the suitability and the reliability of different plant parameterizations for physically-based modeling applications. Subsequently, three flow resistance or drag force models were evaluated with the new data. The main findings of this study are as follows:

The stem, leaf and total areas of the trees confirmed to be suitable characteristic dimensions for estimating flow resistance, as the variation in the corresponding normalized drag forces was smaller than that for the dry and wet masses as well as the volume. The interspecies variation of the parametersχand CDwas small. It remains to be investigated to what extent the parameter values are species-specific and how they depend on growing conditions. The results showed that at low velocities the stem drag of foliated trees reduced in comparison to that under the defoliated condition due to a more efficient reconfiguration of the stem caused by the leaf mass. This implied that the actual foliage drag at low velocities can be somewhat larger than that estimated by FF=Ftot-FS. Variation in the ratio of the leaf area to the stem area was found for trees of different sizes, and the share of the leaf area appeared to increase for the smallest specimens. The largest scale-dependent variation in the investigated parameters was found for the total drag per dry mass and the stem drag per stem volume.

Acknowledgements

Visiting researchers Johann Peter Rauch and Clemens Weissteiner from the University of NaturalResources and Life Sciences, Vienna, collected and provided the 3-D EMF data on the plant structure for our use. We would like to thank Peggy Zinke who kindly provided additional flexural rigidity data, and Catherine Wilson and Jochen Aberle for providing the original Alnus leaf and stem area data of Xavier[9]. The authors also thank the trainees Anja Zogan and Ferran Garcia for helping with the experiments. This work was supported by the Academy of Finland and Maa- ja vesitekniikan tuki ry.

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Notations

10.1016/S1001-6058(14)60068-8

* Biography: JALONEN Johanna (1984-), Female, Ph. D. Candidate