Proceedings of the Seventh International Conference on Hydroscience and Engineering, Philadelphia, PA, September 2006.  http://hdl.handle.net/1860/732If vegetated regions become part of a river’s flow field, the hydraulic resistance of vegetation affects
the overall conveyance. Several descriptions exist to describe this type of flow; among them are
empirical relations and relations that are process-based. In the current work three expressions are
considered that have equal input parameters, similar levels of complexity but different theoretical
backgrounds. The performance of the three methods is evaluated by comparison with flow
measurements (collected from literature), and limits are given for their practical use

Augustijn, Denie C.M.

Hulscher, Susanne J.M.H.

Huthoff, Fredrik

English

Hulscher, Suzanne J.M.H.

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The 7th Int.  Conf. on Hydroscience and Engineering (ICHE-2006), Sep 10 –Sep 13, Philadelphia,USA 1 
 
 
 
 
 
 
HYDRAULIC RESISTANCE OF VEGETATION IN RIVER FLOW APPLICATIONS 
 
 
Fredrik Huthoff1, Denie C.M. Augustijn2 and Suzanne J.M.H. Hulscher3 
 
 
ABSTRACT 
 
If vegetated regions become part of a river’s flow field, the hydraulic resistance of vegetation affects 
the overall conveyance. Several descriptions exist to describe this type of flow; among them are 
empirical relations and relations that are process-based. In the presented work three expressions 
were considered that have equal input parameters, similar levels of complexity but different 
theoretical backgrounds. The performance of the three methods was evaluated by comparison with 
flow measurements (collected from literature), and limits are given for their practical use.  
 
1. INTRODUCTION 
 
The hydraulic resistance of vegetation can play a major role in the hydrodynamics of rivers with 
extensive natural floodplains. Vegetation penetrates the flow field and thereby causes drag and, 
subsequently, energy losses. Traditionally, empirical relations are used to take into account the 
hydraulic resistance of vegetation (e.g. Chow 1959). These methods are easy to incorporate in flow 
models of rivers. However, their range of applicability is limited to situations that they were 
calibrated for. In contrast to purely empirical flow relations, process-based flow relations have a 
general character, allowing a more consistent treatment over a wide range of situations. In the 
current paper, we investigate whether three methods that were determined for flow over idealized 
submerged vegetation (including two with theoretical foundations) also describe the hydraulic 
response to real vegetation adequately. For this purpose, data from a wide range of laboratory flume 
experiments with both natural and artificial vegetation is collected (from literature). 
 
2. MODELS FOR HYDRAULIC RESISTANCE OF VEGETATION 
 
Three methods were compared that describe the effects of (idealized) vegetation on a flow field. The 
three methods are all relatively new, depend on equal input parameters and were originally 
determined for flow through (idealized) rigid vegetation. Also, the required computational effort for 
the three methods is similar. Subsequent sections explain the main characteristics of the different 
methods. 
 
                                                 
1
 PhD Candidate, Department of Water Engineering and Management, Faculty of Engineering Technology, University 
of Twente, PO BOX 217, 7500 AE Enschede, the Netherlands (F.Huthoff@utwente.nl) 
River Hydraulics Consultant, HKV Consultants, PO BOX 2120, 8203 AC Lelystad, the Netherlands. 
2
 Assistant Professor, University of Twente, the Netherlands (D.C.M.Augustijn@utwente.nl) 
3
 Professor, University of Twente, the Netherlands (S.J.M.H.Hulscher@utwente.nl) 
  2 
 
 
Figure 1 Definition sketch of geometrical and dynamical parameters. 
 
2.1 Method 1: Two-layer scaling approach (Huthoff et al. 2006) 
 
In the method proposed by Huthoff et al. (2006) flow over and through the vegetation is treated 
separately (i.e a two-layer approach). Based on a simple force balance and scaling considerations of 
turbulent velocity fluctuations, depth-averaged flow velocities within the submerged vegetation 
layer (or resistance layer, see Figure 1) and in the free flowing layer (surface layer) above the 
roughness elements are estimated. Combining flow velocity expressions for the surface and the 
vegetation layer yields an expression for the normalized total-depth averaged flow velocity: 
 
3/2





 −−
+=
s
kh
h
kh
h
k
u
U
S
 (1) 
Here the depth of flow h exceeds the height of the vegetation k (for definition sketch, see 
Figure 1). The separation between individual vegetation elements s also determines the 
characteristic velocity in the vegetation layer uS: 
 
DC
gi
su
D
S
2
=  (2) 
Equation (2) gives the depth-averaged flow velocity in case of flow trough emergent vegetation, 
with g the gravitational acceleration, i the water surface slope, D the stem diameter and CD the drag 
coefficient. Note that for large flow depths eq. 1 reduces to Manning’s equation (i.e. if h>>k). 
 
2.2 Method 2: Depth-integrated velocity profile (Klopstra et al. 1997) 
 
This method is based on depth-integration of an analytical velocity profile for flow through 
submerged (rigid) vegetation. Originally proposed by Klopstra et al. (1997), and modified by 
Huthoff and Augustijn (2006), the model equations are: 
 
s
s
s
r
s u
U
h
kh
u
U
h
k
u
U −
+=  (3) 
Where the normalized depth-integrated flow velocity is calculated by weighed addition of the 
normalized average flow velocity in the vegetation layer Ur (or resistance layer) and the normalized 
average flow velocity in the surface layer Us: 
  3 
 











~~


+Υ
−Υ
−
+−Υ+=
1
14ln
2
1121
k
k
k
s
r
khku
U 
 (4) 
 
( )








−


~~

 +−
−
+−+−
+Υ= 1ln
2 s
sss
k
s
s
h
hkh
kh
hkh
b
hkh
u
U
κ
 (5) 
Here,  is von Karman’s constant ( = 0.41). The dimensionless velocity at the top of the vegetation 
layer is given by: 
 




 −
+=Υ

kh
k 1 , (6) 
which includes the length scale  
 bα= . (7) 
Additional required parameters to solve eqs. 3-7 are: (i) an equivalent roughness height for flow 
over the vegetation layer 
 
4/14/33.4 bhs α= , (8) 
(ii) a turbulent length scale at the top of the vegetation layer  
 )(240.0 khb
sh
−+
=α , (9) 
and (iii) a drag length 
 
DC
sb
D
2
= . (10) 
 
2.2 Method 3: Based on genetic algorithm (Baptist et al. 2006) 
 
Using a genetic algorithm Baptist et al. (2006) derived a simple analytical flow description based on 
results of a detailed numerical model. Strictly speaking this description is derived empirically. 
However, it enforces rejection of unrealistic dependencies by taking into account the dimensions of 
relevant parameters. Their procedure yielded the following expression for Chézy’s roughness 
coefficient: 
 





+=
k
hg
DkC
g
sC
D
log22 , (11) 
which corresponds to a normalized depth-averaged flow velocity 
 





+=
k
h
s
DhC
k
h
u
U D
s
ln2 2 , (12) 
 
3. COMPARISON OF MODELS 
 
The performance of the three methods was evaluated against 129 flow measurements performed in 
laboratory flumes (taken from literature, see Baptist 2005 for used data). These experiments were 
conducted with various vegetation heights k and various separations between individual vegetation 
elements s, and included both flexible and rigid vegetation. Table 1 gives an overview of the 
characteristics of the used data. Note the diversity in reported drag coefficients CD, which in itself is 
a key issue when describing the hydraulic resistance of flow through vegetation (e.g. Nepf 1999, 
Järvelä 2004).  The separation between vegetation s follows from the surface density m of the 
vegetation (i.e. s2 = 1/ m). None of the data included in Table 1 were previously used to calibrate 
any of the vegetation resistance models mentioned in section 2. 
  4 
 
Table 1 Characteristics of flume experiments (F: flexible vegetation, R: rigid vegetation). 
 
D m s k CD s/CDD Author(s) Nr. of Exp. mm m-2 cm cm - - 
Kouwen et al. (1969) F  27 5 5000 1.4 6-10 3 0.9 
Ree and Crow (1977) F 30 5 1076-1464 2.6-3 20-30 1 5.2-6.1 
Murota et al. (1984) F 8 0.24 4000 1.6 4.8-5.8 2.75 24.0 
Tsujimoto and Kitamura (1990) R 8 1.5 2500 2.0 4.6 1.46 9.1 
Tsujimoto et al. (1993) F 12 0.62 10000 1.0 6.1-6.5 2 8.1 
Ikeda and Kanazawa (1996) F 7 0.24 20000 0.7 40-45 1 29.5 
López and Garcia (1997) R 6 6.4 42-388 5.1- 15.4 7-17 1.13 7.0-21.3 
Meijer (1998) F 7 5.7 254 6.3 155-164 1.805 6.1 
López and Garcia (2001) R 12 6.4 42-384 5.1-15.4 12 1.13 7.1-21.3 
Järvelä (2003) F 12 3 512-12000 0.9-4.4 16-30 1 3-14.7 
 
To compare the performance of the three methods, the relative error in velocity predictions 
was plotted against the relative vegetation separation in the corresponding experiment (s/CDD, see 
also Table 1). Figure 2 shows the results if including all measurements from the experiments listed 
in Table 1 (also shown are the standard deviation of the relative error  and the mean error ). It can 
be seen that predicted values of all three methods correspond reasonably well with a wide range of 
experimental data. Errors for the three methods range from  = 27% for method 2 (Klopstra et al 
1997, which describes most flow detail) to 37% in method 1 (Huthoff et al. 2006). Overall, method 
2 shows the smallest systematic error ( = 5%), but does not give statistically significant different 
result from method 3 (at a 5% confidence interval). Method 1 does give significantly different 
results and tends to underestimate flow velocities ( = -10%). 
 
 
Figure 2 Three vegetation resistance methods and their predicted depth-averaged flow velocities 
compared to measured values (Upredict and Uref). The horizontal axis shows relative separations 
between individual vegetation elements (s/CDD); from dense (left) to sparse vegetation coverage 
(right). Also shown are mean error () and error standard deviations () of predicted flow velocities. 
 
  5 
For method 1 large deviations were observed for predicted velocities if vegetation coverage 
was very dense or very sparse (see Fig. 1). For very dense surface coverage (i.e. when s/CDD <5) 
methods 2 and 3 performed well, but method 1 predicted flow velocities that were always too small. 
The corresponding datasets are those by Kouwen (1969) and the R4 experiments of Järvelä (2003), 
where flows over flexible vegetation (wheat) were considered. Possibly, in these experiments the 
flow field in between and just above the vegetation layer had not developed into the fully turbulent 
regime yet. Using the separation between vegetation elements as a typical length scale, the 
corresponding Reynolds number was of the order 103. The assumption that the average flow velocity 
in the surface layer is determined by turbulent mixing therefore no longer holds. The presence of 
leaves or flexibility is also not incorporated in expression eq. 1, but these effects were absorbed into 
values of the drag coefficient for Kouwen’s data (where CD = 3).  
Overestimation of flow velocities for very sparse vegetation is possibly due to bed resistance 
effects that were not taken into account. Eq. 1 can easily be modified to include bed resistance 
effects (see Huthoff et al. 2006). Naturally, this requires additional knowledge about present bed 
roughness characteristics (e.g. the equivalent roughness height). Method 3 already predicts flow 
velocities for sparse densities satisfactorily; incorporation of bed effects would only introduce larger 
discrepancies with measured values (not shown here). 
Figure 3 shows the performance of the three methods if only considering the experiments that 
were conducted with intermediate vegetation densities. In this analysis, the experiments with very 
dense vegetation by Kouwen et al. (1969) and Järvelä (2003) were omitted, as were the experiments 
with very sparse vegetation by Ikeda and Kanazawa (1996). The result is that still the three methods 
show a standard deviation of the relative error of about 30%. However, method 1 now has a 
significantly smaller systematic error of  = -2% (at 5% confidence interval). 
 
 
 
Figure 3 Performance of methods for intermediate vegetation density. 
 
The shown experiments in Figure 2 have relative vegetation separations in the range 5 < 
s/CDD < 25. Natural vegetation types that correspond with such densities include bushes, reed, 
sedges, orchards and brushwood (see vegetation types in van Velzen et al. 2003, or Huthoff and 
Augustijn 2006). Sparse vegetation where s/CDD > 25 is very uncommon, and besides, in such 
situations the bed resistance in between the individual elements starts to dominate. Very dense 
  6 
vegetation is fairly common in nature: grasslands often have densities where s/CDD < 5. The 
hydraulic resistance of grass-covered floodplains is thus no longer adequately described by the 
method 1. In such cases methods 2 and 3 give more reliable results. 
 
 
 
Figure 4 Performance of methods as function of relative flow depth. 
 
In Figure 4 the performance of the three methods is shown as a function of the relative flow 
depth (for experiments with intermediate vegetation densities only). Among the three methods no 
obvious trend can be discerned of model performance as related to relative flow depth. 
 
4. CONCLUSIONS 
 
Three methodologies to predict flow velocities in presence of submerged vegetation were compared 
with a large set of different laboratory measurements. The collected laboratory experiments included 
flow studies over natural and artificial vegetation, in some cases the vegetation was rigid, in some 
flexible. Among the three methods, method 2 (Klopstra et al. 1997) gives the best performance if 
compared with the entire dataset, although the results of method 3 (Baptist et al. 206) are not 
significantly different. The two-layer scaling method (method 1, Huthoff et al. 2006) gives the best 
results if only focusing on vegetation distributions that have intermediate spatial densities (i.e. for 
situations with relative vegetation separations 5 < s/CDD < 25).   
 The simple mathematical forms of the three vegetation resistance methods make them suitable 
for quick evaluation of a river’s hydraulic response to obstructing vegetation. The range of densities 
where the method of Huthoff et al. (2006) performs well covers a wide range of naturally occurring 
vegetation types. Only for very dense vegetation types as grasslands, this method appears to be 
unreliable. In such cases it is recommended to use either the methods by Baptist et al. (2006) or 
Klopstra et al. (1997), which do not give significantly different results. Regardless of the method 
used, predicted flow velocities have a standard deviation of about 30%.  
 
 
 
 
  7 
ACKNOWLEDGEMENTS 
 
This research is supported by the Technology Foundation STW, applied science division of NWO 
and the technology program of the Ministry of Economic Affairs (the Netherlands). 
 
REFERENCES 
 
Baptist, M. J. (2005), “Modelling Floodplain Biogeomorphology”, PhD thesis, Delft University of 
Technology. 
Baptist, M. J., Babovic, V., Uthurburu, J. R., Keijzer, M., Uittenbogaard, R. E., Mynett, A. and Verwey, A. 
(2006). “On inducing equations for vegetation resistance”, Journal of Hydraulic Research, accepted. 
Chow, V.T. (1959). Open Channel Hydraulics, McGraw-Hill Publishing Company, New York. 
Huthoff, F. and Augustijn, D.C.M. (2006). “Hydraulic resistance of vegetation: predictions of average flow 
velocities based on a rigid-cylinders analogy”, University of Twente, CE&M research report 2006R-
001/WEM-003, ISSN 1568-4652. 
Huthoff, F., Augustijn, D.C.M. & Hulscher, S.J.M.H. (2006). “Depth-averaged flow in presence of 
submerged cylindrical elements”. In: Riverflow 2006, Proceedings of the Third International 
Conference on Fluvial Hydraulics, Lisbon, Portugal, Vol. 1, 575-582. 
Ikeda, S and Kanazawa, M. (1996), “Three-dimensional organized vortices above flexible water plants”, 
Journal of Hydraulic Engineering 122(11), 634-640. 
Järvelä, J. (2003). “Influence of vegetation on flow structure in floodplains and wetlands”. In: River, Coastal 
and Estuarine Morphodynamics, Proceedings of the Third IAHR Symposium, Barcelona, Spain, Vol 2. 
845-856. 
Järvelä, J. (2004). “Determination of flow resistance caused by non-submerged woody vegetation”. Journal of 
River Basin Management, 2(1), 61-70. 
Klopstra, D., Barneveld, H.J., van Noortwijk, J.M. and van Velzen, E.H. (1997). “Analytical Model for 
Hydraulic Resistance of Submerged Vegetation”, In: Managing Water: Coping with scarcity and 
abundance, Proceedings of the 27th IAHR Congress, San Fransisco, 775-780. 
Kouwen, N., Unny, T. and Hill, H.M. (1969) , “Flow retardance in vegetated channels”, Journal of Irrigation 
and Drainage Division, 95(IR2), 329-342. 
López, F. and Garcia, M.H. (1997). “Open channel flow through simulated vegetation: turbulence modelling 
and sediment transport”, Technical report WRP-CP-10, Hydrosystems Laboratory, University of 
Illinois. 
López, F. and Garcia, M.H. (2001). “Mean flow and turbulence structure of open-channel flow through non-
emergent vegetation”, Journal of Hydraulic Engineering, 127(5), 392-402. 
Meijer D.G., (1998a), “Modelproeven overstroomd riet”, Technical Report PR177, HKV Consultants, 
Lelystad, the Netherlands. (in dutch). 
Murota, A., Fukuhara, T. and Sato, M. (1984). “Turbulence structure in vegetated open channel flows”. 
Journal of Hydroscience and Hydraulic Engineering, 2(1), 47-61. 
Nepf, H. M.  (1999) “Drag, turbulence, and diffusion in flow trough emergent vegetation”. Water Resources 
Research, 35(2), 479-489. 
Ree, W.O. and Crow, F.R. (1977). “Friction factors for vegetated waterways of small slope”, Technical report 
ARS-S-151, Agricultural Research Service, U.S. department of Agriculture. 
Tsujimoto, T. and Kitamura, T. (1990). “Velocity profile of flow in vegetated bed channels”, KHL 
progressive Report 1, Kanazawa University. 
Tsujimoto, T., Okada, T. and Kontani, K. (1993) , “Turbulent structure of open channel flow over flexible 
vegetation”, KHL progressive report 4, Kanazawa University. 
van Velzen, E. H., Jesse, P., Cornelissen, P. and Coops, H. (2003), “Stromingsweerstand vegetatie in 
uiterwaarden”, Handbook hydraulic resistance of vegetation, Technical report 2003.028, RIZA, 
Arnhem, The Netherlands. (in dutch). 
 


Hydraulic resistance of vegetation in river flow applications

Huthoff, Freek

Augustijn, Dionysius C.M.

University of Twente Research Information

The 7th Int.  Conf. on Hydroscience and Engineering (ICHE-2006), Sep. 10 – Sep. 13, Philadelphia, USA 1       HYDRAULIC RESISTANCE OF VEGETATION IN RIVER FLOW APPLICATIONS   Fredrik Huthoff1, Denie C.M. Augustijn2 and Suzanne J.M.H. Hulscher3   When vegetated regions become part of a river’s flow field, the hydraulic resistance of vegetation affects the overall conveyance. Several descriptions exist to describe this type of flow, among which are empirical relations and relations that are physics-based. Empirical relations are often simple in form but have the drawback that their use is limited to the situation where they were determined. On the other hand, theoretical descriptions become increasingly complex (large computational efforts) and pose practical difficulties when gathering necessary input data. In the current work a new scaling expression of the average flow field is put forward that combines advantages of existing flow equations: (i) it is physics-based, (ii) it is dependent on readily measurable quantities and (iii) it requires little computational effort. The performance of the new expression is compared to existing expressions, and limits are given for its practical use. Vegetation that penetrates a flow field causes drag in the layer occupied by the vegetation. Based on scaling considerations of the forces involved, depth-averaged flow velocities within the vegetation layer and in the free flowing layer above the roughness elements are estimated. The conditions in the two separate flow layers yield a new description of the overall depth-averaged flow velocity (U), which is entirely determined by measurable geometrical boundaries:  3/2 −−+=skhhkhhkuUS (1) Where the depth of flow h exceeds the height of the vegetation k. The separation between individual vegetation elements s also determines the characteristic scaling velocity in the vegetation layer uS:  DCgisuDS2=  (2) With g the gravitational acceleration, i the bed slope, D the stem diameter and CD the drag coefficient. Note that for large flow depths eq. 1 reduces to Manning’s equation (i.e. if h>>k). Two other methods that rely on the same input parameters for describing vegetative flow resistance are compared to the new description (eq. 1): • The adapted Klopstra method (Klopstra et al. 1997). This method is based on depth-integration of a velocity profile for flow through submerged vegetation. See Huthoff & Augustijn (2006) for details on the adaptation of Klopstra’s method.  • The Baptist method (Baptist et al. 2006). A simple analytical flow description is deduced from outcomes of a detailed numerical model, based on a genetic algorithm.                                                  1 PhD Candidate, Department of Water Engineering and Management, Faculty of Engineering Technology, University of Twente, PO BOX 217, 7500 AE Enschede, the Netherlands (F.Huthoff@utwente.nl) River Hydraulics Consultant, HKV Consultants, PO BOX 2120, 8203 AC Lelystad, the Netherlands. 2 Associate Professor, University of Twente, the Netherlands (D.C.M.Augustijn@utwente.nl) 3 Professor, University of Twente, the Netherlands (S.J.M.H.Hulscher@utwente.nl) The 7th Int.  Conf. on Hydroscience and Engineering (ICHE-2006), Sep. 10 – Sep. 13, Philadelphia, USA 2 The performance of the three methods is evaluated against 177 flow measurements from laboratory flumes (taken from literature, see Baptist et al. 2006 for references). These experiments were conducted with various vegetation heights and various spacing between individual vegetation elements (s/CDD), and included both flexible and rigid vegetation. The results are shown in Fig. 1.    Figure 1 Three vegetation resistance methods and their predicted depth-averaged flow velocities compared to measured values (Upredict and Uref). The horizontal axis shows relative spacings between individual vegetation elements (s/CDD); from dense (left) to sparse vegetation coverage (right). Also shown are mean error (µ) and error standard deviations (σ) of predicted flow velocities.  Predicted values of the newly proposed method correspond reasonably well with a wide range of experimental data (Fig. 1), as do predictions of Baptist’s and Klopstra’s methods. Errors for the three methods range from σ = 24% for Klopstra’s method (which describes most flow detail) to 32% in the new method. Overall, Klopstra’s method shows the smallest systematic error (µ = 4%) while the method proposed by Baptist often underestimates flow velocities (µ = -19%).  The simple mathematical form of the newly proposed method makes it suitable for a quick evaluation of a river’s hydraulic response to obstructing vegetation. However, due to increasing errors in case of dense or sparse vegetation coverage, it is advised to restrict its application to flows through intermediate vegetation densities only (i.e. for situations where 5<s/CDD<25).   REFERENCES  Baptist, M. J., Babovic, V., Uthurburu, J. R., Keijzer, M., Uittenbogaard, R. E., Mynett, A. and Verwey, A. (2006). “On Inducing Equations for Vegetation Resistance”, Journal of Hydraulic Research, accepted. Huthoff, F. and Augustijn, D.C.M. (2006). “Hydraulic Resistance of Vegetation: Predictions of Average Flow Velocities based on a Rigid-cylinders Analogy”, University of Twente, CE&M research report 2006R-001/WEM-003, ISSN 1568-4652. Klopstra, D., Barneveld, H.J., van Noortwijk, J.M. and van Velzen, E.H. (1997). “Analytical Model for Hydraulic Resistance of Submerged Vegetation”, In: Managing Water: Coping with scarcity and abundance, Proceedings of the 27th IAHR Congress, San Fransisco, 775-780. 

Analytical Model for Hydraulic Resistance of Submerged Vegetation”, In: Managing Water: Coping with scarcity and abundance,

Hydraulic Resistance of Vegetation: Predictions of Average Flow Velocities based on a Rigid-cylinders Analogy”,

On Inducing Equations for Vegetation Resistance”,

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Hydraulic Resistance of Vegetation in River Flow Applications

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