ASSESSING VEGETATION RESISTANCE FROM OBSERVEDTEMPORAL WATER SURFACE PROFILES OF FLOOD FLOWS IN
RIVERS
Fumiyoshi Ohnuma1, Shoji Fukuoka 2 and Hiroshi Fujisawa3
1

Graduate School of Science and Engineering, Chuo University,
1-13-27, Kasuga, Bunkyo-ku, Tokyo, Japan (ohnuma_f@civil.chuo-u.ac.jp)
2
Professor, Research and Development Initiative, Chuo University，
1-13-27, Kasuga, Bunkyo-ku, Tokyo, Japan (sfuku@tamacc.chuo-u.ac.jp)
3
Director of River Department, Kyushu Regional Development Bureau, Ministry of Land, Infrastructure andTransport, 2-10-7, Hakataekihigashi, Hakata-ku, Fukuoka, Japan

ABSTRUCT
The behavior of temporal change in water surface profiles manifests any hydraulicphenomena in river course resulting from cross-sectional change, resistance of vegetation andriver bed variation during floods. Vegetation permeability coefficients and Manning’s
roughness coefficients for flood flows are estimated by unsteady two-dimensional flow
analysis and observed data of temporal water surface profiles. Characteristics of vegetation
resistance affected by vegetation conditions and channel scales were clarified using thesecomputed results. The method for assessing the vegetation resistance is presented fromanalytical results using observed temporal water surface profiles.
Key Words: river management, vegetation permeability coefficient, Manning’s roughness coefficient,characteristics of vegetation resistance, unsteady two-dimensional flow analysis

1． INTRODUCTION
Vegetations play a significant role in channels to reduce impacts of flood flow onbanks and form river environment and ecosystem. On the other hand, vegetations produce
local high velocity near banks and increase in water levels. Therefore, vegetations areimportant for both flood control and river environment (Fukuoka 2005). Fukuoka and Fujita(1998) investigated in detail hydraulic effects of vegetations on flood flow by flume
experiments. Similarly, many studies have been done on flow with vegetation in relation withriver management.
The resistance to flood flow in rivers consists of vegetation resistance and channelbottom resistance which are included in the equations of motion of the two-dimensional flow
as follows.
⎛⎞2(τ s , τ n ) = ⎜⎜ gn1 / 3 + gh 2a ⎟⎟
⎝h

K

⎠

u 2 + v 2 (u , v )(1)

Where, K = vegetation permeability coefficient; n = Manning’s roughness coefficient; h= water depth; ha = min( h , htree ); (u, v ) = velocity components (s, n ) . In the conventional
two-dimensional non-uniform flow analysis, some problems arise in the estimation of theflow resistance by two reasons: one is for observation errors of water discharge and flood
trace levels and the other is for the method of analysis. Vegetation permeability coefficients,
therefore, differ from every flood. Fukuoka and Watanabe (2006) developed on unsteady two-dimensional flow analysis method with observed temporal water surface profiles, which
represents well the essential characteristics of flood flow. In this unsteady flow analysis,
vegetation permeability coefficient and Manning’s roughness coefficient were determinedreasonably for flood flow. The authors showed that Manning’s roughness coefficient was
independently given by geometry and boundary resistance of rivers, irrespective of vegetation
conditions. Then, the vegetation permeability coefficients are determined by the unsteady
two-dimensional flow analysis so as to reproduce the observed temporal water surface
profiles of flood flows (Fukuoka and Fujisawa 2007a, Fukuoka and Sato 2007b).
In this study, vegetation resistance characteristics during flood are investigated fromthe unsteady two-dimensional flow analysis (Fukuoka and Watanabe 2006, Fukuoka andFujisawa 2007a, Fukuoka and Sato 2007b). Then, vegetation permeability coefficients
corresponding to channel’s scales and vegetation conditions are examined. Finally waterlevels and velocity vectors are used for indices of an assessment method of rivers withvegetations.
2． CONDITIONS OF CHANNELS AND VEGETATIONS
The area studied in the Tone River (104.0km-131.0km) is shown in Figure 1. Figure 2
shows observation reach in the Watarase River (3.0km-5.5km). The Watarase River is one of
the tributaries of the Tone River and joins the Tone River at 132.5km. There are vegetations,mainly willow, on flood channel throughout those areas and most of them are higher thanbank crown level. Fukuoka and Watanabe (2006) conducted the two-dimensional analysis forseveral floods in the Tone River and Edo River. In this paper, based on their results, weinvestigate vegetation resistance in the Tone River on September, 1998 and the Watarase
River on September, 2007. Recent major floods in the Tone River and Edo River are shown in
Table 1, including heavy floods in 1998 and 2007. Cross-sectional shape at 130.0km in theTone River and observed water levels are shown in Figure 3. Since the Tone River has had no
heavy floods from 1982 to 1998, willows on flood channel grew up so high. Then, thevegetation become a main resistance element to flood flows.
Tone Riverflow

Edo River
Kurihashiflow● Water level observation station■ Vegetations

Mefukibashi

Noda

5.0(km)0.0

Figure 1 Planform and channel conditions of the studied areas of the Tone River and Edo River.
flow● Water level
observation
station■ Vegetations

Shin-akamabashi
Daini-haisuimon

0.0

1.0(km)Figure 2 Planform and channel condition of the studied area of the Watarase River.

Table 1 Recent major floods in the Tone River and Edo River.
Typoon
No.
18
5
15
6
22
23
9

Year/Month1982/91998/92001/92002/7
2004/10
2004/10
2007/9

-15

-10

-5

Observed maximam water discharge(m3 /s)
Kurihashi (Tone R.)
Noda (Edo R.)
11,606
2,872
10,431
2,449
7,980
2,020
8,555
1,622
4,563
1,333
4,025
1,210
1,934
8,933

Time(hour)

0

5

10

15

20

25

30

35

Elevat ion(m)251998 Cr osssectional shape

H.W.L.

20

1998 Obser ved
water level15
102007 Obser ved
water level

5
-200

0

200

400

600

Transverse distance(m)

800

1000

Figure 3 Observed water levels and cross-sectional shape at 130.5km in the Tone River.
20
Water level (m)

18
16
14
12
9/16 17:00
9/17 5:00

9/16 21:00
Flood trace level10

9/17 1:00
Observed water level

8
6

128

123

118
113
Longitudial distance (km)

108

103

(a) Tone River
17
Water level (m)

15
13
11
9
9/17 0:00
9/18 0:00

9/17 8:00
Flood trace level7

9/17 16:00
Observed water level

5
3

60

55

50
45
Longitudial distance (km)4035(b) Edo River
Figure 4 Computed temporal water surface profiles and observed water levels for flood in
1998.
20.0
19.0
Observed water level

9/7 16:00

9/7 20:00

9/8 0:00

18.0

9/8 4:00

Water level (m)

21.0

17.0
6

5.5

5

4.5
4
Longitudial distance (km)

3.5

3

2.5

Figure 5 Computed temporal water surface profiles and observed water levels for floodin the Watarase River in 2007.

Vegetation permeability
coefficient (m/s)

80
70
Edo River60

Tone River

50
40
30
0.00

0.10

0.20

0.30

0.40

0.50

0.60

Vegetation area/Flood channel area

・s)

0.045

-1/3

coefficient (mManning's roughness

Figure 6 Relationship between vegetation permeability coefficient and the ratio ofvegetation area to flood channel area.

0.035
Tone River(1998)
Tone River(2004)
Watarase River(2007)

0.025

E do r iver(1998)
E do River (2004)

0.015
0

20
40
60
Vegeta tion permeability coefficient (m/s )80

Figure 7 Relationship between vegetation permeability coefficient and Manning’s
roughness coefficient.
Vegetation permeability coefficients K are determined by the unsteady twodimensional flow analysis so that observed water surface profiles coincide well withcalculated ones (Figure 4, Figure 5). Figure 6 shows the relationship between vegetation
permeability coefficient and the ratio of vegetation area to flood channel area for the 1998
flood. It shows that vegetation permeability coefficient is smaller as the ratio of vegetation
area to flood channel area is larger. Since, the vegetation resistance expressed in Eq. (1)becomes large when vegetation permeability coefficient is small, vegetation resistancebecome larger as the ratio of vegetation area to flood channel area is larger. The relationshipbetween vegetation permeability coefficient and Manning’s roughness coefficient is shown in
Figure 7. Small-scale flood in 2004 is also included in Figure 7. Since, reeds on flood channel
were main resistance element to 2004 flood flows, vegetation permeability coefficients are
small in comparison with those of the other floods. Tables 2-4 shows characteristics ofvegetation and channel. Those data are used in the later investigation.
3． RESISTANCE CHARACTERISTICS OF VEGETATIONS ON FLOOD FLOWSVegetations in rivers decrease the cross-sectional velocity by mixing flows within thevegetation area and flow outside vegetations and increase the flow resistance. Vegetation
resistance seems to be related to the scale of channel as well as vegetation conditions. The
vegetation resistance to flood flow may be explained by vegetation permeability coefficients
K by solving unsteady two-dimensional flow equations.
For describing the relation of channel scale and vegetation scale, the ratio ofvegetation width to channel width and the ratio of vegetation resistance term to sum of all theterms in the equations of motion at the time of peak discharge are chosen on the coordinate of
Figure 8. It shows that the ratio of vegetation resistance term to sum of all the terms in theequations of motion of the Watarase River is greater than other larger rivers, although theTable 2 Channel and vegetation properties in the Tone River.
Vegetation
T-R-1
T-R-2
T-R-3
T-R-4
T-R-5
T-R-6
T-R-7
T-R-8
T-L-1
T-L-2
T-L-3
T-L-4
T-L-5
T-L-6
T-L-7
T-L-8
T-L-9
T-L-10T-L-11Vegetation width: Bw (m)Main channel width:Bmc (m)Channel width: B (m)

12
51
92
38
56
7
57
32
169
83
90
78
61
80
81
66
75
105
38

207
291
313
274
255
296
223
246
210
339
347
271
254
253
264
302
279
285
243

740
658
701
565
545
511
537
523
709
773
965
535
541
499
525
525
507
575
578

B w/B
0.02
0.08
0.13
0.07
0.10
0.01
0.11
0.06
0.24
0.11
0.09
0.15
0.11
0.16
0.15
0.13
0.15
0.18
0.07

B w/B mc
0.06
0.18
0.29
0.14
0.22
0.02
0.26
0.13
0.81
0.24
0.26
0.29
0.24
0.32
0.31
0.22
0.27
0.37
0.15

B mc /B
0.28
0.44
0.45
0.49
0.47
0.58
0.41
0.47
0.30
0.44
0.36
0.51
0.47
0.51
0.50
0.57
0.55
0.50
0.42

K (m/s)
70
70
55
60
55
50
50
50
55
40
40
40
55
55
55
55
55
55
55

B mc /B
0.32
0.27
0.24
0.18
0.27
0.24
0.31
0.28
0.24
0.30
0.28
0.24
0.23

K (m/s)
55
50
50
60
40
65
60
60
60
60
40
45
60

B mc /B
0.26
0.26
0.26

K (m/s)15
15
20

Table 3 Channel and vegetation properties in the Edo River.
Vegetation
E-R-1
E-R-2
E-R-3
E-R-4
E-R-5
E-R-6
E-L-1
E-L-2
E-L-3
E-L-4
E-L-5
E-L-6
E-L-7

Vegetation width: Bw (m)Main channel width:Bmc (m)Channel width: B (m)

55
80
76
123
48
87
66
54
65
118
81
91
60

110
94
91
65
95
81
108
100
87
108
102
87
80

347
353
374
356
353
344
346
350
371
363
360
354
348

B w/B
0.16
0.23
0.20
0.35
0.14
0.25
0.19
0.15
0.18
0.33
0.23
0.26
0.17

B w/B mc
0.50
0.86
0.83
1.91
0.51
1.07
0.61
0.54
0.75
1.09
0.80
1.05
0.76

Table 4 Channel and vegetation properties in the Watarase River.
Vegetation width: Bw (m)Main channel width:Bmc(m)Channel width: B (m)

37
110
15

62
61
61

241
239
239

Vegatation
resistance/
Channel bottom
resistance

Vegetation
W-R-1
W-R-2
W-L-1

B w/B
0.15
0.46
0.06

12
10
8
6
4
2
0

B w/Bmc
0.59
1.80
0.24

Tone River
Edo River
Watarase River

0

0.1
0.2
0.3
0.4
Vegetation width/Channel width

0.5

Vegetation resistanceterm/The sum of allterms in equation of
motionFigure 8 Relationship between vegetation resistance and channel scale at the time of peakdischarge.
0.5
0.4

ToneRiver
EdoRiver
WataraseRiver

0.3
0.2
0.1
0
0

0.1
0.2
0.3
0.4
Vegetation widt h/Channel width

0.5

Figure 9 Relationship between vegetation resistance and bed resistance against channel
scale at the time of peak discharge.

Vegetation
permeability
coefficient: K(m/s)

70
60
50
40
30
20
10
0

Tone River
Edo River
Ota River
Watarase River
0

200

400
600
Channel width (m)

800

1000

Figure 10 Relationship between channel width and vegetation permeability coefficient.
ratio of vegetation width to channel width is within the same range. This is because thevegetation in smaller channel such as the Watarase River affects strongly on flood flow.
Figure 9 shows the relationship between the ratio of vegetation width to channel width andthe ratio of vegetation resistance to channel bed resistance in each river. The ratio ofvegetation resistance to channel bed resistance in the Watarase River is greater than the others.
Figure 10 shows the relationship between vegetation permeability coefficient and scale ofchannel in the Tone, Edo, Watarase and Ota Rivers (Gotoh and Fukuoka, 2007c). Values ofvegetation permeability coefficient tend to decrease as the channel width is smaller. It meansthat the vegetation resistance increases relatively in smaller channels.
It is shown that the unsteady two-dimensional flow analysis using observed water
surface profiles during floods provides a good explanation for vegetation resistance
represented by the vegetation permeability coefficient in rivers.
4． METHOD FOR ASSESSING EFFECTS OF VEGETATIONS ON FLOOD FLOW
Longitudinal distribution of water level is the most important index to understandchannel condition for the flood control. The method for assessing vegetation effect wasinvestigated in 123.0km-129.0km of the Tone River shown in Figure 11. Figure 12 shows
calculated water surface profile of peak discharge for the 1998 flood estimated by the

123.0kmflow■ Vegetations
129.0kmFigure 11 Planform and channel condition of the observed area of the Tone River.
Vegetation condition

20.0
19.5
19.0
18.5
18.0
17.5
17.0

water level increase
129

128

127

126
125
Longitudial distance (km)

124

123

Figure 12 Observed water level and vegetation distribution.

Water level (m)Left flood channel
Right flood channel

123.0km

123.0km■ Vegetations□ Cutting downflow

■ Vegetations□ Cutting downflow

129.0km

129.0kmFigure 13 Planform and channel condition of
the observed area (Case1).

Figure 14 Planform and channel conditionof the observed area (Case2).

Vegetation condition

Left flood channel
Right flood channel

Cutting down in Cas e2
Cutting down in Case2

Cutting down in Cas e1

20 .0
Case2

19 .5

Ca se0

19 .0
18 .5
18 .0

Water le vel (m)

Case1

17 .5
17 .0
129

128

12 7

126
125
Longitud ial d istance (k m)

12 4

123

Figure 15 Calculated water levels and vegetation distribution.
unsteady two-dimensional flow analysis (Case0). From Figures 11 and 12, the computed
water level increases in 125.5km and 127.5km, which seems to be caused by resistance ofvegetations on right flood channel in 124.5km-125.5km and by contracted section of main
channel in 126.5-127.5km.
Based on the unsteady two-dimensional flow analysis, vegetation effect on flood flow
is investigated from water surface profiles and velocity fields. Here, Case 1 and Case 2
simulated by altering vegetation permeability coefficient evaluate the influences of cutting
down at the right flood channel in 124.5km-126.5km (Figure 13) and both flood channels in
126.5-127.5km (Figure 14), respectively. The unsteady two-dimensional flow analysis by
Fukuoka and Watanabe (2004) proved to be a useful method for determine the vegetation
permeability coefficients and evaluating precise temporal water discharges at any point. Here,the temporal water discharge is given as the boundary condition at upstream end instead ofobserved temporal water level flow simulations of cutting down because water level changes
by cutting down.
Figure 15 shows the comparison between computed water surface profiles at eachpeak discharges of Case 1, Case2 and Case 0 and decreases in water levels by the cutting
down. Decrease in water level is about 10cm in Case1 and 5cm in Case 2 at the upstream ofvegetations in objective. Figure 16 and Figure 17 show differential velocity vectors fromvelocity vector of Case 0. In those figures, blue arrow shows that the velocity difference is
0.0m/s-0.3m/s, and red ones above 0.3m/s. Both cases show velocity increase in cutting downarea. Figure 16 shows velocity difference of Case 1 from the velocity of Case 0. Velocity
vectors increase at the boundary of main channel and right flood channel and decrease inmain channel and left flood channel in 124.5km-125.5km. It seems to reduce flow velocity
toward left flood channel in 124.0km-126.0km. Figure 17 shows velocity difference of Case 2

124.0km

125.0km
123.0km126.0km0.3(m/s)

Velocity vector (0.0m/s-0.3m/s)

0.5(m/s)

Velocity vector (0.3m/s-)

127.0km■□

128.0km

Vegetations
Cutting down

Figure 16 Computed differential velocity vector field (Case 1 –Case0).
124.0km

125.0km
123.0km126.0km0.3(m/s)

Velocity vector (0.0m/s-0.3m/s)

0.5(m/s)

Velocity vector (0.3m/s-)

127.0km

128.0km■□

Vegetations
Cutting down

Figure 17 Computed differential velocity vector field (Case2 –Case0).

from Case 0 and velocity increase at main channel contracted section in cutting down areasand velocity decrease on flood channel at the end of contracted section. The latter is causedby turbulent mixing of the activated flow at the boundary of flood channel and flows on flood
channel.
The effects of vegetation on flood flow are clarified by the flow simulation of cutting
down. Significant change in longitudinal distribution of water levels (water surface profiles)
and velocity vectors is confirmed by this analysis method.

5． CONCLUSIONS
The authors investigated vegetation resistance characteristics and a method forassessing vegetation effect on flood flow in the Tone River, Edo River and Watarase River on
the basis of unsteady two-dimensional flow analysis using observed temporal water surface
profiles. The primary conclusions in this research are as follows.
(1)In river with vegetations, Manning’s roughness coefficient is determined by boundary
shape of channel and then, vegetation permeability coefficient is determined by the unsteady
two-dimensional flow analysis so as to reproduce the observed temporal water surface
profiles. Flow resistance determined by this method provides a reasonable explanation forriver flow with vegetations.
(2) Ratio of vegetation resistance term to sum of all terms in the equations of motion increases
in smaller channel even though the ratio of vegetation width to channel width is almost thesame. And so is the ratio of vegetation resistance to channel bed resistance.
(3)Vegetation permeability coefficients decrease as channel scale becomes small.
(4)Vegetation effect on flood flow was assessed by simulating the flow of cutting down

altering vegetation permeability coefficient and using temporal water discharge as boundary
condition at upstream end. It is shown that water levels and velocity vectors are useful as theindices of the assessment of the flow with vegetations.

REFERENCES
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Vol.13, pp.333-338.
Fukuoka, S., Sato, H., Fujisawa, H. and Ohnuma, F. (2007b), “Assessment of permeability
coefficient of vegetation and roughness coefficient under various floods and channel
conditions”, Annual Journal of Hydraulic Engineering, JSCE, Vol.51, pp.607-612.
Gotoh, T., Fukuoka, S. and Nigo, S. (2007c), “Vegetation destruction by flood flow inchannel and evaluation of discharge hydrographs”, Proceedings of 62th Annual Meetingsof JSCE 2007, pp.187-188 (CD-ROM).
Fukuoka, S., Watanabe, A., Tabata, K., Kazama, S. and Gocho, H. (2006), “Evaluation ofhydrograph of flood discharge and roughness coefficient of the branched section in theTone River and the Edo River”, Annual Journal of Hydraulic Engineering, JSCE, Vol.50,
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Fukuoka, S. and Fujita, K. (1990), Hydraulic effect of luxuriant vegetation on flood flow,
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