Transport of large woody debris in the presence of obstacles

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Geomorphology 76 (

Transport of large woody debris in the presence of obstacles

D. Bocchiola *, M.C. Rulli 1, R. Rosso 2

Department of Hydrologic, Roads, Environmental and Surveying Engineering, Politecnico di Milano,

L. Da Vinci Square 32, 20133 Milano, Italy

Received 23 November 2004; received in revised form 6 July 2005; accepted 2 August 2005

Available online 20 December 2005

Abstract

Flume experiments were carried out to investigate the motion of large woody debris (LWD) in rivers as influenced by the

presence of obstacles. Non-rooted, defoliated LWD was modelled by placing properly scaled wooden dowels placed into

controlled water flow. Obstacles were represented by wooden rods randomly placed into the flume with a specified probability

distribution. The results provide the probability of lodging of the dowels and statistics of the distance travelled. Their

relationships with flow rate and depth, dowel length and spatial density of the obstacles is explored. This yields a general

theoretical framework to approach LWD transport in rivers by combining random factors with deterministic dimensionless

variables.

D 2005 Elsevier B.V. All rights reserved.

Keywords: Large woody debris; Wood transport; Wood trapping; Wood jams

1. Introduction

The transport of large woody debris (henceforth

referred to as LWD) has many implications in river

geomorphology. LWD interacts with erosion and sedi-

mentation processes (Fetherston et al., 1995; Jeffries et

al., 2003), channel morphology (Keller and Swanson,

1979; Murgatroyd and Ternan, 1983; Jackson and

Sturm, 2002; Gomi et al., 2003; Murray and Paola,

2003) and channel hydraulics (Young, 1991; Shields

and Gippel, 1995; Braudrick et al., 1997; Braudrick and

0169-555X/$ - see front matter D 2005 Elsevier B.V. All rights reserved.

doi:10.1016/j.geomorph.2005.08.016

* Corresponding author. Tel.: +39 02 23996292; fax: +39 02

23996207.

E-mail addresses: [email protected] (D. Bocchiola),

[email protected] (M.C. Rulli), [email protected]

(R. Rosso).1 Tel.: +39 02 23996292; fax: +39 02 23996207.2 Tel.: +39 02 23996226; fax: +39 02 23996207.

Grant, 2000; Manga and Kirchner, 2000; Bocchiola et

al., 2002; Haga et al., 2002). The budget of woody

debris at the basin scale is of interest (Benda and Sias,

2003), particularly considering its interaction with the

river flow regime (Abbe and Montgomery, 2003). LWD

has a strong influence on the morphology of low order

channels, where flow depth and width are comparable

in size with the diameter and length of the woody debris

pieces (e.g. Fetherston et al., 1995) and wood can

provide a control on sediment budget (Gomi et al.,

2003).

In lowland rivers, the deposition of LWD and the

presence of river discontinuities, such as bends or

narrow sections, enables sediment deposition, thus trig-

gering bnurseQ areas for the colonization of vegetation

(Fetherston et al., 1995; Jeffries et al., 2003) and even

for the formation of river islands (e.g. Gurnell et al.,

2000a,b). Wood provides the habitat for fish-bearing

and riverine species (Jackson and Sturm, 2002) and it

2006) 166–178

D. Bocchiola et al. / Geomorphology 76 (2006) 166–178 167

has an influence on water temperatures, water flows and

nutrient fluxes (e.g. Welty et al., 2002). Several studies

have been carried out to map the spatial distribution of

LWD using in situ surveys (Wing et al., 1999; Kraft and

Warren, 2003) and remote sensing (Aspinall, 2002;

Marcus et al., 2002). Some pioneering attempts have

been made to assess the relationship between wood

accumulation processes and river geomorphology

(Jackson and Sturm, 2002; Abbe and Montgomery,

2003) and to investigate some statistics of the observed

LWD distribution (e.g. to test their randomness or

spatial organization, see Kraft and Warren, 2003). Brau-

drick and Grant (2000), Manga and Kirchner (2000),

Bocchiola et al. (2002) and Hygelund and Manga

(2003), among others, investigated the interaction of

wood and water flow in rivers. Additionally, Smith et

al. (1993) and Manga and Kirchner (2000) have studied

the influence of LWD transport on water shear stress

and sediment erosion.

During a flood LWD is swept and redistributed

throughout the river network. The redistribution pro-

cess depends on the hydraulic characteristics and ge-

ometry of the individual channels, this including in-

channel structures, such as steps, pools, large boulders

and wood jams. Therefore, the interaction of LWD with

irregular channel patterns plays a major role in deter-

mining LWD dynamics in rivers.

The present paper deals with the interaction of

LWD with channel obstacles. These are associated

with multifaceted bed morphology of braided rivers

and with boulders and vegetation in mountain rivers.

The presence of obstacles also affects the LWD trans-

portation in the floodplain. Here, vegetation is often

poorly managed, so it can grow undisturbed during

periods of low flows, but it can obstruct the transport

of wood pieces during large flood events that occur

with low frequency.

The key factor here is the interaction of the moving

logs with the obstacles, as conditioned by water depth

and velocity. This is approached here by developing

controlled experiments in a laboratory flume. These are

accurately designed in order to investigate the process

of LWD lodging and the distance travelled by the logs.

The results from these experiments are used to develop

a simple theoretical framework capable of providing

quantitative estimates of the complex interaction of

LWD with channel obstacles.

2. Previous studies on LWD transport in rivers

LWD consists of wood pieces 1 m or more in length

or 0.1 m or more in diameter (see Jackson and Sturm,

2002 for the definition of LWD). The initiation of

motion and redistribution of LWD throughout the

river network during flood events was studied by Brau-

drick et al. (1997), Braudrick and Grant (2001) and

Haga et al. (2002), who investigated the relationship

between the distance travelled by a single LWD piece

and the local properties of the flow. Travel distance

depends on LWD size (i.e. its representative length and

diameter and also the presence of rootwads) and den-

sity, the water depth and velocity, and the channel bed

roughness. The presence of bends, changes in channel

conveyance (i.e. channel width) and/or obstacles to

motion also have a significant influence on the path

of LWD.

LWD generally moves further in high order streams

(i.e. larger streams) and shorter pieces move further

than longer ones (e.g. Nakamura and Swanson, 1994).

In headwater streams, the logs longer than the bank-full

width tend to be stable and are removed only during

large flood events or due to decay (e.g. Haga et al.,

2002). Also, large boulders can interact with the trans-

port of the logs by trapping key pieces, leading to the

formation of jams (e.g. Faustini and Jones, 2003). The

major control of LWD transport in headwater streams is

the greatest water depth achieved during a flood event

(e.g. Braudrick and Grant, 2001; Haga et al., 2002). If it

exceeds the bfloating thresholdQ, the logs are more

likely to travel out of the reach. Following Abbe et

al. (1993), a log tends to stop and reside when the water

depth is lower than about half log diameter.

Channel morphology is a key factor in LWD dy-

namics. In straight reaches with deep water the wood

pieces flush rapidly, as they do not touch the bed and,

therefore, they do not encounter noticeable energy dis-

sipation. In sinuous reaches, the wood pieces can be

deposited due to frequent contact with the banks or to

the secondary flows in the outside of the channel bends

(Fetherston et al., 1995). In braided lowland rivers, the

presence of bars tends to bcaptureQ the wood pieces

(e.g. Gurnell et al., 2000a,b), because of the presence of

areas with shallow water and, in case, of the formation

of river islands.

Braudrick and Grant (2001) introduced the concept

that the probability of LWD to be deposited depends on

some particular flow variables and on the piece size.

They investigated the motion and the deposition pat-

terns of wood dowels (1.27–2.54 cm in diameter, 0.3 to

0.9 m in length) in a 7 m long, 1.22 m wide gravel bed

flume, with meanders and alternate bars. They intro-

duced a bdebris roughnessQ parameter, defined as a

weighted average of three variables, namely the ratio

between the piece length and the average channel width

D. Bocchiola et al. / Geomorphology 76 (2006) 166–178168

(Llog /wav), the ratio between the piece length and the

average channel radius of curvature (Llog /Rc) and the

ratio between the bbuoyantQ depth to the average chan-

nel depth (db /dav). This roughness has been related to

the distance travelled by the dowels. Haga et al. (2002)

carried out a field experiment in a mountain stream in

Japan, monitoring the distance travelled by regularly

shaped logs, depending on the flood history for 1 year.

They considered Small Coarse Woody Debris, i.e. logs

with length smaller than the stream width, and showed

that the distance travelled by the logs is strictly related

to the water depth at the peak flow. A log deposited

during an event with given water depth generally

moves only once a new event with a greater water

depth occurs. When the flow depth is smaller than the

log diameter, the logs are usually transported for a short

distance. Finally, the logs are transported further when

the water depth exceeds their diameter.

3. Key issues in transport of LWD

3.1. Stability of wood

As a first step, one must assess the combined flow

depth and velocity conditions that trigger the motion

of a piece of LWD (Braudrick and Grant, 2000). The

authors of the present paper carried out flume experi-

ments to assess the initiation of motion of wood logs

in rivers (Bocchiola et al., 2004, in press). A short

survey of these experiments is reported here (see also

Fig. 1). These experiments tested the initiation of

motion of dowels positioned both parallel and perpen-

dicular to flow direction. These two different initial

positions lead to motion either by sliding or by rolling

on the bed. The experimental results for the incipient

Fig. 1. LWD stability chart and flow conditions in the

motion are well accommodated by the following di-

mensionless equation:

Y4 ¼ 1:26

1þ 2:49XS;R4ð1Þ

with the subscript S, R, denoting the occurrence of

sliding and rolling, respectively. For both cases (slid-

ing and rolling), the variable Y* is given by:

Y4 ¼ qwdw

qlogDlog

: ð2Þ

Here dw denotes the depth of water (with density

qw) necessary to move a log with diameter Dlog and

mass density qlog and it is associated with undisturbed

flow conditions (see Braudrick and Grant, 2000). The

dimensionless variable X* depends on the type of

motion and it is:

XS4 ¼1

2

U2w

gLlog

1

cosatanU� sinað Þ ð3Þ

for sliding, where a is the bed slope, Uw is the undis-

turbed flow velocity, Llog is the log length and U is the

friction angle of the dowels on the channel bed. When

rolling is the prevailing mechanism of the initiation of

motion is given by:

XR4 ¼1

2

U2w

gDlog

1

cosatand� sinað Þ ð4Þ

where d is the friction angle at rolling (i.e. the angle at

which rolling occurs under gravity). The fitting of Eq.

(1) to the observed data is shown in Fig. 1.

One can refer to Bocchiola et al. (2004, in press)

for the scaling issues and the range of validity of Eq.

(1). The value of the intercept for X*=0, i.e. for very

experiment on LWD transportation (PR, JF, FF).

Fig. 2. Example of dowel rolling inside the flume.

Table 1

Properties of the dowels

Dowel qlog,d Llog D log U d

[kg m�3] [m] [m] [8] [8

D1 750 0.050 0.014 34 11

D2 728 0.075 0.014 34 11

D3 798 0.100 0.014 34 11

D4 834 0.125 0.014 34 11

D5 787 0.150 0.014 34 11

D6 780 0.250 0.014 34 11


low flow velocity, is Y*=1.26. The multiplier for Y* in

Eqs. (2) and (3) is found by best fitting of the flume

experiments, and the estimated value of 2.49 is an

estimate of the drag coefficient exerted by the water

flow on the log. These results provide rules for wood

motion initiation that differ notably from those intro-

duced by Braudrick and Grant (2000), mainly in the

case of rolling (i.e. when the logs are perpendicular to

flow).

3.2. Types of motion of LWD

Two major modes occur in the motion of a piece of

LWD driven by river flow (e.g. Braudrick et al., 1997;

Braudrick and Grant, 2001; Haga et al., 2002). First, the

piece of wood can move in contact with the bed, by

rolling or sliding. Second, floating occurs when water is

deep enough to achieve wood buoyancy. One needs a

criterion to discriminate these two different situations,

depending on water depth and flow velocity. Haga et al.

(2002) followed the approach by Braudrick and Grant

(2000) and introduced the dimensionless variable

h*=qwdw /qlogdlog as the controlling factor discrimi-

nating between floating and rolling or sliding. One

notes that h*=Y*. The associated bflotation threshold’’

is h*=1; when h* exceeds unity, motion occurs by

floating. This is obviously associated with the expected

buoyancy force in hydrostatic conditions. One notes

that the above mentioned experiments (see Fig. 1)

yield a larger value of the flotation threshold, i.e.

Y*=1.26. This occurs because of the local perturbation

of the flow profile induced by the log. In fact, the log

raises the water depth upstream, and it lowers the water

depth downstream (Bocchiola et al., 2004, in press).

Therefore, the log is immersed to an average depth

lower than the undisturbed dw. As a result, the buoy-

ancy force is less than that occurring under hydrostatic

conditions, so flotation occurs for a larger flow depth.

Therefore, one assumes here that wood moves in con-

tact with bed for Y*V1.26 and by flotation for

Y*N1.26.

4. The experiments

4.1. Flume settings

Fig. 2 shows a picture of the experimental set-up,

where a dowel mimics the motion of a piece of LWD

under the influence of water flow in a straight channel

with known bed slope and roughness. The experimental

flume is 1 m wide and 30 m long, with a bed slope of

0.006. A 2 m panel is fixed to the flume bed, covered

with sand (D50=2 mm). One notes that sediment trans-

port interacts with wood transport in rivers. This inter-

action is neglected here, because one must first assess

the mechanics of log motion in absence of sediment

load. Accordingly, these experiments were carried out

using a fixed channel bed. The 2 m panel was mounted

in a position so that the water depth and velocity were

almost constant along its whole extent; this was

assessed using flow profile calculations and it was

further tested by local measurements. No relevant

back water effect was observed due to the gate at the

flume’s end.

4.2. Adopted dowels and validity of the incipient motion

criterion

The simple case of non-rooted, defoliated LWD is

considered here, well represented by handmade dowels.

Table 1 shows the major features of the test dowels.

These are made of Beech (Fagus sylvatica) with aver-

age dry density qL=779 kg m�3. Six different lengths

were used to conduct the experiments (see Table 1). A

set of experiments was carried out to check the accu-

racy of Eq. (1) in predicting the initiation of motion for

]

Fig. 3. Distribution of the obstacles in plane.

able 3

ummary of the experimental hydraulic conditions

ydraulic

onditions

owel

dw Uw XR* Re Fr Y* Xe* LL*

[m] [ms�1] [d ] [d ] [d ] [d ] [d ] [d ]

R D1 0.013 0.27 1.34 1.4E +04 0.76 1.03 1.25 0.19

R D2 0.013 0.27 1.34 1.4E +04 0.76 1.09 1.28 0.29


the test dowels. The incipient motion of the dowels was

detected by eye (as in Bocchiola et al., in press and

similarly to Braudrick and Grant, 2000) and the asso-

ciated values of X* and Y* were computed from flow

measurements. The results are shown in Fig. 1 and also

reported in Table 2. One notes that Eq. (1) provides a

reasonable fit of the results.

4.3. Obstacles

Wood rods are placed vertically into the water and

mounted onto some drilled wood beams, so that they

can be pulled out of the water when necessary. The

spacing among the obstacles was set according to

observations of the spatial density of near channel

standing trees in a field survey of the Branega

River, Liguria (Northern Italy), within the framework

of the bINTERREG 3B DESERNETQ project (see

Rulli et al., 2004). Based on the available dowels’

size and the constraints given by the flume size, the

linear scale ratio for trees’ spatial density was assumed

to be 1 :19. This yields a scaled average inter-obstacle

distance in the flume of L0=0.26 m. This is the

average value of the distance between a rod and its

nearest neighbour, or the average available room for a

dowel across two adjacent rods. The obstacles are

randomly distributed in space (i.e. their coordinates

are extracted independently from a bivariate uniform

distribution, see Fig. 3). Although the spatial distribu-

tion of the trees in nature is likely to be more com-

plex, the uniform probability distribution is taken here

for simplicity. Specific analysis of the vegetation pat-

terns is needed to assess more complex distributions.

Also, different settings of the obstacles (i.e. different

randomly generated distributions of the obstacles)

could be considered.

The obstacle rods have a diameter of 0.01 m, so the

obstruction caused by the obstacle is negligible as

compared with channel width (1 /100).

Table 2

Stability of the dowels

Dowel dw Uw dw Uw

Sliding Sliding Rolling Rolling

[m] [ms�1] [m] [ms�1]

D1 0.016 0.24 0.011 0.14

D2 0.014 0.22 0.011 0.15

D3 0.013 0.22 0.012 0.16

D4 0.014 0.23 0.011 0.15

D5 0.016 0.24 0.012 0.16

D6 0.014 0.23 0.012 0.16

4.4. Scaling issues

Some scaling issues need to be discussed. The

Froude number, Fr, and the Reynolds number, Re, of

the flow field are to be considered (see Table 3). The

first ranges from 0.76 to 0.95, while the second ranges

from 1.4�104 to 5.3�104. These provide conditions

similar to those observed in lowland rivers for low

water depths (e.g. Braudrick and Grant, 2000; Hyge-

lund and Manga, 2003). Also, Fr and the Re are

consistent with those used to build the stability curve

(Bocchiola et al., in press) therefore assuring validity of

the stability criteria. Applying the scale ratio of the

flume to the dowels (1 :19), the rescaled length of the

shortest dowel (0.05 m) is about 1 m (0.95 m). This is

consistent with the lowest limit for LWD (e.g. Jackson

and Sturm, 2002). The length of the other, longer

dowels is scaled accordingly; the length of 0.25 m for

the longest dowel corresponds to about 5 m (4.75 m)

R D3 0.013 0.27 1.34 1.4E +04 0.76 1.02 1.25 0.38

R D4 0.013 0.27 1.34 1.4E +04 0.76 0.96 1.22 0.48

R D5 0.013 0.27 1.34 1.4E +04 0.76 1.11 1.28 0.58

F D1 0.020 0.41 3.15 3.3E +04 0.93 1.65 3.15 0.19

F D2 0.020 0.41 3.15 3.3E +04 0.93 1.65 3.15 0.29

F D3 0.020 0.41 3.15 3.3E +04 0.93 1.65 3.15 0.38

F D4 0.020 0.41 3.15 3.3E +04 0.93 1.52 3.15 0.48

F D5 0.020 0.41 3.15 3.3E +04 0.93 1.72 3.15 0.58

F D6 0.020 0.41 3.15 3.3E +04 0.93 1.71 3.15 0.96

F D1 0.027 0.49 4.58 5.3E +04 0.95 2.24 4.58 0.19

F D2 0.027 0.49 4.58 5.3E +04 0.95 2.35 4.58 0.29

F D3 0.027 0.49 4.58 5.3E +04 0.95 2.35 4.58 0.38

F D4 0.027 0.49 4.58 5.3E +04 0.95 2.50 4.58 0.48

F D5 0.027 0.49 4.58 5.3E +04 0.95 2.39 4.58 0.58

F D6 0.027 0.49 4.58 5.3E +04 0.95 2.33 4.58 0.96

T

S

H

c

d

P

P

P

P

P

J

J

J

J

J

J

F

F

F

F

F

F


for the prototype. Therefore, the experiment can be

thought representative of the behaviour of pieces of

LWD as observed in field surveys.

When considering the dynamic equilibrium of the

logs, one must account for the scaling in the vertical

direction (i.e. related to the dowels’ diameter). From

Eq. (1), the scaling is obtained by taking proper values

of X* and Y*, so the experiments are essentially at 1 :1

scale (i.e. the diameter of the log, the flow velocity and

depth and the bed friction angle need not to be scaled,

but through X* and Y*). When the logs start moving,

the interaction between the vertical and plane scales

depends on the logs’ velocity. As a first approximation,

the result (i.e. stop or not) of the bcollisionQ between a

dowel and an obstacle depends on the velocity reached

by that dowel. For given flow depth and velocity (i.e.

X* and Y*), the moving dowel will reach its highest

(limit) velocity and no more acceleration will occur.

This requires the dowel to travel a given distance. If this

distance is less than the average distance between the

obstacles, the experimental set-up is capable of repro-

ducing the impact of the dowels with the obstacles.

Because some preliminary tests showed the dowels

looked to reach a steady (limit) velocity after covering

a few centimetres, one assumes that these experiments

can mimic reasonably well the real situation occurring

in nature.

4.5. Methods of observation

The procedure for the wood transport experiment

was as follows. Steady values of depth and velocity

were established using the flume circulation facility.

Then, each dowel was positioned inside the channel

and left free to move under the action of the flowing

water. The dowels were positioned perpendicular to

main flow direction, as they were observed to be capa-

ble of self pivoting in a few centimetres, so self asses-

sing their motion very quickly. To mimic a random

effect with respect to the placement of the obstacles,

fifteen different starting positions were examined, tak-

ing different distances from the right side wall of the

flume (i.e. fifteen different values of the abscissa in Fig.

3). These were taken at steps of 5 cm, starting from 15

cm and stopping at 85 cm, to avoid the side effect of the

flume walls. Three runs were carried out for each

starting position.

Three mechanisms of LWD transport are examined.

These are bpure rollingQ (PR), i.e. when the dowel is

touching the channel bed (Y*b1.26); bjust floatingQ(JF), i.e. a condition when the dowel is floating but

the value of Y* is close to the flotation threshold

(Y*i1.26); and bfully floatingQ (FF), i.e. when the

water depth exceeds notably the floating threshold

(Y*N1.26). Three different modes of LWD motion

are associated with the values of X* and Y* shown in

Fig. 1.

A total number of 810 runs were carried out in order

to investigate the different modes of LWD motion and

the different lengths of the dowels. In Table 3 a sum-

mary is given of the experimental conditions.

5. Experimental results

5.1. Observed motion patterns

When the motion of the dowels is in contact with

the bed (for Y*V1.26), the motion mainly occurs by

rolling; and sliding only occurs as a transient process

with very short duration. When the dowel is initially

placed perpendicular to flow, it simply starts rolling.

When the dowel is placed stream-wise, it starts mov-

ing by sliding, until it pivots against some obstacle, or

more likely, because of bed grain roughness. Pivoting

makes the dowel turn perpendicular to the flow. In

case of floating, if the dowel is initially oriented

parallel to the flow, it simply starts floating, acceler-

ating until it reaches a steady state velocity, equating

the surface flow velocity (Braudrick and Grant, 2001).

Conversely, if the dowel is perpendicular to flow,

rolling or standing, it is lifted by the current and it

starts turning, driven by the uneven distribution of

velocity across the flow section. Then, it self-adjusts

its direction to match the flow direction and it con-

verges towards the centreline (see Braudrick and

Grant, 2001, Fig. 2).

5.2. Lodging against obstacles

Two different types of lodging mechanism are ob-

served. These are shown in Fig. 4 and will be referred

to as bbridgingQ and bleaningQ. The first occurs when a

dowel stops by literally bridging between two different

rods. This is a somewhat stable position and it is likely

that, unless some further perturbation occurs (i.e. wood

breaking or very high flows), the wood is going to be

bstoredQ for a long period. With the second option,

bleaningQ occurs when a dowel just leans against a

single rod. This usually occurs when the dowel

approaches the rod at about its centre of gravity, so

achieving a balance of the pivoting forces. Leaning of

the dowels was observed to last in time. In fact, in no

case was a leaning dowel seen to move away after it

had stopped. Therefore, one can assume that leaning is

Fig. 4. Deposition of the wood dowels. Flow direction from right to

left (a) Bridging, Br. (b) Leaning, Le.

able 4

ummary of the experimental results

odging dowel L* rL* Br Le Stop Out

[d ] [d ]

R D1 4.02 2.05 0 43 43 2

R D2 2.93 1.48 0 45 45 0

R D3 2.04 1.01 0 45 45 0

R D4 2.00 0.43 2 43 45 0

R D5 1.96 0.35 0 45 45 0

F D1 4.10 2.12 2 9 11 34

F D2 3.72 1.97 1 15 16 29

F D3 3.80 1.96 3 18 21 24

F D4 3.49 1.66 5 15 20 25

F D5 3.05 1.42 4 24 28 17

F D6 2.51 1.55 17 14 31 14

F D1 – – 0 3 3 42

F D2 – – 1 5 6 39

F D3 – – 1 4 5 40

F D4 3.79 1.95 4 6 10 35

F D5 3.29 1.79 8 9 17 28

F D6 2.67 1.64 8 8 16 29


an effective lodging mechanism. However, the wood is

expected to move as soon as a perturbation (i.e. an

increase in flow depth or velocity) occurs.

These two different modes of lodging can lead to

different processes in rivers. For instance, a bridging

LWD can provide a possible bkey logQ for the formation

of jams. Qualitative experiments showed that when a

moving dowel meet a bridging bkey logQ, the latter is

seldom moved away and in the long run, it leads to the

formation of a jam. In contrast, when a moving dowel

encounters a leaning bkey logQ, the latter can be swept

away or not, depending on the size and momentum of

the moving dowel. In the case where a bkey logQ stands,an accumulation of LWD can start.

The chance that a dowel is deposited by bridging is

associated with its length. A short dowel is not likely to

bridge, as it is unlikely that it meets two rods separated

by a distance smaller than its length. A longer dowel

instead can meet two rods that are separated by a

distance smaller than its length and bridge them.

In the present paper, the events of bleaningQ and

bbridgingQ are assumed to be equivalent from the per-

spective of searching for the probability of lodging,

because they both lead to the deposition of a dowel.

However, these two modes must be approached sepa-

rately in order to understand the lodging process.

5.3. Probability of lodging and lodging position

In Table 4 some statistics are given about the ob-

served lodging dowels. These are the number of stops

(i.e. of retained dowels), divided into leaning (Le) and

bridging (Br). In some cases the dowel travels out of the

obstacle area (Out). In the case of rolling, PR, the dowel

D6 is not reported because it moves for a short track

and, therefore, no significant results can be obtained.

Dowel D6 was used only in the case of floating because

it was capable of travelling for a significant distance.

One notices that the number of stops due to bridging

increases with the dowel’s length. Also, the bridging

mode of LWD capture is observed mainly in case of

floating, JF and FF (31 and 22 cases, respectively) and

only two cases occurred for rolling, PR. This means

that when a log is rolling, the simple touch of an

obstacle is sufficient to stop it. In case of floating,

touching only one obstacle is sometimes insufficient

to stop the log, which can pivot and stop only if another

obstacle is found. Notice further that the number of

boutflowsQ of the dowels (Out in Table 4) is practically

null for the rolling case, while it increases noticeably

T

S

L

P

P

P

P

P

J

J

J

J

J

J

F

F

F

F

F

F

Fig. 5. Spatial distribution of the observed stops and related proba

bility for increasing dowels’ length (top-down) in case of pure rolling

PR. The area of the light circles is proportional to the probability dtostopT (also given in the labels). Unlabelled dots are rods where dnostopT happens for the considered dowel’s length in PR conditions

Notice the spatial sparseness of the stopping of short length dowels

(Llog=0.05 m top) and the increasing segregation effect (i.e. spatia

concentration of the stopping points) as L log increases (see Llog=0.15

m, bottom). Dowel D6 is not considered as it practically always stops

at the first obstacle (explained in the text).


for the JF and FF cases. This indicates that in case of

floating, i.e. for high water depth, logs tend to travel at

length. This is consistent with previous studies on LWD

(e.g. Haga et al., 2002).

Figs. 5–7 show the stopping position of the retained

dowels. For each obstacle, the table reports the proba-

bility that a dowel retained inside the domain stops

there. Consider first the case of PR shown in Fig. 5.

Here, almost all the dowels were retained, therefore

providing a somewhat higher number of samples (45

or so for each dowel). For the shortest dowel (D1, top)

the probability of stopping is quite constant in the

whole domain; this means that the dowel has more or

less the same probability of stopping against each of the

obstacles. Moving towards longer dowels (e.g. D5,

bottom), the probability of stopping increasingly con-

centrates towards the first obstacles. Given equivalent

hydraulic conditions (i.e. the same, or very similar, X*

and Y*), longer dowels have a higher probability to

impact on some obstacle, stopping thereby.

A smaller number of samples is available in the case

of Just Floating, JF, because the dowels often flowed

out of the measuring area (see Fig. 6 and Table 4).

However, one sees a behaviour similar to that shown in

Fig. 5. For the shortest dowels (D1, D2 and D3, top) the

stopping probability is evenly distributed in space. For

the longest dowels (D4, D5 and D6, bottom), the area

with the highest stopping probability shifts progressive-

ly towards the first obstacles. Particularly, dowel D6

(0.25 m), stops with a probability of 70% against the

first obstacles (LTb1 m). Neither is this effect due to a

low amount of samples, as the number of retained

dowels increases with length (e.g. for D6, 31 stop

events are observed). This finding means that increas-

ing the force for motion, a smaller number of dowels is

retained but the longest dowels tend to stop with the

highest frequency (see Table 4 for total number of

stops) close to the starting point (i.e. travelling for

short distances). The result for the fully floating dowels

(FF) are shown in Fig. 7. One notes that the shortest

dowels are seldom retained (Table 4, dowels D1, D2,

D3) and a significant sample (at least 10 stop events) is

available only for the dowels D4, D5 and D6. Increas-

ing the dowel length results in the highest stopping

probability shifting upstream towards the first obsta-

cles. Namely, while D4 (Llog=0.125 m) stops in the

first half of the track (LTb1 m) with a probability of

50%, D5 (Llog=0.15 m) stops thereby with a probabil-

ity of 59% or so and D6 (Llog=0.25 m) with a proba-

bility of 88%.

From Figs. 5–7, one notes that the distance travelled

by a dowel of a given length is not constant under the

-

,

.

l

same flow conditions, but it can be represented only as

a random variable with a specified probability distribu-

tion. Neither is this effect due to different starting


positions (e.g. value of x in Fig. 3) as dowels starting

from the same positions generally stop in different

places.

ig. 7. Spatial distribution of the observed stops and related proba-

ility for increasing dowel length (Top-down) in case of Fully Float-

g, FF. The area of the light circles is proportional to the probability

o stopT (also given in the labels). Unlabelled dots are rods where dnotopT happens for the considered dowel’s length in FF conditions.

gain here a segregation effect is spotted as Llog increases, witnessed

y the highest probabilities observed for the closest rods (see

log=0.25 m, bottom), meaning that the longest dowels tend to travel

r the shortest distances. Dowels D1–D3 are not considered as they

re seldom retained and, therefore, no significant percentages can be

iven (explained in the text).

F

b

in

dts

A

b

L

fo

a

g

One notes that the parameterization of this probability

distribution would require a much larger sample size

than that presented in this preliminary study. This is

because one must assess the dependence of the para-

meters on the flow conditions, dowel size and obstacle

density.

Fig. 6. Spatial distribution of the observed stops and related proba-

bility for increasing dowel length (Top-down) in case of Just Floating,

JF. The area of the light circles is proportional to the probability dtostopT (also given in the labels). Unlabelled dots are rods where no stophappens for the considered dowel’s length in JF conditions. Notice

again the segregation effect as Llog increases, witnessed by the highest

probabilities observed for the closest rods (see Llog=0.25 m, bottom),

meaning that the longest dowels tend to travel for the shortest

distances.

Fig. 8. Average distance travelled by the dowels trapped into the

domain L*.


6. Theoretical approach

6.1. Key variables

The definition of a representative distance is neces-

sary in the interpretation of the dowels’ motion into the

flume. In principle, one could consider the length (ab-

solute value) of the vector linking the starting point to

the lodging one. However, here, only the stream-wise

coordinate is considered (i.e. LT in Fig. 3). This implies

that different starting and lodging position are regarded

as equivalent as far as they possess the same LT, irre-

spective of their x coordinate is. Here, only the stream-

wise travelled distance is considered, independently

from the lateral migration of the LWD. The presence

of clustering zone is also neglected in this case. The

travelled distance is assumed here to be a function of

the characteristic distance between obstacles, L0, of the

dowel’s length, LLog, and of the force applied by the

flow. Three dimensionless groups are therefore intro-

duced. The first is:

L4 ¼ LT=L0 ð5Þ

i.e. the ratio between the travelled distance LT and the

average inter-obstacles distance L0. The second is the

bobstruction ratioQ between the log’s length Llog and L0:

L4 ¼ Llog=L0: ð6Þ

The third group is the excess of force with respect to

the critical equilibrium condition. This can be written

as:

Xe4 ¼ XR4� Xc4

¼ XR4�1:26

Y4� 1

�=2:49 Y4V1:26

�

Xe4 ¼ XR4 Y4N1:26: ð7Þ

For Y* smaller than 1.26, the dowels move by roll-

ing on the bed. The greater the value of X* with respect

to its critical value, the stronger the dowel is pushed by

the flow. When Y* exceeds the floating threshold, 1.26,

the dowel starts floating. Because there is no friction

force exerted by the bed on the floating dowel, the

equilibrium statement of Eq. (1) no longer holds.

Under the assumption that the dowel moves at a thresh-

old flow velocity, the variable describing its motion is

Uw. However, in the group XR* of Eq. (2) the denom-

inator is constant; therefore, considering X* is tanta-

mount as considering Uw, apart from a pure scaling

factor. In case of floating the critical value Xc* is zero.

The idea here is that the dimensionless distance trav-

elled by the dowel L* is a function of LL* and Xe*.

Here, only L0 is taken to be representative of the

distance between the obstacles. One assumes that the

distribution of such distances influences the lodging

probability and location. Here, however, the authors

tentatively try to analyse the dependence of the lodging

process on L0. Notice also that it is not straightforward

that one can easily provide a full description of the

distribution of the observed obstacles in channels (e.g.

the distribution of boulders in rivers, or the distribution

of trees and bushes in floodplains) and a parsimonious

approach, using one only variable, seems appropriate.

6.2. Analysis

The random path of a dowel in a river in presence

of obstacles can be represented in terms of the aver-

age L* and the standard deviation rL* of the dimen-

sionless travelled length L* and of the probability and

type of lodging. Their relationship with the excess of

force Xe* and the log’s obstruction ratio LL* can be

assessed using exploratory statistics of observed data.

Here, a linear regression analysis is carried out, not to

determine the best fitting functions but rather to ex-

plore the capability of the selected variables of

explaining the observed variability of the process,

thus providing a basis for further modelling studies.

Due to the relatively small amount of data here

considered, there is no point in undertaking compar-

isons between complex fitting models, which would

not be conclusive anyway.

Table 3 shows the values of Y*, XR* and the excess of

force, Xe*; these are spatial averages along the flume.

Also, the obstruction ratio of the logs LL* is reported.

Table 4 reports the values of L* for the three examined

flow conditions, PR, JF and FF and the corresponding

standard deviation, rL*. The average L* and the stan-

Fig. 11. Observed probability dto stopT and stop type, depending on

LL*, FF.Fig. 9. Mean square error of the distance travelled by the dowels

trapped into the domain rL*.


dard deviation rL* of the distance travelled by the

retained dowels are plotted against LL* in Figs. 8 and

9, respectively. One notes that the higher the force Xe

(i.e. going from PR to FF), the longer the average

travelled distance L*. Also, an increasing obstruction

ratio LL* is associated with decreasing L*. This shows

that the average distance travelled by LWD in the

presence of obstacles depends on the force exerted by

the water and on the length of the LWD, scaled to the

average distance between obstacles. The standard devi-

ation rL* increases as Xe increases, while it decreases

with increasing LL* (see Fig. 9). Here, the range of

distances travelled widens with an increase of the

water force and narrows with an increase of the length

of the LWD piece.

For JF and FF, the probability that a dowel stops

inside the study area is plotted against LL* in Figs. 10

and 11. This tends to one with increasing dowel’s

length. This is consistent with the idea that long logs

are deemed to stop (i.e. probability close to one).

Conversely, short logs are likely to travel out of the

domain. For increasing force, i.e. increasing Xe*, the

probability that a dowel travels out of the area tends to

increase as well. However, the values of this probability

Fig. 10. Observed probability dto stopT and stop type, depending on

LL*, JF.

are possibly dependent on the size (length) of the

domain adopted here (i.e. 2 m).

The percentage of the observed lodging modes (Br

or Le) is plotted against LL* in Figs. 10 and 11, for Br

and Le, respectively. Although the data show a certain

degree of scatter, it is seen that the percentage of Br

increases with dowel length LL* and that the percentage

of Le decreases consequently. Notice that the two prob-

abilities are bound to intercept the y axis at a value of 0

for Br and of 1 for Le because a very short log can stop

only by leaning.

Table 5 shows the result of data regression analysis

under the present approach. It is seen that the values of

R2 (from 0.61 to 0.94) are quite high, thus indicating

that the association of dimensionless variables adopted

here can provide an insight of the investigated process-

es. The highest values of R2 are associated with the

prediction of the lodging probability. These indicate

that one could consider the wood accumulation process

in rivers using a rather simple dimensionless approach

involving a small set of variables. One notes that Brau-

drick and Grant (2001) investigated the average trav-

able 5

egression analysis of the observed statistics with respect to the force

e* and the dowels’ length LL*

ariable/reg. Coeff. [d ] St. Er. [d ] p-val [d ] R2 [d ]

* Intercept 3.128 0.302 1.0E�04

Xe* 0.461 0.097 6.1E�04

LL* �2.693 0.529 3.5E�04 0.75

L* Intercept 1.211 0.272 9.9E�04

Xe* 0.365 0.088 1.6E�03

LL* �1.432 0.478 1.2E�02 0.61

top Intercept 1.000 – –

Xe* �0.245 0.012 1.0E�04

LL* 0.419 0.080 1.0E�04 0.94

e Intercept 1.000 – –

Xe* �0.312 0.120 2.0E�02

LL* �0.023 0.018 2.2E�01 0.76

T

R

X

V

L

r

S

L


elled distance (m) of the dowels by visual correlation

with Llog /wav, Llog /Rc and db /dav (see page 273, Fig.

8a, b, c). They also performed a linear regression

analysis between the bdebris roughnessQ and the dis-

tance travelled by the wood dowels, but they found

somewhat poor determination coefficient R2 (less than

0.1, see page 272, Table 5). Also, Braudrick and Grant

(2001) visually correlated the percentage of retained

wood into the flume (number of trials with retained

wood) with Llog /wav, Llog /Rc and db /dav (pag. 277,

Fig. 9a, b, c). They did not find any significant corre-

lation (see page 276). Although the experiment by

Braudrick and Grant (2001) is somewhat different

from the present one, it is noted that the theoretical

approach presented here improves substantially the pre-

vious approaches to LWD transportation in rivers. In

this sense, this study represents an improvement in the

field of LWD transport models and can be considered a

reliable basis for further research.

7. Conclusions

The transport of LWD into a reach where obstacles

are present is a complex process, involving a combina-

tion of random factors and deterministic mechanisms.

The present approach involves a simplified sketch of

vegetation, river geomorphology and hydraulic geom-

etry of stream flows, in order to describe the situation

when dead or living in-channel vegetation is present, or

morphologic constraints provide altered conveyance.

The distance travelled by a piece of LWD is a random

variable, whose expectation and variance depend on the

length of the piece, the inter-obstacle spacing and the

force exerted by the current. The probability that a

piece of LWD is stopped and also its stopping mode,

either by leaning against one obstacle or by bridging

two obstacles, also depends on the length of the LWD

and on the flow conditions. The simple theoretical

framework presented in Section 6 shows that LWD

transport process can be explored using an appropriate

dimensionless approach based on well-defined physical

quantities. As compared with previous investigations,

this approach provides a more comprehensive descrip-

tion of the key variables involved, also introducing a

simple and effective theoretical framework for model-

ling and predictive purposes. Because the distribution

of LWD influences the formation of wood structures in

rivers, these results are of interest for both researchers

and river managers.

Further developments will include the definition of

the general shape of the travelled length distributions

and of their dependence on the control variables

introduce here. Also, the study of more complex

LWD geometry, including roots and foliage, should

be considered. Further, the formation of jams requires

specific focus, because of its high potential in en-

hancing flood risk, especially in those rivers where

man-made structures yield supplementary obstacles to

the water flow and to LWD. Eventually, the present

results, although preliminary, can provide an interest-

ing insight of LWD transport in rivers and, more

generally speaking, can contribute to the understand-

ing of the interaction between woody debris and river

morphology.

Acknowledgments

The authors kindly acknowledge Eng. Davide

Motta, Chiara Narciso and Alessandro Greppi for

their contribution to this research, in partial fulfillment

of their Master’s thesis at Politecnico di Milano. Also,

the authors thank Dr. Silvia Bozzi and Dr. Matteo

Spada for their contribution in the research. This

work was supported by the GNDCI of the National

Research Council (CNR) of Italy (contract n.

00.00545.PF42), by INRM through the project

bAnalysis of hydrological and sedimentological re-

sponse in burned areasQ and by the Liguria region

through the bINTERREG 3B DESERNETQ project.

Funding for the present work was also granted from

the European Community, through the project

bIRASMOSQ (Contract FP6-2004-Global-3-018412).

The authors acknowledge two anonymous reviewers

for their accurate work that helped to improve the

quality of the paper.

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