Review

A review of surface erosion and sediment delivery models for unsealed roads

Baihua Fu a, Lachlan T.H. Newham a,*, C.E. Ramos-Scharro ́n b

a The Integrated Catchment Assessment and Management Centre, The Fenner School of Environment and Society, The Australian National University, Linneaus Way, Building 48A,

Canberra ACT 0200, Australia

bDepartment of Geography and the Environment, University of Texas-Austin, 1 University Station, A3100, Austin, TX 78712, USA

article info

Article history:

Received 21 April 2009

Accepted 22 July 2009

Available online 14 August 2009

Keywords:

Modelling

Road erosion

Unsealed road

Sediment

Road drainage

Sediment delivery

abstract

This paper reviews available models for estimating surface erosion and sediment delivery to streams

from unsealed roads. It summarises current progress and identifies directions for ongoing research and

model development. The paper provides a framework for assessing road erosion and sediment delivery

models and it includes an overview of road erosion and sediment delivery processes and how they are

commonly represented in models. Seven road models are reviewed in terms of their representations of

erosion and sediment delivery processes, assumptions, application and limitations. While simple models

are thought to be more useful and easily applied for land management purposes, more complex models

provide a basis for building and consolidating scientific knowledge. This article reveals some of the

limitations and needs of existing road erosion models. These include limitations of their ancestor

hillslope erosion models, the imbalance between representation of erosion processes versus sediment

delivery, a lack of representation of subsurface flow interception and the lack of model testing and

uncertainty analysis. One of the most fundamental limitations to developing improved models of road

erosion and delivery is access to data of an appropriate standard.

2009 Elsevier Ltd. All rights reserved.

1. Introduction

The significance of unsealed roads to off-site water quality

decline is widely acknowledged, especially in forested catchments

(Anderson and MacDonald, 1998; Croke et al., 1999b; Forsyth et al.,

2006; Grayson et al., 1993; Motha et al., 2004; Ramos-Scharro ́n and

MacDonald, 2007c). Erosion rates from unsealed roads have been

shown to be much greater than in adjacent undisturbed hillslope

areas. For example, Ramos-Scharro ́n and MacDonald (2007b) and

Croke et al. (1999b) observed erosion rates of four and six orders of

magnitude higher than from undisturbed hillslope areas in the U.S.

Virgin Islands, and coastal southeast Australia, respectively. The

development of cost-effective land management decisions requires

an adequate understanding of road erosion and sediment delivery

processes for effective planning and execution of mitigation activities. Road erosion and sediment delivery models provide a quantitative tool to assess and guide those activities.

The general approaches used to quantify erosion from roads

include field-based roadside or streammonitoring, sediment tracing

experiments and the use of road erosion models. Roadside sediment

traps provide useful information on coarse sediment yields (i.e. sand

and gravel) but they are prone to losses of the finer sediment fractions (i.e. clay and silt) (Robichaud and Brown, 2002; RamosScharro ́n and MacDonald, 2007b). Highly variable bedload inputs

and the unpredictable efficiency of sediment traps results in high

uncertainty in measured sediment yields when sediment trap data

is used to estimate total sediment yields (Sheridan and Noske, 2007).

Other more reliable but field-intensive and expensive monitoring

methods are available. For example, Sheridan et al. (2006) use

a design consisting of a bedload trap, a tipping bucket for measuring

discharge, and a split sampler for measuring suspended load. Stream

monitoring techniques can provide information on the integrated

effect of variable sources of erosion but the contribution from roads

at the catchment scale is often difficult to specify due to the mixing of

sediment from multiple sources and the complexity of processes

controlling sediment routing and deposition.

Environmental tracers such as fallout radionuclides have been

used successfully in forest road erosion studies to isolate the

sediment contribution of roads at catchment scales (Wallbrink

et al., 2002). However, many sediment tracing results are affected

by factors such as stream water geochemistry, organic matter and

particle-size sorting (Foster and Lees, 2000). The influence of these

factors can make interpretation of sediment tracing results difficult

(Fu et al., 2006).

* Corresponding author. Tel.: þ61 2 6125 8129; fax: þ61 2 6125 8395.

E-mail address: lachlan.newham@anu.edu.au (L.T.H. Newham).

Contents lists available at ScienceDirect

Environmental Modelling & Software

journal homepage: www.elsevier.com/locate/envsoft

1364-8152/$ – see front matter 2009 Elsevier Ltd. All rights reserved.

doi:10.1016/j.envsoft.2009.07.013

Environmental Modelling & Software 25 (2010) 1–14
Models have the advantages of allowing catchment-scale

assessment which is an important consideration for prioritising

catchment management effort. Model results can be used to

reconstruct the effects of past disturbances, assess current conditions or estimate future management scenarios. Models used to

assess other aspects of water quality have been extensively developed and applied in the last half century, and are therefore more

highly developed and have been more thoroughly tested than road

erosion models.

The purpose of this review is to take stock of recent progress in

road erosion modelling and to provide guidance for future research

and model development. The review is constrained to focus on

techniques for estimating surface erosion and delivery of roadderived sediment to streams. No consideration is given to in-stream

processes.

2. Overview of road erosion and sediment delivery processes

The integrated effect of erosion and sediment delivery dictates

the amount of sediment reaching a stream or any other waterbody.

For the purpose of this paper, road erosion is defined as sediment

detachment and deposition processes occurring on the surface of

road features, including cutslopes, ditches and fillslopes; sediment

delivery specifically refers to the delivery of eroded sediment from

road features to stream networks. Mass wasting processes are not

considered here.

2.1. Definition of road features

Unsealed roads lack surface protection afforded by tar- or

cement-based materials. A typical unsealed road cross section

contains all or a subset of the features shown in Fig. 1. A consistent

nomenclature is used throughout this paper but terms may vary

locally.

The road surface is the compacted area used to support traffic. A

ditch is the drainage structure along one or both sides of a road that

acts as a conduit for runoff and associated sediment. Road surfaces

can be insloped, outsloped or crowned. Insloped roads deliver

runoff to the ditch while outsloped roads deliver runoff to the

fillslope, usually via a diffuse pathway. Ditches are usually absent

on low traffic, outsloped roads. Crowned roads deliver part of their

runoff to a ditch and part to a fillslope. Cutslopes are the slope of

a cutting, while a fillslope is the slope of a fill. The hillslope connecting the fillslope to a stream is referred to as the lower hillslope

area, while the hillslope above cutslopes is referred to as an upper

hillslope area.

The two most common drainage structures used for unsealed

roads are: (i) mitres/push-outs and (ii) culverts. A mitre/push-out is

an excavated drain constructed at an angle to the road, allowing

runoff to drain away from the road surface and onto a fillslope or

a lower hillslope area. A culvert is a conduit constructed under the

road surface that delivers runoff from a ditch on the upper hillslope

side of a road. A road segment is that length of road draining to

a drainage structure or stream-crossing. The width of the road

surface is the distance between the break from the cutslope or the

ditch to the road surface, to the break of slope from road surface to

the ditch or the fillslope. The contributing road surface area is the

upslope area of road that connected to a drainage point. It is usually

determined by the combination of the effective road width and the

road segment length.

2.2. Factors affecting erosion from unsealed roads

Sediment can be eroded from all road features. On unsealed

roads, road surface erosion is generally the dominant source of

sediment (e.g. Ramos-Scharro ́n and MacDonald, 2007b), and much

more common than mass wasting (Ketcheson et al., 1999). The

factors affecting surface erosion from roads include rainfall intensity and duration, snowfall, the characteristics of surface materials,

the hydraulic characteristics of the road surface, road slope, traffic,

construction and maintenance, and the contributing road area

(MacDonald and Coe, 2008). Rainsplash and flow energy are the

primary energy sources that cause surface erosion of road features

in most areas.

Snowfall can also influence erosion processes. Snow cover,

especially when prolonged, reduces erosion by shielding the road

surface from raindrop energy and by slowing overland flow at the

snow–soil interface. The result is that surface erosion rates on roads

during snowmelt are considerably less than during rainfall events.

This is illustrated by Vincent (1985) who showed that the road

surface sediment yields caused by snowmelt in the mountains of

Idaho, U.S. were less than 10% of the total annual sediment

production, while the remaining 90% was caused by rainfall.

Snow also affects the road surface hydrology. Although snowmelt rates are usually relatively lower than rainfall rates, the

additional runoff generated during rain-on-snow events and the

increased duration of saturated conditions can be a trigger of

increased erosion, mass wasting and suspended sediment yields in

Fig. 1. A typical cut-and-fill road cross section and features. The dashed lines indicate the hillslope profile prior to the construction of the road.

2 B. Fu et al. / Environmental Modelling & Software 25 (2010) 1–14
streams (Bulygin et al., 2006; Harr, 1981; Pentz and Kostaschuk,

1999; Rekolainen, 1989; Weigert et al., 2003).

The surface materials of unsealed roads are often locally sourced

and may contain a high proportion of fine particles that are easily

eroded. The erodibility of road surface materials is determined by

many attributes including cohesiveness, particle-size distribution,

organic matter content, and permeability (Geeves et al., 2000).

Road surfaces that have low cohesiveness, high silt or fine sand

content, low rock or gravel content, and low organic content tend to

be most erodible (Geeves et al., 2000). Unsealed road surfaces have

typically low infiltration rates due to compaction, which lead to

higher level of infiltration excess overland flow than on undisturbed hillslope areas (Croke et al., 1999a; Ramos-Scharro ́n and

MacDonald, 2007c). With little vegetation cover, unsealed road

surfaces typically have much greater erosion rates than adjacent

hillslope areas. Concentrated flows in ruts have been observed to be

a dominant sediment source from unsealed roads (Elliot et al.,

1999a) but exceptions have been noted (e.g. Sheridan and Noske,

2007).

Slope steepness has long been recognised as an important factor

in soil erosion by water (Wischmeier and Smith, 1965) with steeper

roads tending to have greater erosion rates. Ramos-Scharro ́n and

MacDonald (2005) demonstrated that sediment yield increases

exponentially with increasing road slope for roads that are regularly graded (at least once every two years). Luce and Black (1999)

found that sediment yield normalised by slope length is linearly

related to the square of the road slope.

Traffic volume has been observed to be one of the major factors

affecting surface erosion from unsealed roads (Grayson et al., 1993;

Luce and Black, 1999; Ramos-Scharro ́n and MacDonald, 2005; Reid

and Dunne, 1984; Sheridan and Noske, 2007; Ziegler et al., 2001b).

This is because the coarse particles on the road surface can be

broken down by vehicles through crushing and abrasion. Fine

particles below the surface layer may also be pumped to the surface

by compaction caused by traffic (Reid, 1981; Dube ́ et al., 2004).

More frequent traffic (Croke et al., 2006; MacDonald et al., 2001),

heavier vehicles (Sheridan and Noske, 2007), and traffic during wet

weather (Coker et al., 1993; Ziegler et al., 2001b) all result in higher

sediment yields. As an illustration, Croke et al. (2006) found that

sediment yields (normalised by road length and slope) are up to 30

times greater on high traffic roads than low traffic roads in coastal

southeast Australia.

Newly constructed roads often have higher surface erosion rates

than older roads. This is likely due to the protection afforded by

vegetation and/or rock armouring of the road surface, cutslopes,

ditches and fillslopes on older surfaces (Megahan, 1974). Some

maintenance activities such as grading may also increase road

runoff and surface erosion in the first few years due to disturbance

of the road surface (Forsyth et al., 2006; Luce and Black, 1999).

Sugden and Woods (2007) reported 63% and 86% declines of sediment yields in the second and third year, respectively, after grading

in western Montana, U.S. A similar trend is also reported for forest

roads in the U.S. Virgin Islands (Ramos-Scharro ́n and MacDonald,

2005). However, it is important to note that not all road maintenance activities increase sediment yields. Well maintained roads

may also be better drained, resulting in lesser sediment delivery to

streams in the long term.

The role of cutslopes on road erosion, including generating

additional runoff and sediment, has been investigated in several

studies (Croke et al., 2006; La Marche and Lettenmaier, 2001;

MacDonald et al., 2001; Megahan et al., 2001; Riley, 1988).

MacDonald et al. (2001) reported that subsurface flow interception

from cutslopes increases road runoff, and hence road surface

erosion, and is mainly controlled by the area of the upper hillslope.

Cutslope erosion caused by rainsplash, surface flow and mass

failure can also be significant in some areas. For example, sediment

yields of up to about 250 t ha1 yr1 were reported from granitic

cutslopes on forest roads in Idaho, U.S. (Megahan et al., 2001).

These yields are roughly equivalent to the road surface erosion rates

of 200–250 t ha1 yr1 reported for the same area (Ketcheson et al.,

1999). Several characteristics of the cutslope, including slope,

height, vegetation cover, geology and soils were identified as

affecting erosion rates from the cutslope (Collison and Anderson,

1996; Megahan et al., 2001). Collison and Anderson (1996) found

that vegetation cover played a significant role in controlling cutslope stability together with the permeability of the soil, soil

strength and the cutslope height. However, Megahan et al. (2001)

reported that the slope of the cutslope may be a more significant

factor than its height in affecting sediment yields. No studies were

found that investigated the delivery potential of sediment generated from cutslopes independent of the road surface, but delivery

ratios of up to 75% have been assumed by Ramos-Scharro ́n and

MacDonald (2007b). This is likely due to the difficulty in distinguishing sediment from cutslopes and road surfaces once mixed.

An analysis of particle-size fractions may suggest the delivery

potential of cutslope sediment. Sediment tracing techniques may

also be useful to discriminate sediment from cutslope and road

surface sources.

Studies of erosion from ditches and fillslopes are less detailed

than studies of road surfaces and cutslopes. This is likely due to

a perceived small long-term contribution to road erosion and the

difficulty in distinguishing sediment from ditches and road surfaces

once mixed. Nevertheless, ditches and fillslopes are potentially

important sediment sources particularly when erosion is caused by

scour from road runoff. Ditches may deepen or widen, or be filled

with deposited sediment during rainfall events (Croke et al., 2006;

Lane and Sheridan, 2002). Sediment eroded from the road surface

and deposited in ditches or on fillslopes can be remobilised in

subsequent rainfall events. Croke et al. (2006) reported that while

coarse sediment is usually trapped in ditches during most low to

moderate rainfall, it is washed off in large events (rainfall intensity

greater than 110 mm h1

). Uncompacted fillslopes are prone to

sheet and rill erosion and scour, especially from concentrated flow

from drainage outlets. Lane and Sheridan (2002) suggested that

fillslope erosion was primarily responsible for bedload sediment

downstream of a road-stream crossing in the Central Highlands of

Victoria, Australia, during a five-month period of monitoring.

Mass wasting processes may be significant sediment sources

from cutslopes and fillslopes, especially in steep and wet forested

regions (Sidle et al., 2006). Such processes include instantaneous

and progressive mass failures (Megahan et al., 1978, 1983; Swanson

and Dyrness, 1975; Wemple et al., 2001) and dry creep (Megahan,

1978). Mass wasting processes are most often observed on cut-andfill roads but may also be triggered by high drainage concentrations

from ridge-top roads (Montgomery, 1994). Mass wasting occurs as

a result of processes that differ from those responsible for surface

erosion and hence models of mass wasting warrant separate evaluation to those of road surface erosion. This paper focuses on

models of surface erosion only.

2.3. Road surface erosion rates

Road surface erosion rates have been previously reviewed (Dube ́

et al., 2004; Ramos-Scharro ́n and MacDonald, 2005, 2007c). These

reviews considered a range of roads with different locations,

lithologies, climate zones, road conditions and traffic levels. Dube ́

et al. (2004) reviewed 17 road erosion studies, most conducted in

mountainous regions of the western U.S.. The annual sediment

yields ranged from 0.4 g m2 mm1 yr1 (mm refers to rainfall) for

non-traffic roads to 860 g m2 mm1 yr1 for fine gravel surface

B. Fu et al. / Environmental Modelling & Software 25 (2010) 1–14 3
roads under moderate to heavy use (Dube ́ et al., 2004). RamosScharro ́n and MacDonald (2007c) reviewed studies of small scale

erosion from unsealed roads. The sediment concentrations they

reported ranged from less than 100 mg L1 to up to 227,000 mg L1

.

These reviews suggest a very large range of road erosion rates

across different areas. Table 1 provides a summary of estimated

road erosion rates from studies published since 2000.

2.4. Road sediment delivery to stream networks

Almost all unsealed road surfaces are erodible, but not all

eroded materials reach streams. This is due to deposition between

the original location of the sediment, drains and streams. Factors

affecting the efficiency of sediment delivery from roads include the

placement and type of drainage structures, the distance from

drainage outlets to streams, contributing area, hillslope slope and

degree of concavity and the trapping efficiency of obstructions

(Megahan and Ketcheson, 1996).

As shown in Fig. 1, surface flow is usually drained to ditches,

after which it is redirected by mitres/push-outs or culverts. Roadderived sediment can reach the stream directly at road-stream

crossings, and indirectly via diffuse, partial or fully gullied pathways. Diffuse and partly gullied flow pathways are less effective

than fully gullied pathways in delivering sediment to streams

(Croke and Mockler, 2001; La Marche and Lettenmaier, 2001).

The most efficient form of sediment delivery occurs at roadstream crossings where virtually all generated sediment is delivered to a stream (Croke et al., 2005; Lane and Sheridan, 2002). Lane

and Sheridan (2002) investigated the impacts of road-stream

crossings on downstream water quality in the Central Highlands of

Victoria, Australia, and showed that a coarse-fragment metalled

road increased suspended sediment loads by 250% downstream

from a road-stream crossing. Most of the sediment was observed to

be sourced from the fillslope and the unsealed road side.

Partial or fully gullied pathways occur when fillslopes and/or

lower hillslopes are eroded by road runoff. Croke and Mockler

(2001) used contributing road length and the slope of the lower

hillslope at the drain outlet to derive a gully initiation threshold for

cut-and-fill roads. Fillslope curvature was also reported by La

Marche and Lettenmaier (2001) to be an important contributing

factor to gully formation below culverts.

The least efficient road-stream connection is via diffuse pathways. Major factors affecting the delivery of sediment via diffuse

pathways include rainfall intensity and duration, volume of erosion,

contributing road area, lower hillslope properties such as slope and

vegetation cover, and road to stream distance (Croke et al., 1999a;

Hairsine et al., 2002; Megahan and Ketcheson, 1996).

3. Modelling road erosion

3.1. Types of road models

The representation of physical processes and complexity vary

greatly in road models, so multiple categorisations are required to

separate and describe road models. Road models may be categorised into two families depending on the modelling approach:

empirical and physics-based models. Empirical models are based

on statistical relationships between responses and independent

variables, and they are derived from empirical observations (Merritt et al., 2003). Physics-based models are based on a hydrological

response model that simulates infiltration and runoff routing, and

mass or energy conservation equations that describe erosion and

sediment delivery processes often in a high level of detail (Merritt

et al., 2003).

Table 1

A summary of reported sediment yields from studies published post-2000. Note that traffic estimates are reported directly from the original publication and direct comparison

between studies is difficult.

Sources Location Spatial scale Method Road

surface

Average

rainfall

(mm yr1

)

Traffic (Annual

return passes)

Contributing

area (m2

)

Slope

(%)

Sediment

load

(t yr1

)

Annual sediment

erosion rate

(g m2 mm1 yr1

)

Annual-averaged data

Sheridan and

Noske, 2007

Victoria,

Australia

Segment

(surface þ ditch)

Drain outlet

monitoring – as

per Sheridan

et al. (2006)

Unsealed 723 1319 (light vehicles) 711 4 1.4 2.7

892 54 (light vehicles) 558 12 0.7 1.4

1161 51 (light vehicles) 415 11 1.1 2.3

Gravel 855 3369 (heavy vehicles) 1000 4 0.5 0.6

MacDonald

et al., 2001

U.S. Virgin

Islands, St. John

Segment

surface þ ditch)

Filter fabric dam

and culvert socks

Unsealed 1150 Very high (leading to

tourist camp)

760 9 4.0 4.6

Medium 405 4 0.1 0.2

Low 630 14 1.5 2.1

Sidle et al.,

2004

Peninsular

Malaysia.

Segment

(surface þ ditch þ

cutslope þ fillslope)

Volumetric

estimation via

observation of soil

pedestal heights

Unsealed 2654 High 4140 – 113  8 10.3  0.8

Sources Location Spatial scale Method Road

surface

Rainfall

intensity

(mm hr1

)

Duration

(min)

Traffic Contributing

area (m2

)

Slope

(%)

Sediment

load (kg)

Hourly sediment

erosion rate

(g m2 mm1 hr1

)

Event-based data

Croke et al.,

2006

Bermagui,

Australia

Segment

(surface þ ditch)

Rainfall simulator

and flume – as

per Bos et al. (1991)

Unsealed 75 30 Main access road 200 4 110 3.7

110 * 30 Main access road 200 4 150 3.4

Segment (surface þ

ditch þ cutslope)

75 30 Feeder access road 600 5 50 0.6

110 * 30 Feeder access road 600 5 40 0.3

Ziegler et al.,

2001a

Pan Khum

village,

Thailand

Plot (surface) Rainfall simulator Unsealed 107 61.2 – 3 14 6 19.1

108* 10.6 – 3 14 1 0.5

115 46.5 – 3 26 16 35.9

*: Successive events.

4 B. Fu et al. / Environmental Modelling & Software 25 (2010) 1–14
Depending on the temporal scale of model simulation, a road

model can be categorised as event-based or continuous. Eventbased models simulate erosion and delivery as a result of single

rainfall-runoff events, while continuous models estimate sediment

yields resulting from multiple rainfall-runoff events. Outputs from

continuous models are sometimes reported as annual average

volumes. Empirical models are generally continuous models and

physics-based models are usually event-based.

Models may also be categorised on the basis of their spatial scale

of application into plot, segment and catchment-scale models.

Most road models are developed for their application on segment

scales and include descriptive parameters that characterise major

road features. Plot-scale road models focus on detailed quantification of infiltration runoff and erosion processes on a particular road

feature such as the road surface. Catchment-scale models consider

roads as a component of a catchment and often involve all road

features, including the upper and lower hillslopes.

Depending on the capability of the model to predict sediment

production rates for various size classes, road models are classified

into single-size and multiple-size models. Models that do not

differentiate between particle sizes are regarded as single-size

models. Multiple-size models estimate sediment yields for a range

of particle-size distributions. Multiple-size models are potentially

advantageous in water quality studies because many sedimentassociated pollutants are preferentially attached to fine particles

(Aksoy and Kavvas, 2005), and particle size is also an important

factor that controls sediment delivery. However, data computations

and process representations are greater for multiple-size models.

As described in Section 2.1, a road contains many features.

Single-feature models estimate erosion and delivery from a single

road feature, most often the road surface. Multi-feature models

include two or more road features.

3.2. Typical road model

A road model typically includes an erosion and a delivery

module. The simplest road models generally consider inputs from

surface erosion only, and model the delivery of sediment by

a sediment delivery ratio (SDR)-like approach. Unlike a traditional

catchment-scale SDR approach, the ratio of sediment delivery to

a stream to the total sediment generated from a road feature is

defined here as SDRR-S. Moderately complex road models usually

consider cutslopes as sediment sources. They also investigate

features of fillslopes or lower hillslopes, such as length and steepness, as components in delivering sediment to a stream. The most

complex models include representation of detailed erosion

processes on both cutslopes and road surfaces, and a larger number

of components in sediment delivery, such as transport and deposition through ditch and fillslope, gully initiation, and sediment

particle-size sorting. Fig. 2 shows a ‘generalised’ road model and

indicates the levels of complexity associated with various

approaches. Note that complexity is also influenced by the level of

spatial detail inherent in the application of a model. A simple model

that is applied in a highly spatially disaggregated fashion has

resulting relatively high overall complexity.

4. Existing road models

Four empirical models and three physics-based models are

reviewed here in terms of their process representation, assumptions, applicability and limitations. These models are selected on

the basis of their current use and/or development, and diversity of

process representation. All the models were developed in the last

half century and have sufficient technical documentation to enable

informed comparison.

4.1. Empirical road models

4.1.1. WARSEM

The Washington Road Surface Erosion Model (WARSEM) is an

empirical model used to estimate long term average road-derived

sediment delivered to the stream network. It was developed by the

Washington State Department of Natural Resources (Dube ́ et al.,

2004). WARSEM was developed as an Access database application,

but has been integrated into a GIS model (SEDMODL) (Dube ́ et al.,

2004). WARSEM is an iteration of the earlier R1-R4 and BOISED

models and shares many common characteristics with those

models. R1-R4 and BOISED were developed for application in the

northern Rocky Mountains, U.S. (Ketcheson et al., 1999).

WARSEM is spatially distributed by road segment and the

sediment outputs have a single size fraction. It considers multiple

features including the ditch, cutslope and the road surface. WARSEM can be applied at large catchment scales and the effects of

a variety of best management practices enable the model to be used

to aid catchment decision making.

The acknowledged assumptions of the model include that: road

segments over 200 feet (approximately 60 m) from a stream do not

deliver sediment; fillslope erosion is negligible; and the ditch and

road surface respond similarly to the input factors (Dube ́ et al.,

2004).

4.1.1.1. Erosion module. A maximum of 15 data inputs are required

but these vary according to the intended purpose of the modelling

exercise (Dube ́ et al., 2004). These inputs include annual average

rainfall, road surface materials, vegetation cover, slope, traffic and

maintenance, and the contributing area for road surface, cutslope

and ditch. The majority of data inputs are specified for individual

segments of a road network.

A base erosion rate is estimated from average annual rainfall

corrected for snowfall and modified by factors values derived from

published studies (Dube ́ et al., 2004). The equations of WARSEM are

(Dube ́ et al., 2004):

E 1⁄4 ðRs þ CsÞ  Ag (1)

where E is total sediment delivered to a stream from each road

segment (t yr1

), Rs is road surface and ditch sediment delivered to

a stream from each road segment (t yr1

), Cs is cutslope sediment

Cutslope Road surface 

Ditch 

Stream 

Fillslope / lower 

hillslope

Gully 

Erosion module 

Delivery module 

Fig. 2. Conceptual framework of road models indicating low (double solid line),

moderate (solid line) and high (dashed line) levels of complexity.

B. Fu et al. / Environmental Modelling & Software 25 (2010) 1–14 5
delivered to a stream from each road segment (t yr1

), and Ag is

a road age factor (dimensionless). And,

Rs 1⁄4 G  Sf  T  L  W  S  Er  SDRRS (2)

Cs 1⁄4 G  Cf  L  H  Er  SDRRS (3)

Er 1⁄4 a  Rb (4)

where G is a geologic erosion factor (dimensionless), Sf is a road

surfacing factor (dimensionless), T is a traffic factor (dimensionless), L is the segment length (feet), W is the road surface and ditch

width (feet), S is a road slope factor (dimensionless), Er is an erosion

rate based on a rainfall factor (t acre1 yr1

), SDRR-S is an empirical

sediment delivery factor (dimensionless) described later, Cf is

a cutslope cover factor (dimensionless), H is cutslope height (feet),

R is average annual rainfall (inches), and a and b are empirical

parameters.

4.1.1.2. Delivery module. The delivery of road-derived sediment to

a stream is modelled using a SDRR-S, determined by the downslope

distance between the drainage outlets and the stream, based on the

study of Megahan and Ketcheson (1996). Values of 100%, 35% and

10% are given when the distances between road drainage and

stream are 0, 1–100, and 101–200 feet, respectively (Dube ́ et al.,

2004).

4.1.2. USLE and modifications

The Universal Soil Loss Equation (USLE) (Wischmeier and Smith,

1965, 1978) is a commonly-used hillslope-erosion model that was

developed in the 1950s for application on agricultural land in the

eastern U.S.. The outputs of USLE are annually-averaged and singlesized. The USLE has been modified in the last few decades and its

modifications include the Modified Universal Soil Loss Equation

(MUSLE) (Williams, 1975) and the Revised Universal Soil Loss

Equation (RUSLE) (Renard et al., 1991, 1997). The USLE and its

modifications are empirical models used to estimate net erosion,

hence they do not consider sediment delivery processes.

The greatest limitation of the use of USLE and its modifications

for road erosion modelling is that even though it is based on

statistical relationships from over 10,000 plot scale observations,

none of these originate from road segments. Consequently, using

these models to estimate erosion from unsealed road surfaces is

questionable, mainly due to the differences in soil properties and

usage between agriculture lands and unsealed road surfaces. Road

surfaces are typically more compacted than agriculture lands

(Ziegler et al., 2000). Traffic levels, which are not currently

considered in the USLE, are one of the most important factors

contributing to road surface erosion. In contrast, levels of vegetation cover and tillage effects are important factors to be considered

for the estimation of erosion from agriculture soils. The RUSLE has

been reported to overestimate sediment yields by an order of

magnitude for soil erosion from snig tracks in eastern Australia

(Croke and Nethery, 2006). Although some studies have applied

USLE or its modifications on unsealed roads (e.g. Farabi and James,

2005; Megahan et al., 2001; Sheridan et al., 2006), none are supported by detailed testing of the factor values.

4.1.2.1. Erosion module. The USLE estimates erosion based on five

empirical input variables: rainfall erosivity, surface material erodibility, slope, area and cover:

A 1⁄4 R  K  L  S  C  P (5)

where A is the long term average annual soil loss (t ha1 yr1), R is

the rainfall erosivity factor (MJ mm ha1 hr1 yr1

), K is soil erodibility factor (t hr MJ1 mm1

), L is hillslope length factor (dimensionless), S is hillslope slope factor (dimensionless), C is land use

factor (dimensionless), and P is the support practices factor

(dimensionless) (Foster et al., 1981; Wischmeier and Smith, 1978).

Traffic and maintenance factors may potentially be modelled via

the USLE P factor but no published studies were found to support

such an approach. Further, Sheridan et al. (2008) argued that the K

factor is inappropriate for road applications because it over-represents the significance of rill processes.

It is recommended that the USLE should not be used for estimating road surface erosion until formal tests and modification of

the model are conducted. Nevertheless, the USLE provides a simple

framework for the estimation of erosion rates. In fact, WARSEM can

be seen as a modification of the USLE because WARSEM is framed

within a similar model structure as the USLE, but with modified

approaches to calculate the factor values and the inclusion of

additional factors specially designed for road surface erosion.

4.1.3. ROADMOD

ROADMOD uses a vector-based GIS to predict annual roadderived sediment yield by an empirical relationship between road

erosion rates and road surface conditions and a series of network

algorithms (Anderson and MacDonald, 1998). The empirical relationships were specifically developed for the U.S. Virgin Islands.

ROADMOD is a spatially distributed model (by road segment)

whose outputs are annual-averaged and single-sized.

The major limitation of ROADMOD is that the sediment

production algorithm was determined by measuring the crosssectional area of ‘missing’ road surface material (including rill

erosion and compaction) since construction and grading at a single

location. Therefore, its applicability to conditions different to those

for which it was developed is questionable. The model assumes

that sediment deposition on the road surface is negligible, that no

significant sediment is contributed from the cutslopes, ditches and

fillslopes, and that erosion rates are consistent over space and time

(Anderson and MacDonald, 1998).

4.1.3.1. Erosion module. The road surface is the only sediment

source considered in ROADMOD. The controlling factors used for

model inputs are road slope and contributing road area. An

empirical study suggested that sediment yield is linearly related to

the road drainage area and road slope (Anderson and MacDonald,

1998):

E 1⁄4 a þ b  A  S (6)

Here E is annual average sediment yield from per metre road

surface (m3 m1 yr1

), A is the contributing road area (m2), S is the

road slope (m m1

), and a and b are empirical parameters. Total

sediment yield (m3 yr1

) from a road segment is calculated by

multiplying E by the segment length L (m). An assumed bulk

density parameter is used to convert the volumetric estimate to

a mass.

ROADMOD uses a vector GIS road network with road segments

as the basic mapping units. Model parameters are assigned to each

digitised road segment. ROADMOD estimates annual sediment

yield from each segment using Equation (6). After identifying the

network outlet, the sediment delivered to each outlet is estimated

by totalling sediment yield from all contributing road segments.

4.1.3.2. Delivery module. Sediment delivery processes in ROADMOD are estimated by using three assumed SDRs, depending on the

sediment delivery pathway. A value of 1.0 is assigned when

6 B. Fu et al. / Environmental Modelling & Software 25 (2010) 1–14
sediment is delivered directly by ditches and culverts into the

stream network, 0 when the runoff is directed to vegetated hillslopes, and 0.5 when the runoff discharges to unvegetated hillslopes or mangrove swamps (Anderson and MacDonald, 1998). The

SDR concept is slightly different in this case where delivery directly

from the road to the marine environment is modelled.

4.1.4. STJ-EROS road submodel

The St John sediment budget model (STJ-EROS) is a GIS-based,

catchment-scale model based on empirical data and application of

a SDR (Ramos-Scharro ́n and MacDonald, 2007a). The model

predicts sediment yields from coastal watersheds into the marine

environment for sediment originating from unsealed roads, stream

banks, tree throw, and undisturbed hillslopes. Only the road and

the sediment delivery submodels are reviewed in this article. The

road submodel of STJ-EROS is spatially distributed by road segment,

and the model outputs are annual-averaged and multiple-sized.

The empirical models for estimating road surface erosion

developed by Ramos-Scharro ́n and MacDonald (2005) assumed

that rainfall, road length, width and slope, and grading frequency

can explain most of the variation of sediment yield from the road

surface. Sediment yield from cutslopes are assumed uniform, and

a uniform silt-size particle correction is applied.

A comparative study has been conducted between STJ-EROS and

ROADMOD (Ramos-Scharro ́n and MacDonald, 2007a). Both models

were applied in catchments in the U.S. Virgin Islands (RamosScharro ́n and MacDonald, 2007a). It was argued that STJ-EROS

provided a more accurate prediction of road sediment because it

was based on better field observation data, and the predicted values

of STJ-EROS were closer to observed sediment yield values (RamosScharro ́n and MacDonald, 2007a).

4.1.4.1. Erosion module. Two features are modelled in STJ-EROS: the

road surface and the cutslope. Sediment yields from the road

surface are estimated based on empirical relationships between

sediment yields (estimated from sediment trap data), precipitation

and road characteristics (Ramos-Scharro ́n and MacDonald, 2005).

Input variables for erosion from the road surface include rainfall,

slope, and contributing road area. Empirical parameters differ for

roads with different grading frequencies. Erosion from cutslope

areas is assumed to be 9% of the total road segment sediment yield

(Ramos-Scharro ́n and MacDonald, 2007a). The equations used to

estimate sediment yields from road surfaces and cutslopes are

shown below. Sediment yields from all road segments in a catchment are accumulated to estimate total sediment yields from roads

and cutslopes:

E 1⁄4 Rs þ Cs (7)

Rs 1⁄4 a þ b  Sm  R  L  W  St (8)

Cs 1⁄4 ðPc=ð1 PcÞÞ  Rs (9)

Here E is total sediment yield from the road surface and cutslope

(kg), Rs and Cs are sediment yields from the road surface and cutslope, respectively (both in kg), S is road slope (m m1

), R is annual

rainfall (cm), L is road length (m), W is road width (m), St is a silt

content adjustment factor, Pc is the proportion of cutslope sediment

to the total sediment yields (0.09), and a, b and m are empirical

parameters. The empirical relationship (Equation (8)) is based on

data collected from sediment traps, hence a St factor is used to

adjust for the likely underestimation of fine particles lost when

sediment traps are used to estimate yields (Ramos-Scharro ́n and

MacDonald, 2007a). This factor differs for different grading

frequency classifications.

4.1.4.2. Sediment delivery. STJ-EROS estimates sediment delivery

from roads not to the stream network but to the marine environment, similar to the ROADMOD model. A user-defined SDR is used

to account for hillslope, channel and coastal wetland storage

between the road and the marine environment (Ramos-Scharro ́n

and MacDonald, 2007a). The SDRs are determined by the potential

retention of wetland environments (Ramos-Scharro ́n and MacDonald, 2007a). In general, SDRs of 0.4–1.0 are assigned to areas

that drain directly to the sea. Areas that drain to the sea through

coastal wetland or salt pond pathways have SDRs of 0–0.5. A SDR of

0 is given for areas that lack a surface pathway to the marine

environment (Ramos-Scharro ́n and MacDonald, 2007a).

4.2. Physics-based road models

4.2.1. WEPP

The Water Erosion Prediction Project (WEPP) is a physics-based

model that estimates soil loss and sediment yields from hillslope

erosion at hillslope or small catchment scales (Flanagan and

Nearing, 1995). WEPP was originally designed for application in

agricultural areas but has also been used for estimating erosion

from forest roads. WEPP is a spatially-distributed, daily-continuous

model that produces annual-averaged and multiple-sized outputs.

For application to roads, WEPP can include multiple features such

as road surface, cutslope, ditch, fillslope and lower hillslope.

WEPP:Road (Elliot et al., 1999b) is a web-based interface for

modelling individual road segments.

4.2.1.1. Erosion and delivery modules. WEPP has a hydrology

component which provides inputs (such as rainfall intensity, infiltration and runoff) for the erosion component (Flanagan and

Nearing, 1995). The erosion component of WEPP then combines

modelling of erosion processes and delivery to the stream network.

The estimated sediment yield at the bottom of the hillslope is

modelled as being delivered to streams. Sediment loadings are

estimated by calculating soil detachment and deposition rates from

interrill and rill areas (Foster et al., 1995). Interrill erosion is

determined by rainfall intensity, interrill runoff rate, interrill

erodibility and an interrill sediment delivery ratio (Foster et al.,

1995). Rill erosion is estimated as a function of hydraulic shear

stress, soil critical shear stress and sediment transport capacity.

Detachment occurs when hydraulic shear stress is greater than soil

critical shear stress and sediment load is less than sediment

transport capacity (Foster et al., 1995).

In road modelling applications, the road surface, fillslopes and

lower hillslope areas are modelled separately by defining them as

different Overland Flow Elements (OFE). Each OFE has unique soil

and vegetation parameters assigned. These parameters determine

different rill and interrill erosion rates.

WEPP, as a physics-based model, requires the estimation of

parameters such as rainfall volume and intensity, infiltration, slope,

and soil texture and erodibility parameters (Flanagan and Nearing,

1995). WEPP:Road simplifies data input which allows users to

specify selected climate, soil texture, gravel addition, road topography, drain spacing, road design and surface condition, and ditch

condition (Elliot et al., 1999b). Both rainfall and snowfall are

considered for generating daily weather inputs for the WEPP model

(Elliot et al., 1999b).

4.2.2. KINEROS2

The Kinematic Runoff and Erosion Model (KINEROS) is

a dynamic, event-based runoff and erosion model developed by

the Agricultural Research Service, U.S. Department of Agriculture

for typically small-scale applications (Woolhiser et al., 1990).

KINEROS2 is the second generation of KINEROS, containing

B. Fu et al. / Environmental Modelling & Software 25 (2010) 1–14 7
modified modules to quantify runoff and erosion processes

(Smith et al., 1995). KINEROS2 is a physics-based, spatiallydistributed, multiple-size but single-feature model. It is suitable

for application for infiltration-excess-dominated sites, and when

sediment transport varies during storms (Ziegler et al., 2001a).

The outputs of the model include time-varying runoff, sediment

yield and sediment concentration for a rainfall-runoff event.

KINEROS2 was not developed specifically for road surfaces, but

a recent study has proven that it can be applied to estimate

runoff and sediment yields from unsealed roads at the subsegment scale (Ziegler et al., 2001a, 2002). Its application at

larger scales is constrained by a lack of understanding of accumulated flow on road segments (Ziegler et al., 2002). The

particular road study did not attempt to evaluate its capacity to

simulate sediment delivery from road-related features to the

stream network.

4.2.2.1. Erosion module. In application of KINEROS2 to road erosion,

a road section is assumed either to be a single rectangular surface

with fixed length and width, or to be parallel flow planes for rutted

roads. The later is a more physically justifiable assumption but the

high variability in the morphology of drainage pathways from

unsealed roads is not explicitly modelled. Like all process-based

models, KINEROS2 begins by calculating excess precipitation as the

difference between rainfall rates and infiltration capacity. Infiltration capacity follows Smith and Parlange (1978) and is calculated as

a function of the hydraulic properties of the material and the

infiltrated depth; downslope runoff routing follows a kinematic

wave approach (Chow, 1998). KINEROS2 does not model erosion

based on rill and interrill processes but rather uses the concepts of

rainsplash and hydraulic shear stress to calculate erosive capacity.

When rainfall rate exceeds infiltration rate and ponding occurs,

rainsplash erosion is a function of the square of rainfall intensity

and soil erodibility, and is inversely related to surface water depth.

When no runoff is generated on the surface, rainsplash erosion is

assumed to be zero.

Hydraulic erosion represents the sediment exchange between

flowing water and the soil surface, and is estimated as the difference between local sediment concentration and transport capacity

(Smith et al., 1995). Sediment generated at any point along a road

surface flow path is estimated by solving a mass balance equation

similar to that used for kinematic runoff routing (Smith et al., 1995).

4.2.3. GA-UH/GA-KW coupled with sediment rating curve

The Green-Ampt – Unit Hydrograph (GA-UH) and the GreenAmpt – Kinematic Wave (GA-KW) models are two event-based

hydrological approaches used to simulate surface runoff from an

unsealed road surface. These models were used jointly with sediment rating curves to estimate sediment yields from a road segment

in the U.S. Virgin Islands (Ramos-Scharro ́n and MacDonald, 2007c).

The Green-Ampt infiltration and kinematic wave equations are

physics-based, while the unit hydrograph and sediment rating

curves are empirical. The coupled models only estimate erosion

from the road surface. The model outputs are single-sized.

4.2.3.1. Erosion module. Both models begin by calculating excess

rainfall as the difference between rainfall rates and infiltration

capacity estimated by the Green-Ampt equation (Scott, 2000).

Excess rainfall is then routed to the road drainage outlet by an

empirically-derived unit hydrograph (UH) or a kinematic wave

(KW) routing approach (Ramos-Scharro ́n and MacDonald, 2007c).

Sediment yield is simulated by multiplying road discharge by the

sediment rating curve. A sediment rating curve is the equation

resulting from statistical regression of measured suspended sediment concentration and instantaneous runoff rates.

One disadvantage of the UH approach is that it requires data

from the particular road segment to develop the unit hydrograph,

while the KW, at least in theory, does not have such previous data

requirements. Hydraulic parameters are needed for both of these

infiltration-runoff models, and these include hydraulic conductivity, maximum infiltration rate, and surface roughness, among

others. Tests showed that both models performed in a similar

fashion when compared to measured discharge rates. Much error in

model performance was due to inaccuracies in estimating infiltration during the initial stages of rainfall events, and the models

performed better for larger storms than for small rainfall events

(Ramos-Scharro ́n and MacDonald, 2007c).

Many assumptions are used in the GA-UH and GA-KW models to

simplify the hydrological and sediment transport processes. With

regards to the suspended sediment rating curve, the model

assumes sediment concentration is exponentially related to

discharge rates at the outlet of a road segment. This assumption

greatly simplifies the model but may result in poor performance

when the correlation between discharge rate and sediment

concentration is poor. In a particular application of this approach to

a road segment in the U.S. Virgin Islands, poor correlation was

found between suspended sediment concentration and discharge

when discharge exceeded 5 mm h1 (Ramos-Scharro ́n and

MacDonald, 2007c). As a result, the application of such a model at

high discharge rates, when most sediment is expected to be

exported from the road, is limited. The use of sediment rating

curves may also lead to overestimation of sediment yields when

a rating curve is developed under a sediment transport-limited

situation, but used in a sediment supply-limited situation. Road

sediment supply can be altered by several factors including sediment exhaustion during individual flow events and changes in

surface conditions caused by traffic and maintenance activities

(Ziegler et al., 2001b).

5. Discussion

5.1. Comparison of reviewed models

The models reviewed in the previous section represent a range

of currently available road erosion and delivery models. The models

vary in their temporal and spatial scales, the road features

considered, the processes they represent and their data requirements see Table 2.

5.1.1. Model families and data requirements

Four of the models reviewed (WARSEM, USLE, ROADMOD, and

STJ-EROS) can be categorised as empirical. These models are based

on a statistical analysis of the correlation between sediment yields

from a road segment and a range of variables describing local

climate, road characteristics, and management activities. Among

these variables, road slope and surface area (or road length) are

used in three of the four models, suggesting the importance of

these variables in estimating sediment yields from road surface

erosion. Due to the assumptions underlying ROADMOD and

STJ-EROS, they apply only to conditions from where they were

developed. In contrast, WARSEM and USLE could be more easily

adaptable as they were developed based on a more extensive

database and therefore incorporate parameters that allow for predicting sediment yields from more variable conditions. Empirical

models are usually associated with high levels of spatial and

temporal aggregation and have lesser data requirements than

physics-based models (Jakeman et al., 1999).

GA-UH and GA-KW coupled with sediment rating curve models

can be classified as a combination of physics-based and empirical

models. These models contain a physics-based rainfall-runoff

8 B. Fu et al. / Environmental Modelling & Software 25 (2010) 1–14
module and empirically-derived sediment concentration – runoff

rating curve. These models generally require more complex data

inputs than exclusively-empirical models.

The physics-based road models reviewed include WEPP and

KINEROS2. These models solve equations describing runoff and

sediment generated from the road surface. Considerable data are

required to apply physics-based models, and such data are often

not available outside experimental sites. Default parameter values

can be assumed in some instances, increasing the potential range of

applicability of such models.

5.1.2. Temporal and spatial scales

The temporal scales of road models are largely correlated to

their spatial scales. Most temporally lumped models such as those

based on annual average simulation have been applied at larger

spatial scales. In contrast, event-based models are commonly used

to study individual road segments. However, these segment-based

models have been (or have the potential to be) expanded to a road

network. Although a model such as KINEROS2 provides insight into

sediment yield response at a high time resolution and can be

expanded to predict responses at a small catchment scale, its

parameter calibration requirements are very difficult to achieve.

Therefore, this type of event-based, high spatial and temporal

resolution model is more apt for research applications than for land

management purposes.

5.1.3. Features and process representation

Section 2.1 described a typical cut-and-fill road segment which

contains a cutslope, road surface, fillslope and a variety of drainage

structures (Fig. 1). The local geometry and material properties of all

these features influence the processes controlling road erosion and

sediment delivery. However, not all of these features are considered

in road models. WARSEM and WEPP contain the most complete

modelling of road features and processes; other models consider

only a subset, predominantly the road surface. Generally both

sediment generation and delivery are simulated, with a few exceptions such as the USLE and KINEROS2, where only sediment generation is considered.

The consideration of erosion from cutslopes in road models is

very limited, partly due to the perceived or actual low contribution

of cutslopes to total road erosion in many areas (Elliot and Tysdal,

1999; Ramos-Scharro ́n and MacDonald, 2007a). It is also due to

a variety of processes affecting cutslope erosion (surface erosion by

rain, freeze-thaw, piping and mass wasting) and also the difficulty

of modelling the transport of sediment produced by cutslopes to

the drainage outlet.

Fillslope erosion is typically considered in sediment delivery

processes, but this feature is modelled least often in the erosion

component of the reviewed models. This can be attributed to its

generally perceived small sediment contribution and logistical

difficulties in implementing field studies. In other soil erosion

studies, fillslopes may be modelled in the same way as undisturbed

hillslopes, but significant differences are likely in vegetation cover

and soil erodibility. Megahan et al. (1991) found, during a plot-scale

study in Idaho, U.S., that fillslope surface erosion is dominantly

influenced by ground cover density and snowfree period rainfall

erosivity. A limitation of current models is the few studies that have

investigated the impact of accumulated flow from road drains to

fillslope erosion (Croke and Mockler, 2001), an exception being

Elliot and Tysdal (1999).

5.1.4. Management applications

Most models are intended as tools to assess current conditions

(impact), to evaluate best management practices or to help identify

field data collection and resource management priorities. For

example, USLE, WEPP and their modifications have been applied in

forest road surface erosion assessment in Australia (Ryan et al.,

2003) and the U.S. (Heller and Norman, 2005; Riedel and Vose,

2003). WARSEM can be used to investigate best management

practices on forest roads by simulating the effects of changes in

surfacing, traffic, cutslope vegetation cover, and installation of

sediment traps (Dube ́ et al., 2004).

Models containing stochastic variables can be used to define the

probabilities associated with different rates of erosion. However,

none of the models reviewed here use a probabilistic approach for

prediction. Distributed WEPP, a WEPP Internet interface for forest

and rangeland erosion after disturbance, was developed to present

the probability of sediment yields (Elliot et al., 2001). The approach

may be used in WEPP to provide probabilities for road erosion.

Megahan et al. (1991) used Monte Carlo simulation to predict the

probability of occurrence of sediment yields from granitic fillslopes

in Idaho, U.S., under various levels of ground cover density. Such

probabilistic modelling may prove useful for land managers to

define the risks from road erosion, as well as to assess management

alternatives.

5.2. Limitations and recommendations

5.2.1. Modification of existing erosion models

Most attempts to develop new road erosion studies adapt the

theories of existing erosion processes on hillslopes and catchment,

and therefore inherit a similar mathematical structure to their

ancestor models. The new road erosion models adopt two major

approaches: empirical modelling which derives relationships

between sediment yields and a range of controlling factors; and

physics-based modelling which predicts the hydrologic behaviour

of the road surfaces and uses the response to calculate erosion as

the difference between erosive potential and surface resistance.

Table 2

A comparison of the models included in this review.

Models Type Data

requirementsa

Temporal scale Spatial scale Modelled features Process representationb Sediment

size fraction

WARSEM Empirical Medium Annual average Road network Surface, drain,

cutslope, fillslope

Erosion and delivery Single

USLE and modifications Empirical Small Annual average Road network Surface, cutslope Erosion only Single

ROADMOD Empirical Medium Annual average Road network Surface Erosion and delivery Single

STJ-EROS Empirical Medium Annual average Road network Surface, cutslope Erosion and delivery Multiple

WEPP Physics-based Large Annual average Road segment Surface, drain,

cutslope, fillslope

Erosion and delivery Multiple

KINEROS2 Physics-based Large Event based Plot-small catchment Surface Erosion only Multiple

GA-UH and

GA-KW þ rating curve

Coupled physics-based

and empirical

Medium Event based Road segment Surface Erosion and delivery Single

a Data requirements are based on the number of model inputs and parameters, as well as the accessibility to these values, including the involvement of filed work. b Process representation includes the consideration of road surface erosion and the delivery of sediment from road to stream.

B. Fu et al. / Environmental Modelling & Software 25 (2010) 1–14 9
Empirical models are useful for estimating annual loads and for

identifying erosion ‘hot spots’ within a catchment. In contrast,

physics-based models simulate single-event or inter-storm sediment loads, which could be used for quantifying the impact of

a road segment in the water quality of a particular river. The limitations of the ancestor models also apply to the modified road

models, some of which are summarised in Merritt et al. (2003).

A successful application of the empirical modelling approach

largely depends on the correct identification of critical factors that

influence sediment loads. Factors such as rainfall, effective contributing road area, road slope, traffic, and road maintenance activities

are commonly used. Although empirical models require a relatively

smaller number of parameters, they have the following limitations:

i) confidence in their application is limited to the environmental circumstances from which the empirical relationships

were generated (Merritt et al., 2003);

ii) temporal variation of rainfall, runoff and erosion processes is

generally not considered (Merritt et al., 2003); and

iii) the heterogeneity of road/catchment characteristics and nonlinearities of the system is largely simplified and hence up- or

down-scaling application of the original models is difficult.

Physics-based models have the advantage of being applicable to

different environments, potentially producing greater depth of

information on hydrology and erosion processes. Theoretically,

principles of physics remain unchanged regardless of location;

hence if properties of road soils can be adequately determined at

a site, they can be applied to another site as long as local climate

and road characterization data are available for calibration. This is

illustrated by the successful application and testing of the WEPP:-

Road model to roads in a Pinus plantation forest in southeast

Queensland, Australia even though the model was developed for

the U.S. (Forsyth et al., 2006). Reasonable agreements between

WEPP estimates and field observations were also found in a hillslope scale study in southeast New South Wales, Australia (Croke

and Nethery, 2006).

Physics-based modelling has several disadvantages. It almost

always requires estimation/calibration of more parameters than

empirical modelling. The numerous assumptions that describe the

hydrology and erosion processes limit the application of such

models at large scales (Beven, 1989). This is mainly because the

equations of most physics-based models are based on the physics of

small scale homogeneous systems, and therefore their applicability

to larger scale heterogeneous systems require methodical testing.

Other problems that may limit the widespread applicability of

physics-based road erosion models include:

i) large computational demands;

ii) the need to develop input databases that describe the spatial

variability of model variables appropriately;

iii) the requirement for accurate hydrological prediction; and

iv) the need to implement an adequate monitoring strategy that

would allow for variable and parameter calibration, as well as

for model testing.

Despite the large number of existing physics-based erosion

models for hillslope and catchment applications, the number and

diversity of these models for unsealed roads is relatively small. The

successful adaptation of selected physics-based models to road

erosion and sediment delivery studies indicates the potential of

incorporating roads into pre-existing hillslope models without

major alterations to their structure. None of the physics-based road

models reviewed here can account for the hydrological and erosion

processes occurring on surfaces other than the road surface.

5.2.2. Imbalance between modelling erosion and delivery

Most road erosion studies have been undertaken to assess offsite water quality problems. Hence there is a clear need to consider

both erosion from roads and the processes that govern sediment

delivery from roads to streams. However, in most models, there is

a significant bias towards the erosion process, with much less

consideration given to delivery processes. This is largely due to the

difficulty of obtaining monitoring data to quantify or test road-tostream connectivity across a range of physical environments.

Thorough evaluations of the outputs of road models, particularly in

their capacity to estimate the amount of the road-derived sediment

reaching a stream, are largely limited. Among the models considered here the delivery component can be considered to be the least

reliable.

The most common, and sometimes only, variable to determine

sediment delivery from road to stream is the distance between road

and stream. However, this ignores other factors, such as the

contributing road area and rainfall intensity (Hairsine et al., 2002),

gully initiation (Croke and Mockler, 2001), groundcover, slope, and

the presence or absence of runoff-detaining features along the flow

path. An empirical model of sediment delivery from road to stream

has been developed by Megahan and Ketcheson (1996) for forest

roads in Idaho in the western U.S.. The travel distance of sediment

from unsealed roads are estimated based on the volume of

deposited sediment, the capacity of the hillslope to retain sediment, the slope of the lower hillslope, and the upslope contributing

area (Megahan and Ketcheson, 1996).

In southeastern Australia, Hairsine et al. (2002) developed an

event-based conceptual model called ‘Volume to breakthrough’

model (Vbt) which predicts the probability of road-derived runoff

reaching a stream through diffuse overland flow. Input variables of

the Vbt model include the distance from the drain to the stream,

contributing road area, rainfall and infiltration rates, and the

duration of the rainfall event (Hairsine et al., 2002). The Vbt model

was originally developed as a hydrology connectivity model, but

with further effort a sediment delivery component could be

incorporated. Such work is currently underway in the Lower Cotter

Catchment of Australia (Thompson et al., 2008).

A counter argument to the use of both erosion and delivery

modelling could be made that modelling the likely locations of

highest sediment generation from a road network can be by itself

effective in identifying opportunities to control erosion. Field

inspection of such sites may quickly reveal whether the generated

sediment is being delivered to areas of concern in problematic

quantities, and whether the best solution is improved road

management or improved off-road practices such as detention

ponds. Similarly, modelling the sediment delivery potential of

road segment is also useful to identify potential road segments for

further investigation or monitoring on sediment generation, and

to assess alternative road or drainage locations to control roadderived sediment from entering streams (e.g. Eastaugh et al.,

2008).

5.2.3. Buildup-washoff process in erosion

The phenomenon of high sediment concentration at the early

stage of a runoff event is usually referred to as the ‘first flush’ in

water quality studies, especially in urban areas. It occurs when

loose sediment accumulates between storm events. The amount of

readily transportable sediment gradually declines with time during

a storm event. A buildup-washoff function is commonly used to

represent such processes (Chen and Adams, 2007; Zoppou, 2001).

The simulation of buildup-washoff processes is potentially important for temporally distributed models, or when the sediment

contribution during buildup-washoff period is significant in longterm sediment generation.

10 B. Fu et al. / Environmental Modelling & Software 25 (2010) 1–14
The buildup-washoff process often occurs on the surface of

unsealed roads (Ziegler et al., 2001a), or as temporary sediment

storage in ditches and other channelized features, but may also

arise on steep cutslopes of granitic bedrock and shallow noncohensive soil, where long-term weathering processes weaken

particle bonds allowing for continuing mass wasting for long

periods of time (Megahan et al., 1983). Very few event-based road

models account for processes affecting road surface conditions

between rainfall events. Ziegler et al. (2001a, 2002) noted that road

sediment supply is dynamic because inter-storm processes and

traffic create loose materials on top of compacted surfaces. During

storm events, loose materials, whose supply is determined by interstorm sediment detachment processes, are eroded first. After

removal of loose materials, the road sediments are supplied by the

compacted road surface, which is affected by intra-storm events

(Ziegler et al., 2001a). Sediment concentration spikes may occur

during the first five minutes of storm events (Ziegler et al., 2001a).

This implies the significance of inter-storm sediment detachment

processes on road modelling, which are generally ignored in many

road models.

Three types of buildup functions are identified in water quality

modelling: linear, power and exponential (Rossman, 2005). The

exponential decay relationship between the available sediment and

the duration of time has been widely used (Chen and Adams, 2007),

and may be profitably used for road erosion modelling. However,

representation of buildup-washoff in most road models is still very

limited and is a particular limitation for application of event models

in areas of high rainfall variability. Access to data good enough for

parameterisation of buildup-washoff processes is essential.

A variation on the buildup-washoff approach has been used by

Megahan (1974) to describe the long-term decrease of sediment

erosion on unsealed roads following surface disturbance such as

road construction. Megahan’s model has been supported by several

subsequent studies (Ramos-Scharro ́n and MacDonald, 2005; Sugden and Woods, 2007).

5.2.4. Subsurface flow interception

There are two primary mechanisms by which roads may affect

catchment hydrology: generation of infiltration excess runoff from

road surfaces and the interception of subsurface flow by the cutslope (Bowling and Lettenmaier, 2001). The focus of this paper is on

surface erosion, but the significance of intercepted runoff on road

surface erosion and sediment transport, as well as mass wasting,

presents significant opportunity for further research.

The effects of forest roads on hydrological processes have been

the focus of several studies including Luce (2002), Negishi et al.

(2008), Sidle et al. (2006) and Wemple et al. (2001). For example,

Negishi et al. (2008) reported that intercepted subsurface flow

contributed nearly 30% of the sediment and 80% of runoff on

a forest road in Malaysia. In areas where cutslope interception of

subsurface flow is substantial, the volume of flow conveyed by road

ditches and culverts during and between storm events may add

considerably to road surface runoff. For example, a high proportion

of road runoff was reported from subsurface runoff intercepted by

cutslopes during snowmelt periods in mountainous areas in central

Idaho, U.S. (Megahan, 1972).

None of the seven models reviewed accounts for the effects of

roads on sub-surface flow interception by cutslopes. The need to

incorporate this effect of forest roads has been highlighted by

several studies. For example, Busteed et al. (2005) found that the

WEPP WATERSHED model underestimated road runoff by nearly

fifty percent, and most of this error was due to inaccuracies during

large storms. This may partly be explained by the failure to estimate

additional runoff intercepted by cutslopes. The latest release of the

WEPP model has the capability to quantify subsurface flow rates

along forested hillslopes (Covert et al., 2005), but no studies have

yet attempted to use this tool to assess the role of road cutslope

interception in generating surface runoff. Similarly, the Distributed

Hydrology-Soil-Vegetation Model (DHSVM) is a physics-based

hydrological model that accounts for both surface and subsurface

flow on forest roads (Bowling and Lettenmaier, 2001). Further

investigation is required as to the applicability of such models for

estimating subsurface flow interception and the ensuing implications on sediment generation and delivery processes.

5.2.5. Model testing and uncertainty analysis

Model testing and uncertainty analysis are critical for developing an understanding of model outputs. However, they are

seldom reported for road erosion and delivery models. Most

empirical models are validated from datasets collected at the sites

used for their development. Very few are applied or tested widely

in other places. Even fewer road studies attempt to quantify the

uncertainty of road model outputs. Notable exceptions include: (i)

the study of Ketcheson et al. (1999) in which an assessment of the

accuracy of the R1–R4 and BOISED models is presented; (ii) testing

of KINEROS2 by Ziegler et al. (2001a); and (iii) guidance on the

reliability of the WEPP:Road model that is provided in the documentation of that model (Elliot et al., 1999b). Other attempts at

model testing include the comparison of the ROADMOD model

outputs against measured sediment yields as reported in RamosScharro ́n and MacDonald (2005).

A large and increasingly sophisticated literature describes

general model testing and uncertainty analysis and suggests good

modelling practices (Jakeman et al., 2006; Saltelli et al., 2000).

Much that can be learned from the literature on model testing,

uncertainty analysis and modelling practice is directly applicable to

road models. For example, the sources of uncertainty of water

quality models and accumulation of uncertainty described by Beck

(1987) are directly applicable to road models. Limiting factors for

model testing and uncertainty analysis include access to data of

sufficient quantity, spatial and temporal resolution and reliability

for comparison against model outputs, and the large inherent

variability in the data.

In addition to traditional monitoring and measurement, sediment tracing techniques may also be useful for model testing,

especially at the catchment scale (e.g. Wallbrink et al., 2002; Motha

et al., 2003). For example, Motha et al. (2003) successfully used

geochemistry and radionuclide tracers to discriminate sediment

contributions from undisturbed forest, forest harvest areas, and

gravelled and ungravelled road surfaces for a small forest catchment of southeastern Australia. The results of this study can

potentially be used to test catchment-scale road models applied for

the same area. Sediment tracing can also aid in separating the

relative sediment contributions originating on cutslopes and fillslopes from those produced on the road surface if significantly

different tracer properties of these sources can be identified.

5.2.6. Guidelines for model selection

The first step in model selection is to determine the kinds of

questions the model is intended to address. A model may be needed

to aid management of unsealed roads, or for scientific research on

the behaviour of unsealed roads. The types of questions that

managers ask of road erosion and sediment deliverymodels include:

 What is the contribution of unsealed roads to catchment-scale,

suspended, bedload or total sediment yields?

 Which road segments contribute large amounts of sediment to

a stream network?

 How should road drains be constructed or spaced to reduce

impacts on stream water quality?

B. Fu et al. / Environmental Modelling & Software 25 (2010) 1–14 11
 How should new roads be laid out to reduce impacts on stream

water quality?

 How can changes in maintenance, such as grading and resurfacing, affect sediment yields?

 How does traffic affect sediment generation and subsequent

delivery to streams?

Simpler models (in terms of process representation, number of

features modelled, the level of spatial and temporal aggregation

etc.) appear to be preferred for management purposes. More

complex models are potentially useful, particularly in building

understanding of the physical processes at play, but require

a higher level of expertise to be useful for management purposes.

The next step in model selection is to see whether the scope of

the model satisfies both the purpose of the study and the characteristics and data availability of the study area. The model selected

should have spatial, temporal, and accuracy scales suited to the

purpose of the study, while also having the capability to include all

sediment sources perceived to be playing a role in sediment

production and delivery. These requirements imply a priori

knowledge of the study area and a clear conceptual understanding

of the goals of the modelling effort.

All empirical models, including those with empirically derived

SDRR-S, are developed under specific environmental conditions

such as climate, topography, and lithology. The conditions of the

four empirical models reviewed in this paper are summarised in

Table 3. The WARSEM model was developed for areas including

snowfall regions, while ROADMOD and STJ-EROS were developed

in areas with steep slopes, erodible soils and intense rain events.

Even though localised conditions may prevent the widespread use

of these particular empirical approaches to areas other than those

for which the model was developed, their model structure could

prove useful for both researchers and land managers. The

conceptual description of processes implied by the model could be

used as a framework in the development of new models, in the

design of research approaches, and in the development of

prevention and mitigation strategies.

5.2.7. The imperative for monitoring

Access to good data is the greatest limitation to the development

of sediment generation and delivery models for unsealed roads. It is

important that those responsible for commissioning, developing

and applying road models are aware of this limitation and that

modelling studies are supported by well targeted monitoring.

Monitoring is expensive and therefore must be well prioritised.

Monitoring should be considered on a case-by-case basis. The

objectives, the anticipated modelling approach and available

resources should be carefully considered in developing a monitoring program. The key guiding principle should be a clear

understanding of how monitoring data will contribute to model

development and testing.

Monitoring must respond to an a priori understanding of the

potential factors controlling road erosion and delivery processes and

must be conscientious of the general framework and methodology

that will be used to generate, test, or validate a model. For example,

application of an empirical model will require information on how its

factors respond to specific environmental conditions and road

characteristics in its area of application. Monitoring across the

intended range of environmental conditions and road characteristics

would be required for confident application of an empirical model.

The spatial scale of intended model application is also an important determinant of themonitoring required. Sediment yield data, for

example, can be collected in a continuum of increasing spatial scale

from rainfall simulator studies (w1’s m2

) to road segment (102’s m2)

and catchment-scale monitoring (1’s–103

’s km2). In most cases data

collection occurs at a finer scale than that intended for model

application. For example, modelling catchment-scale impacts will

likely require data to support the simulation of sediment generation

and delivery from individual road segments, but its validation

requires data at the catchment scale.

A particular weakness identified in this review is the monitoring

of road-to-stream connectivity. This is evidenced by the lower

complexity of delivery modules relative to erosion models in most

cases. More complex models may or may not be required, but our

poor knowledge of delivery processes inhibits how models are

developed and a balance needs to be established between monitoring of erosion and delivery.

The technical aspects of data collection are beyond the scope of

this review but Bos et al. (1991), Megahan and Ketcheson (1996),

Sheridan et al. (2006), and Ziegler et al. (2001b) provide examples

of data collection approaches that may be modified to meet specified objectives.

6. Conclusion

The importance of unsealed roads to off-site water quality is

being increasingly recognised. The identification of sediment

sources and their delivery potential using mathematical models can

assist in recognising critical sediment source areas, evaluating best

management practices and/or prioritising data collection and

research activities. A range of models have been developed for

estimating surface erosion on unsealed roads but they are typically

at a lesser level of development than corresponding models for

other types of land use activities.

Most models of surface erosion and sediment delivery from

unsealed roads can be categorised as empirical and physics-based

models. Empirical models generally have lower parameter

requirements than physics-based models but are limited in their

widespread application as they only represent a rather restricted

set of conditions. On the other hand, physics-based models have the

potential for more generic applications but the strictness of variable

validation requirements make them unlikely choices for other than

research purposes.

All of the models reviewed here consider sediment generation

from the road surface, but lack consistency in incorporating other

road features. The processes of sediment generation and delivery are

generally explicitly considered but typically less consideration is

given to delivery processes. This is the result of poorer knowledge of

delivery processes and the difficulty in obtaining monitoring data to

test the extent of road-to-stream connectivity for sediment sources.

A set of guidelines have been provided for model selection. In

most instances, the first and most important step in deciding on

Table 3

Summary of the location, climate, topography, lithology, road and land use characteristics of the area where the empirical models were developed.

Characteristics USLE WARSEM ROADMOD and STJ-EROS

Location U.S. Washington State,

northwestern U.S.

St John, U.S. Virgin Islands

Annual rainfall Diverse 100–3000 mm 900–1400 mm

Elevation Diverse 0–4000 m 0–500 m

Road slope Diverse 1–13% 0–37% (R) 1–21% (S)

Dominate lithology Diverse Sedimentary,

volcanic and basalt

Volcanic

Soil Diverse Diverse Shallow gravelly clay

loams

Dominant road users – Truck and light

vehicles

Truck and light vehicles

(traffic is

not modelled)

Dominant land use Agriculture Forest Forest

R: ROADMOD and S: STJ-EROS

12 B. Fu et al. / Environmental Modelling & Software 25 (2010) 1–14
a modelling approach is to determine the question(s) that a model

is intended to address. Model selection should have spatiotemporal scales suited to the purpose of the study and should be

expected to have the expected accuracy required for this purpose.

Simpler models appear to be preferred for management purposes

with more complex models potentially most useful for building

understanding of the dominant processes.

Model testing and uncertainty analysis, while critical to developing understanding of model outputs, are seldom reported for

road erosion and delivery models. To address this concern there is

significant opportunity to take advantage of the literature

describing model testing, uncertainty analysis and good modelling

practice. However, a fundamental requirement for model testing

and ongoing model development is access to data of an appropriate

standard to support model development and testing. In collecting

data to support model development the key guiding principle is

a clear understanding of how monitoring data will contribute to

model development and testing.

Significant opportunities exist for future research activities to

support modelling of surface erosion and sediment delivery.

Building knowledge in the following areas is of high priority: (i)

sediment delivery processes from roads to streams; (ii) the

importance of buildup-washoff processes in controlling inter- and

intra-storm sediment availability; (ii) the effects of roads on

hydrologic processes at spatial scales larger than the road segment,

especially the effects of subsurface flow interception; and (iv) how

to incorporate information from sediment tracer experiments into

the model development process.

Acknowledgements

The comments of the several anonymous reviewers were of

great assistance in improving the structure and content of the

paper. We would also like to thank Drs Ingrid Takken, Jacky Croke

and Chris Thompson for sharing their wealth of knowledge on road

erosion and providing valuable advice and helpful comments on

earlier drafts of the paper. We would also like to thank Professors

Tony Jakeman and John Norton for their helpful comments on the

paper. Dr John Field has also provided much assistance to the

authors and his inputs are gratefully acknowledged. The assistance

of Mr Clive Hilliker in the preparation of the artwork is appreciated

as is as the editorial assistance provided by Dr Sue Holzknecht.

References

Aksoy, H., Kavvas, M.L., 2005. A review of hillslope and watershed scale erosion and

sediment transport models. CATENA 64 (2–3), 247–271.

Anderson, D.M., MacDonald, L.H., 1998. Modelling road surface sediment production using a vector geographic information system. Earth Surface Processes and

Landforms 23 (2), 95–107.

Beck, M.B., 1987. Water quality modelling: a review of the analysis of uncertainty.

Water Resources Research 23 (8), 1393–1442.

Beven, K., 1989. Changing ideas in hydrology – the case of physically-based models.

Journal of Hydrology 105 (1–2), 157–172.

Bos, M.G., Replogle, J.A., Clemmems, A.J., 1991. Flow measuring flumes for open

channel systems. Transactions of the American Society of Agricultural Engineers Michigan, USA.

Bowling, L.C., Lettenmaier, D.P., 2001. The effects of forest roads and harvest on

catchment hydrology in a mountainous maritime environment. In: Wigmosta, M.S., Burges, S.J. (Eds.), Land Use and Watersheds: Human Influence on

Hydrology and Geomorphology in Urban and Forest Areas. Water Science and

Application, vol. 2. American Geophysical Union, Washington, DC, pp. 145–164.

Bulygin, S., Tarasov, V., Radov, S., 2006. Soil erosion in agricultural landscapes of

Donbas. Eurasian Soil Science 39 (10), 1144–1147.

Busteed, P.R., Turton, D.J., Nettles, J., 2005. Erosion from an established forest road in

the Ouachita Mountains. In: Gassman, P.W. (Ed.), Watershed Management to

Meet Quality Standards and Emerging TMDL, Proceedings of the Third

Conference 5–9 March 2005, pp. 101–109.

Chen, J., Adams, B.J., 2007. A derived probability distribution approach to stormwater quality modeling. Advances in Water Resources 30 (1), 80–100.

Chow, V.T., 1998. Handbook of Applied Hydrology. McGraw-Hill, New York, N.Y.

Coker, R.J., Fahey, B.D., Payne, J.J., 1993. Fine sediment production from truck traffic,

Queen Charlotte Forest, Marlborough Sounds, New Zealand. Journal of

Hydrology, New Zealand 31, 56–64.

Collison, A.J.C., Anderson, M.G., 1996. Using a combined slope hydrology/stability

model to identify suitable conditions for landslide prevention by vegetation in

the humid tropics. Earth Surface Processes and Landforms 21 (8), 737–747.

Covert, S.A., Robichaud, P.R., Elliot, W.J., Link, T.E., 2005. Evaluation of runoff

prediction from WEPP-based erosion models for harvested and burned forest

watersheds. Transactions of the ASAE 48 (3), 1091–1100.

Croke, J., Hairsine, P., Fogarty, P.,1999a. Runoff generation and re-distribution in logged

eucalyptus forests, south-eastern Australia. Journal of Hydrology 216 (1–2), 56–77.

Croke, J., Hairsine, P., Fogarty, P., 1999b. Sediment transport, redistribution and

storage on logged forest hillslopes in south-eastern Australia. Hydrological

Processes 13 (17), 2705–2720.

Croke, J., Mockler, S., 2001. Gully initiation and road-to-stream linkage in a forested

catchment, southeastern Australia. Earth Surface Processes and Landforms 26

(2), 205–217.

Croke, J., Mockler, S., Fogarty, P., Takken, I., 2005. Sediment concentration changes in

runoff pathways from a forest road network and the resultant spatial pattern of

catchment connectivity. Geomorphology 68 (3–4), 257–268.

Croke, J., Mockler, S., Hairsine, P., Fogarty, P., 2006. Relative contributions of runoff

and sediment from sources within a road prism and implications for total

sediment delivery. Earth Surface Processes and Landforms 31 (4), 457–468.

Croke, J., Nethery, M., 2006. Modelling runoff and soil erosion in logged forests:

scope and application of some existing models. CATENA 67, 35–49.

Dube ́, K., Megahan,W., Mccalmon, M., 2004. Washington Road Surface Erosion Model

(WARSEM) Manual. Department of Natural Resources, State of Washington.

Eastaugh, C.S., Rustomji, P.K., Hairsine, P.B., 2008. Quantifying the altered hydrologic

connectivity of forest roads resulting from decommissioning and relocation.

Hydrological Processes 22 (14), 2438–2448.

Elliot, W.J., Foltz, R., Luce, C., 1999a. Modeling low-volume road erosion. Transportation Research Record 1652, 244–249.

Elliot, W.J., Hall, D.E., Scheele, D.L., 1999b. WEPP interface for predicting forest road

runoff, erosion and sediment delivery. Technical Documentation. U.S.D.A. Forest

Service.

Elliot, W.J., Robichaud, P.R., Hall, D.E., Cuhaciyan, C.O., Pierson, F.B., Wohlgemuth, P.,

2001. A probabilistic approach to modeling erosion for spatially-varied conditions, American Society of Agricultural Engineers Annual Meeting, Sacramento,

California July 2001. Paper No. 01-8006. 16 pp.

Elliot, W.J., Tysdal, L.M., 1999. Understanding and reducing erosion from insloping

roads. Journal of Forestry 97 (8), 30–34.

Farabi, H., James, R., December 2005. Using GIS, terrain attributes and hydrologic

models to predict the risk of soil erosion and stream water deterioration caused

by forest roads. In: Zerger, A., Argent, R.M. (Eds.), MODSIM 2005 International

Congress on Modelling and Simulation. Modelling and Simulation Society of

Australia and New Zealand, Melbourne.

Flanagan, D.C., Nearing, M.A. (Eds.), 1995. USDA – Water Erosion Prediction Project:

Hillslope Profile and Watershed Model Documentation. NSERL Report No.10.

USDA-Agricultural Research Service, National Soil Erosion Research Laboratory,

West Lafayette, Indiana.

Forsyth, A.R., Bubb, K.A., Cox, M.E., 2006. Runoff, sediment loss and water quality

from forest roads in a southeast Queensland coastal plain Pinus plantation.

Forest Ecology and Management 221 (1–3), 194–206.

Foster, G.R., Flanagan, D.C., Nearing, M.A., Lane, L.J., Risse, L.M., Finkner, S.C., 1995.

Hillslope erosion component. In: Flanagan, D.C., Nearing, M.A. (Eds.), USDA –

Water Erosion Prediction Project: Hillslope Profile and Watershed Model

Documentation. National Soil Erosion Research Laboratory, West Lafayette.

Foster, G.R., McCool, D.K., Renard, K.G., Moldenhauer, W.C., 1981. Conversion of the

universal soil loss equation to SI metric units. Journal of Soil and Water

Conservation 36 (6), 355–359.

Foster, I.D.L., Lees, J.A., 2000. Tracers in geomorphology: theory and applications in

tracing fine particulate sediments. In: Foster, I.D.L. (Ed.), Tracers in Geomorphology. John Wiley & Sons, Ltd, Chichester.

Fu, B., Field, J.B., Newham, L.T., 2006. Tracing the source of sediment in Australian

coastal catchments. In: Fitzpatrick, R.W., Shand, P. (Eds.), Regolith 2006-

Consolidation and Dispersion of Ideas. Western Australian, CRC LEME, Perth.

Geeves, G.W., Leys, J.F., Mctainsh, G.H., 2000. Soil erodibility. In: Charman, P.E.V.,

Murphy, B.W. (Eds.), Soils: Their Properties and Management. Oxford University

Press, Oxford.

Grayson, R.B., Haydon, S.R., Jayasuriya, M.D.A., Finlayson, B.L., 1993. Water quality in

mountain ash forests – separating the impacts of roads from those of logging

operations. Journal of Hydrology 150 (2–4), 459–480.

Hairsine, P.B., Croke, J.C., Mathews, H., Fogarty, P., Mockler, S.P., 2002. Modelling

plumes of overland flow from logging tracks. Hydrological Processes 16 (12),

2311–2327.

Harr, R.D., 1981. Some characteristics and consequences of snowmelt during rainfall

in western Oregon. Journal of Hydrology 53 (3–4), 277–304.

Heller, S., Norman, S., 2005. 2004 Forest Road BMP Upgrade Monitoring Program.

USDA-Forest Service, Lake Tahoe Basin Management Unit.

Jakeman, A.J., Green, T.R., Beavis, S.G., Zhang, L., Dietrich, C.R., Crapper, P.F., 1999.

Modelling upland and instream erosion, sediment and phosphorus transport in

a large catchment. Hydrological Processes 13 (5), 745–752.

Jakeman, A.J., Letcher, R.A., Norton, J.P., 2006. Ten iterative steps in development

and evaluation of environmental models. Environmental Modelling & Software

21 (5), 602–614.

B. Fu et al. / Environmental Modelling & Software 25 (2010) 1–14 13
Ketcheson, G.L., Megahan, W.F., King, J.G., 1999. ‘‘R1–R4’’ and ‘‘BIOSED’’ sediment

prediction model tests using forest roads. Journal of the American Water

Resources Association 35 (1), 83–98.

La Marche, J.L., Lettenmaier, D.P., 2001. Effects of forest roads on flood flows in the

Deschutes River, Washington. Earth Surface Processes and Landforms 26 (2),

115–134.

Lane, P.N.J., Sheridan, G.J., 2002. Impact of an unsealed forest road stream crossing:

water quality and sediment sources. Hydrological Processes 16 (13), 2599–2612.

Luce, C.H., 2002. Hydrological processes and pathways affected by forest roads:

what do we still need to learn? Hydrological Processes 16 (14), 2901–2904.

Luce, C.H., Black, T.A., 1999. Sediment production from forest roads in western

Oregon. Water Resources Research 35 (8), 2561–2570.

MacDonald, L.H., Coe, D.B.R., 2008. Road sediment production and delivery:

processes and management. In: Proceedings of the First World Landslide

Forum, International Programme on Landslides and International Strategy for

Disaster Reduction. United Nations University, Tokyo, Japan, pp. 381–384.

MacDonald, L.H., Sampson, R.W., Anderson, D.M., 2001. Runoff and road erosion at

the plot and road segment scales, St John, US Virgin Islands. Earth Surface

Processes and Landforms 26 (3), 251–272.

Megahan, W.F., 1972. Subsurface flow interception by a logging road in mountains

of Central Idaho. In: Csallany, S.C., McLaughlin, T.G., Striffler, W.D. (Eds.),

Proceedings of a Symposium on Watersheds in Transition. American Water

Resources Association, Urbana, Illinois.

Megahan, W.F., 1974. Erosion over time: a model. USDA-Forest Service, Research

Report INT-156, Intermountain Research Station, Ogden Utah.

Megahan, W.F., 1978. Erosion processes on steep granitic road fills in Central Idaho.

Soil Science Society of America Journal 42 (2), 350–357.

Megahan, W.F., Day, N.F., Bliss, T.M., 1978. Landslide occurrence in the western and

central northern Rocky Mountain physiographic province in Idaho. In:

Youngberg, C.T. (Ed.), Forest Soils and Land Use: Proceedings of the Fifth North

American Forest Soils Conference, Colorado State University. Department of

Forest and Wood Science, Colorado State University, Fort Collins, pp. 116–139.

Megahan, W.F., Ketcheson, G.L., 1996. Predicting downslope travel of granitic

sediments from forest roads in Idaho. Journal of the American Water Resources

Association 32 (2), 371–382.

Megahan, W.F., Monsen, S.B., Wilson, M.D., 1991. Probability of sediment yields from

surface erosion on granitic roadfills in Idaho. Journal of Environmental Quality

20 (1), 53–60.

Megahan, W.F., Seyedbagheri, K.A., Dodson, P.C., 1983. Long-term erosion on

granitic roadcuts based on exposed tree roots. Earth Surface Processes and

Landforms 8 (1), 19–28.

Megahan, W.F., Wilson, M., Monsen, S.B., 2001. Sediment production from granitic

cutslopes on forest roads in Idaho, USA. Earth Surface Processes and Landforms

26 (2), 153–163.

Merritt, W.S., Letcher, R.A., Jakeman, A.J., 2003. A review of erosion and sediment

transport models. Environmental Modelling & Software 18 (8–9), 761–799.

Montgomery, D.R., 1994. Road surface drainage, channel initiation, and slope

stability. Water Resources Research 30 (6), 1925–1932.

Motha, J.A., Wallbrink, P.J., Hairsine, P.B., Grayson, R.B., 2003. Determining the

sources of suspended sediment in a forested catchment in southeastern

Australia. Water Resources Research 39 (3), 1056. doi:10.1029/2001WR000794.

Motha, J.A., Wallbrink, P.J., Hairsine, P.B., Grayson, R.B., 2004. Unsealed roads as

suspended sediment sources in an agricultural catchment in south-eastern

Australia. Journal of Hydrology 286, 1–18.

Negishi, J.N., Sidle, R.C., Ziegler, A.D., Noguchi, S., Abdul Rahim, N., 2008. Contribution of

intercepted subsurface flow to road runoff and sediment transport in a loggingdisturbed tropical catchment. Earth Surface Processes and Landforms 33,1174–1191.

Pentz, S.B., Kostaschuk, R.A., 1999. Effect of placer mining on suspended sediment in

reaches of sensitive fish habitat. Environmental Geology 37 (1), 78–89.

Ramos-Scharro ́n, C.E., MacDonald, L.H., 2005. Measurement and prediction of

sediment production from unpaved roads, St John, US Virgin Islands. Earth

Surface Processes and Landforms 30 (10), 1283–1304.

Ramos-Scharro ́n, C.E., MacDonald, L.H., 2007a. Development and application of

a GIS-based sediment budget model. Journal of Environmental Management 84

(2), 157–172.

Ramos-Scharro ́n, C.E., MacDonald, L.H., 2007b. Measurement and prediction of

natural and anthropogenic sediment sources, St. John, U.S. Virgin Islands.

CATENA 71, 250–266.

Ramos-Scharro ́n, C.E., MacDonald, L.H., 2007c. Runoff and suspended sediment

yields from an unpaved road segment, St. John, US Virgin Islands. Hydrological

Processes 21 (1), 35–50.

Reid, L.M., 1981. Sediment production from gravel-surfaced roads, Clearwater basin,

Washington. Publication FRI-UW-8108. University of Washington Fisheries

Research Institute: Seattle, WA.

Reid, L.M., Dunne, T., 1984. Sediment production from forest road surfaces. Water

Resources Research 20, 1753–1761.

Rekolainen, S., 1989. Effect of snow and soil frost melting on the concentrations of

suspended solids and phosphorus in two rural watersheds in Western Finland.

Aquatic Sciences – Research Across Boundaries 51 (3), 211–223.

Renard, K.G., Foster, G.R., Weesies, G.A., McCool, D.K., Yoder, D.C., 1997. Predicting

soil erosion by water: a guide to conservation planning with the Revised

Universal Soil Loss Equation (RUSLE). Agriculture Handbook. No. 703. U.S.

Department of Agriculture, Washington, DC.

Renard, K.G., Foster, G.R., Weesies, G.A., Porter, J.P., 1991. RUSLE: revised universal

soil loss equation. Journal of Soil and Water Conservation 46, 30–33.

Riedel, M.S., Vose, J.M., 2003. Collaborative research and watershed management

for optimization of forest road best management practices. In: Irwin, C.L.,

Garrett, P., Mcdermott, K.P. (Eds.), Proceedings of the 2003 International

Conference on Ecology and Transportation. Center for Transportation and the

Environment, North Carolina State University, Raleigh, US.

Riley, S.J., 1988. Soil loss from road batters in the Karuah State Forests, eastern

Australia. Soil Technology 1, 313–332.

Robichaud, P.R., Brown, R.E. 2002. Silt fences: an economical technique for measuring

hillslope soilerosion. RMRS-GTR-94, US Forest Service, Fort Collins, CO.

Rossman, L.A., 2005. Storm water management model: user’s manual version 5.0.

EPA/600/R-05/040. United States Environmental Protection Agency, Cincinnati.

Ryan, P.J., Murphy, S., McKenzie, N.J., 2003. Assessing Soil Erosion Hazard for

Australian Forest Management. Forest & Wood Products Research & Development Corporation, Victoria.

Saltelli, A., Chan, K., Scott, E.M., 2000. Sensitivity Analysis. Wiley, Chichester.

Scott, H.D., 2000. Soil Physics: Agricultural and Environmental Applications. Iowa

State University Press, Iowa, USA.

Sheridan, G.J., Noske, P.J., 2007. A quantitative study of sediment delivery and

stream pollution from different forest road types. Hydrological Processes 21 (3),

387–398.

Sheridan, G.J., Noske, P.J., Lane, P.N.J., Sherwin, C.B., 2008. Using rainfall simulation

and site measurements to predict annual interrill erodibility and phosphorus

generation rates from unsealed forest roads: validation against in-situ erosion

measurements. CATENA 73 (1), 49–62.

Sheridan, G.J., Noske, P.J., Whipp, R.K., Wijesinghe, N., 2006. The effect of truck

traffic and road water content on sediment delivery from unpaved forest roads.

Hydrological Processes 20 (8), 1683–1699.

Sidle, R.C., Sasaki, S., Otsuki, M., Noguchi, S., Nik, A.R., 2004. Sediment pathways in

a tropical forest: effects of logging roads and skid trails. Hydrological Processes

18 (4), 703–720.

Sidle, R.C., Ziegler, A.D., Negishi, J.N., Nik, A.R., Siew, R., Turkelboom, F., 2006. Erosion

processes in steep terrain-truths, myths, and uncertainties related to forest management in Southeast Asia. Forest Ecology and Management 224 (1–2), 199–225.

Smith, R.E., Goodrich, D.C., Quinton, J.N., 1995. Dynamic, distributed simulation of

watershed erosion: the KINEROS2 and EUROSEM models. Journal of Soil and

Water Conservation 50 (5), 517–520.

Smith, R.E., Parlange, J.Y., 1978. A parameter-efficient hydrologic infiltration model.

Water Resources Research 14 (3), 533–538.

Sugden, B.D., Woods, S.W., 2007. Sediment production from forest roads in western

Montana. Journal of the American Water Resources Association 43 (1), 193–206.

Swanson, F.J., Dyrness, C.T., 1975. Impact of clear-cutting and road construction on

soil erosion by landslides in the western Cascade Range, Oregon. Geology 3 (7),

393–396.

Thompson, C.J., Takken, I., Croke, J., 2008. Hydrological and sedimentological connectivity of unsealed roads. In: Schmidt, J., Cochrane, T., Phillips, C., Elliott, S., Davies, T.,

Basher, L. (Eds.), Sediment Dynamics in Changing Environments. Proceedings of

a symposium held in Christchurch, New Zealand, 1–5 December 2008, vol. 325.

International Association of Hydrological Sciences Publication, pp. 524–531.

Vincent, K.R., 1985. Runoff and erosion from a logging road in response to snowmelt

and rainfall. M.S. thesis, University of California, Berkeley, USA.

Wallbrink, P.J., Roddy, B.P., Olley, J.M., 2002. A tracer budget quantifying soil

redistribution on hillslopes after forest harvesting. CATENA 47 (3), 179–201.

Weigert, A., Wenk, G., Ollesch, G., Fritz, H., 2003. Simulation of snowmelt erosion

using the EROSION 3D model. Journal of Plant Nutrition and Soil Science 166

(1), 128–130.

Wemple, B.C., Swanson, F.J., Jones, J.A., 2001. Forest roads and geomorphic process

interactions, Cascade Range, Oregon. Earth Surface Processes and Landforms 26

(2), 191–204.

Williams, J.R., 1975. Sediment yield predictions with universal equation using runoff

energy factor. In: Present and Prospective Technology for Predicting Sediment

Yields and Sources. Proceedings of the Sediment Yield Workshop, USDA Sedimentation Lab, Oxford, Mississippi, 28–30 November 1972. USDA-Agricultural

Research Service, pp. 244–252. ARS-S-40.

Wischmeier, W.H., Smith, D.D., 1965. Predicting rainfall erosion losses from cropland east of the Rocky Mountains. In: Agricultural Handbook, vol. 282. U.S.

Department of Agriculture, Washington, DC.

Wischmeier, W.H., Smith, D.D., 1978. Predicting rainfall erosion losses – a guide to

conservation planning. In: Agricultural Handbook, vol 537. U.S. Department of

Agriculture, Washington, DC.

Woolhiser, D.A., Smith, R.E.,Goodrich, D.C.,1990. KINEROS, A Kinematic Runoff and Erosion

Model: documentation and user manual. USDA-Agricultural Research Service, No. 77.

Ziegler, A.D., Giambelluca, T.W., Sutherland, R.A., 2001a. Erosion prediction on

unpaved mountain roads in northern Thailand: validation of dynamic erodibility modelling using KINEROS2. Hydrological Processes 15 (3), 337–358.

Ziegler, A.D., Giambelluca, T.W., Sutherland, R.A., 2002. Improved method for

modelling sediment transport on unpaved roads using KINEROS2 and dynamic

erodibility. Hydrological Processes 16 (15), 3079–3089.

Ziegler, A.D., Sutherland, R.A., Giambelluca, T.W., 2000. Runoff generation and

sediment transport on unpaved roads, paths, and agricultural land surfaces in

northern Thailand. Earth Surface Processes and Landforms 25 (5), 519–534.

Ziegler, A.D., Sutherland, R.A., Giambelluca, T.W., 2001b. Interstorm surface preparation and sediment detachment by vehicle traffic on unpaved mountain

roads. Earth Surface Processes and Landforms 26 (3), 235–250.

Zoppou, C., 2001. Review of urban storm water models. Environmental Modelling &

Software 16 (3), 195–231.

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