A METHODOLOGY FOR PLANNING ROAD BEST MANAGEMENT PRACTICES

COMBINING WEPP: ROAD EROSION MODELING AND SIMULATED 

ANNEALING OPTIMIZATION

By

JAMES ANDERSON EFTA

B.S. Resource Conservation, The University of Montana, Missoula, MT, 2006

Thesis

presented in partial fulfillment of the requirements

for the degree of

Master of Science

in Forestry

The University of Montana

Missoula, MT

August 2009

Approved by:

Perry Brown, Associate Provost for Graduate Education

Graduate School

Woodam Chung, Chair

Department of Forest Management, College of Forestry and Conservation

Solomon Dobrowski

Department of Ecosystem and Conservations Sciences, College of Forestry and 

Conservation

Andrew Wilcox

Department of Geosciences
ii

Efta, James, M.S., Summer 2009 Forestry

A Methodology for Planning Road Best Management Practices Combining WEPP: Road 

Erosion Modeling and Simulated Annealing Optimization

Chairperson: Woodam Chung

Erosion from forest roads is a known problem in mountainous terrain. To abate these

negative consequences, physical Best Management Practices (BMPs) are implemented, sometimes with no knowledge of erosion hot spots. With the need to minimize water

quality impacts while at the same time accounting for multiple considerations and 

constraints, road BMP planning at the watershed scale is a difficult task. To assist in this

planning process, a methodology is presented here that combines WEPP: Road erosion

predictions with simulated annealing optimization. Under this methodology, erosion

predictions associated with BMP options for a segment comprise the objective function

of an optimization problem. This methodology was tested on a watershed in the Lake

Tahoe Basin. WEPP: Road input data was gathered through road surveys. Modeling

results predicted relatively little sediment leaving the forest buffer, as a result of

numerous well-maintained BMPs and the dry climate found in the watershed. A

sensitivity analysis for all WEPP: Road input parameters is presented, which provides

insight into the general applicability of these erosion estimates as well as the relative

importance of each input parameter. After evaluating erosion risk across the entire

watershed, applicable BMPs were assigned to problem road segments and WEPP: Road

was used to predict change in sediment leaving the buffer with BMP implementation at a

given site. These predictions, combined with budget constraints as well as equipment

scheduling considerations, were incorporated into an algorithm using simulated annealing 

as its optimization engine. Three modeled scenarios demonstrate the viability of this

methodology in reducing total sediment leaving the road buffer over a planning horizon. Of the 173 segments surveyed, 38 segments could be treated using generic BMPs. For all

three scenarios, BMP-SA reduced sediment leaving the buffer by as much as 70% over

the course of a 20-year planning horizon. For the 38 segments treated with BMPs, sediment was reduced by greater than 90% over the planning horizon. This methodology

is a viable approach for streamlining watershed-scale road network BMP planning, despite its heavy reliance on road erosion estimates. 
iii

ACKNOWLEDGEMENTS

First and foremost, I would like to thank Woodam Chung for his tireless work

ethic, constant willingness to answer my questions, and unending patience with me. Your 

teaching, encouragement, and advising will long be remembered. My committee

members, Solomon Dobrowski and Andrew Wilcox, both have my thanks for their

instruction and feedback over the past two years. 

I would also like to thank Randy Foltz, Bill Elliot, and Jun Rhee at the Rocky

Mountain Research Station in Moscow for their cooperation through the course of this

research project. The Pacific Southwest Research Station, by providing funding, made

this research possible.

Catherine Schoen, Jim Harris, and Paul Potts at the Lake Tahoe Basin

Management Unit have my thanks for meeting and conversing with me on multiple

occasions and providing invaluable insight for my research.

The College of Forestry and Conservation at The University of Montana has my

appreciation for providing a welcoming and challenging work and learning environment

over the past six years. Faculty, staff, and fellow students, thank you. 

Last, but certainly not least, I cannot express enough gratitude to my family and

friends for their encouragement and support while I have pursued this degree. 
iv

TABLE OF CONTENTS

Abstract ii

Acknowledgements iii

Table of Contents iv

List of Tables and Figures vii

1. Introduction/Literature Review 1

1.1 Introduction 1

1.2 Literature Review 3

1.2a Effects of Road Construction 3

1.2b Factors Affecting Severity of Road Impacts 5

1.2c Mitigation of Road Impacts Using Best Management Practices

8

1.2d Road Erosion Prediction Using Models 11

1.2e Natural Resource Planning and Decision Support Tools 13

1.3 Literature Review Summary 18

1.4 References 19

2. An Analysis of WEPP: Road Parameter Sensitivity 25

2.1 Abstract 25

2.2 Introduction 26

2.3 Description of WEPP: Road Interface 28

2.4 Methods 29

2.5 Results/Discussion 31
v

2.5a Qualitative Parameters 31

2.5b Quantitative Parameters 38

2.6 Conclusions 40

2.7 References 42

3. A Methodology for Planning Road Best Management Practices Combining WEPP: 

Road Erosion Modeling and Simulated Annealing Optimization 45

3.1 Abstract 45

3.2 Introduction 46

3.3 Study Site 47

3.4 Methods 49

3.4a Field data collection 49

3.4b Data acquisition using GIS/preparation for model input 51

3.4c “Hot spot” identification and verification 53

3.4d Simulated annealing modeling framework 54

3.5 Results 60

3.5a WEPP: Road erosion modeling results 60

3.5b BMP-SA modeling results 65

3.6 Discussion 72

3.6a Discussion of WEPP: road modeling results 72

3.6b Discussion of BMP-SA modeling results 77

3.7 Conclusions 78

3.8 References 81
vi

Appendixes A

A. Example Solution from BMP-SA Algorithm A

B. Flowchart Describing Adapted Simulated Annealing Algorithm

N

C. Example Input Table for BMP-SA Algorithm O
vii

LIST OF TABLES AND FIGURES

Tables

Table 1. WEPP: Road input parameters and possible values or parameter ranges 29

Table 2. Control road segment used for WEPP: Road sensitivity analysis 30

Table 3. WEPP: Road control segment predictions 31

Table 4. Classification of road segments with greater than 0 lbs/yr sediment leaving

buffer into risk rating classes 53

Table 5. Priority of BMP assignment for a given road segment 56

Table 6. Further criteria used when assigning BMPs to problematic road segments 

56

Table 7. Installation costs, maintenance costs, and maintenance frequencies associated 

with assigned BMPs 57

Table 8. Predicted sediment leaving road and sediment leaving buffer in ton/yr and

ton/acre/yr in Glenbrook Creek, NV. 61

Table 9. Forest road erosion rates from multiple published studies 75

Table 10. Reduction in predicted sediment leaving the buffer using BMP-SA model

78

Figures

Figure 1. Example of solution value change with iteration number in a minimization 

problem using simulated annealing optimization 17

Figure 2. WEPP: Road predictions of sediment leaving the road under four road designs

33

Figure 3. WEPP: Road predictions of sediment leaving the buffer under four road designs

33

Figure 4. WEPP: Road predictions of sediment leaving the road under different road 

surface types 36
viii

Figure 5. WEPP: Road predictions of sediment leaving the buffer under three road 

surface types 36

Figure 6. WEPP: Road predictions of sediment leaving the road under no traffic, low 

traffic, and high traffic scenarios 37

Figure 7. WEPP: Road predictions of sediment leaving the buffer under no traffic, low 

traffic, and high traffic scenarios 37

Figure 8. WEPP: Road predictions of sediment leaving the road in silt loam soil under 

multiple quantitative parameter scenarios 39

Figure 9. WEPP: Road predictions of sediment leaving the buffer in silt loam soil under 

multiple quantitative parameter scenarios 39

Figure 10. Map of study area 48

Figure 11. Example initial solution formulated from a list of alternative BMPs on a road 

segment 59

Figures 12 and 13. Examples of neighborhood solutions formulated from the initial 

(current) solution 59

Figure 14. Map of erosion risk by road segment, Glenbrook Creek forest road network

61

Figure 15. Erosion rates for sediment leaving native surface road segments at various 

segment lengths, Glenbrook Creek, NV. 62

Figure 16. Erosion rates for sediment leaving native surface roads at various road 

gradients, Glenbrook Creek, NV. 62

Figure 17. Erosion rates for sediment leaving the buffer from native surface roads at 

various buffer lengths, Glenbrook Creek, NV. 63

Figure 18. Average erosion rates for three road surface types, Glenbrook Creek, NV. 

64

Figure 19. Average erosion rates for native surface roads in three soil types, Glenbrook 

Creek, NV. 65

Figure 20. Sediment leaving road buffer through planning horizon with increasing initial

budget per period, new BMP installation only model scenario. 66
ix

Figure 21. Number of BMPs installed in period one at varying initial budgets per period, new BMP installation only model scenario. 66

Figure 22. Number of BMPs installed in each period at varying initial budgets per period, 

new BMP installation only model scenario. 67

Figure 23. Sediment leaving road buffer through planning horizon with increasing initial

budget per period for new BMP installation and maintenance model scenario. 68

Figure 24. Number and type of BMPs installed on treatable road segments at varying

initial budgets per period for new BMP installation and maintenance model scenario. 

69

Figure 25. Number and types of BMPs installed in period one at varying initial budgets

per period for new BMP installation and maintenance model scenario. 69

Figure 26. Number of BMPs installed in each period at varying initial budgets per period

for new BMP installation and maintenance model scenario. 70

Figure 27. Sediment leaving buffer through course of planning horizon at varying initial

budgets per period for existing BMP maintenance, new BMP installation, and new BMP

maintenance model scenario. 71

Figure 28. Number and type of BMPs installed in period one at varying initial budgets

per period for existing BMP maintenance, new BMP installation, and new BMP

maintenance model scenario. 71

Figure 29. Number of BMPs installed per period at varying initial budgets per period for

existing BMP maintenance, new BMP installation, and new BMP maintenance model

scenario. 72
1

1. INTRODUCTION/LITERATURE REVIEW

1.1 Introduction

Forest roads fulfill a critical service through providing access to public lands. If

road mileage is a metric of perceived importance of remote land access, the 380,000

miles of United States Forest Service (USFS)-administered forest roads could be

interpreted as invaluable (USDA Forest Service 2009). Negative impacts of these roads, however, are extensive. These impacts encompass biological effects as well as hydrologic

and geomorphic changes. To minimize negative road impacts, managers frequently implement Best

Management Practices (BMPs). In practice, physical BMPs (e.g. drain dips, cross- draining culverts, rip rap) are installed based on professional judgment in the field. Often, 

no data on sediment leaving the road surface or sediment leaving the buffer- thereby 

entering a stream- is used to guide judgment. One way to address this issue is to apply

some form of road erosion prediction model. These models range from relatively simple, two or three variable empirically-based prediction equations (such as those reported by 

Megahan and Ketcheson (1996)) to complicated, process-based computer models such as

WEPP: Road (Elliot et al. 1999). By applying some form of erosion prediction model to

road segments, managers can identify erosion hot spots and prioritize treatment. While applying hydrology models to road segments provides insight into where

treatment is most critical, these models do not provide any help in determining what

treatment is most effective. In addition, given budget constraints, managers must decide 

what BMPs are most cost-effective to install right now and what BMPs can be installed

on other sites in the future. Existing BMPs must be maintained to ensure continued
2

effectiveness; otherwise catastrophic road failure could result. Further challenges stem 

from the logistics associated with project planning for BMP installation, since it is

cheaper to install and maintain BMPs in near proximity in the same time period. At a

small scale, these issues are tractable. Planning BMPs for large watersheds, however, while taking into account all possible treatment options and management considerations, becomes exceedingly difficult. 

Heuristic optimization provides a starting point from which these problems can be

addressed. Heuristic optimization, in solving an objective function while taking into

account numerous side constraints, allows complicated planning problems to be solved

over relatively short computation time. A variety of heuristic optimization techniques

have been applied to forest planning issues for several decades, but have only more

recently been incorporating environmental constraints (Weintraub et al. 2000). 

Presented in this thesis is a methodology that combines road erosion modeling with

heuristic optimization with the intent of improving watershed-scale road BMP planning. Since the study site for demonstrating this methodology was in the Lake Tahoe Basin, literature references and procedures used herein cater to those conditions found in the

Lake Tahoe Basin. Note, however, that the general concept can be applied to any

watershed. 

The following section is a literature review of road prism and adjacent hill slope

hydrology, erosion modeling, road BMP implementation, and optimization techniques. Following the literature review is a manuscript presenting a WEPP: Road sensitivity

analysis. The final section of this thesis, also a manuscript, presents model results for

WEPP: Road erosion modeling combined with simulated annealing optimization.
3

Simulated annealing optimization, through iterative comparison of neighborhood

solutions, was used here to find a near-optimum BMP implementation and maintenance

scenario while accounting for multiple constraints (for a complete description of

simulated annealing, see Chapter 1.2e). With this research, I demonstrate that combining

road erosion prediction modeling with heuristic optimization techniques can improve

road BMP planning and implementation over a planning horizon.

1.2 Literature Review

1.2a Effects of Road Construction

Forest roads (hereafter referred to as “roads”) can be defined as a subset of roads

that “are characterized as being narrow, not covered with asphalt, lightly traveled, and

remote (Forman and Alexander 1998).” While more primitive and designed to access 

rougher terrain than other roads (Forman and Alexander 1998), these roads must also

accommodate larger vehicles to facilitate activities such as timber harvest, recreation, grazing, and mining (Akay et al. 2005, Switalski et al., 2003, Forman, 2000). While

Forman and Alexander’s definition excludes asphalt surfaced roads, the definition used

through the course of this thesis will include paved road segments, since the Lake Tahoe

Basin provides a notable exception to this definition by using asphalt paving on its road

network. 

The effects of road erosion begin with the first groundbreaking for a roadbed. Vegetation is removed from the future road bed, exposing soil to greater raindrop impact. 

Nutrient-rich topsoil is also removed, creating a positive feedback loop that leads to less

plant regeneration and greater exposure of organic matter-deficient soils to erosive forces. 
4

Soil compaction aggregates the soil’s susceptibility to erosion (Grismer and Hogan 2004,

Switalski et al. 2004). 

Roads crosscutting hillslopes reroute groundwater to the surface through the road’s

cutslope, causing an increase in overland flow (Luce 2002). With increases in road

density (number of roads per unit area) come increases in drainage density, since roads

can become drainage paths themselves (Wemple et al. 1996). Roads tend to increase the

amount of runoff delivered to streams and also increase in-stream erosion (Jones et al. 2000, Maholland 2002). As a result, frequency and magnitude of small stream peak flows 

increases (Maholland 2002, Luce 2002). 

Roads become a chronic fine source of sediment in a watershed (Luce 2002) and

can greatly increase the potential for landslides and mass flows in forested watersheds

(Grigal 2000, Jones et al. 2000), at times to such an extent that mass flow becomes the

predominant sediment source for streams (Megahan and Hornbeck 2000). 

Culverts are potentially responsible for several of the hydrologic, geomorphic, and

biological consequences of roads. If improperly sized, culverts will increase water speed

and subsequent erosive potential of runoff (Maholland 2002). With this increase in

erosive potential, new channels may form as a result of culvert placement and

permanently alter stream network structure (Wemple et al. 1996). In addition, culverts

have been found to be entry points for sediment and other stream pollutants (Forman and

Alexander 1998). Improperly placed culverts can become plugged, rerouting water to

other stream channels or directly down the road, and potentially causing washouts, severe 

gully erosion, or potentially even landslides when the drainage system becomes
5

completely overwhelmed (Forest Practices Advisory Committee (FPAC 2000)). Culverts

may serve as an impediment to upstream fish passage (FPAC 2000). 

Beyond fish passage issues, other biological impacts are also of concern when

discussing roads and their effects on the landscape. Roads create a medium for

introduction of invasive plant species (FPAC 2000, Switalski et al. 2004). Chronic inputs

of fine sediment tend to cause increased stream turbidity, which can cause problems for

fish, aquatic vegetation, and macro-invertebrates (Forman and Alexander 1998). Roads, especially at culverts, can block movement of large wood pieces downhill, which are

important for stream habitat. A buildup of wood and debris above a culvert could

eventually result in a culvert blowout and debris flow downhill (FPAC 2000). In terms of

wildlife, roads disrupt contiguous habitat sections and create barriers to movement and

migration (Forman and Deblinger 2000). Noise pollution is also an issue, causing more

problems for some species than others (Forman and Alexander 1998).

1.2b Factors Affecting Severity of Road Impacts

Parent materials and soil type influence road erosion potential. Sugden and Woods

(2007) found that the average annual sediment yield from Belt Metasediments is similar

to the amount of erosion found in basalt, sandstone, and other sedimentary materials in

the Northwest United States, but far less than for granitic parent materials like those

tested in the Idaho Batholith by other researchers. Research in the Lake Tahoe Basin has

shown volcanic parent materials to be even more erodible than the granitic parent

materials that also dominate the basin’s lithology (Grismer and Hogan 2005a). Glacial till 

parent materials are similar in sediment contribution to the Belt Supergroup studied by
6

Sugden and Woods (2007). In general, finer soils tend to contribute more sediment for

runoff than coarser-textured soils (Luce and Black 1999, Grismer and Hogan 2005a). 

Physical location and construction of a road also plays a role in a road’s

susceptibility to erosion. Packer (1967) found that the distance to the closest obstruction

below the road prism is directly related to how much sediment reaches a stream channel

from the road. Greater distance between roads and streams means, in all likelihood, more

obstructions, and therefore less sediment delivered. This fact, however, is also contingent 

upon the degree of hydrologic connectivity to the stream network (Wemple et al. 1996). 

Presence or absence of aggregate surfacing, depth of that surfacing, and quality of

that surfacing can affect road erosion rates (Swift 1984, Foltz and Truebe 2003). Steeper

slopes and longer road segments will increase road erosion rates (Sugden and Woods

2007, Luce and Black 1999). Aspect of slope will influence available water, and as a

result will also control potential surface erosion (Packer 1967). In addition, road

geometry (insloped versus outsloped or crowned road profile, road width) will also serve

as a control on sediment production (Luce and Black 1999, Packer 1967). Location of

sediment origin on the road prism partially regulates road sediment travel distance

(Megahan and Hornbeck 2000). 

Cutslope height and angle will vary sediment yield, as will presence or absence of

vegetation on the cutslope, in the ditch, and on the road’s fill slope (Luce and Black

1999). The amount of cutslope runoff contribution relative to the road bed itself is not

generally agreed upon by researchers (Luce 2002). Cutslope interception of subsurface

flow and the consequent contribution of subsurface flow to road runoff and surface

erosion may be a major contributor to road surface erosion in wetter climates and
7

landscapes (Wemple and Jones 2003, Luce 2002). Slope length, soil depth, subsurface

topography, and cutslope height relative to total depth of cutslope to bedrock all dictate

degree of groundwater interception and surface runoff (Wemple and Jones 2003). 

Road location on a slope can play an important role in determining erosion

potential. Roads located high on a slope are more susceptible to erosion as a result of

receiving a greater amount of precipitation due to orographic effect (Maholland 2002). Roads high on a slope, however, tend to be minimally connected to streams (due to

minimal stream channel formation) and therefore have a lower proportional impact on

stream sedimentation (Jones et al. 2000, Bloom 1998). Roads, however, can concentrate

flow, creating channels higher on the slope than if no roads were present (Forman and

Alexander, 1998). Roads located on the mid- and low-slope can be major contributors of

sediment to stream channels (Maholland 2002, Bloom 1998). In western Oregon, mid- slope roads tend to be net sources of sediment, whereas valley floor roads tend to be net

sinks (Jones et al. 2000). 

New roads tend to produce more sediment than old roads, and newly disturbed

roads (for example, roads that have been recently graded) produce more sediment than

undisturbed roads (Megahan and Kidd 1972, Swift 1984, Grigal 2000). 

Traffic on forest roads is a dominating factor in the amount of sediment produced

(Reid and Dunne 1984). Ruts, by channeling runoff directly down the road grade, increase erosion potential (Swift 1984, Grigal 2000). With these factors in mind, road

maintenance regimen will influence road erosion potential (Swift 1984). 

Climate plays a major role in controlling road erosion potential. Rainfall intensity

and duration affect surface erosion (Grigal 2000). In areas where snowmelt is not the
8

dominant form of precipitation, snowmelt runoff may not exceed forest soil infiltration

rates or soil critical shear stress values, making it a minor contributor to sedimentation

(Elliot 2006). In contrast, the majority of sediment reaching downstream water bodies

from upland sources may come during spring snowmelt in environments where snow is

the dominant form of precipitation (Simon et al. 2006).

Adjacent forest management practices can affect sediment production from roads. Fewer trees adjacent to a given road section will produce more water yield than a thicker

forest stand and consequently shed more water to the road grade (Luce and Black 1999, 

Megahan and Hornbeck 2000, Grigal 2000). In most cases, sediment production from

roads has been found to greatly exceed the amount of sediment produced by the timber

harvest for which they were built to access (Megahan and Kidd 1972, Sugden and Woods 

2007). 

With all of these factors taken into consideration, it is clear that transportation

network planning plays a crucial role in how much sediment is produced by forest road

networks (Krogstad and Schiess 2000, FPAC 2000).

1.2c Mitigation of Road Impacts Using Best Management Practices

To address and minimize effects of road erosion, scientists and managers have

formulated standards, or Best Management Practices (BMPs), as guidelines for how

projects should be conducted and constructed. “Best Management Practices or ‘BMPs’ 

are those principals and engineering design practices that will protect water quality as

well as the function of the road when properly applied (Keller and Sherar 2007).” Besides 

roads, BMPs practices have also been formulated for a number of landscape management 
9

practices, for example agriculture (Brown et al. 2007), hazard fuel reduction (O’Connell 

2006), grazing (Wyoming Department of Environmental Quality 1997), and mining (U.S. 

EPA 2000).

Road BMPs can be structural/physical or planning in nature. Examples of

structural/physical road BMPs include culverts, drain dips or waterbars, and resurfacing. 

Planning BMP examples include maintenance frequency or limiting what length of road

surface can be graded at one time (USDA Forest Service 2000).

Physical BMPs used in the Lake Tahoe Basin: Since Lake Tahoe is a unique

management situation (spanning two states, multiple national forests, and being

susceptible to heavy user traffic), the Lake Tahoe Basin has its own USFS management 

district- the Lake Tahoe Basin Management Unit (LTBMU)- along with a number of

other planning agencies. To ensure compliance with its BMPs, the LTBMU has initiated

an annual monitoring program to evaluate effectiveness of mandated BMPs. In general, LTBMU BMPs have been effective according to their evaluation criteria (Brill et al. 2009, Heller and Norman 2005).

Structural/physical BMPs used frequently in the Lake Tahoe Basin include (but are

not limited to) culverts, gravel, native and rocked ditches, riprap, drain dips, and

pavement. Discussions pertinent to those BMPs assigned to problem road segments in the 

Lake Tahoe Basin study watershed are below (for further detail, see Chapters 2 and 3). Pavement: In terms of surfacing, paving roads will prevent sediment entrainment

from the road bed, but in turn will create an impervious surface that may concentrate

water and sediment into drainage structures (Maholland 2002). Nonetheless, paving may
10

be the best sediment mitigation solution for high-traffic roads (Reid and Dunne 1984, Clinton and Vose 2004). Paving short road segments in mountainous terrain is a costly 

endeavor (USDA Forest Service 2008), and as such is used relatively infrequently.

Drain dips: Drain dips fall into the broad category of surface cross drains. By 

interrupting hydraulically contiguous sections of road, segment length, which has been

found to be an important variable in determining sediment production on forest roads

(e.g. Luce and Black 2001a, Coe 2006), is minimized. Beyond segment length, 

appropriate drain dip spacing is dictated by a number of different factors, including

(among others) surfacing material characteristics, climate, and road grade (Copstead et al. 

1998).Outsloping: Under this road profile design, runoff is not concentrated into a point

source; rather, runoff is dispersed off the shoulder along the entire length of the road

segment. By dispersing runoff and sediment in this fashion, sediment is less likely to

reach a stream (Luce and Black 2001a, Elliot et al. 2009). While a highly effective BMP, outsloping is not appropriate in all situations (such as on wet or steep roads with heavy

truck traffic) and requires more intensive maintenance than other BMPs (USDA Forest

Service 2008). Road decommissioning: If a road segment is unnecessary, it can be permanently

removed from the road network (Switalski et al 2004). Road decompaction and prism

restoration are becoming more popular options following decommissioning (Luce 2002, Switalski et al. 2004). The Lake Tahoe Basin recently finished a period of extensive

forest road decommissioning, and as such is no longer widely applying this BMP (P. Potts personal communication). 
11

1.2d Road Erosion Prediction Using Models

General overview of hydrologic models: To assess runoff and erosion, researchers

and managers have enlisted the help of mathematical hydrologic models for many years

(Sorooshian et al. 2008, Loague and VanDerKwaak 2004). These models fall into several 

broad categories: empirical versus process (physics)-based, stochastic versus

deterministic, and lumped versus distributed. 

In use since the 1970’s, the Universal Soil Loss Equation (USLE) is a widely used

empirically-based erosion prediction model (Wischmeier and Smith 1978). The Revised

Universal Soil Loss Equation (RUSLE) and the Modified Universal Soil Loss Equation

(MUSLE) are two more recent improvements on the original model (Brooks et al. 2003). 

Empirical models do not make full use of our understanding of hydrologic system

dynamics. Process-based models, in contrast, incorporate knowledge about the physics of

a system to derive more detailed yet generalizable predictions of runoff and sediment

(Renschler 2003).

As a sub-category of process-based models, stochastic models draw variable inputs

from probability distributions. In contrast, deterministic models define input variables as

being free from random variation (Loague and VanDerKwaak 2004). A further

subdivision within hydrologic models stems from whether the model treats spatial

watershed variability in a lumped versus distributed fashion. While distributed models

allow for spatial variability in climate and hydrologic processes across a watershed, lumped models do not. Accounting for spatial variability produces a more accurate

representation of watershed-scale hydrologic processes. As a tradeoff, these models can
12

be highly complex as a result of requiring detailed spatially-explicit data and may 

demand greater computation resources (Sorooshian et al. 2008).

Distributed Hydrology-Soil-Vegetation Model (DHSVM) (Wigmosta et al. 1994),

and Système Hydrologique Européen Sediment Yield Component (SHESED) (Wicks and 

Bathurst 1996) are examples of fully process-based models currently in use. The Water

Erosion Prediction Project (WEPP) (Flanagan and Nearing 1995), also a fully process- based hydrologic model, has over 400 input parameters. Originally designed for

agriculture, it has been adapted for use in forest conditions (Elliot et al. 2006) and has

been applied to a variety of watersheds with success at a variety of scales (Amore et al. 2004). 

Hydrologic modeling and road erosion: Empirical and process-based models alike

have been developed to predict road erosion. Several studies have developed road

sediment volume and travel prediction equations from empirical data (e.g. Megahan and

Ketcheson 1996, Anderson and MacDonald 1998). These empirical models are

computerized in some instances; ROADMOD and STJ-EROS, two GIS-based models

capable of predicting road erosion, calculate erosion using empirical relationships

(Ramos-Scharron and MacDonald 2007). 

As process-based hydrologic models have become more prevalent, so too have

process-based road erosion prediction tools. SWAT, while not spatially-explicit, is 

capable of predicting road erosion (Neitsch et al. 2005) (Despite being generally 

considered a physics-based model, SWAT’s erosion computations are based on empirical
13

models). Doten and others’ (2006) modification of DHSVM to accommodate road

sediment was the first spatially-explicit physics-based model to incorporate road erosion. 

With process-based models have come complexity and inaccessibility to untrained

users. WEPP: Road, a user-friendly web-based interface for WEPP, has been developed

by the Rocky Mountain Research Station (Elliot et al. 2004) to address this problem. This 

marks the first adaptation of a process-based model specifically for predicting sediment 

from road segments. WEPP: Road requires few input parameters, many of which can be

acquired without field surveys. The interface allows users from a variety of technical

backgrounds to effectively predict impacts associated with road-related management

decisions. By providing a range of climates (and the option to alter climates to represent 

site-specific conditions), surface types, traffic levels, and road designs, WEPP: Road is

applicable virtually anywhere in the U.S.

1.2e Natural Resource Planning and Decision Support Tools

Forest and natural resource planning, especially when accounting for multiple uses, has become ever more complex over time (Rönnqvist 2003). Optimization strategies

(including application to forest roads) have been employed since the 1970’s to address

multiple management goals and environmental constraints in forest planning (Weintraub

et al. 1995, Rönnqvist 2003, Weintraub 2006).

Optimization strategies consist of either exact solutions or heuristics (Kirkpatrick et

al. 1983). Linear programming, integer programming, and mixed integer programming

are all common exact solution methods. While exact solutions are often preferred, problem complexity may require excessive computation power or time (Kowalski 1995). 
14

In these cases, heuristics are favorable. While not guaranteed to find the exact solution, heuristics produce near optimum solutions during multiple process repetitions with less

computing time (Lin and Kernighan 1973). 

With increasing concern for environmental impact of forest operations has come

incorporation of impact mitigation strategies into the planning process (Weintraub et al. 2000). Sedimentation associated with timber harvest has been accounted for since the

1970’s using linear programming techniques (Hof and Bevers 2002). Application of

heuristic optimization specifically to environmental concerns, including sedimentation

associated with roads, has only occurred more recently (Chung 2002, Weintraub et al. 2000). 

Optimization and road impact analysis: Multiple projects to date have incorporated

BMPs and/or associated erosion potential into cost-benefit analyses for road management

planning. Aruga and others (2005) optimized road alignments using a Tabu Search

algorithm. To incorporate road impact concerns, road sediment was accounted for with 

empirically-derived erosion equations. BMPs assigned to road segments included road 

surface material, culvert location (segment length), and outsloped road design. This 

research emphasized new road construction and incorporated erosion concerns as a side

constraint. 

 Taking a stream restoration perspective, Madej and others (2006) compared the

effectiveness of a genetic algorithm (a heuristic technique) with dynamic programming

(an exact solution technique) to assess the cost effectiveness of road removal treatments

on a watershed scale. While both search techniques provided similar answers, the genetic
15

algorithm was deemed to have several advantages over dynamic programming because it

provides a set of effective solutions rather than only one solution. As a result, managers 

have a choice of which solution to use when wishing to account for other factors besides

just sediment savings. Sediment savings associated with various treatments was

accounted for by physically measuring voids left in road prism, native hillslopes, and

channels following a 12-year storm event. 

Modeled road erosion predictions have been incorporated into forest transportation

planning problems. To date, all research incorporating these predictions has used WEPP:

Road to model road sediment. Rackley and Chung (2008) applied a dollar amount to

WEPP: Road erosion estimates to incorporate environmental concerns into

NETWORK2000, a forest transportation planning tool. Since environmental constraints

had to be assigned a dollar amount within their modeling framework, Rackley and

Chung’s research provided an indirect assessment of these constraints. 

In another application of WEPP: Road to a forest transportation planning problem, Contreras and others (2008) used WEPP: Road sediment predictions to incorporate road

sediment as a side constraint into an Ant Colony Optimization (ACO) metaheuristic. While modeled sediment was directly assessed (not assigned a dollar value), it was not

the objective function of the planning problem. 

No studies to date have exclusively emphasized sediment concerns associated with

BMP implementation on existing forest road networks. While process-based models have 

been used to estimate erosion, they have only been used to assess side constraints in

forest transportation planning problems. The logical evolution of watershed-scale road

network planning problems is to formulate sedimentation concerns as objective functions
16

within the planning problem. Furthermore, process-based road erosion predictions, being

the current state-of-the-art, could be used in the place of empirical equations.

Though multiple heuristics could be used to solve similar planning problems, simulated annealing (Kirkpatrick et al. 1983) is a primary candidate for addressing forest

road BMP planning. For uncomplicated planning problems not concerned with

transportation network planning, the use of more complex heuristics is unwarranted. Simulated annealing is simple compared with other heuristics, yet effective, and can be

applied to a variety of optimization problems (Kirkpatrick et al. 1983, Tarp and Helles

1997).

Description of Simulated Annealing: Simulated annealing loosely resembles

cooling metal leaving a forge. Beginning and ending temperatures are specified before 

starting the search, as is cooling rate. When the search starts, two solutions are generated. The second of these solutions is a neighborhood solution to the initial (current) solution, where one element of the initial solution has been altered. The objective function values 

for these two solutions are then compared. 

If the alternative (new) solution value is indeed better than the initial solution, the

new solution is stored as the current solution. The next iteration of the algorithm

generates a new solution by again altering one element of the current solution. In the

case that the alternative solution is not better than the initial solution, an acceptance

probability is generated using the following equation: 
17

Depending on whether the objective function is to minimize or maximize a value, the relationship between the acceptance probability and a randomly generated number

will dictate whether the worse new solution will be accepted and used as the current

solution in the next algorithm iteration. In accepting a worse solution, simulated 

annealing provides for the possibility that the worse solution may serve as a link to a

better solution that would not be found as quickly using a random search. 

After a set number of iterations, temperature is cooled at the set cooling rate. As

temperature becomes smaller, the interval of difference between the new and current

temperature must be smaller in order for a worse solution to be accepted. This creates a

solution space that becomes less variable as algorithm iterations increase and temperature 

decreases. Upon reaching stopping criteria (often defined as maximum number of

iterations or minimum temperature), the algorithm stops and a best solution is reported.

Figure 1. Example of solution value change with iteration number in a minimization problem using

simulated annealing optimization.

20

25

30

35

40

45

0 2000 4000 6000 8000 10000 12000 14000 16000 18000

Be

st solutio

n

valu

e

Number of iterations
18

Simulated annealing has been used to solve complicated natural resource planning

problems that include both spatial adjacency and temporal constraints. Example 

applications include forest harvest scheduling (e.g. Lockwood and Moore 1993, Liu et al. 2000) and land-use allocation associated with mine reclamation (Aerts and Heuvelink

2002). In terms of road-related applications, simulated annealing has been used to

optimize forest road vertical alignment within forest road construction decision support

tools (Akay and Sessions 2005). Additionally, Coulter et al. (2005) used simulated

annealing to optimize forest road maintenance and upgrade projects on Oregon State

University research forests. To date, no projects have addressed spatially-explicit BMP 

installation and maintenance scheduling with the exclusive intention of minimizing water

quality degradation using simulated annealing. 1.3 Literature Review Summary

Surface hydrology associated with road networks is fairly well-understood. To

address negative impacts associated with roads, BMPs have been implemented on road

networks. Examples of BMPs used on forest roads in the Lake Tahoe Basin include 

outsloping, paving, and drain dips. Road erosion models come in multiple different

forms, ranging from empirical to process-based. Researchers have begun bridging the gap 

between identification of problematic road segments and planning of BMP

implementation. There is a lack of planning tools available for directly addressing road

sedimentation and planning applicable BMPs on existing road networks. Combining

process-based road erosion modeling with heuristic optimization, specifically simulated

annealing, provides a possible framework for this needed tool. 
19

1.4 References

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J. Geographical Information Science 16(6): 571-587. 

Akay, A.E., and Sessions, J. 2005. Applying the Decision Support System, TRACER, to 

Forest Road Design. Western Journal of Applied Forestry 20(3): 184-191.

Akay, A., Boston, K., and Sessions, J. 2005. The evolution of computer-aided road

design systems. International Journal of Forest Engineering 16(2): 73-79.

Amore, E., Modica, C., Nearing, M.A., and Santoro, V.C. 2004. Scale effect in USLE

and WEPP application for soil erosion computation from three Sicilian basins. Journal of

Hydrology 293: 100-114.

Anderson, D.M., and MacDonald, L.H. 1998. Modelling road surface sediment

production using a vector geographic information system. Earth Surface Processes and

Landforms 23: 95-107. 

Aruga, K., Sessions, J., and Miyata, E.S. 2005. Forest road design with soil sediment

evaluation using a high-resolution DEM. Journal of Forest Research 10: 471-479. 

Bloom, A.L. 1998. An Assessment of Road removal and Erosion Control Treatment

Effectiveness: A Comparison of 1997 Storm Erosion Response between Treated and

Untreated Roads in Redwood Creek Basin, Northwestern California. MSc. Thesis, Humboldt State University, Arcata California. 

Brill, N., Harris, J., and Norman, S. 2009. 2008 Best Management Practices Evaluation

Program Report. USDA Forest Service, Lake Tahoe Basin Management Unit.

Brooks, K. Ffolliott, P., Gregersen, H., and DeBano, L. Hydrology and the Management

of Watersheds: Third Edition. 2003: Iowa State Press. 

Brown, L., Boone, K., Nokes, S., Ward, A. Agricultural Best Management Practices. AEX-464-91. Ohio State University Extension Fact Sheet: Food, Agricultural and

Biological Engineering. http://ohioline.osu.edu/aex-fact/0464.html. Accessed 13

September 2007. Chung, W. 2002. Optimization of cable logging layout using a heuristic algorithm for network

programming. PhD Thesis. Oregon State University, Corvallis, Oregon.

Clinton, B.D., and Vose, J.M. 2003. Differences in Surface Water Quality Draining Four

Road Surface Types in the Southern Appalachians. Southern Journal of Applied Forestry 

27(2): 100-106. 
20

Contreras, M.A., Chung, W., and Jones, G. 2008. Applying ant colony optimization

metaheuristic to solve forest transportation planning problems with side constraints. Canadian Journal of Forest Research 38: 2896-2910.

Copstead, Ronald L.; Johansen, David Kim; Moll, Jeffry. 1998. Water/Road Interaction: 

Introduction to surface cross drains. Report 9877 1806-SDTDC. San Dimas, CA: U.S.

Department of Agriculture, Forest Service,Technology and Development Program. 15 p.

Akay, A.E., and Sessions, J. 2005. Applying the Decision Support System, TRACER, to 

Forest Road Design. Western Journal of Applied Forestry 20(3): 184-191.

Doten, C.O., Bowling, L.C., Lanini, J.S., Maurer, E.P., and Lettenmaier, D.P. 2004. A 

spatially distributed model for the dynamic prediction of sediment erosion and transport

in mountainous

forested watersheds. Water Resources Research 42: W04417. 

Elliot, W. J. 2004. WEPP internet interfaces for forest erosion prediction. Jour. Am. Water Res. Assoc. 40(2):299-309.

Elliot, W.J. 2006. The roles of natural and human disturbances in forest soil erosion. In: 

Owens, P.N.; Collins, A.J. (eds.). Soil Erosion and Sediment Redistribution in River

Catchments. Wallingford, Oxfordshire, UK: Commonwealth Agricultural Bureau

International. 177-185.

Elliot, W.E.; Foltz, R.B.; Robichaud, P.R. 2009. Recent findings related to measuring and 

modeling forest road erosion. In Anderssen, R.S.; Braddock, R.D.; Newham, L.T.H., eds. Proceedings of the 18th World IMACS / MODSIM Congress, Cairns, Australia, 13-17 

July 2009. International Congress on Modelling and Simulation. Interfacing Modelling

and Simulation with Mathematical and Computational Sciences. 

Flanagan, D.C., and Nearing, M.A. (Eds.). 1995. USDA-water erosion prediction project: 

hillslope profile and watershed model documentation. NSERL Report #10, USDA-ARS 

National Soil Erosion Research Laboratory, West Lafayette, Indiana, 298pp.

Foltz, R.B. and M.A. Truebe, 2003. Locally Available Aggregate and Sediment

Production. Transportation Research Record 1819, Paper No. LVR8-1050.

Forest Practices Advisory Committee, 2000. Report of the Forest Practices Advisory 

Committee on Salmon and Watersheds, Oregon Department of Forestry. Section B:

Forest Roads.

Forman, R.T. 2000. Estimate of the Area Affected Ecologically by the Road System in

the United States. Conservation Biology 14(1): 31-35. 

Forman, R.T. and Alexander, L. 1998. Roads and their Ecological Effects. Annual

Review of Ecological Systematics 29: 207-231. 
21

Forman, R.T.T. and Deblinger, R.D. 2000. The Ecological Road-Effect Zone of a

Massachusetts (U.S.A) Suburban Highway. Conservation Biology 14(1): 36-46. 

Grigal, D.F. 2000. Effects of Extensive Forest Management on Forest Productivity. Forest Ecology 138: 167-185.

Grismer and Hogan. Simulated Rainfall Evaluation of Revegetation/Mulch Erosion

Control in the Lake Tahoe Basin—1: Method Assessment, 2: Bare Soil Assessment, 3: 

Soil Treatment Effects. Land Degrad. Develop. 15: 573–588 (2004), Land Degrad. Develop. 16: 397–404 (2005),Land Degrad. Develop. 16: 489–501 (2005).

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

USDA Forest Service, Lake Tahoe Basin Management Unit. 

Hof, J., and Bevers, M. 2002. Spatial Optimization in Ecological Applications. Columbia

University Press: New York. 

Jones, J.A., Swanson, F.J., Wemple, B.C., and Snyder, K.U. 2000. Effects of Roads on

Hydrology, Geomorphology, and Disturbance Patches in Stream Networks. Conservation

Biology 14(1): 76-85. 

Keller, G. & Sherar, J. Low-Volume Roads Engineering: Best Management Practices

Field Guide.

http://ntl.bts.gov/lib/24000/24600/24650/Index_BMP_Field_Guide.htm. Accessed 11

September 2007. Kirkpatrick, S., Gelatt, C.D., and Vecchi, M.P. 1983. Optimization by Simulated

Annealing. Science 220(1948): 671-680. 

Kowalski, K. 2005. On the structure of the fixed charge transportation problem. Int. J. Math. Educ. Sci. Technol. 36: 879–888.

Krogstad, F. and Schiess, P. 2000. Haul routing: an overlooked factor in environmentally 

driven road decommissioning. In Technologies for New Millennium Forestry: 

Proceedings of the 23rd Annual Meeting of the Council on Forest Engineering. Kelowna, British Columbia, Canada, September 11-14, 2000.

Lane, L.J., Shirley, E.D., Singh, V.P., 1988. Modelling erosion on hillslopes. In:

Anderson, M.G. (Ed.), Modelling Geomorphological Systems. Wiley, Chichester

(Chapter 10).

Lin, S. and Kernighan, B.W. 1973. An Effective Heuristic Algorithm for the Traveling- Salesman Problem. Operations Research 21(2): 498-516. 
22

Liu, G., Lockwood, J.D., and Warden, C.W. 2000. A target-oriented approach to forest 

ecosystem design- changing the rules of forest planning. Ecological Modelling 127: 269- 281. 

Loague, K., and VanDerKwaak, J.E. 2004. Physics-based hydrologic response

simulation: platinum bridge, 1958 Edsel, or useful tool. Hydrological Processes 18: 2949- 2956.

Lockwood, C. & Moore, T. 1993. Harvest scheduling with spatial constraints: a 

simulated annealing approach. Can. J. For. Res. 23: 468-478.

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

roads: what do we still need to learn? Hydrol. Process. 16: 2901–2904. Luce, C.H. and Black, T.A. 1999. Sediment production from forest roads in western

Oregon. Water Resources Research 35(8): 2561-2570. 

Luce, C.H., and Black, T.A. 2001a. Spatial and Temporal Patterns in Erosion from Forest 

Roads. In Influence of Urban and Forest Land Uses on the Hydrologic-Geomorphic 

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23

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25

2. AN ANALYSIS OF WEPP: ROAD PARAMETER SENSITIVITY

2.1 Abstract

WEPP: Road is a user-friendly interface to a process-based road erosion model

that is applicable virtually anywhere in the U.S. The sensitivity analysis presented here

provides a perspective for identifying those parameters that are most important to collect

accurately during road surveys. In addition, the analysis provides insight into the central

physical concepts that drive WEPP: Road predictions. Forty road segments were

generated where one parameter was altered in each segment from its control value. Quantitative parameters were altered to plus and minus 10% and 30% of their control

value. All 40 segments were input into WEPP: Road under all soil options using the same 

climate. 

WEPP: Road erosion rate estimates were substantially different between soil 

types. These differences could be explained through a combination of soil cohesive 

strength and particle size. WEPP: Road predicted an increase in sediment leaving the

road and sediment leaving the buffer with a change in road surface from native to paved. Any change in rock content above 50% in WEPP: Road yielded no change in erosion rate 

predictions. Road length and width were the most sensitive quantitative parameter inputs

for estimates of both sediment leaving the road and sediment leaving the buffer. Generally, WEPP: Road estimates matched published data. 
26

2.2 Introduction

Forest roads fulfill a critical service through providing access to remote public

and private lands, often in rugged terrain (Forman and Alexander 1998, Switalski et al. 2003). While providing important functions, forest roads have numerous negative

consequences. These effects include biological impacts (e.g. FPAC 2000, Switalski et al. 2004, Forman and Deblinger 2000), changes to hillslope hydrology (e.g. Jones and Grant

1996, Maholland 2002, Luce 2002), and geomorphic consequences (e.g. Wemple et al. 1996, Montgomery 1994, Jones et al., 2000). Runoff and erosion prediction (hydrologic) models are one method by which

consequences of watershed erosion can be mitigated. With hydrologic models, future

events can be forecast and previous hydrologic events can be analyzed. Managers and

planners can minimize environmental damage resulting from management decisions 

(Singh and Woolhiser 2002). Through prediction of sediment loss, thousands of dollars in 

economic loss may be prevented as a result of property damage, incorrect placement of a

road or drainage structure, or restoration of an area following an ill-conceived 

management decision. 

For years, empirical models such as the Universal Soil Loss Equation

(Wischmeier and Smith 1978), and Revised Universal Soil Loss Equation (Renard et al. 1997) were widely used to make erosion estimates. Empirical models, while simple, do

not make full use of our understanding of hydrologic system dynamics (Renschler 2003). 

Process- and physics-based models, in contrast, incorporate knowledge about the physics

of a system to derive more detailed yet generalizable predictions of runoff and sediment

(Renschler 2003). The Water Erosion Prediction Project (WEPP) (Flanagan and Nearing
27

1995) is one of many process-based hydrologic models currently in use. Originally 

designed for agriculture, it has been adapted for use in forest conditions (Elliot et al. 2006) and has been applied to a variety of watersheds with success at multiple scales 

(Amore et al. 2004).

To address the need for a relatively simple, user-friendly road erosion model, WEPP: Road was developed by the Rocky Mountain Research Station in Moscow, ID

(Elliot 2004). WEPP: Road provides a web-based graphic user interface requiring few

input parameters, many of which can be acquired without field surveys. The interface

allows users from a variety of technical backgrounds to effectively predict impacts

associated with road-related management decisions. By providing a range of climates

(and the option to alter climates to represent site-specific conditions), surface types, traffic levels, and road designs, WEPP: Road is applicable virtually anywhere in the U.S. 

Understanding how a given parameter will affect road erosion estimates is

important for model users. Given limited resources, WEPP: Road users may be unable to

measure all necessary input parameters in the field at every site of interest. Knowing

which parameters are essential to accurately measure gives users a better idea of where to 

best allocate resources. In addition, it is important to understand sources of prediction

variability in assessing model outputs when trying to achieve the best possible erosion

predictions. 

The sensitivity analysis presented here fills this need. From this sensitivity

analysis, identified sources of prediction variability can inform users of the general

concepts that drive the WEPP model. Additionally, WEPP: Road’s predictive capability

can be validated by analyzing whether predictions agree with current literature. 
28

2.3 Description of WEPP: Road Interface:

WEPP: Road is an interface to the WEPP model specifically catering to road

hydrology and sediment production estimation. Numerous climate base station records

are available in the climate library. To accommodate local climate variation, base station

data can be altered using the Parameter-elevation Regression based on Independent

Slopes (PRISM) model, which modifies precipitation based on linearly regressed

relationships with elevation (Daly et al. 2004). WEPP: Road estimates runoff and soil

loss on three overland flow elements: the roadbed itself, a fill slope, and the road buffer

(hill slope area between the base of the fill slope and the nearest water source) (Elliot et

al. 1999). Four soil types can be modeled by WEPP: Road: clay loam, silt loam, sandy

loam, and loam. Four road designs (insloped, bare ditch, insloped, vegetated ditch, outsloped, unrutted, and outsloped, rutted), three road surface types (native, graveled, or

paved), and three traffic levels (none, low, and high) are provided as options in the 

WEPP: Road interface. Other input parameters include road gradient, road length, road

width, fill slope gradient, fill slope length, buffer gradient, buffer length, and percent rock 

content (defined as the percent volume of rock fragments greater than 2 mm in diameter

in the soil substrate (H. Rhee personal communication)). While the default simulation

time is 30 years, the user can specify longer time periods if desired (Table 1). WEPP: Road outputs include a summary of input values as well as predicted 

runoff from rain events, predicted runoff from winter storm events, sediment leaving the

road prism (road), and sediment leaving the buffer.
29

Table 1. WEPP: Road input parameters and possible values or parameter ranges.

WEPP: Road input 

parameter

Possible values/allowable 

range

Climate N/A

Soil type Silt loam

Sandy loam

Clay loam

Loam

Road design Insloped, bare ditch

Insloped, vegetated or 

rocked ditch

Outsloped, unrutted

Outsloped, rutted

Surface type Native

Graveled

Paved

Traffic level None

Low

High

Road width 1 ft - 300 ft

Road length 1 ft - 999 ft

Road gradient .3% - 99%

Fill slope length 1 ft - 999 ft

Fill slope gradient .3% - 99%

Buffer length 1 ft - 999 ft

Buffer gradient .3% - 99%

Coarse rock content 0% - 100%

Years of simulation time 1 yr - 200 yrs

2.4 Methods

WEPP: Road inputs for this analysis were chosen based on average values

frequently seen on forest roads in the western United States. The control segment can be

found in Table 2. 
30

Table 2. Control road segment used for WEPP: Road sensitivity analysis. 

Design Surface, 

traffic 

Road 

grad 

(%) 

Road 

length 

(ft) 

Road 

width 

(ft) 

Fill 

grad 

(%) 

Fill 

length 

(ft) 

Buff 

grad 

(%) 

Buff 

length 

(ft) 

Rock 

cont 

(%) 

Insloped, 

bare 

ditch

native 

low 7 300 12 50 10 20 300 50

After establishing a control segment, new road segments were created, each with 

one input parameter altered from the control. Qualitative parameters (road design, surface, and traffic level) were altered such that every possible parameter value was

represented in a segment. Each quantitative parameter was altered to plus and minus 10% 

and 30% of the control parameter value. In doing so, a wide range of forest road

conditions commonly seen on the ground could be evaluated. Using these criteria, a total

of 40 test segments were developed. Interaction between input parameters was not tested.

The 40 segments were run in WEPP: Road Batch, an alternative WEPP: Road

interface which allows the user to estimate sediment leaving the road and buffer for up to

200 segments simultaneously. All 40 segments were run with each of the four soil texture 

options. “TAHOE CA” base station climate data (available in the WEPP: Road Batch

climate library) was used for the simulation. Monthly average precipitation values from

this base station data were increased using PRISM based on elevation at a central location 

within the Glenbrook Creek watershed, NV. (For justification of study site, see Chapter

3.3.)
31

2.5 Results/Discussion

A comparison of control segment erosion predictions for each soil type is shown

in Table 3. Loam soils were predicted to produce greater than double the sediment

leaving the road in sandy loam soils. Clay loam and silt loam soils were predicted to

produce 1.5 and 1.9 times more sediment leaving the road than sandy loam soils, respectively. WEPP: Road estimated 2.4 times more sediment leaving the buffer in clay

loam than in sandy loam soils and approximately 1.5 times more sediment leaving the

buffer in silt loam and loam soils than in sandy loam soils. Research suggests that forest

soils with higher silt contents are more readily erodible (Luce and Black 2001a), 

indicating that WEPP: Road estimates match empirical studies.

Table 3. WEPP: Road control segment predictions. 

Clay 

loam

Silt 

loam

Sandy 

loam Loam

Sediment leaving 

road (lbs) 1002 1302 658 1342

Sediment leaving 

buffer (lbs) 78 49 33 50

2.5a Qualitative parameters: 

Figure 2 shows WEPP: Road predictions of sediment leaving the road for the four

different road design templates available in the model. The insloped, bare ditch road

design was predicted to produce more sediment leaving the road per year than any other

road design. The difference in sediment prediction between outsloped, unrutted and

outsloped, rutted road profiles reflects the importance of proper maintenance (Swift 1984, Grigal 2000).
32

Modeled behavior of the different soil types across the four road designs was

consistent except for sandy loam on the outsloped, unrutted road segment. Greater 

sediment leaving the road in sandy loam soils relative to other soil types could be

attributed to the lower cohesive strength of sandy loam compared to the other soil types

(Brady 1990). As a result, sandy loam can be more easily entrained than the other soil

types over short distances. Continuous flow path length on the road bed is shortest on the

outsloped, unrutted road design. Assuming that short flow paths favor greater coarse soil

sediment transport, since coarser (sandier) soils are deposited after traveling shorter

distances relative to other soil types, WEPP: Road predictions are appropriate. 

Predictions of sediment leaving the buffer (Figure 3) demonstrate the utility of 

outsloping road segments as a Best Management Practice that minimizes road sediment. This modeled result is backed by published literature (Megahan and Ketcheson 1996, Luce and Black 2001a, Elliot et al. 2009). With the exception of clay loam, predicted 

sediment leaving the buffer was similar or nearly identical between insloped, vegetated

ditch profiles and outsloped, rutted profiles. Clay loam, with a smaller particle size

distribution relative to the other soil types, can be entrained over longer distances given

the same amount of runoff. 
33

Figure 2. WEPP: Road predictions of sediment leaving the road under four road designs. 

Figure 3. WEPP: Road predictions of sediment leaving the buffer under four road designs. 

WEPP: Road predictions of sediment leaving the road in different surface types

are shown in Figure 4. Predictions indicated that graveled road surfaces are more

effective at reducing sediment leaving the road than pavement. Since the road design in

the control segment was insloped with a bare ditch, all sediment leaving the road on

paved segments must be attributed to ditch erosion. In all cases, pavement increased

0

200

400

600

800

1000

1200

1400

1600

Insloped, 

bare ditch

Outsloped, 

unrutted

Insloped, 

vegetated 

ditch

Outsloped, 

rutted

Se

dim

e

nt le

avin

groad

per ye

ar, lbs

Road design

clay loam

silt loam

sandy loam

loam

0

10

20

30

40

50

60

70

80

90

Insloped, 

bare ditch

Outsloped, 

unrutted

Insloped, 

vegetated 

ditch

Outsloped, 

rutted

Se

dim

e

nt le

avin

gth

e

b

uffer per ye

ar,

lbs

Road design

clay loam

silt loam

sandy loam

loam
34

sediment leaving the road, with the greatest increase being in sandy loam soils. Pavement, being essentially impervious to infiltration, generates more and flashier runoff

than graveled or native surface roads. Despite having less available source sediment, WEPP: Road predictions indicate that paved segment runoff can be substantial enough to

produce greater sediment leaving the road from ditch erosion alone than total sediment

leaving the road from a native surface segment. Sandy loam, being more readily

entrained, will produce more sediment leaving paved road segments than other soil types. 

WEPP: Road predicted sediment leaving the buffer in loam soils on paved

segments to be less than that on native surface segments; the same holds true for silt loam 

soils (Figure 5). Sandy loam and clay loam do not follow this trend. The greater predicted 

runoff leaving paved road segments can easily entrain clay loam for longer distances

prior to deposition, thereby explaining the increase in sediment leaving the buffer on clay

loam segments relative to silt loam and loam soils. As for sandy loam, the combination of 

increased runoff and more entrained sediment leaving the road relative to other soil types

could explain the disparate amount of sediment leaving the buffer in this soil type. Reid and Dunne observed paved segments producing less than 1% of sediment

generated on a heavily used gravel segment (1984). In another study conducted in

Georgia and South Carolina, paved road segments were found to produce less than 5% of

the Total Suspended Solids (TSS) leaving unimproved gravel road segments (Clinton and 

Vose 2003). These results were found on slopes greater than 20% in unknown soil types

with riprap on drainage surfaces. For both of these studies, ditch roughness and

maintenance regime assumptions were not clearly conveyed.
35

WEPP: Road is not capable of modeling effects of BMPs on downslope drainage

surfaces, which may explain buffer erosion predictions being greater than those predicted

below other surface types. To clarify whether the bare ditch component of the road

design was responsible for elevated WEPP: Road erosion predictions from the road

surface, the paved segment road design was changed to “insloped, vegetated or rocked

ditch” and again modeled for erosion using WEPP: Road. Traffic level on the graveled

surface segment was altered to “high” and modeled again using WEPP: Road. Figure 4

also includes these model predictions. WEPP: Road predicted less sediment leaving the

road from the paved segment than the high traffic graveled segment, but predictions

ranged from 54-85% of that found on high traffic graveled segments. 

While no conclusion can be made regarding WEPP: Road’s prediction of

sediment leaving paved segment road buffers, WEPP: Road may be overestimating

sediment leaving the ditches of paved road segments. Not all parameters associated with

field tested segments, however, are known. More information about the condition of

paved segments used in field studies, especially regarding their ditches, must be

compared to WEPP: Road model assumptions to detect whether sediment leaving the

road is truly being overestimated.
36

Figure 4. WEPP: Road predictions of sediment leaving road under different road surface types. All road 

designs are insloped, bare ditch except for the paved segment with an insloped and vegetated or rocked 

ditch. All segments were modeled using low traffic assumptions except for one graveled segment. 

Figure 5. WEPP: Road predictions of sediment leaving the buffer under three road surface types. 

Effects of traffic level on WEPP: Road predictions can be found in Figures 6 and

7. WEPP: Road predicted an exponential increase in sediment leaving the road and

sediment leaving the buffer with increases in traffic. WEPP: Road assumes high traffic to

be equivalent to sediment available on a newly constructed road or during an active

logging operation. Low traffic, in contrast, is assumed to generate one quarter of the

sediment generated during an active logging operation (B. Elliot personal

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

2,000

Native Graveled, 

low traffic

Paved Insloped, 

vegetated 

ditch paved

Graveled, 

high traffic Se

dim

e

nt le

aivn

groad

pe

ar ye

ar,

lbs

clay loam

silt loam

sandy loam

loam

0

10

20

30

40

50

60

70

80

90

100

Native Graveled Paved Se

dim

e

nt le

avin

g

b

uffer per ye

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Road surface

clay loam

silt loam

sandy loam

loam
37

communication). With such assumptions, WEPP: Road predictions related to traffic

follow closely with literature-supported findings (e.g. Reid and Dunne 1984, Foltz 1996, Bilby et al. 1989). 

Figure 6. WEPP: Road predictions of sediment leaving the road under no traffic, low traffic, and high 

traffic scenarios. 

Figure 7. WEPP: Road predictions of sediment leaving the buffer under no traffic, low traffic, and high 

traffic scenarios.

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

None Low High

Se

dim

e

nt le

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gth

e road

per ye

ar, lbs

Traffic level

clay loam

silt loam

sandy loam

loam

0

20

40

60

80

100

120

140

160

180

200

None Low High

Se

dim

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nt le

avin

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Traffic level

clay loam

silt loam

sandy loam

loam
38

2.5b Quantitative parameters:

In all three soil types, sensitivity trends between parameters are identical. 

Accordingly, only WEPP: Road predictions in silt loam soil are shown below. 

Road length was the most sensitive of the six parameters in terms of change in

predicted sediment leaving the road, followed by road gradient and road width (Figure 8). These results suggest that BMPs which reduce segment length stand to reduce sediment

leaving the road more than BMPs that alter other quantitative road parameters. Fill slope 

gradient and length were predicted to have minimal effect on sediment leaving the road. Rock content, if greater than 50%, has no effect on predicted sediment leaving the road.

Free rocks on the soil surface have been shown to dissipate the kinetic energy of

runoff (Descroix et al. 2001). Research has found forest soils with rock fragment cover

greater than 50% to take longer to generate runoff and to protect finer subsurface soils

from being entrained by runoff (Cerda ́ 2001). Martínez-Zavala and Jordán report an

increase in infiltration rate and exponential decrease in soil loss rate with increase in rock 

fragment cover (2008). While the research cited above would suggest that WEPP: Road

predictions disagree with published literature, Kidwell and others (1997) report, as per

Poesen et al.’s findings (1990), that degree of embeddedness acts as a control on

infiltration rate; rock fragments embedded under the soil surface restrict infiltration rate

and also therefore time to production of overland flow. This physical control appears to

be the driver behind WEPP: Road predictions of sediment production at percent rock

contents less than 50%. WEPP: Road uses default values when modeling roads 

containing 50% rock content or greater (H. Rhee personal communication), explaining

the lack of change in predicted erosion at rock contents greater than 50%. 
39

Figure 8. WEPP: Road predictions of sediment leaving the road in silt loam soil under multiple quantitative 

parameter scenarios. Multiplier represents control value of a given parameter (1) as well as +/- 10% (1.1 

and .9) and +/-30% (1.3 and .7) that value. Figure 9. WEPP: Road predictions of sediment leaving the buffer in silt loam soil under multiple 

quantitative parameter scenarios. Multiplier represents control value of a given parameter (1) as well as +/- 10% (1.1 and .9) and +/-30% (1.3 and .7) that value.

Since all parameters controlling sediment leaving the road influence sediment

volume available for downslope transport, all eight quantitative parameters could

0

500

1000

1500

2000

2500

0.7 0.9 1 1.1 1.3

Se

dim

e

nt le

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per ye

ar, lbs

Multiplier

road gradient

road length

road width

rock content

fill slope gradient

fill slope length

0

20

40

60

80

100

120

140

0.7 0.9 1 1.1 1.3

Se

dim

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nt le

avin

g

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ar, lbs

Multiplier

road gradient

road length

road width

fill slope gradient

fill slope length

buffer gradient

buffer length

rock content
40

potentially affect WEPP: Road predictions for sediment leaving the buffer (Megahan and

Ketcheson 1996). For that reason, all quantitative parameters have been included in

Figure 9. As with sediment leaving the road, road length was the most sensitive

parameter. Buffer gradient and road width both had a positive relationship with sediment

leaving the buffer. Buffer length, in contrast, had a negative relationship with sediment

leaving the buffer. Buffer length was more sensitive than both buffer gradient and road

width. As with predictions for sediment leaving the road, fill slope length and fill slope

gradient had little bearing on sediment leaving the buffer. Rock content had the same

effect on sediment leaving the buffer as it did with sediment leaving the road; there was

no change in sediment leaving the buffer with change in rock content above 50% due to

WEPP: Road model assumptions. Multiple studies highlight the importance of road segment length and also 

interactivity with slope on the road bed and buffer in explaining sediment transport from

forest roads (e.g. Luce and Black 1999, Luce and Black 2001a, Elliot et al. 2009). In

addition, Coe (2006) found segment surface area, and thereby segment length, to be a

significant explanatory variable for sediment production from forest roads in the Western

Sierras. With these studies considered, WEPP: Road predictions match empirical 

research. 

2.6 Conclusions

Generally, differences in WEPP: Road erosion predictions between soil types

appear to be governed by relations between soil cohesive strength and particle size. Soils

with lower cohesive strengths can more easily entrained by runoff, but are prone to

earlier deposition due to their more massive particle size. 
41

WEPP: Road erosion predictions for paved road segments were not intuitive. Further investigation of field condition of paved road segment ditches in published

literature and WEPP: Road model assumptions are necessary to resolve this potential

discrepancy. In addition, WEPP: Road is limited in its capacity to model roads in soils

with greater than 50% rock content.

WEPP: Road predictions may deviate as much as +/- 50% from measured values

in the field (Elliot et al. 1999). With this fact in mind, the often-used slogan “garbage in, garbage out” becomes highly pertinent for managers wishing to achieve accurate

predictions with this model. It is critical that managers collect accurate input data for use

in WEPP: Road. Averaging values over large areas could substantially alter WEPP: Road

results, rendering predictions invalid. In doing so, valuable resources- economic, 

environmental, or otherwise- may be wasted. 

This sensitivity analysis is not a validation of WEPP: Road. Rather, it is meant to

give further insight into parameter behavior under multiple conditions. Reasons for model 

predictions from these test road segments were hypothesized here but, to date, have not

all been confirmed by model developers. 

The sensitivity analysis presented here provides further background from which

users can evaluate WEPP: Road erosion and predictions. With this analysis, users can

also channel limited resources into collecting parameters which stand to most affect the

erosion prediction of interest (sediment leaving the road versus sediment leaving the

buffer). Finally, erosion prediction deviation from direct observation can be evaluated

through this sensitivity analysis and critical interpretation of model performance.
42

2.7 References

Amore, E., Modica, C., Nearing, M.A., and Santoro, V.C. 2004. Scale effect in USLE

and WEPP application for soil erosion computation from three Sicilian basins. Journal of

Hydrology 293: 100-114.

Bilby, R.E., Sullivan, K. & Duncan, S.H. 1989. The generation and fate of road-surface 

sediment in forested watersheds in southeastern Washington. Forest Science 35(2): 453- 468. 

Brady, N.C. 1990. The Nature and Properties of Soils, Tenth Edition. New York:

MacMillan Publishing Company. 

Cerda ́ , A. 2001. Effects of rock fragment cover on soil infiltration, interrill runoff and 

erosion. European Journal of Soil Science 52(1): 59–68.

Clinton, B.D., and Vose, J.M. 2003. Differences in Surface Water Quality Draining Four 

Road Surface Types in the Southern Appalachians. Southern Journal of Applied Forestry 

27(2): 100-106. 

Daly, C., Neilson, R.P., and Phillips, D.L. 1994. A Statistical-Topographic Model for 

Mapping Climatological Precipitation over Mountainous Terrain. J. Appl. Meteor. 33:

140-158.

Descroix, L., Viramontes, D., Vauclin, M., Gonzalez Barrios, J.L., and Esteves, M. 2001. 

Influence of soil surface features and vegetation on runoff and erosion in the Western 

Sierra Madre (Durango, Northwest Mexico). Catena 43(2)L 115-135. 

Elliot, B., Senior research engineer, Rocky Mountain Research Station – Moscow Forest

Sciences Lab, Moscow ID. Personal communication, 12 August 2009. Elliot, W. J. 2004. WEPP internet interfaces for forest erosion prediction. Jour. Am.

Water Res. Assoc. 40(2):299-309.

Elliot, W., Robichaud, P., Flanagan, D, Dun, S., Wu, J. 2006. Adapting the Water

Erosion Prediction Project (WEPP) Model to Forest Conditions. Paper #062150, 2006

ASABE Annual International Meeting, Portland, OR. 

Elliot, W.J., Hall, D.E., and Scheele, D.L. 1999. WEPP:Road: WEPP Interface for 

Predicting Forest Road Runoff, Erosion and Sediment Delivery Technical 

Documentation. http://forest.moscowfsl.wsu.edu/fswepp/docs/wepproaddoc.html. 

Accessed 2 June 2009. Elliot, W.E.; Foltz, R.B.; Robichaud, P.R. 2009. Recent findings related to measuring and 

modeling forest road erosion. In Anderssen, R.S.; Braddock, R.D.; Newham, L.T.H., eds. Proceedings of the 18th World IMACS / MODSIM Congress, Cairns, Australia, 13-17 
43

July 2009. International Congress on Modelling and Simulation. Interfacing Modelling

and Simulation with Mathematical and Computational Sciences. 

Foltz, R.B. 1996. Traffic and no-traffic on an aggregate surfaced road: sediment

production differences. Presented at the FAO Seminar on Environmentally Sound Forest

Roads, June 1996, Sinaia, Romania. 13 p.

Forest Practices Advisory Committee, 2000. Report of the Forest Practices Advisory 

Committee on Salmon and Watersheds, Oregon Department of Forestry. Section B:

Forest Roads.

Forman, R.T. and Alexander, L. 1998. Roads and their Ecological Effects. Annual

Review of Ecological Systematics 29: 207-231. 

Forman, R.T.T. and Deblinger, R.D. 2000. The Ecological Road-Effect Zone of a

Massachusetts (U.S.A) Suburban Highway. Conservation Biology 14(1): 36-46. 

Grigal, D.F. 2000. Effects of Extensive Forest Management on Forest Productivity. Forest Ecology 138: 167-185.

Jones, J.A. and Grant, G.E. 1996. Peak flow responses to clear-cutting and roads in small 

and large basins, western Cascades, Oregon. Water Resources Research 32(4): 959-974. 

Jones, J.A., Swanson, F.J., Wemple, B.C., and Snyder, K.U. 2000. Effects of Roads on 

Hydrology, Geomorphology, and Disturbance Patches in Stream Networks. Conservation 

Biology 14(1): 76-85. 

Kidwell, M.R., Weltz, M.A., and Guertin, D.P. 1997. Estimation of Green-Ampt 

Effective Hydraulic Conductivity for Rangelands. Journal of Range Management 50(3): 

290-299. 

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

we still need to learn? Hydrological Processes 16: 2901–2904.

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

Oregon. Water Resources Research 35(8): 2561-2570.

Luce, C.H., and Black, T.A. 2001a. Spatial and Temporal Patterns in Erosion from Forest 

Roads. In Influence of Urban and Forest Land Uses on the Hydrologic-Geomorphic 

Responses of Watersheds, Edited by M.S. Wigmosta and S.J. Burges. Water Resources

Monographs, American Geophysical Union, Washington, D.C. pp. 165-178. 

Luce, C. H. and T. A. Black. 2001b. Effects of traffic and ditch maintenance on forest

road sediment production. In Proceedings of the Seventh Federal Interagency

Sedimentation Conference, March 25-29, 2001, Reno, NV. pp. V67-V74.
44

Maholland, B. 2002. Geomorphic Assessment of Natural and Anthropogenic

Sediment Sources in an Eastern Sierra Nevada Watershed. Thesis, University of Nevada

Reno. 

Martinez-Zavala, L., and Jordan, A. 2008. Effect of rock fragment cover on interrill soil 

erosion from bare soils in Western Andalusia, Spain. Soil Use and Management 24(1):

108–117. Megahan, W.F., and Ketcheson, G.L. 1996. Predicting downslope travel of granitic

sediments from forest roads in Idaho. Water Resources Bulletin 32(2): 371-382. 

Renard, K.G., Foster, G.R, Weeies, G.A., McCool, D.K., and Yoder, D.C. 1997. 

Predicting soil erosion by water: A guide to conservation planning with the revised 

universal soil loss equation (RUSLE). USDA Washington, DC: Agric. Handb. 703. 

Rhee, H., Rocky Mountain Research Station- Moscow Forest Sciences Laboratory 

Research Engineer. Email communication 15 March 2008 and 10 August 2009.

Singh, V.P., and Woolhiser, D.A. 2002. Mathematical Modeling of Watershed

Hydrology. Journal of Hydrologic Engineering 7(4): 270-292.

Swift, L.W. 1984. Gravel and Grass Surfacing Reduces Soil Loss From Mountain Roads. Forest Science 30(3): 657-670. Switalski, T.A., Bissonnette J.A., DeLuca T.H., Luce C.H., and Madej, M.A. 2004. Benefits and impacts of road removal. Front Ecol Environ 2(1): 21-28. 

Renschler, C.S. 2003. Designing geo-spatial interfaces to scale process models: the

GeoWEPP approach. Hydrological Processes 17: 1005-1017.

Wemple, B.C., Jones, J.A., and Grant, G.E. 1996. Channel Network Extension by

Logging Roads in Two Basins, Western Cascades, Oregon. Water Resources Bulletin

32(6): 1195-1207. 
45

3. A METHODOLOGY FOR PLANNING ROAD BEST MANAGEMENT 

PRACTICES COMBINING WEPP: ROAD EROSION MODELING AND 

SIMULATED ANNEALING OPTIMIZATION

3.1 Abstract

To minimize erosion from roads, managers install and maintain physical Best

Management Practices (BMPs). BMP installation on a watershed scale is a difficult task

because of the need to account for multiple constraints, such as available budget, BMP

maintenance, and equipment scheduling. A methodology for addressing this challenge is 

presented here that combines WEPP: Road erosion modeling and simulated annealing 

optimization. Field surveys of forest roads at Glenbrook Creek, NV provided inputs for

WEPP: Road and subsequent identification of erosion risk potential. Appropriate BMPs

were identified for segments posing an erosion risk. These BMPs, associated sediment, costs, and maintenance frequencies were input into a model using simulated annealing as

a heuristic search backbone. The algorithm minimized sediment leaving the road buffer

over the course of the planning horizon by comparing potential BMP installation and

maintenance scenarios. Preexisting BMP maintenance costs, new BMP installation costs

and maintenance regimens, and equipment scheduling considerations were accounted for

within the algorithm. Three scenarios at multiple initial budget levels were modeled to

demonstrate the utility of this methodology. 

Of the 173 surveyed segments, 38 segments were available to have BMPs 

installed. The best possible solution yielded a reduction in sediment leaving the buffer

over the course of the planning horizon by 70%. This methodology can be applied to any

watershed, but relies heavily on the perceived accuracy of road erosion predictions.
46

3.2 Introduction

Forest roads, when imposed on the landscape, often become the most prominent

source of erosion in mountainous watersheds (Burroughs 1990). Roads can magnify

erosion rates by multiple orders of magnitude (e.g. Megahan and Ketcheson 1996, Megahan and Kidd 1972). Frequently, roads increase sediment delivery to streams in a

given watershed and alter geomorphic processes both in and out of the stream channel

(e.g. Montgomery 1994, Jones et al. 2000, Wemple et al. 1996). Impacts of road- generated fine sediment entering streams include increased turbidity (Forman and

Alexander 1998) and impairment of fish habitat (FPAC 2000). Roads become a chronic

source of fine sediment to downstream water bodies (Luce 2002). 

It could be argued that few places in the western United States are as aware of the

downstream consequences of upstream management actions as the Lake Tahoe Basin. Lake Tahoe has been declared an Outstanding Natural Resource Water by the U.S. Environmental Protection Agency. As a result of precipitous losses in water clarity over

the past 25 years, Lake Tahoe is currently designated as an impaired water body under

Section 303(d) of the Clean Water Act (Roberts and Reuter 2007). In order to stem this

decline in water clarity, it is imperative that innovative solutions for mitigating fine

sediment inputs to Lake Tahoe be conceived. 

To minimize road erosion, managers frequently implement Best Management

Practices (BMPs). In practice, physical BMPs (e.g. drain dips, cross-draining culverts, rip 

rap) are installed based on professional judgment in the field. Often, no data on sediment

leaving the road surface or sediment leaving the buffer (that portion of the hill slope lying 

between the fill slope and the nearest waterway) is used to guide judgment. One way to
47

mitigate this issue is to apply a road erosion model such as WEPP: Road (Elliot et al. 1999). WEPP: Road provides a user-friendly process-based model via web interface for

managers to evaluate erosion from forest roads. 

While WEPP: Road provides a highly cost-effective means of evaluating road

erosion using relatively few measurements made in the field, new BMP implementation

on a watershed scale is a daunting task. Given budget constraints, managers must

evaluate which sites stand to benefit most from BMP implementation right now as well as 

planning future BMP implementation. In addition, existing BMPs must be maintained to

ensure continued effectiveness, along with any new BMPs. Further complications arise

from the logistics associated with project planning for BMP installation because it would

be cheaper to install and maintain BMPs in near proximity in the same time period. 

Here, a solution to this problem is presented that combines WEPP: Road-derived 

erosion data with simulated annealing optimization to spatially optimize BMP placement

across the road network. In doing so, this methodology minimizes road-related sediment

entering streams in a given watershed while taking into account budget constraints and

spatial adjacency considerations over the course of a planning horizon. 

3.3 Study Site

Lake Tahoe, on the California-Nevada border, lies between the Sierra Nevada

Range to the west and the Carson Range to the east. Elevations range from approximately 

6900 feet to nearly 11,000 feet. Average maximum air temperature from 1915- 1998 was

56 degrees F and average minimum temperature was 30 degrees F. Precipitation in the
48

basin ranges from 70 to 90 inches per year on the west side of the basin to 30 to 40 inches 

on the east side, with most precipitation falling as snow (Rowe et al. 2002). Figure 10. Map of study area. The Glenbrook Creek watershed encompassed the majority of the study area

(Figure 10). Glenbrook Creek is close to Carson City, NV, making it an important

recreation access point for the Lake Tahoe Basin. In addition, the Rocky Mountain

Research Station is parameterizing WEPP: Road using rainfall simulation data from

Glenbrook Creek. With these factors in mind, Glenbrook Creek was deemed an

appropriate watershed for this study. 
49

Glenbrook Creek, on the east side of the Lake Tahoe Basin, lies approximately 15 

miles west of Carson City, NV and 20 miles north of South Lake Tahoe, CA. The

watershed ranges in elevation from approximately 6200 feet to 8800 feet at its furthest

upslope extent. Soils are primarily granitic in origin (Grismer and Hogan 2004). Average 

annual precipitation at the TAHOE CA SNOTEL site, which lies at lake elevation 12

miles northwest of and across the lake from Glenbrook Creek, is approximately 31 

inches. 

A gated housing development near the mouth of Glenbrook Creek was excluded

from the study area. The portion of Forest Road 14N32 connecting with Highway 50 at

Spooner Summit was included in the study area since it served as a major access point to

the watershed. The gated road segment to the west of Highway 50, known as the “Old

Lincoln Highway,” was initially surveyed using GPS but never modeled for road erosion

since it was only used for administrative access.

3.4 Methods

3.4a Field data collection:

Field data collection was conducted in July 2008. Of the 7.6 miles of road

surveyed (5.6 miles of those roads being in the Lake Tahoe Basin), 173 hydraulically 

contiguous road segments were identified. WEPP: Road input parameters determined or

measured in the field for each of these segments included: - Identification of road segment “from” nodes and “to” nodes

- GPS coordinates for “from” and “to” nodes

- Road gradient
50

- Road surface type

- Coarse rock content - Fillslope gradient - Fillslope length - Soil texture

- Road width

- Road design (insloped or outsloped, rutted or unrutted, bare or vegetated ditch) “From” nodes and “to” nodes were identified for each road segment. “To” nodes 

were always delivery points, or the perceived segment outlet for runoff and sediment. “From” nodes comprised the entrance or beginning segment locations for runoff and

sediment entrainment. Segments were delineated between two existing drainage

structures, from a slope break or high point to a drainage structure, from a high point to a

low point, or between a drainage structure and a low point.

GPS points were taken using a GPS flash card adapter for a Dell Axim Personal

Digital Assistant. Road gradient and fillslope gradient were both manually measured with 

a clinometer. Widths and lengths were all taken using a logger’s tape delineated in tenths

of feet. When necessary, slope and length/width measurements were averaged over the

length of the segment. Coarse rock content and soil texture were both performed on soil

adjacent to the road grade itself. Coarse rock content was established using a 2 mm sieve

by taking a ratio between total soil volume and rock volume greater than 2 mm diameter. Soil texture was evaluated using the hand-texturing procedure developed by Thein

(1979). 
51

3.4b Data acquisition using GIS/preparation for model input:

For GIS-derived input parameters, vector data was provided by the Tahoe

Regional Planning Agency (TRPA) and the 10 m Digital Elevation Model (DEM) was

obtained from the Lake Tahoe GIS Data Clearinghouse (http://tahoe.usgs.gov/). WEPP: Road parameters derived from GIS data or from Lake Tahoe Basin

Management Unit (LTBMU) data included segment length, buffer slope, buffer length, and road traffic level. Segment length was found by first reprocessing the GPS-derived 

road layer into segments based on hydraulic connectivity observed on the ground, then

using a GIS to calculate the length of those segments. 

Delivery points for insloped segments were always assumed to be “to” nodes. 

Since sediment delivery from outsloped segments occurs along the entire length of the

segment, delivery points for these segments were designated at the middle of the

segment. Buffer length and slope for each segment were calculated from these delivery

points. Since WEPP: Road will not accept slopes exceeding 100% and road lengths

exceeding 1000 feet, values exceeding these thresholds were replaced with 99 and 999, respectively. In locations where there was no fill slope, WEPP defaults of .3% slope and

one foot were used.

Buffer slope and buffer length were found using a software program developed by 

the Forest Operations Research and Management Sciences Group at The University of

Montana. Using road network delivery points, a raster stream layer, and a flow path raster

derived from a DEM, this program calculated buffer length as total flow path distance to 

the nearest stream. Buffer slope was calculated for each road segment using this flow 

path distance. 
52

Road segments were processed in WEPP: Road Batch according to soil texture. Sandy clay loam and silty clay loam were grouped together and processed as being “clay

loam” soil type (H. Rhee personal communication). “TAHOE CA” was chosen for the

climate, being the closest available climate base station within the WEPP: Road climate

library. Based on elevation at a central location in the watershed, monthly precipitation

values were increased based on the PRISM model (accessible through the WEPP: Road

interface). Since climate data stored for use with the FS WEPP interfaces include only 

monthly values, WEPP: Road uses the CLIGEN weather generator to produce daily 

climate data for the desired simulation time (Elliot et al. 1999). Thirty years of daily

climate data were generated for these simulations. Road traffic level was held constant at

“low” for all segments (Briebart et al. 2006). A sensitivity analysis of WEPP: Road (Chapter 2) and current literature suggest

that road length and width, road gradient, soil type, and surface type all serve as

important controls on sediment leaving the road. Those same factors, coupled with buffer

gradient and length, control sediment leaving the buffer. To explore the linkage between

these factors and WEPP: Road predictions in Glenbrook Creek, relationships between

erosion rate (which normalizes erosion values across segments of all lengths and widths)

and these parameters were evaluated along with absolute prediction values for Glenbrook

Creek. Where necessary, erosion rates were calculated using average surface areas; total

road length within a surface or soil type was multiplied by average road width for that

soil or surface type. 
53

3.4c “Hot spot” identification and verification:

Following WEPP: Road Batch processing, results were reviewed to identify

which segments had the greatest amount of sediment leaving the buffer. Natural breaks in 

a histogram were used to determine “hot spots”, or those segments that were contributing

large amounts of sediment to Glenbrook’s streams. Those segments that were not

classified as high risk segments were classified as moderate or low risk segments. The

LTBMU supported our risk rating criteria (C. Shoen personal communication). The 

breakdown is shown in Table 4. Field verification of the high risk road segments within the Glenbrook Watershed

was conducted in September 2008. A LTBMU roads engineer accompanied us during

field verification. During this process, we assessed the legitimacy of each hot spot by

identifying the overriding characteristic causing the segment to be an erosion risk.

Segments were deemed legitimate hot spots for reasons ranging from steepness of the

segment to length of segment to lack of surface durability. In addition to validating 

erosion risk from modeled road segments, applicable treatments were assigned to the

road segments visited. 

Table 4. Classification of road segments with greater than 0 lbs/yr sediment leaving buffer into risk rating

classes. 

Risk rating

Number of

segments in 

class

Low bound 

(lbs/yr 

sediment 

leaving 

buffer)

High 

bound 

(lbs/yr 

sediment 

leaving 

buffer)

Miles of 

road in risk 

class

Percent of 

total road 

mileage 

surveyed

High risk 9 130 1300 0.9 12

Moderate 

risk 30 12 130 1.5 19

Low risk 35 1 11 1.8 21
54

3.4d Simulated annealing modeling framework:

Simulated annealing, developed by Kirkpatrick and others (1983), uses a modified 

Monte Carlo simulation that loosely resembles metal cooling after leaving a forge. This 

optimization technique solves problems through comparison of neighborhood solutions. An integral component of the algorithm is its linkage to temperature; initial and final

temperatures, along with a cooling rate, are defined within the algorithm. Acceptance 

probabilities, also linked to temperature, provide for the possibility of accepting worse

solutions during iterative solution comparison. A flowchart explaining the adapted

simulated annealing algorithm framework to this planning problem is in Appendix B. The objective function of this optimization problem was to minimize sediment

leaving the buffer through the course of the planning horizon [Eq. 1] while accounting for 

budget as a constraint [Eq. 2].

Minimize

, ( 1)

Subject to

, = 1

where 

Z: total sediment leaving the buffer through the course of the planning horizon

j: planning period

H: length of planning horizon

i: segment number

N: total number of segments on the road network

, sediment leaving the buffer from segment i during planning period j
55

, : cost of BMP treatment scheduled for segment i in planning period j

: budget for planning period j

( )

: discount term

Sediment was minimized by applying appropriate BMPs to treatable road

segments. Appropriate BMPs were prioritized based on existing condition of the road

network (Table 5). These priorities were established through a field visit with LTBMU

roads engineers as well as personal communication with other USFS roads engineers. Of

the 74 road segments producing greater than zero sediment leaving the buffer per year, 38 

could be assigned treatments. 36 segments could not be assigned BMPs because they

were either paved (assumed to be an “end-point” BMP) or had some combination of

conditions which prevented assignment of BMP treatments. For example, outsloping was

not considered an appropriate BMP for graveled segments and drain dips were not

applied to segments already outsloped. 

Within the algorithm, an initial budget per period was specified. This initial

budget was the maximum that could be spent on BMP installation and maintenance in a

given planning period. Planning horizon was specified as 20 years, with planning period

being one year. 

Each segment had four possible BMP treatment options available, with one option 

being “none”, or no BMP assigned to the segment. Only one option per segment could be 

selected for implementation by the algorithm. If greater than four options were possible

on a given road segment, the three options (besides none) that produced the greatest

reduction in sediment leaving the road buffer were used. Further criteria used to assign

BMPs on the road network are shown in Table 6. 
56

Table 5. Priority of BMP assignment for a given road segment

Condition Priority 1 Priority 2 Priority 3

Buffer slope > fill 

slope Outslope Drain dips Pave

Road Slope > 17% Pave Drain dips Outslope

Note: Drain dips applicable on any segment greater than 150 feet in length. 

Table 6. Further criteria used when assigning BMPs to problematic road segments. 

BMP Comment

Outslope Delivery point reassigned to center of road segment. Not 

applicable on paved or graveled segments.

Pave If paving is already installed on a segment, no further BMPs 

can be installed.

Drain dips

Segment length iteratively divided in half until segment 

length is less than 150 feet or sediment leaving buffer is zero. 

Drain dips not applicable on outsloped segments.

In the case of drain dips, multiple options could be assigned. On segments longer 

than 150 feet, segments were divided in half to represent a hydrologic break between the 

two segments. These segments were iteratively divided in half until segment length was 

less than 150 feet or sediment leaving the buffer equaled zero. 

Installation costs, maintenance costs, and maintenance frequencies associated

with a given BMP assignment can be found in Table 7. For each potential BMP scenario

on a given segment, WEPP: Road was used to predict sediment leaving the buffer. These 

predictions, along with the costs and maintenance frequencies associated with each BMP

scenario, were formatted into an input table for the BMP-SA algorithm. See Appendix C

for an example BMP-SA input table. 
57

Table 7. Installation costs, maintenance costs, and maintenance frequencies associated with assigned

BMPs. These costs were compiled through a combination of personal communication with USFS personnel 

and the USFS Region 4 Cost Estimating Guide for Road Construction (USDA 2008).

BMP Installation 

cost ($)

Equipment 

move-in

costs

($)

Maintenance 

cost ($)

Equipment 

move-in costs 

for 

maintenance 

($)

Maintenance 

frequency 

(yrs)

Outsloping 3000/mile 1000 1000/mile 500 3

Drain dips 100/each 500 100/each 500 5

Pavement 245000/mile 1500 15000/mile 500 7

Applicable BMP installation and maintenance scenarios were created from this

list of BMP options. BMP-SA first randomly assembled an initial, or current, solution

where one treatment option was selected for every segment. A neighborhood solution

was then formulated where one element of the current solution was altered (Figures 11- 13). Sediment generated from these alternative solutions was compared within the

algorithm as temperature was cooled. If the neighborhood solution was better than the

current solution, the current solution was always accepted and used to formulate the next

neighborhood solution for comparison. If a neighborhood solution was worse than the

current solution, an acceptance probability was calculated that was linked to the

temperature at the time of comparison using the following equation:
58

Depending on the acceptance probability, the neighborhood solution could be

accepted as the current solution despite producing more sediment than the previous

solution over the course of the planning horizon. With this iterative comparison of

solutions, a near-optimum BMP installation and maintenance scenario was formulated 

upon reaching the stopping conditions dictated within the algorithm.

To account for equipment scheduling on adjacent road segments, clusters of

segments were created. Road segments with delivery points within 1000 feet of each

other were grouped into a single cluster both manually and using a subroutine within the

BMP-SA algorithm. For road work conducted in the Lake Tahoe Basin, it costs $500 for

each piece of equipment that must be moved into the basin (P. Potts personal

communication). It was assumed that the same piece of equipment could be used for

maintenance and installation of all BMPs of the same type within a cluster. Thus, equipment move-in costs were incurred only once within each cluster. In accounting for

these costs, assumptions were made as to how many pieces of equipment were required

to install each BMP. 

While computing the objective function, BMP-SA discounted sediment leaving

the buffer by four percent per year. Discounting by four percent is standard practice in

natural resources economic analysis involving U.S. Forest Service investments (Row et

al. 1981). 
59

BMP Segment Period

Sediment 

leaving buffer 

(tons)

Outslope 10 2 .010

Drain dip 27 4 .002

Pavement 13 8 .035

Figure 11. Example initial solution formulated from a list of alternative BMPs on a road segment. Initial solutions are randomly formulated within BMP-SA.

BMP Segment Period Sediment leaving 

buffer (tons)

Outslope 10 2 .010

Drain dip 27 12 .002

Pavement 13 8 .035

Figures 12 and 13. Examples of neighborhood solutions formulated from the initial (current) solution. Neighborhood solutions are formulated by changing one

element of the initial (current) solution, either period of installation (Figure 12) or BMP installed (Figure 13). In this case, the BMP that was installed or the type

of BMP installed can be changed. With BMP-SA, current and neighborhood BMP solutions are iteratively compared. The algorithm compares two solutions, and 

if a neighborhood solution is worse than the current solution, an acceptance probability is calculated such that, based on temperature, the neighborhood solution

may be accepted as the current solution. In doing so, BMP-SA can arrive at a consistent near-optimum BMP implementation and management scenario more

quickly than if purely random search techniques were employed. 

BMP Segment Period

Sediment 

leaving buffer 

(tons)

Outslope 10 2 .010

None 27 4 .032

Pavement 13 8 .035
60

Three BMP implementation and maintenance scenarios were modeled: New BMP 

installation only, new BMP installation and maintenance, and existing BMP maintenance

along with new BMP installation and maintenance. In those modeling scenarios

accounting for BMP maintenance, BMPs were assumed to be maintained in perpetuity at 

their assigned frequencies. When included, existing BMPs were assumed to start their 

maintenance cycle in period one. Each scenario was modeled using multiple budget

levels to assess model behavior under different budget conditions.

3.5 Results

3.5a WEPP: Road erosion modeling results:

Of the 173 segments analyzed in the study area, 99 of them (accounting for 3.6

miles of the study area) were predicted to produce zero sediment leaving the buffer over 

the 30-year modeling period. Per- segment sediment outputs ranged from .7 tons per year

to 0 tons per year, with a mean of less than .1 tons per year. WEPP: Road predicted a 

total of 55.0 tons per year of sediment leaving the road and 3.0 tons of sediment leaving

the buffer per year (Table 8). Rates of sediment loss were lower within Glenbrook than

across the entire study area. Erosion risk did not seem to follow any spatial pattern

(Figure 14). In terms of general trends related to specific road segment parameters, no

relationship could be established between road width and erosion rate. Segment length

and road gradient, in contrast, showed weak positive relationships (R

2 = .26 and .14, respectively) with erosion rate for sediment leaving the road (Figures 15 and 16). 
61

Table 8. Predicted sediment leaving road and sediment leaving buffer in ton/yr and ton/acre/yr in 

Glenbrook Creek, NV. Average road width across the entire study area was used to calculate ton/acre/yr 

values. 

Study Area

Sediment Leaving Road Sediment Leaving Buffer

ton/yr ton/acre/yr ton/yr ton/acre/yr

Entire Study Area 55.0 6.1 3.0 0.3

Glenbrook 

Watershed 22.7 3.4 1.6 0.2

Note: tons are English short tons (1 short ton = 2000 pounds).

Figure 14. Map of erosion risk by road segment, Glenbrook Creek forest road network.
62

Although there was no correlation between buffer gradient and sediment leaving

the buffer, a negative logarithmic trend was evident between sediment leaving the buffer

and buffer length (R2 = .21) (Figure 17). 

Figure 15. Erosion rates for sediment leaving native surface road segments at various segment lengths, 

Glenbrook Creek, NV. Erosion rates were calculated using WEPP: Road erosion estimates.

Figure 16. Erosion rates for sediment leaving native surface roads at various road gradients, Glenbrook 

Creek, NV. Erosion rates were calculated using WEPP: Road erosion estimates.

y = 0.0227x - 1.7947

R2 = 0.2632

-10

0

10

20

30

40

50

60

70

80

90

100

0 200 400 600 800 1000 1200

Erosio

nrate (to

n/ acre/ yr) Segment length (feet)

y = 0.5221x - 1.1747

R2 = 0.1364

-10

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20 25

Erosio

nrate (to

n/ acre/ yr) Road gradient (%)
63

Figure 17. Erosion rates for sediment leaving the buffer from native surface roads at various buffer lengths, 

Glenbrook Creek, NV. Erosion rates were calculated using WEPP: Road erosion estimates.

Average erosion rates on three road surface types are presented in Figure 18. Native surface roads had an average erosion rate of 7.4 ton/acre/yr, which was higher 

than that estimated by WEPP: Road for graveled and paved segments. Paved segments

erosion rates were estimated at 5.1 ton/acre/yr for sediment leaving the road. Erosion rate

for sediment leaving the buffer adjacent to paved segments was higher than in the other 

two surface types, at .6 ton/acre/yr. 

y = -0.222ln(x) + 1.4664

R2 = 0.2121

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

0 200 400 600 800 1000 1200

Se

dim

e

nt le

avin

g

b

uffer(to

n/ acre/ yr) Buffer length (feet)
64

Figure 18. Average erosion rates for three road surface types, Glenbrook Creek, NV. Erosion rates were 

calculated using WEPP: Road erosion estimates.

WEPP: Road estimated segments in loam soils to have an average erosion rate of

18.3 ton/acre/yr for sediment leaving the road, three and a half times that of segments in

clay loam and sandy loam soils (Figure 19). Segments in clay loam were predicted to

have the next greatest erosion rate for sediment leaving the road at 4.9 ton/acre/yr, followed by sandy loam with 3.8 ton/acre/yr. Segments in loam soils were also projected

to have the greatest erosion rates for sediment leaving the buffer, at .5 ton/acre/yr, 

followed by sandy loam (.3 ton/acre/yr) and clay loam (.1 ton/acre/yr), respectively. 

1.8

7.4

5.1

0.2 0.3 0.6

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

Gravel Native Paved

Erosio

nrate (to

n/ acre/ yr) Road surface type

Sediment leaving road

Sediment leaving buffer
65

Figure 19. Average erosion rates for native surface roads in three soil types, Glenbrook Creek, NV. Erosion 

rates were calculated using WEPP: Road erosion estimates.

3 .5b BMP-SA modeling results:

New BMP installation only: Trend in sediment leaving the buffer with increasing

initial budget per period (hereafter referred to as “budget”) is shown in Figure 20. Sediment leaving the buffer produced a negative exponential trend with increasing 

budget. Note that the theoretical minimum number of BMPs installed is zero. Below

$3,000, the model failed to find a feasible solution within one hour. The best solution was achieved when all 38 segments had BMPs applied to them

in period one. Sediment was reduced from 41.7 tons over the course of the planning

horizon to 11.5 tons through the course of the planning horizon. With this modeled

scenario, all 38 BMPs were installed in period one when budget equaled $20,000 (Figure

21). Increasing budget beyond this level yielded no reduction in sediment leaving the

buffer. 

4.9

18.3

3.8

0.1 0.5 0.3

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

16.00

18.00

20.00

clay loam loam sandy loam

Erosio

nrate (to

n/ acre/ yr) Soil type

Sediment leaving road

Sediment leaving buffer
66

Figure 20. Sediment leaving road buffer through planning horizon with increasing initial budget per period, 

new BMP installation only model scenario. Figure 21. Number of BMPs installed in period one at varying initial budgets per period, new BMP

installation only model scenario. Number of BMPs installed in period one increased with initial budget per period. Proportion of segments with outsloping chosen as an appropriate BMP also increased

with budget. In several instances, solutions at two different budgets yielded decreases in

sediment leaving the buffer while having the same number of BMPs installed in period

one. In all of these instances, number of segments where outsloping was installed as a

BMP was greater in the solution producing less sediment leaving the buffer. Outsloping

11.4

11.6

11.8

12

12.2

12.4

12.6

12.8

13

0 5000 10000 15000 20000 25000 30000 35000 40000

Se

dim

e

nt le

avin

g

b

ufferthro

u

gh

co

urse

of pla

n

nin

g

h

orizo

n(to

n

s)

Initial budget per period ($)

0

5

10

15

20

25

30

35

40

3

0

0

0

400050006000700080009000

1000011000120001300014000150001600017000180001900020000Num

b

er of B

M

Psinstalle

d in

p

erio

d

one

Initial budget per period ($)

outsloping

7 drain dips

3 drain dips

drain dips
67

is a highly effective BMP for reducing sediment leaving the road and buffer, but also

tends to be more expensive than drain dips (Luce and Black 2001a, Elliot et al. 2009, USDA 2008). 

Figure 22 shows the number of segments where BMPs were installed in each

period. At $3,000, all BMPs were installed in the first seven periods. As budget

increased, the number of periods required for all BMPs to be installed was reduced. 

Figure 22. Number of BMPs installed in each period at varying initial budgets per period, new BMP

installation only model scenario. New BMP installation and maintenance: The new BMP installation and

maintenance modeling scenario displayed a negative exponential trend similar to the

trend displayed with previous modeled scenario (Figure 23). Below $6,000, the model

failed to produce feasible solutions in one hour. 0

5

10

15

20

25

30

35

40

3

0

0

0

400050006000700080009000

1000011000120001300014000150001600017000180001900020000Num

b

er of B

M

Psinstalle

d through

course

of planninghorizon

Initial budget per period ($)

Period 7

Period 6

Period 5

Period 4

Period 3

Period 2

Period 1
68

Figure 23. Sediment leaving road buffer through planning horizon with increasing initial budget per period

for new BMP installation and maintenance model scenario. As with the previous modeling scenario, minimum sediment leaving the buffer

through the course of the planning horizon was 11.5 tons. The less-than-perfect negative

exponential trend seen in Figure 23 served as evidence of the solution quality- computation time tradeoff that occurs with heuristic optimization. Had the model been

run for longer periods of time at each budget level, the curve would likely be completely

smooth. With this scenario, all 38 BMPs can be installed in period one at a $34,000

budget.

Figure 24 shows the distribution of types of BMPs installed at varying budgets. While no distinct pattern was evident, at $6,000 budget two segments had no treatment

chosen as the best possible option. This result indicates that budget was so limited that

neither BMP installation nor maintenance was feasible for these two segments. Had there

been sufficient budget available for installation, the model would have installed BMPs on 

these segments late in the planning horizon so as to avoid maintenance costs. 

11.4

11.6

11.8

12

12.2

12.4

12.6

12.8

Se

0 5000 10000 15000 20000 25000 30000 35000 40000 45000

dim

e

nt le

avin

g

b

ufferthro

u

gh

co

urse

of pla

n

nin

g

h

orizo

n(to

n

s)

Initial budget per period ($)
69

Figure 24. Number and type of BMPs installed on treatable road segments at varying initial budgets per

period for new BMP installation and maintenance model scenario. Figure 25 presents the number and types of BMPs installed in period one at

varying budgets for the new BMP installation and maintenance scenario. Again, number 

of outsloped segments installed in period one relative to drain dips increased with budget. 

Cost-benefit tradeoffs similar to those seen in the previously modeled scenario could also

be found here. Figure 25. Number and types of BMPs installed in period one at varying initial budgets per period for new 

BMP installation and maintenance model scenario. 0

5

10

15

20

25

30

35

40

N

u

m

ber of BM

Psin

stalle

d

Initial budget per period ($)

none

outsloping

7 drain dips

3 drain dips

drain dips

0

5

10

15

20

25

30

35

40

N

u

m

ber of BM

Psin

stalle

din

period

o

n

e

Initial budget per period ($)

outsloping

7 drain dips

3 drain dips

drain dips
70

The number of segments treated during a given planning period at varying

budgets is presented in Figure 26. As with the previously modeled scenario, the number

of BMPs installed in period one increased with budget. 

Figure 26. Number of BMPs installed in each period at varying initial budgets per period for new BMP

installation and maintenance model scenario. Note that no treatment is applied to two segments at $6,000

initial budget per period. 

Existing BMP maintenance and new BMP installation and maintenance: The best

solution achieved with this scenario was the same as with the previous two modeled

scenarios- 11.5 tons of sediment leaving the buffer over the course of the planning

horizon (Figure 27). Maintenance of existing BMPs required approximately $35,000

minimum initial budget. Period 13, with numerous preexisting BMPs having maintenance 

frequencies of 2, 3, or 4 years (installed in period one), required the greatest initial

budget. As a result, any new BMPs with a three-year maintenance frequency (such as

outsloping) could not be installed in period one until budget was increased beyond this

minimum level.

0

5

10

15

20

25

30

35

40

N

u

m

ber of BM

Psin

stalle

dthro

u

gh

co

urse

of pla

n

nin

g

h

orizo

n

Initial budget per period ($)

Period 8

Period 7

Period 6

Period 5

Period 4

Period 3

Period 2

Period 1
71

Figure 27. Sediment leaving buffer through course of planning horizon at varying initial budgets per period

for existing BMP maintenance, new BMP installation, and new BMP maintenance model scenario. Again, sediment leaving the buffer decreased exponentially with increase in

budget. With this scenario, a budget of $57,000 was necessary for all BMPs to be

installed in period one. 

Figure 28. Number and type of BMPs installed in period one at varying initial budgets per period for

existing BMP maintenance, new BMP installation, and new BMP maintenance model scenario. When installation of new BMPs and maintenance of all BMPs was accounted for, the number of BMPs installed in period one increased linearly as budget increased

11.4

11.6

11.8

12

12.2

12.4

12.6

30000 35000 40000 45000 50000 55000 60000 65000 70000

Se

dim

e

nt le

avin

g

b

uffer

thro

u

gh

co

urse

of pla

n

nin

g

h

orizo

n(to

n

s)

Initial budget per period ($)

0

5

10

15

20

25

30

35

40

3

6

0

0

0

370003800039000400004100042000430004

4000

45000460004700048000490005000051000520005300054000550005600057000 Num

b

er of B

M

Psinstalle

d in p

erio

d

one

initial budget per period ($)

outsloping

7 drain dips

3 drain dips

drain dips
72

(Figure 28). As a result of accounting for maintenance costs, the solution became more

constrained, making the BMP installation scenario less variable than with the previous

scenario. Outsloped segments increased with budget as with the two previously modeled

scenarios. 

Figure 29. Number of BMPs installed per period at varying initial budgets per period for existing BMP

maintenance, new BMP installation, and new BMP maintenance model scenario. In general, number of periods required to install BMPs on all segments decreased

with increase in budget (Figure 29). 3.6 Discussion

3.6a Discussion of WEPP: Road modeling results:

The outstanding BMP infrastructure on Glenbrook Creek’s forest roads partially

explains the lack of spatial trend in erosion risk prediction. The LTBMU’s BMP

installation and maintenance regimen, coupled with the dry climate found in this

watershed, explains the minimal amount of sediment predicted to be leaving the road and

buffer. 

0

5

10

15

20

25

30

35

40

3

6

0

0

0

370003800039000400004100042000430004

4000

45000460004700048000490005000051000520005300054000550005600057000 Num

b

er of B

M

Psinstalle

d through

course

of planninghorizon

Initial budget per period ($)

Period 5

Period 4

Period 3

Period 2

Period 1
73

Though correlations between sediment leaving the road and buffer for segment

length, road gradient, and buffer length were not strong, the trends do suggest agreement

between WEPP: Road predictions and empirical research (Luce and Black 1999, Luce

and Black 2001a). Note that regressions were not fitted with the intention of predicting

parameter response within WEPP: Road; rather, regressions were used to evaluate

whether parameter response within WEPP: Road matched empirical research. Modeled differences in sediment leaving the road and buffer for the three surface

types were not anticipated. While the reduction in sediment leaving the road and buffer in 

graveled segments compared to native segments was expected, pavement, having an

impervious surface, should produce even less sediment leaving the road than graveled

segments. This was not the case with WEPP: Road predictions for Glenbrook Creek. Numerous paved segments in Glenbrook Creek had unvegetated ditches, which could

partially explain why the erosion rate for sediment leaving the road was greater than

double that found on graveled segments. Due to more and flashier runoff leaving paved

segments, buffer sediment can be more readily entrained than on road segments with

other surface types. In some cases, paved segments in Glenbrook Creek had armored

drainage surfaces below the road, but these BMPs cannot be modeled in WEPP: Road. As 

a result, road segments with this surface type were generally predicted to have higher 

average erosion rates for sediment leaving the buffer than the other two surface types. No 

conclusions can be drawn regarding accuracy of predictions for sediment leaving the

buffer. Published field research coupled with a sensitivity analysis of WEPP: Road

suggest that the model may be overestimating sediment leaving paved road segments.
74

Further investigation is necessary, however, to determine whether sediment leaving

paved segments is truly being overpredicted. Particle size relationships and soil cohesive strengths govern WEPP: Road’s

erosion predictions across different soil types (Chapter 2). Forest soils highest in silt

content have been found to be most erodible, having less cohesive strength than clay-rich 

soils and smaller particle sizes than sandy soils (Luce and Black 2001a). With loam soils

having the greatest silt content of these three soil types, WEPP: Road’s estimate of

sediment leaving the road in this soil type is appropriate though quite large. In contrast, estimates for sediment leaving the buffer were suspect. Segments in clay loam, having 

less massive particle sizes, could be expected to post the greatest losses from the buffer. This discrepancy, coupled with the high erosion rate estimate for sediment leaving the

road, is likely due to the high slopes, long contiguous segment lengths, and few BMPs

found on segments in loam soils. Similar confounding factors may be influencing erosion 

rate in other soil types. Field validation using stratified sampling would be necessary to

discern the true effect of all three soil types on sediment leaving the road and buffer. 

Segment length, road gradient, buffer length, and surface type appear to be the

primary drivers for predicted erosion in the Glenbrook watershed. The weak, nonexistent, or confounded signals from specific parameters affecting severity of erosion impact

highlight the interplay of multiple factors in dictating sediment losses from a given road

segment. These results also reflect the complexity of process-based road erosion

prediction.
75

Comparison of predictions with empirical studies: WEPP: Road Batch results fall 

within the range of empirical results found in other studies. Megahan and Kidd (1972)

measured less than .1 ton/acre/yr of background erosion in granitics of the Idaho

Batholith, which are less erodible than the volcanic substrates found in the Lake Tahoe 

Basin (Grismer and Hogan, 2004) but similar to the much of the parent material found in 

Glenbrook Creek. In contrast, erosion rates greater than 40 ton/acre/yr are routinely

observed on forest roads (Grace 2008). Table 9 contains some published erosion rates for

reference. (For more published reference values, see Elliot and Foltz 2001).

Table 9. Forest road erosion rates from multiple published studies. Note that these rates come from a

variety of climates, soil types, road designs, traffic levels, study designs, and sample sizes. Rates from 

either native or graveled surface roads. Reported numbers are averages unless specified otherwise. Values

are included here as a general reference against predicted WEPP: Road values. 

Authors/source Erosion rate 

(ton/acre/yr) Traffic Comments

Megahan and 

Kidd 1972 32.0 Logging/Truck Idaho Batholith, newly constructed roads

Foltz 1996 1.4 Logging western Oregon, good aggregate 

(graveled road)

Luce and Black 

2001b

4.4 Logging/Truck western Oregon, not graded, less 

than one year study

Fransen et al. 

2001 4.0 Unknown New Zealand, granitic, included cutslope contribution

Sugden and 

Woods 2007 2.4 Logging/Truck Belt Supergroup, western Montana

Sugden and 

Woods 2007 2.3 Logging/Truck Glacial till, western Montana

These general numbers can be compared with empirical results specific to the

Lake Tahoe area. On the west slope of the Sierra Nevada range, Coe (2006) found a mean 

erosion rate of 1.4 ton/acre/yr on native surface roads over three wet seasons

(approximately October through June). During the first wet season of data collection, where average annual precipitation was near the long-term average of 1300 mm, 3.6 
76

ton/acre of sediment were measured leaving the road. In comparison, WEPP: Road

erosion predictions yielded an average rate of 7.4 ton/acre/yr across all native surface

segments in the study area. Precipitation in Coe’s study site was approximately one and a

half times the average annual precipitation generated by PRISM for WEPP: Road erosion

estimates in Glenbrook Creek (33.2 inches, or approximately 843 mm). Average road

gradients, segment lengths, and parent materials were comparable for both studies, but

road designs and traffic levels for segments in Coe’s study are unknown. Coe’s study

segments were in primarily loam soils. 

Graveled segments in the Coe study also yielded a lower average erosion rate of

.5 ton/acre/yr, compared to 1.8 ton/acre/yr predicted over 30 years in Glenbrook Creek. For both native surface and graveled segments, WEPP: Road estimates for sediment 

leaving the road in Glenbrook Creek are higher than regional empirical values. No empirical values for sediment leaving road segment buffers in the Lake Tahoe

Basin could be found. To give some perspective to estimates for sediment leaving the

buffer, Simon and others found 9.7 ton/yr of fine sediment entering Lake Tahoe from

Glenbrook Creek in 2003. Evaluated against WEPP: Road outputs, forest roads in this

watershed are responsible for approximately 16% of Glenbrook Creek’s yearly sediment 

load.

WEPP: Road is in the process of being parameterized specifically for the Lake

Tahoe Basin by the Rocky Mountain Research Station in Moscow. This parameterized

model version may mitigate some of the differences between empirical research and

modeled predictions. Currently, the TAHOE CA SNOTEL site is the closest base station
77

available within the WEPP: Road climate library. Site-specific climate data may also

reduce prediction disagreement with field-derived data. 

3.6b Discussion of BMP-SA modeling results:

Despite the potential deviation of some erosion predictions from reality, BMP-SA 

and its associated methodology are applicable no matter whether predictions agree with

absolute values found in the field. BMP-SA uses predicted relative differences between

two treatments to identify the most appropriate BMP implementation and maintenance

scenario. Assumptions within the model never change, so though absolute values may be

incorrect, relative predicted differences between segments (and associated BMPs) will be 

consistent.

The best possible BMP installation scenario was achieved with all three modeling

scenarios, albeit at higher budget levels when maintenance of new and existing BMPs

was accounted for. Under the best possible solution, sediment leaving the buffer was

reduced by greater than 72% if compared to buffer sediment outputs should no treatments 

be installed through the course of the planning horizon (Table 10). With respect to the 38

treated segments, sediment was reduced by nearly 93% if compared to buffer sediment

outputs should no treatments be installed through the course of the planning horizon. This 

savings is substantial considering that the Glenbrook watershed is in a dry climate and

already has numerous well-maintained BMPs. Assuming that managers are aware of hot

spots on the road network, installing and maintaining BMPs without using this model

could yield significant sediment savings. Budget, maintenance, and equipment scheduling 
78

constraints, however, would not be accounted for. Also, sediment may not be minimized

to the greatest degree possible. 

Using the best available cost estimates for road BMP installation and

maintenance, sediment leaving the buffer can be minimized at $57,000 budget per period

through the course of a twenty-year planning horizon. This result assumes that existing

BMPs and new BMPs are regularly maintained during the horizon. All BMPs must be

installed during period one to maximize sediment savings. 

Table 10. Reduction in predicted sediment leaving the buffer using BMP-SA model. 

Portion of study 

area

Sediment leaving 

buffer with no new 

BMPs installed (tons 

through planning 

horizon)

Sediment leaving 

buffer with best 

possible BMP 

installation scenario 

(tons through 

planning horizon)

Percent reduction

Entire study area 41.7 11.5 72.4%

38 treatable 

segments 32.5 2.3 92.9%

Note: sediment has been discounted using 4% discount rate. 

There were no instances where paving was chosen as an applicable new BMP. In

every instance where pavement was a potential BMP option, WEPP: Road model outputs

indicated that pavement increased sediment leaving the buffer above existing levels. Other researchers have had similar results in applying WEPP: Road to paved road

segments in the Lake Tahoe Basin (Briebart et al. 2006). 

3.7 Conclusions

When forest road BMP planning issues are approached from the one- or few- segment perspective, watershed-scale sedimentation, maintenance, and equipment
79

planning concerns cannot be addressed. At the watershed scale, however, accounting for

all of these issues and concerns for every road segment becomes highly complicated and, in some cases, may be simply too complex to address using conventional methods. The

methodology presented here makes watershed-scale forest road BMP planning feasible. Multiple constraints can be accounted for consistently for every segment across the entire 

road network. 

This research tested a methodology for increasing efficiency of BMP planning on 

a forest road network. Road-related sediment leaving the forest buffer was minimized

over the course of a planning horizon while accounting for budget constraints as well as

equipment scheduling considerations. The solutions presented here used modeled WEPP: 

Road erosion data from a high-density road survey as well as guidelines for prioritizing 

appropriate BMPs for a given road segment. To minimize sediment leaving the road

buffer, this data was input into an adapted simulated annealing optimization algorithm. Under the best BMP implementation scenario, predicted sediment leaving the road buffer

was reduced by greater than 70% over the course of a planning horizon. From these tests, 

it can be concluded that WEPP: Road erosion modeling combined with simulated 

annealing optimization provides a viable approach to water quality issues associated with

sedimentation from forest roads. While the data used here is from the Lake Tahoe Basin, this methodology can be applied to any watershed. This methodology is also applicable at 

a scale greater than a single watershed, though problem complexity may substantially

increase.

Sediment savings with BMP-SA was considerable, in part because little sediment

was predicted to leave the road buffer from the Glenbrook Creek watershed. If predicted
80

sediment leaving the road buffer was greater, percent decrease in sediment leaving the

buffer as a result of BMP installation could be lower. In a watershed without a well- developed BMP infrastructure, however, there would more potential for a tool like BMP- SA to minimize sediment leaving the buffer. 

There are two critical assumptions of this modeling exercise. One is that BMPs

must be maintained at appropriate intervals in perpetuity, otherwise money spent

installing BMPs is not worthwhile. In addition, this modeling process relies on the

accuracy of road sedimentation prediction for determining problematic road segments

and the effects of BMP installation on sediment savings. WEPP: Road is an easy-to-use, 

process-based model interface for estimating road sediment losses and has gained

widespread use among researchers and managers. It is important to note that WEPP:

Road estimates have been shown to deviate from field measurements by +/- 50% (Elliot

et al. 1999). Accordingly, the importance of having accurate model inputs cannot be

understated. 

BMP implementation is often site-specific in nature. For that reason, some hot 

spots may not be able to be treated using one of only a handful of generic BMPs; only

professional judgment in the field may provide the ideal option in such situations. With 

this point in mind, coupled with all of the above assumptions and limitations, the results

of BMP-SA are not meant to replace professional judgment in the field. Rather, this tool

is meant to assist in the decision-making process associated with forest road management 

and planning. By implementing a methodology and/or tools like those used here, managers can identify where to focus limited resources to achieve the greatest economic

and environmental benefit across multiple spatial and temporal scales. 
81

3.8 References

Briebart, A., Harris, J., and Norman, S. 2006. Forest Road BMP Upgrade Monitoring

Report 2003-2005. USDA Forest Service, Lake Tahoe Basin Management Unit.

Brooks, K. Ffolliott, P., Gregersen, H., and DeBano, L. Hydrology and the Management

of Watersheds: Third Edition. 2003: Iowa State Press. 

Burroughs, E.R., Jr. 1990. Predicting onsite sediment yield from forest roads. Proceedings of Conference XXI, International Erosion Control Association, Erosion

Control: Technology in Transition. Washington, DC, February 14-17, 1990. 223-232. 

Coe, D. 2006. Sediment production and delivery from forest roads in the Sierra Nevada, California. MSc Thesis, Colorado State University, Fort Collins, CO.

Elliot, W.J., Hall, D.E., and Graves, S.R. 1999. Predicting sedimentation from forest

roads. Journal of Forestry, August 1999, 97(8):23-29.

Elliot, W.J., Hall, D.E., and Scheele, D.L. 1999. WEPP:Road: WEPP Interface for 

Predicting Forest Road Runoff, Erosion and Sediment Delivery Technical 

Documentation. http://forest.moscowfsl.wsu.edu/fswepp/docs/wepproaddoc.html. 

Accessed 2 June 2009. Elliot, W.J.; Foltz, M. 2001. Validation of the FS WEPP Interfaces for Forest Roads and

Disturbances. ASAE paper number 01-8009. St. Joseph, MI: ASAE. 16 p.

Elliot, W.E.; Foltz, R.B.; Robichaud, P.R. 2009. Recent findings related to measuring and 

modeling forest road erosion. In Anderssen, R.S.; Braddock, R.D.; Newham, L.T.H., eds. Proceedings of the 18th World IMACS / MODSIM Congress, Cairns, Australia, 13-17 

July 2009. International Congress on Modelling and Simulation. Interfacing Modelling

and Simulation with Mathematical and Computational Sciences. 

Fransen, P.J., Philips, C.J., and Fahey, B.D. 2001.Forest Road Erosion in New Zealand:

Overview. Earth Surface Processes and Landforms 26: 165-174. 

Foltz, R.B. 1996. Traffic and no-traffic on an aggregate surfaced road: sediment

production differences. Presented at the FAO Seminar on Environmentally Sound Forest

Roads, June 1996, Sinaia, Romania. 13 p.

Forest Practices Advisory Committee, 2000. Report of the Forest Practices Advisory

Committee on Salmon and Watersheds, Oregon Department of Forestry. Section B:

Forest Roads.

Forman, R.T. and Alexander, L. 1998. Roads and their Ecological Effects. Annual

Review of Ecological Systematics 29: 207-231. 
82

Grace, J.M. 2008. Determining the Range of Acceptable Forest Road Erosion. ASABE 

Paper No. 083984. St. Joseph, Mich.: ASABE.

Grismer, M.E. and Hogan, M.P. 2004. Simulated Rainfall Evaluation of

Revegetation/Mulch Erosion Control in the Lake Tahoe Basin—1: Method Assessment. Land Degradation and Development 15: 573-588. 

Jones, J.A., Swanson, F.J., Wemple, B.C., and Snyder, K.U. 2000. Effects of Roads on

Hydrology, Geomorphology, and Disturbance Patches in Stream Networks. Conservation

Biology 14(1): 76-85. 

Kirkpatrick, S., Gelatt, C.D., and Vecchi, M.P. 2003. Optimization by Simulated

Annealing. Science 220(4598): 671-680.

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

we still need to learn? Hydrological Processes 16: 2901–2904.

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

Oregon. Water Resources Research 35(8): 2561-2570. 

Luce, C.H., and Black, T.A. 2001a. Spatial and Temporal Patterns in Erosion from Forest 

Roads. In Influence of Urban and Forest Land Uses on the Hydrologic-Geomorphic 

Responses of Watersheds, Edited by M.S. Wigmosta and S.J. Burges. Water Resources

Monographs, American Geophysical Union, Washington, D.C. pp. 165-178. 

Luce, C. H. and T. A. Black. 2001b. Effects of traffic and ditch maintenance on forest

road sediment production. In Proceedings of the Seventh Federal Interagency

Sedimentation Conference, March 25-29, 2001, Reno, NV. pp. V67-V74.

Megahan, W.F. and Ketcheson, G.L. 1996. Predicting Downslope Travel of Granitic 

Sediments from Forest Roads in Idaho. Water Resources Bulletin 32(2): 371-382. 

Megahan, W.F. and Kidd, W.J. 1972. Effects of Logging and Logging Roads in Erosion

and Sediment Deposition on Steep Terrain. Journal of Forestry 7: 136-141. 

Metropolis, N., Rosebluth, A.R., Rosenbluth, M.N., Teller, A.H., Teller, E. 1953. Equation of State Calculations by Fast Computing Machines. Journal of Chemical

Physics 21(6): 1087-1092.

Potts, P. 2008. LTBMU Roads Engineer, U.S. Forest Service. Personal communication, 18 March 2008. 

Rhee, H., Rocky Mountain Research Station- Moscow Forest Sciences Laboratory 

Research Engineer. Email communication, September 3, 2008.
83

Roberts, D.M., and Reuter, J.E., lead authors. 2007. Draft Lake Tahoe Total Maximum 

Daily Load Technical Report, California and Nevada. California Water Quality Control

Board, Lahontan Region and Nevada Division of Environmental Protection. 

Row, C., Kaiser, H.F., and Sessions, J. 1981. Discount Rate for Long-Term Forest

Service Investments. Journal of Forestry. 79(6): 367-369, 376.

Rowe, T.G., Saleh, D.K., Watkins, S.A., Kratzer, C.R., 2002. Streamflow andWater- Quality Data for Selected Watersheds in the Lake Tahoe Basin, California and Nevada,

Through September 1998. Water Resources Investigations Report 02-4030. U.S.

Geological Survey, Carson City, p. 118 pp.

Schoen, C. 2008. LTBMU Roads Engineer, U.S. Forest Service. Personal

communication, September 10, 2008. 

Simon, A., E.J. Langendoen, R.L. Bingner, R. Wells, A. Heins, N. Jokay and I. Jaramillo. 

2003. Lake Tahoe Basin Framework Implementation Study: Sediment Loadings and 

Channel Erosion. USDA-ARS National Sedimentation Laboratory Research Report. No. 

39. 377 p.

 Sugden, B. and Woods, S. 2007. Sediment Production from Forest Roads in Western

Montana. Journal of American Water Resources Association 43(1): 193-206.

Thein, S.J. 1979. A flow diagram for teaching texture by feel analysis. Journal of Agron. Edu. 8:54-55.

USDA Forest Service: Pacific Southwest Research Station. 2000. Lake Tahoe Watershed

Assessment. Murphy, D.D. and Knopp, C.M., eds. General Technical Report PSW-GTR- 175. 

Venn, T., Natural Resource Economist, College of Forestry and Conservation, The

University of Montana. Personal communication May 2009. 

Wemple, B.C., Jones, J.A., and Grant, G.E. 1996. Channel Network Extension by

Logging Roads in Two Basins, Western Cascades, Oregon. Water Resources Bulletin

32(6): 1195-1207. 

USDA Forest Service: Intermountain, Southwest, and Rocky Mountain Regions. 2008

Cost Estimating Guide for Road Construction. 
A

Appendixes

A. Example Solution from BMP-SA Algorithm

Notes about solution:

This is a raw solution output. The fact that the solution starts at Period 0 and ends

at Period 19 is an artifact of algorithm programming, since arrays store values starting at

0. Results are correct despite this discrepancy; simply add 1 to each period value. 

Nonzero values for periods where there is no installation or maintenance activity 

is due to addition and subtraction of floating point values. Note that, in all instances

where this occurs, values are zero to at least the second decimal place.

Pre-existing BMP codes: - rld: rock-lined ditch

- nd: native ditch

- god: gravel on drain dip

________________________________________________________________________ BMP SIMULATED ANNEALING ALGORITHM RESULTS

The best solution has a sediment output over the course of the planning horizon of: 

11.512097 tons

Cost of the best solution over the course of the planning horizon: 127083.781250 dollars

Initial budget: 57000.000000 dollars per period

THE SOLUTION:

PERIOD 0

install BMP 3draindips on segment 6 at install cost 300.000000

install BMP outslope on segment 7 at install cost 89.520454

install BMP draindip on segment 31 at install cost 100.000000

install BMP draindip on segment 33 at install cost 100.000000

install BMP outslope on segment 38 at install cost 72.805679

install BMP outslope on segment 41 at install cost 50.951530

install BMP draindip on segment 49 at install cost 100.000000

install BMP draindip on segment 52 at install cost 100.000000

install BMP 3draindips on segment 59 at install cost 300.000000

install BMP draindip on segment 60 at install cost 100.000000

install BMP draindip on segment 62 at install cost 100.000000

install BMP draindip on segment 65 at install cost 100.000000

install BMP draindip on segment 66 at install cost 100.000000

install BMP 3draindips on segment 67 at install cost 300.000000

install BMP draindip on segment 69 at install cost 100.000000

install BMP draindip on segment 71 at install cost 100.000000
B

install BMP draindip on segment 79 at install cost 100.000000

install BMP draindip on segment 80 at install cost 100.000000

install BMP draindip on segment 93 at install cost 100.000000

install BMP outslope on segment 95 at install cost 133.189194

install BMP outslope on segment 96 at install cost 122.434662

install BMP outslope on segment 108 at install cost 143.797150

install BMP outslope on segment 112 at install cost 123.576141

install BMP 3draindips on segment 113 at install cost 300.000000

install BMP draindip on segment 115 at install cost 100.000000

install BMP outslope on segment 116 at install cost 486.000000

install BMP draindip on segment 117 at install cost 100.000000

install BMP 7draindips on segment 119 at install cost 700.000000

install BMP draindip on segment 120 at install cost 100.000000

install BMP draindip on segment 121 at install cost 100.000000

install BMP outslope on segment 127 at install cost 1143.000000

install BMP draindip on segment 133 at install cost 100.000000

install BMP draindip on segment 134 at install cost 100.000000

install BMP outslope on segment 136 at install cost 91.398865

install BMP outslope on segment 141 at install cost 47.919949

install BMP outslope on segment 142 at install cost 390.000000

install BMP 7draindips on segment 146 at install cost 700.000000

install BMP draindip on segment 174 at install cost 100.000000

Treatment cost for period 0: 32494.597656 dollars

NOTE: preexisting BMP cost already accounted for, so it won't show up in treatment cost

PERIOD 1

Treatment cost for period 1: 0.000000 dollars

NOTE: preexisting BMP cost already accounted for, so it won't show up in treatment cost

PERIOD 2

maintain preexisting BMP rld on segment 66 at maintenance cost 94.500000

maintain preexisting BMP rld on segment 67 at maintenance cost 94.500000

maintain preexisting BMP rld on segment 68 at maintenance cost 94.500000

maintain preexisting BMP rld on segment 70 at maintenance cost 94.500000

maintain preexisting BMP rld on segment 72 at maintenance cost 94.500000

maintain preexisting BMP rld on segment 109 at maintenance cost 94.500000

Treatment cost for period 2: -0.000977 dollars

NOTE: preexisting BMP cost already accounted for, so it won't show up in treatment cost

PERIOD 3
C

maintain BMP outslope on segment 7 at maintenance cost 29.840151

maintain preexisting BMP outsloping on segment 8 at maintenance cost 43.489964

maintain preexisting BMP gravel on segment 32 at maintenance cost 154.104172

maintain preexisting BMP outsloping on segment 32 at maintenance cost 35.023674

maintain preexisting BMP gravel on segment 34 at maintenance cost 34.347500

maintain BMP outslope on segment 38 at maintenance cost 24.268560

maintain BMP outslope on segment 41 at maintenance cost 16.983845

maintain preexisting BMP gravel on segment 42 at maintenance cost 161.444168

maintain preexisting BMP outsloping on segment 50 at maintenance cost 25.320456

maintain preexisting BMP gravel on segment 66 at maintenance cost 175.522491

maintain preexisting BMP gravel on segment 67 at maintenance cost 351.648315

maintain preexisting BMP gravel on segment 68 at maintenance cost 76.655334

maintain preexisting BMP gravel on segment 70 at maintenance cost 112.001663

maintain preexisting BMP gravel on segment 72 at maintenance cost 115.975838

maintain preexisting BMP gravel on segment 80 at maintenance cost 175.290009

maintain preexisting BMP outsloping on segment 81 at maintenance cost 57.188446

maintain preexisting BMP outsloping on segment 94 at maintenance cost 19.917046

maintain BMP outslope on segment 95 at maintenance cost 44.396400

maintain BMP outslope on segment 96 at maintenance cost 40.811554

maintain BMP outslope on segment 108 at maintenance cost 47.932384

maintain preexisting BMP gravel on segment 109 at maintenance cost 49.375500

maintain BMP outslope on segment 112 at maintenance cost 41.192047

maintain preexisting BMP gravel on segment 114 at maintenance cost 80.570831

maintain BMP outslope on segment 116 at maintenance cost 162.000000

maintain BMP outslope on segment 127 at maintenance cost 381.000000

maintain preexisting BMP outsloping on segment 135 at maintenance cost 185.059280

maintain BMP outslope on segment 136 at maintenance cost 30.466288

maintain preexisting BMP outsloping on segment 138 at maintenance cost 60.063633

maintain BMP outslope on segment 141 at maintenance cost 15.973315

maintain preexisting BMP outsloping on segment 143 at maintenance cost 20.971781

maintain BMP outslope on segment 142 at maintenance cost 130.000000

maintain preexisting BMP outsloping on segment 148 at maintenance cost 48.701519

Treatment cost for period 3: 6964.864258 dollars

NOTE: preexisting BMP cost already accounted for, so it won't show up in treatment cost

PERIOD 4

maintain preexisting BMP nd on segment 34 at maintenance cost 400.000000

maintain preexisting BMP nd on segment 42 at maintenance cost 400.000000

maintain preexisting BMP nd on segment 50 at maintenance cost 400.000000

maintain preexisting BMP nd on segment 53 at maintenance cost 400.000000

maintain preexisting BMP nd on segment 63 at maintenance cost 400.000000

maintain preexisting BMP rld on segment 66 at maintenance cost 94.500000

maintain preexisting BMP rld on segment 67 at maintenance cost 94.500000

maintain preexisting BMP rld on segment 68 at maintenance cost 94.500000
D

maintain preexisting BMP rld on segment 70 at maintenance cost 94.500000

maintain preexisting BMP rld on segment 72 at maintenance cost 94.500000

maintain preexisting BMP rld on segment 109 at maintenance cost 94.500000

maintain preexisting BMP nd on segment 114 at maintenance cost 400.000000

Treatment cost for period 4: 0.000549 dollars

NOTE: preexisting BMP cost already accounted for, so it won't show up in treatment cost

PERIOD 5

maintain BMP 3draindips on segment 6 at maintenance cost 300.000000

maintain preexisting BMP dd on segment 8 at maintenance cost 150.000000

maintain BMP draindip on segment 31 at maintenance cost 100.000000

maintain preexisting BMP dd on segment 32 at maintenance cost 150.000000

maintain BMP draindip on segment 33 at maintenance cost 100.000000

maintain preexisting BMP dd on segment 34 at maintenance cost 150.000000

maintain preexisting BMP dd on segment 42 at maintenance cost 150.000000

maintain BMP draindip on segment 49 at maintenance cost 100.000000

maintain preexisting BMP dd on segment 50 at maintenance cost 150.000000

maintain BMP draindip on segment 52 at maintenance cost 100.000000

maintain preexisting BMP dd on segment 53 at maintenance cost 150.000000

maintain BMP 3draindips on segment 59 at maintenance cost 300.000000

maintain BMP draindip on segment 60 at maintenance cost 100.000000

maintain preexisting BMP dd on segment 61 at maintenance cost 150.000000

maintain BMP draindip on segment 62 at maintenance cost 100.000000

maintain preexisting BMP dd on segment 63 at maintenance cost 150.000000

maintain BMP draindip on segment 65 at maintenance cost 100.000000

maintain BMP draindip on segment 66 at maintenance cost 100.000000

maintain preexisting BMP dd on segment 67 at maintenance cost 150.000000

maintain BMP 3draindips on segment 67 at maintenance cost 300.000000

maintain preexisting BMP dd on segment 68 at maintenance cost 150.000000

maintain BMP draindip on segment 69 at maintenance cost 100.000000

maintain preexisting BMP dd on segment 70 at maintenance cost 150.000000

maintain BMP draindip on segment 71 at maintenance cost 100.000000

maintain preexisting BMP dd on segment 72 at maintenance cost 150.000000

maintain BMP draindip on segment 79 at maintenance cost 100.000000

maintain BMP draindip on segment 80 at maintenance cost 100.000000

maintain preexisting BMP dd on segment 81 at maintenance cost 150.000000

maintain BMP draindip on segment 93 at maintenance cost 100.000000

maintain preexisting BMP dd on segment 94 at maintenance cost 150.000000

maintain BMP 3draindips on segment 113 at maintenance cost 300.000000

maintain preexisting BMP dd on segment 114 at maintenance cost 150.000000

maintain BMP draindip on segment 115 at maintenance cost 100.000000

maintain BMP draindip on segment 117 at maintenance cost 100.000000

maintain BMP 7draindips on segment 119 at maintenance cost 700.000000

maintain BMP draindip on segment 120 at maintenance cost 100.000000
E

maintain BMP draindip on segment 121 at maintenance cost 100.000000

maintain BMP draindip on segment 133 at maintenance cost 100.000000

maintain BMP draindip on segment 134 at maintenance cost 100.000000

maintain BMP 7draindips on segment 146 at maintenance cost 700.000000

maintain BMP draindip on segment 174 at maintenance cost 100.000000

Treatment cost for period 5: 17599.998047 dollars

NOTE: preexisting BMP cost already accounted for, so it won't show up in treatment cost

PERIOD 6

maintain BMP outslope on segment 7 at maintenance cost 29.840151

maintain preexisting BMP outsloping on segment 8 at maintenance cost 43.489964

maintain preexisting BMP gravel on segment 32 at maintenance cost 154.104172

maintain preexisting BMP outsloping on segment 32 at maintenance cost 35.023674

maintain preexisting BMP gravel on segment 34 at maintenance cost 34.347500

maintain BMP outslope on segment 38 at maintenance cost 24.268560

maintain BMP outslope on segment 41 at maintenance cost 16.983845

maintain preexisting BMP gravel on segment 42 at maintenance cost 161.444168

maintain preexisting BMP outsloping on segment 50 at maintenance cost 25.320456

maintain preexisting BMP gravel on segment 66 at maintenance cost 175.522491

maintain preexisting BMP rld on segment 66 at maintenance cost 94.500000

maintain preexisting BMP gravel on segment 67 at maintenance cost 351.648315

maintain preexisting BMP rld on segment 67 at maintenance cost 94.500000

maintain preexisting BMP gravel on segment 68 at maintenance cost 76.655334

maintain preexisting BMP rld on segment 68 at maintenance cost 94.500000

maintain preexisting BMP gravel on segment 70 at maintenance cost 112.001663

maintain preexisting BMP rld on segment 70 at maintenance cost 94.500000

maintain preexisting BMP gravel on segment 72 at maintenance cost 115.975838

maintain preexisting BMP rld on segment 72 at maintenance cost 94.500000

maintain preexisting BMP gravel on segment 80 at maintenance cost 175.290009

maintain preexisting BMP outsloping on segment 81 at maintenance cost 57.188446

maintain preexisting BMP outsloping on segment 94 at maintenance cost 19.917046

maintain BMP outslope on segment 95 at maintenance cost 44.396400

maintain BMP outslope on segment 96 at maintenance cost 40.811554

maintain BMP outslope on segment 108 at maintenance cost 47.932384

maintain preexisting BMP gravel on segment 109 at maintenance cost 49.375500

maintain preexisting BMP rld on segment 109 at maintenance cost 94.500000

maintain BMP outslope on segment 112 at maintenance cost 41.192047

maintain preexisting BMP gravel on segment 114 at maintenance cost 80.570831

maintain BMP outslope on segment 116 at maintenance cost 162.000000

maintain BMP outslope on segment 127 at maintenance cost 381.000000

maintain preexisting BMP outsloping on segment 135 at maintenance cost 185.059280

maintain BMP outslope on segment 136 at maintenance cost 30.466288

maintain preexisting BMP outsloping on segment 138 at maintenance cost 60.063633

maintain BMP outslope on segment 141 at maintenance cost 15.973315
F

maintain preexisting BMP outsloping on segment 143 at maintenance cost 20.971781

maintain BMP outslope on segment 142 at maintenance cost 130.000000

maintain preexisting BMP outsloping on segment 148 at maintenance cost 48.701519

Treatment cost for period 6: 6964.864746 dollars

NOTE: preexisting BMP cost already accounted for, so it won't show up in treatment cost

PERIOD 7

Treatment cost for period 7: -0.000366 dollars

NOTE: preexisting BMP cost already accounted for, so it won't show up in treatment cost

PERIOD 8

maintain preexisting BMP nd on segment 34 at maintenance cost 400.000000

maintain preexisting BMP nd on segment 42 at maintenance cost 400.000000

maintain preexisting BMP nd on segment 50 at maintenance cost 400.000000

maintain preexisting BMP nd on segment 53 at maintenance cost 400.000000

maintain preexisting BMP nd on segment 63 at maintenance cost 400.000000

maintain preexisting BMP rld on segment 66 at maintenance cost 94.500000

maintain preexisting BMP rld on segment 67 at maintenance cost 94.500000

maintain preexisting BMP rld on segment 68 at maintenance cost 94.500000

maintain preexisting BMP rld on segment 70 at maintenance cost 94.500000

maintain preexisting BMP rld on segment 72 at maintenance cost 94.500000

maintain preexisting BMP rld on segment 109 at maintenance cost 94.500000

maintain preexisting BMP nd on segment 114 at maintenance cost 400.000000

Treatment cost for period 8: 0.000000 dollars

NOTE: preexisting BMP cost already accounted for, so it won't show up in treatment cost

PERIOD 9

maintain BMP outslope on segment 7 at maintenance cost 29.840151

maintain preexisting BMP outsloping on segment 8 at maintenance cost 43.489964

maintain preexisting BMP gravel on segment 32 at maintenance cost 154.104172

maintain preexisting BMP outsloping on segment 32 at maintenance cost 35.023674

maintain preexisting BMP gravel on segment 34 at maintenance cost 34.347500

maintain BMP outslope on segment 38 at maintenance cost 24.268560

maintain BMP outslope on segment 41 at maintenance cost 16.983845

maintain preexisting BMP gravel on segment 42 at maintenance cost 161.444168

maintain preexisting BMP outsloping on segment 50 at maintenance cost 25.320456

maintain preexisting BMP gravel on segment 66 at maintenance cost 175.522491

maintain preexisting BMP gravel on segment 67 at maintenance cost 351.648315

maintain preexisting BMP gravel on segment 68 at maintenance cost 76.655334

maintain preexisting BMP gravel on segment 70 at maintenance cost 112.001663
G

maintain preexisting BMP gravel on segment 72 at maintenance cost 115.975838

maintain preexisting BMP gravel on segment 80 at maintenance cost 175.290009

maintain preexisting BMP outsloping on segment 81 at maintenance cost 57.188446

maintain preexisting BMP outsloping on segment 94 at maintenance cost 19.917046

maintain BMP outslope on segment 95 at maintenance cost 44.396400

maintain BMP outslope on segment 96 at maintenance cost 40.811554

maintain BMP outslope on segment 108 at maintenance cost 47.932384

maintain preexisting BMP gravel on segment 109 at maintenance cost 49.375500

maintain BMP outslope on segment 112 at maintenance cost 41.192047

maintain preexisting BMP gravel on segment 114 at maintenance cost 80.570831

maintain BMP outslope on segment 116 at maintenance cost 162.000000

maintain BMP outslope on segment 127 at maintenance cost 381.000000

maintain preexisting BMP outsloping on segment 135 at maintenance cost 185.059280

maintain BMP outslope on segment 136 at maintenance cost 30.466288

maintain preexisting BMP outsloping on segment 138 at maintenance cost 60.063633

maintain BMP outslope on segment 141 at maintenance cost 15.973315

maintain preexisting BMP outsloping on segment 143 at maintenance cost 20.971781

maintain BMP outslope on segment 142 at maintenance cost 130.000000

maintain preexisting BMP outsloping on segment 148 at maintenance cost 48.701519

Treatment cost for period 9: 6964.864746 dollars

NOTE: preexisting BMP cost already accounted for, so it won't show up in treatment cost

PERIOD 10

maintain BMP 3draindips on segment 6 at maintenance cost 300.000000

maintain preexisting BMP dd on segment 8 at maintenance cost 150.000000

maintain BMP draindip on segment 31 at maintenance cost 100.000000

maintain preexisting BMP dd on segment 32 at maintenance cost 150.000000

maintain BMP draindip on segment 33 at maintenance cost 100.000000

maintain preexisting BMP dd on segment 34 at maintenance cost 150.000000

maintain preexisting BMP dd on segment 42 at maintenance cost 150.000000

maintain BMP draindip on segment 49 at maintenance cost 100.000000

maintain preexisting BMP dd on segment 50 at maintenance cost 150.000000

maintain BMP draindip on segment 52 at maintenance cost 100.000000

maintain preexisting BMP dd on segment 53 at maintenance cost 150.000000

maintain BMP 3draindips on segment 59 at maintenance cost 300.000000

maintain BMP draindip on segment 60 at maintenance cost 100.000000

maintain preexisting BMP dd on segment 61 at maintenance cost 150.000000

maintain BMP draindip on segment 62 at maintenance cost 100.000000

maintain preexisting BMP dd on segment 63 at maintenance cost 150.000000

maintain BMP draindip on segment 65 at maintenance cost 100.000000

maintain preexisting BMP rld on segment 66 at maintenance cost 94.500000

maintain BMP draindip on segment 66 at maintenance cost 100.000000

maintain preexisting BMP dd on segment 67 at maintenance cost 150.000000

maintain preexisting BMP rld on segment 67 at maintenance cost 94.500000
H

maintain BMP 3draindips on segment 67 at maintenance cost 300.000000

maintain preexisting BMP dd on segment 68 at maintenance cost 150.000000

maintain preexisting BMP rld on segment 68 at maintenance cost 94.500000

maintain BMP draindip on segment 69 at maintenance cost 100.000000

maintain preexisting BMP dd on segment 70 at maintenance cost 150.000000

maintain preexisting BMP rld on segment 70 at maintenance cost 94.500000

maintain BMP draindip on segment 71 at maintenance cost 100.000000

maintain preexisting BMP dd on segment 72 at maintenance cost 150.000000

maintain preexisting BMP rld on segment 72 at maintenance cost 94.500000

maintain BMP draindip on segment 79 at maintenance cost 100.000000

maintain BMP draindip on segment 80 at maintenance cost 100.000000

maintain preexisting BMP dd on segment 81 at maintenance cost 150.000000

maintain BMP draindip on segment 93 at maintenance cost 100.000000

maintain preexisting BMP dd on segment 94 at maintenance cost 150.000000

maintain preexisting BMP rld on segment 109 at maintenance cost 94.500000

maintain BMP 3draindips on segment 113 at maintenance cost 300.000000

maintain preexisting BMP dd on segment 114 at maintenance cost 150.000000

maintain BMP draindip on segment 115 at maintenance cost 100.000000

maintain BMP draindip on segment 117 at maintenance cost 100.000000

maintain BMP 7draindips on segment 119 at maintenance cost 700.000000

maintain BMP draindip on segment 120 at maintenance cost 100.000000

maintain BMP draindip on segment 121 at maintenance cost 100.000000

maintain BMP draindip on segment 133 at maintenance cost 100.000000

maintain BMP draindip on segment 134 at maintenance cost 100.000000

maintain BMP 7draindips on segment 146 at maintenance cost 700.000000

maintain BMP draindip on segment 174 at maintenance cost 100.000000

Treatment cost for period 10: 17600.000000 dollars

NOTE: preexisting BMP cost already accounted for, so it won't show up in treatment cost

PERIOD 11

Treatment cost for period 11: -0.000244 dollars

NOTE: preexisting BMP cost already accounted for, so it won't show up in treatment cost

PERIOD 12

maintain BMP outslope on segment 7 at maintenance cost 29.840151

maintain preexisting BMP outsloping on segment 8 at maintenance cost 43.489964

maintain preexisting BMP gravel on segment 32 at maintenance cost 154.104172

maintain preexisting BMP outsloping on segment 32 at maintenance cost 35.023674

maintain preexisting BMP gravel on segment 34 at maintenance cost 34.347500

maintain preexisting BMP nd on segment 34 at maintenance cost 400.000000

maintain BMP outslope on segment 38 at maintenance cost 24.268560

maintain BMP outslope on segment 41 at maintenance cost 16.983845
I

maintain preexisting BMP gravel on segment 42 at maintenance cost 161.444168

maintain preexisting BMP nd on segment 42 at maintenance cost 400.000000

maintain preexisting BMP nd on segment 50 at maintenance cost 400.000000

maintain preexisting BMP outsloping on segment 50 at maintenance cost 25.320456

maintain preexisting BMP nd on segment 53 at maintenance cost 400.000000

maintain preexisting BMP nd on segment 63 at maintenance cost 400.000000

maintain preexisting BMP gravel on segment 66 at maintenance cost 175.522491

maintain preexisting BMP rld on segment 66 at maintenance cost 94.500000

maintain preexisting BMP gravel on segment 67 at maintenance cost 351.648315

maintain preexisting BMP rld on segment 67 at maintenance cost 94.500000

maintain preexisting BMP gravel on segment 68 at maintenance cost 76.655334

maintain preexisting BMP rld on segment 68 at maintenance cost 94.500000

maintain preexisting BMP gravel on segment 70 at maintenance cost 112.001663

maintain preexisting BMP rld on segment 70 at maintenance cost 94.500000

maintain preexisting BMP gravel on segment 72 at maintenance cost 115.975838

maintain preexisting BMP rld on segment 72 at maintenance cost 94.500000

maintain preexisting BMP gravel on segment 80 at maintenance cost 175.290009

maintain preexisting BMP outsloping on segment 81 at maintenance cost 57.188446

maintain preexisting BMP outsloping on segment 94 at maintenance cost 19.917046

maintain BMP outslope on segment 95 at maintenance cost 44.396400

maintain BMP outslope on segment 96 at maintenance cost 40.811554

maintain BMP outslope on segment 108 at maintenance cost 47.932384

maintain preexisting BMP gravel on segment 109 at maintenance cost 49.375500

maintain preexisting BMP rld on segment 109 at maintenance cost 94.500000

maintain BMP outslope on segment 112 at maintenance cost 41.192047

maintain preexisting BMP gravel on segment 114 at maintenance cost 80.570831

maintain preexisting BMP nd on segment 114 at maintenance cost 400.000000

maintain BMP outslope on segment 116 at maintenance cost 162.000000

maintain BMP outslope on segment 127 at maintenance cost 381.000000

maintain preexisting BMP outsloping on segment 135 at maintenance cost 185.059280

maintain BMP outslope on segment 136 at maintenance cost 30.466288

maintain preexisting BMP outsloping on segment 138 at maintenance cost 60.063633

maintain BMP outslope on segment 141 at maintenance cost 15.973315

maintain preexisting BMP outsloping on segment 143 at maintenance cost 20.971781

maintain BMP outslope on segment 142 at maintenance cost 130.000000

maintain preexisting BMP outsloping on segment 148 at maintenance cost 48.701519

Treatment cost for period 12: 6964.864258 dollars

NOTE: preexisting BMP cost already accounted for, so it won't show up in treatment cost

PERIOD 13

Treatment cost for period 13: -0.001923 dollars

NOTE: preexisting BMP cost already accounted for, so it won't show up in treatment cost
J

PERIOD 14

maintain preexisting BMP rld on segment 66 at maintenance cost 94.500000

maintain preexisting BMP rld on segment 67 at maintenance cost 94.500000

maintain preexisting BMP rld on segment 68 at maintenance cost 94.500000

maintain preexisting BMP rld on segment 70 at maintenance cost 94.500000

maintain preexisting BMP rld on segment 72 at maintenance cost 94.500000

maintain preexisting BMP rld on segment 109 at maintenance cost 94.500000

Treatment cost for period 14: -0.002686 dollars

NOTE: preexisting BMP cost already accounted for, so it won't show up in treatment cost

PERIOD 15

maintain BMP 3draindips on segment 6 at maintenance cost 300.000000

maintain BMP outslope on segment 7 at maintenance cost 29.840151

maintain preexisting BMP dd on segment 8 at maintenance cost 150.000000

maintain preexisting BMP outsloping on segment 8 at maintenance cost 43.489964

maintain BMP draindip on segment 31 at maintenance cost 100.000000

maintain preexisting BMP dd on segment 32 at maintenance cost 150.000000

maintain preexisting BMP gravel on segment 32 at maintenance cost 154.104172

maintain preexisting BMP outsloping on segment 32 at maintenance cost 35.023674

maintain BMP draindip on segment 33 at maintenance cost 100.000000

maintain preexisting BMP dd on segment 34 at maintenance cost 150.000000

maintain preexisting BMP gravel on segment 34 at maintenance cost 34.347500

maintain BMP outslope on segment 38 at maintenance cost 24.268560

maintain BMP outslope on segment 41 at maintenance cost 16.983845

maintain preexisting BMP dd on segment 42 at maintenance cost 150.000000

maintain preexisting BMP gravel on segment 42 at maintenance cost 161.444168

maintain BMP draindip on segment 49 at maintenance cost 100.000000

maintain preexisting BMP dd on segment 50 at maintenance cost 150.000000

maintain preexisting BMP outsloping on segment 50 at maintenance cost 25.320456

maintain BMP draindip on segment 52 at maintenance cost 100.000000

maintain preexisting BMP dd on segment 53 at maintenance cost 150.000000

maintain BMP 3draindips on segment 59 at maintenance cost 300.000000

maintain BMP draindip on segment 60 at maintenance cost 100.000000

maintain preexisting BMP dd on segment 61 at maintenance cost 150.000000

maintain BMP draindip on segment 62 at maintenance cost 100.000000

maintain preexisting BMP dd on segment 63 at maintenance cost 150.000000

maintain BMP draindip on segment 65 at maintenance cost 100.000000

maintain preexisting BMP gravel on segment 66 at maintenance cost 175.522491

maintain BMP draindip on segment 66 at maintenance cost 100.000000

maintain preexisting BMP dd on segment 67 at maintenance cost 150.000000

maintain preexisting BMP gravel on segment 67 at maintenance cost 351.648315

maintain BMP 3draindips on segment 67 at maintenance cost 300.000000

maintain preexisting BMP dd on segment 68 at maintenance cost 150.000000
K

maintain preexisting BMP gravel on segment 68 at maintenance cost 76.655334

maintain BMP draindip on segment 69 at maintenance cost 100.000000

maintain preexisting BMP dd on segment 70 at maintenance cost 150.000000

maintain preexisting BMP gravel on segment 70 at maintenance cost 112.001663

maintain BMP draindip on segment 71 at maintenance cost 100.000000

maintain preexisting BMP dd on segment 72 at maintenance cost 150.000000

maintain preexisting BMP gravel on segment 72 at maintenance cost 115.975838

maintain BMP draindip on segment 79 at maintenance cost 100.000000

maintain preexisting BMP gravel on segment 80 at maintenance cost 175.290009

maintain BMP draindip on segment 80 at maintenance cost 100.000000

maintain preexisting BMP dd on segment 81 at maintenance cost 150.000000

maintain preexisting BMP outsloping on segment 81 at maintenance cost 57.188446

maintain BMP draindip on segment 93 at maintenance cost 100.000000

maintain preexisting BMP outsloping on segment 94 at maintenance cost 19.917046

maintain preexisting BMP dd on segment 94 at maintenance cost 150.000000

maintain BMP outslope on segment 95 at maintenance cost 44.396400

maintain BMP outslope on segment 96 at maintenance cost 40.811554

maintain BMP outslope on segment 108 at maintenance cost 47.932384

maintain preexisting BMP gravel on segment 109 at maintenance cost 49.375500

maintain BMP outslope on segment 112 at maintenance cost 41.192047

maintain BMP 3draindips on segment 113 at maintenance cost 300.000000

maintain preexisting BMP dd on segment 114 at maintenance cost 150.000000

maintain preexisting BMP gravel on segment 114 at maintenance cost 80.570831

maintain BMP draindip on segment 115 at maintenance cost 100.000000

maintain BMP outslope on segment 116 at maintenance cost 162.000000

maintain BMP draindip on segment 117 at maintenance cost 100.000000

maintain BMP 7draindips on segment 119 at maintenance cost 700.000000

maintain BMP draindip on segment 120 at maintenance cost 100.000000

maintain BMP draindip on segment 121 at maintenance cost 100.000000

maintain BMP outslope on segment 127 at maintenance cost 381.000000

maintain BMP draindip on segment 133 at maintenance cost 100.000000

maintain preexisting BMP outsloping on segment 135 at maintenance cost 185.059280

maintain BMP draindip on segment 134 at maintenance cost 100.000000

maintain BMP outslope on segment 136 at maintenance cost 30.466288

maintain preexisting BMP outsloping on segment 138 at maintenance cost 60.063633

maintain BMP outslope on segment 141 at maintenance cost 15.973315

maintain preexisting BMP outsloping on segment 143 at maintenance cost 20.971781

maintain BMP outslope on segment 142 at maintenance cost 130.000000

maintain BMP 7draindips on segment 146 at maintenance cost 700.000000

maintain preexisting BMP outsloping on segment 148 at maintenance cost 48.701519

maintain BMP draindip on segment 174 at maintenance cost 100.000000

Treatment cost for period 15: 24564.867188 dollars

NOTE: preexisting BMP cost already accounted for, so it won't show up in treatment cost

PERIOD 16
L

maintain preexisting BMP nd on segment 34 at maintenance cost 400.000000

maintain preexisting BMP nd on segment 42 at maintenance cost 400.000000

maintain preexisting BMP nd on segment 50 at maintenance cost 400.000000

maintain preexisting BMP nd on segment 53 at maintenance cost 400.000000

maintain preexisting BMP nd on segment 63 at maintenance cost 400.000000

maintain preexisting BMP rld on segment 66 at maintenance cost 94.500000

maintain preexisting BMP rld on segment 67 at maintenance cost 94.500000

maintain preexisting BMP rld on segment 68 at maintenance cost 94.500000

maintain preexisting BMP rld on segment 70 at maintenance cost 94.500000

maintain preexisting BMP rld on segment 72 at maintenance cost 94.500000

maintain preexisting BMP rld on segment 109 at maintenance cost 94.500000

maintain preexisting BMP nd on segment 114 at maintenance cost 400.000000

Treatment cost for period 16: -0.001190 dollars

NOTE: preexisting BMP cost already accounted for, so it won't show up in treatment cost

PERIOD 17

Treatment cost for period 17: -0.000977 dollars

NOTE: preexisting BMP cost already accounted for, so it won't show up in treatment cost

PERIOD 18

maintain BMP outslope on segment 7 at maintenance cost 29.840151

maintain preexisting BMP outsloping on segment 8 at maintenance cost 43.489964

maintain preexisting BMP gravel on segment 32 at maintenance cost 154.104172

maintain preexisting BMP outsloping on segment 32 at maintenance cost 35.023674

maintain preexisting BMP gravel on segment 34 at maintenance cost 34.347500

maintain BMP outslope on segment 38 at maintenance cost 24.268560

maintain BMP outslope on segment 41 at maintenance cost 16.983845

maintain preexisting BMP gravel on segment 42 at maintenance cost 161.444168

maintain preexisting BMP outsloping on segment 50 at maintenance cost 25.320456

maintain preexisting BMP gravel on segment 66 at maintenance cost 175.522491

maintain preexisting BMP rld on segment 66 at maintenance cost 94.500000

maintain preexisting BMP gravel on segment 67 at maintenance cost 351.648315

maintain preexisting BMP rld on segment 67 at maintenance cost 94.500000

maintain preexisting BMP gravel on segment 68 at maintenance cost 76.655334

maintain preexisting BMP rld on segment 68 at maintenance cost 94.500000

maintain preexisting BMP gravel on segment 70 at maintenance cost 112.001663

maintain preexisting BMP rld on segment 70 at maintenance cost 94.500000

maintain preexisting BMP gravel on segment 72 at maintenance cost 115.975838

maintain preexisting BMP rld on segment 72 at maintenance cost 94.500000

maintain preexisting BMP gravel on segment 80 at maintenance cost 175.290009

maintain preexisting BMP outsloping on segment 81 at maintenance cost 57.188446
M

maintain preexisting BMP outsloping on segment 94 at maintenance cost 19.917046

maintain BMP outslope on segment 95 at maintenance cost 44.396400

maintain BMP outslope on segment 96 at maintenance cost 40.811554

maintain BMP outslope on segment 108 at maintenance cost 47.932384

maintain preexisting BMP gravel on segment 109 at maintenance cost 49.375500

maintain preexisting BMP rld on segment 109 at maintenance cost 94.500000

maintain BMP outslope on segment 112 at maintenance cost 41.192047

maintain preexisting BMP gravel on segment 114 at maintenance cost 80.570831

maintain BMP outslope on segment 116 at maintenance cost 162.000000

maintain BMP outslope on segment 127 at maintenance cost 381.000000

maintain preexisting BMP outsloping on segment 135 at maintenance cost 185.059280

maintain BMP outslope on segment 136 at maintenance cost 30.466288

maintain preexisting BMP outsloping on segment 138 at maintenance cost 60.063633

maintain BMP outslope on segment 141 at maintenance cost 15.973315

maintain preexisting BMP outsloping on segment 143 at maintenance cost 20.971781

maintain BMP outslope on segment 142 at maintenance cost 130.000000

maintain preexisting BMP outsloping on segment 148 at maintenance cost 48.701519

Treatment cost for period 18: 6964.863281 dollars

NOTE: preexisting BMP cost already accounted for, so it won't show up in treatment cost

PERIOD 19

Treatment cost for period 19: 0.001938 dollars

NOTE: preexisting BMP cost already accounted for, so it won't show up in treatment cost
N

B. Flowchart Describing Adapted Simulated Annealing Algorithm

No Ye No Stop, report best solution

Lower temperature

Time to change 

temperature?

Have stopping criteria been reached? Ye

s No Ye

s

Input initial budget per period, length of 

planning horizon; Define initial temperature 

Compute cost of maintaining existing 

BMPs over course of planning horizon, 

subtract from initial budget

Develop initial (current) solution, including maintenance regime Formulate new solution and maintenance regime: change BMP or period of 

installation for one road segment in current solution Compute sediment leaving buffer over 

course of planning horizon for each solution Compute proximity between segments

Compute acceptance probability Does the new solution save more sediment than the current solution? Go to next iteration; update current solution N

o Ye

s Accept solution?
O

C. Example Input Table for BMP-SA Algorithm

segment number BMP type installation cost maintenance cost maintenance frequency sediment leaving buffer _______________________________________________________________________

6 none 0 0 0 0 draindip 100 100 5 0.001 outslope 128.4272706 42.8090902

3 0 3draindips 300 300 5 0

7 none 0 0 0 0 draindip 100 100 5 0 outslope 89.52045294 29.84015098

3 0 none 0 0 0 0

31 none 0 0 0 0 draindip 100 100 5 0.001 none 0 0 0 0 none

0 0 0 0

33 none 0 0 0 0 draindip 100 100 5 0.002 none 0 0 0 0 none

0 0 0 0

38 none 0 0 0 0 outslope 72.80567942 24.2685598 3 0.005 none 0 0 0

0 none 0 0 0 0

41 none 0 0 0 0 outslope 50.95153236 16.98384412 3 0 none 0 0 0

0 none 0 0 0 0

49 none 0 0 0 0 draindip 100 100 5 0 outslope 210.00 70.00 3 0

none 0 0 0 0

52 none 0 0 0 0 draindip 100 100 5 0 pave 14494.16309 887.397766 7

0.012 outslope 177.00 59.00 3 0

59 none 0 0 0 0 draindip 100 100 5 0.023 outslope 399.00 133.00 3 0

3draindips 300 300 5 0

60 none 0 0 0 0 draindip 100 100 5 0 outslope 171.00 57.00 3 0

none 0 0 0 0

62 none 0 0 0 0 draindip 100 100 5 0 outslope 471.00 157.00 3 0

none 0 0 0 0

65 none 0 0 0 0 draindip 100 100 5 0.001 none 0 0 0 0 none

0 0 0 0

66 none 0 0 0 0 draindip 100 100 5 0.012 none 0 0 0 0 none

0 0 0 0
P

67 none 0 0 0 0 draindip 100 100 5 0.04 3draindips 300 300 5 0.009

none 0 0 0 0

69 none 0 0 0 0 draindip 100 100 5 0.034 none 0 0 0 0 pave

7479.089355 457.903442 7 0.2115

71 none 0 0 0 0 draindip 100 100 5 0.026 pave 7758.704102 475.022705 7

0.1355 none 0 0 0 0

79 none 0 0 0 0 draindip 100 100 5 0 none 0 0 0 0 none

0 0 0 0

80 none 0 0 0 0 draindip 100 100 5 0.008 none 0 0 0 0 none

0 0 0 0

93 none 0 0 0 0 draindip 100 100 5 0.022 none 0 0 0 0 none

0 0 0 0

95 none 0 0 0 0 draindip 100 100 5 0.024 outslope 133.1892 44.3964

3 0.0065 none 0 0 0 0

96 none 0 0 0 0 draindip 100 100 5 0.025 outslope 122.4346618 40.81155392

3 0.009 none 0 0 0 0

108 none 0 0 0 0 draindip 100 100 5 0.021 outslope 143.7971559 47.93238529

3 0.001 none 0 0 0 0

112 none 0 0 0 0 draindip 100 100 5 0.017 outslope 123.5761412 41.19204706

3 0.001 none 0 0 0 0

113 none 0 0 0 0 draindip 100 100 5 0.063 3draindips 300 300 5 0.016

none 0 0 0 0

115 none 0 0 0 0 draindip 100 100 5 0 none 0 0 0 0 none

0 0 0 0

116 none 0 0 0 0 draindip 100 100 5 0 outslope 486.00 162.00 3 0

none 0 0 0 0

117 none 0 0 0 0 draindip 100 100 5 0 outslope 354.00 118.00 3 0

none 0 0 0 0

119 none 0 0 0 0 pave 46355.11 2835 7 0.933 3draindips 300 300 5 0.009

7draindips 700 700 5 0
Q

120 none 0 0 0 0 draindip 100 100 5 0 none 0 0 0 0 none

0 0 0 0

121 none 0 0 0 0 draindip 100 100 5 0 outslope 294.00 98.00 3 0

none 0 0 0 0

127 none 0 0 0 0 draindip 100 100 5 0.001 outslope 1143.00 381.00 3

0 none 0 0 0 0

133 none 0 0 0 0 draindip 100 100 5 0 pave 23765.00 1440.00 7

0.024 none 0 0 0 0

134 none 0 0 0 0 draindip 100 100 5 0 none 0 0 0 0 none

0 0 0 0

136 none 0 0 0 0 draindip 100 100 5 0.017 outslope 91.39886177 30.46628725

3 0.004 none 0 0 0 0

141 none 0 0 0 0 outslope 47.91994706 15.97331569 3 0 none 0 0 0

0 none 0 0 0 0

142 none 0 0 0 0 outslope 390.00 130.00 3 0.0045 3draindips 300 300 5 0.09

7draindips 700 700 5 0.028

146 none 0 0 0 0 draindip 100 100 5 0.117 3draindips 300 300 5 0.03

7draindips 700 700 5 0.004

174 none 0 0 0 0 draindip 100 100 5 0 none 0 0 0 0 none

0 0 0 0