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Decision analysis and cost effectiveness analysis applied to forest road restoration in coastal British… Allison, Clay Stanley 2000

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Decision Analysis and Cost Effectiveness Analysis Applied to Forest Road Restoration in Coastal British Columbia Clay Stanley Allison B.A., The University of Calgary, 1974 M.A., The University of Calgary, 1978 A Thesis Submitted In Partial Fulfillment Of The Requirements For The Degree Of Master of Science in The Faculty of Graduate Studies Department of Forest Resources Management We accept this thesis as conforming to the required standard  The University Of British Columbia April 2000 © Clay Stanley Allison, 2000  In presenting  this  degree at the  thesis  in partial  University of  freely available for reference copying  of  department publication  this or  fulfilment  of  British Columbia, and study.  of this  his  or  her  requirements  I agree  that the  I further agree  thesis for scholarly purposes by  the  may be  representatives.  It  thesis for financial gain shall not  is  Phc^<^ /IfZOQcCr'S  The University of British Columbia Vancouver, Canada  Date  DE-6 (2/88)  MaA^A  ZLK.ZOO O  advanced  that permission for extensive granted  allowed  permission.  Department of  an  Library shall make it  by the  understood be  for  HA */*^ <j»*S  that without  head  of  my  copying  or  my written  Abstract Evaluating investments in projects designed to restore the natural system and prevent expected loss from events such as landslides is difficult because of the complexity of the natural system and chance. Using a road deactivation project in coastal British Columbia as a case study, I demonstrate the use of decision analysis to organize the complexity of the natural system. The resulting structure provided a series of focal points for an expert group to develop consensus estimates of the probability of a landslide and the expected loss for a sample of road segments in the study area. The forest road was segmented by Terrain Stability Class and divided into 171 road segments approximately one hundred meters in length. A sample of 17 road sections was used to estimate the relationship between expected net benefit and road deactivation cost. Cost effectiveness analysis was used to weigh the expected net benefit of road deactivation with the deactivation cost. The cost effectiveness analysis showed that cumulative expected net benefit reaches a maximum then declines as additional road segments are deactivated. As a result there is a difference between the maximum cumulative expected net benefit and the total expected net benefit. The results of the cost effectiveness analysis did not significantly change when the return interval of the rainstorm, the discount rate, and the amount of the loss due to the landslide were varied. The results show that it is possible to distinguish between road segments offering high expected net benefits from road segments offering no expected net benefits. Seventeen road segments (10% of the 171 road segments) represented 98% ($7,870,000 of $8,000,000) of the cumulative expected net benefits from road deactivation and 18% of the cumulative cost ($87,000 of $490,000). Sixty-nine segments (40% of 171 road segments) had expected net benefit-cost ratios zero and below and represented 39% of the cumulative cost ($190,000 of $490,000). The results also show that there is a relationship between road deactivation cost and expected net benefits for Terrain Stability Classes IV and V. The evaluation approach relied on information that is currently available including air photographs, contour maps, and road assessments conducted in the field together with expert opinion. On a larger scale, the approach would be inexpensive to implement while offering the opportunity to better target the investment of resources, possibly saving up to seventy or eighty percent of road construction project costs.  Table of Contents Abstract  ii  Table of Contents  iii  List of Tables  v  List of Figures  vi  Acknowledgements  ix  Dedication  x  Chapter 1.- Introduction  1  The Objectives of the Study Chapter 2 - Addressing Elements That Cloud the Assessment of Road Deactivation  3 6  Complexity of Natural Processes  6  Rainfall and Landslides  7  Road Deactivation Planning and Regulations  9  Risk Perception  14  Economic Concepts and Road Deactivation  16  Chapter 3 - Characterizing Road Deactivation Benefits and Costs  21  Road Deactivation Objectives in British Columbia and Neighbouring Jurisdictions  21  Identifying Impact Areas  25  Scenarios of Impact Characterized  28  Proximity to the Road Impact Characterization  28  Hillslope Impact Characterization  28  Headwater Impact Characterization  29  Main Channel Impact Characterization  30  Elements of Loss included in the Characterizations of Impact  31  Index of Expected Loss due to Localized Channel and Stream Impacts  31  Index of Expected Fish Loss  31  Index of Expected Water Quality Loss  33  Index of Expected Timber Loss  34  Road Deactivation Costs  37  iv Chapter 4 - Decision Analysis and Road Deactivation  39  Decision Analysis  39  Probability Estimation  40  Chapter 5 - Cost Effectiveness Analysis of Road Deactivation  45  Cost Effectiveness Analysis  45  Deactivation Benefits and Costs  47  Sensitivity Analysis of Cost Effectiveness Analysis Results  57  Varying the Discount Rate  58  Varying the Loss Amount  63  Varying the Rainstorm Return Interval  68  Varying the Probability of a Landslide Occurring After a Rainstorm Has Occurred  71  Chapter 6 - Limitations and Conclusions  77  The Analysis Results Re-Examined Using Incremental Expected Net Benefit  77  Bounding the Analysis  84  Bibliography  87  V  List of Tables Table 2-1 Risk Rating Used to Establish Work Priority for Road Deactivation in BC  12  Table 3-1 Some Road Deactivation Considerations  23  Table 3-2 Watershed Loss Categories and Factors Used to Characterize Loss  25  Table 3-3 Definition of Landslide Impact Areas and Severity Classes  26  Table 3-4 Index of Expected Localized Physical Impact and Fish Loss  33  Table 3-5 Index of Expected Water Quality Loss  34  Table 3-6 Index of Expected Timber Resource Loss  36  Table 3-7 Summary of Indexes of Expected Loss by Impact Area  37  Table 4-1 Probability of a Landslide for a Random Sample of Road Segments  44  Table 5-1 Baseline Distribution (Discount Rate set at 4.25%) of Road Segments by Expected Net Benefit-cost Ratios  56  Table 5-2 The Distribution of Road Segments by Expected Net Benefit-cost Ratio Ranges and Terrain Stability Class using Different Discount Rates  60  Table 5-3 Distribution of Road Segments in Three Benefit-cost Ratio Ranges as a Result of Varying Discount Rate  63  Table 5-4 The Distribution of Road Segments by Expected Net Benefit-cost Ratio Ranges and Terrain Stability Class using Different Expected Loss Amounts  66  Table 5-5 Distribution of Road Segments in Three Benefit-cost Ratio Ranges as a Result of Varying Estimated Loss Amount  67  Table 5-6 The Distribution of Road Segments by Expected Net Benefit-cost Ratio Ranges and Terrain Stability Class using Different Estimates of the Rainstorm Return Interval  69  Table 5-7 Distribution of Road Segments in Three Benefit-cost Ratio Ranges as a Result of Varying Rainstorm Return Interval  71  Table 5-8 The Distribution of Road Segments by Expected Net Benefit-cost Ratio Ranges and Terrain Stability Class using Different Estimates of the Probability of a Landslide  73  Table 5-9 Distribution of Road Segments in Three Benefit-cost Ratio Ranges as a Result of Varying the Probability of Landslide  76  vi  List of Figures Figure 1-1 Elements of the Access Planning Process that Lead to the Deactivation Plan and the Final Outcome of the Access Plan Figure 1-2 Road Deactivation Study Area  2 *t  Figure 2-1 The Data Points are the Estimated Mean Rainfall Intensities for Storms of Return Intervals from 2 Years to 100 years and for a Landslide Threshold  9  Figure 2-2 Risk Perception Links the Economic Environment to the Physical Environment  15  Figure 4-1 Probability Estimation Logic Chart  42  Figure 4-2 The Expert Group's Estimates of the Probability of a Landslide Without Road Deactivation Compared to the Probability of a Landslide With Road for 17 Randomly Chosen Road Segments. Six Road Segments were Selected from each Terrain Class  43  Figure 5-1 Decision Framework for Expected Loss in the Current Year  48  Figure 5-2 Sample Regression Plot Log 10 of Expected Benefit to Cost  52  Figure 5-3 Combined Terrain IV & V Regression Plot Log 10 Expected Benefit to Cost  52  Figure 5-4 Cost Effectiveness Baseline Results (Discount Rate set at 4.25%) Showing Cumulative Expected Net Benefit to Cost Produced by Sorting the Road Segments in Order of their Expected Net Benefit-cost Ratios  54  Figure 5-5 Alternative Cost Effectiveness Frontiers Showing Cumulative Expected Net Benefit to Cost Produced by Ranking the Road Segments in Order of their Expected Net Benefit-cost Ratios and Varying the Discount Rate  59  Figure 5-6 Alternative Cost Effectiveness Frontiers Showing Cumulative Expected Net Benefit to Cost Produced by Ranking the Road Segments in Order of their Expected Net Benefit-cost Ratios and Varying the Estimated Loss Amounts  64  Figure 5-7 Alternative Cost Effectiveness Frontiers Showing Cumulative Expected Net Benefit to Cost Produced by Ranking the Road Segments in Order of their Expected Net Benefit-cost Ratios and Varying the Rainstorm Return Interval  68  vii Figure 5-8 Alternative Cost Effectiveness Frontiers Showing Cumulative Expected Net Benefit to Cost Produced by Ranking the Road Segments in Order of their Expected Net Benefit-cost Ratios and Varying the Expert Group's Probability of a Landslide  72  Figure 6-la Terrain Class III Alternative Distribution of Road Segments Showing Expected Incremental Expected Net Benefit to Cost Produced by Ranking the Road Segments in Order of their Expected Net Benefit-cost Ratios and Varying the Discount Rate  80  Figure 6-lb Terrain Class IV Alternative Distribution of Road Segments Showing Expected Incremental Expected Net Benefit to Cost Produced by Ranking the Road Segments in Order of their Expected Net Benefit-cost Ratios and Varying the Discount Rate  80  Figure 6-lc Terrain Class V Alternative Distribution of Road Segments Showing Expected Incremental Expected Net Benefit to Cost Produced by Ranking the Road Segments in Order of their Expected Net Benefit-cost Ratios and Varying the Discount Rate  81  Figure 6-2a Terrain Class III Alternative Distribution of Road Segments Showing Expected Incremental Expected Net Benefit to Cost Produced by Ranking the Road Segments in Order of their Expected Net Benefit-cost Ratios and Varying the Amount of the Loss  81  Figure 6-2b Terrain Class IV Alternative Distribution of Road Segments Showing Expected Incremental Expected Net Benefit to Cost Produced by Ranking the Road Segments in Order of their Expected Net Benefit-cost Ratios and Varying the Amount of the Loss  82  Figure 6-2c Terrain Class V Alternative Distribution of Road Segments Showing Expected Incremental Expected Net Benefit to Cost Produced by Ranking the Road Segments in Order of their Expected Net Benefit-cost Ratios and Varying the Amount of the Loss  82  Figure 6-3a Terrain Class III Alternative Distribution of Road Segments Showing Expected Incremental Expected Net Benefit to Cost Produced by Ranking the Road Segments in Order of their Expected Net Benefit-cost Ratios and Varying the Return Interval of the Rainstorm  83  viii Figure 6-3b Terrain Class IV Alternative Distribution of Road Segments Showing Expected Incremental Expected Net Benefit to Cost Produced by Ranking the Road Segments in Order of their Expected Net Benefit-cost Ratios and Varying the Return Interval of the Rainstorm  83  Figure 6-3c Terrain Class V Alternative Distribution of Road Segments Showing Expected Incremental Expected Net Benefit to Cost Produced by Ranking the Road Segments in Order of their Expected Net Benefit-cost Ratios and Varying the Return Interval of the Rainstorm  84  ix  Acknowledgements The journey to complete this thesis has truly been a walk down a long crooked road composed of tempting detours. I willingly took some detours and my committee members steered me clear of many others, Professor David Tait, Professor Roy Sidle, Professor Doug Golding, and Pat Slaney, MELP. Thank you for your patience, guidance and wisdom. My guide to the application of decision analysis to the natural system was Professor David Tait. Professor Roy Sidle applied his equally gifted mind to melding his knowledge of hydrology to decision analysis. While it seems hardly sufficient, thank you both. Dennis Lozinsky and Wayne Ketty provided both the information and the opportunity for me to learn about current road deactivation practice and to build the thesis around a recently completed forest road deactivation project. Mr. Lozinsky and Mr. Ketty perspectives have shaped the thesis approach and their contributions made the thesis stronger. Decision analysis requires the ability to sort through detail and puzzles, I was helped by two of the best, Stan Allison and Shane Allison. To prove expert opinion could be used to assess the probability of expected loss, an expert group was required. The group, who freely volunteered their time and their insights to made the approach work, Jonathan Fannin, Dan Hogan, Wayne Ketty, Mike Lichtensteiger, Roy Sidle, David Tait, Bruce Thomson, and Weimin Wu. The persistence of Dan Hogan, Bruce Thomson, Wayne Ketty, Roy Sidle, and David Tait was appreciated. When I needed to talk through some of my half finished thoughts several people listened patiently and offered counsel including Brian Sieben, Rita Winkler, Hardy Bartle, Jim Johnston, and Lynn Husted. Finally, the only reason the thesis reads as well as it does is because of the editorial efforts of David Tait, Roy Sidle, and Jackie Johnston.  Dedication  To the contribution and support of three generations of Allisons.  1  Chapter 1 Introduction Prudent strategies are needed throughout British Columbia to assess the magnitude of resource loss in watersheds that have been adversely impacted by forestry activity and to manage the large investment necessary to address the backlog of such watersheds. (Slaney and Martin, 1997). One aspect of this strategy is to determine how much to invest or spend once the decision has been taken to deactivate a forestry road or more probably, a road network. The answer is not obvious. Clouding the answer are factors like determining the appropriate planning time frame, defining important resources and attributes, and measuring the expected benefits. Additionally but significantly, the element of chance influences how we reach the desired road deactivation objectives.  Factors that obscure decisions on how much to spend on road deactivation include the age of the road and the way it was originally constructed, because the road construction approach can increase the risk of road-related landslides (McCammon, 1996; Moore, 1994). Most forest roads built in the 1970's constructed a horizontal running surface by excavating a into the hillslope and using some of the excavated material together with some logging debris as fill on the downslope side of the road prism. During construction the natural surface and subsurface drainage system was modified and excess excavated material simply pushed over the side. In some areas the excavated material used in the road fill was held in place by the root strength of old growth stumps, other vegetation, debris that remained after logging, and retaining walls built of logs anchored by large stumps (Moore, 1994). Because the logging debris and root networks of stumps decompose, the risk to slope stability increases with time (Sidle et al. 1985). The decay increases the probability of road-related landslides and increase the chance that the fill material will become saturated (Doyle et al. 1998). Slope stability is a major concern of the forest industry in the mountainous terrain of coastal British Columbia (Sidle et al. 1985; Schwab, 1998). Loss of stability can result in the displacement of soil, rock, and debris downslope threatening resource values such as stream habitat and forest site productivity.  2  Contributing to the difficulty of determining how much to spend on road deactivation is the fact that deactivation is an element of a larger planning process: road access planning. British Columbia regulations allow for three access management strategies (Moore, 1994): 1)  The road remains open and is upgraded to current standards. The open road requires periodic inspection and maintenance.  2)  Based upon access needs (i.e., duration and type) the road is deactivated to one of the following: - Temporary level (regular use suspended for up to three years), - Semi-permanent level (regular use suspended for up to three years on winter roads, roads with a potential for debris torrents, and those roads in isolated areas as well roads in areas where harvesting is temporarily suspended), - Permanent level (road to be closed permanently).  3)  The road is left alone if the roadway site where the road has been over grown or the access is very difficult.  Range of Deactivation from Full Deactivation to No Deactivation  Range of Possible Sites Road Access  Future Road  Requirements  Usage  Objectives  Deactivation Plan, Some Elements  Range of Deactivation  Final Outcome  Treatments Options  Range of Possible Climate Scenarios  Budget Constraints  Figure 1-1 Elements of the Access Planning Process that Lead to the Deactivation Plan and the Final Outcome of the Access Plan.  3  Access planning begins by estimating future road use and setting objectives that describe the desired future condition of the road (Figure 1-1). As an example, it may be decided that the road network is no longer required, in which case future road maintenance will no longer be required and the road will not contribute to landslides or excessive surface erosion. After setting objectives, managers develop a deactivation plan. The deactivation plan involves several linked elements including the type of the deactivation, the range of possible site conditions, treatment alternatives, climate, and budget constraints. Underlying each consideration is an array of possible outcomes and probabilities of occurrence leading to multiple possible final outcomes. To simplify Figure 1-1, factors such as severity of the possible landslide impacts are not displayed as elements to be considered when developing the final outcome of the planning process, possibly suggesting that, the planning processes results in a single final outcome. Multiple possible outcomes are possible; for example, the severity of the landslide impact depends in part upon the existing capacity of the natural system (at the time of the landslide) to withstand the consequences of the landslide. The impact on the aquatic habitat of a flush of sediment into a stream depends on the volume of water flowing in the stream, the available suspended sediment carrying capacity, and potential storage sites (Swanston, 1991). While the planning process would be more accurately reflected by including in Figure 1-1 all possible combinations of the planning elements together with uncertainty, the figure would be of little use to managers wishing to distinguish between the benefits and costs of the final outcome alternatives. One way to systematically approach decisions about road deactivation is decision analysis (Raiffa, 1970). Decision analysis is a method of comparing alternative deactivation choices and the range of expected outcomes or loss. The difference between the average expected loss of not undertaking deactivation and the average expected loss of undertaking deactivation can be thought of as the savings achieved, or the expected benefit of undertaking road deactivation.  777c? Objectives  of the Study  The purpose of the study is to demonstrate that the complexity of road deactivation decisions can be organized by applying decision analysis. The resulting structure will allow  4  experts to reach a c o n s e n s u s on the expected probability of a landslide occurring for a given s e g m e n t of road and (given that this landslide occurs) t h e a v e r a g e expected loss f r o m the landslide. T h e secondary purpose of the study is to d e m o n s t r a t e that results of decision analysis c a n benefit budgeting related to road deactivation by distinguishing a m o n g road s e g m e n t s that offer large benefits f r o m those that offer m o d e r a t e to low benefits. Further, that the cost of deactivating a s e g m e n t of road is related to the expected benefit f r o m deactivating it. T h e demonstration uses, as a case study, 17 kilometres of forest road deactivation in coastal British C o l u m b i a c o m p l e t e d under Forest Renewal BC's W a t e r s h e d Restoration Program. T h e total t e n d e r cost w a s $588,367 or $35,064 per kilometre. T h e projects are located in the following sub-drainages:  Misery  Creek at an elevation of 4 0 0 m to 1 2 0 0 m ( 4 9 ° 4 8 ' lat., 1 2 3 " 4 5 ' long.) and C h i c k w a t Creek at an elevation of 3 0 0 m to 1 2 0 0 m ( 4 9 ° 5 0 ' lat., 1 2 3 ° long.) (Figure 1-2).  Figure 1-2 Road Deactivation Study A r e a  5  Figure 1-2 Road Deactivation Study Area The remaining sections of this thesis are structured in the following manner. •  Chapter 2 introduces the elements addressed to undertake the analysis of road deactivation including natural complexity, rainfall frequency and landslides, road deactivation planning and regulation, risk, and economics.  •  Chapter 3 introduces deactivation costs and discusses how resource losses were estimated.  •  Chapter 4 briefly presents decision tree analysis and the decision analysis framework for road deactivation. I describe the process used to determine probability of land slide occurring and the probability of expected loss.  •  Chapter 5 introduces the cost-effectiveness analysis model, a simple linear relationship between expected benefits and costs of road deactivation for a sample of randomly selected road segments. The linear relationship is built upon the structure developed in the decision analysis (Chapter 4). The linear relationship is applied to 17 km of deactivated road, allowing a cost-effectiveness frontier to be plotted. I then discuss the results of the cost-effectiveness analysis together with the sensitivity of the results to changes in the underlying variables.  •  Chapter 6 summarizes the limitations, results and conclusions of the study.  6  Chapter 2 Addressing Elements That Cloud the Assessment of Road Deactivation Assessing the physical impact of a single intervention such as road is difficult because watersheds are in a constant state of change that occurs naturally and simultaneously at various scales of space and time (O'Neil et al.1995; Gunderson et al. 1995). The task becomes more arduous with the addition of natural system complexity, the regulations and range of deactivation actions developed to address natural system complexity, society's perception of the changes resulting from road deactivation, and the manner in which risk perceptions feed into the economic environment (Botkin, 1990). The assessment of road deactivation requires that the uncertain events influencing the assessment be organized in a systematic manner and the possible consequences examined. Simplifying assumptions were used to address the natural system complexity and scenarios of change were characterized. Significant factors influencing the occurrence of a road-related landslide, such as rainfall intensity and duration, were bounded.  Complexity of Natural Processes The natural processes in the watershed can be represented as a set of nested, inter-linked processes where larger processes (e.g., stream flow) are composed of several underlying processes that are interrelated (e.g., surface and subsurface flows). The underlying processes are, in turn composed of other processes (e.g., subsurface flow is formed from ground water flow and saturated and unsaturated soil moisture movement). To make the task of analysis even more complicated, each of these nested processes is linked to other ecological processes (e.g., subsurface flow is linked to soil chemistry, soil biota, and water quality). In natural systems these environmental and ecological processes are linked, sometimes tightly and sometimes loosely. Site specific interactions that vary through time and space shape the structure and function of an individual watersheds (Yozzo et al. 1996). But the apparent steady equilibrium of a natural watersheds is caused not only by a balance of large processes. Equilibrium is also the product of the chance balancing of a  7  multitude of smaller processes that shape the structure and function of the watershed (Lertzman et al. 1992; Gunderson et al. 1995). The complexity of the natural system was reduced by designating four areas in the watershed as the areas potentially impacted by a road-related landslide and presupposing that the total loss from the landslide is the sum of the loss in each area. The experience and knowledge of a group of professionals was used to integrate system complexity and the possibility of change from a road-related landslide in each of the designated areas. It was assumed that the probability estimates would not change over the planning time frame.  Rainfall and Landslides Storms delivering large amounts of rainfall are regularly associated with landslides in British Columbia (Schwab, 1998). The strong influence of topography on the amount of rainfall delivered to coastal British Columbia results in substantial local variations (Church, 1998). Ninety-nine rainfall monitoring stations are located across the Province, virtually none of them at higher elevations. The gauged stations have monitored precipitation inputs for one to twenty-four hour intervals for an average of seventeen years. Ninetynine gauges at lower elevations are insufficient to construct a map that systematically reveals local variations in mountainous topography (Alila, 1994; Church, 1998). Further, extrapolating from short term rainfall records creates additional uncertainty (Alila, 1994). Simply put, the longer the return interval (the expected length of time between rainstorms of similar intensity and duration) the wider the range of uncertainty. These issues surrounding the accuracy of rainfall estimation, however, are beyond the scope of this study. The issues are raised to draw attention to the uncertainty in the estimating procedures and thereby to limitations of results provided by such analysis. The closest rain gauge site to my study area is located several kilometers to the west on the coast, thus the data are not directly applicable. For the study, I developed rainfall estimates for storms of varying return intervals using regional isoline maps of both the mean and standard deviation of the annual rainfall extremes contained in the Rainfall Frequency Atlas (Hogg and Carr, 1985). Estimates of the mean and standard deviation of  8  the a n n u a l e x t r e m e s for the s t u d y areas w e r e inferred f r o m t h e respective maps.  These  e s t i m a t e d rainfall a m o u n t s w e r e increased by a factor of 2.0, as r e c o m m e n d e d by H o g g a n d Carr (1985), to a u g m e n t for the orographic effects on annual precipitation.  For a rainfall duration of 6 hours with an a v e r a g e intensity of eight m m per hour or greater the probability of recurrence is o n c e every 20 years or 0.05 (Figure 2-1).  For t h e s a m e 6-  hour d u r a t i o n , a s t o r m with an average intensity of 9.2 m m per hour or greater w o u l d have a probability of recurrence of 100-year return or 0.01 Figure 2-1.  For any  c o m b i n a t i o n of s t o r m d u r a t i o n (1 t o 24 h o u r s ) a n d a v e r a g e intensity (0 t o 1 6 m m per hour) t h e probability t h a t t h e c o m b i n e d duration a n d intensity will occur can be e s t i m a t e d and it is possible to plot curves representing similar probabilities of o c c u r r e n c e f o r all points t h r o u g h o u t t h e 24 hour duration s e q u e n c e (Figure 2-1).  Estimated m e a n rainfall  intensities for 2, 6, 12 a n d 24 hours periods with recurrence intervals of 2, 5, 10, 15, 20, 25, 50, a n d 100 years w e r e calculated and displayed in Figure 2-1 ( H o g g and Carr,  1985).  In addition to t h e s e curves, a relationship (for saturated conditions) b e t w e e n rainfall m a g n i t u d e a n d s t o r m return interval derived for a d a t a b a s e of landslides w o r l d w i d e w a s d e v e l o p e d (Sidle et al. 1985; Caine, 1980). T h i s t h r e s h o l d provides a basis for predicting shallow, rapid failures in the a b s e n c e of data other t h a n m e a n intensity a n d duration of rainfall f o r a particular s t o r m (Sidle e t a l . 1985). In g e n e r a l , Figure 2-1 d e m o n s t r a t e s t h a t over a 24-hour period average rainfall intensity for a particular return period (probability of occurrence) d i m i n i s h e s as duration increases; thus, the t h r e s h o l d rainfall intensity needed to trigger a landslide also decreases.  For short s t o r m durations (e.g., o n e to t w o hours)  only low probability, high intensity storms are projected to trigger landslides.  For  durations of six to t w e l v e hours, rainfall intensities associated with s t o r m s equal to or above. A t e n - y e a r return interval (P=0.1) lie a b o v e the threshold a n d are thus a s s u m e d to trigger a landslide. For a 24-hour s t o r m , rainfall intensities w i t h return intervals of greater t h a n 25-years are n e e d e d to trigger a landslide.  9  16  0 -I  1  1  !  !  1  1  1  !  !  1  \-  1  3  5  7  9  11  13  15  17  19  21  23  Rainfall D u r a t i o n ( h o u r s ) • 2 year return interval m 5 year return interval A 10 year return interval — - -o - • 15 year return interval — - X - - 20 year return interval o 25 year return interval — 50jrear return interval x 100 year return interval —•—Threshold above which Rainfall Intensity is expected to Cause Landslides  Figure 2-1 The Data Points are the Estimated Mean Rainfall Intensities for Storms of Return Intervals from 2 Years to 100 years (Hogg and Carr, 1985) and for a Landslide Threshold (Caine 1980; Sidle et al. 1985)  Considering these data a rainfall event that could trigger landslides in the study area was characterized as having a 20 years (P= 0.05). This characterization did not specify a storm duration because the incremental difference between the mean rainfall intensity at 6, 12, and 24 hour periods was small. Alternatively the expert group (who estimated landslide probabilities) was asked to use their experience in the study area and to consider a rainstorm of the intensity that occurs once every twenty years and relate the impact of this storm to the study area.  Road Deactivation Planning and Regulations All forestry roads in steep terrain reduce the stability of hillslopes (Sidle et al. 1985). Depending upon the extent of the excavation or cut into the hillslope the forest road surface may be fully, or partially, formed by the original hillslope strate with the remainder of the road surface formed by excavated material resting as fill material on the natural slope (Moore, 1994). In the past, road construction was done using heavy equipment  10  (e.g., bulldozers or line shovels) that offered little control of fill material and contributed to slope instability through oversteepening or overloading steep slopes. Oversteepening occurs by changing the natural slope geometry through placing excavated material downslope of the road prism. Overloading occurs by piling excavated material on top of natural ground cover. Oversteepening and overloading increase the potential volume of material in a landslide. Slope stability can be further compromised by factors such as rainfall or road-related conditions including oversteepened cut slopes, loss of road fill support, poor drainage control causing road water to be re-directed onto slopes, and removal of material from the toe of the slope (Moore, 1994; Moll, 1996). The importance of fill condition was emphasized in a recent Oregon Department of Forestry study on the effectiveness of Oregon's forest practices rules during two extreme storms in 1996 (Dent et al. 1997). This study is the largest such ground-based investigation conducted in Oregon to date. Crews surveyed 136 miles of stream channel and documented approximately 600 landslides. These data were combined with land management history and with road construction and maintenance specifications. Conclusions of interest for this study include the following: •  Most of the road-related landslides occurred in areas with particularly high natural rates of landslides and debris flows.  •  About half of the road-related landslides were associated in some way with road drainage. The other half were mainly related to fill conditions and slope steepness. The height of the cut into the slope (versus the width of the cut that is used to form the road surface) appears to have been the best correlation with landslide occurrence, even for landslides below roads (Dent et al. 1997).  In British Columbia field assessments are used to determine and record the existing condition of a road that may be deactivated. The assessments are used to identify and address site specific problems and form the basis for the road deactivation plan in addition to providing extra information for the access planning process. Assessment of the hillslope is conducted from the top of the slope down to the valley floor. Typically, one or two people walk the road to measure and inventory road condition. The road length is segmented, perhaps into lengths as short as ten meters. The team notes signs of stress (e.g., tension cracks in the sidecast material) and other features that may lead to a road-  11  related failure (e.g., damaged drainage culverts). Based upon this detailed information a deactivation design is developed. A deactivation strategy for placing roads into temporary storage (e.g., installation of waterbars costing $0.15 to $0.60 per meter of road depending upon spacing) versus full deactivation (e.g., retrieving fill material and placing it on the road bench at a cost of $18 to $35 per meter) has substantial budget implications. In this example temporary storage is significantly more inexpensive as compared to the cost of full deactivation. Road deactivation planning in British Columbia follows from road access planning for defined areas containing specific road networks. The access planning process addresses several issues including the following: Identifying the current and future vehicle types and users, and the amount of use, Determining who will be responsible for maintaining the road and for maintenance funding, Determining whether the road can be kept open with anticipated funding sources. The deactivation strategy chosen depends upon several factors which, in turn, influence road deactivation design. They include the risk to timber and non-timber values, strategies for managing access, and the road condition. When field assessments have been completed, access strategies may be modified accordingly. Some deactivation strategies require the use of heavy equipment, and the actions often leave the road impassable. In cases where the access management plan calls for permanent deactivation, the regulatory objective of the deactivation project is that the roadway and cleared width be left in a state that is unlikely to induce a landslide and where "natural drainage" has been restored. As a result of achieving these objectives the deactivated road is usually rendered impassible to heavy equipment and effectively becomes an obstacle that bars heavy equipment access. A top-down approach to permanent deactivation is carried out on the road (i.e., from the highest elevation to the lowest) to avoid the costs and environmental damage incurred in reopening a permanently deactivated road. Possible costs may be those of re-establishing the road together with possible environmental costs of renewed slope disturbance. In keeping with the top-down approach, funding is allocated based upon elevation. If limited funding is available for a particular watershed, higher reaches of the road network will receive priority compared to  12  lower level roads. Additionally, a significant proportion of the cost of road deactivation is for renting heavy equipment to perform the deactivation work and transporting the equipment to the site. These costs heavily influence the decision to complete all the deactivation work in a particular watershed before moving to the next project. Regulations in British Columbia pertaining to road deactivation require a risk assessment that is used to place priorities on the sequence of work to be undertaken. A risk rating has been developed and is the product of hazard and consequence (Moore, 1994). Moore (1994) defines "hazard" as the increased chance of landslides and surface soil erosion processes (erosion) and the deposition of eroded soil materials in streams (sedimentation). "Consequence" refers to the chance that a given hazard will affect resource, social, and economic values that are on a site, downslope of it, or downstream from it. Table 2-1 shows how risk rating is derived from ratings of "hazard" and "consequences" on road segments examined during field assessments. Table 2-1 Risk Rating Used to Establish Work Priority for Road Deactivation in BC (Appendix E, Moore, 1994). Risk Rating Consequence Rating  Hazard Rating  Risk Rating  High  High  High  Moderate  High  Moderate  High  High  Very High  High  Low  Moderate  Moderate  Moderate  Moderate  Low  High  Moderate  Moderate  Low  Low  Low  Moderate  Low  Low  Low  Low  The hazard rating can be established using either terrain stability maps or the recommendation of a professional engineer or geoscientist (Moore, 1994). Terrain stability maps describe areas of slope stability with respect to stable, potentially unstable, and unstable terrain within a particular landscape. For example, Terrain Stability Classes I & I I have a low hazard rating; Class III a moderate hazard rating; Class IV a moderate to high rating; and Class V a high hazard rating. Consequence ratings, described in terms of high, moderate, and low impact, are established by considering several resource and socio-  13  economic values including the following (Moore, 1994): Resource values: - Stream resource values - Water quality and supply - Fish habitat - Wildlife habitat and migration - Forest site productivity Socio-economic values: - Human life; private property or equipment; downslope railways, highways and other roads - Utilities - Landscape values - Recreation values Once access requirements are established and deactivation begins, the engineering work must be in compliance with the Forest Practices Code of British Columbia, and the scope of the work must meet with Ministry of Forests approval. The Forest Practices Code of British Columbia and accompanying regulations and standards describe a set of goals and provide guidelines about how these goals are to be attained (British Columbia Ministry of Forests and Ministry of Environment Lands and Parks, 1994). The code requires the Ministry of Forests district manager to prepare a road deactivation plan prior to conducting any permanent or semi-permanent deactivation (Section 64-8). A prescription design is required to satisfy the district manager that the actions are necessary to adequately manage and conserve the forest resources of the Province before temporary deactivation can be done (Section 64-9). Prescription designs must specify any site-specific deactivation measures necessary to minimize soil erosion (Section 64-10). The Chief Forester establishes deactivation standards for various types of roads (Section 207-1) by referencing the legislation, such as the Forest Act and the Forest Road Engineering Guidebook (British Columbia Ministry of Forests, 1993 b). The Forest Road Engineering Guidebook, for example, provides direction on how to meet the requirements of the Forest Practices Code and accompanying regulations by providing information together with recommended procedures for designing, building, and maintaining forest roads. The Watershed Restoration Program's Resource Road Rehabilitation Handbook: Planning and Implementation Guidelines (Interim Methods) (Moore, 1994) provides additional information to assist in problem identification and prescribe treatments to remedy them  14  but is superseded by The Forest Practices Code of British Columbia Act Guidebooks where overlap occurs. The complexity introduced by the range of possible road deactivation actions and the regulations developed to guide their use was bounded by focusing the study on a road deactivation plan for the area approved for funding under Forest Renewal's Watershed Restoration Program. The road deactivation plan for the area included estimates of the fill material resting on the natural slope that the plan developers believed would contribute to a landslide should one occur. Drawing upon the existing regulations, terrain stability maps at a scale of 1 to 5000 provided the expert group with a common reference upon which to build consensus on the probability of a road related landslide occurring and the expected loss.  Risk Perception The Forest Practices Code of British Columbia Act and accompanying regulations give guidelines, techniques, and tools to design road deactivation. In general, these guidelines provide latitude with respect to the design of site-specific deactivation measures. The guidelines are open to the user's interpretation of the Ministry's preference for risk and the technical assessment of risk of failure at the deactivation site where risk can be thought of as the product of the range of possible losses and the related probabilities. "How safe is safe enough?" is answered through the user's interpretations of risk that is embedded, but not clearly specified, in the road deactivation design put forward for approval to the Ministry of Forests. This is problematic because without a transparent statement of risk it is not clear how to weigh the benefits of road deactivation against the costs of road deactivation.  The answer to the question "How safe is safe enough?" depends partly on how we assess risk and how we perceive risk given the interaction of the physical environment with the economic environment. One component of the natural system includes the watershed and the forest road being considered for deactivation together with the resource values, structure, and functions possibly changed by a landslide. The other component represents the range of possible road deactivation actions and road deactivation outcomes (Figure 2-  15  2) (Morgan, 1990). Chance can influence either or both of the components. How the individual perceives risk in either component is a personal determination that influences how the individual values the outcome. Risk perception illustrated in Figure 2-2 links economics with the physical environment and requires that estimates of risk be quantified to allow efficient resource allocation.  Figure 2-2 Risk Perception Links the Economic Environment to the Physical Environment (Morgan, 1990) Research shows that experts and non-experts have different perceptions about risk as it is related to some technologies (Slovic, 1987). Risk perception, derived in part from closely held beliefs and past experience, leads many people to rely on fallible indicators such as memories of past landslide events or imagined consequences of the hazard (e.g., extinction of a species). Not surprisingly, risk perceptions appear to change slowly over time persisting in the face of contrary evidence, because closely held beliefs may be used to screen new, potentially conflicting information. Once formed, initial impressions tend to structure the way that subsequent evidence is interpreted. The complexity introduced by risk perception was simplified by focusing the scope of perception and obtaining estimates of risk from the consensus of a group of experts knowledgeable about the area and landslide processes. The experts where asked to  16  estimate the probability of loss in proximity to the road, on the hillslope, in the headwater channel and in the main channel given that a landslide in a specified road section. The continuum of possible loss in each area was characterized as low, medium, and high.  Economic Concepts and Road Deactivation In general, efficient allocation of resources in the budgeting process rests upon the economic concept of scarcity and multiple competing needs for scarce resources. Investments in natural resources, like other capital investments, make sense if the future expected benefits outweigh the costs of the investment. Over time, economic benefits of natural resources from watersheds appear in two forms. One is a flow of income from resource management activities (e.g., timber harvesting, fishing) and the other is the stock value of the watershed as an asset (i.e., the discounted future income stream). The cost of road deactivation can be viewed as a re-investment in the watershed to enhance stock value. The stock value may change along with changes in the prices of the natural resources (capital gains). Additionally, stock value may change along with changes in the physical quantities and qualities of the resources (i.e., either because of reductions caused by harvesting or additions as the result of deactivation activities) and through natural growth or decline. To maximize present value of the watershed, the two benefit streams should be considered simultaneously (Clarke and Munro, 1975). The importance of this approach to natural resource management, termed the capital theoretic model, is well established (Munro, 1992). In the economic literature the 'capital theoretic' model refers to dynamic as opposed to static analysis and uses optimal control theory to apply modern capital theory (i.e., growth theory) to investment analysis. Applications to forestry are problematic since the value of individual trees changes with time. Furthermore, at the forest scale the stand is not uniform in age or volume. Yet another difficulty to be overcome if we are to apply this approach to road deactivation is that the large number of variables in the watershed increases the complexity of the mathematics and may inadvertently cloud the transparency of the economic analysis. Practical considerations of applying the capital theoretic approach to road deactivation are beyond the scope of this study. The topic is raised to draw attention to the income (flow)  17  and asset (stock) concepts and the considerable influence on future generations of decisions made today. An example is a watershed where the roads are not deactivated or maintained and road-related landslides occur that significantly impact the watershed resources. As a result, the resources may not be available for use for an extended period of time. Also there is a chance that the watershed may not return to the pre-disturbance condition for several decades. A further economic consideration raised by road deactivation is that some resource management goals can be measured in dollar terms while others cannot, making it difficult to measure net economic benefit (net economic benefit is the difference between expected economic benefit from road deactivation and the cost to deactivate the road). Values that cannot be measured in dollar terms (non-monetary values) include the broad range of non-market social benefits or costs (i.e., opportunity cost, option value, existence value, and bequest value). A great deal of research has been directed toward improving methods for measuring non-monetary values, but none of the methods have been widely accepted (Ferguson, 1996; Greeley-Polhemus Group, 1991; Roessler and McDaniels, 1994). The difficulty with measuring net benefits stems from the theoretical foundation of investment theory and its extension to ecological management. It is an area of fundamental disagreement among economists. Two key assumptions of investment theory are: 1)  Resources can be substituted one for another.  2)  Public undertakings are generally similar to private investments that typically reach maturity in one generation or less and generate ordinary income.  The first major assumption of investment theory treats all resources as homogeneous by allowing one resource to be substituted for another (e.g., timber for scenic values). This assumption reduces the issues involved to those concerning the cost of the resource or the price paid. If the concept of scarcity is allowed, resources have multi-attribute properties (e.g., quantity, quality) (Randall, 1987). Scarcity suggests that there are different types of resources (e.g., water quality thresholds, red listed species) and substitution among resource types in terms of their value is not possible, at least not in time frames of any consequence to human society.  18  The implication of the second assumption, that public undertakings reach maturity in one human generation, is that the expected benefit from all investments can be expressed in dollar terms and that a dollar today is worth more than a dollar in the future (following Fisher's notion of present values) (Zerbe and Dively,1994). The inference for ecological investments such as road deactivation is that events that occur in several generations will have only a slight influence on present values. The concept of present value was first popularised in the 1950's where the application was rapidly extended to operational project management decision making. Central to this concept is the notion that market forces determine the appropriate discount rate, and the investment together with the expected cash flows are discounted over the project life (i.e., calculating the present value of a piece of manufacturing equipment with a productive life of 20 years). The higher the discount rate, the lower the value given to future costs and benefits. For a 30-year time frame the present value of costs and benefits can be changed by a factor of five depending upon the discount rate chosen (Row et al.1981). Ecological economists would argue that after one human lifetime, intergenerational issues enter into the decision context (Norton, 1995). For example, from the point of view of intergenerational equity it can be argued that discounting is unethical and that the appropriate social rate of discount should be either zero or very low. In such cases the applicable discount rate reflects society's time preference of money rather than a market-determined rate (Islam and Gigas, 1997). Simply put, the social rate of discount is a reflection of society's time preference of money or the rate of interest (usually lower than the market rate of interest) that is set by the government to reflect the rate of return society expects from a particular investment. Where it is determined that a market-based discount rate will be used as part of net present value calculations, there is general agreement that public sector investments differ from private sector investments resulting in a need for a social rate of discount to be applied to public sector investments to reflect society's time preference of money. No consensus has been reached, however, on how to measure society's time preference of money (Heaps, 1989; Row et al.1981). Several measurement options are available including: •  The percent rate of return that the resources would have otherwise provided in the private sector. It is argued that this rate reflects the opportunity cost of capital or the  19  value foregone by the private sector in having the capital shifted to the public sector. In economics, "opportunity cost" is a fundamental concept (Zerbe and Dively, 1994). Opportunity cost for road deactivation is the return that could have been produced if the money and resources had not been invested in road deactivation. In practice, opportunity cost is measured by the value of inputs used in producing the final product, such as the deactivated road. This implies that for a public project to be beneficial, the expected net rate of return would meet or exceed the opportunity cost of capital. •  Row et al. (1981) and Heaps (1989) argue that the private sector opportunity cost of capital overstates the social discount rate. Consequently, when calculating the social discount rate, the private opportunity cost of capital should be adjusted for factors such as corporate taxes. Further, the discount rate should not reflect the average measures of opportunity cost on all private investments but be more carefully calculated to reflect the opportunity cost of capital for investments at the margin (i.e., the most recent projects).  •  Rather than using the financial market to determine the appropriate social discount rate, Islam and Gigas (1997) argue that the appropriate rate should reflect ecological considerations. That is, issues of sustainability, including intergenerational equity, environmental risks, and irreversibility of the environmental impacts of an investment, must be incorporated into the calculation of the social discount rate.  In the extreme case the theoretical gap between ecological economics and investment theory driven by market forces is quite wide. Economic issues associated with this gap far exceed the scope of this study. One such issue is the appropriate duration to analyze the benefits received from road deactivation. In practice it appears that by undertaking road deactivation the British Columbia populace has demonstrated a recognition of some aspects of the ecological economics. Public acceptance of some of the arguments of ecological economics highlights the need to develop tools to better integrate economics and the environment to allow rationale decision making with respect to environmental investments such as road deactivation.  20  The application of economic theory to road deactivation presumed that the conditions assumed for the initial year remain constant over the fifty planning period. The analysis uses a static model not allowing the uniqueness of resource values or estimates of expected loss by the expert group to change with time. While experience with restoration projects suggests that the direction of recovery depends on the level of disturbance (Havas, 1995), the static model assumes that after a landslide the impacted area returns to a pre-disturbance equilibrium.  21  Chapter 3 Characterizing Road Deactivation Benefits and Costs Whether or not to deactivate a road and the extent to which the road should be deactivated is based upon a consideration of watershed values gained or lost by society (Cairns, 1995). Defining the values and the continuum of loss that society attaches to the values is not easy, because the values are a compendium of interests based upon closely held beliefs of individuals. An indication of society's values and the associated losses are reflected by the factors considered in road deactivation programs in British Columbia and neighbouring jurisdictions. The continuum of loss associated with a road related landslide can be viewed as consisting of three classes (high medium and low) each characterized by scenarios describing possible loss. The dollar loss estimates associated with each scenario reflect an index of loss and are not intended as precise measures of loss. The loss indexes present a reasonable upper bound on the potential amount of loss. Characterizing the amount of loss allows us to weigh against each other the expected values of the watershed if it is left in the existing condition and the expected values of the watershed if the roads are deactivated.  Road Deactivation Objectives in British Columbia and Neighbouring Jurisdictions As noted in Chapter 2, describing watershed values gained or lost is complicated by risk perception. Consider the possible difference in public and private landowners' perceptions of risk in the United States. In very general terms, on US National Forest lands a uniform standard of protection is applied across the landscape. On public lands the burden of proof lies with the resource users, such as harvesting companies, to prove that deviation from the uniform standard of protection will not adversely impact the desired environmental goals. In contrast, on private lands (setting aside legislation such as the Endangered Species Act) the landowner chooses the level of protection that complies with or exceeds a set of minimum protection standards. On private land, the burden of proof rests with the public to prove that a higher level of protection is required to achieve desired environmental goals.  22  A comparison of management strategies on public versus private land suggests that on public land society perceives that deviating from the uniform standard will not yield sufficient benefit to offset the potential loss. That is, the perception of risk is higher than expected gain, risk in this use is a function of probability and all possible outcomes. Furthermore, the way in which the loss (gain) is perceived may result in very different measures of risk because risk perception is based on individual preferences and closely held beliefs (Slovic, 1987). While the large issue of risk perception is not directly addressed in this study, the concept weaves into the discussion. Risk perception, by touching the key components of the analysis, such as the probability estimation process and definitions of resource loss, influences the context within which road restoration is viewed and valued (Botkin, 1990). The United States Army Corps of Engineers (Harrington and Feather, 1996) define the context within which restoration is viewed and valued by establishing the "significance" of the deactivation project, that is, verifying the ecological, economic, and social contexts within which restoration is verified. Verification provides a systematic accounting method to establish the values deemed to be important that are used to determine the costeffectiveness of the project. Some US Forest Service Regions are currently evolving a strategy for road deactivation/re-engineering and stream restoration that establishes the significance of the restoration on a whole forest basis versus a site-by-site or a project-byproject basis. Planning processes used to identify values and the associated losses presumably underlie road deactivation currently underway out in British Columbia, non-US Forest Service lands in Oregon and Washington, and Regions 5 and 6 of the US Forest Service. An indication of the values and the associated losses is reflected in the factors considered by road deactivation programs. Some of the factors considered (i.e., access) are common across all regions while others, (i.e., revegetation) are regionally specific (Table 3-1). The factors listed for the non-US Forest Service lands in Washington and Oregon are derived road inventory criteria. The factors listed for British Columbia are those used to determine work sequence priorities (Moore, 1994). The considerations listed for the US Forest Service (USFS) are the high level goals for road deactivation (Moll, 1996).  23  T a b l e 3-1 S o m e R o a d Deactivation Considerations N o n - U S Forest Service Lands in W a s h i n g t o n Roads associated with unstable slopes Fish passage (barriers) Water quality standards violations Geology/soils Hydrology of area Climate (flow potential) Proximity of road to other resources, (e.g.,valley road) Locations of roads in the watershed Number of stream crossings Washouts of stream crossings/fish passage N o n - U S Forest Service Lands in O r e g o n Landslides in sidecast material entering streams Turbid drainage water entering streams Stream crossing structures Sidecast (where risk of failure is high) Potential for sediment delivery to a stream Surface drainage General road description Condition of each stream crossing structure Symptoms of erosion along the road Risk of landslides entering the stream British C o l u m b i a Risk to human life Downstream impacts to property Road user safety Delivery of sediment to fish bearing and community drinking water streams Loss of forest site productivity High quality visual resources Access to control natural resources Protection of road infrastructure R e g i o n s 5 a n d 6 of t h e US Forest Service State Access Drainage Erosion Stability Revegetation  24  The California Department of Forestry performance standards for forest roads attempt to prevent or minimize sediment "input" into the drainage system, as do forest road regulations in other jurisdictions. In California, watershed restoration activities on the hillslope focus primarily on prevention (i.e., reducing the potential of high risk sites to input sediment into the drainage system). For the most part the prevention focus ignores sites that are currently delivering or have a past history of delivering sediment to the drainage system. A general planning approach for organizing the broad range of considerations in road deactivation programs is presented by the National Research Council (NRC) (National Research Council, 1992). The success of the NRC approach depends on identifying key ecological processes within a particular ecosystem and understanding those processes in relation to the objectives of the project (Yozzo et al. 1996). This approach was used to organize the range of considerations presented in Table 3-1. In general, in all regions road deactivation considerations include controlling surface erosion, minimizing mass wasting hazards, and restoring slope hydrology by treating high risk road drainage sites (uncoupling the road and stream drainage systems and returning water intercepted by the road network to the subsurface as quickly as possible). Each consideration is linked to the an underlying interaction of watershed structure and function. For example, the advantages of returning the surface water to shallow groundwater is that, relative to water flowing on the surface, subsurface water is delivered to the stream channel at lower rates. This may reduce winter peak flows and maintain base flow in the summer months. Erosion from road surfaces should also be reduced. Applying the National Research Council general planning approach to the information contained in Table 3-1, the desired ecological states in the watershed include: • • •  Fish passage and reduced sediment inputs; Reduced landslide potential in general, and in particular, from abandoned roads Protection of the capital investment in the road network.  Each of the desired ecological states can be associated with attributes that are adversely impacted by road-related slope failures and erosion include: • •  Access Vegetation  25  • • •  Natural drainage patterns Aquatic values Other resource values  For each of these attributes it is possible to consider the expected loss associated with no road deactivation and the expected loss after completing road deactivation, with the difference being expected benefit of road deactivation. The attributes are represented in Table 3-2 as loss categories together with factors used to characterize cost. For each of these attributes it is possible to consider the expected loss associated with no road deactivation and the expected loss after completing road deactivation, with the difference being the expected benefit of road deactivation. The attributes are represented in Table 3-2 as loss categories together with factors used to characterize cost.  Table 3-2 Watershed Loss Categories and Factors Used to Characterize Loss Loss  Category  Access  Measures Cost to repair or rebuild  Aquatic values Habitat  Cost to remove in-stream sediment and debris Cost to rebuild habitat  Water Quality  Cost to treat the water to meet potable water standards  Fish Loss  Commercial market value Cost of lost future productivity  Vegetation Loss  Cost to restock Commercial value of timber Scheduling costs  Other Resources  Dependent on resource  Identifying Impact Areas To develop a conceptual model of estimated loss from a road-related landslide, the watershed was segmented into four geographic/geomorphic areas: 1) the area in proximity to the road, 2) the hillslope area downslope of the road, 3) headwater channels,  26  and 4) main channels. These areas are referred to as impact areas and are defined in Table 3-3. The loss in each area is assumed to be additive. The additive assumption is an abstraction of natural conditions in the watershed and may underestimate the total impact of a landslide. In nature the impact categories are linked and the impacts in one area may compound the impact in another area. For example, impact in 'proximity to the road' may contribute to the size of the impact in the 'hillslope area'. From an analytical perspective the naturally occurring linkages between areas is problematic because the relationship between areas is not sufficiently well defined. Table 3-3 Definition of Landslide Impact Areas and Severity Classes Landslide Impact Areas Impact Area  Levels of Landslide Severity Applied in each Impact Area  Definition  Severity Class i)  A) Proximity to Road  Starting at 20 m down slope from the road and extending to the stream or headwater channel.  B) Hillslope  C) Headwater  The road or road prism to a distance of 20 m down slope  Channel  D) Main Channel  The length of first and second order channels.  The third order and higher stream channel and substrate.  No loss to low loss  ii) Low to moderately high loss iii) Moderately high to very high loss i)  No loss to low loss  ii)  Low to moderately high loss  iii) Moderately high to very high loss i)  No loss to low loss  ii)  Low to moderately high loss  iii) Moderately high to very high loss i)  No loss to low loss  ii)  Low to moderately high loss  iii) Moderately high to very high loss  The severity of loss in each area can be represented as a continuous array (i.e., from no loss to high loss). For analytical purposes this array has been segmented into three broad groups of loss referred to as severity classes (1= no loss to low loss; 2= low to moderately high loss; and 3= moderately high to very high loss), and scenarios characterizing loss for each severity class. The scenarios reflect general rather than specific conditions allowing the application of the same set of scenarios to the entire study area. The focus of the scenarios was the damage of road-related landslides on the hillslope and watershed described in terms of the watershed attributes and measures (Table 3-2). As an example, the effect of a landslide in the 'headwater and main channel impact areas' are described in terms of sediment movement and resulting loss of vegetation. Similarly, the effect of a  27  landslide in the 'hillslope' is described in terms of vegetation loss, sediment entering the channel and the aquatic impact. The scenarios exclude loss of access as a significant attribute because the access management plan for the study area determined that there was no future access requirement. This consideration aside, access values influence the scope of road deactivation and reduce expected net benefit from other, less extensive forms of road deactivation as compared to full deactivation. The scenarios used to describe potential impact were developed based upon the natural characteristics of the study area such as the geographic/geomorphic conditions. The study area sub-drainages, located along the southwest coast of British Columbia within the Southern Pacific Range of the Coast Mountains, are part of the Sunshine Coast Timber Supply Area. The inland topography of the Sunshine Coast is generally mountainous and characterized by high rainfall. Precipitation is concentrated in the winter. A high proportion of the winter rain and snow melt runs off (Church, 1998). Much of this runoff, particularly in headwaters, is generated via infiltration into highly permeable forest soils and subsequent subsurface flow (Sidle et al. 2000). Slope stability is influenced by subsurface drainage and perturbations therein. (Sidle, 1984; Montgomery et al. 1997; Tsubeyama et al. 2000). Contingent on other events, extreme precipitation (single large or multiple small rainstorms) can saturate the soil and contribute to landslides on open hillslopes and/or through debris flows in headwater channels (Sidle and Swanston, 1982; Schwab, 1998).  The study area is primarily within the Coastal Western Hemlock, Mountain Hemlock, and Alpine Tundra biogeoclimatic zones (Nuszdorfer and Boettgerl994). Higher elevation forest species are western hemlock mertsiana),  amabilis fir  western redcedar {Pseudotsuga),  {Tsuga heterophylla),  {Abies amabilis),  {Thujaplicata).  yellow cedar  mountain hemlock  {Chamaecyparis  {Tsuga  nootkatensis),  and  Lower elevation stands are mixed Douglas-fir  western hemlock {Tsuga  heterophylla),  and western red cedar. The area  is primarily rated as a medium growing site with some low and poor growing sites where high water tables or rock are limiting factors. In the upper elevation areas the highest timber values are on well-drained sidehill areas where there is minimal interference with natural drainage. Much of the study area timber supply was harvested in the 1970's.  28  Scenarios of Impact Characterized Scenarios of possible landslide damages were characterized for each severity of landslide in each impact area. The characterizations were used to establish relative indexes of resource loss associated with low, medium and high severity of landslide impact in each impact area. The indexes of loss provide a conservative upper bound on the possible loss rather than a precise measure of the amount of loss. (Sensitivity analysis was conducted to test the sensitivity of the cost effectiveness results to change in the amount of expected loss. It was found that the results of the cost effectiveness analysis did not change. To systematically construct the loss indexes an accounting approach was used to develop the relative magnitudes of loss. The results shown in the summary section (see later Table 37, reflect that timber resource loss was of significant concern in the proximity to the road and hillslope impact areas. The loss index for the proximity to the road and hillslope impact areas was relatively lower that the indexes characterized for the headwater and main channel impact areas. The loss index for headwater and main channel impact areas were based upon the characterizations of physical structure loss, fish loss and water quality loss. The characterizations of physical structure loss, fish loss and water quality loss produced the largest magnitudes of loss. Proximity to the Road Impact Characterization Loss is characterized as the loss of timber resource and the cost to revegetate the impacted area. Landslides of low (less than 30 m in volume) and moderate severity 3  (between 30 and 100 m in volume) were considered to have no cost (i.e., no timber 3  resource loss). Along 100 m of road length a landslide of high severity or the equivalent smaller multiple landslides varying in width from one to three meters (Johnson et al. 2000) were assumed to travel 20 m downslope and impact an area of 160 m (8m by 20m) with 2  consequent damage to timber resources. In terms of volume, a landslide of high severity was characterized as greater than 100 m . 3  Hillslope Impact Characterization Loss is characterized as the loss of the timber resource and the cost to revegetate the impacted area. A landslide of low severity (or the equivalent smaller multiple landslides varying in width from one to three meters) was assumed to travel 21 m downslope from  29  the edge of the road and impact an area of 210 m (10 m by 21 m). A landslide of 2  moderate severity (or the equivalent smaller multiple landslides) was assumed to travel downslope 34 m and impact an area of 340 m (10 m by 34 m). A landslide of high 2  severity (or the equivalent smaller multiple landslides) was assumed to travel 50 m downslope and impact an area of 500 m (10 m by 50 m). 2  Headwater Impact Characterization Loss is characterized as loss of channel structure in first- and second-order streams and increased sediment into the stream. A landslide of low severity was characterized by a landslide(s) coming to rest at the mouth of the headwater channel causing minimal impact. On the other hand, a landslide of moderate severity (or the equivalent smaller multiple landslides) would enter the headwater channel and continue halfway down the channel as a debris flow. Sediment deposited by the landslide debris flow is assumed to contribute to increased levels of suspended sediment ranging from 25-200 m for the 3  remainder of the storm season (i.e., November through February). A landslide of high severity (or the equivalent smaller multiple landslides) passing through the headwater channel as a debris flow impacting the full length of the headwater channel. Sediment deposited by the landslide debris flow in the main channel is assumed to contribute to increased levels of suspended sediment ranging from 100-400 m for eight months. 3  During large rainstorms, the structure within headwater stream channels, such as large woody debris and large boulders, disperses the energy of the water flowing to the main channel. In addition, Hogan et al. (1998) argue that headwater streams contribute to the formation of a critical link between terrestrial and aquatic ecosystems. Ideally, a measure of the loss associated with a road-related landslide/ debris flow that impacts headwater channels is the cost to restore the headwater to resemble the pre-landslide state. Loss of structure in headwater channels, however, is not normally considered when calculating loss attributed to a road-related landslide or when planning restoration (pers. com. J. Richardson, 1999, UBC). Restoration cost estimates for headwater channels are not readily available, and restoration techniques have not been refined, so cost estimates may overestimate actual cost. As an alternative loss was estimated as the approximate value of timber remaining  30  in a riparian buffer strip if the buffer strip was not harvested to protect the stream (as is now required by Forest Practices Code of British Columbia). In the study area, the average length of the headwater channel is 335 m (measured from the point the landslide could potentially enter the headwater channel to the main channel) for a random sample of road segments. The Forest Practices Code recommends buffer strips of up to three meters in width for streams classified S5 and S6 with no fish presence and that fall outside the reserve zone where no forest activity may take place. Where landslides of moderate and high severity impact the headwater, loss was characterized as equivalent to the loss of timber resources for areas of 500 and 1005 m , respectively (1005 m is the average 2  2  length of the headwater, 335 m times the buffer width, 3 m). Main Channel Impact Characterization Loss is characterized as localized damage, fish loss, and increased sediment into the stream in third-order and larger streams. A landslide debris flow of low severity (or the equivalent smaller multiple landslides) was considered to cause minimal impact. A landslide of moderate severity (or the equivalent smaller multiple landslides) was assumed to deliver 400 m of sediment and debris to the main channel, destabilize 25 m of stream 3  bank, and impacting 4 km of stream length on a diminishing basis with time. Sediment deposited was assumed to increase levels of suspended sediment for 8 months. A landslide of high severity (or the equivalent smaller multiple landslides) was assumed to deliver 800 m of sediment and debris to the main channel, destabilize 50 m of stream 3  bank, and impacting 8 km of stream length on a diminishing basis with time. Sediment deposited was assumed to increase levels of suspended sediment for 16 months. The characteristics of a stream, such as the distribution of substrate, are contingent upon various hydraulic, hydrologic, biological, geomorphic, and geologic processes. The particular combination of conditions that provide for clean, loose, suitably-sized spawning gravel can be disturbed by activities related to logging and road construction (Slaney and Zaldokas, 1997). A broad range of loss estimates is possible when a landslide (or the equivalent smaller multiple landslides) enters the main channel because loss is a function of several linked factors including landslide severity, large woody debris, tributary junction characteristics, location of impacts, stream discharge rate, and channel gradient. A roadrelated landslide entering a stream channel may increase the level of suspended and  31  bedload sediment carried by the stream as well as the volume of boulders and woody debris in the stream. Depending upon the timing of fine sediment inputs in relation to fish life cycles, spawning productivity may decline or fine sediment may bury eggs in the spawning gravel. Alternatively, the sediment may act to displace the habitats of aquatic invertebrates, the primary source of food for salmonoids (Richardson and Hinch, 1998). Deposits of sediment and debris may cause the stream channel to undergo morphological change including altering the streambed, banks, and large woody debris supply (Slaney and Zaldokas, 1997).  Elements of Loss included in the Characterizations of Impact Index of Expected Loss due to Localized Channel and Stream Impacts The cost of localized channel and stream impacts of a landslide are approximated from the cost to remove sediment, rock, and woody debris as well as the cost of stream bank stabilization. The cost of in-stream landslide debris removal is influenced by road access, the distance from the impacted site to the disposal site, and the cost of mobilizing the necessary equipment. The characterization of the cost of localized channel and stream impacts of a landslide assumes that 400m is the equivalent of 50 truckloads requiring 20 3  hours of equipment time at $340 per hour (one excavator at $130 per hour and three dump trucks at $70 per hour per truck). It is also assumed that road access is available and debris is hauled to a disposal site one kilometre away (pers.com D. Murray July 27, 1999 Kerr Wood Leidal). Bank stabilization techniques may be classified as one of three structural types: 1) rock methods, 2) vegetative methods, and 3) integrative methods. Associated with each technique is a range of cost estimates that depend upon the project size, location, and follow-up maintenance requirements. In this study the cost of bank stabilization is based on using rock methods (i.e., lining the streambank) and it is assumed that the rock is available locally and delivered to the impacted area at a cost of $35 per m . 3  Index of Expected Fish Loss Some of the roads in the study area are located in a watershed that drains into Chichwat Creek. Chickwat Creek flows into the Tazoonie River and shortly thereafter the Tazoonie  32  empties into Narrows Inlet. Department of Fisheries and Oceans (DFO) escapement records reflect a total escapement of 28,000 salmon at the mouth of the Tazoonie River (pers. com. K. Hyta, July 1999, DFO). The characterization of the expected fish loss focused on the Chickwat Creek portion of the study where the annual market value of salmon (if they were all caught) would be $560,000 providing the average weight per salmon is 5 kilograms with a market value $4.00 per kilogram (Scarfe, 1996). In the Chickwat Creek sub-drainage the road deactivation area is close to the mouth of the Tazoonie River. Road-related landslides have the potential to impact both resident and returning fish migration for some distance upstream. Several factors including the timing of the landslide related to the life cycle of the fish would influence the magnitude of loss of fish and the impact on future spawning. Several site-specific conditions influence the density offish in reaches of the stream (pers. com. Richardson, 1999, UBC), which greatly complicate the assessment of landslide impact on resident fish at varying stages of life. In addition, factors typically beyond the control of road deactivation practices, such as ocean survival and harvesting of fishing confound the assessment of landslide impact on expected future spawning. Estimation of the expected loss offish draws attention to considerations of scale (both in time and space) in valuing loss from road-related landslides. The equivalent of the estimated current resident fish loss was included in the total expected loss as an approximation of loss caused by diminished future productivity in the impacted reach.  To bound the range of fish loss estimates it was assumed that there were 1500 smolts per kilometer and that 10% of the fish return to spawn (pers. com. M. Bradford, July 1999, Department of Fisheries and Oceans). An equal number of spawners caught by commercial fishers would have an average value of $6000 per kilometer. A landslide/debris flow of high severity delivering 800 m of sediment to the main channel 3  would severely impact the entire stream reach from the study site to the ocean (approximately 8 km) resulting in an expected loss of $48,000. To recognize that the in subsequent years the landslide may impact returning fish populations, the loss was doubled. Total expected loss is $96,000. Similarly, a landslide of moderate severity that delivers 400 m to the main channel severely impacts four km of stream length with an 3  expected loss of $24,000. To recognize the possible impact of the landslide in subsequent years the impact of the landslide was doubled. Total expected loss is $48,000. Physical  33  restoration cost and fish loss by impact area and severity of landslide is summarized in Table 3-4. Table 3-4 Index of Expected Localized Physical Impact and Fish Loss Main Channel I m p a c t Area Localized I m p a c t  Loss (Cost)  Low Impact Total Loss (low)  $  0  Moderate Impact Debris Removal  400m of debris =  $ 6,800  Bank stabilization  25 m in length =  $22,500  3  Total Loss (moderate)  $29,300  High Impact Debris Removal  800m of debris  Bank stabilization  50 m in length $45,000  $13,600  3  Total Loss (high)  $58,600  Fish Loss  Loss (Cost)  Low Impact Total Loss (low)  $  0  Moderate Impact Immediate impact  4 x $6000/ km =  Future Harvest  $24,000 $24,000  Total Loss (moderate)  $48,000  High Impact Immediate impact  8 x $6000/ km =  $48,000  Future Harvest  $48,000  Total Loss (high)  $96,000  Index of Expected Water Quality Loss Water quality loss was characterizated in terms of the volume of sediment entering the natural drainage system and the cost to treat the water related to increases in suspended sediment. Factors, such as the transport capacity of the natural system at the time of the landslide and the rate of stream flow, influence the magnitude of the cost. Treating the water for increased sediment loads caused by a landslide is generally not contemplated in  34  road deactivation planning nor is it practical. As an alternative estimate, the range of water quality loss was estimated as the replacement cost of drinking water incurred by a small community (i.e., the cost of switching drinking water sources from a stream with very high suspended sediment levels to a source with less sediment (pers com. K. Rood, Aug. 1999, Northwest Hydraulic Consultants Ltd.). The capital cost of the alternative water supply was amortised over 20 years at 3% interest, one option being to drill ground water wells. For ground water supplies, a monthly capital cost is assumed to be $155; the monthly operating cost is $445; and the total monthly operating cost is $600. The second option is to pump water from an alternative stream source. The monthly capital cost is assumed to be $940; the monthly operating cost is $460; and the total monthly cost is $1,400. Water quality loss related to landslides/debris flows of moderate severity is estimated as $600 per month and for landslides/debris flows of high severity as $1,400 per month. Water quality losses are shown in Table 3-5. Table 3-5 Index of Expected Water Quality Loss H e a d w a t e r I m p a c t Area  Main Channel I m p a c t Area  Low Impact Volume  10-30m  30-60m  3  Total Loss (low)  $  3  0  $  0  Moderate Impact Volume  25-200m 4 months  100-800m 8 months  3  Total Loss (moderate)  3  $2,400  $ 4,800  High Impact Volume  100-400m 8 months  Total Loss (high)  >800m 16 months  3  3  $4,800  $22,400  Index of Expected Timber Loss Timber loss is characterized in terms of the value of the existing timber cover that could be displaced by a landslide. Over a 47-year period Reid (1998) found that landslide scars usually revegetate after about seven years and 90% were revegetated in nine years (the range of duration being 3 to 13.5 years). In about nine percent of the samples, the landslide reduced the site's ability to grow trees for an extended period of time (16 of 171  35  landslides remained unvegetated for over 40 years, possibly because of repeated occurrence of landslides or extensive surface erosion on the landslide scar at the same site) (Reid, 1998). As a result, road-related landslides have the potential to displace the existing timber cover and reduce or eliminate productivity on the landslide path. The loss may also extend to the forest scale and have social cost (i.e., loss of scenic value) or influence the annual allowable cut. The expected market value, used to characterize timber loss associated with a road-related landslide, depends upon a combination of natural and biological influences such as the interaction of particular tree species with site characteristics, that affect the volume of timber produced on the site. The expected dollar value of the timber volume is determined by future market conditions. For the study area, the expected dollar value was estimated using the Ministry of Forest TIPSY computer model (Table Interpolation Program for retrieving Stand Yield information) (Mitchell et al.1998). The model integrates a biological model of timber growth and yield with a model of future forest market conditions. The TIPSY model requires the following information: • • • •  species information (species, species composition, and site index) stand specification (stand regeneration type and delay, initial density, and silviculture treatment) discount rate operational adjustment factors (OAFs): OAF1 is applied to reduce yields because of unproductive areas such as swamps and rock outcrops; OAF2 is applied to reflect natural losses incurred by biotic forces, including disease, as the stand matures.  Information on tree species and site characteristics are used by the model to choose one of 440 yield tables in its database or to interpolate between the closest yield tables. The British Columbia Ministry of Forests Tree and Stand Simulator model (TASS) produced the growth and yield tables for managed stands used in TIPSY. TASS is an individual tree, distance-dependent model that simulates the growth of trees in three dimensions (Mitchell et al.1998). Forest cover maps were used to identify a representative species mix and site index for the study area. Based upon the larger forest cover polygons, a species mix of 40% coastal  36  western hemlock, 40% coastal Douglas-fir, and 20% western redcedar with a site index of 23 was selected as representative of the study area. The operational adjustment factors were set to zero. As a result the timber growth for the area may be overestimated. The estimates however will provide an indication of the upper bound of the growth potential per hectare for the estimated site index. Assuming that the future market prices are the Table 3-6 Index of Expected Timber Resource Loss Proximity to Road Impact Area  Hillslope Impact Area  Headwater Impact Area  Low Impact Site Level Loss  T215m x 7= $1505 R215m x .05=$ 11 Total $1516 2  2  Other Loss  $1516  Total Loss (low)  $  0  $3032  $  0  Moderate Impact Site Level Loss  R 160m x .05=$ 8  T340m x7= $2380 R340m x .05= $ 17 Total $2397  2  2  2  Other Loss  T (6x 335)3.5= $ 7,035  $2397  Total Loss (moderate)  $  8  $4794  $ 7,035  High Impact Site Level Loss  T 160m x 7= $1120 R 160m x.05=$ 8 Total $1128  T 5 0 0 m x 7 = $3500 R 500m x.05=$ 25 Total $3525  Other Loss  $1128  $3525  Total Loss (high)  $2256  2  2  2  2  T (6 X 335)7= $14,070  $7050  $14,070  T= Timber value, R= Revegetation cost using a planting cost of $501 per hectare  same as the current market prices (TIPSY model default), for a physical rotation age of 100 years, gross harvest revenues is approximately $70,000 per hectare or $7 m were 2  obtained Thus, timber loss at the site level associated with road related landslides is characterized as $7 m of impacted area. The $7 m is the maximum possible loss and 2  2  intended to conservatively bound the upper limit of the timber loss associated with a roadrelated landslide at the site level. Other dimensions of timber resource loss, such as loss at the forest scale were approximated by doubling the loss at the site level. Total timber  37  loss is considered to be $14 m . Table 3-6 summarizes estimated timber loss by impact 2  area and landslide severity. Table 3-7 Summary of Indexes of Expected Loss by Impact Area Proximity to Road Impact Area  Hillslope Impact Area  Headwater Impact Area  Main Channel Impact Area  Low Impact  Timber Fish Physical Water Total Loss (low)  $3,032  $  0  $3032  $  0  $  0  Moderate Impact  Timber Fish  $  8  $4,794  Physical Water Total Loss (moderate)  $  8  $4794  $2,256  $7,050  $7,035 $2,400  $48,000 $29,300 $ 4,800  $9,435  $82,100  $14,070  $ 96,000 $ 58,600  $ 4,800  $ 22,400  $18,870  $177,000  High Impact  Timber Fish Physical Water Total Loss (high)  $2256  $7050  Road Deactivation Costs Approximately 17 km of forest road located in two watersheds about four km apart were included in this study (Figure 1-2, page 5). In British Columbia a physical assessment of the roads is required prior to road deactivation. During the field assessment for the study area a survey crew divided the roads into about 1700 segments that were distinguished by well-defined geographic/geomorphic boundaries, specific road networks, or other logical means (Moore, 1994). For each road segment the data collected included: • the length of the road segment (the chained distance)  38  • • • •  recommended deactivation actions rating of how complicated undertaking the work would be work priority rating the volume of material resting on the hillslope supporting part of the road running surface (volume of sidecast), and • indicators of active or potential road-related problems. Because the length of the road segments were not uniform, the road segments were grouped into approximately 171 road segments of about 100 m in length. Based upon the information gained during the field assessment, deactivation actions that reflect the cost of the access management planning objectives, risk assessment, and the need to comply with the British Columbia Ministry of Forest regulations (see Chapter 2) are specfied together with the degree of difficulty of undertaking these tasks. The deactivation actions such as water bar installation are specified for each segment. A water bar refers to a shallow ditch crossing the road at an angle to the ditchline to capture and divert road surface water and intercepted substrate drainage off the road and into the ditchline or across the road (Moore, 1994). Cost estimates for deactivation actions were supplied by the forest company undertaking road deactivation in the region. Other costs, such as project management or professional fees were ignored because the costs are not proportional to the number of road lengths deactivated. The cost data supplied by the forestry company identified by action type the implementation cost according to the degree of difficulty (low, moderate or high). Depending upon the type of action, the measurement units of the cost estimates were by unit, by volume per cubic meter, or by distance per meter.  39  Chapter 4 Decision Analysis and Road Deactivation. Road deactivation actions combined with the natural processes at work in the watershed can lead to several possible outcomes. The analysis of this complicated interaction can begin by using the concept that change in the natural environment could result from natural processes and from road deactivation activities. Chance can be a separate consideration impacting either the natural processes or road deactivation activities or both (Chapter 2). Viewed in this manner, the application of decision analysis to the interaction of the natural processes and road deactivation becomes more transparent. Decision analysis is an approach to systematically organize the uncertain events that may occur and the possible consequences of those events (Raiffa, 1970). Once a decision tree is established, the structure enables an expert group to focus on chance and systematically step through the sequence of events that influence their estimates of the probability that a landslide would occur and the expected loss on a sample of road segments.  Decision Analysis Beginning at a specific road segment the sequence of uncertain events, possible outcomes, and associated losses as a consequence of a road-related landslide can be represented using a decision tree. The decisions and chance events that the road deactivation designer encounters are arranged in sequential order. A decision junction (usually represented by a square) distinguishes the alternative choices available to the designer. A chance junction (usually represented as circle) branches into the alternative possibilities that could happen by chance. At each chance junction are the probability assessments for each of the possible branches. Tracing any path to its end will yield the associated loss. Using an averaging or folding back procedure, it is possible to determine the average loss associated with the choice to deactivate the road segment (Raiffa, 1970). The decision analysis structure brings into focus that the total expected loss for each road segment is derived from events occurring at the tips of the decision tree. Characterizing loss from a road-related landslide as being additive simplifies the decision tree used to organize the road deactivation decision. Because of this simplification, outcomes that  40  involve multiple areas (i.e., proximity to the road, hillslope, headwater, and main channel) may be treated as if they were isolated events. The alternative to characterizing losses as being additive is to consider all possible combinations of impacted areas defined in this study (i.e., proximity to the road, hillslope, headwater, and main channel) as unique possible events. This would result in multiple possible outcomes each requiring estimates of probability and loss. As the level of complexity increases, the task of discerning between increasingly finer measures of probability and loss becomes increasingly difficult.  Probability Estimation All road segments in the study area were not analysed because of resource limitations. A small randomly sample of roads was identified (18 road lengths in total, six road lengths from each of the three most unstable terrain classes). The sample size reflected a desire to not exceed the time constraints of the expert group used to estimate probabilities of landslide occurrence and the expected losses. The group brought together expertise from diverse areas including road deactivation, decision analysis, hillslope and landslide process, and geotechnical and engineering. Members of the group volunteered their expertise and time to the study; not all group members attended all sessions. The expert group members consisted of: • • • •  Jonathan Fannin Dan Hogan Wayne Ketty Mike Lichtensteiger  • • • •  Roy Sidle David Tait Bruce Thomson Weimin Wu  Three meetings were held with the expert groups. The first meeting refined the sampling process and the method of estimating the probabilities. Following the advice of the expert group, the 17 kilometres of forest road in the study area consisting of 171 road segments were stratified using the Coastal Terrain Stability Classification System. The rationale for the stratification was that terrain classification provides a common set of reference conditions upon which the experts could base their probability estimates. Because of this, the experts gained additional confidence in their estimates and could more easily reconcile divergent opinions. The Coastal Terrain Stability Classification System is based upon data  41  on surfacial materials, landforms, geomorphic processes, slope angle, soil texture, moisture regime, landscape position, vegetation, and bedrock types (Moore, 1994). The study area had 171 road segments made up of 95 road segments in Terrain Class III, 53 road segments in Terrain Class IV, and 23 road segments in Terrain Class V. Class III is defined as areas where minor stability problems can develop. Class IV is defined as areas having a moderate to high likelihood of slope failure following road construction. Class V is defined as areas having a high likelihood of slope failure following road construction (Moore, 1994). The available data for the Chickwat Creek area indicated that roads were primarily located in a class III or IV terrain, while data for the Misery Creek area indicated that road segments fell into Terrain Classes III, IV, and V. At the second and third meetings with the expert group we estimated probabilities for the sample of 18 road segments. The group members had varying levels of familiarity with the study area. In total the expert group estimated 306 probabilities, choosing to begin the assessment at the top of the hillslope and considering the same road segment twice, once without deactivation and once with deactivation. In this way, we determined all probability estimates for a road segment before moving along the road toward the next road segment in the sample. When first considering a road segment, the group was asked to consider several factors and to develop a consensus on the probability of a road-related landslide occurring (Figure 4-1). For this part of the work, the group used a topographic map at a scale of 1:20,000 displaying road networks, streams, and terrain stability class, along with topographic map sheets at a scale of 1:5000. The group also had information about surficial materials in a 1:50,000 map as well as information from the Level II Forest Road Assessment results, air photos (taken at 5758 m with a 304-mm focal lens), and rainfall estimates for a storm with a recurrence interval of 20 years. Additionally, the group was given the distances from the road to the headwater channel, the distances through the headwater channel to the main channel, and the distances from the road to the main channel. Critical to the estimation process was a short video of a recent landslide in the study area taken from a helicopter and photographs and information about deactivation sites provided by a member of the expert group who had on-site operational experience.  42  Probability Estimation Logic  Low  Figure 4-1 Probability Estimation Logic Chart Assuming a landslide had occurred, the expert group first focused on the proximity to the road impact area. Using the characterizations of landslide impact (high, medium and low) the probabilities of impact were estimated (Figure 4-1). Once this was accomplished, and using these probabilities as a reference, the group considered the characterizations of landslide impact (high, medium and low) for the hillslope impact area and estimated the probabilities of impact. This pattern was repeated for the headwater and main channel impact areas (Figure 4-1). The difference between the probability estimates with deactivation and without deactivation for the 17 road segments is shown in Figure 4-2. Grouped by terrain class (Table 4-1), the road segments are ranked in ascending order by probability of a landslide occurring without road deactivation. The results presented in Figure 4-2 and Table 4-1 represent an incomplete picture of after road deactivation. Not shown are the probabilities associated with the change in expected loss. These probabilities also influence the final outcome. As an example, for road segment Sample 6 there is significant reduction in the  43  probability that a landslide would occurr after road deactivation. For road segment 6 there was little change in the probabilities that the landslide would impact the proximity to the road, hillslope, headwater channel, the main channel. For all impact areas however, considerable change occurred in the probabilities assigned to severity of loss (high, medium, and low) after deactivation. In general for all road segments there was no discernible trend in the decrease in the probability of expected loss after road deactivation.  0.6 Probability 0.4 -  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  Road Sections Stratified by Terrain Class • T e r r a i n Class 3 Probability of a Landslide for Road Sections 1 to 6 Without Road Deactivation • T e r r a i n Class 4 Probability of a Landslide for Road Sections 7 to 12 Without Road Deactivation • T e r r a i n Class 5 Probability of a Landslide for Road Sections 13 to 17 Without Road Deactivation ^ T e r r a i n Class 3 Probability of a Landslide for Road Sections 1 to 6 With Road Deactivation D  T e r r a i n Class 4 Probability of a Landslide for Road Sections 7 to 12 With Road Deactivation  " T e r r a i n class 5 Probability of a Landslide for Road Sections 13 to 17 With Road Deactivation  Figure 4-2 The Expert Group's Estimates of the Probability of a Landslide Without Road Deactivation Compared to the Probability of a Landslide With Road for 17 Randomly Chosen Road Segments. Six Road Segments were Selected from each Terrain Class. Once the probability estimates for the sample road segments had been developed it was possible to calculate the expected benefit for each of the road segments (Table 4-1) using the indexes of loss and compare the expected benefit for each road segment to the cost of deactivating it.  44  Table 4-1 Probability of a Landslide for a Random Sample of Road Segments Road  Road Segment  Terrain Class  Length  North 300  Probability. Probability of Slide. of Slide. With Without Deactivation Deactivation  200-300  3  104  0.15  North 320  0-320  3  94  Misery 400-2  1269  3  Misery 430  0-430  Misery 430  Cost /100m  Benefit /100m  0  3,778  27  0.30  0.05  3,195  1,253  91  0.30  0  1,953  457  3  100  0.40  0  4,778  321  169  3  120  0.65  0.2  3,500  6,548  North 300  2413  3  101  0.8  0.25  3,039  124,060  North 310  573  4  102  0.1  0.02  1,862  35  North M/L  1700  4  130  0.1  0.02  1,615  52  North M/L  832  4  106  0..25  0.10  3,381  8,578  North 90  391  4  90  0.50  0.30  3,821  32,404  North 90  85-90  4  96  0.90  0.50  3,579  134,156  North 100  103-100  4  97  0.95  0.20  2,899  14,833  North 50  0-50  5  57  0.15  .050  2,908  1,516  Misery 400-2  214  5  105  0.80  0.20  3,530  65,015  North 41  408  5  102  0.90  0.25  4,110  96,690  Misery 400-1  2649  5  85  1.00  0.55  4,086  84,508  Misery 400-2  850  5  104  1.00  0.50  4,300  66,810  45  Chapter 5 Cost Effectiveness Analysis of Road Deactivation Cost effectiveness analysis provides a means to determine the least costly option to achieve the standard of road deactivation desired by comparing the cumulative expected net benefit of road deactivation with the cumulative deactivation cost. Plotting the ratio of expected net benefit to deactivation cost, for each road segment, ranked high to low produces a cost effectiveness frontier on a chart where cumulative cost is plotted on the x axis and cumulative expected net benefit is plotted on the y axis. The cost effectiveness frontier demonstrates the relationship between cumulative expected net benefit and cumulative cost of deactivation. If the relationship for all road segments were equal the cost effectiveness frontier would be linear. The results of the cost effectiveness analysis for the study area show that a small number of road segments generate large expected net benefit, while a larger number of road segments generate no expected net benefit, and that on average the magnitude of expected net benefit is related to Terrain Stability Class. In all but one case, the cost effectiveness results were not sensitive to change in the discount rate, the probability of a rainstorm and the amount of the expected loss from a landslide. As compared to the base case scenario, when the cost effectiveness analysis was conducted with a discount rate set to 0.05% there was noticeable change in the shape of the cost effectiveness frontier.  Cost Effectiveness Analysis After the decision to deactivate the forest roads in an area has been made, there are two possible approaches that can be used to determine the most cost efficient allocation of resources. •  Establish deactivation standards and then conduct cost effectiveness analysis to determine the least costly option for achieving this standard.  •  Consider a variety of deactivation treatments combined in different ways to achieve various levels of fulfillment of the road deactivation goals in conjunction with cost effectiveness analysis.  46  The US Army Corps of Engineers has adopted a version of the second approach. Their efforts focus on developing the least costly means of achieving several levels of rehabilitation, any one of which may be determined to be appropriate and justified (Greeley-Polhemus Group, 1991). While this approach has intuitive appeal, the first of the two approaches is the most applicable to this study given the current regulatory structure applied to road deactivation in British Columbia. Cost effectiveness analysis allows choice among road deactivation alternatives on the basis of (marginal) cost, providing the measure of outcome is consistent. In a well functioning or perfectly competitive market and a market that is at equilibrium, the correct amount of any given good (e.g., road deactivation) is produced at the lowest possible cost. In economic theory this is termed an efficient resource allocation. In the larger picture, where an efficient resource allocation exists, marginal cost is identical with the "opportunity cost" (or "economic cost") to society of using the resources to create this "good" rather than other goods. Opportunity cost refers to the fact that whenever there are competing needs for a resource, devoting the resource to one use deprives others of the opportunity of using it (Pearce, 1990). The analysis began by considering several factors for a sample of road segments including the probability of a large rainstorm, the probability of a landslide, and the estimated losses should a landslide occur. Expected loss with deactivation was calculated and subtracted from the expected loss without deactivation to calculate the expected benefit of undertaking road deactivation for the sample of road segments. Net benefit for each road segment was calculated by subtracting the cost of deactivating each road segment from the expected benefit for each road segment. Net benefit was used consistently throughout the analysis to maintain consistency with decision analysis where net benefit is the focus. Using net benefit in the cost effectiveness analysis produces net benefit-cost ratios that vary to a minimum of minus one. The mean benefit for Terrain Class III road segments in the sample was used to estimate the expected benefit for all Terrain Class III road segments in the study area. The estimated expected benefit for all Terrain Classes IV and V road segments in the study area was estimated using a linear relationship derived from the expected benefit and  47  deactivation cost of Terrain Class IV and V road segments in the sample. In the study area a comparison of the expected net benefit with the respective cost to deactivate the road segment demonstrates the cost effectiveness of the decision to deactivate the road segment. The following paragraphs discuss the steps involved in the cost effectiveness analysis, the results of the cost effectiveness analysis, and a sensitivity analysis comparing the results to changes in some key variables underlying the analysis.  Deactivation Benefits and Costs Several factors including the probability of a large rainstorm, probability of a landslide, and the estimated losses should a landslide occur influence the expected net benefits associated with the choice to deactivate the road segment (Figure 5-1). A planning time frame of fifty-years is proposed as the appropriate planning period for the cost effectiveness analysis in the study area because fifty-years approximates the length of time before the second growth timber in the study area may be harvested and the roads rebuilt. Including the concept of time into the analysis raises the problem that losses from landslides could be considered as functions of time. As an example, the dollar value of timber growth escalates towards the end of the fifty-year planning timeframe as the existing growth on the site reaches maturity. At any point during the first twenty years of the planning timeframe, the present value of the timber in the study area will not be large. Further if we assume that multiple landslides occur on the same site, the loss of timber value would be the present value of the growth of the trees during the time interval between landslides. If the time interval were very small, dollar loss would be insignificant, which may understate the loss attributed to the most recent landslide. To clarify the analysis, albeit at the cost of some precision in the calculation of loss, expected loss from a landslide was characterized as a fine, or levy, rather than as a function of time. In other words, each time a landslide occurs, a fine is levied. Regardless of the timing of the landslide (whether the day after deactivation or twenty years after deactivation) the dollar amount of the fine is the same. The dollar amount of the fine approximates the loss of resource values in each impacted area depending upon the severity of the landslide impact (Chapter 3). Because treating loss as a fine is an abstraction from reality and may overestimate the resource loss over the planning  48  timeframe, the estimates of expected loss are considered a reasonable upper bound to the expected amount of resource loss. Decision  Road Rainstorm Segment Event (W)  Landslide (S)  Impact Area (A)  Severity Loss/Cost of Impact (L)  P{Su\ A) p(s  p(A \s){4)n  n  }  Proximity to Road  4) A)  L{S )  p{s , A )  L(S )  U  p(s\w){3)a 2  |  P(A \S)(5) 2  •  2  A) 2  Hillslope  2]  L(S  22  )  A) 2  Road # 430 •  A) P(A \S)(6) • 3  Headwater  P{Sl2  A)  L(S )  p(s  4)  L{Sx)  i3  3  P(S^ A) P(4|S)(7)D  32  L{SJ  P(S 2 A) 4  M. Channel - /  A)  (8)  L(0)  (9)  L(0)  Figure 5-1 Decision Framework for Expected Loss in the Current Year The risk associated with the decision to deactivate the road can be thought of as the sum of the expected risk in the current year and the discounted value of expected risk in subsequent years. The calculation of expected loss in the current year followed the  49  decision framework used by the expert group to estimate the probability of a loss for a road segment (Figure 5-1). Loss is anticipated to occur at the beginning of the year. The respective decision junctions are discussed in the following paragraphs. In each year subsequent to the current year through to year 50, the road segment is re-exposed and subject to the risk of a landslide (junctions (1) through (9) inclusive) (Figure 5-1). Because loss is characterized as a fine, the expected (average) loss for the road segment in any given year is the current (average) expected loss plus the discounted expected (average) loss in the next year. Loss in years subsequent to the current year is treated as an infinite annuity. The following points explain the junctions (1) through (9) inclusive in Figure 5-1 Junction 1 represents a road segment today. The two branches reflect the occurrence or non-occurrence of a significant rainstorm (W) in that year that occurs with a probability P(w). Junction 2 is reached if a significant rainstorm occurs. The two branches reflect the occurrence, or non-occurrence of a road-related landslide (S), with a probability p(s\w). In other words p(s\w) represents the probability of a landslide (S) conditional on the fact that a significant (W) has occurred. Junction 3 shows the four branches that reflect the proportion of time the road-related slide impacts the road (Ai), the hillslope (A ), the headwater (A ), and the main 2  3  channel (A4). These proportions are expressed as probabilitiesP(A \S), X  P(A \S), 2  p(A \s), and P(A \S). i  4  These probabilities are not independent.  Junctions 4, 5, 6, and 7 reflect the severity levels of landslide impact in each of the impact areas. These probabilities are expressed as p(s \A ), or the probability of a j IJ  I  level of landslide damage in area /given that a landslide event has taken place in area i. These probabilities are independent. Terminal values of junctions 4, 5, 6, and 7 carry a cost/loss that is equal toL(s ) or the y  loss or penalty resulting from a landslide of severity/in area f. It is assumed that in subsequent years the road is re-exposed the same set of uncertain events and possible outcomes. That is, to a risk of future slides that will have a risk R  50  (expected loss) discounted one year that is R/(l+d) where d\s the discount rate. The expected loss from a road-related landslide today is the sum of the discounted values from year 1 through year 50.To determine the present value of the road segment at junction 1 we begin at the tips of the decision tree and average back. The expected loss associated with junctions 4, 5, 6, or 7 is given by: 1) The average loss at junction 3 is the average total loss of equation 1 (above) with the weights equal to P(A,\S)  2)  t  PiA^tHsM^)}  Tips 8 and 9 reflect situations where no landslide-related event the current year. The expected present value related to the road segment (Junction 1) is calculated as the expected or average loss that occurs in the current year (equation 3) treated as an infinite annuity (equation 4).  3)R = P(w)p{s\w)f /»U|5jt{p(sj4^)} • j  p(w)p{s\w)f  j  4)7? =  p(4|5)iH^Kfe)} ;=1  1=1  d  Equation 4 provides an expression for the risk of the decision paths to either deactivate or not to deactivate the road segment. The difference between expected loss without deactivation and the expected loss with deactivation is the expected benefit of road deactivation. Equation 4 was used to derive two data sets (the expected loss with and without road deactivation) for the random sample of 17 road segments using the following variables; a rainstorm with the probability of occurring once every twenty years (0.05 probability of occurring annually), a 4.25% discount rate, loss amounts equal to those described in Table 3-7 (page 38), and probabilities (landslide occurrence and severity of impact) equal  51  to those estimated by the expert group. The expected benefit of road deactivation (the difference between the expected loss with and without deactivation) is compared to the cost to deactivate the respective road segment in Figure 5-2. One of the road samples, Road 41, segment 192, sample number 4-5, located in Terrain Class V, was dropped from the analysis because the expert group found that no deactivation treatment had been carried out as the road bed had been naturally reclaimed by vegetation and the deactivation contractor thought that deactivation actions would destabilize the area. Because no money was spent on the sample segment, no benefit would accrue from deactivation. The range of expected benefits for the sample of road segments was much larger than the range of deactivation costs. To better study the relationship between the expected benefit and cost, the expected benefit was log transformed and a linear relationship was plotted 10  between the logarithm of the expected benefit and cost for road segments in Terrain Class III, IV and V. The observed linear relationships between the logarithm of the expected benefit and deactivation cost for road segments in Terrain Classes IV and V were investigated using least squares analysis (Zar, 1984). No relationship between the logarithm of the expected benefit and cost was observed for Terrain Class III {r =.0633). 2  On the other hand the /^for Terrain Class IV and V was fairly high (0.89) for Class IV and 0.77 for Class V). Covariance analysis of the slope of Terrain Class IV and V plots revealed that for a 95 percent confidence interval no statistical difference between the classes existed. Based on these results: •  Terrain Classes IV and V were combined into one group.  •  No relationship was proposed between expected benefit and cost for Terrain Class III.  52  6.00  7  Terrain V 0.0012X  + 0.0748  R = 0.7688 2  •  Terrain Class I I I  •  Terrain Class IV  A  Terrain Class V  Terrrain I I I y = -0.0003X + 4.2449 R —0.0633 J  Terrain IV : 0.0015X - 0.9048 _RL=.0.8944  0.00  1000.00  2000.00  3000.00  4000.00  5000.00  Cost of Road Deactivation  Figure 5-2 Sample Regression Plot Log 10 of Expected Benefit to Cost  • Terrain Class III  3.00  a Terrain Classes IV and V  o  S 2.00  1.00  0.00 -I 0.00  :  .  ,  1000.00  2000.00  3000.00  _  ,  ,  I  4000.00  5000.00  6000.00  Cost of Road Deactivation  Figure 5-3 Combined Terrain IV & V Regression Plot LoglO Expected Benefit to Cost  53  Figure 5-3 presents the results of a regression of the log^ transformed expected benefits of the combined Terrain Classes IV and V. The linear relationship proposed is logio (expected benefit) = 0.0014(cost) - 0.4823 (r = 0.877). This relationship was used 2  to calculate expected benefit for each road segment in the Terrain Class IV and V grouping for the baseline cost effectiveness analysis . The average expected benefit for Terrain Class III is 3.1, or $1259.02. This value was used to calculate expected benefit for each road segment in each Terrain Class grouping for the baseline cost effectiveness analysis. Because of the nature of the log scale used to relate expected benefit to cost, as the cost of deactivating a road segment increases the potential magnitude of error in the predicted expected benefit grows. The sample range of expected benefits from road segments was $40 to $190,000; thus the sample is little guidance for prediction of expected benefit values that are significantly beyond $190,000. To compensate, the expected benefit from a road segment was capped. That is, predicted expected benefit was limited to the maximum sample expected benefit plus $500,000 for a total of $690,000. In the baseline cost effectiveness analysis expected benefit was capped for 10 road segments. The expected benefits were transformed into expected net benefit by subtracting the deactivation cost. Ranking the road segments in order of their expected net cost benefit ratios from highest to lowest and plotting cumulative expected net benefit and cumulative cost (Figure 5-4) produces a cost effectiveness frontier. The baseline cost effectiveness analysis frontier shows that the relationship between expected net benefit and road deactivation cost is not linear. Initial expenditures on deactivation generate significant benefits. As expenditure increases, amounts of the incremental increase in expected net benefit decrease and the cost effectiveness frontier abruptly flattens. Expenditures beyond this point do not increase expected net benefit and, as cost increases, a point is reached where the expected net benefit declines. The total cumulative expected net benefit for the baseline analysis after all road segments had been deactivated was $8,000,000 and the total cumulative cost was $490,000. The baseline cost effectiveness frontier (Figure 5-4) shows that cumulative expected net  54  benefit increases significantly up to about $90,000 in cumulative cost and approximately $7,900,000 in cumulative expected net benefit. After sharp increase almost no expected net benefit is accumulated with further expenditure. As costs continue to increase a point is reach where expected net benefit declines (Figure 5-4). The cost effectiveness frontier consisted of 171 road segments, 95 located in Terrain Class III, 53 in Terrain Class IV, and 23 in Terrain Class V. Of the 95 road segments located in Terrain Class III, 22 had expected net benefit-cost ratios zero and above, ranging to a high of approximately 14.5 because net benefit-cost ratios are being used the some of the remaining road segments in Terrain Class III had ratios a which approached minus one.  $9,000,000 $8,000,000 $7,000,000 % $6,000,000  c  2  %  z $5,000,000 •  1 $4,000,000 •5 $3,000,000  E  $2,000,000  $1,000,000  $0 $0  $100,000  $200,000  $300,000  $400,000  $500,000  $600,000  Cumulative Cost  Figure 5-4 Cost Effectiveness Baseline Results (Discount Rate set at 4.25%) Showing Cumulative Expected Net Benefit to Cost Produced by Sorting the Road Segments in Order of their Expected Net Benefit-cost Ratios Of the 53 road segments in Terrain Class IV, 28 had expected net benefit-cost ratios zero and above, ranging to a high of 140. Of the 23 road segments in Terrain Class V, 19 had a expected net benefit-cost ratio zero and above, ranging to a high of 155.  55  For all Terrain Classes, 69 road segments had expected net benefit-cost ratios zero and above representing 40% of the total of 171 road segments. Of the 69 road segments, 60% (42) had expected net benefit-cost ratios between 0 and 5; 17% (12) had benefitcost ratios that exceeded 51 (Table 5-1). Seventeen road segments, all located in Terrain Class IV and V (10% of 171 road segments), were expected to deliver 8% ($7,870,000) of the cumulative expected net benefit from road deactivation ($8,000,000) at 18% of the cumulative cost ($87,000 of $490,000). These seventeen road segments had expected net benefit-cost ratios above 21. To gain an understanding of this group of road segments and the deactivation actions taken, a sample of ten road segments was assessed, all located on Road 400. Prior to deactivation, Road 400, located in the Misery Creek Drainage, began at an elevation of 530 m and ascended to 900 m over a distance of 2,800 m. During the ascent the road crossed the same drainage network seven times. In general the characteristics of the road segments included large volumes of fill material used to support the road running surface (70 to 170 m^ of sidecast), numerous tension cracks, gullies in need of reconstruction, and road beds requiring reconstruction. The types of deactivation actions undertaken included removal of sidecast and transport of the sidecast to a local deposit site. The road segments were within 100 m of a main channel. The expert group felt that the road segments offered high probability of a large landslide or a number of small landslides, possibly delivering a large volume of debris and sediment to the drainage system. For example, the expected probability of a landslide occurring on the three Terrain Class V segments was 80%, 100%, and 100%. When the landslide occurred the expected probability of damage on the hillslope was 0% (0% because the landslide would directly enter the headwater channel), 100%, 100%, and the expected probability of headwater channel damage was 100%, 15%, 0% (0% because the landslide would directly enter the main channel). The expected probability of impact to a main channel was 60%, 98%, and 100%. There was an expected 50% to 60% probability that the severity of landslide impact to a headwater channel would be classified as high. Similarly, there was an expected 10% to 40% probability that the severity of landslide impact to a main channel would be classified as high.  56  Table 5-1 Baseline Distribution (Discount Rate set at 4.25%) of Road Segments by Expected Net Benefit-Cost Ratios Baseline B/C Ratio Range  Number of Road Segments Terrain  Terrain  Terrain  Class III  Class IV  Class V  <0  73  25  4  102  0to5  14  20  8  42  6 to 10  5  1  6  11 to 15  3  1  Total  4  16 to 20 21to30  1  1  2  3  31 to 40  1  41 to 50  1  > 51  5  7  12  53  23  171  Total  95  1  Looking at the cost effectiveness frontier as described in Table 5-1, 102 road segments had expected net benefit-cost ratios less than zero and ranging to -0.99 (73 road segments in Terrain Class III, 25 in Terrain Class IV, and 4 in Terrain Class V). Road segments located in Terrain Classes IV were in two clusters. Those between zero and 0.53 were mixed with road segments from Terrain Class III and those between -0.86 and 0.99 were mixed with Terrain Class V. Eleven Terrain Class IV road segments were mixed with Terrain Class V, road segments and lay at the most negative end of the benefit-cost ratio distribution, deactivation costs ranged from $200 to $2,200 per 100 m with gross expected benefit ranging from $1 to $300. All Terrain Class V road segments with expected net benefit-cost ratios less than zero lay at the most negative end of the benefitcost ratio distribution. Fifteen 15 Terrain Class IV and V road segments with the most negative benefit-cost ratios lay at the end of the cost effectiveness frontier (Figure 5-4). Ten of these road segments were located on the North Mainline Road in the Chickwat Creek drainage. The road began at an elevation of 450 m and ascended to 800 m over a distance of 3,400 m. In general low volumes of fill material were associated with these road segments. Deactivation  57  treatments included installation of water bars (shallow troughs excavated crossing the road running surface) and culverts, reconstructing gullies, cleaning ditch lines and retrieval of small amounts of sidecast. The road segments were greater than 200 m from the main channel and most of the sidecast present was considered to be stable during the field assessment. Some road segments were in close proximity to a headwater channel (100 m or less). In these cases the potential distance that a landslide could travel in the headwater channel to the main channel was greater than 180 m. The expert group felt that there was a low probability of a large landslide or a number of small landslides occuring along the road sections that might deliver a large volume of debris and sediment to the drainage system. For example, the expected probability of landslides occurring on two Terrain Class IV road segments on the North Mainline was 10% for segment I and 25% for segment II. When a landslide occurred, the expected probability of damage on the hillslope for segment I was 15% and for segment II 25% and the expected probability of damage in a headwater channel for segment I was 0% and for segment II 50%. The expected probability of impact to a main channel for segment I was 75% and for segment II 40%. There was a low probability of high damage in the either the headwater or the main channel consequently the net expected benefit for deactivation of the road segment was very low.  Sensitivity Analysis of Cost Effectiveness Analysis Results To analyze how robust the baseline cost effectiveness analysis results (Figure 5-4) are to changes in the values the discount rate, amount of the expected loss, and the return interval of the rainstorm a series of sensitivity analysis were conducted. Sensitivity analysis alters a single variable while holding the other variables at their baseline rates and the change in the cost effectiveness results are examined. As an example, changing the discount rate from 4.25% to 0.5% results in a cost effectiveness frontier that is patterned after the baseline frontier (41 road segments accounted for 90% of expected net benefit and 29% of cumulative cost)(Figure 5-5).  58  The key probability estimates included in the cost effectiveness analysis (Equation 4 on page 51) are: p(s\w)  probability of a landslide given a weather event  P^s)  probability of the landslide affecting one of the impact areas  p(s \A )  probability of the severity of the landslide impact  P(jv)  probability of rain storm return interval  IJ  I  P(fV) was used by the expert group to determine p(s\w) in turn; p(s\w) was used by the expert group to generate P(AJ\S) and  p{s \A ). IJ  I  For example, the severity of impact  in proximity to the road influenced the probability of impact and probabilities of severity of impact on the hillslope and in the headwater channel. It is possible that the expert group either over- or under-estimated the risk. This bias would be reflected in all the probability estimates because the estimates are conditional probability estimates, only one,P(w), was included in the sensitivity analysis. To test the sensitivity of the results to r\sk,P(w) is varied to include storms with a 15-year (P = .067) and 50-year (P = .020) return intervals. Other key variables of the cost effectiveness analysis include the discount rate and the loss associated with the severity of impact. The baseline cost effectiveness analysis assumed a discount rate equal to the government's cost of money. That is a social discount rate equal to return on public Government of Canada real return bonds, 4.25 (Cote et al.1996). Following the discussion of discount rates in Chapter 2 the discount rate was varied to include a private rate of return of 8%, plus a 2% and 0.05% social discount rate which are expressions of the time preference of money allowing for intergenerational concerns and environmental sustainability. To examine the sensitivity of the findings to changes in the cost indexes loss in each impact area was varied plus 20%, minus 20%, and plus 100%. Varying the Discount Rate Three alternative discount rates were examined, 0.5%, 2%, and 8% and the results were compared with the baseline analysis (4.25%) results (Table 5-2 and Figure 5-5). Total  59  cumulative expected net benefit increased by 90% with a discount rate of 0.5% and by 25% with a discount rate of 2%. Inversely, cumulative expected net benefit decreased by 25% when the discount rate was increased to 8%. Compared with the baseline cost effectiveness analysis, setting the discount rate at 0.5% caused the cost effectiveness frontier to rise more gradually, reaching an expected net benefit-cost ratio of one when cumulative cost reached $435,000 (as opposed to $153,000 when the discount rate was 4.25%) and reaching an expected net benefit-cost ratio of zero when cumulative cost reached $474,000 (as compared to $188,000). Setting the discount rate at 2% and 8% varied the total cumulative expected net benefit for all road segments but did not substantially change the shape of the cost effectiveness frontiers as compared to the baseline cost effectiveness analysis. For an 8% discount rate, however the cost effectiveness frontier's descent beyond an expected net benefit-cost ratio less than zero as compared to the baseline, was steeper.  $18,000,000 T  .  • Baseline 4.25% • Discount Rate 0.5% A Discount Rate 2% a Discount Rate 8%  %  9  $4,000,000  %Q—  $2,000,000  V $0  -I $0  , $100,000  , $200,000  , $300,000  , $400,000  , $500,000  $600,000  Cumulative Cost  Figure 5-5 Alternative Cost Effectiveness Frontiers Showing Cumulative Expected Net Benefit to Cost Produced by Ranking the Road Segments in Order of their Expected Net Benefit-cost Ratios and Varying the Discount Rate  60  In general the shape of the cost effectiveness frontiers resembled the baseline cost effectiveness frontier where cumulative expected net benefit reaches a maximum then declines as additional road segments are deactivated. As a result there is a difference between the maximum cumulative expected net benefit and the total expected net benefit that varies with the amount of expected loss. The difference can be observed by looking at the road segments with the highest expected benefit-cost ratios. For example with a discount rate of 0.5% total cumulative expected net benefit was $15,700,000, 17 road segments account for 64% of expected net benefit and for 14% of cumulative cost. With a discount rate of 2% total cumulative expected net benefit was $10,100,000, 17 road segments account for 93% of expected net benefit and for 18% of cumulative cost. With a discount rate of 8% total cumulative expected net benefit was $6,000,000, 17 road Table 5-2 The Distribution of Road Segments by Expected Net Benefit-cost Ratio Ranges and Terrain Stability Class using Different Discount Rates Discount Rate  Number of Road Segments  0.05%  B/C Ratio Range  Terrain Class III  <0  Terrain Class IV  Terrain Class V  10  4  14  1  86  Oto 5  77  8  6 to 10  8  14  11 to 15 16 to 20  1  Total  22  1  2  3  3  1  5  21to30  4  31 to 40  2  1  3  41 to 50  2  3  5  4  > 51  9  9  11  29  Total  95  53  23  171  61  Table 5-2 continued, The Distribution of Road Segments by Expected Net Benefit-cost Ratio Ranges and Terrain Stability Class using Different Discount Rates Discount Rate 2.0%  N u m b e r o f Road Segments Terrain  Terrain  Terrain  Class I I I  Class IV  Class V  <0  49  12  4  65  0 to 5  37  25  4  66  6  3  9  2  2  5  B/C Ratio Range  6 to 10  Total  l l to 15  1  16 to 20  5  5  21to30  1  2  31 to 40  2  2  41 to 50 > 51 Total  95  Discount Rate 8.0%  7  10  17  53  23  171  N u m b e r o f Road Segments Terrain  Terrain  Terrain  Class I I I  Class IV  Class V  <0  78  32  6  116  0to5  15  13  7  35  6 to 10  2  1  B/C Ratio Range  l l to 15  Total  3 1  1  16 to 20  1  2  3  21to30  1  1  2  1  1  5  5  10  53  23  171  31 to 40 41 to 50 >51 Total  95  segments account for 102% of expected benefit and for 18% of cumulative cost. For comparison, in the baseline analysis total cumulative expected net benefit was $8,000,000, 17 road segments accounted for 98% of expected net benefit and 18% of cumulative cost. When the discount rate was set at 0.5%, 157 road segments had expected net benefit-  62  cost ratios zero and above, and represented 97% of cumulative cost, while 14 road segments had expected net benefit-cost ratios below zero. When the discount rate was set at 2%, 106 road segments had expected net benefit-cost ratios zero and above representing 58% of cumulative cost, while 65 road segments had expected net benefitcost ratios below zero. When the discount rate was set at 8%, 55 road segments had expected net benefit-cost ratios zero and above representing 31% of cumulative cost, while 116 road segments had expected net benefit-cost ratios below zero. (For comparison, in the baseline analysis 69 road segments had expected net benefit-cost ratios of zero and above representing 39% of cumulative cost, and 102 road segments had expected net benefit-cost ratios below zero). With a decrease in the discount rate, the value of the deactivation benefits increase, as does the number of road segments offering a positive return. This is demonstrated when the discount rate was set at 0.5% and 2%. Virtually all Terrain Class IV and V road segments had a positive expected net benefit-cost ratio. Change is most notable at the middle and at either end of the expected net benefit-cost ratio distribution as demonstrated by Table 5-3. Table 5-3 reflects four discount rates (including the baseline discount rate 4.25%, Table 5-1) and the percentage distribution of road segments in three expected net benefit-cost ratio ranges. Table 5-3 displays the distribution of road segment by the number of road segments in selected expected net benefit-cost ratio ranges by discount rate. Increasing the interest rate shifts the number of road segments toward the (-.99 to 0) and (0 to 5) expected net benefit-cost ratio ranges with the greatest impact being noticed in Terrain Class III (see Table 5-3). In Terrain Class III when the discount rate is 2% and greater, there is an absence of road segments with cost benefit ratios greater than 51 and a relatively equal distribution of road segments in Terrain Classes IV and V. In Terrain Class III when the discount rate is close to zero there is an absence of road segments with cost benefit ratios less than zero.  63  Table 5-3 Distribution of Road Segments in Three Benefit-cost Ratio Ranges as a Result of Varying Discount Rate Rate (%)  % of Total Road Segments in the B/C Ratio Range (< 0).  % of Total Road Segments in the ' % of Total Road Segments in the B/C B/C Ratio Range Ratio Range (0 to 5) (>51)  0.05  8  50  i  17  2  38  39  i  10  4.25  60  25  :  7  8  68  20  i  6  % Distribution of Road Segments in the B/C Ratio Range (< 0) by Terrain Class III 0.05  % Distribution of Road Segments in the B/C Ratio Range (0 to 5) by Terrain Class  IV  V  III  IV  71  24  90  9  1  V  % Distribution of Road Segments in the B/C Ratio Range (> 51) by Terrain Class III  IV  V  31  31  38  2  75  22  3  56  38  6  41  59  4.25  71  25  4  33  48  19  42  58  8  67  28  5  43  37  20  50  50  Varying the Loss Amount  Three alternative loss indexes were used in the sensitivity analysis, (loss + 100%, loss + 20%, and loss - 20%) and the results compared the results to the baseline analysis results where the total cumulative expected net benefit was $8,000,000 (Table 5-4 and Figure 56). Total cumulative expected net benefit increased by 25% to $9,900,000 when the amount of loss was increased by 100%. Total cumulative expected net benefit increased by 6% to $8,500,000 when the amount of loss was increased by 20%, and decreased by 9% to $7,200,000when the amount of loss was decreased by 20%. In all cases, loss + 100%, loss + 20%, and loss - 20%, the shape of the cost effectiveness frontiers  64  $12,000,000  $10,000,000  VQnntBnnnBnnfflsnssxEooDonB £  $8,000,000 UU.I.I.UC—  •  Baseline  x Loss - 20%  $6,000,000  O Loss + 20% + Loss +100%  $4,000,000  $2,000,000  $0 $0  $100,000  $200,000  $300,000  $400,000  $500,000  $600,000  Cumulative Cost  Figure 5-6 Alternative Cost Effectiveness Frontiers Showing Cumulative Expected Net Benefit to Cost Produced by Ranking the Road Segments in Order of their Expected Net Benefit-cost Ratios and Varying the Estimated Loss Amounts resembled the baseline cost effectiveness frontier where cumulative expected net benefit reaches a maximum then declines as additional road segments are deactivated. As a result there is a difference between the maximum cumulative expected net benefit and the total expected net benefit that varies with the amount of expected loss. The difference can be observed by looking at the road segments with the highest expected benefit-cost ratios. For example, where the expected loss was increased by 100% 17 road segments account for 100% of expected net benefit and for 18% of cumulative cost. When expected loss was increased by 20% 17 road segments account for 98% of expected benefit and for 18% of cumulative cost. Where expected loss was decreased by 20% 17 road segments account for 93% of expected benefit and for 18% of cumulative cost. (For comparison in the baseline scenario, 17 road segments accounted for 98% of expected benefit and 18% of cumulative cost). When the loss amount was increased by 100%, 99 road segments had expected net benefit-cost ratios of zero and above and represented 54% of cumulative cost while 72 road segments had expected net benefit-cost ratios  65  below zero. This is a pattern similar to that observed when the discount rate was set at 2%, that is, increasing the value of the deactivation benefits and shifting virtually all Terrain Class IV and V road segments to a positive return status. When the loss was increased by 20%, 80 road segments had expected net benefit-cost ratios zero and above; representing 45% of cumulative cost; 91 road segments had expected net benefit-cost ratios below zero. When the loss was decreased by 20%, 62 road segments had expected net benefit-cost ratios of zero and above and represented 34% of cumulative cost; 109 road segments had expected net benefit-cost ratios below zero. For the baseline conditions, 69 road segments had expected net benefit-cost ratios of zero and above representing 39% of cumulative cost; 102 had ratios below zero. Varying the loss amount modified the distribution of road segments by expected net benefit-cost ratio in each Terrain Class at the middle and either end of the benefit-cost ratio distribution as demonstrated in Table 5-5. When the net benefit-cost ratios exceed 51 the distribution in Terrain Classe IV and V is approximately evenly split iegardless of the amount of loss. Where the net benefit-cost ratios are less than zero, regardless of the amount of expected loss amount, the distribution of road segments by terrain class remained similar. (Also, a similar distribution of road segments across the three ranges of net benefit-cost ratios for loss plus 20% and loss plus 100% exists). When the expected loss amount were varied by plus or minus 20%, the absolute impact in each of the benefit-cost ratio ranges was similar. Increasing the amount of loss by 100% however, did not have the same proportional impact.  66  Table 5-4 The Distribution of Road Segments by Expected Net Benefit-cost Ratio Ranges and Terrain Stability Class using Different Expected Loss Amounts Expected Loss + 100%  Number of Road Segments Terrain  Terrain  Terrain  Class III  Class IV  Class V  <0  56  13  4  73  0 to 5  30  25  4  59  6  3  9  1  2  4  B/C Ratio Range  6 to 10 11 to 15  1  16 to 20  5  21to30  3  Total  5 1  4  31 to 40 41 to 50 > 51 Total  95  Expected Loss + 20%  7  10  17  53  23  171  Number of Road Segments Terrain Class III  Class IV  Terrain Class V  0<  71  17  4  92  Oto 5  16  27  7  50  6 to 10  4  1  2  7  11 to 15  2  B/C Ratio Range  16 to 20  Terrain  2 1  21to30  1  31 to 40  1  Total  1 1  1  3  5  6  7  13  53  23  171  41 to 50 >51 Total  95  67  Table 5-4 continued, The Distribution of Road Segments by Expected Net Benefit-cost Ratio Ranges and Terrain Stability Class using Different Expected Loss Amounts Expected Loss - 20%  Number of Road Segments Terrain  Terrain  Terrain  Class III  Class IV  Class V  0<  79  30  4  113  0 to 5  11  15  9  35  6 to 10  3  1  11 to 15  2  B/C Ratio Range  Total  4 2  16 to 20 21to30  1  3  4  31 to 40  1  1  2  5  6  11  53  23  171  41 to 50 > 51 Total  95  Table 5-5 Distribution of Road Segments in Three Benefit-cost Ratio Ranges as a Result of Varying Estimated Loss Amount Loss Variance  % of Total Road Segments in the B/C Ratio Range (< 0).  % of Total Road Segments in the B/C Ratio Range (0 to 5)  +100  43  35  10  + 20  54  29  8  Base  60  25  7  -20  66  20  6  % Distribution of Road Segments in the B/C Ratio Range (< 0) by Terrain Class  % Distribution of Road Segments in the B/C Ratio Range (0 to 5) by Terrain Class  III  IV  V  III  IV  V  +100  77  17  6  51  42  + 20  77  18  5  32  Base  71  25  4  -20  70  27  3  % of Total Road Segments in the B/C Ratio Range 0 51)  % Distribution of Road Segments in the B/C Ratio Range (> 51) by Terrain Class III  IV  V  7  41  59  54  14  41  59  33  48  19  42  58  31  43  26  50  50  68  $10,000,000  $9,000,000  • —era  $8,000,000  $7,000,000  2  $6,000,000 TWrrmTiiiiiiT-  M  • Baseline 20 Year Return  $5,000,000  • Storm 15 Year Return A Storm 50 Year Return a  $4,000,000  • — A  $3,000,000  $2,000,000  $1,000,000  $0 $0  $100,000  $200,000  $300,000  $400,000  $500,000  $600,000  Cumulative Cost  Figure 5-7 Alternative Cost Effectiveness Frontiers Showing Cumulative Expected Net Benefit to Cost Produced by Ranking the Road Segments in Order of their Expected Net Benefit-cost Ratios and Varying the Rainstorm Return Interval Varying the Rainstorm Return Interval Two alternative rainstorm return intervals that could trigger landslides were considered in the sensitivity analysis, 15 years and 50 years, and the results were compared to the baseline analysis (20 year return interval) results where the total cumulative expected net benefit was $8,000,000 (Table 5-6 and Figure 5-7). Total cumulative expected net benefit increased by 10% to $8,700,000 when the return interval was reduced to 15 years and total cumulative expected net benefit decreased by 32% to $5,400,000 when the return interval was increased to 50 years. For return intervals of both 15 years and 50 years, the shape of the cost effectiveness frontiers resembled the baseline cost effectiveness frontier. As a result, there is a difference between the maximum cumulative expected net benefit and the total expected net benefit that varies with the rainstorm return interval. The difference can be observed by looking at the road segments with the highest expected benefit-cost ratios. When the return interval was set at 15 years, 17 road segments accounted for 97% of cumulative expected net benefit ($8,400,000 of $8,700,000) and  69  18% of c u m u l a t i v e cost. W h e n t h e return interval w a s 50 years, 17 road s e g m e n t s  $5,400,000)  and  18% of c u m u l a t i v e cost. In t h e baseline scenario, 17 road s e g m e n t s a c c o u n t e d for  98%  a c c o u n t e d for  103% of  of e x p e c t e d net benefit  cumulative e x p e c t e d net benefit  ($7,800,000  of  $8,000,000)  and  ($5,600,000 18% of  of  c u m u l a t i v e cost.  W h e n the s t o r m return interval w a s d e c r e a s e d to 15 years, 86 road s e g m e n t s had e x p e c t e d net benefit-cost ratios of zero a n d a b o v e a n d r e p r e s e n t e d 47%  of cumulative  cost; 85 road s e g m e n t s h a d e x p e c t e d net benefit-cost ratios b e l o w z e r o . T h i s is a pattern similar to t h a t o b s e r v e d w h e n loss associated w i t h landslide i m p a c t w a s increased by 100%  or t h e d i s c o u n t rate w a s set at 2%, t h a t is, shifting virtually all T e r r a i n Class IV a n d  V road s e g m e n t s to a positive e x p e c t e d net benefit-cost ratio. In a pattern similar to that o b s e r v e d w h e n t h e d i s c o u n t rate w a s set at 8%,  increasing the rainstorm return interval to  50 years, resulted in 50 road s e g m e n t s w i t h e x p e c t e d net benefit-cost ratios of zero and a b o v e a n d r e p r e s e n t e d 29%  of c u m u l a t i v e cost; 121 road s e g m e n t s had e x p e c t e d net  benefit-cost ratios b e l o w zero. (By w a y of c o m p a r i s o n , for the baseline 69 road segments, had net benefit-cost ratios of zero a n d a b o v e representing 39% of c u m u l a t i v e cost, and 102 had e x p e c t e d net benefit-cost ratios b e l o w zero).  T a b l e 5-6 T h e Distribution of R o a d S e g m e n t s by Expected Net Benefit-cost Ratio R a n g e s a n d T e r r a i n Stability Class using Different Estimates of t h e Rainstorm Return Interval Return Interval 15 Y e a r B/C Ratio R a n g e  N u m b e r of R o a d S e g m e n t s Terrain  Terrain  Terrain  Class III  Class IV  Class V  Total  <0  67  14  4  85  Oto 5  19  28  6  53  6 to 10  3  3  3  9  11 to 15  3  16 to 20  3  3 1  4  21to30 31 to 40  1  1  41 to 50  1  2  3  >51  6  7  13  53  23  171  Total  95  70  Table 5-6 continued, The Distribution of Road Segments by Expected Net Benefit-cost Ratio Ranges and Terrain Stability Class using Different Estimates of the Rainstorm Return Interval Return Interval 50 Y e a r B/C Ratio R a n g e  N u m b e r of R o a d S e g m e n t s Terrain  Terrain  Terrain  Class III  Class IV  Class V  Total  <0  79  35  7  121  0 to 5  16  11  6  33  l l to 15  1  3  4  16 to 20  1  1  2  1  1  5  5  10  53  23  171  6 to 10  21to30 31 to 40 41 to 50 > 51 Total  95  Varying the rainstorm return interval also modified the middle and at either end of the benefit-cost ratio distribution as demonstrated in Table 5-7. When benefit-cost ratios exceeded 51 there is an approximately even split in the distribution regardless of rainstorm return interval for Terrain Classes IV and V. Where benefit-cost ratios fell below zero the distribution of road segments by terrain class did not remain.  71  Table 5-7 Distribution of Road Segments in Three Benefit-cost Ratio Ranges as a Result of Varying Rainstorm Return Interval Return  % of Total Road Segments in the B/C Ratio Range (< 0).  % of Total Road Segments in the B/C Ratio Range (0 to 5)  % of Total Road Segments in the B/C Ratio Range 0 51)  15 yr  50  31  8  20 yr  60  25  7  50 yr  66  19  6  % Distribution of Road Segments in the B/C Ratio Range (< 0) by Terrain Class  % Distribution of Road Segments in the B/C Ratio Range (0 to 5) by Terrain Class  III  IV  V  III  IV  V  15 yr  79  16  5  36  53  20 yr  71  25  4  33  50 yr  65  30  5  48  % Distribution of Road Segments in the B/C Ratio Range (> 51) by Terrain Class III  IV  V  11  46  54  48  19  42  58  33  19  50  50  Varying the Probability of a Landslide Occurring After a Rainstorm Has Occurred When the expert group estimated the probability of landslide and the probabilities of the expected loss, several conditional probabilities were used. That is the probability of the weather event (P(w) was used by the expert group to determine p(s\w), in turn P(S\W)  was used by the expert group to generate ^(41^)  a r |  d P{Sy\4)- Because  probabilities are conditional, only the climate event was selected in the sensitivity analysis. The following paragraphs demonstrate that varying the expected probability of the landslide produces similar results to those observed when the rainstorm interval was changed. Four alternative measures of the probability of a landslide were used in the sensitivity analysis and were compared to the baseline results where the total cumulative expected net benefit was $8,000,000 (Table 5-8 and Figure 5-8). The alternative measures of the probability of a landslide were the expert group's estimate of the probability of a landslide minus 80%, minus 20%, plus 20%, and plus 80%. The alternative measures offered the possibility that some of the probability estimates would exceed one or would be negative. To avoid the possibility, where the probability estimates exceed one, they were rounded  72  down to one and where the probability estimates were negative, they were assumed to be zero. The total cumulative expected net benefit decreased by 50% to $3,900,000 as the probabilities were decreased by 80%. 10000000  9000000  8000000  7000000  m 6000000  n Benefit Ratio • Baseline  &  X Landslide + 20%  5000000  x Landslide + 80% +• Landslide - 20%  4000000  o Landslide - 80% • Storm 15 Year Return A Storm 50 Year Return  3000000  2000000  1000000  o  m-  100000  200000  300000  400000  500000  600000  -1000000 C u m u l a t i v e Cost  Figure 5-8 Alternative Cost Effectiveness Frontiers Showing Cumulative Expected Net Benefit to Cost Produced by Ranking the Road Segments in Order of their Expected Net Benefit-cost Ratios and Varying the Expert Group's Probability of a Landslide  The total cumulative expected net benefit decreased by 10% to $7,200,000 as the probabilities were decreased by 20%. The total cumulative expected net benefit increased by 3% to $8,200,000 in each case as the probability of failure were increased 80% and 20% respectively. The estimated probabilities of a landslide occurring assigned to seven road segments in the sample of 17 road segments used to estimate the relationship between net expected benefit and road deactivation cost, were high (P >.08 ). As a result there is little change in the total cumulative expected net benefit when the probabilities of a landslide occurring were increased. All of the seven road segments except one were located in Terrain Stability Classes IV and V and represented some of the highest net benefit road segments included in the sample set. Increasing the probability of a landslide  73  on these road s e g m e n t s resulted in only a small proportion of the intended c h a n g e being captured before the probability of a landslide a p p r o a c h e d 1. A s a result, the expected benefit f r o m deactivating these road s e g m e n t s w a s not appreciably c h a n g e d and the cost effectiveness frontier closely a p p r o x i m a t e d the baseline cost effectiveness frontier.  Decreasing the probability of a landslide on these road s e g m e n t s resulted in a larger portion of the intended c h a n g e being captured, w h i c h decreased the total cumulative e x p e c t e d net benefit. W h e r e t h e probability of a landslide w a s r e d u c e d by 8 0 % , t h e cost effectiveness frontier produced w a s similar to the cost effectiveness frontier produced w h e n the discount rate w a s set at 8 % .  T h a t is, w h e r e the e x p e c t e d net benefit-cost ratio  w a s less t h a n zero, t h e cost effectiveness frontier decline w a s steeper as c o m p a r e d to the baseline cost effectiveness frontier.  T a b l e 5-8 T h e Distribution of Road S e g m e n t s by Expected Net Benefit-cost Ratio Ranges and T e r r a i n Stability Class using Different Estimates of the Probability of a Landslide Probability of a Landslide + 80% B/C Ratio R a n g e  N u m b e r of Road S e g m e n t s  Terrain  Terrain  Terrain  Class III  Class IV  Class V  Total  <0  70  18  4  92  Oto 5  16  26  8  50  6 to 10  4  1  1  6  11 to 15  3  1  16 to 20  2  4 2  21to30 31 to 40  1  41 to 50  1  > 51  5  7  12  53  23  171  Total  95  3  4 1  74  Table 5-8 continued, The Distribution of Road Segments by Expected Net Benefit-cost Ratio Ranges and Terrain Stability Class using Different Estimates of the Probability of a Landslide Probability o f a Landslide + 20%  Number o f Road Segments  Terrain  Terrain  Terrain  Class I I I  Class IV  Class V  <0  79  35  7  121  0to5  16  11  6  33  11 to 15  1  3  4  16 to 20  1  1  2  1  1  5  5  10  53  23  171  B/C Ratio Range  Total  6 to 10  21to30 31 to 40 41 to 50 > 51 Total  95  Probability o f a Landslide 20% B/C Ratio Range  Number o f Road Segments  Terrain  Terrain  Terrain  Class I I I  Class IV  Class V  Total  <0  79  30  5  114  0to5  16  15  8  39  6 to 10  1  11 to 15  1 1  1  16 to 20 21to30  1  2  3  31 to 40  1  1  2  5  6  11  53  23  171  41 to 50 > 51 Total  95  75  Table 5-8 continued, The Distribution of Road Segments by Expected Net Benefit-cost Ratio Ranges and Terrain Stability Class using Different Estimates of the Probability of a Landslide Probability o f a Landslide 80% B/C Ratio Range  Number of Road Segments  Terrain  Terrain  Terrain  Class I I I  Class IV  Class V  Total  <0  83  41  4  124  Oto 5  16  6  8  30  1  1  2  1  1  1  3  6 to 10 11 to 15 16 to 20 21to30  2  31 to 40  1  1  41 to 50 > 51 Total  99  2  4  6  53  19  171  In the case where probability was decreased by 80% 17 road segments accounted for 107% of the expected benefit ($4,200,000 of $3,900,000) and for 18% of cumulative cost. When probability decreased by 20%, 17 road segments accounted for 100% of expected benefit ($7,200,000 of $7,200,000) and for 18% of the cumulative cost. In the case where probability was increased by 20%, 17 road segments accounted for 98% of the expected benefit ($8,000,000 of $8,200,000) and for 18% of the cumulative cost. Where probability was increased by 80%, 17 road segments account for 103% of expected benefit ($7,900,000 of $8,200,000) and for 18% of cumulative cost. In the baseline scenario, 17 road segments represented 98% of the expected benefit and 18% of cumulative cost. When the probability was decreased by 20%, 59 road segments had benefit-cost ratios of zero and above and represented 34% of the cumulative cost while 112 road segments had expected net benefit-cost ratios below zero. When the probability was decreased by 80%, 44 road segments had benefit-cost ratios of zero and represented 24% of the cumulative cost; 126 road segments had expected net benefit-cost ratios below zero. In the baseline scenario, 69 road segments had expected net benefit-cost  76  ratios of zero and above representing 39% of the cumulative cost, and 102 had expected net benefit-cost ratios below zero). Varying the probability of a landslide modified the middle and both ends of the benefit-cost ratio distribution (Table 5-9). Varying the probability plus or minus 20% resulted in a similar distribution of road segments where the benefit-cost ratios exceed 51. Change is noticeable if the benefit-cost ratios fall between zero and five. Table 5-9 Distribution of Road Segments in Three Benefit-cost Ratio Ranges as a Result of Varying the Probability of Landslide Rate (%)  % of Total Road Segments in the B/C Ratio Range (< 0).  % of Total Road Segments in the B/C Ratio Range (0 to 5)  % of Total Road Segments in the B/C Ratio Range (>51)  +80  54  35  10  +20  54  35  10  Base  60  29  8  -20  72  25  7  -80  68  20  6  % Distribution of Road Segments in the B/C Ratio Range (< 0) by Terrain Class  % Distribution of Road Segments in the B/C Ratio Range (0 to 5) by Terrain Class  % Distribution of Road Segments in the B/C Ratio Range (> 51) by Terrain Class  III  IV  V  III  IV  V  IV  V  +80  76  20  4  32  52  16  42  58  +20  76  20  4  32  52  16  42  58  Base  71  25  4  33  48  19  42  58  -20  63  33  4  42  23  35  25  75  -80  68  26  6  41  38  21  56  44  III  77  Chapter 6 Limitations and Conclusions The results of the cost effectiveness analysis (Chapter 5) were facilitated by establishing some boundaries to focus the analysis. Based upon these boundaries the analysis demonstrates that it is possible to distinguish the road segments that are expected to yield significant expected net benefits from the road segments that are not expected to offer any expected net benefits after road deactivation. Upon close examination expected net expected benefits, on average, are related to Terrain Stability Class. The relationship between expected net benefit and Terrain Stability Class is more easily observed by examining first, the incremental expected net benefits generated by each road segment, and second, the sensitivity of the incremental expected net benefit to change in the discount rate, the loss amount, and the rainstorm return interval. Used in conjunction with decision analysis, the relationship between expected net benefits and Terrain Class provides the basis for managers to develop operational rules for road deactivation planning.  The Analysis Results Re-Examined Using Incremental Expected Net Benefit The results of the study confirm the value of decision analysis used in conjunction with cost effectiveness analysis. The results of the cost effectiveness analysis are clearly displayed in a plot of the incremental expected net benefit from each road segment ranked by expected net benefit to cost ratios (high to low) and plotted against cumulative road deactivation cost. Forty percent of the road segments (69 of 171) had expected net benefit-cost ratios zero and below, representing 39% of the cumulative cost ($190,000 of $490,000). Seventeen road segments all located in Terrain Class IV and V (10% of 171 road segments) delivered 98% ($7,870,000 of $8,000,000) of the cumulative expected net benefit from road deactivation representing 18% of the cumulative cost ($87,000 of $490,000). Changing the key variables underlying the analysis does not substantially change the baseline results, but cause some minor reordering of the road segments.  78  Figures 6-1, 6-2, and 6-3 demonstrate the sensitivity of the baseline results to changes in the rate of discount, the loss amount and the rainstorm return interval. Changing the rate of discount, the loss amount and the rainstorm return interval, changed the expected incremental net benefit from each road section and the net benefit-cost ratio which was used to order the road segments in each plot. Noticeable is the large incremental gain for some of the road segments and the small or negative gain for the balance of road segments. Only when the discount rate is set very low (0.05) is there marked difference in the pattern of incremental expected net benefit. Lowering the discount rate increases the number of road segments contributing to incremental gain and more of the road segments achieve the maximum expected net expected benefit allowed in the analysis for each road segment ($690,000). As a result of lowering the discount rate, 90% of cumulative expected net benefit is delivered by road segments costing approximately 39% ($190,000) in cumulative cost. Grouped by Terrain Class one sees an observable pattern to the incremental expected net benefit from the road segments (Figures 6-1, 6-2, and 6-3). If expected net incremental benefit is viewed as a continuum where values range from high to below zero, the high values are predominantly associated with road segments located in Terrain Class V (Figure 6-3), and the zero and negative values are associated with road segments located in Terrain Class III (Figure 6-1). In both Terrain Classes there are exceptions. In Terrain Class V some road segments have low to negative expected incremental expected net benefit, and in Terrain Class III some road segments have expected incremental expected net benefit greater than zero. The expected incremental expected net benefit from road segments in Terrain Class IV ranges from high to negative. The observed relationship between the expected net benefit, deactivation cost, and Terrain Stability Class suggests the following operating criteria for road deactivation planning that includes decision analysis: 1)  Undertake road deactivation on all road segments in Terrain Class V unless the results of the risk analysis suggest negative expected net benefit. Conduct further analysis of the road segments with negative expected net benefit to determine if there are other factors that should be included in the decision process.  79  2)  Undertake road deactivation on all road segments in Terrain Class IV unless the results of the risk analysis suggest zero and/or negative expected net benefit. Conduct further analysis of the road segments with negative expected net benefit to determine if there are other factors that should be included in the decision process.  3)  Undertake no road deactivation on all road segments in Terrain Class III unless the results of the risk analysis suggest positive expected net benefit. Conduct further analysis of the road segments with positive expected net benefit.  The information to conduct decision analyses and to estimate probabilities is available for most areas of British Columbia. That information includes road assessment and deactivation plans, maps and air photos and the expertise of professional knowledge about the region in which the road deactivation project is located. Loss amounts were characterized by incorporating available information and expert opinion to establish conservative estimates of maximum loss indexes. Because the information to establish expected risk is currently available, the cost and time required to conduct decision and cost effectiveness analysis is minimal, particularly when weighed against the potential offered by more efficient allocation of the resources allocated to road deactivation.  80  $800,000  $700,000  $600,000  z  a E =  $400,000  • Baseline 4.25% • Discount 0.5% A Discount 2% • Discount 8%  $300,000  I  X $200,000 LU  $100,000  $0  -4B0$3  $50,000  IBB- — 'I— ( y n r ' — W U $100,000 $150,000 $200,000 $250,000 $300,000 $350,000 $400,000 $450,000 $50(  -B—M-l-l  -$100,000  Cumulative Cost  Figure 6-la Terrain Class III Alternative Distribution of Road Segments Showing Expected Incremental Expected Net Benefit to Cost Produced by Ranking the Road Segments in Order of their Expected Net Benefit-cost Ratios and Varying the Discount Rate $800,000 -r  - -  $700,000  $600,000  f  $500,000  f  $400,000  • Baseline 4.25% • Discount 0.5% A Discount 2%  I 2 jj  • Discount 8% $300,000  >< $200,000  $100,000  'S  $0 $100,000  $200,000  M-i $300,000  $400,000  $500,000  $60d 000  -$100,000 Cumulative Cost  Figure 6-lb Terrain Class IV Alternative Distribution of Road Segments Showing Expected Incremental Expected Net Benefit to Cost Produced by Ranking the Road Segments in Order of their Expected Net Benefit-cost Ratios and Varying the Discount Rate  81  800000  T  • • A •  200000  Baseline 4.25% Discount 0.5% Discount 2% Discount 8%  500000  Cumulative Cost  Figure 6 - l c Terrain Class V Alternative Distribution o f Road Segments Showing Expected Incremental Expected Net Benefit t o Cost Produced by Ranking t h e Road Segments in Order o f their Expected Net Benefit-cost Ratios and Varying t h e Discount Rate $800,000  — — —  $700,000  $600,000  •3 $500,000  E  B  $400,000  •  Baseline  *: Loss - 20%  E  8  o Loss + 20%  =  $300,000  fi  $200,000  + Loss +100%  $100,000  $0 4 $D  $50,000  $100,000  $150,000  $200,000  $250,000  $300,000  $350,000  $400,000  $450,00o" $50C!,000  -$100,000 Cummulative Cost  Figure 6-2a Terrain Class I I I Alternative Distribution of Road Segments Showing Expected Incremental Expected Net Benefit t o Cost Produced by Ranking t h e Road Segments in Order of their Expected Net Benefit-cost Ratios and Varying t h e Amount o f the Loss  82  $800,000  $700,000  tma»  Oflt + • •  $600,000 Ex $500,000 ct ed In  • x o +  $400,000  cr 6  mt  $300,000  Baseline Loss - 20% Loss + 20% Loss +100%  al Ne $200,000  $100,000  !rt1tiilHJiiwttet»fife—H—S-)5-r $100,000 -$100,000  $200,000  $300,000  $400,000  $500,000  $6001000  J  Cumulative Cost  Figure 6-2b Terrain Class IV Alternative Distribution of Road Segments Showing Expected Incremental Expected Net Benefit to Cost Produced by Ranking the Road Segments in Order of their Expected Net Benefit-cost Ratios and Varying the Amount of the Loss 800,000  700,000  E  x  600,000  pe 500,000  rt  ed In 400,000  mt  • X o +  300,000  Baseline Loss - 20% Loss + 20% Loss +100%  al N  e  200,000  100,000  100,000  200,000  300,000  400,000  500,000  600 000  -100,000 Cumulative Cost  Figure 6-2c Terrain Class V Alternative Distribution of Road Segments Showing Expected Incremental Expected Net Benefit to Cost Produced by Ranking the Road Segments in Order of their Expected Net Benefit-cost Ratios and Varying the Amount of the Loss  83  $800,000  $700,000  $600,000  I c  $500,000  % 5  $400,000  • Baseline 20 Year Return • Storm 15 Year Return A Storm 50 Year Return  i  g  i I  =  $300,000  fi  $200,000  $100,000 $0 $p  -SH-B-B-GSB-I $50,000 $100,000 $150,000 $200,000 $250,000 $300,000 $350,000 $400,000 $450,000 $500,000  -$100,000 Cumulative Cost  Figure 6-3a Terrain Class I I I Alternative Distribution o f Road Segments Showing Expected Incremental Expected Net Benefit t o Cost Produced by Ranking t h e Road Segments in Order of their Expected Net Benefit-cost Ratios and Varying t h e Return Interval o f the Rainstorm $800,000  $700,000  $600,000  %  $500,000  f  $400,000  • Baseline 20 Year Return  8 E 2  o Storm 15 Year Return A Storm 50 Year Return  £  $300,000  x  $200,000  $100,000 A  •  BO-  $0 $100,000  $200,000  $300,000  $400,000  $500,000  $60d,1,000  -$100,000 Cumulative Cost  Figure 6-3b Terrain Class IV Alternative Distribution of Road Segments Showing Expected Incremental Expected Net Benefit t o Cost Produced by Ranking t h e Road Segments in Order of their Expected Net Benefit-cost Ratios and Varying t h e Return Interval o f t h e Rainstorm  84  700000  600000  %  500000  • Baseline 20n Year Return • Storm 15 Year Return A Storm 50 Year Return  200000  , aaa » •  100000  100000  200000  300000  400000  500000  -100000 Cumulative Cost  Figure 6-3c Terrain Class V Alternative Distribution o f Road Segments Showing Expected Incremental Expected Net Benefit t o Cost Produced by Ranking t h e Road Segments in Order o f their Expected Net Benefit-cost Ratios and Varying t h e Return Interval o f the Rainstorm  Bounding the Analysis Decision analysis and cost effectiveness analysis have been used to address the question, How much money should be spent on road deactivation in a given area? The approach has produced results that appear to be self evident and support the prevailing thoughts of road deactivation professionals interviewed during this study. At the outset of the study, however, the task of verifying the perceptions of road deactivation professionals was not self evident. The challenges of the complexity of the natural system, risk perception, government regulation, and the constraints of economic theory combined to produce a complicated decision environment. Decision analysis provided the structure to organize a view of the natural system complexity that an expert group could use to estimate probability of a landslide and expected loss. A relationship between expected net benefits and deactivation costs by Terrain Stability Class was estimated for a random sample of road segments. The relationship was used to estimate expected net benefits for all road segments in the study area.  85  The analysis was possible because, to address complexity, the decision was bounded. Some of these boundaries are discussed in the following paragraphs. Further, using expert knowledge it was not necessary to tease apart the impact of change caused by natural processes and change caused by road deactivation actions. Similarly, it was not necessary to tease apart the role of chance in the natural system and the influence of chance on the effectiveness of road deactivation actions. In practice the natural processes relevant to the road deactivation decision would be determined through a strategic planning process that preceded the deactivation planning. To connect the study results with current road deactivation practice, the concept of significance (Apogee Research, 1995) was introduced together with the National Research Council planning approach (National Research Council, 1992). A set of natural resource values maintained or protected by road deactivation, drawn from road deactivation programs in British Columbia and some neighboring jurisdictions, was identified. Using these values characterizations of loss resulting from forest road related landslides were developed. The watershed was divided into four areas that would be potentially impacted by a road-related landslide, the expected loss in each of the four areas was characterized by three scenarios or indexes of loss (high, medium, and low), and dollar values were estimated. Road segments of approximately 100 m were defined using the characteristics of the road. The deactivation costs for each road segment was determined using the field assessment reports. Probabilities were approximated using the consensus estimates of an expert group. Focusing on a random sample of 17 road segments, the expert group estimated the probability of a landslide, the probabilities of landslide impact in the four areas potentially affected by a road-related landslide, and the conditional probabilities of expected loss in each of the four areas. The estimates could have been improved had the expert group undertaken a field assessment of the study area. The sample size of 17 road segments was smaller than desired, and the results could have been improved had a larger sample been used. In addition the cost of deactivation for the study was determined using one deactivation plan for the area. The results of the analysis could be extended by contrasting alternative deactivation designs, if such designs are available.  86  Decision analysis assisted the expert group to focus on specific events and estimate the probability of the event occurring. The results of the analysis could have been improved by broadening the decision tree to include other factors, such as soil moisture conditions prior to a rainstorm, or the possibility that, with time, the road and the hillslope may attain a stable equilibrium. The expected risk for the decision to undertake road deactivation for each road segment is the risk in the current year plus the discounted future risk. Monetary losses were estimates of the maximum possible losses and were presented as relative indexes of loss to conservatively bound the upper limit of loss. Because loss was treated as a levy or fine, future risk was treated as an infinite annuity simplifying the calculation of expected risk. Unless significant effort was spent characterizing loss, it is not clear whether a more complicated treatment of future risk was warranted.  87  Bibliography Alila, Y. (1994). "A Regional Approach for Estimating Design Storms in Canada," PhD, University of Ottawa, Ottawa. 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