170 Stewart et al.: QTRA and Risk-based Cost-benefit of Tree Assessment that economic assessment is the sole criterion for decision making. However, if a decision was to retain the trees for non-quantifiable reasons (e.g., heritage value, tourism) then Table 3. Net benefit of risk mitigation that reduces risk by ΔR = 75%. All currency is represented in Australian dollars (AUD$). Risk of Harm (ROH) per $0 tree per year without risk mitigating measures 1/20 1/100 1/1,000 1/10,000 1/100,000 Figure 6. Net benefit of tree removal. Table 2. Net benefit of tree removal as function of Risk of Harm (ROH) and cost of tree removal including opportunity costs (CΔR ). All currency is represented in Australian dollars (AUD$). ROH per tree per year 1/20 1/100 1/1,000 1/10,000 1/100,000 1/1,000,000 1/10,000,000 Cost of tree removal including opportunity costs (C∆R $1,200 ) $2,200 $249,050 $49,050 $4,050 -$450 -$900 -$945 -$950 $248,050 $48,050 $3,050 -$1,450 -$1,900 -$1,945 -$1,950 $6,200 $244,050 $44,050 -$950 -$5450 -$5,900 -$5,945 -$5,950 Note: Each entry represents benefit minus cost result for each ROH and value of tree amenity. Entries that are positive would be considered cost-effective to implement risk mitigating measures. Example 2: Net benefit of risk mitigating measure Rather than removing the tree, it is possible to employ a risk mitigation strategy to reduce the exposure of people to a potential hazard. This might include, for example, restricting vehicle access to an adjacent road, redirecting pedestrian traffic, or closing the street on high wind days. The study authors assume a 75% reduction in target prob- ability, equivalent to a risk reduction of ∆R = 75%. The cost of risk mitigation measures may be $15,000 per year. Maintenance costs associated with root damage to pave- ment and services costs $250 per year. Hence, C∆R = $15,250 efit of retaining the trees may be public amenity, which may vary from E(B) = $1,000 to E(B) = $5,000 per year. Net Benefit is calculated from Equation 9 using the pa- rameters described in Table 3. If the ROH is 1/100 or greater, then risk mitigating measures are cost effective. However, the benefits of such measures reduces as ROH decreases, even when the public amenity and benefit of retaining the tree is valued at E(B) = $5,000 per year. If the ROH is 1/100, the net benefit for tree removal is $49,050 (assuming no loss of amenity), and $22,500 if risk mitigating measures are put in place that reduce risk by 75% (compare Table 2 and Table 3). It follows that a decision aimed at only maxi- mizing net benefit would be to remove the tree—assuming per year, and Closs = $5 million as assumed above. A ben- ©2013 International Society of Arboriculture 1/1,000,000 1/10,000,000 $172,250 $22,250 -$11,500 -$14,875 -$15,213 -$15,246 -$15,250 $173,250 $23,250 -$10,500 -$13,875 -$14,213 -$14,246 -$14,250 $177,250 $27,250 -$6,500 -$9,875 -$10,213 -$10,246 -$10,250 Note: Each entry represents benefit minus cost result for each ROH and value of tree amenity. Entries that are positive would be considered cost-effective to implement risk mitigating measures. risk mitigating measures are also cost-effective and justifi- able with a net benefit of at least $22,250. Clearly, differ- ent cost inputs will lead to different results and decisions. Improvements to QTRA The priority for improvement lies in more accurate and robust as- sessment of failure probabilities, as this is the parameter in the risk equation subject to the highest uncertainty (and error). This means more scientific approaches are needed, and that results are bench- marked with known risks to ensure that results pass a reality check. Hazard identification is an important first step to under- stand the cause of tree failure, and then the frequency and se- verity of these events. This might involve assessing the annual probability that a wind speed exceeds a certain value, or rain- fall exceeds a specific value. Statistical and probabilistic mod- els for natural hazards are well researched and documented. For example, Wang and Wang (2009) provide stochastic wind field models for most locations in Australia for cyclones and storms. If the tree under consideration is similar in age, condition, and exposure to other trees, then the failure probability may be derived as [10] Probability of Failure = n(failed trees over time period T) N × T per year where n() is the number of failed trees over time period T, N is the total number of failed and unfailed trees, and T is time mea- sured in years. It is preferable to consider time periods in excess of one year, as this will average out the failure probability over time and is more likely to consider the effect of extreme events. The larger the sample size (N × T) the more confi- dence there is in the calculation. It follows from binomial theory that the 90% confidence limits of such as a result is [11] Probability of Failure ±1.645 Probability of Failure × 1- Probability of Failure( N × T ) Taking the Laman Street figs as an example, if n(failed trees) is 2 over T = 10 years, and the total number of trees is N = 16, then the probability of failure given by Equation 10 is 0.0125 or 1/80. Value of tree amenity E(B) per year $1,000 $5,000
July 2013
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