426 category “Impact Score” appeared to only influence the output by 3%, which raised questions as to the value of this input. The analysis showed that the QTRA W method applied different weightings to its inputs to the full QTRA method, with “Target” accounting for 45%, “Probability of Failure” account- ing for 31%, and “Size of Part” accounting for 21% of the variance, indicating that in many instances, dif- ferent risk ratings under the same circumstances would be produced, depending on the method (full or wheel) used. Whilst most tree risk assessment methods used similar input categories, the multivariate stepwise regression of the Monte Carlo simulation demon- strated that significant differences existed between methods because of scaling, range of input catego- ries, and the mathematics. With the exception of the full version of QTRA, TRE, and TRAQ, no method provided an explanation of its weighting, scaling, or mathematics. Risk assessors often assume that out- puts of methods provide a full range of possibilities and that all output scores are equally likely, but the analyses show this is not the case. Few of the method authors clearly discussed the reasons behind the range, weighting, and mathematics of their methods, but TRAQ and QTRA do it better than most. It seemed that few, if any, authors of the assessment methods had analysed the effects of the inputs on the subsequent measurement of risk. Fair and reasonable explanations may exist, but in failing to provide them, many methods lack transparency, which could leave them open to legal criticism or challenge. The Monte Carlo simulation permitted the cre- ation of probability distribution profiles. The purpose of the distribution profiles was to determine the range of values generated by the input ranges, scaling, and underlying mathematics, and the probable frequency of these output values, in order to represent these as a probability distribution curve. The distribution output charts presented in each method’s summary indicated that some methods tend to produce larger frequencies of particular output values, that few methods pro- duced flat or even output distributions, and that in some instances, methods could not produce a full range of output values. For instance, USDAFS 2 had a theoretical output range of 0 to 6; however, because of the mathematics used, this method cannot produce the output value 5, and generated the numbers 2 and 0 at 2.5 times the frequency of other values. TRAQ could not generate 7 of the outputs in its assigned ©2020 International Society of Arboriculture Norris and Moore: How Tree Risk Assessment Methods Work range from 1 to 16. Two methods had the possibility of producing a zero risk output, which raised the question as to whether it is possible to rate any tree- related risk as zero. Given the size, age, and context of trees that are subjected to risk assessment, it would seem probable that there is always some element of risk, no matter how small that risk might be, especially for trees growing in public spaces. In analysing the sensitivity data, while each method was unique and different from the others, they could be placed into 3 broad groups (Table 7): • Group 1 methods produced a normal distribution with most values around the mean. • Group 2 methods produced outputs at the lower end of the risk scale. • Group 3 methods produced outputs evenly, if not continuously, across the risk scale (with Private 3 producing outputs at the lower end of the risk scale as in Group 2). This grouping shows that the method chosen to risk assess a tree can impact the score derived. For example, Group 2 methods will usually provide a lower risk rating, while Group 1 methods will tend to provide a score closer to the mean for the range of possible scores, and Group 3 methods provide scores evenly across their range. The variations identified between methods in both the ranked order and stan- dardised score approaches strongly aligned, suggest- ing that both approaches identified similar aspects of each method. This research defined risk as a variant of R = Li × Co, and methods were assessed in relation to the formula. Using the data generated from the multivariate regres- sion analysis, the various inputs for each method were placed into the consequences or likelihood cate- gories. There is no reason that the weightings for like- lihood and consequences should be equal; and this did not apply in any instance (Figure 3). The closest to balanced methods were QTRA (Co:Li = 0.51), TRE QT (Co:Li = 0.51), and TRAQ (Co:Li = 0.66). Private 2 (Co:Li = 0.69) was mathematically the clos- est to balanced, but its “Other” category weakened the effect of other inputs. USDAFS 2 (Co:Li = 0.00), Private 3 (Co:Li = 0.00), Threats (Co:Li = 0.04), and QTRA W (Co:Li = 0.07) were very strongly weighted to the likelihood inputs. For 14 of the 16 methods, the weighting favoured likelihood over consequence inputs, and only HCC (Co:Li = 2.19) and Kenyon (Co:Li = 2.66) favoured consequences, with both using a “damage factor” as a final modifier. Some
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