We were curious that the Draft EIS provides identical numbers for all the alternatives for river encounters and time in sight during the summer when we felt there should be some difference between these alternatives. Does it make sense that the preferred alternative has more daily launches and a wider variety of trip lengths than the no-motor alternative C and yet both have the same wilderness quality? This is not consistent with our previous calculations and our intuition.
We started with what should we measure? The two measures used are river group encounters and time in sight. Both of these are favored by the commerical industry because it places them in a good light (although there are also some legitimate reasons to use them). But some of the alternatives consider groups of eight people. Replacing a 32 person commercial oar trip with two noncommercial oar trips each with eight people would probably result in more river encounters and time in sight. Most people would probably find the latter is more consistent with a wilderness which contradicts these measures. The other problem is that both measures used as a comparison of alternatives are amenable to manipulation, either intentional or unintentional. Too many river encounters? Just have those two groups row (or motor) a little closer together and suddenly river encounters have decreased. So we decided to use a measure that is invariant to group size which is the average daily encounters in number of people.
If we launch on an 18 day trip we know that 7 day motor trips that launch for the next 11 days have to pass us somewhere. This difference in trip lengths or speeds in physical terms is the convective component of average daily encounters. There is also a component of groups nearby randomly speeding up and slowing down relative to each other which in physical terms is Brownian motion or the diffusive component of the average daily encounters. While the convective component is a firm number the diffusive component requires estimates of the probability of contacting nearby groups. The total average daily encounters is the sum of the convective and diffusive components.
It is probably best to separate out the convective and diffusive components since the choice of contact probability can change the relative importance of each component. For the convective component the average number of people encountered is dramatically reduced when trip speeds are similiar. This is consistent with our intuition although some may be surprised at the degree of reduction. Well what if we added just a few fast motor trips? Looking at the commercial motor row we see that such a trip, if it existed, would encounter a lot of people. This demonstrates that gradually phasing out fast motor trips is not a viable alternative.
Looking at the diffusive component we see that perhaps surprisingly the no motor alternatives again have the smallest average number of people contacted daily. This is a function of the number of launches and the sizes of groups and is a bit more complicated but the calculation shows the clear result. The probability of contact can change the relative importance of the two components but should not have any effect on the differences we see within each component. We see that given this choice of probability of contact that for noncommercial standard groups the total average daily encounters for the preferred alternative is more than double the highest no-motor alternative. Most people would notice a significant difference between encountering an average number of 146 people each day to just encountering 64. It is difficult to envision any changes to this analysis that would result in a significant change in the differences between the preferred alternative and the no motor alternatives.
| Alternatives | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| A | B | C | D | E | F | G | H | RRFW | |
| No Change From Current | No Motors, Low Use |
No Motors, High Use |
Mixed Motors/ Oars, Low Use |
Spread Out Current, More Non-Comm |
50/50 Comm/ Non-Comm Motors/ No-Motors |
Mixed Motors/ Oars, High Use |
Preferred Alternative | 4 Trips Daily Year-Round Wilderness | |
| Summer Launches (pp 38-52 Draft EIS) | |||||||||
| Commercial Motor | 417 | 0 | 0 | 308 | 369 | 305 | 325 | 369 | 0 |
| Commercial Oar | 117 | 246 | 243 | 123 | 108 | 110 | 94 | 106 | 246 |
| Noncommercial Standard | 129 | 123 | 246 | 123 | 123 | 124 | 123 | 123 | 246 |
| Noncommercial Small | 0 | 123 | 0 | 62 | 62 | 31 | 62 | 62 | 0 |
| Launches Per Day | |||||||||
| Commercial Motor | 3.39 | 0.00 | 0.00 | 2.50 | 3.00 | 2.48 | 2.64 | 3.00 | 0.00 |
| Commercial Oar | 0.95 | 2.00 | 1.98 | 1.00 | 0.88 | 0.89 | 0.76 | 0.86 | 2.00 |
| Noncommercial Standard | 1.05 | 1.00 | 2.00 | 1.00 | 1.00 | 1.01 | 1.00 | 1.00 | 2.00 |
| Noncommercial Small | 0.00 | 1.00 | 0.00 | 0.50 | 0.50 | 0.25 | 0.50 | 0.50 | 0.00 |
| Maximum Size (p 36 Draft EIS) | |||||||||
| Commercial Motor | 43 | 25 | 30 | 30 | 40 | 32 | |||
| Commercial Oar | 39 | 25 | 30 | 25 | 25 | 30 | 30 | 32 | 16 |
| Noncommercial Standard | 16 | 16 | 16 | 16 | 16 | 16 | 16 | 16 | 16 |
| Noncommercial Small | 8 | 8 | 8 | 8 | 8 | 8 | |||
| Maximum Summer Trip Length (p 36 Draft EIS) | |||||||||
| Commercial Motor | 18 | 10 | 8 | 10 | 8 | 10 | |||
| Commercial Oar | 18 | 16 | td | 16 | 14 | 16 | 14 | 16 | 18 |
| Noncommercial Standard | 18 | 16 | 16 | 16 | 16 | 16 | 14 | 16 | 18 |
| Noncommercial Small | 18 | 16 | 16 | 16 | 16 | 16 | 14 | 16 | |
| Average Trip Length (p G-13 Draft EIS) | |||||||||
| Commercial Motor | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 | 7 |
| Commercial Oar | 13 | 13 | 13 | 13 | 13 | 13 | 13 | 13 | 13 |
| Noncommercial Standard | 18 | 16 | 16 | 16 | 16 | 16 | 14 | 16 | 18 |
| Noncommercial Small | 18 | 16 | 16 | 16 | 16 | 16 | 14 | 16 | 18 |
| Average Daily Encounters (Number Of People) | |||||||||
| Convective Component | |||||||||
| Commercial Motor | 58.2 | 73.71 | 91.91 | 47.2 | 44.6 | 46.3 | 39.7 | 49.4 | 77.71 |
| Commercial Oar | 73.7 | 5.5 | 7.4 | 33.5 | 46.2 | 38.5 | 50.3 | 48.9 | 12.3 |
| Noncommercial Standard | 99.4 | 9.4 | 11.1 | 39.9 | 54.7 | 46.9 | 54.5 | 59.2 | 8.9 |
| Noncommercial Small | 99.41 | 9.4 | 11.11 | 39.9 | 54.7 | 46.9 | 54.5 | 59.2 | 8.91 |
| Diffusive Component | |||||||||
| Commercial Motor | 112.6 | 48.11 | 59.31 | 60.0 | 73.8 | 65.6 | 80.6 | 80.5 | 41.61 |
| Commercial Oar | 114.2 | 38.1 | 47.3 | 60.0 | 75.8 | 65.6 | 84.6 | 80.5 | 35.2 |
| Noncommercial Standard | 123.4 | 41.7 | 52.9 | 63.6 | 79.4 | 71.2 | 90.2 | 86.9 | 35.2 |
| Noncommercial Small | 129.81 | 44.9 | 59.31 | 66.8 | 82.6 | 74.4 | 93.4 | 90.1 | 41.61 |
| Total Encounters | |||||||||
| Commercial Motor | 170.7 | 121.81 | 151.31 | 107.1 | 118.4 | 111.9 | 120.3 | 129.9 | 119.31 |
| Commercial Oar | 187.9 | 43.6 | 54.7 | 93.5 | 122.0 | 104.1 | 134.9 | 129.5 | 47.5 |
| Noncommercial Standard | 222.8 | 51.1 | 64.0 | 103.5 | 134.1 | 118.1 | 144.7 | 146.1 | 44.1 |
| Noncommercial Small | 229.21 | 54.3 | 70.41 | 106.7 | 137.3 | 121.3 | 147.9 | 149.3 | 50.51 |
The convective component should be zero if all trips travel at the same overall speed; i.e. the same trip length. The increment for each additional day should be the number of groups times the maximum group size of the other groups. The total is the sum over each type of group and then this has to be divided over the length of the trip.
Once the convective component is removed the rest of the calculation can assume that all trips travel at the same speed. For the diffusive component we have to estimate the likelihood that there will be contact of another group that launched on the same day. We estimated that probability on any particular day at 40%. For groups that launched a day apart we used a probability of 20%. A probability of 5% is used for groups that launched 2 days apart.
Many contacts are multiple contacts between two groups that occur on the same day (another source of interpretation and manipulation) which may only be approximated by using Brownian motion. The actual average observed contacts can be impacted by multiple contacts especially around places like Phantom Ranch. If this is a problem then it would suggest that restrictions around exchanges at Phantom Ranch would be more appropriate than altering the management of the entire river.
It is assumed that each group of a particular type travels the river at the same overall speed (trip length). In reality they do travel at somewhat different speeds and these differences can cause additional contacts between groups. However, the Draft EIS suggests that most trips of a particular type are within plus or minus one day of the average. Looking at the alternatives with small differences between travel times of different types of groups it appears that the smaller differences within each group would not significantly change the conclusions of this model.
This analysis does not take into account the variability in number of launches each day in alternative A. This puts alternative A on an equal basis with the rest of the alternatives for the purposes of this analysis.
This calculation assumes that all trips are from Lees Ferry to Diamond Creek while in some alternatives a significant number of people will leave the river at Whitmore by helicopter. Although this model does not consider Whitmore it can be argued that Whitmore should be a separate analysis and that broad decisions about overall use of the river should consider all alternatives on an equal basis which is without Whitmore.
The formulas used in the calculations are in the source code of the table in this web page. The calculations are fairly simple which has the benefit that it is hard to manipulate and distort the results but has the disadvantage that they may not model more complex aspects of river trips. However any section of the river that distorts things away from the underlying physics is also likely amenable to management controls. While this simple model is appropriate for broad decisions among alternatives more complex models such as the Grand Canyon Simulator are necessary for final analysis and more specific decisions about whether management objectives are met.
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