In calculating WTP, we now used the weighted perception probability values created from the ordered probit models (table 10) as a substitute for the “raw” Water Clarity and Water Color perception values in the truncated negative binomial model of perceptions (table 9, column 3). Equation 26 shows how the weighted perception is calculated, where the P (j) change as TSI (SD) changes (equation 24). Any change in TSI (SD) will change the weighted perception probability values; these new values were used to calculate the number of trips at the baseline and improved TSI (SD) values. The standard welfare measure for a Poisson model then applies (equation 28).
Improving water clarity by reducing TSI (SD) by 25%
When our highest TSI(SD) value (79.8) at Utah Lake is reduced by 25%, its new TSI(SD) value would be 59.85. Thus we would expect that the mean perception (Water
Clarity) value to move from 3.54 to 3.11 (table 14, last row). Similarly, our lowest TSI(SD)
value is 32.2 at Strawberry Reservoir; a 25% improvement reduces this to 24.23. Using our linking model, the probability weighted water quality perception moves from 2.37 to 2.14 (table 14, row 2). Calculations are shown for other lakes in table 14.
45 Table 14 Mean WTP using “Linked biophysical to perception model” reduction in TSI (SD) by 25%
Lake Visitors Baseline
TSI(SD) Improved TSI(SD) Baseline Weighted Perceptions Improved Weighted Perceptions MWTP after reducing TSI(SD) by 25% Strawberry Reservoir 47 32.3 24.23 2.37 2.14 $55.96 (-$23.61 — $135.53) Bear Lake 62 34.1 25.58 2.42 2.17 $52.27 (-$22.31 — $126.86)
Flaming Gorge Res. 16 36.5 27.38 2.49 2.23 $46.88
(-$28.12 — $121.88)
East Canyon Res. 18 42.5 31.88 2.66 2.36 $64.17
(-$16.66 — $145.02)
Deer Creek Res. 31 42.8 32.1 2.67 2.37 $76.32
(-$19.77 — $172.41) Rockport Reservoir 12 43.9 32.93 2.70 2.39 $75.51 (-$20.80 — $171.83) Jordanelle Reservoir 19 44.8 33.6 2.72 2.41 $81.55 (-$21.35 — $184.44) Pineview Reservoir 41 50.4 37.8 2.87 2.53 $83.90 (-$18.13 — $185.94)
Willard Bay Res. 35 68.8 51.6 3.31 2.91 $105.13
(-$16.94 — $227.20)
Utah Lake 54 79.8 59.85 3.54 3.11 $117.55
(-$17.19 — $252.28) 95% confidence bounds stated in parentheses
46 Comparing table 14 (columns five and six) to table 13 (columns one and two) we
can see that a change of 25% in TSI(SD) does not correspond to the same level of changes when observing the Improved Clarity to Improved Weighted Perception. While the initial values for clarity and weighted perceptions are relatively close, a 25% change in TSI (SD) does not correspond to a one-unit change in perception when “passed
through” the linking model. While the MWTP values of table 14 appear to have the same ratio difference between table 12 and 13, the MWTP values in table 14 are much closer to the values from the biophysical model (table 12). As the MWTP values start to increase, the difference between values of both tables also rises. The confidence interval on table 14 is relatively smaller than that of table 12.
Improving water clarity by reducing TSI (SD) to center value of improved trophic classification
Table 3 shows that the range of TSI values between each trophic classification is not the same so it may be reasonable to believe that reducing TSI (SD) to the middle of the next “better” trophic status would be a reasonable policy goal. For example, if TSI (SD) for a lake is 78 (hypereutrophic), it would change to 60 (eutrophic). Lakes with TSI (SD) values lower than 40 (oligotrophic) would not change. If the TSI (SD) were equal to a value ranging from 40 to 50, the new value would be changed to the mean of our lakes in the oligotrophic trophic classification since the middle level of the oligotrophic trophic classification (20) and is below any values found in the dataset for TSI (SD).
47 Table 15 Mean WTP using “link biophysical to perception model” change TSI (SD) to center value of improved trophic classification
Lake Visitors Baseline
TSI(SD) Improved TSI(SD) Baseline Weighted Perceptions Improved Weighted Perceptions
MWTP after changing Trophic Classification for TSI(SD)
Strawberry Reservoir 47 32.3 32.3 2.37 2.37 $ -
Bear Lake 62 34.1 34.1 2.42 2.42 $ -
Flaming Gorge Reservoir 16 36.5 36.5 2.49 2.49 $ -
East Canyon Reservoir 18 42.5 35 2.66 2.45 $44.66
(-$11.29 — $100.61 )
Deer Creek Reservoir 31 42.8 35 2.67 2.45 $55.07
(-$13.91 — $124.06) Rockport Reservoir 12 43.9 35 2.7 2.45 $60.64 (-$16.42 —$137.71) Jordanelle Reservoir 19 44.8 35 2.72 2.45 $70.97 (-$18.36 — $160.30) Pineview Reservoir 41 50.4 45 2.87 2.73 $34.43 (-$6.91 — $75.77)
Willard Bay Reservoir 35 68.8 45 3.31 2.73 $152.34
Utah Lake 54 79.8 60 3.54 3.11
(-$26.51 — $331.20) $116.55 ($-17.01 — 250.10) 95% confidence bounds stated in parentheses
48 In the previous table we can see that even though we modified the way that changes
in TSI (SD) occur, it appears that the improved weighted perceptions (table 15, column 6) is not really close to the improved clarity perception values (table 13, column 4). The first 3 rows of table 15 do not present MWTP since there were no change in their TSI(SD) since those lakes are classified as oligotrophic. Compared to table 12, the values provided on the previous table have a narrower confidence interval, though one should note that the MWTP changes are not uniform since moving to the center value of a better trophic classification can represent different value changes for each lake. For example, Pineview Reservoir had an improvement in TSI(SD) of 5.4 units, while Willard Bay Reservoir had a change of 23.8 units. One may observe that the “larger” change for Willard Bay Reservoir generated a much larger increase in welfare than Pineview Reservoir, even though both reservoirs were moving from “eutrophic” status to “mesotrophic” status. The MWTP for improving Willard Bay Reservoir is over four times as large as the MWTP to improve the quality of Pineview Reservoir.
Improving water clarity by changing TSI (SD) by 1.5 meters
If we observe table 3, we can see that the range of values between each trophic classification is not the same, but on average each of those classifications are roughly 1.5 meters (4.92 feet) apart in measured Secchi depth. We now estimate MWTP for 1.5 meters improvement in clarity.
49 Table 16 Mean WTP using “link biophysical measure to perception” based on change in meters
Lake Visitors Baseline
TSI(SD) Improved TSI(SD) Baseline Weighted Perceptions Improved Weighted Perceptions MWTP after improving water clarity by 1.5 meters Strawberry Reservoir 47 32.3 29.42 2.37 2.29 $19.74 (-$8.12 — $47.60) Bear Lake 62 34.1 30.87 2.42 2.33 $19.46 (-$8.10 — $47.01)
Flaming Gorge Reservoir 16 36.5 32.75 2.49 2.39 $18.80
(-$11.06 — $48.67)
East Canyon Reservoir 18 42.5 37.17 2.66 2.51 $31.37
(-$7.78 — $70.52)
Deer Creek Reservoir 31 42.8 37.4 2.67 2.52 $37.72
(-$9.33 — $84.78) Rockport Reservoir 12 43.9 38.13 2.7 2.54 $38.69 (-$10.21 — $87.60) Jordanelle Reservoir 19 44.8 38.73 2.72 2.56 $43.10 (-$10.80 — $96.98) Pineview Reservoir 41 50.4 42.15 2.87 2.65 $53.54 (-$11.07 — $118.15)
Willard Bay Reservoir 35 68.8 49.69 3.31 2.86 $118.32
(-$19.49 — $256.13)
Utah Lake 54 79.8 51.9 3.54 2.91 $175.48
(-$28.24 — $379.20) 95% confidence bounds stated in parentheses
50 Just as in table 14 and 15, table 16 confidence interval is narrower than that of table
12. It appears that table 16 MWTP values appears to get approach the values in table 12 as MWTP increases. Just as in table 14, MWTP values rises as one goes down the rows in table, this can be attributed to the fact that constant level changes give the impression of higher improvements in “dirtier” lakes when compared to cleaner lakes After using the last approach where Secchi depth was changed by 1.5 meters, a visual examination appears to show that none of the three models fully captures how a change in biophysical measure would correspond to unit change in the perception model. In order to fully understand whether any of those models are close to explaining such changes we will use the convolution method. Using the perception model and each of the three linked models, we estimated new WTP distributions using standard bootstrapping techniques of repeated sampling with replacement. Based on Poe, Giraud, and Loomis (2005), we use the convolution method by calculating various sampling schemes of the difference ,
where X is the WTP distribution of the perception model and Y is the WTP distribution for the linked model, where the indicator z would designate which of the three models would be used (change by 25%; change to the middle of trophic classification; change in meters). The significance of the differences is computed by the number of negative values as a proportion of all paired differences. The null hypothesis is that the difference between the distributions is equal to 0. The model related to change in TSI (SD) by 25% was the only model where the null hypothesis was not rejected at the 5% confidence level, its value was 0.080. The models related to change in trophic classification and change in meters and had the respective 0.041 and a 0.047 level of significance. The table below exemplifies the results of the test.
Table 17 Comparison of WTP distributions of weighted models to WTP distribution of baseline perceptions model
Linked Model Test Statistic Different WTP Distribution
Reduce TSI(SD) by 25% 0.08 No
Reduce TSI(SD) to center of
trophic classification 0.04 Yes
Reduce TSI(SD) based on 1.5 meters improvement in Sight
depth 0.05 Yes
Since the linked model where the TSI (SD) is reduced by 25% can also be directly compared to the distribution of our baseline biophysical model we also compared such distribution. Its value was 0.43, meaning that we could not rejected the null hypothesis that the distributions are different from each other.
CONCLUSION
In this study we have attempted to understand changes in trip behavior by exploring the relationship between the biophysical measures of water quality and people’s perception of water quality. Water quality in travel cost models have generally been estimated in one of two ways: Using biophysical measures or using perceived water quality. The first approach requires the analyst to assume that biophysical measures can be perceived by the respondent, and the second presumes that a measure of perceived water quality can be ‘translated’ back to some metric that is useful to the natural scientists. What is missing is the link between biophysical and perceived measures of water quality, and how changes in biophysical measures relate to a person’s perception of water quality. Further, the two approaches for including water quality in a travel cost model could lead to different models and thus, different welfare estimates associated with changes in water quality.
Using the knowledge that water clarity is related to TSI (Secchi depth), and that TSI (Chlorophyll) accounts for the greenish tint in the water, simple models that link perceptions and biophysical measures were estimated. We used the “linkage” models three different ways: (i) postulating a fixed percentage change in the biophysical measures, (ii) postulating fixed change of 1.5 meters in Secchi depth measure (improved water clarity) at all lakes, (iii) postulating an improvement to the next best level of quality, where the improvement was to the mid-point of the next best trophic classification. After calculating all three different ways of changing biophysical measures, we used the convolution method to understand the difference between the distribution of WTP estimated with the original perceptions model and the three estimates that account for the link between biophysical and perception measures. The model using the percentage levels [approach (i)] was the only model where
the null hypothesis that the difference between WTP distributions was equal to zero was not rejected. The same approach (i) was also compared with the original biophysical model WTP distribution the null hypothesis again was not rejected.
Future studies should focus on a closer examination of the model linking biophysical and perception measures. Increasing the sample size would be beneficial to understanding overall perception levels. Some lakes in the data only had a unique visitor or a couple visitors. While this is not enough to remove such individuals from our sample, increasing the sample size would help to create a more representative model of perceptions across a broader variety of lakes. Further, the different preferences and activities of people, as revealed by different primary activities, may affect perceptions of water quality. Our linkage models did not investigate this possibility. The implication is that if a certain lake is being used primarily for warm water fishing and the anglers are interested in a certain variety of fish, the water quality level desired may be different than when compared to swimmers or boaters. Even though the results did not show a perfect link when using the convolutions model, this paper shows that such a link should be analyzed. The use of a large dataset would be beneficial to better understand such a link and in identifying the prospective differences between lakes and groups visiting the lakes. Different levels of water quality may be preferred by different groups. Finally this paper raises the question of whether regulators should focus on maintaining the water quality level desired based on primary activity of lake or improving all lakes to the same water quality level.
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60 Appendix 1
Lake Name TSI(SD) TSI(Chla) Mean
Clarity Mean Shades of Green Number of Visitors Fish Lake 32.11 23.62 2.75 2.00 4 Strawberry Reservoir 32.31 34.34 2.66 2.38 47 Bear Lake 34.10 23.60 2.39 1.68 62 Marsh Lake 36.44 32.25 1.00 2.00 1
Flaming Gorge Reservoir 36.49 34.47 2.44 1.81 16
Duck Fork Reservoir 37.40 23.80 1.00 1.00 1
Tony Grove Reservoir 37.68 31.85 2.00 1.50 2
Huntington Reservoir 38.46 27.45 2.00 2.00 1
Lyman Lake 38.78 28.54 2.33 1.33 3
Tropic Reservoir 39.34 21.57 2.00 2.00 1
Porcupine Reservoir 40.15 32.92 2.60 1.60 5
Silver Lake Flat 40.69 27.14 2.75 2.25 4
Starvation Reservoir 41.02 35.11 2.75 1.75 4
Mantua Reservoir 41.51 40.80 2.78 2.44 9
Navajo Lake 41.53 24.74 2.14 2.14 7
Tibble Fork Reservoir 42.08 20.06 3.11 2.33 9
Mirror Lake 42.11 32.04 2.00 1.80 5
Whitney Reservoir 42.50 31.92 3.00 1.50 2
East Canyon Reservoir 42.51 34.90 2.78 2.11 18
Joes Valley Reservoir 42.61 23.32 1.00 3.00 1
Deer Creek Reservoir 42.84 43.69 2.65 2.06 31
Quail Creek Reservoir 43.06 21.61 2.56 2.11 9
Causey Reservoir 43.51 26.24 3.00 3.00 3
Scout Lake 43.64 27.26 1.00 2.00 1
Moon Lake 43.70 42.61 3.00 2.00 1
Big Sand Wash
Reservoir 43.71 27.20 3.00 2.00 1
Rockport Reservoir 43.91 39.49 3.08 2.17 12
Currant Creek Reservoir 44.01 27.90 2.67 2.67 3
Jordanelle Reservoir 44.82 38.09 2.89 2.26 19
Washington Lake 45.25 29.07 2.75 2.00 4
Smith and Morehouse
Reservoir 45.49 29.44 2.25 1.75 4
Sand Hollow 45.58 25.59 1.50 1.50 4
Woodruff Creek
Trial Lake 46.04 29.95 1.67 1.67 3
Panguitch Lake 46.11 49.72 2.50 2.00 4
Kens Lake 46.69 30.57 2.50 2.00 2
Puffer Lake 46.75 40.08 3.00 2.00 1
Wall Lake 47.15 27.16 3.00 2.00 1
Huntington Lake North 47.31 19.77 4.00 1.00 1
LaBaron Reservoir 47.74 39.77 3.00 3.00 1
Scofield Reservoir 47.77 68.01 2.17 2.00 6
Echo Reservoir 47.98 41.01 3.00 1.89 9
Mill Hollow Reservoir 48.19 45.95 3.00 2.00 1
Bridger Lake 48.21 46.56 3.50 2.00 2
Butterfly Lake 48.25 37.24 2.00 2.00 1
Blanding City Reservoir 48.96 27.19 2.00 2.00 2
Yankee Meadow Reservoir 49.23 48.84 1.50 1.50 2 Settlement Canyon Reservoir 49.81 38.54 3.00 1.50 4 Spirit Lake 49.90 40.59 3.00 2.00 1 Pelican Lake 50.25 40.84 2.00 2.50 2 Lower Gooseberry Reservoir 50.39 38.29 3.00 2.00 1 Pineview Reservoir 50.40 40.89 3.00 2.00 41
Birch Creek Reservoir 50.76 44.59 3.00 2.00 1
Red Fleet Reservoir 50.91 35.43 2.00 2.00 2
Hyrum Reservoir 51.58 39.94 3.10 2.10 10
Gunlock Reservoir 52.47 38.53 3.00 1.75 4
Piute Reservoir 52.49 40.34 2.50 2.00 2
East Park Reservoir 52.92 32.92 3.00 2.00 1
Upper Enterprise
Reservoir 53.74 51.12 2.00 1.50 2
Palisades Lake 53.99 32.79 2.80 2.40 5
Matt Warner Reservoir 54.64 58.96 3.00 2.00 1
Newcastle Reservoir 54.69 55.84 3.00 3.00 1
Payson Lake 55.01 44.48 3.00 2.00 4
Grantsville Reservoir 55.54 37.31 4.00 3.00 1
Baker dam reservoir 56.51 57.54 3.00 2.00 1
Kents Lake 59.28 50.94 2.00 2.00 1
Salem Pond 60.28 61.94 3.00 3.00 1
Gunnison Reservoir 61.07 32.93 3.00 3.00 1
Newton Reservoir 62.64 52.18 3.33 2.00 3
Yuba 63.54 45.19 3.67 2.00 3
Otter Creek Reservoir 65.52 47.59 3.00 2.33 3
Mona Reservoir 76.78 50.70 2.00 2.00 1 Gunnison Bend Reservoir 78.43 26.51 4.00 2.00 3 Cutler Reservoir 78.74 60.15 4.00 1.50 2 Utah Lake 79.81 60.82 3.65 2.24 54 Fish Lake 32.11 23.62 2.75 2.00 4 Strawberry Reservoir 32.31 34.34 2.66 2.38 47 Bear Lake 34.10 23.60 2.39 1.68 62 Marsh Lake 36.44 32.25 1.00 2.00 1
Flaming Gorge Reservoir 36.49 34.47 2.44 1.81 16