IMPERVIOUS SURFACE AND MACROINVERTEBRATES IN THE SOUTH ATLANTA METROPOLITAN AREA.
Although many professional stream ecologists have established a relationship between a stream's watershed characteristics and its macroinvertebrate community, data collected by volunteer citizen scientists have not frequently been used to examine this relationship. Volunteer stream monitoring programs can provide data with little to no funding, and sometimes for longer time periods and a broader geographic scale than government agencies are able. Despite the coarser taxonomic resolution and simpler biotic indices of volunteer protocols, a few studies have demonstrated that volunteers can provide scientifically valid data. Fore et al. (2001) reported that volunteers were as accurate at identifying macroinvertebrates as professionals when properly trained, and that their simple volunteer index was correlated with a professional multimetric index, if less precise. Engel and Voshell (2002) also found that volunteers are just as reliable as professionals when properly trained in collection and identification, but the simple volunteer index used by Virginia Save Our Streams did not correlate to professional indices, so they developed a new one. Using volunteer rapid assessment protocols in Georgia (Georgia Adopt-A-Stream 2009), Stahley and Kodani (2011) found that streams draining parking lots have less diverse macroinvertebrate communities dominated by tolerant species, compared to streams in forest preserves. Using one volunteer group's data, the current study investigated how several streams' watersheds affected the health of their macroinvertebrate communities. The strength of that relationship, any emergent patterns in the communities' response to watershed damage, and the shape of the response curve were key matters of interest in this study.
When discussing the health of a stream's macroinvertebrate community, impervious surfaces and urbanization go together. Arnold and Gibbons (1996) reviewed the history of impervious surfaces in the United States and pointed out that imperviousness increased in the mid-twentieth century as roads were paved and that it became associated with areas having high population density. Interestingly, they even mention that imperviousness could be studied more widely in the future with geographic information systems (GIS), and subsequently, the emergence of better coverage and lower costs has enabled deeper investigation. In New England, percentage impervious surface area within a watershed was 96-98% correlated with urban intensity (McMahon and Cuffney 2000; Coles et al. 2010). In Maryland they were 94% correlated (Utz et al. 2009). Allan (2004) warned that urbanization is complex, and that it can bring with it a complex mix of many intertwined factors such as higher stream temperatures, a mix of toxins, and habitat changes. Although it is not completely synonymous with urbanization, imperviousness can be thought of as a simple environmental index that can summarize all the complexity that comes with urban development, with its mix of land uses, various ways of managing storm water, and diverse sources of pollution (Arnold and Gibbons 1996).
One pattern that regularly emerges from the literature is that as damage to the watershed increases, pollution-sensitive taxa such as mayflies, stoneflies, and caddisflies decrease, whereas tolerant taxa such as midges increase (Paul and Meyer 2001; Georgia Adopt-A-Stream 2009). In Utah, Gray (2004) reported that the abundance of sensitive macroinvertebrates decreased while tolerant species increased as the area around the Provo River urbanized over 24 years. In a detailed study of the Piedmont, Highlands, and Coastal Plain regions of Maryland, Utz et al. (2009) found that even different species of macroinvertebrates within the same order or family can respond to imperviousness differently, depending on their regional location. Most stoneflies (Plectoptera) were negatively affected by urbanization in the Coastal Plain and Piedmont, but less than one third of the nonbiting midge flies (Chironomidae) were. In the Atlanta metropolitan area, Gregory and Calhoun (2007) reported that stoneflies had the strongest negative response to urbanization of any single taxon in their study (Spearman's rank coefficient Rs -0.86), followed closely by beetles (Coleoptera, Rs -0.69) and mayflies (Ephemeroptera, Rs -0.66), whereas midges and dipterans actually increased (both Rs +0.68).
Despite the varying responses of individual taxa, macroinvertebrate community metrics universally show a strong negative response to watershed damage. Studying agricultural, mixed-agricultural, mixed-urban, and urban streams in the Piedmont region of Maryland, Moore and Palmer (2005) reported a strong negative relationship between impervious surface and taxa richness ([R.sup.2] = 0.70). Ourso and Frenzel (2003) report that the Hilsenhoff family-level biotic index (Hilsenhoff 1988), a rapid assessment protocol used by professional benthologists to quickly evaluate a stream, is 72% correlated to impervious surface area. Being designed for volunteers, Georgia Adopt-A-Stream's (2009) macroinvertebrate index (referred to as the water quality index or WQI) only requires taxonomic identification of macroinvertebrates to order, and assigns pollution tolerant species 1 point, moderately tolerant species 2 points, and intolerant species 3 points. Despite being designed for use by volunteers, Georgia Adopt-a-Stream's WQI has been occasionally used by ecologists in publications (Barnett et al. 2007; Stahley and Kodani 2011). This study used Georgia Adopt-A-Stream's macroinvertebrate index to investigate the strength of the relationship between a stream's health and the impervious surface of the surrounding watershed.
In addition, some previous studies indicated that watersheds can sustain a certain amount of damage from impervious surfaces--a threshold--before damage to macroinvertebrate communities occurs. This threshold is usually small. In reviewing literature, Paul and Meyer (2001) found that some studies reported a threshold between 10 and 20% impervious surface area. Ourso and Frenzel (2003) studied urbanizing watersheds in Alaska, and found that percent impervious area as little as 5% negatively affected several physical, chemical, and biological factors within a stream. In China, Wang et al. (2012) also reported a 5% threshold for impervious surface damage to a stream macroinvertebrate community. In their study of streams in the Piedmont region of north central Georgia, Roy et al. (2003) suggested that sensitive taxa are lost above 15% urban land cover. On the other hand, in a very thorough study of urban intensity and macroinvertebrates in New England watersheds around Boston, Coles et al. (2010) found that only one group, collector-gatherers, showed a threshold response, but other indices such as EPT, noninsect taxa, and tolerance values conformed to linear models. Allan (2004) hypothesized that the relationship between the biological condition of a stream and an anthropogenic gradient could be linear, nonlinear, or a threshold. A goal of this current study was to determine the nature of Georgia Adopt-A-Stream's WQI response to impervious surface.
MATERIALS AND METHODS
Twenty research sites within Clayton, Henry, and Spalding Counties in the south Atlanta metropolitan area were visited from January 2007 through September 2014 (Figure 1). All sites were on small, wadeable streams, in a variety of environments including forests, wetlands, suburban day-use parks, housing subdivisions, and parking lots. Sites were visited from 1 to 8 times.
Macroinvertebrate samples were collected using the methods outlined in Georgia Adopt-A-Stream's (2015) volunteer sampling protocols. D-frame nets were used for capturing macroinvertebrates in muddy bottom streams, and kick seines in rocky bottoms streams. Samples were sorted to either class or order, and although protocol only required reporting rare (1-9), common (10-99), or dominant ([greater than or equal to] 100) taxa, the actual number of individuals within each taxon found was recorded. Noting actual numbers of individuals allowed for calculation of indices such as the percentage of mayflies, stoneflies, and caddis, commonly referred to as EPT, as well as percentages of individual taxa. Because recent changes to the Georgia Adopt-A-Stream (2015) collection protocol made a distinction between case-building (sensitive = 3 points) and net-spinning caddis (somewhat sensitive = 2 points), it made sense to try calculating an index similar to EPT, excluding net-spinners, henceforth referred to as MSC. Only one EPT and one MSC were calculated for each site, pooling all the data from all the site visits. WQI, a macroinvertebrate index reflecting water quality, was totaled as follows: 3 points was assigned for the presence of each sensitive taxon, 2 points for somewhat sensitive taxa, and 1 point for pollution tolerant taxa (Table I; Georgia Adopt-A-Stream 2015).
In cases when sites were visited multiple times, a separate WQI was calculated for each visit. After counting, the live macroinvertebrates were returned to their stream. Specimens were preserved in ethanol only if needed for further study, and Voshell's A Guide to Common Freshwater Invertebrates of North America (2002) was used to confirm taxonomic identification. SRI's ArcGIS 10.0 geographical information system was used to delineate watersheds for each study site (ESRI 2011). A digital elevation model was available free of charge from the National Elevation Dataset (NED), which enabled creation of a three-dimensional map of the study area (U.S. Geological Survey 2016). Data for impervious surfaces was available for free from the National Land Cover Database (USGS 2014)--this map layer allowed quantification of the percentage of each watershed that was impervious to water. All of our macroinvertebrate data were entered into the Georgia Adopt-A-Stream database (2015) and are freely available to the public, as well as the locations, descriptions, and maps for each study site. Coordinates for each study site are included in appendix I.
The data, which consisted of the sites' WQI and the percent imperviousness of the associated watershed, were analyzed in Minitab 17 Statistical Software (2010). Simple linear and polynomial regression models were explored by examining residuals, significance testing, and forward stepwise curve fitting as per Zar (2010).
To understand how the macroinvertebrate communities related to impervious surfaces, taxa were examined first individually, then in groups, and finally as a whole assemblage. Individual taxa exhibited different relationships to impervious surfaces, and the more interesting ones are shown in Figure 2. Three taxa seemed to exhibit a maximum tolerance for imperviousness: case-building caddis (<17%), stoneflies (<27%), and clams (<40%). It should be noted that even below their apparent maximum imperviousness, these three taxa were greatly variable in their occurrence from site to site. A level of imperviousness below 27%, for instance, was not a guarantee of finding stoneflies, although they never appeared above this level. Other taxa, notably mayflies, net-spinning caddis, and midges, could be found sporadically in watersheds of low, medium, and high levels of imperviousness. Mayflies were present irregularly at all levels of imperviousness, but were less abundant in watersheds with highest imperviousness. Midges were also found at almost every study site, but when sites had greater than 22% imperviousness, they consistently made up between 12 to 40% of the associated communities.
Percent EPT, the traditional index used to indicate water quality in macroinvertebrate studies, did not exhibit any clear pattern with regard to imperviousness (Figure 3). MSC, which included mayflies, stoneflies, and only the case-building caddis, had a somewhat triangular distribution. At low imperviousness, MSC could be high, medium, or low, but as imperviousness increased it appeared that MSC diminished.
In addition to EPT and MSC, macroinvertebrates data were also grouped according to pollution tolerance and graphed against imperviousness (Figure 4). Tolerant and moderately-tolerant taxa were found in all of the sites, whereas intolerant taxa were absent from two sites, both of which had higher imperviousness.
The average macroinvertebrate WQI for study sites in this study ranged from 2.6 to 25.0 (Table II). Individual observations of WQI ranged from 0 to 25 (Table II). The water quality index measures the macroinvertebrate species richness at each study site, with pollution sensitive species receiving 3 points, somewhat-tolerant species receiving 2 points, and tolerant species receiving 1 point. Based on their average WQI, five of the sites rated as poor, seven were fair, another seven were good, and only one was excellent. Watershed imperviousness ranged from 3% to 53%. The watersheds for our sites varied greatly in size: Angel Creek at Reynolds Nature Preserve was the smallest at just 5 hectares, whereas Big Cotton Indian Creek at J.P. Mosely Park was the largest at 13,383 hectares.
For this study, there was no evidence for a meaningful relationship between WQI and watershed size, even when plotted as both a simple linear regression and quadratic regression (Figure 5). [R.sup.2] was only 0.16 for a linear model, and just 0.22 for curvilinear model. There were very few large watersheds sampled, but even for the smaller watersheds (those under 5,000 hectares in area), WQI ranged greatly and showed no apparent pattern. Multiple regression revealed that imperviousness was a significant factor, but watershed size was not (Table III).
When WQI was plotted against imperviousness, the residuals were nonnormal and followed a curvilinear trend, which suggested the possibility of a curvilinear function (Gotelli and Ellison 2013), and these issues were resolved with a quadratic model. Lowess regression of WQI against imperviousness produced a regression line similar to a quadratic function when F = 0.5 (the standard default for Lowess regressions) was selected (Appendix II). Stepwise regression (Zar 2010) was employed to find a polynomial equation (Table IV). First, a simple linear regression yielded a Y-intercept of 21.27 and a slope of -0.3452, both of which differed significantly from zero, so the null hypothesis was rejected, and both terms were determined to be important for the regression. In the second step, the coefficient of the [imperviousness.sup.2] term was tested and was also significantly different from zero. Lastly, in the third step, the imperviousness3 term did not reject the null hypothesis, meaning adding this term did not significantly improve the regression model, so the stepwise process was complete.
Table V shows the regression analysis for the quadratic equation. The Imperviousness term was not significant, but Zar (2010) recommends leaving this in the quadratic equation for the best fit line because it affects the calculation of residuals. With a probability of 0.009, the test for lack-of-fit rejected the null hypothesis of linearity. Four observations were identified as outliers, and their removal did affect the probability of the summary statistics. Removing the outliers decreased S, the standard error of the regression, from 4.74 to 3.65 (Frost 2014), R2 increased from 60.45% to 76.64%, and most interestingly, the test for lack-of-fit ended up with a probability of 0.065, thus confirming the quadratic model.
Some interesting trends appeared in the plot of WQI versus percent imperviousness (Figure 6). First, it is important to note that at each site, WQI was highly variable between site visits. The best fit line took a path which increased very slightly through the sites with imperviousness ranging from 3 to 8%, reached a peak WQI value of 17.4 at 8% imperviousness, and then decreased strongly as it moved through sites with higher imperviousness.
Interpretation of the Regression
These data, which included multiple observations over the study period for several of the sites, not only produced an [R.sup.2] value typical of all regressions, but also allowed for testing the goodness-of-fit. When the data in this study had 4 outlying observations removed, the sum of squares for the lack-of-fit test decreased by half and the associated probability rose to 0.065. It is therefore concluded that the quadratic model fit the data. Not only did WQI and impermeable surface have a strong relationship, but the quadratic model provided a better fitting line for the data than either the linear or cubic models, and provided a relatively high coefficient of determination ([R.sup.2]=0.77), and fit the curve nicely (Figure 6). Furthermore, including all of the data in the regression, with several individual WQIs for each site rather than averaging all of them to provide a single Y for each X, was the correct thing to do. Zar (2010, 349) points out that with more values of Y at each X, statistical power is improved. Alternatively, means that grouped all the observations for each study site could have been reported, thus eliminating all of the outliers, but this would result in fewer observations overall, with a loss of both information and the ability to test for linearity (Freund 1971; Zar 2010, 349). Naturally, the WQI for each site varied from time to time, and the S statistic, also known as the standard error of the regression, provided a clue as to how much. S was 3.65, which is about 30% of the overall average WQI of 11.8. About 95% of observations should fall within two times this value, which would be 7.3. Thus, the 95% confidence interval, being 7.3, was narrower than the value of the overall mean of 11.8--certainly a better situation than if it were wider. Still the WQI within each study site varied quite a bit over time, as evidenced by Hidden Valley (Table VI) which had a minimum WQI of 14 (fair) and a maximum of 27 (excellent). Even larger variation in WQI has been reported in another study in Georgia--Barnett et al. (2007) reported WQIs that ranged from 2 (poor) to 23 (excellent) for one particular site on the Alapahoochee River. The question of the effects of time, particularly of seasonality and year-to-year variation on a stream's macroinvertebrates, is a very valid one, but it will have to wait until enough data have been collected. With just 60 observations spread over nine years at 20 different sites, this particular set of data is not up to the task, but with more data, the question of these temporal factors could be answered.
So, if impervious surface cannot by itself entirely explain a site's WQI, then what else might contribute? Watershed size did not appear to affect WQI, as the very few large watersheds examined had WQI values well within the range of the many small ones (Figure 5), and a multiple regression analysis failed to detect size as a statistically significant factor (Table III). Another examination of individual taxa may provide a clue. In figure 2, it was clear that some macroinvertebrates were highly affected by imperviousness, and some were not. Despite being a "sensitive" taxon, in this study mayflies defied explanation and sometimes appeared where imperviousness was high. Anecdotally, my students and I found mayflies clinging onto branches within the stream with some degree of predictability. It is reasonable that the abundance of mayfly-harboring woody debris may be more reliably predicted by the presence of a protected stream buffer with a mature canopy, or perhaps even stream restoration efforts, rather than simple watershed imperviousness. Georgia Adopt-A-Stream recently introduced an in-stream assessment protocol, so future volunteer data will include a stream habitat score that will be based upon characteristics such as stream buffer, vegetative cover, and substrate variety. In addition to habitat quality, meteorological variables in the environment, such as temperature and rainfall, as well as in-stream changes in habitat such as erosion could change a stream's WQI from season to season and year to year.
The Relationship Between Impervious Surface and Macroinvertebrates
For this particular study, the relationship between impervious surface and the macroinvertebrate community index appeared to be curvilinear, with the vertex of the curve at 8% imperviousness. As such, these data supported Allan's (2004) hypothesis that a stream's condition could possibly respond in a nonlinear fashion to anthropogenic changes in the environment. Consistent with previous findings (Stahley and Kodani 2011), knowledge of streamside land use had some predictive power of the macroinvertebrate community for small watersheds, but it is impossible to accurately predict a site's macroinvertebrate index just by knowing its associated streamside habitat. With an [R.sup.2] of 0.632, the Georgia Adopt-A-Stream macroinvertebrate index correlates reasonably well with percent impervious area. This compared favorably with Ourso and Franzel's (2003) reported correlation index of [R.sup.2] = 0.7266 for the Hilsenhoff family-level biotic index (HFBI), a rapid assessment protocol, frequently used by professional benthologists to quickly evaluate a stream's health (Hilsenhoff 1988). This is also in agreement with Moore and Palmer (2005), who found macroinvertebrate diversity strongly related to percent imperviousness with their [R.sup.2] of 0.70. That so many studies have reported similar coefficients of determination again says that impervious surface must be important, but clearly it does not explain all of the variation in a stream's macroinvertebrate community.
Recall that, as to the question of a minimum threshold of damage to a macroinvertebrate community, the literature reports varying results. Moore and Palmer (2005), found no damage threshold in their study of Maryland streams, whereas Paul and Meyer (2001) report a threshold of 10-20%. Studies in China (Wang et al. 2012) and Alaska (Ourso and Frenzel 2003), suggest a 5% threshold, but both include several study sites having very low percent impervious area, approaching 0%. In this study, only three study sites had imperviousness less than 5%--the Panola Mountain watershed had 3% imperviousness, Pates Creek and Angel Creek both had 4%with WQI varying greatly for each of these sites. Several authors (Gotelli and Ellison 2013; van Emden 2008; Zar 2010) caution against drawing conclusions outside the range of predictors or X values used to construct a regression model, so caution is warranted. Although WQI clearly decreased when imperviousness exceeded 8%, the question of exactly what happens in Georgia watersheds with imperviousness between 0 and 8% still remains. More data are needed.
Recommendations for Future Studies
There is clearly a need for further studies, and there are specific ways that future efforts could be focused to improve the understanding of how watersheds affect macroinvertebrate communities. First, in order to decisively settle the question of how imperviousness relates to a stream's macroinvertebrate community, data from two types of watersheds are needed: those that have nearly 0% imperviousness, and those that have imperviousness above 48%. This study was not able to test for the X or Y intercepts, but future studies could be directed towards finding such watersheds of interest, targeting them for data collection with this goal in mind. Second, in order to increase statistical power and account for seasonal variation, quarterly macroinvertebrate sampling should be sought out and encouraged. Third, in-stream habitat scores should be reported whenever possible, as these could also be used in improvement of the regression model. Fortunately, Georgia Adopt-A-Stream has recently implemented a habitat assessment protocol, and data are beginning to be recorded.
Finally, this study made use of volunteer data, which generally seems to be under-utilized--a point also defended by Fore et al. (2001). Although professional grade metrics for macroinvertebrate communities incorporate greater taxonomic precision, this study suggests that the Georgia Adopt-A-Stream water quality index can provide a reasonable estimation of a stream's health when compared to impervious surface within a watershed. Volunteer protocols typically trade some taxonomic resolution to reduce the time and expertise needed to monitor a stream. Such a trade-off is a good one because storm water managers can use these data to highlight areas that need further investigation--a wise idea if fiscal resources for professional crews are limited. Additionally, by involving citizen-scientists, volunteer monitoring programs can help to increase awareness of stream and watershed health. Lastly, scientists would do well to remember that volunteer data are still data. Just as a jigsaw puzzle requires many tiny pieces to see a whole picture, there are some valid and important questions that science can answer only with data carefully collected by volunteers who care about their local streams.
The author thanks Georgia Adopt-A-Stream, Lake Spivey Rotary Club, Reynolds Nature Preserve, Henry County Storm Water Management Department, City of Griffin Storm Water Management Department, and Clayton State University for their cooperation and support of this study. The author also thanks his many research student for their help and inspiration, including (in chronological order) Anne Stahley, Brett Williams, Jennifer Webb, Denisse Iacobucci, Kevin Washington, Samantha Ortega, Johnny Ly, Chau Hau, Justin Agan, Crystal Seckendorf, Loc Bui, and Vickie Vo. Lastly, several people, including several anonymous reviewers provided very helpful comments that were crucial in the development of this manuscript.
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Coordinates of the Study Sites in UTM, Zone 16N,Number of Visits, Average, Minimum, and Maximum WQI Number Average Minimum SiteName Northing Easting of Visits WQI WQI Angel Creek 3721119 745984 6 16 13 Big Springs Park 3705074 765296 1 11 -- Camp Creek Bridge 3716489 770203 1 25 -- Coker Creek 3717014 763525 1 13 -- Crooked Creek 3720905 746083 1 14.5 6 CSU 3720628 747780 8 2.6 0 Gardner Park 3715856 756738 5 9 3 Griffin Golf Course 3681154 754486 1 6 -- Hidden Valley 3722614 758377 7 20 14 Indian Springs 3718286 747574 7 6 2 JP Mosely Park 3715000 763054 2 19.5 16 Lake City Hall 3721601 746345 3 3.7 2 Liberty Baptist 3717781 754281 2 12 7 Maddox Rd 3717998 749585 3 16.3 13 Panola Mtn SP 3724099 762857 2 22 22 Pates Creek Park 3709583 756304 1 19 -- Rum Creek 3711424 754930 1 17 -- Southlake Mall 3718353 745483 1 14 -- Stockbridge HS 3716788 759552 5 18.6 16 Maximum SiteName WQI Angel Creek 21 Big Springs Park -- Camp Creek Bridge -- Coker Creek -- Crooked Creek 23 CSU 4 Gardner Park 15 Griffin Golf Course -- Hidden Valley 27 Indian Springs 10 JP Mosely Park 23 Lake City Hall 5 Liberty Baptist 17 Maddox Rd 22 Panola Mtn SP 22 Pates Creek Park -- Rum Creek -- Southlake Mall -- Stockbridge HS 23
Lowess regression of WQI vsersus imperviousness. The Lowess regression process does not provide a model equation for the data, but it produced a curve-fitted line notably similar to the quadratic model when the default value of F = 0.5 was selected. F = 0.9 produced what amounts to two straight lines, whereas F = 0.1 yielded a seemingly haphazard pattern.
Christopher H. Kodani Clayton State University
2000 Clayton State Blvd., Morrow, Georgia, 30260 email@example.com
Table I. Pollution Tolerance and Points of Georgia Adopt-A-Stream's WQI (*) (Georgia Adopt-A-Stream 2015) Sensitive Taxa Somewhat Sensitive Taxa Tolerant Taxa (3 points) (2 points) (1 point) Stonefly Nymphs Common Net Spinning Caddisflies Midge Fly Larvae Mayfly Nymphs Dobsonfly/Hellgrammite & Fishfly Black Fly Larvae Water Penny Larvae Dragonfly & Damselfly Nymphs Lunged Snails Riffle Beetle Larvae Crayfish Aquatic Worms and Adults Crane Flies Leeches Aquatic Snipe Flies Aquatic Sow Bugs Caddisflies (Case- Scuds building) Clams & Mussels Gilled Snails (*) Water quality rating (WQI) was calculated as the sum of all categories: excellent > 22, good 17-22, fair 11-16, and poor < 11. Table II. Study Sites Ranked by Average WQI Percentage Average Site Water Quality Watershed Rank WQI Visits Rating Imperviousness 1 25.0 1 Excellent > 22 6 2 22.0 2 Good 17-22 3 3 20.0 7 10 4 19.5 2 17 5 19.0 1 4 6 18.6 5 23 7 17.0 1 17 8 17.0 1 9 9 16.6 6 Fair 11-16 4 10 16.3 3 38 11 14.5 2 9 12 14.0 1 33 13 13.0 1 7 14 12.0 2 32 15 11.0 1 53 16 9.0 5 Poor < 11 27 17 6.0 1 40 18 6.0 7 42 19 3.7 3 48 20 2.6 9 48 Watershed Name Rank (Size in ha) 1 Camp Creek (1,785) 2 Panola Mountain (97) 3 Hidden Valley (279) 4 JP Mosely Park (13,383) 5 Pates Creek (3,194) 6 Stockbridge HS (8,036) 7 Rum Creek (3,759) 8 Tussahaw Creek (5,849) 9 Angel Creek (5) 10 Maddox Road (929) 11 Crooked Creek (29) 12 Southlake Mall (1,133) 13 Coker Creek (28) 14 Liberty Baptist (2,410) 15 Big Springs Park (64) 16 Gardner Park (288) 17 Griffin Golf Course (73) 18 Indian Springs (69) 19 Lake City Hall (205) 20 Clayton State U (27) Table III. Multiple Regression of WQI versus Watershed Size and Imperviousness Source DF Adj SS Adj MS F-Value P-Value Regression 2 488.67 244.34 17.24 < 0.001 (*) Watershed Size 1 43.61 43.61 3.08 0.097 (*) Imperviousness 1 368.52 368.52 26.00 < 0.001 (*) Error 17 240.95 14.17 -- -- (*) Total 19 729.63 -- -- -- (*) (*) Indicates significant at [alpha] = 0.05 Table IV. Coefficients for Terms in the Stepwise Regression Regression Equation Term CoefficientSE Coefficient t-Value Linear Constant 21.27 1.30 16.42 Imperviousness -0.3452 0.0410 -8.42 Quadratic Imperviousness (2) -0.00950 0.00343 -2.77 Cubic Imperviousness (3) 0.000030 0.000320 0.09 Regression Equation P-Value Linear < 0.001 (*) < 0.001 (*) Quadratic 0.008 (*) Cubic 0.925 ([dagger]) ([dagger]) Note that the cubic term is not significant. (*) Indicates significant at [alpha] = 0.05
Table V. Regression Analysis for the Quadratic Equation Y = -0.00714 Imperviousness (2) + 0.046 Imperviousness + 18.10.
Source DF ADJ SS ADJ MS F-Value P-Value Regression 2 1955.86 977.929 43.56 < 0.001 (*) Imperviousness 1 1.61 1.609 0.07 0.790 (*) Imperviousness (2) 1 113.79 113.788 5.07 0.028 (*) Error 57 1279.74 22.452 -- -- Lack-of-Fit 16 633.99 39.624 2.52 0.009 (*) Pure Error 41 645.76 15.750 -- -- Total 59 3235.60 -- -- -- Model Summary: S = 4.74; [R.sup.2] = 60.45%; [R.sup.2] (adj) = 59.06%; [R.sup.2] (pred) = 55.83% Four outliers removed Y = - 0.0102 Imperviousness (2) + 0.167 Imperviousness + 17.92. Source DF ADJ SS ADJ MS F-Value P-Value Regression 2 2309.96 1154.98 86.92 < 0.001 (*) Imperviousness 1 19.01 19.01 1.43 0.237 (*) Imperviousness (2) 1 203.03 203.03 15.28 < 0.001 (*) Error 53 704.25 13.29 -- -- (*) Lack-of-Fit 15 296.16 19.74 1.84 0.065 (*) Pure Error 38 408.09 10.74 -- -- (*) Total 55 3014.21 -- -- -- (*) Model Summary: S = 3.65; [R.sup.2] = 76.64%; [R.sup.2] (adj) = 75.75%; [R.sup.2] (pred) = 74.04% (*) Indicates significant at [alpha] = 0.05
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|Author:||Kodani, Christopher H.|
|Publication:||Georgia Journal of Science|
|Date:||Mar 22, 2018|
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