TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters



## Appendix B-12: Multiple Regres sion Model for Stream SCITSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters

B12-1 

### Appendix B-12. Multiple Reg ression Model for Stream SCI Multiple regression models can effectively model the extent to which different environmental factors (e.g., nutrient concentra tions, habitat quality) account fo r variations in the stream condition index (SCI). Predictions from such models can then inform nutrient criterion decisions.

Concurrent measurements of SCI and different environmental factors were provided by the Florida Department of Environmental Protection (FDEP) in the Excel file “Stream file2 for Xufeng_021009.” Samples were collected at 249 dis tinct stations, coded as different STORET numbers. One to three samples were colle cted from each station. To characterize the environmental conditions at each station, averages were calculated over all samples at a given site for the following measurements: log total nitrogen (TN), log total phosphorus (TP), log specific conductivity, habita t score, log color, and pH. Each station was also characterized by its geographic location (degrees la titude and longitude) and by a Landscape Disturbance Intensity Index (LDI). Once average conditions at each stat ion were calculated, they were combined with individual sampled values of SCI, giving a to tal of 344 samples with complete environmental and biological data.
The strengths of correlation betw een most environmental variable s were moderate (Table B12- 1). As expected, log TP and l og TN were strongly correlated ( r = 0.52).
Because log TP and log TN were strongly correlated, their relati onships with SCI were modeled separately by fitting two multiple regression mode ls. Each model included either log TP or log TN plus all the other covariates for which da ta were available as explanatory variables.
Model results for log TN:

Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 78.67225 63.96867 1.230 0.21961 logtn -10.74999 3.90684 -2.752 0.00625 ** hab 0.26784 0.04349 6.159 2.1e-09 *** LDI -0.94130 0.58045 -1.622 0.10582 pH -0.01423 1.49463 -0.010 0.99241 LONGITUDE 0.65861 0.74644 0.882 0.37823 LATITUDE 0.06150 0.87522 0.070 0.94402 logcond -8.53654 3.55382 -2.402 0.01685 * color 2.27513 2.57929 0.882 0.37837

--- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 14.4 on 335 degrees of freedom Multiple R-squared: 0.3704, Adjusted R-squared: 0.3554 F-statistic: 24.63 on 8 and 335 DF, p-value: < 2.2e-16TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters

B12-2 Model results for log TP:

Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 66.31642 64.53766 1.028 0.30490 logp -0.19659 1.92279 -0.102 0.91863 hab 0.26958 0.04423 6.095 3.01e-09 *** LDI -1.08353 0.58908 -1.839 0.06675 . pH 0.60466 1.52958 0.395 0.69286 LONGITUDE 0.56124 0.75620 0.742 0.45850 LATITUDE 0.40722 0.87909 0.463 0.64350 logcond -10.77206 3.49839 -3.079 0.00225 ** color 0.15219 2.64265 0.058 0.95411

--- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 14.56 on 335 degrees of freedom Multiple R-squared: 0.3562, Adjusted R-squared: 0.3408 F-statistic: 23.17 on 8 and 335 DF, p-value: < 2.2e-16
In both models, the relationship between SCI and habitat score (hab) and log conductivity (logcond) was significantly different from zero. Log TN (logtn) also was significantly associated with SCI ( p < 0.01), whereas log TP was not.

The R 2 values for both models were not high ( R 2 = 0.37 and 0.36); however, the degree to which the models accounted for variability in SCI should be interpreted with resp ect to the variability that one expects to explain with environmental variables. More specifically, SCI values calculated from samples collected from the same site are known to vary substantially. In a different analysis, the standard deviation of this within-site variability of SCI values was estimated as 13.4 (FDEP 2007, page 23). This with in-site variability cannot be explained by differences in environmental conditio ns across sites, and therefore the R 2 value should be adjusted to account for k nown, within-site variance.

R 2 values can be adjusted to account for within- versus across-site variance by decomposing the total observed variance in SCI values. The total observed variance of SCI observations in the data set was 321.5. Of this variance, 179.6 (i.e., 13.4 2 ) can be attributed to within-site variance, leaving an across-site variance of 141.9 to be ex plained by the regression models. In the log TN model, the variance explained by the model can be calculated by s ubtracting the variance of the residuals (202.4) from the total observe d variance (321.5), giving 119.1. Then, an R 2 value that expresses the proportion of the across-site variability that is explained by the model can be computed as the variance explained by th e model divided by the across-site variance: 119.1/141.9 = 0.84.
In the log TN model, both habitat score and l og conductivity were signifi cantly associated with SCI values, and therefore sele cting a TN criterion value to achieve a minimum SCI value requires that one assume repres entative values of conductivity and habitat score. FDEP has determined that SCI = 40 is a threshold above which sites meet their designated use for supporting aquatic life. This SCI threshold can be used with the regression model shown above to compute candidate TN criterion values. First, values for predictor variable that were not statistically significant (i.e., LD I, pH, latitude, longitude, and color) are fixed at their mean values, and SCI is fixed at 40, giving the following equation:TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters

B12-3 mean mean mean mean mean Color Cond Latitude Longitude pH LDI Habitat TN log28.2

log54.8 0615.0 659.0 0142.0 941.0 268.0log7.107.7840



  

   

This equation can be simplified to

Cond Habitat TN log54.8 268.0log7.107.2740

  
If one specifies a habitat score and a log conductivity in this e quation, a log TN criterion value can be calculated that, on average, is associated with SCI = 40. This calculation is summarized in Figure B12-1, where the symbols indicate observed values of habitat scor e and log conductivity, and the contour lines indicate TN criterion values associated with SCI = 40 and with a particular combination of habitat score and log conductivity va lue. Each contour line is labeled by a log TN value, which can be interpreted as a candidate crit erion value. Each contour line is also labeled in parentheses with the percentile of the observed TN distributi on represented by the candidate criterion value. For example, approximately 55% of observed TN values in the data set were less than log TN = 0 (TN = 1 mg/L).
In the upper left quadrant of th e plot, conductivity values are high and habitat scores are low, both of which were associated with reductions in SCI value. Consequently, the log TN values required to achieve SCI = 40 for these sites were very low. Estimated candidate criterion values for log TN in these sites were less than one, a concentration lower than any concentration observed in the data set.

Table B12-1. Correlations between Environmental Variables log TP log TN log cond Habita t log color LDI Latitude Longitude log TN 0.52 log cond 0.38 0.32 Habitat -0.27 -0.12 -0.29 log color 0.26 0.39 -0.21 0.15 LDI 0.28 0.14 0.38 -0.69 -0.27 Latitude -0.36 -0.38 -0. 61 0.25 -0.06 -0.27 Longitude 0.41 0.45 0.56 -0.07 0.3 0.16 -0.66 pH 0.25 0.04 0.77 -0.3 -0.48 0.37 -0.42 0.29TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters

B12-4 Figure B12-1. Observed values of habitat score versus log( conductivity). Cont ours indicate candidate TN criterion values associated with each combination of habitat and conductivity values. The percentile of the obser ved TN distribution associated with each candidate criterion value is shown in parentheses.