USGS Scientific Investigations Report 2010–5008 Use of Continuous Monitors and Autosamplers to Predict Unmeasured Water-Quality Constituents in Tributaries of the Tualatin River, Oregon

Table 15. Preliminary model statistics for correlation of Escherichia coli bacteria with continuous parameters at Dairy Creek at Highway 8 near Hillsboro, Oregon, 2002–04.

[Regression models are of the form E. coli = a*Turb+ b*Q + c*SC + d, where a, b, and c are model coefficients and d is the intercept, Turb, Q, and SC are the explanatory variables turbidity (in Formazin Nephelometric Units), discharge (in cubic feet per second), and specific conductance (in microsiemens per centimeter), respectively, and E. coli is the dependent variable, in colonies per 100 milliliters. Where E. coli is log transformed, a bias transformation factor (BCF; Duan, 1983) is multiplied by 10^(log^{E. coli}⁾ to get the final value. Model 7b was not included in the model selection scheme because stage and discharge are surrogates for one another, but model 7b was built separately to evaluate the use of stage as an independent variable to compensate for backwater effects on discharge at the Dairy Creek site. RMSE values are in colonies per 100 milliliters. The maximum Variance Inflation Factor (VIF) indicates the largest VIF obtained for any one variable in the correlation. Abbreviations: E. coli, Esherichia coli bacteria; n, number of samples; Adj.-R², adjusted R², a coefficient of determination which adjusts for degrees of freedom and penalizes the use of too many explanatory variables; f, a function of indicated constituents; log, base 10 logarithm; RMSE, root mean square error; NA, VIFs are not applicable because only one independent variable was used]

Model No. and form	Model calibration								Model validation—Goodness-of-fit evaluation
	Value of coefficient, when used					Correlation statistics			Model validation—Goodness-of-fit evaluation
	a	b	c	d	BCF	n	Adj.-R²	Maximum VIF	Mean error	Validation RMSE	Coefficient of determination	Nash-Sutcliffe coefficient	z-statistic from sign test
Scenario 1	Calibration data set—Autosamplers only								Validation data set—Clean Water Services ambient monitoring data
1. logE. coli =f(Turb, SC)	0.035	–	-0.025	5.14	1.05	37	0.871	1.3	185	694	0.10	-4.1	0.31
2. logE. coli =f(Turb, Q, SC)	0.036	-0.0001	-0.025	5.15	1.05	37	0.867	2.9	118	735	0.09	-3.3	0.63
3. logE. coli =f(Q, SC)	–	0.005	-0.029	5.71	1.12	38	0.715	1.2	11	653	0.10	-2.4	1.1
4. logE. coli =f(Turb)	0.049	–	–	1.69	1.1	37	0.695	NA	-122	331	0.01	-0.15	0.93
Scenario 2	Calibration data set—Peak autosampler plus first monthly and high flow monitoring samples from Clean Water Services dataset								Validation data set—Remaining monthly Clean Water Services ambient monitoring + non-peak autosampler data
5. logE. coli =f(SC)	–	–	0.013	0.713	1.29	17	0.342	NA	94	567	0.02	-3.2	1.2
6. logE. coli =f(Turb, SC)	0.017	–	0.013	0.497	1.45	17	0.309	1.0	161	667	0.03	-4.8	2.4
7a. logE. coli =f(Q, SC)	–	-0.0004	0.011	0.981	1.37	16	0.378	1.2	19	329	0.02	0.13	1.8
7b. logE. coli =f(Stage, SC)	–	-0.0001	0.011	0.828	1.36	32	0.391	¹1.4	-2	331	0.02	0.21	0.9
8. logE. coli =f(Turb, Q, SC)	0.017	0.00001	0.013	0.494	1.45	17	0.256	¹1.2	71	338	0.07	-0.26	2

¹ Exceeds a threshold VIF value, calculated as {1/(1– (Adj.-R²)} and indicates possible multicollinearity.