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 13. Preliminary model statistics for correlation of total suspended solids with continuous parameters at Dairy Creek at Highway 8 near Hillsboro, Oregon, 2002–04.

[Regression models are of the form TSS = 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 TSS is the dependent variable, total suspended solids, in milligrams per liter. Where TSS is log transformed, a bias transformation factor (BCF; Duan, 1983) is multiplied by 10^(logTSS) to get the final value. The maximum Variance Inflation Factor (VIF) indicates the largest VIF obtained for any one variable in the correlation. Abbreviations: 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; –, not included in the regression]

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. logTSS=f(Turb)	0.025	–	–	0.709	1.03	38	0.704	–	-2.2	5	0.07	-0.16	3.5
2. logTSS=f(Turb, Q)	0.019	0.002	–	0.642	1.02	38	0.745	2.1	-3.9	6.1	0.10	-0.57	5.2
3. logTSS=f(Turb, SC)	0.025	–	0.0009	0.696	1.03	38	0.695	1.4	-2.2	5	0.06	-0.17	3.5
4. logTSS=f(Turb, Q, SC)	0.019	0.002	0.0009	0.524	1.02	38	0.738	¹2.3	-4	6.3	0.03	-0.64	5
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. logTSS=f(Turb)	0.051	–	–	0.415	1.02	20	0.758	–	0.07	4.6	0.06	0.06	2.5
6. logTSS=f(Turb, Q)	0.051	0.0001	–	0.396	1.02	20	0.757	¹2.7	-0.49	4.9	0.13	0.08	1
7. logTSS=f(Turb, SC)	0.053	–	0.0007	0.304	1.02	20	0.754	1.1	-1.4	4.6	0.14	0.04	1.3
8. logTSS=f(Turb, Q, SC)	0.054	0.0002	0.0009	0.251	1.02	20	0.758	1.3	-1.5	4.9	0.19	0.11	1.6

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