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 11. Preliminary model statistics for correlation of total phosphorus with continuous parameters at Fanno Creek near Durham, Oregon.

[Regression models are of the form TP = a*Turb+ b*Q + c*SC + d, where a, b, and c are regression 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 TP is the dependent variable, total phosphorus concentration, in milligrams per liter. In some models, as indicated by the model form column, the dependent or explanatory variables were log transformed. Where TP is log transformed, a bias transformation factor (BCF; Duan, 1983) is multiplied by 10^(logTP) to get the final value. RMSE values are in milligrams per liter. 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; USGS, U.S. Geological Survey; –, 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. logTP=f(Turb, SC)	0.007	–	0.003	-1.63	1.01	54	0.893	1.3	-0.003	0.075	0.24	-0.1	1.1
2. logTP=f(logTurb, logSC)	0.752	–	2.05	-6.47	1.02	54	0.813	1.7	-0.039	0.092	0.05	-0.67	5.2
3. TP=f(Turb, SC)	0.004	–	0.001	-0.2	–	54	0.905	1.3	-0.007	0.072	0.20	-0.01	1.3
Scenario 2	Calibration data set—Complete autosampler storm samples + USGS 2001–07								Validation data set—Clean Water Services ambient monitoring data
4. logTP=f(Turb, SC)	0.006	–	0.002	-1.34	1.03	140	0.645	1.7	-0.008	0.064	0.29	0.19	1.7
Scenario 3	Calibration data set—Peak autosampler plus first monthly and high flow monitoring samples from USGS and Clean Water Services datasets								Validation data set—Remaining monthly low flow USGS + Clean Water Services ambient monitoring + non-peak autosampler data
5. logTP=f(Turb, SC)	0.005	–	0.001	-1.19	1.02	99	0.575	¹1.6	-0.02	0.067	<0.01	-0.14	3.1
6. logTP=f(Turb, Q, SC)	0.005	-0.00003	0.001	-1.18	1.02	95	0.582	¹2.0	-0.021	0.067	<0.01	-0.16	4

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