Table 14. Preliminary model statistics for correlation of total phosphorus with continuous parameters at Dairy Creek at Highway 8 near Hillsboro, Oregon, 2002–04.

[Regression models are of the form TP = 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 TP is the dependent variable, total phosphorus, in milligrams per liter. Where TP is log transformed, a bias transformation factor (BCF; Duan, 1983) is multiplied by 10^(logTP) to get the final value. Data sets for correlation included: peak discharge samples from the autosampler deployment, plus monthly and high flow monitoring samples from Clean Water Services databases. Stage is used in place of discharge with the Clean Water Services data because discharge data are not provided by Oregon Water Resources Department when stage is greater than 10 feet. 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; –, not included in the regression]

Model No. and form	Model calibration								Model validation—Goodness-of-fit evaluation
	Value of coefficient, when used					Correlation statistics
	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, Q, SC)	0.021	-0.0008	0.009	-2.26	1.01	37	0.808	12.9	0.023	0.06	0.55	-2.1	0.49
2. logTP=f(Turb, SC)	0.018	–	0.009	-2.32	1.01	37	0.788	1.3	0.015	0.1	0.38	-4.9	1.8
3. logTP=f(Turb, Q)	0.017	-0.001	–	-1	1.01	37	0.535	12.7	0.025	0.05	0.08	-0.86	3.5
4. logTP=f(Turb)	0.012	–	–	-1.03	1.02	37	0.503	–	0.005	0.04	0.00	-0.09	2
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. logTP=f(SC)	–	–	0.003	-1.35	1.01	19	0.557	–	-0.001	0.04	0.27	0.26	2.2
6. logTP=f(Turb, SC)	-0.012	–	0.004	-1.32	1.01	30	0.711	1.0	-0.0006	0.04	0.15	0.07	3.2
7.logTP=f (Q, SC)2	–	-0.00007	0.004	-1.44	1.02	31	0.683	1.1	-0.0008	0.03	0.18	0.14	3.2
8. logTP=f (Stage, SC)3	–	0.004	0.004	-1.45	1.04	39	0.375	11.4	-0.002	0.03	0.20	0.17	1.6
9. logTP=f(Turb, Stage, SC)	-0.006	-0.007	0.003	-1.22	1.01	19	0.533	1.2	-0.002	0.04	0.04	-0.1	2.9

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

² High discharge (and accompanying samples) excluded, where stage greater than 10 feet.

³ High stage data available. Note increase in number of samples. Residuals wide-spread for high stage samples.

First posted June 18, 2010