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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
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.

First posted June 18, 2010

For additional information contact:
Director, Oregon Water Science Center
U.S. Geological Survey
2130 SW 5th Ave.
Portland, Oregon 97201
http://or.water.usgs.gov

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