Discussion

The use of continuously measured parameters as surrogates for unmeasured constituents, including real-time applications, has increased in recent years. Rasmussen and others (2008) published regression models for 19 constituents, including whole-water and dissolved solutes such as various major ions (calcium, magnesium, and sulfate) nutrients, and bacteria (bacteria, fecal coliform, and enterococcus) at 5 sites in Kansas. The program in Kansas has been successful enough that results of the regression predictions are posted online in real time, and coefficients of determination for the regression models mostly range from about 0.6 to greater than 0.9. However, the streams in Kansas, which are known to consistently carry appreciable sediment loads and to have relatively steady flow, are different from Tualatin River tributaries in Oregon. In the Tualatin River basin, most streams are considerably smaller than the streams monitored in Kansas and many have rapid, short-term responses to rainfall runoff (due to their highly urbanized upstream land uses) or highly variable streamflows (given the prolonged dry climate in summer and prolonged wet periods in winter). It was not clear, therefore, that the modeling approaches taken in Kansas and elsewhere could be successfully applied in the Tualatin River basin.

Given the uncertainty over application of the predictive regression techniques to conditions in the Tualatin River tributaries, this study followed a proof-of-concept approach. Regression models and predictions were developed for this report as examples of the type of results that could be obtained for selected Tualatin River tributaries, if additional data were collected to better represent the range of conditions at those sites. Although all the sites (target and non-target) in the study are considered important for management of non-point runoff, the target sites (on Fanno Creek and Dairy Creek) were selected for detailed analysis because they represent land use types (urban and agricultural, respectively) of interest from a management standpoint. Furthermore, additional stream-chemistry data were available for these sites from Clean Water Services (and for Fanno Creek, from USGS) beyond the temporary autosampler deployments used in this study. However, the resulting regression models for these sites are considered preliminary because the available data do not adequately represent the range of conditions expected at these sites, particularly high flows that often lead to high concentrations and loads. Therefore, several models are shown and discussed for each site, any of which could, with sufficient additional data, become the most useful model form for predicting the indicated parameter. Water-quality constituents associated with suspended particulates, notably TSS, TP, and E. coli bacteria, were modeled (as dependent variables) because they are the constituents of greatest interest to local regulators and resource managers, and because they may be most effectively modified through land use management, whereas dissolved constituents such as nitrate or phosphate may be more controlled by groundwater and microbiological processes.

Neither historical dataset (from Clean Water Services and USGS) was originally collected for the purposes used in this report, so neither dataset represented optimal input data for calibration or validation of regression models. High-flow conditions, which in particular cause high concentrations and loads of TSS, TP, and E. coli bacteria, are under-represented. The regression models and coefficients discussed in this report, therefore, are considered examples or starting points for future modeling efforts. Furthermore, the aggregation of data from multiple laboratories that was done for Fanno Creek introduced additional uncertainty, particularly for predictions of TSS, for which the input calibration and validation datasets used a combination of TSS analysis from Clean Water Services and suspended sediment concentration analysis from USGS laboratories. No data were available upon which to base any adjustment of USGS suspended sediment concentration data to compare with the TSS analysis by Clean Water Services. Any inherent differences were incorporated into the regression model uncertainties and the magnitude of the prediction intervals.

Several sites in the Tualatin River basin continuously measure streamflow and stream stage, and water‑quality monitors collect temperature, specific conductance, dissolved oxygen, pH, and turbidity data, and, at some sites, chlorophyll a (see http://or.water.usgs.gov/tualatin/monitors/). Of these, specific conductance, turbidity, and streamflow most directly indicate short-term physical changes in the stream that may result in water-quality changes, and are the most likely candidates to be used as surrogates for water‑sample chemical data. Seasonality also was explored with the incorporation of sine and cosine transformations of sample date.

Most results from the regressions for the highly urbanized Fanno Creek site were consistent with findings from Anderson and Rounds (2003), who determined that TSS from three sites in Fanno Creek was significantly correlated with several parameters, including discharge, turbidity, and total dissolved solids (a surrogate for specific conductance). Similarly, TP was significantly correlated with total dissolved solids and turbidity, and E. coli bacteria was significantly correlated with turbidity. In this study, models for TSS, TP, and E. coli bacteria were primarily a function of turbidity, with discharge and specific conductance typically having various influences on the models. Despite sometimes impressive adjusted-R² values for model calibration, the goodness-of-fit statistics from the model validation exercise generally reflected poor agreement with the validation datasets. This poor agreement with the validation datasets was particularly true for the Nash‑Sutcliffe coefficient, a measure of model errors that is more stringent than the coefficient of determination for the model. The validation datasets in this study, however, are primarily composed of low-flow samples and do not adequately evaluate the response of the models to high flows, so the actual fit during these conditions is unknown.

Results from Dairy Creek at Highway 8, with primarily undeveloped or agricultural land upstream, were equivocal and likely reflect the limited dataset. No data were available from routine or sporadic studies by the USGS (unlike at Fanno Creek), and no winter data were available for any of the independent variables except stage during 2002–04. Furthermore, backwater conditions at Dairy Creek during late autumn and winter may have a major effect on any correlations that involve discharge and may necessitate separate models for free-flowing as opposed to backwater flow regimes at that site. Using discharge as an independent variable at these high stages would require a different method of stream gaging (for example, measuring stream velocity and deriving a rating for velocity with discharge). Velocity also may be a useful independent variable at this site. The slower velocities associated with backwater produce much less turbulence than the faster velocities associated with unimpeded streamflow thus affecting the quantity of suspended sediment and other particulates. Therefore, correlations of streamflow, turbidity, or specific conductance with TSS, TP, E. coli bacteria, and other parameters likely would be different under backwater conditions. The effect of backwater on correlations with dissolved constituents such as orthophosphorus or nitrate-nitrogen may depend on its effect on different sources such as groundwater discharge at high stage. For example, redox or other conditions in temporarily saturated soils could cause changes in the release of nutrients, dissolved minerals, or dissolved organic carbon (which could affect turbidity and specific conductance) if backwater conditions are prolonged.

The lack of significance of sine and cosine terms in any of the regression models may indicate that the other independent variables inherently capture most of the seasonal signal contained in the data. To the extent that seasonal processes such as riparian or upland growth would affect runoff patterns, the continuous records of turbidity, specific conductance, and discharge also should reflect these factors and may more directly measure the indirect seasonal patterns. Additionally, Dairy Creek, with its larger upstream area of agricultural land use and pervious surfaces, generally would be more susceptible to seasonal patterns than Fanno Creek; however, regression modeling was less successful overall at this site than at Fanno Creek. The lack of appropriate high‑flow data and difficulties with backwater may have caused problems with the regression-based models at the Dairy Creek site that masked sine- or cosine-dependent seasonal patterns. Finally, dissolved constituents that are more directly functions of biological processing may be more likely than TSS and TP to exhibit seasonal fluctuations (for example, nitrate production from nitrification, or dissolved orthophosphate uptake during primary production; Anderson and Rounds, 2003). For future modeling efforts, particularly those involving dissolved chemical species, seasonal aspects should be evaluated using sine and cosine terms as independent variables.

Using the Regression Equations

Assuming future development of regression models is successful for some constituents at sites in the Tualatin River basin, the models can be used in several ways. The primary expected use is to evaluate peak concentrations in the modeled streams in response to hydrologic events, and thereby anticipate related water-quality effects or conditions in the mainstem Tualatin River. To fully evaluate effects on the Tualatin River, constituent loads (in mass per year) exported from the tributaries should be calculated or estimated as well; a simple matter if the monitoring station and a streamflow gaging station are located together (for example, Uhrich and Bragg, 2003). Regulators may compare predicted concentrations with benchmarks such as regulatory criteria or TMDL-based requirements, but model uncertainty (for example, the range of possible concentrations indicated by prediction intervals around a given predicted value) should be considered in any such comparison. Water managers may also wish to evaluate predicted concentrations as a potential response of stream restoration or other land-use management changes in the drainage basin. After several years of data collection and iterations of model calibrations, it may be possible to use such models to detect trends in water quality over time. If model coefficients or functional forms change consistently over time in ways that are insensitive to simple increases in the number of samples available for calibration, then such changes could indicate new or reduced sources, steady changes in the association of a particular constituent with another, or other process-based changes in the drainage basin. For example, model forms at a site that are constant for TSS but that have declining coefficients for turbidity in a TP model could indicate that the source of TP has changed and may be less dependent on suspended particulates.

Suggestions for Future Study

The initial plan for this study was to use autosamplers, deployed in conjunction with, and potentially triggered by, continuous monitors to collect high-density data over the course of several storms at individual sites, six of which had been identified in the larger tributaries to the Tualatin River. These deployments would provide data spanning a broad range of environmental conditions and that could be used to establish initial regression models. The planned sampling was limited, however, by available resources such that only two sites could be sampled for each storm; furthermore, the sampled storms proved to be relatively small and did not produce the desired range of hydrologic responses in the sampled streams. Additional constraints were imposed by limited, seasonal deployments of the continuous monitors at some sites, resulting in fewer continuously monitored data being collected with autosamplers at the highest streamflows. Streamflow or stage was not directly available at two sites (Beaverton and Rock Creeks), and was subject to backwater at another site (Dairy Creek at Highway 8), so only a few measurements were available for use as a surrogate for those sites.

Site Considerations

To build on the findings from this study, several considerations could improve data collection procedures and help select locations at which success would be most likely. These include

1. Permanent or long-term installations of equipment such as streamflow and stream-stage sensors, continuous monitors, and (or) autosamplers, during all seasons and streamflow conditions, and maintenance of stage discharge rating curves and electronic databases for streamflow and continuous monitors under high and low streamflow conditions. When streamflow cannot be directly monitored at a site, estimation of discharge from upstream or nearby gaging stations requires a more thorough approach than the simple summation and routing that was used at some non-target sites in this study;
2. Availability of telemetry or other remote communication with monitors and autosamplers to enhance the quality of monitor data, reduce downtime, anticipate stream conditions that might result in autosamplers triggering, and allow determination of the status of sample collection. Such communication, together with currently available database software, allows the real-time display of calculated concentrations, loads, and prediction intervals in other locations around the Nation (for example, see http://nrtwq.usgs.gov/ks/);
3. Avoidance of backwater conditions that may render regression models inapplicable under certain situations; alternatively, the development of models that apply seasonally or under specific streamflow conditions;
4. Avoidance of local influences that do not adequately represent drainage basin conditions, but which may exert disproportionately strong influence on water quality at the sampling or monitoring sites, such as nearby tributary inputs, localized erosion or other sediment sources, point sources, or impoundments.

Samples were collected from Fanno and Dairy Creeks and several additional sites. Regression models were not explored for these additional sites, however, because insufficient storm data were available for 2002-03, or other individual considerations, and because water managers were more interested in Fanno and Dairy Creek. Chicken Creek did not respond readily to storms during the period of study, and seemed to have a groundwater-dominated hydrologic response that resulted in low concentrations of suspended materials. Likewise, Gales Creek at Old Highway 47, with a primarily forested upstream drainage basin, did not show a substantive hydrologic response to storms during periods of monitor deployment. Beaverton and Rock Creeks did not have stream gages at the same sites where the monitors and autosamplers were deployed, and efforts at simple mass‑balance routing of streamflow from upstream gaging stations, including tributaries, were unsuccessful for the purposes of this study. Within a short distance upstream of the Rock Creek sampling site, a streambank was actively eroding during high-flows, and that episodic contribution of suspended sediment may not have been representative of upstream sediment and chemistry sources. Although these streams may be subjects of future studies, careful selection of sampling locations and equipment installation will be needed to provide data of sufficient seasonality and quality for successful development of regression models.

Autosamplers

Autosamplers allow the collection of unattended samples during inconvenient times or unsafe conditions and the collection of time-series samples over the course of a storm hydrograph. However, autosamplers are expensive and require maintenance (for example, for intake clogging, battery and ice replacement, and programming). They also have sampling reliability issues (for example, inadvertent triggering when the stream hydrograph does not match the desired pattern, [that is, false starts], or conversely not triggering when the stream response should have dictated the desired sampling), and quality assurance concerns. As a result, although autosamplers can change the types and frequency of samples collected and make certain sample-collection schedules logistically possible, they do not necessarily reduce the expense of sampling. Finally, the use of multiple samples collected during a few storm hydrographs for regression modeling may result in serial correlation issues, artificially inflating the value of coefficients-of-determination (R²) for regression models, and indicating a level of model robustness that may not be warranted.

Despite these issues, autosamplers can be highly useful for developing a robust dataset for refining the regression models started in this study. Primary uses for autosamplers could include

1. Unattended sampling at nights, weekends, or other situations that are difficult to sample manually;
2. Sampling in streams with rapid hydrological responses, when it may be difficult to get to the site before the peak discharge;
3. Collecting enough samples during a storm hydrograph, together with continuous monitor or streamflow data, to allow screening for key samples for laboratory submission, on the basis of peak discharge or turbidity values;
4. Collecting samples at multiple sites during a single storm, if enough autosamplers are available for deployment;
5. Collecting samples from locations that are inconvenient or unsafe for human sampling, such as manholes or culverts; and
6. Exploring within-storm variability of selected water-quality constituents, such as comparing constituent concentrations as streamflow increases and decreases during storms.

Quality assurance data collected for this study indicate that autosamplers can be used for collection of representative samples in Tualatin River basin streams, but additional tests during high streamflow conditions and at additional sites are warranted. Appropriate tests include evaluation of sample holding times, especially for bacteria and during warm weather, additional determination of cross section coefficients at high flows and at various sampling sites, and additional tests of equipment contamination or carryover when sample tubing has been deployed for extended periods.

Water Sample Collection

Historical data from USGS and Clean Water Services databases were helpful for evaluating whether or not useful regression models can be developed for Fanno Creek, Dairy Creek, and elsewhere. These databases extended the range of conditions represented in the models, increased the number of samples and thereby the degrees-of-freedom of the regressions, supported the use of several scenarios of data aggregation to better understand the constraints of available data, and allowed validation of the developed models with independent data not used for model calibration. The historical data were collected to meet other objectives, however, and therefore were not as useful in this study for predictive purposes as might be desired. The primary limitation was the lack of samples collected during storms or other high-flow periods. Clean Water Services data were collected in a routine manner as part of an established ambient monitoring program, during which samples were sometimes collected during storm runoff, but collection was not designed specifically for those conditions. USGS data collection at Fanno Creek was mostly routine, although several additional high-flow samples had been collected as part of other studies (see Anderson and Rounds, 2003). No historical USGS data that could be used for this study were available from Dairy Creek near Highway 8. Also, USGS data did not include E. coli bacteria so regression models for bacteria had fewer samples to use. Additional uncertainty may have been introduced to the Fanno Creek analysis by combining analytical results from USGS and Clean Water Services databases, representing different laboratory methodologies—most likely for the suspended sediment concentration and total suspended solids data, which could not be compared because of a lack of available data from concurrent samplings.

To build on the models initiated in this report, and to develop robust regressions that can be useful for understanding concentrations and (or) loading of water-quality constituents, additional high-flow samples are needed to extend the range of conditions represented. The baseline conditions are well represented in the available data (for example, figure 3), and probably can be easily predicted. The models discussed in this report do a reasonable job of predicting a range of baseline conditions, especially for Fanno Creek, such that routine sample collection could theoretically be scaled back (regulatory considerations aside) with minimal loss of understanding of stream conditions.

Although redesigning the Clean Water Services ambient monitoring program is beyond the scope of this report, the simple addition of several samples each year from high flow conditions would allow the model results from this study to be revisited and improved upon, particularly if those samples included the most extreme conditions. If the use of surrogates for predictive modeling as outlined here were the sole objective of a modified sampling plan, at least for selected sites, it might include elements such as

1. Reducing the routine sampling frequency at each site to twice-monthly intervals, especially during low-flow periods;
2. Installing autosamplers that are designed to capture instantaneous (not flow-weighted) samples during storms, thus allowing the selection of samples for laboratory analysis (based on streamflow or turbidity, for example), and sampling during weekends and evenings, ideally with remote interrogation or activation capabilities;
3. Sampling of selected storms manually, particularly the most extreme events each year, with an added focus on collecting cross sectional data for evaluating the representativeness of the autosampler’s intake location;
4. Evaluating analytical procedures, especially for E. coli bacteria, to ensure that resulting data will meet the needs of model development;
5. Developing predictive models for other stream constituents, such as chlorophyll, dissolved orthophosphate, or nitrogen either as total nitrogen, nitrate-nitrogen, or ammonia-nitrogen; and
6. Considering additional independent variables such as continuously monitored water temperature, optical measurements of chlorophyll or ultraviolet fluorescence, or local precipitation data.

Model Development and Selection

Log transformation of dependent variables was an important step in the development of most predictive models for this study, an approach that is similar to those from other studies. Distributions of many environmental parameters are log-normal in nature, so such transformations often are consistent with stream processes (Helsel and Hirsch, 1992). Additionally, log transformation has the practical benefit of eliminating negative results when model predictions are converted back to normal units. However, log transformation can introduce a bias that needs to be corrected. Duan’s Bias Correction Factor (Duan, 1983), or BCF, which converts the logarithmic residuals from the regression process into normal space and then averages them, has been used frequently in recent studies (Uhrich and Bragg, 2003; Anderson, 2007; Rasmussen and others, 2008) and is used by the USGS as part of a national protocol for surrogate prediction by regression models (Rasmussen and others, 2009). Other steps in the maintenance of data and regression modeling include graphical evaluation of the relations between independent and dependent variables (for example, figure 5), removal of outliers (if careful attempts to resolve them were unsuccessful), and evaluation of residuals for homoscedasticity (constant variance across the range of data; Rasmussen and others, 2009).

When predicting surrogate concentrations using regression models such as those presented in this report, model uncertainty should be considered. In this study, 95 percent prediction intervals are included in figures showing time-series based on the continuously measured independent variables (for example, figure 6). For log-transformed dependent variables, lower and upper prediction interval values initially were in logarithmic terms and needed the bias correction applied after conversion to normal units in the same way as the actual predicted independent values. Although many models did not perform well for predicting the exact value of the independent variables in the validation datasets, the prediction intervals almost always encompassed the validation data. It is therefore important to display the range covered by the lower and upper prediction intervals, and equally important for water managers to consider that the actual concentration of an unmeasured constituent could fall anywhere within the portrayed interval range.

In this report, regression models were compared against an independent validation dataset through the determination of several goodness-of-fit statistics (table 8), including RMSE, a coefficient of determination analogous to the model’s R², and the Nash-Sutcliffe coefficient, which measures the contribution of the predicted values to the measured variance. This approach appears somewhat unique among recent studies that predict surrogate values from continuous monitors, but provides a critical assessment of the model’s performance against an independent dataset. The available datasets for model validation in this study were not adequate to assess model performance at the high values, most of which was during stormflow periods, so the goodness-of-fit statistics presented in this report would change if the same models were evaluated with a more complete dataset.

The use of continuous parameters such as discharge, stage, turbidity, or specific conductance for estimation of additional constituents has inherent risks of multicollinearity, wherein the independent variables are correlated, potentially causing spurious regression results or confounding the values of regression coefficients. Multicollinearity is a potential risk because many of the physical processes that affect these continuous parameters, such as discharge and turbidity, are related. Multicollinearity can be measured through the use of variance inflation factors (VIFs), which provide a measure of the independence of the individual variables, and generally is reduced with increasing numbers of samples (Draper and Smith, 1998). Assessment of multicollinearity is not straightforward, however, and must be done in conjunction with specific study objectives. In this study, VIFs were all less than general rules-of-thumb (that is, less than 5–10) that are sometimes cited (Helsel and Hirsch, 1992). Critical VIFs were calculated according to the SAS Institute’s method (1989) by using the model’s adjusted-R² in equation 3, and compared with the VIFs for the individual parameters. As a result, multicollinearity was potentially indicated for at least one or two models for each estimated parameter at each site because the respective adjusted-R² values were low. The collection of additional data to increase the sample size and the number of values (constituent data) measured during storm conditions would be expected to reduce the likelihood of multicollinearity among independent variables in future studies.

Model selection schemes initially used backward stepwise regression to identify potential explanatory variables, followed by the use of Mallow’s Cp to reduce the likelihood of producing models that were overfitted (Helsel and Hirsch, 1992). The Best Subsets algorithm, which is widely available in many statistical software packages, makes formal use of Mallow’s Cp along with alternating inclusion and exclusion of independent variables to achieve a parsimonious model (Draper and Smith, 1998). Future work on model selection also could benefit from a more broad-based selection scheme that uses all the information available from regression statistics to identify the most robust and parsimonious models, and to minimize the use of extraneous independent variables. An example model selection metric that could be useful is Akaike’s Information Criterion, or AIC (Burnham and Anderson, 2002), which provides numerous scores and weights to identify the best model from a suite of potential regression models. Regardless of which of these schemes is used, however, the process can be expected to be iterative, particularly with exploration of transformation schemes and evaluation of seasonal variation by using sine and cosine transformations, while concurrently watching for potential problems with multicollinearity and serial correlation.

First posted June 18, 2010