Purpose and Scope

This report summarizes the OLS regression models used to compute continuous 15-minute TP and suspended-sediment concentrations and loads at two USGS streamgages: the Williamson River below Sprague River near Chiloquin (USGS site ID 11502500; U.S. Geological Survey, 2023) and the Sprague River near Chiloquin (USGS site ID 11501000; ; U.S. Geological Survey, 2023; fig. 1). At the Williamson River site, surrogate regression models were updated with additional years of data for a total period of record from WY 2014–20, and a new TP regression model was developed at the Sprague River site for a total period of record from WY 2018–20. The models use turbidity as a surrogate for TP and SSC concentrations, and the streamflow data are used to compute continuous TP and suspended-sediment loads at both locations. Details for SSC regression methods and results are described in the two associated data releases (Schenk, 2023a, b).

Description of Study Area

The upper Klamath River Basin, including the Upper Klamath Lake, Williamson River, and Sprague River subbasins (fig. 1), encompasses about 3,770 square miles. The basin is in south-central Oregon and occupies a broad, faulted, volcanic plateau that spans the boundary between the Cascade Range and the Basin and Range geologic provinces (Gannett and others, 2007). A regional groundwater study by Gannett and others (2007) in the larger upper Klamath River Basin comprising the entire drainage basin upstream from Iron Gate Dam on the Klamath River provides detailed basin setting, regional groundwater movement, historical precipitation patterns, water budgets, and geologic framework of the basin. An additional study in the Sprague River subbasin provides detailed information on geomorphologic conditions and flood-plain and near-channel vegetation (O’Connor and others, 2015).

The Williamson River and Sprague River subbasins combined constitute 79 percent of the total drainage area and about 50 percent of the streamflow to Upper Klamath Lake (Walker and Kann, 2022). Forested land is the predominant land-use type in the Williamson River (80 percent) and Sprague River (68 percent) subbasins. Agriculture in both river subbasins is minimal in terms of overall watershed area, with about 9 and 8 percent of subbasin land use listed as pasture and grass hay for the Williamson River and Sprague River subbasins, respectively, and 2 percent of each of the subbasins listed as irrigated lands. However, agricultural grazing activities that occur near the Sprague and Williamson Rivers and their tributaries reduce riparian vegetation as well as widen and shallow the channel cross sections, which can lead to increased sediment and nutrient inputs to the fluvial systems.

On an annual basis, the Sprague River provides a substantial amount of streamflow to the Williamson River (Hess and Stonewall, 2014). Upstream from the confluence of the Williamson and Sprague Rivers, Spring Creek provides most of the streamflow to the Williamson River at base flow, and the Williamson River between the outlet of the Williamson River canyon and the Sprague River confluence is a system with a large component of groundwater discharge that responds relatively slowly to storm events and snowmelt runoff (Gannett and others, 2007).

Turbidity

Continuous turbidity data were collected during the study period at both sites, using Forest Technology Systems DTS-12 turbidity sensors deployed in the water column, which reported turbidity in Formazin Nephelometric Units (FNU). The turbidity sensors used near-infrared light sources in the range of 780–900 millimeters (mm) with a single detector at 90 degrees to the light beam. Management of turbidity sensors and processing and approval of data followed USGS protocols in Wagner and others (2006) and Rasmussen and others (2009). Turbidity data were collected every 15 min at both sites and were stored in the USGS National Water Information System using method codes specific to the instrument type (U.S. Geological Survey, 2023). Turbidity sensors were equipped with wipers and were programmed to wipe the sensor face prior to taking a measurement. One limitation of the DTS-12 sensors is that the wiper is not activated at temperatures less than 2 degrees Celsius (°C), a condition that often is encountered during the winter at both sites, although generally during periods when both flow and turbidity are low.

Streamflow Data

Streamflow was measured following USGS guidelines, and streamflow discharge data were computed using USGS guidelines (Turnipseed and Sauer, 2010) and reported in cubic feet per second (ft³/s) every 15-min.

Total Phosphorus and Suspended-Sediment Sample Collection

Sample collection and processing at both sites followed USGS protocols outlined in the National Field Manual (Edwards and Glysson, 1999) or USGS techniques and methods publications on the collection of water-quality data (Wilde and others, 2002; Wilde, 2006). Equal-width increment (EWI) methods were used to collect samples for WY 2008–2018; equal-discharge increment (EDI) methods were used to collect samples for WY 2019–20. These techniques sample at multiple locations along the channel cross section and are representative of the cross-section composite concentrations in the channel. At the Williamson River site, all samples were collected from the cableway, and at the Sprague River site samples were collected from a bridge using a three- or four-wheel crane. Samples were collected using a DH-95 isokinetic sampler suitable for collecting depth-integrated water-quality samples. EWI/EDI samples used a DH-95 isokinetic sampler when stream velocities exceeded 0.46 meters per second (m/s; 1.5 feet per second [ft/s]). When stream velocities were less than 0.46 m/s (1.5 ft/s), either a grab sample was collected from the left bank or a multiple vertical non-isokinetic sample was collected from either the cableway (Williamson River site) or the bridge (Sprague River site) by removing the isokinetic sample nozzle from the sampler and collecting water from 3 to 5 locations in the cross section. Sample water was composited into a 3-liter (L) acid washed plastic bottle and transferred to a churn splitter. Samples intended for TP analysis were transferred from the churn splitter into 125-milliliter (mL) white plastic bottles and preserved with 4.5 normality sulfuric acid. Samples for dissolved phosphorus were also collected from the churn splitter and filtered through a 0.45-micrometer (µm) in-line capsule filter using a peristaltic pump with acid-washed tubing, collected in an amber plastic bottle. All field samples were stored on ice and delivered to the Klamath Tribes Sprague River Water Quality Lab (SRWQL) on the same day the samples were collected.

SSC sample collection methods were similar to TP sample collection using a DH-95 sampler. The main difference in sample collection methods between SSC and TP was that SSC sample water was composited into a 3-L polypropylene bottle, not a churn splitter. The 3-L bottle was then sent to the SRWQL for analysis of sediment concentration in milligrams per liter (mg/L) and percent of sample less than 62.5 microns. Additional details on SSC sample collection methods can be found in two associated data releases and model archives for sediment surrogate regressions at the Sprague and Williamson Rivers (Schenk, 2023b, a).

Discrete Sample Quality Assurance

Quality assurance (QA) samples were collected periodically at both sites as replicate and blank samples. Replicates were collected either as split-replicates or sequential-replicates. Split-replicate samples were collected from the same churn during sample processing, representing a split of one EWI sample, and providing an estimate of variability introduced in the laboratory analysis. Sequential-replicate samples were collected as two separate sample volumes during the EWI samples and processed separately and provide a combined estimate of variability owing to both field and laboratory sources. Sequential replicate samples collected during storm events represented rapidly changing hydrologic conditions and, therefore, were more variable than the split-replicate samples because of the additional time required to collect two sample volumes, during which actual concentrations of constituents in the stream are expected to change. Equipment blank samples were collected at each site to test the cleanliness of sample equipment and for field contamination. Eleven QA samples were collected during WY 2014–20 at the Williamson River site, representing 27 percent of the total number of samples collected, and 7 QA samples were collected during WY 2018–20 at the Sprague River site, representing 28 percent of the total number of samples collected.

All discrete TP samples used in the regression analysis were reviewed using the WQReview package in R (Mills and Penn, 2022). This process involved evaluating replicate sample results and blank sample results to determine if data quality was acceptable for release to the public. Additional information on QA procedures for SSC can be found in the model archive summaries for both sites (Schenk, 2023b, a).

Surrogate Regression Methods

Surrogate regression models for TP were evaluated at both sites. Error statistics were developed for nine models for the Sprague River and seven models for the Williamson River, and a best-fit model was selected to produce time series of TP. Turbidity and streamflow were evaluated as explanatory variables, and TP was evaluated as the dependent variable. Linear, multiple linear, and nonlinear models with various axis transformations were developed and tested. The best model was chosen relying primarily on model standard prediction error (MSPE) to evaluate model differences, but also considered other factors such as root mean square error (RMSE), coefficient of determination (R²), and to limit homoscedastic errors.

Owing to the amount of time required for the collection of an EWI/EDI sample, multiple turbidity and streamflow values were recorded during the period of sample collection. To generate data pairs of potential explanatory variables (turbidity or streamflow) for the TP model calibration dataset, the nearest approved unit values of turbidity and streamflow were paired to the sample time associated with the TP sample within a matching window of plus or minus 15 min.

Total Phosphorus and Suspended-Sediment Load Calculations

Final time series of TP and SSC concentrations calculated from the regression models were used to calculate instantaneous values of TP loads (TPL) and suspended-sediment loads (SSL) in tons per second using equations 1 and 2:

Instantaneous TP loads in tons per second were aggregated monthly by summing the daily TP loads for each month of interest, and then were converted to kilograms. At the Williamson River site, 59 days of missing turbidity data occurred between May 3 and June 30, 2015, which did not allow for calculating unit values of TP and SSC using turbidity regression models. To calculate missing days of TP loads, an exponential regression was developed relating daily TP loads in tons to mean daily streamflow as well as for upper- and lower-90 percent prediction intervals (fig. 2). The exponential regressions were then used to compute daily TP loads and daily prediction intervals for the 59 days of missing turbidity data and are considered estimated values.

Sprague River Near Chiloquin Total Phosphorus Regression Model

A regression with the square root of turbidity as the independent variable was selected as the best-fit regression model to compute TP for the study period (table 1; fig. 3). The calibration dataset used for the model is shown in table 2. The model was applied to the time series of turbidity collected at the Sprague River site to compute time series concentrations of TP for WY 2018–20 during which TP samples were collected. During this period, the maximum recorded turbidity was 94.7 FNU, and the maximum turbidity sampled during sample collection was 76.1 FNU on March 26, 2018. Only 0.14 percent (150-unit values) of the computed TP values were computed with turbidity values that exceeded the limits of the regression (turbidity values greater than 76.1 FNU). Computed time series of TP concentrations and 90 percent prediction intervals are shown in figure 4.

The best-fit SSC surrogate model at the Sprague River site used log-transformed turbidity as the explanatory variable (Schenk, 2023a).

Williamson River Below Sprague River Total Phosphorous Regression Model

A linear TP-turbidity model was selected as the best-fit regression model to compute TP for the study period (table 1; fig. 5). The calibration dataset for this model is shown in table 3. The linear model was applied to the time series of turbidity collected at the Williamson River site to compute time series concentrations of TP for WY 2014–20 and supersedes the prior-published model from water year (WY) 2014–15 (table 1). During WY 2014–20, the maximum recorded turbidity was 71.8 FNU, and the maximum turbidity sampled during sample collection was 59.1 FNU on March 26, 2018. Only 0.07 percent (176 unit values) of the computed TP values were computed with turbidity values that exceeded the limits of the regression (turbidity values greater than 59.1 FNU). Computed TP concentrations and 90 percent prediction intervals for the time series are shown in figure 6. The model reported in this report supersedes the model published in Schenk and others (2016). The current model was used to revise previously published data since the initial model was developed with only 10 observations, was applied to a short time period (WY 2014–15; table 1), and was a proof-of-concept effort.

Total Phosphorus and Suspended-Sediment Loads to Upper Klamath Lake from the Sprague and Williamson Rivers

Annual TPL and SSL at the Williamson and Sprague Rivers using the methods described in this report are shown in tables 4 and 5 and figures 7A, and 8A. Data are reported from WY 2018–20 for the Sprague River TP loads, and WY 2014–20 for the Williamson River TP and suspended-sediment loads at both sites. Mean annual streamflow at the streamgages is also reported in table 4 to examine the load values in a hydrologic context.