Continuous Streamflow and Water-Quality Monitoring

The USGS began collecting continuous (15-minute interval) streamflow data at the Topeka site during November 2015 (U.S. Geological Survey, 2022) using standard USGS methods (Sauer and Turnipseed, 2010; Turnipseed and Sauer, 2010). These data are available in near-real time (hourly) from the USGS National Water Information System database at https://doi.org/10.5066/F7P55KJN (U.S. Geological Survey, 2022) by using station number 06888990.

The USGS began collecting continuous (15-minute interval) water-quality data at the Topeka site in November 2018. During November 2018 through June 2021, a YSI EXO2 water-quality monitor (YSI, Inc., 2017) was deployed by suspension from a building structure about 1 to 3 feet below the water surface on the southern bank of the Kansas River (fig. 3). Limited access and safety concerns prevented the use of bridge deployment at the centroid of flow (optimal deployment method used at the Wamego and De Soto sites; Williams [2021]). The water-quality monitor was equipped with water temperature, specific conductance, pH, dissolved oxygen, turbidity, and chlorophyll and phycocyanin fluorescence sensors. The water-quality monitor was operated and maintained using standard USGS methods (Wagner and others, 2006; Bennett and others, 2014). All continuous water-quality data are available in near-real time (hourly) from the USGS National Water Information System database at https://doi.org/10.5066/F7P55KJN (U.S. Geological Survey, 2022) by using station number 06888990.

Discrete Water-Quality Sampling

Water-quality samples were collected at the Topeka site on a biweekly to monthly basis during November 2018 through June 2020, on a monthly to bimonthly basis during July 2020 through June 2021, and during selected reservoir release and runoff events. Using this fixed-schedule sampling approach, water-quality samples were collected over the range of study period streamflows (fig. 2). Initially, during November 18, 2018, through February 5, 2019, three water-quality samples were collected 0.2 mi downstream from the continuous water-quality monitor location using depth- and width-integrated sampling techniques (U.S. Geological Survey, 2006) from a watercraft. This location was selected for safety reasons because of proximity of an upstream low-head dam (0.1 mi downstream from the continuous water-quality monitor location). Remaining samples were collected from the continuous water-quality monitor location because of greater accessibility throughout the study period streamflow range. Therefore, during February 19, 2019, through June 2021, all samples, excluding E. coli bacteria, were collected from the water-quality monitor location using a US DH–95 or US D–95 sampler (Edwards and Glysson, 1999) with depth-integrated sampling techniques (U.S. Geological Survey, 2006). Samples of E. coli bacteria were collected from the same location using a sterile, autoclaved bottle in a weighted basket. The water-quality monitor location provided the greatest safety and allowed for consistent sampling methodology and location regardless of streamflow conditions. All water-quality samples were analyzed for total dissolved solids, major ions, hardness as calcium carbonate, total nitrogen (particulate plus dissolved nitrogen), total Kjeldahl nitrogen (TKN; total concentration of organic nitrogen and ammonia), total phosphorus, chlorophyll a, total suspended solids, suspended sediment, and E. coli bacteria.

Total dissolved solids, major ions, hardness as calcium carbonate, nutrients (nitrogen and phosphorus species), and total suspended solids were analyzed by the USGS National Water Quality Laboratory in Lakewood, Colorado, using the methods documented by Fishman and Friedman (1989). Chlorophyll a was analyzed by the USGS National Water Quality Laboratory in Lakewood, Colo., using U.S. Environmental Protection Agency Method 445.0 (Arar and Collins, 1997). Suspended-sediment concentration was analyzed at the USGS Iowa Sediment Laboratory in Iowa City, Iowa, following methods documented by Guy (1969). Samples of E. coli bacteria were analyzed by the USGS Kansas Water Science Center following the methods documented by Myers and others (2014). All of these data are available from the USGS National Water Information System database at https://doi.org/10.5066/F7P55KJN (U.S. Geological Survey, 2022) by using station number 06888990.

Phytoplankton community composition and abundance, microcystin (a cyanotoxin), and geosmin and 2-methylisoborneol (taste-and-odor compounds) samples also were collected during each water-quality sampling. However, additional data collected during cyanobacteria, microcystin, and taste-and-odor events are necessary to obtain representative model-calibration datasets for model development at the Topeka site. Water-quality sampling and analytical methodology for these constituents are described in greater detail by Foster and Graham (2016) and Graham and others (2018).

Quality Assurance and Quality Control of Continuous and Discrete Water-Quality Data

All continuous and discrete water-quality data collected during November 2018 through June 2021 were reviewed and approved quarterly, following USGS guidance (U.S. Geological Survey, 2016, 2017). Continuous water-quality data occasionally were corrected or deleted because of fouling, sensor calibration drift (Wagner and others, 2006; Bennett and others, 2014), equipment malfunction, or temporary removal of the water-quality monitor to avoid loss or damage during below-freezing surface-water temperatures. During November 2018 through June 2021, about 3 percent of the water-temperature, pH, dissolved oxygen, and phycocyanin fluorescence records and about 4 percent of the specific conductance, turbidity, and chlorophyll fluorescence records at the Topeka site were missing or deleted because of excessive fouling.

Quality-control (QC) samples were collected for about 10 percent of all discrete water-quality samples. Concurrent replicate QC samples were collected to characterize variability in sample results that could potentially be introduced by sample-collection methods, sample processing techniques, and analytical method (Rasmussen and others, 2014; Mueller and others, 2015). Relative percentage difference (RPD) was used to quantify differences in noncensored (data reported as greater than or equal to the laboratory minimum reporting limit [MRL]) constituent concentrations or densities among concurrent replicate pairs and was calculated by dividing the absolute difference of a replicate pair of samples by their mean value and multiplying by 100 (Zar, 1999). Concurrent replicate RPDs met QC objectives if a constituent’s median RPD was less than or equal to 5 percent for total dissolved solids, major ions, and hardness as calcium carbonate; less than or equal to 10 percent for nutrients (nitrogen and phosphorus species), chlorophyll a, total suspended solids, and suspended-sediment concentration; and less than or equal to 30 percent for E. coli bacteria (Williams, 2021). Three concurrent replicate pairs were collected from the Topeka site during November 2018 through June 2021. QC objectives were met for concurrent replicate pairs for all constituents used for model development documented in this report. Median RPDs among concurrent replicate pairs for total dissolved solids, major ions, and hardness as calcium carbonate were less than 1 percent. Nutrient (nitrogen and phosphorus species) and chlorophyll a median concurrent replicate RPDs were less than 4 percent. Median concurrent replicate RPDs were less than 9 percent for total suspended solids and suspended-sediment concentration. The median RPD among E. coli bacteria concurrent replicates was 20 percent. Variability among E. coli bacteria concurrent replicate densities can increase if samples are insufficiently mixed during sample processing (Myers and others, 2014).

Three field blank samples were collected from the Topeka site during November 2018 through June 2021 to characterize bias caused by sampling procedures and analytical methods (Mueller and others, 2015). QC objectives were met if field blank sample concentrations were less than or equal to the associated MRL. Field blank sample concentrations were less than or equal to MRLs with the exception of one sample analyte. Chloride was the single constituent that had at least one detection (0.03 milligram per liter [mg/L]) greater than the MRL (0.02 mg/L) in all blank samples collected during the study period. Equipment- and procedure-blank samples were collected for all E. coli bacteria samples during November 2018 through June 2021. No E. coli bacteria detections were in any equipment- or procedure-blank samples during the study period.

Concomitant field and in situ water-quality monitor (YSI EXO2) physiochemical properties were measured during discrete sampling events to compare sample-collection methods (depth- and width-integrated [collection method used during November 18, 2018, through February 5, 2019] and depth-integrated [collection method used during February 19, 2019, through June 2021]). Cross-sectional profile water-quality physiochemical properties were measured about 1 foot below the water surface alongside the depth- and width-integrated discretely collected samples; these samples coincided with the 84th, 81st, and 52d percentiles of daily mean study period streamflows. Two sets of vertical-profile cross-sectional water-quality physiochemical properties were measured at several depths at each cross-section location; these two vertical-profile cross-sectional measurements coincided with the 19th and 69th percentiles of daily mean study period streamflows. The Topeka site’s stream conditions were arbitrarily considered to be well mixed if field-measured profile and in situ measurement statistics (water temperature, specific conductance, and dissolved oxygen means and pH medians) were within 5 percent. RPDs among concomitant cross-sectional and in situ continuous water-quality monitor statistics were calculated to determine if the initial depth- and width-integrated samples were comparable to the depth-integrated samples collected at the in situ continuous water-quality monitor location. RPDs among concomitant cross-sectional profile and in situ continuous water-quality monitor measurement statistics were less than 4 percent. RPDs among concomitant vertical-profile cross-sectional and in situ continuous water-quality monitor statistics were equal to or less than 3 percent. This information indicated that the Kansas River at the Topeka site likely was generally well mixed; therefore, all water-quality samples, regardless of sample-collection technique, were considered during model development.

Development of Regression Models

Models that related continuous in situ water-quality sensor measurements, streamflow, and seasonal components to discrete sample water-quality constituent concentrations or densities using linear regression analysis and data collected during November 2018 through June 2021 were developed. All regression models were developed using R programming language, version 4.2.0 (R Core Team, 2022). Models were developed using ordinary least squares estimation for constituents with model-calibration datasets containing no left-censored data (data reported as less than the laboratory MRL). Ordinary least squares estimation was used to develop models that compute continuous concentrations or densities of total dissolved solids, calcium, magnesium, sodium, sulfate, chloride, hardness as calcium carbonate, total nitrogen (particulate plus dissolved nitrogen), TKN, total phosphorus, chlorophyll a, suspended sediment, and E. coli bacteria. These constituents were selected for model development based on evaluation of model-diagnostic statistics, relevance to water-treatment managers, association with State water-quality criteria or impairments, previously published Kansas River models (Rasmussen and others, 2005; Foster and Graham, 2016; Williams, 2021), and overall dataset suitability for model development. If censored data were present in a constituent’s model-calibration dataset, then Tobit regression estimation was used to develop models using the absolute maximum likelihood estimation procedure (Hald, 1949; Cohen, 1950; Tobin, 1958; Helsel and others, 2020). Absolute maximum likelihood estimation was used to develop the model that computes continuous concentrations of total suspended solids. Percentages of censored data and the model estimation method for each water-quality constituent are reported in table 1 and appendixes 1–14.

Chlorophyll a and E. coli bacteria sample data included some results qualified as “estimated” in accordance with standard laboratory quality-assurance procedures. Estimated results were investigated as potential outliers by confirming correct database entry, evaluating laboratory analytical performance, and reviewing all field notes associated with the samples in question (Rasmussen and others, 2009). Estimated results within the chlorophyll a and E. coli bacteria model-calibration datasets are identified in appendixes 11 and 14, respectively; were not determined to have errors associated with sample collection, processing, or analysis; and were therefore considered valid.

Potential explanatory variables that were considered during linear regression model development were continuous streamflow, water temperature, specific conductance, dissolved oxygen, turbidity, chlorophyll and phycocyanin fluorescence, and seasonal components (sine and cosine variables). Potential explanatory variables were evaluated individually and in combination and were interpolated by discrete water-quality sample time within the 15-minute continuous record. Explanatory variable data were not interpolated by sample time if the sample time coincided with a gap in the continuous record (because of excessive fouling, equipment malfunction, or equipment removal) that exceeded 2 hours (Williams, 2021). If gaps in the continuous record exceeded 2 hours and prevented interpolation based on discrete water-quality sample time, then data collected using water-quality monitors during discrete sample collection were used for inclusion in the model-calibration dataset.

Preliminary linear regression models were evaluated based on range and distribution of continuous and discrete model-calibration data, patterns in residual plots, and the following model diagnostic statistics: adjusted coefficient of determination (R²), pseudo-R² (computed for Tobit regression models only; McKelvey and Zavoina, 1975), Mallows’ C_p (Mallows, 1973), root mean square error (RMSE), and prediction error sum of squares (PRESS; Rasmussen and others, 2009; Helsel and others, 2020). The best linear regression model was selected for each response variable (total dissolved solids, calcium, magnesium, sodium, sulfate, chloride, hardness as calcium carbonate, total nitrogen [particulate plus dissolved nitrogen], TKN, total phosphorus, chlorophyll a, total suspended solids, suspended sediment, and E. coli bacteria) when variance explained by the model (adjusted R² or pseudo-R²) was maximized and greater than or equal to 0.60, model precision was high and model bias was low (Mallows’ C_p), uncertainty in model computations was minimized (RMSE and PRESS), and heteroscedasticity (irregular scatter) was minimal in residual plots (Rasmussen and others, 2009; Helsel and others, 2020). Potential explanatory variables were not included in the final selected regression model if they had a probability greater than 0.05. Model simplicity and previously published explanatory variables at other Kansas River sites (Rasmussen and others, 2005; Foster and Graham 2016; Williams, 2021) also were considered during the model selection process.

Logarithmic transformations (logarithm with base 10 [log] transformations) of the response and explanatory variables were used during model development if heteroscedasticity was apparent in plots of response variable residuals compared to model computed values (shown in appendixes 1–14). If log transformations were used in the final selected model, a bias correction factor was computed and used for the retransformation of log-transformed computations back into their original units (Duan, 1983) to reduce inherent negative bias introduced by log transformations (Helsel and others, 2020).

Multiple explanatory variables for a given linear regression model were considered if the additional variable increased the variance (as indicated by adjusted R² or pseudo-R²) explained by the model by at least 5 percent, decreased Mallows’ C_p, minimized RMSE and PRESS, and minimized heteroscedasticity in residual plots. Additionally, multiple explanatory variables were considered for inclusion in the final selected model if their variance inflation factors (Marquardt, 1970) were less than 4, indicating minimal multicollinearity (O’Brien, 2007; Vatcheva and others, 2016; Helsel and others, 2020).

Potential outliers initially were identified by viewing bivariate plots of the model-calibration data for each set of response and explanatory variables (Rasmussen and others, 2009). Studentized residuals from preliminary models were inspected for values greater than three or less than negative three (Pardoe, 2020). Values outside of that range were considered potential outliers and were investigated. Additionally, computations of leverage, Cook’s distance, and difference in fits statistics were used to estimate potential outlier effect on the final selected regression model (Cook, 1977; Helsel and others, 2020). Outliers were investigated for potential removal from the model-calibration dataset by confirming correct database entry, evaluating laboratory analytical performance, and reviewing field notes associated with the sample in question (Rasmussen and others, 2009). Outlier identification and justification for removal are included, when applicable, in appendixes 1–14. Model development methodology is described in additional detail in appendixes 1–14.

Total Dissolved Solids, Major Ions, and Hardness

Specific conductance was the single explanatory variable used to model for total dissolved solids, calcium, magnesium, sodium, sulfate, chloride, and hardness as calcium carbonate at the Topeka site (table 1; appendixes 1–7). Specific conductance, a measure of the surface water’s ability to conduct an electrical current, is positively correlated with total dissolved solids and other charged ionic species (Hem, 1985) and explained about 93–98 percent of the variance (as indicated by adjusted R²) in total dissolved solids, major ions, and hardness as calcium carbonate concentrations (table 1; appendixes 1–7). Specific conductance was also the single explanatory variable used to model for these constituents in previously published models at the Wamego and De Soto sites (Rasmussen and others, 2005; Foster and Graham, 2016; Williams, 2021).

Total Nitrogen, Total Kjeldahl Nitrogen, Total Phosphorus, and Chlorophyll a

Turbidity was the single explanatory variable used to model for total nitrogen, TKN, and total phosphorus at the Topeka site (table 1; appendixes 8–10). Turbidity, a measure of surface-water clarity caused by the presence of suspended and dissolved material, typically increases during precipitation runoff events. Nutrients, as well as other contaminants, tend to physically bind to suspended and dissolved material in the Kansas River (Rasmussen and others, 2005; Graham and others, 2018). Turbidity explained about 74, 92, and 91 percent of variability in total nitrogen, TKN, and total phosphorus concentrations, respectively (table 1). The TKN model may overestimate computed TKN concentrations in the low (0.0 to 0.70 mg/L) and high (3.11 to 4.73 mg/L) ranges and underestimate computed TKN concentrations in the middle range (0.71 to 3.10 mg/L) because of larger scatter observed in plots of residual and regression computed TKN and residual TKN and turbidity (appendix 9). Additional TKN model-calibration data may improve this limitation in the future. Turbidity also was selected as an explanatory variable for nutrient (nitrogen and phosphorus species) models published by Rasmussen and others (2005), Foster and Graham (2016), and Williams (2021) at the Wamego and De Soto sites.

Chlorophyll fluorescence was the single explanatory variable used to model for chlorophyll a at the Topeka site (table 1; appendix 11). Although an unknown level of uncertainty is inherent to fluorescence sensors (because of nonphotochemical quenching, matrix effects, and variable fluorescence responses of differing plankton communities [Foster and others, 2022]), chlorophyll fluorescence makes physical and statistical sense as an explanatory variable for chlorophyll a because chlorophyll a pigments fluoresce when irradiated by certain wavelengths of light emitted from the chlorophyll fluorescence sensor. Chlorophyll fluorescence explained about 81 percent of the variability in chlorophyll a concentration. The chlorophyll a model may overestimate computed chlorophyll a concentration in the upper range based on irregular scatter in the plot of observed and regression computed chlorophyll a (appendix 11). Additional chlorophyll a model-calibration data may improve this limitation in the future. Chlorophyll fluorescence was also the single explanatory variable used to model for chlorophyll a concentration in the models previously published by Williams (2021) at the Wamego and De Soto sites.

Total Suspended Solids and Suspended Sediment

Turbidity was the single explanatory variable used to model for total suspended solids and suspended sediment at the Topeka site (table 1; appendixes 12 and 13). Turbidity was positively correlated with total suspended solids and suspended sediment and explained about 94 and 99 percent of the variance in these constituents, respectively. Turbidity was also the single explanatory variable used to model for these constituents in the models previously published by Rasmussen and others (2005), Foster and Graham (2016; did not publish models for total suspended solids), and Williams (2021) at the Wamego and De Soto sites.

Escherichia coli Bacteria

Turbidity was the single explanatory variable used to model for E. coli bacteria at the Topeka site (table 1; appendix 14), likely because E. coli tend to physically bind to suspended material. Turbidity explained about 79 percent of the variance in E. coli density and was also the single explanatory variable used to model for E. coli models previously published by Rasmussen and others (2005), Foster and Graham (2016; published E. coli model for De Soto site only), and Williams (2021) at the Wamego and De Soto sites.