Continuous Streamflow and Water-Quality Monitoring

Continuous (1-hour maximum interval) streamflow and water-quality physicochemical properties were measured at the Halstead and Sedgwick sites during the study period. Streamflow has been measured at the Halstead and Sedgwick sites since May 1995 and November 1993, respectively. Streamflow was measured using standard USGS methods (Sauer and Turnipseed, 2010; Turnipseed and Sauer, 2010; Painter and Loving, 2015). Water-quality physicochemical properties (continuous surrogates) used for model development in this report included water temperature, specific conductance, pH, dissolved oxygen, turbidity, nitrate plus nitrite, and fDOM.

Since June-October 1988, both sites have been equipped with a YSI Incorporated 6600 Extended Deployment System water-quality monitor (YSI Incorporated, 2012a) to continuously measure (60-minute interval) water temperature, specific conductance, pH, dissolved oxygen (YSI Clark cell or optical dissolved oxygen sensors), and turbidity (YSI 6026 or 6136 optical turbidity sensors). Detailed method descriptions for continuous water-quality monitoring by the USGS Kansas Water Science Center are in Bennett and others (2014). Nitrate sensors (HACH Nitratax plus sc; HACH Company, 2014) were installed at the Sedgwick site in March 2012 and the Halstead site in February 2017. Nitrate sensor data include nitrite and, therefore, are reported and referred to as nitrate plus nitrite concentrations (Pellerin and others, 2013) in this report. Surface-water monitors were installed near the centroid of the stream cross section to best represent stream width conditions and were maintained following standard USGS procedures (Wagner and others, 2006; Rasmussen and others, 2008; Pellerin and others, 2013; Bennett and others, 2014).

Some equipment was upgraded throughout the life of the project. YSI 6136 turbidity sensors were initially installed at both sites in July 2004. A Xylem YSI EXO2 water-quality monitor (YSI Incorporated, 2012b) equipped with water temperature, specific conductance, pH, dissolved oxygen, turbidity, and YSI EXO fDOM sensors was installed in September 2014 at the Sedgwick site and in January 2017 at the Halstead site. Because of differences in turbidity sensor readings between the YSI 6136 and YSI EXO turbidity sensors (Stone and others, 2019), only YSI EXO turbidity sensor data were used for model development in this report although turbidity data were available since June-October 1998. Continuous water-quality data for Kansas are available at the National Water Information System database (U.S. Geological Survey, 2021).

Discrete Water-Quality Data Collection

During 1998 through 2019, about eight discrete surface-water water-quality samples were collected annually at both study sites across a range of Little Arkansas River streamflow conditions using USGS equal-width increment methods (U.S. Geological Survey, 2006; Stone and others, 2012; Rasmussen and others, 2014; Stone and others, 2019). These samples were analyzed for dissolved (number of samples [n] at the Halstead site [Halstead n]=218 and n at the Sedgwick site [Sedgwick n]=345) and suspended solids (Halstead n=186 and Sedgwick n=234); suspended-sediment concentration (Halstead n=178 and Sedgwick n=315); hardness (Halstead n=218 and Sedgwick n=351); alkalinity (Halstead n=34 and Sedgwick n=147); primary ions (bicarbonate [Halstead n=34 and Sedgwick n=147]; calcium [Halstead n=217 and Sedgwick n=351]; sodium [Halstead n=217 and Sedgwick n=351]; chloride [Halstead n=219 and Sedgwick n=360]; and sulfate [Halstead n=217 and Sedgwick n=356]); nutrients (total Kjeldahl nitrogen [Halstead n=168 and Sedgwick n=304] and total phosphorus [Halstead n=168 and Sedgwick n=304]); total organic carbon (Halstead n=130 and Sedgwick n=167); indicator bacteria (E. coli [Halstead n=151 and Sedgwick n=183] and fecal coliform bacteria [Halstead n=216 and Sedgwick n=261]); arsenic (Halstead n=167 and Sedgwick n=312); and atrazine (Halstead n=176 and Sedgwick n=323). Collection and analyses for dissolved and total suspended solids, suspended-sediment concentration, primary ions, nutrients, total organic carbon, arsenic, bacteria, and pesticides followed methods described by Ziegler and Combs (1997), Ziegler and others (1999, 2010), Stone and others (2012, 2016, 2019), and Tappa and others (2015). Indicator bacteria analyses were done using methods described by the U.S. Environmental Protection Agency (2000, 2006a, 2006b) and Myers and others (2014).

Dissolved solids, primary ions, nutrients, total organic carbon, and arsenic samples were analyzed by the Wichita Municipal Water and Wastewater Laboratory and the USGS National Water Quality Laboratory (Denver, Colorado). Suspended-sediment concentrations were analyzed at the USGS Iowa Sediment Laboratory (Iowa City, Iowa) following methods described in Guy (1969). Indicator bacteria samples were analyzed by the USGS Kansas Water Science Center (Lawrence, Kansas). Atrazine was analyzed by the USGS National Water Quality Laboratory. Discrete water-quality data are available at the National Water Information System database (U.S. Geological Survey, 2021).

Quality Assurance and Quality Control

Quality-assurance and quality-control samples were collected routinely during the study period to identify, quantify, and document bias and variability in data resulting from collecting, processing, handling, and analyzing samples (U.S. Geological Survey, 2006). Relative percentage difference (RPD) was calculated to quantify differences in water-quality monitor measurements and discrete sample analyte concentrations detected in replicate water-quality samples. The RPD was calculated by dividing the difference between replicate pairs by the mean and multiplying that value by 100, resulting in a value representing the percentage difference between replicate samples (Zar, 1999).

Water temperature, specific conductance, pH, and dissolved oxygen sensor data did not exceed operational limits and the Xylem YSI EXO turbidity sensor did not exceed the maximum operational limit (4,000 formazin nephelometric units) during the study period. Time-series measurements were occasionally missing or deleted from the dataset because of equipment malfunction, excessive fouling caused by environmental conditions, extreme low- or no-flow conditions, or temporary removal of equipment because of ice. During the study period (January 1998 through December 2019), 3 and 4 percent of the hourly streamflow record, 6 and 3 percent of the water temperature record, 8 and 9 percent of the specific conductance record, 6 and 4 percent of the pH record, 8 and 6 percent of the dissolved oxygen record, 2 and 6 percent of the YSI EXO turbidity record, 4 and 7 percent of the fDOM record, and 1 and 11 percent of the nitrate plus nitrite record were missing or deleted (table 2) at the Halstead and Sedgwick sites, respectively. Most of the missing data were because of low flow or icy conditions and occasionally sensor fouling. The fDOM data were temperature and turbidity corrected following protocols described by Downing and others (2012).

Comparison of field cross-sectional measurements collected during high- and low-flow conditions at the surface-water sites with the continuous data provided verification that bias in continuous data because of monitor location within the stream cross section was minimal. Median RPDs between continuous and field water-quality monitor measurements were less than (<) 2 percent, except for dissolved oxygen (<4 percent), Xylem YSI EXO sensor turbidity (<6 percent), and fDOM (<19 percent; table 3). The largest differences between continuous and field-monitor values commonly occurred when conditions were changing rapidly.

About 10 percent of the discrete water-quality samples were quality-assurance and quality-control samples and included concurrent replicates, field and equipment blanks, and standard reference samples. Concurrent replicate samples were collected to quantify variability potentially introduced by sample collection, processing techniques, and analytical method (Bennett and others, 2014, Mueller and others, 2015). RPDs were not calculated for replicate pairs that had consistent nondetections (both values in the replicate pair were censored) or inconsistent detections (one value in the replicate pair was a detected value and the other value was censored; Mueller and others, 2015); these pair types occurred only in three indicator bacteria replicate pairs. Replicate comparisons included 86 dissolved and total suspended solids pairs, 34 suspended-sediment concentration pairs, 205 primary ion pairs, 70 nutrient pairs, 27 total organic carbon pairs, 68 indicator bacteria pairs (containing 1 inconsistent E. coli bacteria pair detection and 2 consistent fecal coliform bacteria pair nondetections), 32 dissolved arsenic pairs, and 25 atrazine pairs. Median dissolved solids, hardness, calcium, sodium, alkalinity, bicarbonate, chloride, sulfate, and total phosphorus RPDs were <2 percent; median total suspended solids, total Kjeldahl nitrogen, arsenic, atrazine, total organic carbon, and suspended sediment RPDs were <6 percent; median E. coli bacteria RPD was 8.8 percent; and median fecal coliform bacteria RPD was 20 percent (table 3). Largest RPD values generally occurred when the values were near the laboratory reporting level.

Blank samples consisted of deionized water, inorganic blank water, or organic blank water, depending on analyses. During the study period, 63 blank samples for modeled analytes were collected and analyzed for dissolved and suspended solids, hardness, calcium, sodium, chloride, sulfate, total Kjeldahl nitrogen, total phosphorus, total organic carbon, E. coli and fecal coliform bacteria, dissolved arsenic, and atrazine. Suspended solids, hardness, chloride, sulfate, total phosphorus, and arsenic blank samples did not have any detections during the study period. Blank samples with analyte detections included dissolved solids (four detections), calcium and sodium (three detections each), total Kjeldahl nitrogen (five detections), total organic carbon (six detections), E. coli and fecal coliform bacteria (one detection each), and atrazine (two detections table 3). Blank sample analyte detections were at or below either the analytical detection limit or minimum reporting limit except for one dissolved solids detection, one total Kjeldahl nitrogen detection, and one total organic carbon detection. Detection or minimum reporting limit exceedances were near the analytical detection or minimum reporting limit.

Standard reference samples were analyzed by the Wichita Municipal Water and Wastewater Laboratory and analytical results were submitted to the USGS Branch of Quality Systems annually and oftentimes biannually for laboratory-performance evaluation. Standard reference sample data are available at https://bqs.usgs.gov/srs. Most of the reported values were within 10 percent of the most probable value during the study. Median RPDs between laboratory results and most probable values indicated that laboratory data generally were consistent and unbiased.

Regression Model Development

Simple linear (ordinary least squares [OLS]) and Tobit regression analyses were used to develop regression models that related continuously measured physicochemical properties (continuous surrogates), streamflow, and seasonal components to discretely sampled water-quality constituent concentrations or densities (Rasmussen and others, 2009; Helsel and others, 2020). The previously published (Rasmussen and others, 2016) models for dissolved solids, suspended solids, suspended-sediment concentration, hardness, alkalinity, bicarbonate, calcium, sodium, chloride, sulfate, total Kjeldahl nitrogen, total phosphorus, total organic carbon, E. coli bacteria, fecal coliform bacteria, arsenic, and atrazine were updated following methods described in Rasmussen and others (2009, 2016). Additional streamflow-based models (with streamflow and seasonal components) were developed to compute estimates of concentrations or densities during periods when concomitant continuous surrogate measurements were unavailable.

Regression models were developed using OLS estimation for constituents that had datasets without left-censored data (< values). Tobit regression methods were used for fitting linear models for constituents that had datasets with left-censored data using absolute maximum likelihood estimation (AMLE; Hald, 1949; Cohen, 1950; Tobin, 1958; Helsel and others, 2020). Discrete datasets containing left-censored data included total suspended solids (5–8 percent left-censored data), chloride (<1–2 percent left censored data), sulfate (3–4 percent left-censored data), E. coli bacteria (1 percent left-censored data), fecal coliform bacteria (<1 percent left-censored data), dissolved arsenic (<1–2 percent left-censored data), and atrazine (1–3 percent left-censored data). Data and models for this report were analyzed and developed using R (version 4.0.0) programming language (R Core Team, 2020). Tobit regression models were developed using absolute maximum likelihood estimation methods using the smwrQW (v.0.7.9) package in R programming language (R Core Team, 2020).

Model datasets had different numbers of measurements for the following two primary reasons:

Model datasets and modeled constituents included available concomitant real-time physicochemical properties as explanatory variables during model development. Potential explanatory variables were evaluated individually and in combination and included available concomitant continuously measured streamflow, water temperature, specific conductance, pH, dissolved oxygen, turbidity (YSI EXO turbidity sensor), fDOM, and nitrate plus nitrite concentration for the updated models. Periodic functions (seasonal components sine and cosine variables) also were evaluated as potential explanatory variables using day of the year. Explanatory variables were interpolated within the continuous record based on discrete sample time. The maximum time span between two continuous data points used for interpolation was 2 hours.

Potential linear regression models were evaluated based on diagnostic statistics (coefficient of determination [R²], or adjusted R² for OLS-estimated models; pseudo-R² for AMLE-estimated models; Mallow’s C_p for OLS-estimated models; root mean square error for OLS-estimated models; prediction error sum of squares for OLS-estimated models; and residual standard error for AMLE-estimated models), patterns in residual plots, and the range and distribution of discrete and continuous data (Helsel and others, 2020). Updated models were selected regardless of the date ranges of available concomitant real-time surrogate data (table 2) that

If either a sine or cosine seasonality variable was included in the model, a corresponding counterpart also was included in the model. A bias correction factor was calculated for models with logarithmically transformed response variables because transformation of estimates to original units results in a low biased estimate (Duan, 1983; Helsel and others, 2020).

Potential outliers were identified following Rasmussen and others (2009) and Helsel and others (2020). Studentized residuals, leverage, Cook’s D (Cook, 1977), and difference in fits values were used to identify influential data points for OLS-estimated models; and leverage and Cook’s D values were used to identify influential data points for AMLE-estimated models. Studentized residuals are used to identify outliers with high leverage, Cook’s D is a combination of each observation’s leverage and residual value (large values indicate influential observations), and difference in fits is the product of the Studentized residual and leverage (large values indicate influential observations). Removing data points that were based only on outlier criteria may only overestimate the certainty of the model. Data points that were not representative of the dataset and exceeded Cook’s D and difference in fits thresholds for OLS-estimated models and Cook’s D thresholds for AMLE-estimated models were removed from model datasets to avoid erroneous inflation of model-computed values at the upper range of surrogate relations.

Solids and Primary Ions

Specific conductance was the sole explanatory variable for dissolved solids, hardness, alkalinity, bicarbonate, calcium, sodium, chloride, and sulfate at both study sites (tables 4–5). Specific conductance was positively related to dissolved solids and primary ions because specific conductance measures water’s capacity to conduct an electrical current and is related to the concentration of ionized substances in water (Hem, 1992). Model forms (selected explanatory variables) for dissolved solids, hardness, calcium, and sodium were similar to previously published models at both sites (tables 4–5; Christensen and others, 2003; Rasmussen and others, 2016). Updated model forms (selected explanatory variables) for chloride and sulfate were similar to the most recently published models at the Halstead site but did not include streamflow as an explanatory variable like the most recently published models did at the Sedgwick site (table 5, Rasmussen and others, 2016); previously published chloride and sulfate models by Christensen and others (2003) also did not include streamflow as an explanatory variable. Updated model forms (selected explanatory variables) for alkalinity and bicarbonate did not include streamflow as an additional explanatory variable like the most recently published models did at both study sites (tables 4–5, Rasmussen and others, 2016). Earlier published alkalinity and bicarbonate model forms (selected explanatory variables) included streamflow at the Halstead site and streamflow and specific conductance at the Sedgwick site (Christensen and others, 2003).

The amount of variance explained by updated dissolved solids, hardness, calcium, and sodium ranged from 97 to 98 percent (tables 4–5). The amount of variance explained by updated alkalinity and bicarbonate models ranged from 89 percent at the Halstead site to 94 percent at the Sedgwick site (tables 4–5). The amount of variance explained by updated chloride models ranged from 88 percent at the Sedgwick site to 93 percent at the Halstead site (table 5). The amount of variance explained by the updated sulfate models ranged from 84 percent at the Halstead site to 91 percent at the Sedgwick site (table 5). The amount of variance explained by updated primary ions models was within 5 percent of the most recently published models, except for the updated sulfate model at the Halstead site (R² decreased from 0.90 to 0.84, table 5, Rasmussen and others, 2016).

Turbidity was the sole explanatory variable for total suspended solids and suspended-sediment concentration (table 4). Turbidity is caused by suspended and dissolved matter such as clay, silt, finely divided organic material, plankton and other microscopic organisms, organic acids, and dyes. Total suspended solids and suspended-sediment concentration were positively correlated with turbidity (table 4) because turbidity measures light scattered by particulates in water. Model forms for total suspended solids were similar to previously published models at both sites (table 4; Rasmussen and others, 2016; Christensen and others, 2003). Updated model forms (selected explanatory variables) for suspended-sediment concentration at both sites did not include streamflow as an explanatory variable like the most recently published models did (table 4, Rasmussen and others, 2016). Suspended-sediment concentration models published by Christensen and others (2003) included turbidity as the sole explanatory variable at the Halstead site and streamflow and turbidity as explanatory variables at the Sedgwick site.

The amount of variance explained by the updated total suspended solids models ranged from 94 percent at the Sedgwick site to 97 percent at the Halstead site (table 4). The amount of variance explained by the updated suspended-sediment concentration models ranged from 93 percent at the Sedgwick site to 98 percent at the Halstead site (table 4). The amount of variance explained by updated total suspended solids and suspended-sediment concentration models was within 5 percent of the most recently published models (table 4, Rasmussen and others, 2016).

Nutrients and Total Organic Carbon

Turbidity was the sole explanatory variable for total Kjeldahl nitrogen (TKN), total phosphorus, and total organic carbon (table 6). TKN, total phosphorus, and total organic carbon were positively related to turbidity (table 6). TKN (which includes organic nitrogen), total phosphorus (which sorbs to suspended sediment), and total organic carbon contain organic material (which is a substantial component of total suspended solids; Hem, 1992). Updated model forms (selected explanatory variables) for TKN, total phosphorus, and total organic carbon were similar to the most recently published models; however, updated TKN models did not include a seasonal component (table 6; Rasmussen and others, 2016). Updated TKN and total phosphorus model forms (selected explanatory variables) were similar to those published previously by Christensen and others (2003) by having turbidity as the sole explanatory variable.

The amount of variance explained by updated TKN models ranged from 83 percent at the Sedgwick site to 95 percent at the Halstead site (table 6). The amount of variance explained by updated total phosphorus models ranged from 68 percent at the Sedgwick site to 86 percent at the Halstead site (table 6). The amount of variance explained by the updated total organic carbon models ranged from 89 percent at the Sedgwick site to 91 percent at the Halstead site (table 6). The amount of variance explained by updated nutrient and total organic carbon models was within 5 percent of the most recently published models, except for the updated TKN model for the Sedgwick site (decrease of 7 percent), the updated total phosphorus model for the Sedgwick site (increase of 6 percent), and the updated total organic carbon model for the Halstead site (increase of 8 percent; table 6; Rasmussen and others, 2016).

Indicator Bacteria

Turbidity was the sole explanatory variable for E. coli and fecal coliform bacteria and was positively related to indicator bacteria (table 7), likely because bacteria sorbs to suspended particles. Suspended material in streams provide a medium for bacterial accumulation and transport. Updated model forms (selected explanatory variables) for E. coli and fecal coliform bacteria were similar to previously published models (table 7; Christensen and others, 2003; Rasmussen and others, 2016).

The amount of variance explained by updated indicator bacteria models ranged from 73 to 84 percent (table 7). The amount of variance explained by updated E. coli bacteria models increased from 5 percent (updated Halstead site R²=0.73) to 6 percent (updated Sedgwick site R²=0.79) from the most recent published models, and the amount of variance explained by updated fecal coliform bacteria models increased from 11 percent (updated Sedgwick site R²=0.77) to 16 percent (updated Halstead site R²=0.84) (table 7; Rasmussen and others, 2016).

Dissolved Arsenic and Atrazine

Streamflow and water temperature were explanatory variables for dissolved arsenic (table 8). Dissolved arsenic was negatively correlated with streamflow and positively correlated with water temperature (table 8). Updated model forms (selected explanatory variables) for dissolved arsenic were similar to the most recently published model forms (table 8; Rasmussen and others, 2016). Streamflow was the sole explanatory variable for dissolved arsenic in earlier published models (Christensen and others, 2003). The amount of variance explained by updated dissolved arsenic models ranged from 77 percent at the Sedgwick site to 79 percent at the Halstead site (table 8). The amount of variance explained by updated dissolved arsenic models was within 5 percent of the most recent published models (table 8; Rasmussen and others, 2016).

Specific conductance and seasonal components were explanatory variables for atrazine (table 8). Atrazine was negatively correlated with specific conductance at both study sites and model forms (selected explanatory variables) were similar to the most recently published models (table 8; Rasmussen and others, 2016). Previously published atrazine models by Christensen and others (2003) also included specific conductance and seasonal components as explanatory variables. The amount of variance explained by the updated atrazine models was 41 percent at the Halstead site and 54 percent at the Sedgwick site (table 8). The amount of variance explained by updated atrazine models was within 5 percent of the most recent published models (table 8; Rasmussen and others, 2016).