Final SAR Estimates for 2005 and SAR Estimation Equations for 2006

April 2006

One objective of the U.S. Geological Survey (USGS) Tongue River surface-water-quality monitoring network is to estimate and report sodium adsorption ratio (SAR) in real-time on a continuous basis during the March-October irrigation season for sites on the Tongue River and its major tributaries. During 2004-05, this objective was accomplished for many of the sites by estimating SAR from the continuous seasonal record of specific conductance (SC) provided by monitors installed at each network site. SAR in surface water potentially can be related to SC because both properties are a function of the concentrations of major ions in water.

SAR can be estimated using ordinary least squares regression (also known as linear regression) equations developed using SC and SAR data for water-quality samples collected at each site. During the first two years of the monitoring program, some data collected prior to 2004 were used because insufficient recent data from 2004-05 existed. Now that the monitoring network has been in operation for two years, regression equations can be adequately developed using only data for 2004-05, which represents a common time period for all sites.

The objective of this effort is to update previously developed SAR estimation equations using only SC and SAR data for water-quality samples collected in 2004-05. The updated SC-SAR equations have been used to calculate final estimated SAR values for 2005; these values replace the provisional data that were calculated using equations developed in early 2005 and that were provided during 2005. The final daily mean values of estimated SAR are available for retrieval from the USGS National Water Information System (NWIS).

These new SC-SAR regression equations will be used to estimate provisional real-time SAR during 2006 and are presented below. The periods of record and number of samples used to develop the equations for 2005 are listed in table 1.

Equations used to estimate SAR during 2004 can be found here.

Table 1. Summary of the number of water-quality samples collected during various years by the U.S. Geological Survey at sites in the Tongue River surface-water-quality monitoring network. No data are available for any of the sites for 1997-98. Shaded cells and bold text indicate the period of record and number of samples used to develop regression equations for estimating SAR from specific conductance after October 2005. Stations with no shaded cells indicate that estimated SAR will not be provided in real-time during 2006 because the recent data either do not produce a statistically significant relation or are too poorly defined to be reliable.

Tongue River at Monarch, Wyoming (USGS station 06299980)

A SC-SAR equation and 95-percent prediction intervals based on water-quality samples collected during January 2004 to October 2005 have been developed (fig. TRMON1). This regression equation was used to calculate estimated SAR values for the 2005 irrigation season (fig. TRMON2) from continuous SC. The estimated SAR values are within 0.06 SAR units of the laboratory-measured values for water-quality samples, with the exception of one value in May that occurred during a large runoff event.

Figure TRMON1. Relation of specific conductance (SC) and sodium adsorption ratio (SAR) for water-quality samples collected January 2004 to October 2005 at Tongue River at Monarch, Wyoming. Dashed lines indicate 95-percent prediction interval.

Figure TRMON2. Sodium adsorption ratio (SAR) measured in 2005 water-quality samples and estimated from specific conductance (SC) using relation shown in figure TRMON1, Tongue River at Monarch, Wyoming.

Tongue River at State Line, Montana (USGS station 06306300)

A SC-SAR equation and 95-percent prediction intervals based on water-quality samples collected during January 2004 to October 2005 have been developed (fig. TRSL1). This regression equation was used to calculate estimated SAR values for the 2005 irrigation season (fig. TRSL2) from continuous SC. The estimated SAR values are within 0.12 SAR units of the laboratory-measured values for water-quality samples.

Figure TRSL1. Relation of specific conductance (SC) and sodium adsorption ratio (SAR) for water-quality samples collected January 2004 to October 2005 at Tongue River at State line, Montana. Dashed lines indicate 95-percent prediction interval. Note that the y-axis has a logarithmic scale.

Figure TRSL2. Sodium adsorption ratio (SAR) measured in 2005 water-quality samples and estimated from specific conductance (SC) using relation shown in figure TRSL1, Tongue River at State line, Montana.

Tongue River at Tongue River Dam, Montana (USGS station 06307500)

A SC-SAR equation and 95-percent prediction intervals based on water-quality samples collected during January 2004 to October 2005 have been developed (fig. TRDAM1). This regression equation was used to calculate estimated SAR values for the 2005 irrigation season (fig. TRDAM2) from continuous SC. The estimated SAR values are within 0.10 SAR units of the laboratory-measured values for water-quality samples.

Figure TRDAM1. Relation of specific conductance (SC) and sodium adsorption ratio (SAR) for water-quality samples collected January 2004 to October 2005 at Tongue River at Tongue River Dam, Montana. Dashed lines indicate 95-percent prediction interval.

Figure TRDAM2. Sodium adsorption ratio (SAR) measured in 2005 water-quality samples and estimated from specific conductance (SC) using relation shown in figure TRDAM1, Tongue River at Tongue River Dam, Montana.

Tongue River at Birney Day School Bridge, Montana (USGS station 06307616)

A SC-SAR equation and 95-percent prediction intervals based on water-quality samples collected during January 2004 to October 2005 have been developed (fig. TRBDS1). This regression equation was used to calculate estimated SAR values for the 2005 irrigation season (fig. TRBDS2) from continuous SC. The estimated SAR values are within 0.15 SAR units of the laboratory-measured values for water-quality samples, with the exception of one value in early May.

Figure TRBDS1. Relation of specific conductance (SC) and sodium adsorption ratio (SAR) for water-quality samples collected January 2004 to October 2005 at Tongue River at Birney Day School Bridge, Montana. Dashed lines indicate 95-percent prediction interval.

Figure TRBDS2. Sodium adsorption ratio (SAR) measured in 2005 water-quality samples and estimated from specific conductance (SC) using relation shown in figure TRBDS1, Tongue River at Birney Day School Bridge, Montana.

Tongue River below Brandenberg Bridge, Montana (USGS station 06307830)

A SC-SAR equation and 95-percent prediction intervals based on water-quality samples collected during January 2004 to October 2005 have been developed (fig. TRBB1). This regression equation was used to calculate estimated SAR values for the 2005 irrigation season (fig. TRBB2) from continuous SC. The estimated SAR values are within 0.25 SAR units of the laboratory-measured values for water-quality samples.

Figure TRBB1. Relation of specific conductance (SC) and sodium adsorption ratio (SAR) for water-quality samples collected January 2004 to October 2005 at Tongue River below Brandenberg Bridge, Montana. Dashed lines indicate 95-percent prediction interval.

Figure TRBB2. Sodium adsorption ratio (SAR) measured in 2005 water-quality samples and estimated from specific conductance (SC) using relation shown in figure TRBB1, Tongue River below Brandenberg Bridge, Montana.

Tongue River above T & Y Diversion Dam, Montana (USGS station 06307990)

A SC-SAR equation and 95-percent prediction intervals based on water-quality samples collected during November 2004 (start of sampling period) to October 2005 have been developed (fig. TRTY1). This regression equation was used to calculate estimated SAR values for the 2005 irrigation season (fig. TRTY2) from continuous SC. The estimated SAR values are within 0.2 SAR units of the laboratory-measured values for water-quality samples.

Figure TRTY1. Relation of specific conductance (SC) and sodium adsorption ratio (SAR) for water-quality samples collected November 2004 to October 2005 at Tongue River above T & Y Diversion Dam, Montana. Dashed lines indicate 95-percent prediction interval.

Figure TRYTY2. Sodium adsorption ratio (SAR) measured in 2005 water-quality samples and estimated from specific conductance (SC) using relation shown in figure TRTY1, Tongue River above T & Y Diversion Dam, Montana.

Tongue River at Miles City, Montana (USGS station 06308500)

A SC-SAR equation and 95-percent prediction intervals based on water-quality samples collected during January 2004 to October 2005 have been developed (fig. TRMC1). This regression equation was used to calculate estimated SAR values for the 2005 irrigation season (fig. TRMC2) from continuous SC. The estimated SAR values are within 0.70 SAR units of the laboratory-measured values for water-quality samples, with the exception of one value in early June.

The SAR for the sample collected June 9, 2005, appears to be an outlier (fig. TRMC1) and was not used to develop the regression equation. Streamflow at Miles City on June 9 was derived largely from tributaries that flow into the Tongue River downstream from the T & Y Diversion Dam. Water in these tributaries, which included Pumpkin Creek, likely had high SAR values that resulted in an unusually high value at Miles City on June 9.

Figure TRMC1. Relation of specific conductance (SC) and sodium adsorption ratio (SAR) for water-quality samples collected January 2004 to October 2005 at Tongue River at Miles City, Montana. Dashed lines indicate 95-percent prediction interval.

Figure TRMC2. Sodium adsorption ratio (SAR) measured in 2005 water-quality samples and estimated from specific conductance (SC) using relation shown in figure TRMC1, Tongue River at Miles City, Montana.

Goose Creek near Acme, Wyoming (USGS station 06305700)

A SC-SAR equation and 95-percent prediction intervals based on water-quality samples collected during January 2004 to October 2005 have been developed (fig. GOOSE1). This regression equation was used to calculate estimated SAR values for the 2005 irrigation season (fig. GOOSE2) from continuous SC. The estimated SAR values are within 0.12 SAR units of the laboratory-measured values for water-quality samples, with the exception of one value in early May.

Figure GOOSE1. Relation of specific conductance (SC) and sodium adsorption ratio (SAR) for water-quality samples collected January 2004 to October 2005 at Goose Creek near Acme, Wyoming. Dashed lines indicate 95-percent prediction interval.

Prairie Dog Creek near Acme, Wyoming (USGS station 06306250)

A SC-SAR equation and 95-percent prediction intervals based on water-quality samples collected during January 2004 to October 2005 have been developed (fig. PDC1). This regression equation was used to calculate estimated SAR values for the 2005 irrigation season (fig. PDC2) from continuous SC. The estimated SAR values are within 0.23 SAR units of the laboratory-measured values for water-quality samples.

Figure PDC1. Relation of specific conductance (SC) and sodium adsorption ratio (SAR) for water-quality samples collected January 2004 to October 2005 at Prairie Dog Creek near Acme, Wyoming. Dashed lines indicate 95-percent prediction interval.

Figure PDC2. Sodium adsorption ratio (SAR) measured in 2005 water-quality samples and estimated from specific conductance (SC) using relation shown in figure PDC1, Prairie Dog Creek near Acme, Wyoming.

Hanging Woman Creek near Birney, Montana (USGS station 06307600)

A SC-SAR equation and 95-percent prediction intervals based on water-quality samples collected during January 2004 to October 2005 have been developed (fig. HWC1). This regression equation was used to calculate estimated SAR values for the 2005 irrigation season (fig. HWC2) from continuous SC. The estimated SAR values are within 0.4 SAR units of the laboratory-measured values for water-quality samples.

Figure HWC1. Relation of specific conductance (SC) and sodium adsorption ratio (SAR) for water-quality samples collected January 2004 to October 2005 at Hanging Woman Creek near Birney, Montana. Dashed lines indicate 95-percent prediction interval.

Figure HWC2. Sodium adsorption ratio (SAR) measured in 2005 water-quality samples and estimated from specific conductance (SC) using relation shown in figure HWC1, Hanging Woman Creek near Birney, Montana. Missing values from late July through October result from an extended period of no flow.

Otter Creek at Ashland, Montana (USGS station 06307740)

A SC-SAR equation and 95-percent prediction intervals based on water-quality samples collected during January 2004 to October 2005 have been developed (fig. OTTER1). This regression equation was used to calculate estimated SAR values for the 2005 irrigation season (fig. OTTER2) from continuous SC. The estimated SAR values are within 0.6 SAR units of the laboratory-measured values for water-quality samples.

Figure OTTER1. Relation of specific conductance (SC) and sodium adsorption ratio (SAR) for water-quality samples collected January 2004 to October 2005 at Otter Creek near Ashland, Montana. Dashed lines indicate 95-percent prediction interval.

Figure OTTER2. Sodium adsorption ratio (SAR) measured in 2005 water-quality samples and estimated from specific conductance (SC) using relation shown in figure OTTER1, Otter Creek at Ashland, Montana. Missing values of estimated SAR from late July through September result from periods of no flow and problems with the SC monitor.

Pumpkin Creek near Miles City, Montana (USGS station 06308400)

Real-time estimates of SAR were not provided for this site during 2005 owing to the lack of sufficient water-quality data from which to develop a SC-SAR relation. Although 17 samples were collected between January 2004 and October 2005, the relation between SC and estimated SAR is poorly defined, and any estimates of SAR made with the equation would have a large error. Therefore, estimated SAR values will not be available for 2005 from NWIS or provided in real-time during 2006 for this site.

Figure PUMP1. Relation of specific conductance (SC) and sodium adsorption ratio (SAR) for water-quality samples collected January 2004 to October 2005 at Pumpkin Creek near Miles City, Montana. Dashed lines indicate 95-percent prediction interval.