U.S. Department of the Interior U.S. Geological Survey

1. science for a changing world Application of Dimensionless Sediment Rating Curves to Predict Suspended-Sediment Concentrations, Bedload, and Annual Sediment Loads for Rivers and Streams Prepared in cooperation with the Montana Chapter of the American Water Resources Association Scientific Investigations Report 2016-5146 https://pubs.er.usgs.gov/publication/sir20165146 U.S. Department of the Interior U.S. Geological Survey

2. Sediment in Montana Rivers and Streams https://ofmpub.epa.gov/waters10/attains_state.control?p_state=MT&p_cycle=2016

3. What is a Dimensionless Sediment Rating Curve (DSRC)? • Method of scaling unit values in order to make inferences for regions where data are not available • Sediment and streamflow are transformed to dimensionless values by developing a ratio between regional samples and a reference index • The reference index is bankfull streamflow • Dimensionless values of SSC and bedload are plotted against dimensionless values of streamflow to create predictive equations U.S. Department of the Interior U.S. Geological Survey

4. Why develop a Dimensionless Sediment Rating Curve Model? • Dimensionless relations can help understand naturally occurring relations among hydraulic and water-quality properties. • Equations developed from dimensionless relations can be used to estimate SSC and bedload for streams where no data are available. • Costs are reduced by minimizing extensive sediment data collection. • Tool is provided to support decision-making for stream restoration prioritization and for planning and design of river restoration projects. Leopold and others (1964) Dietrich and others (1989) Troendle and others (2001) Padmanabhan and Johnson (2010) U.S. Department of the Interior U.S. Geological Survey

5. Purpose and Scope • Develop relations among streamflow, SSC, and bedload for selected rivers in Minnesota stratified by Pfankuch stability categories of “good/fair” and “poor”. • Compare SSC, bedload, and annual sediment loads estimated from DSRCs developed in Pagosa Springs, CO and regional Minnesota-based DSRCs to measured samples of SSC, bedload, and annual sediment loads from measured data. U.S. Department of the Interior U.S. Geological Survey

6. Study Area and Sampling Sites Advancing and retreating glaciers Northeast (volcanic bedrock) more resistant to glacial erosion Northwest lies in dried lakebed of glacial Lake Agassiz Southwest lies in the channel of glacial River Warren Southeast escaped Wisconsinan glaciation – “driftless” Good/Fair Poor

7. U.S. Department of the Interior U.S. Geological Survey

8. U.S. Department of the Interior U.S. Geological Survey

9. Develop Regional DSRC Models 664 values formatted, QCd, and potential outliers (18 outliers identified – appendix table 1-2 in report) Determine SSC and bedload at bankfull streamflow Check model requirements and assumptions a. sites without significant relations b. linearity and unequal variance 4. Construct the model a. weighted nonlinear least squares (nls function in R) b. intercepts SSC and bedload at bankfull U.S. Department of the Interior U.S. Geological Survey

10. Determining SSC and bedload at bankfull streamflow U.S. Department of the Interior U.S. Geological Survey

11. Wild Rice River at Twin Valley – determination of SSC at bankfull Jackknife resampling statistic identifies and removes bias

12. Suspended-sediment concentration relation to streamflow good/fair and poor stability sites U.S. Department of the Interior U.S. Geological Survey

13. Development of Regional DSRC Models The form of the regional DSRC model: (1 – B1) + B1X1B2 + e1 The intercept and coefficient, B1, are constructed so that when the models’ dimensionless output value is back transformed into dimensional form, the predicted value of SSC or bedload at the corresponding bankfull streamflow will match the estimated SSC and bedload at bankfull streamflow. U.S. Department of the Interior U.S. Geological Survey

14. Pagosa Springs and Minnesota DSRC model equations Suspended-sediment concentration Pagosa Springs DSRC models: SSC (good.fair stability): SSC = 0.0636 + 0.9326Q2.4085 SSC (poor stability): SSC = 0.0989 + 0.9212Q3.659 Minnesota DSRC models: SSC (good.fair stability): SSC = 0.026 + 0.974Q0.951 SSC (poor stability): SSC = 0.066 + 0.934Q1.006 U.S. Department of the Interior U.S. Geological Survey

15. Model Evaluation and Interpretation Multiple measures of goodness-of-fit Proximity of the DSRC models trendline to the 95 percent confidence intervals of the measured data’s regression trendline. Nash-Sutcliffe model efficiency value. Model bias. Deviation of the DSRC models estimated annual sediment loads from the measured data annual sediment loads. U.S. Department of the Interior U.S. Geological Survey

18. Minnesota DSRC model

21. Suspended-sediment concentration, in milligrams per liter EXPLANATION Measured data Pagosa Springs model Minnesota model Site model Site model upper and lower 95% confidence interval Bankfull streamflow

23. Measures of goodness-of-fit How closely do the observed data fit the model? Nash-Sutcliffe Model Efficiencies Nash, J.E. and J. V. Sutcliffe (1970) NSE SSCo = Observed SSC; SSCm = Modeled SSC; SSCo = Mean observed SSC U.S. Department of the Interior U.S. Geological Survey

24. -105 -4.7 -16.4 U.S. Department of the Interior U.S. Geological Survey

25. Pagosa Springs SSC Model Bias (%) Pagosa Springs Bedload Model Bias (%) Model Bias (Rb) Pagosa Springs SSC Model = 37% Minnesota SSC Model = 30% Pagosa Springs Bedload Model = 29% Minnesota Bedload Model = 20%

26. Suspended-sediment loads, in tons per year (2012)

27. Annual bedload, in tons per year (2013)

28. DSRC Model Precautions-Limitations • DSRC model reliability is dependent on representative measure of bankfull streamflow, SSC, and bedload. • DSRC models should not be used to predict loads for extreme streamflows, such as those that exceed twice the bankfull streamflow (Rosgen, var dates). • If relations between SSC and streamflow and between bedload and streamflow are not statistically significant, DSRCs are not applicable and should not be used to predict SSC or bedload (Rosgen, var dates). • If relations between SSC and streamflow and between bedload and streamflow in a particular region substantially deviate from DSRC models, then regionally specific DSRCs should be developed (Rosgen, 2010). U.S. Department of the Interior U.S. Geological Survey

29. Summary • The Minnesota DSRC models regression trendlines were not significantly different than site-specific regression trendlines for 14 out of 16 sites • Pagosa Springs DSRC models had markedly higher slopes than site-specific models and Minnesota DSRCs • For SSC, the Pagosa Springs model was not a good predictor of SSC for half of the sites samples (NSE < 0) • Annual suspended-sediment loads were not significantly different between Minnesota DSRC and site-specific R-LOADEST loads for good/fair sites for 2012 and 2013 and not different for 6 out of 8 sites for poor sites in 2012 and 2013 • Results support application of regionally-based DSRCs for uses such as stream restoration prioritization, planning and design, and estimating annual sediment loads U.S. Department of the Interior U.S. Geological Survey

30. Questions

31. Relation between Suspended-Sediment Concentration and Metallic Contaminants In the Clark Fork at Deer Lodge, Montana