The Effect of the Pool and Riffle on Transport in Rivers by Ian Halket A Thesis submitted to the Faculty of Graduate Studies of The University of Manitoba in partial fulfilment of the requirements of the degree of DOCTOR OF PHILOSOPHY Department of Civil Engineering University of Manitoba Winnipeg Copyright © 2010 by Ian Halket Acknowledgements During the course of my research for this thesis many people gave freely of their time and sage advice. I cannot acknowledge everyone here but I hope they accept my sincere appreciation. I would especially like to thank my supervisors and committee members for their patience and much needed advice. Dr. Peter Rasmussen, Dr. Jay Doering, Dr. David Lobb and Dr. Nazim Cicek were kind enough to offer their criticisms and suggestions during the preparation of the thesis; Dr. Ken Snelgrove gave direction and advice during the initial stage of the thesis. And Dr. Don Trim helped me develop and truth the calculus for the model. Lastly I would like to acknowledge the advice and insightful comments of Dr. Peter Steffler. I would also like to acknowledge Dwight Williamson and Nicole Armstrong and Manitoba Water Stewardship, my partners in the Assiniboine River Water Quality Study, who offered support and funding; Bob Harrison and Alf Warkenton with Manitoba Water Stewardship, who provided hydrological data for the thesis; and Dennis Lazowski of Water Survey of Canada, who provided the data for the Athabasca River. I could not have completed my thesis without the support and encouragement that I received from my colleagues at Red River College, especially Ralph Caldwell, Robert Friessen, Ken Webb and Dale Watts. Lastly, I would like to thank my family, Lisa, Lezlie and Alec for their editorial support, encouragement, understanding and especially their stamina in putting up with my study antics during the time I have been working on this thesis and Ph.D. studies. i For PJ, who always believed. ii Abstract One-dimensional steady flow pollutant transport models assume that the river reach modelled has a uniform cross-sectional shape which manifests as a constant average velocity in the model equations. Rarely do rivers meet this criterion. Their channels are seldom uniform in shape, but rather alternate in a quasi-periodic manner between pool and riffle sections. This bedform sequencing imparts a corresponding variation in the average cross-sectional velocity which is not accounted for in constant velocity transport models. The literature points out that the pool and riffle planform may be the reason for the sometimes poor predictions obtained from these models. This thesis confirms that the fluctuation in average cross-sectional velocity caused by the pool and riffle planform does have a marked effect on transport in rivers. The pool and riffle planform promotes an enhanced decay of a pollutant when a first order biochemical reaction is simulated. This effect becomes more pronounced as flow declines. The reason for this is that travel time in a pool and riffle channel is greater than for a uniformly shaped channel. Current one-dimensional models assume a uniform channel and therefore overestimate the velocity of a substance moving downstream. To show this an equation is developed that describes the variation in average cross-sectional velocity along a pool and riffle channel. The parameters of the equation can be easily evaluated for any river. The equation is incorporated into a mass balance analysis and a new form of the river transport model is derived. Analysis shows that the transport of a substance in a pool and riffle channel is governed by travel velocity which is different from the average cross-sectional velocity iii used in the traditional advection model. Replacing average velocity with travel velocity provides a simple fix for the traditional model. The new transport model is tested on the Athabasca River with excellent results. The variable velocity model successfully simulates the DO dynamics on a 550 kilometre stretch of the river. This suggests that the model has good potential for simulating pollutant transport in other rivers. Since analysis shows that the effect of the pool and riffle planform on contaminant transport is magnified at low flow levels, the model has good potential for use in determining TMDLs for contaminants, because these regulatory levels are set for low flow conditions. iv Table of Contents Abstract ii List of Tables vii List of Figures viii Chapter 1 Introduction 1 Chapter 2 Transport of Pollutants in Rivers 6 2.1 Longitudinal Dispersion 9 2.2 The Spread of a Pollutant Pulse 12 2.3 Time-Concentration Curves and Transient Storage 15 2.4 Discussion 19 Chapter 3 Pool and Riffle 21 3.1 Hydraulic Geometry 25 3.2 The Velocity Reversal Hypothesis 26 3.3 Assiniboine River Study 33 3.4 Discussion 48 Chapter 4 Model Development 52 4.1 Average Velocity Equation for a Pool and Riffle 54 4.2 A Pollutant Transport Moded 58 4.3 Theoretical Analysis 66 4.4 Non-dimensional Analysis 71 4.5 The General Case 75 Chapter 5 Model Calibration and Validation 78 5.1 Athabasca River 82 5.2 History of Studies on the Athabasca 83 5.3 Variable Velocity DO Model 85 5.4 Velocity Reversal Patterns 87 5.5 Uncertainties 98 5.6 Calibration 100 5.7 Sensitivity and Non-Dimensional Analysis 105 5.8 Validation 107 5.9 Discussion 112 Chapter 6 Summary and Conclusion 120 6.1 Future Directions 125 6.2 Conclusion 126 Literature Cited 129 v Appendix 1 Description of Model Structure 147 Appendix 2 Input Values and Results of Athabasca River Modelling 152 vi List of Tables Table 3.1. Hydraulic geometry coefficients and exponents for the hydrometric stations on the Assiniboine River. 35 Table 4.1. Comparison of concentrations for variations in amplitude. 64 Table 4.2. Comparison of hydraulic parameters and flow for the upper reach of the Assiniboine River. 72 Table 4.3. Comparison of differences in concentration between variable velocity and constant velocity advection equations for flow and distance downstream of pollutant input. 72 Table 4.4. Comparison of differences in concentration between variable velocity and constant velocity advection equations. 73 Table 5.1. Value of parameters in Equations 5.3 and 5.4 for a ±25% perturbation. 106 Table 5.2. Results of sensitivity analysis for Station 105616 m. 106 Table 5.3. Non-dimensional analysis for the Athabasca River. 107 Table 5.4 Root mean square and coefficient of determination for the Variable Velocity Model (VVM) and DOSTOC model simulations on the Athabasca River. 112 Table 5.5. Comparison of travel times calculated from HEC2 velocities and travel velocity uT. 114 Table 5.6. Comparison of travel times calculated by average cross-sectional velocity, a, and travel velocity uT. 115 Table 5.7. Flow level ranges and 2b/a ratios for the Athabasca River for the four survey periods. 116 vii List of Figures Figure 2.1. Typical representations of time-concentration curves for a) the advection-dispersion equation and b) measurement of a tracer release. 12 Figure 3.1. Typical pool and riffle sequence. 22 Figure 3.2. The velocity reversal hypothesis. 27 Figure 3.3. Assiniboine River Study Area. 34 Figure 3.4. Comparison of pool and riffle cross-sections at Miniota for a 23 cms flow level. 36 Figure 3.5. Velocity-discharge curves for the Miniota Station. 37 Figure 3.6. Comparison of river channel cross-sectional shape at Miniota Station for 1994, 1995, and 1997 at a 22 cms flow stage. 39 Figure 3.7. Comparison of annual Velocity-discharge curves at Miniota Station for 1993, 1994, and 1996 at the riffle. 40 Figure 3.8. Comparison of annual hydraulic geometry curves at Miniota Station between the pool and riffle sections. 41 Figure 3.9. Velocity-discharge curves for the hydrometric stations at Griswold, St. Lazare and Virden. 42 Figure 3.10. Channel cross-sections near Virden, Manitoba. 44 Figure 3.11. Full range of the velocity reversal pattern at Virden, Manitoba. 44 Figure 3.12. Velocity reversal pattern established from analysis of the records at Shellmouth and Millwood stations. 45 Figure 3.13. Comparison of velocity reversal patterns for the upper and lower reaches on the Assiniboine River. 46 Figure 3.14. Comparison of velocity reversal patterns for the upper, lower and Russel reaches on the Assiniboine River. 47 Figure 3.15. Comparison of average Velocity-discharge curves for the viii East Fork River and Severn River. 49 Figure 4.1. Schematic for deriving the one-dimensional general mass-balance equation for a pool and riffle channel. 59 Figure 4.2. Plot of analytical solution to Equation 4.10 for the lower reach of the Assiniboine River at a 22.4 cms flow stage. 62 Figure 4.3. Comparison of distance-concentration curves for amplitudes varying from 0 to ±0.3 on the Assiniboine River at a flow of 22.4 cms. 63 Figure 4.4. Comparison of distance-concentration curves for the constant velocity model versus the variable velocity model at the 7Q10 flow stage on the Assiniboine River. 65 Figure 4.5a and b. Velocity-distance(a) and velocity-time(b) graphs for a 22.4 cms flow at Virden on the Assiniboine River. 68 Figure 4.6. Travel velocity versus the ratio of the area of the pool to the area of the riffle. 76 Figure 5.1. Athabasca River Basin. (Noton and Allan, 1994). 81 Figure 5.2. Velocity-discharge curves for the Athabasca River used by MacDonald and Hamilton (1988) and Chambers et al. (1996). 88 Figure 5.3a. Hydraulic Geometry at Hinton on the Athabasca River. 89 Figure 5.3b. Hydraulic Geometry at Windfall on the Athabasca River.