Downstream Hydraulic Geometry of Alluvial Rivers

1. DOWNSTREAM HYDRAULIC GEOMETRY of ALLUVIAL RIVERS Pierre Y. Julien Colorado State University New Orleans December 2014 1

2. Objectives Discuss the downstream hydraulic geometry of alluvial rivers in terms of: • Level I – Alluvial river equilibrium • Level II – Spatial width changes • Level III – Temporal width changes

3. I – Alluvial river equilibrium Objectives: Review the Downstream Hydraulic Geometry (DHG) equations for alluvial rivers • Define Downstream Hydraulic Geometry • Review DHG equations • Compare with field measurements • Discuss some limitations of DHG

4. Cross-section geometry

5. Downstream Hydraulic Geometry

6. Some DHG equations

7. Julien-Wargadalam equations

8. Bankfull width and depth

9. Bankfull velocity and slope

10. Performance of different equations

11. I – Alluvial river equilibrium Conclusion: • Downstream Hydraulic Geometry equations provide very good first order approximations of alluvial river equilibrium conditions.

12. Limitations of DHG equations Limitations of the DHG equations include: • What is the dominant, bankfull or effective discharge? • What grain size (d50 or d90…) should be used? • Can DHG equations predict meandering or braiding? Is it also appropriate to ask: • Do rivers have constant W, h or S? • Does equilibrium exist? Lets discuss further the width changes in space and time

13. II – Spatial width changes Objectives: illustrate the changes in river widths and explain how river width can decrease • Illustrate channel width changes in space • Explain the concept of equivalent channel width • Show an example on the Rio Grande

14. Reach of the Rio Grande, NM narrow wide

15. Relationship between channel width and sediment transport

16. Concept of equivalent widths The concept of equivalent channel width stems from the decrease in sediment transport with increased channel width: Hypothesis: • The channel width of river reaches can be different from the equilibrium channel width from the DHG equations – however, to maintain the same sediment transport level, an increase in channel width requires an increase in channel slope.

17. Example on the Rio Grande, NM From Leon et al. ASCE-JHE 135(4), 2009

18. Slope vs width From Leon et al. ASCE-JHE 135(4), 2009

19. Slope vs width-depth ratio From Leon et al. ASCE-JHE 135(4), 2009

20. Wider reaches are steeper! From Leon et al. ASCE-JHE 135(4), 2009

21. II – Spatial width changes Conclusion: • Channel widths can be different from equilibrium conditions, but to satisfy continuity in sediment transport, wider channels require steeper slopes.

22. III – Temporal width changes Objectives: explain how alluvial river widths change over time • Illustrate that the channel widths can change with time • Explain the concept of deviation from equilibrium • Show and example on the Rio Grande • Estimate the time scale for river width adjustments

23. Temporal Changes in Hydraulic Geometry Rio Grande below Cochiti Dam, NM 1935 1972 1992 Braiding Transition Meandering From Richard et al. ASCE-JHE 131(11), 2005

24. Hydraulic Geometry of the Rio Grande From Richard et al. ASCE-JHE 131(11), 2005

25. How do rivers decrease their channel width? 1971 1971 1998 1998

26. Rio Grande – note the channel width changes 1996-2009 1996

27. Rio Grande 2005

28. Rio Grande 2006

29. Rio Grande 2009

30. Temporal width changes Hypotheses: • The alluvial channel width gradually adjusts towards the equilibrium width. • The annual change in channel width is proportional to the deviation from equilibrium, measured as the difference between the current channel width and the equilibrium channel width.

31. Hypothesis 1. Channel widths change towards equilibrium

32. Hypothesis 2. Width changes are proportional to the deviation from equilibrium equilibrium

33. Changes in active channel width Rio Grande, NM (after Richard et al., 2005) Deviation from equilibrium equilibrium Change in active channel width

34. Prediction of Active Channel Widthby Exponential equation (after Richard et al., 2005) Equilibrium width half adjustment Half adjustment Time scale  0.7/k1

35. III – Temporal width changes Conclusions: • Channel widths gradually change toward equilibrium • The annual width change is proportional to the difference between the actual width and the equilibrium width • The time required to reach equilibrium is asymptotic, but half the width adjustment can be reached in 0.7/k years, with for instance k ~ 0.025-0.045 on the Rio Grande.

36. Conclusions I - Downstream Hydraulic Geometry equations • Give very good first order approximations of alluvial river equilibrium II - Spatial changes in channel widths • Channel widths can differ from equilibrium channel widths, and wider reaches require steeper slopes III - Temporal changes in channel widths • Channel widths gradually change toward equilibrium at a rate proportional to the difference between the actual width and the equilibrium width • The time required to reach equilibrium is asymptotic, but half the width adjustment can be reached in 0.7/k years, and k ~ 0.035 on the Rio Grande

37. J. Wargadalam, CSU and DID IndonesiaG. Richard, CSU and Mesa State UniversityC. Leon, CSU and RTIU. Ji, Y.H. Shin and K.Y. Park, CSU and K-WATERD.C. Baird, R. Padilla and J. Aubuchon, USBRJ.S. Lee, Hanbat UniversitySo many others… Acknowledgments

38. Byen Mersi !