Surface Velocity to Depth-Averaged Velocity—A Review of Methods to Estimate Alpha and Remaining Challenges
Abstract
:1. Introduction
2. Methods to Estimate α
2.1. Alpha—Default Value
2.2. Site Alpha from Reference Discharge and Discharge from Surface Velocimetry with αi = 1
2.3. Site Alpha from Extrapolated Velocity Profiles
2.4. Alpha from Log Law Profiles—Extending from Bed to Surface
2.4.1. Alpha from Log Law Profiles—Theory and Derivations
2.4.2. Alpha from Log Law Profiles—Practical Implementation
2.4.3. Alpha from Log Law Profiles—Limitations
2.5. Alpha from Power Law Profiles—Extending from Bed to Surface
2.5.1. Alpha from Power Law Profiles—Theory and Derivations
2.5.2. Alpha from Power Law Profiles—Practical Implementation
2.5.3. Alpha from Power Law Profiles—Limitations
2.6. Alpha Estimation from Site Characteristics
- Natural rivers: ‘For water depth less than 2 m: consider using α = 0.8 with an uncertainty of about ±15% at 90% confidence level. For greater water depth, consider using α = 0.9 with an uncertainty of about ±15% at 90% confidence level.’
- Artificial concrete channels: ‘Consider using α = 0.9 with an uncertainty of about ±15% at 90% confidence level.’
2.7. Alpha—Additional Methods
2.7.1. Alpha from Shape Factor
2.7.2. Alpha from Surface Velocity Fluctuations
3. Stage to Alpha Rating Curves
4. Site Alpha vs. Local Alpha
5. Divided Channel Method
6. How to Select the Optimal Method for Estimating Alpha
7. Remaining Challenges and Future Directions
7.1. Surface Wind
7.2. Secondary Currents
7.3. Other Challenges
7.4. Future Directions
- Re-analysis of existing datasets (e.g., Welber et al. [4]; Hauet et al. [39]) with the inclusion of slope, which is a key driver of the shape of logarithmic velocity profiles (Section 2.4), and thus α.
- Conduct a systematic high-resolution laboratory investigation into the effect of surface wind on velocity profiles and α [62].
- Further investigate the turbulent outer region, secondary currents, compound velocity profiles, and how to practically estimate α using these compound profiles.
- Conduct a detailed field investigation into the spatial heterogeneity of α; the characteristics that make a measurement site suitable for the estimation of α; and the errors that may occur if these characteristics are not present.
- Develop methods to infer flow non-uniformity (e.g., acceleration/deceleration, convergence/divergence, secondary currents, etc.) from the surface velocity field.
8. Summary
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Normal | Smooth | Rough | Very Rough | Extreme Cases | |
---|---|---|---|---|---|
m | 6–7 | 10 | 4 | 2–3 | |
M | 0.143–0.167 | 0.1 | 0.25 | 0.333–0.5 | |
α | 0.86–0.87 | 0.91 | 0.8 | 0.67–0.75 | 0.6–1.2 |
H/d84 | m | M | α |
---|---|---|---|
>30 | 6.25 | 0.16 | 0.86 |
10–30 | 5.26 | 0.19 | 0.84 |
2–10 | 1.72 | 0.58 | 0.63 |
<2 | 0.63 | 1.59 | 0.37 |
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Biggs, H.; Smart, G.; Doyle, M.; Eickelberg, N.; Aberle, J.; Randall, M.; Detert, M. Surface Velocity to Depth-Averaged Velocity—A Review of Methods to Estimate Alpha and Remaining Challenges. Water 2023, 15, 3711. https://doi.org/10.3390/w15213711
Biggs H, Smart G, Doyle M, Eickelberg N, Aberle J, Randall M, Detert M. Surface Velocity to Depth-Averaged Velocity—A Review of Methods to Estimate Alpha and Remaining Challenges. Water. 2023; 15(21):3711. https://doi.org/10.3390/w15213711
Chicago/Turabian StyleBiggs, Hamish, Graeme Smart, Martin Doyle, Niklas Eickelberg, Jochen Aberle, Mark Randall, and Martin Detert. 2023. "Surface Velocity to Depth-Averaged Velocity—A Review of Methods to Estimate Alpha and Remaining Challenges" Water 15, no. 21: 3711. https://doi.org/10.3390/w15213711