Abstract
Quantifying the flow resistance in step-pool streams is of importance for studying the restoration of benthic animals and bedload transport. The Darcy–Weisbach friction factor of the total flow resistance is partitioned into components associated with grains, spills, and loose-packed particles. By extending the two-dimensional hydraulic radius, a new proposed roughness height is applied to evaluate resistance components induced by spills and loose-packed particles. Three morphological patterns induced by different-magnitude floods can be classified to form different flow resistance components, depending on the morphological variation. The three components varying with hydraulic and geometric parameters by considering the closest-1 NSEI and smallest RMSE and MRE have been examined. It is found that the grain resistance factor component, in comparison with other factors, has a slight impact on hydraulic parameters. Hydraulic and geometric parameters have a significant influence on the spill resistance component, accounting for the main proportion of the total resistance. The resistance associated with loose-packed particles correlates with parameters due to the initial random movement of particles and abundant sources.
Similar content being viewed by others
Data availability
All data generated or analyzed during this study are included in the manuscript.
References
Aberle J, Smart GM (2003) The influence of roughness structure on flow resistance on steep slopes. J Hydraul Res 41(3):259–269
Abrahams AD, Li G, Atkinson JF (1995) Step-pool streams: adjustment to maximum flow resistance. Water Resour Res 31(10):2593–2602
Bathurst JC (1978) Flow resistance of large-scale roughness. J Hydraul Div 104(12):1587–1603
Bathurst JC (1985) Flow resistance estimation in mountain rivers. J Hydraul Eng 1111:625–643
Beisel JN, Usseglio-Polatera P, Thomas S, Moreteau JC (1998) Stream community structure in relation to spatial variation: the influence of mesohabitat characteristics. Hydrobiologia 389(1–3):73–88
Billi P, D’Agostino V, Lenzi MA. Marchi L (1998) Bed load, slope and channel processes in a high-altitude alpine torrent. Gravel-Bed Rivers in the Environment, Water Resources Publications, LLC, Highlands Ranch, CO
Canovaro F, Paris E, Solari L (2007) Effects of macro-scale bed roughness geometry on flow resistance. Water Resour Res 43:W10414
Chanson H (1994) Hydraulics of skimming flows over stepped channels and spillways. J Hydraul Res 32(3):445–460
Chartrand SM, Jellinek M, Whiting PJ, Stamm J (2011) Geometric scaling of step-pools in mountain streams: Observations and implications. Geomorphology 129(1–2):141–151
Cheng NS (2011) Representative roughness height of submerged vegetation. Water Resour Res 47:W08517
Chin A (2003) The geomorphic significance of step–pools in mountain streams. Geomorphology 55(1–4):125–137
Chin A, Wohl E (2005) Toward a theory for step pools in stream channels. Prog Phys Geogr 29(3):275–296
Church M, Zimmermann A (2007) Form and stability of step-pool channels: research progress. Water Resour Res 43:W03415
Comiti F, Andreoli A, Lenzi MA (2005) Morphological effects of local scouring in step–pool streams. Earth Surf Proc Land 30(12):1567–1581
Comiti F, Mao L, Wilcox A, Wohl E, Lenzi MA (2007) Field-derived relationships for flow velocity and resistance in high-gradient streams. J Hydrol 340:48–62
Comiti F, Cadol D, Wohl E (2009) Flow regimes, bed morphology, and flow resistance in self-formed step-pool channels. Water Resour Res 45:W04424
Death RG, Zimmermann EM (2005) Interaction between disturbance andprimary productivity in determining stream invertebrate diversity. Oikos 111(2):392–402
Duan XH, Wang ZY, Xu MZ, Zhang K (2009) Effect of streambed sediment on benthic ecology. Int J Sedim Res 24(3):325–338
Essery ITS, Horner MW (1978). The Hydraulic Design of Stepped Spillways, CIRIA Report No. 33, 3nd edition, Jan., London, UK
Ferguson R (2007) Flow resistance equation for gravel- and boulder- bed streams. Water Resour Res 43:W05427
Ferro V, Porto P (2018) Applying hypothesis of self-similarity for flow-resistance law in calabrian gravel-bed rivers. J Hydraul Eng 144(2):04017061
Graf WH (1984) Flow resistance for steep, mobile channels. Proceedings of Workshop ‘Idraulica del territorio montano’, Bressanone: 341–352
Hassan MA, Tonina D, Beckie RD, Kinnear M (2014) The effects of discharge and slope on hyporheic flow in step-pool morphologies. Hydrol Process 29(3):419–433
Hawkins CP, Murphy ML, Anderson N (1982) Effects of canopy, substrate composition, and gradient on the structure of macroinvertebrate communities in cascade range streams of oregon. Ecology 63(6):1840–1856
Hey RD (1979) Flow resistance in gravel-bed rivers. J Hydraul Div 105(4):365–379
Katul G, Wiberg P, Albertson J, Hornberger G (2002) A mixing layer theory for flow resistance in shallow streams. Water Resour Res 38(11):1250
Koloseus HJ, Davidian J (1996) Free-surface instability correlations, and Roughness-concentration effects on flow over hydrodynamically rough surfaces. USGS, Washington. https://doi.org/10.3133/wsp1592CD
Lee AJ, Ferguson RI (2002) Velocity and flow resistance in step-pool streams. Geomorphology 46(1–2):59–71
Lenzi MA (2004) Displacement and transport of marked pebbles, cobbles and boulders during floods in a steep mountain stream. Hydrol Process 18(10):1899–1914
Luo M, Wang X, Yan X, Huang E (2020) Applying the mixing layer analogy for flow resistance evaluation in gravel-bed streams. J Hydrol 589:125119
Luo M, Ye C, Wang X, Huang E, Yan X (2022) Analytical model of flow velocity in gravel-bed streams under the effect of gravel array with different densities. J Hydrol 608:127581
MacFarlane WA, Wohl E (2003) Influence of step composition on step geometry and flow resistance in step-pool streams of the Washington Cascades. Water Resour Res 39(2):1037
Mao L, Lenzi MA (2007) Sediment mobility and bedload transport conditions in an alpine stream. Hydrol Process 21(14):1882–1891
Marcelo H (2008) Sedimentation engineering, Processes, measurements, modeling, and practice. Virginia, ASCE Press, Reston, pp 21–146
Matthaei CD, Townsend CR (2000) Long-term effects of local disturbance history on mobile stream invertebrates. Oecologia 125(1):119–126
Maxwell AR, Papanicolaou AN (2001) Step-pool morphology in high-gradient streams. Int J Sedim Res 16(3):380–390
McCuen RH, Knight Z, Cutter AG (2006) Evaluation of the Nash-Sutcliffe efficiency index. J Hydrol Eng 11(6):597–602
Millar RG (1999) Grain and form resistance in gravel-bed rivers resistances. J Hydraul Res 37(3):303–312
Millar RG, Quick MC (1998) Stable width and depth of gravel-bed rivers with cohesive banks. J Hydr Eng-ASCE 124(10):1005–1013
Molnar P, Densmore AL, McArdell BW, Turowski JM, Burlando P (2010) Analysis of changes in the step-pool morphology and channel profile of a steep mountain stream following a large flood. Geomorphology 124:85–94
Palucis MC, Ulizo TP, Fuller B, Lamb MP (2018) Flow resistance, sediment transport, and development in a steep gravel-bedded river flume. Geomorphology 320:111–126
Powell DM (2014) Flow resistance in gravel-bed rivers: progress in research. Earth Sci Rev 136:301–338
Recking A, Frey P, Paquier A, Belleudy P, Champagne JY (2008) Feedback between bed load transport and flow resistance in gravel and cobble bed rivers. Water Resour Res 44:W05412
Rickenmann D, Recking A (2011) Evaluation of flow resistance in gravel-bed rivers through a large field data set. Water Resour Res 47(7):W07538
Sindelar C, Smart G (2016) Transition flow in step-pool systems: pressure distributions and drag forces. J Hydraul Eng 10:04016035
Smart GM, Duncan MJ, Walsh JM (2002) Relatively rough flow resistance equations. J Hydraul Eng 128:568–578
Stefano CD, Palmeri V, Pampalone V, Ferro V (2019) Dissipative analogies of step-pool features: from rills to mountain streams. CATENA 174:235–247
Strom KB, Papanicolaou AN (2007) ADV measurements around a cluster microform in a shallow mountain stream. J Hydraul Eng 133(12):1379–1389
Tritico HM, Hotchkiss RH (2005) Unobstructed and obstructed turbulent flow in gravel bed rivers. J Hydraul Eng 131(8):635–645
Weichert RB, Bezzola GR, Minor H (2008) Bed morphology and generation of step-pool channels. Earth Surf Proc Land 33:1678–1692
Wilcox AC, Nelson JM, Wohl EE (2006) Flow resistance dynamics in step-pool channels: 2. partitioning between grain, spill, and woody debris resistance. Water Resources Research 42: W05419
Wohl EE, Thompson DM (2000) Velocity characteristics along a small step–pool channel. Earth Surf Proc Land 25:353–367
Xu MZ, Wang ZY, Pan BZ, Zhao N (2012) Distribution and species composition of macroinvertebrates in the hypothetic zone of bed sediment. Int J Sedim Res 27(2):129–140
Zhang C, Xu M, Hassan MA, Chartrand SM, Wang Z (2018) Experimental study on the stability and failure of individual step-pool. Geomorphology 311:51–62
Zhang C, Xu M, Hassan MA, Chartrand SM, Wang Z, Ma Z (2020) Experiment on morphological and hydraulic adjustments of step-pool unit to flow increase. Earth Surf Proc Land 45:280–294
Zhao N, Wang ZY, Pan BZ, Xu MZ, Li ZW (2014) Macroinvertebrate assemblages in mountain streams with different streambed stability. River Res Appl 31(7):825–833
Zimmermann A (2010) Flow resistance in steep streams: an experimental study. Water Resour Res 46:W09536
Acknowledgements
This research is supported by the Second Tibetan Plateau Scientific Expedition and Research Program (Grant No. 2019QZKK020401) and the National Natural Science Foundation of China (Grant No. 51639007 and 41771543). Thanks to two anonymous reviewers and editors for their useful and careful critiques for improving this research.
Funding
This research is supported by the Second Tibetan Plateau Scientific Expedition and Research Program (Grant No. 2019QZKK020401) and the National Natural Science Foundation of China (51639007 and 41771543).
Author information
Authors and Affiliations
Contributions
Ming Luo: Conceptualization, Investigation, Methodology, Formal analysis, Writing- Original Draft, Writing—Review & Editing. Xufeng Yan: Validation, Writing—Review & Editing. Er Huang: Supervision, Funding acquisition, Project administration.
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Ethical statement
This paper complies with the ethical standards of research and methodology.
Code availability
Not applicable.
Additional information
Edited by Dr. Luigi Cimorelli (ASSOCIATE EDITOR) / Dr. Michael Nones (CO-EDITOR-IN-CHIEF).
Rights and permissions
About this article
Cite this article
Luo, M., Yan, X. & Huang, E. Flow resistance evaluation based on three morphological patterns in step-pool streams. Acta Geophys. 71, 359–372 (2023). https://doi.org/10.1007/s11600-022-00850-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11600-022-00850-3