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2025 Vol.58, Issue 4 Preview Page

Research Article

Assessment of bedload empirical equation applicability based on recent bedload meta-analysis data

최신 소류사 메타분석 자료 기반 소류사량 경험식 적용성 분석

Hyoseob Noha
,
Il Won Seobc
,
Yong Sung Parkd*
노 효섭a
,
서 일원bc
,
박 용성d*
aResearch Assistant Professor, Institute of Construction and Environmental Engineering, Seoul National University, Seoul, Korea
bProfessor Emeritus, Department of Civil and Environmental Engineering, Seoul National University, Seoul, Korea
cPrincipal Researcher, Institute of Construction and Environmental Engineering, Seoul National University, Seoul, Korea
dAssociate Professor, Department of Civil and Environmental Engineering, Seoul National University, Seoul, Korea
a서울대학교 건설환경종합연구소 연구조교수
b서울대학교 건설환경공학부 명예교수
c서울대학교 건설환경종합연구소 책임연구원
d서울대학교 건설환경공학부 부교수
*Corresponding Author
30 April 2025. pp. 329-343
PDF XML Citation
Abstract

Accurate estimation of sediment transport is crucial for river management. However, currently, there are no sediment transport equations widely applicable under diverse conditions. This study evaluates the applicability of existing sediment transport equations using the latest sediment transport metadata and analyzes factors influencing their applicability. For laboratory flume data, existing equations demonstrated meaningful explanatory power with the index of agreement (IoA) exceeding 0.65. In contrast, for natural river data, IoA values were mostly below 0.51, indicating limited applicability. This discrepancy is likely due to the greater complexity of hydraulic characteristics in natural rivers and the higher uncertainty in estimating shear stress compared to laboratory conditions. To improve the accuracy of the empirical equation, this study proposes several alternatives; introducing additional explanatory variables, utilizing alternative sediment transport parameters to replace shear stress, and developing equations that account for regime shifts. These approaches are expected to improve the accuracy of sediment transport estimation across various conditions.

Keywords
Sediment transport
Empirical formula
Metadata analysis
Experimental flume
Natural river
Shear stress

하천 관리에서 중요한 인자인 유사량의 산정은 매우 중요하나 다양한 조건에서 적용할 수 있는 신뢰성 높은 소류사량 산정식은 거의 없는 것으로 알려져 있다. 이에 본 연구에서는 최신 소류사량 메타데이터를 활용하여 기존 경험식들의 적용 가능성을 평가하고, 적용성에 영향을 미치는 요인을 분석하였다. 분석 결과, 실험 수로에서 수집한 자료에 대해 기존 경험식들이 일치도 지수 0.65 이상의 유의미한 설명력을 보였으나, 자연 하천 자료에 대해서는 대부분 0.51 이하로 나타났다. 이는 자연 하천의 수리 특성이 실험 수로보다 복잡하고, 하천 마찰 응력 산정의 불확도가 크기 때문으로 판단된다. 산정식의 정확도를 개선하기 위해 추가적인 설명변수를 도입하는 방안, 실측이 어려운 바닥 마찰 응력을 대신할 대체 소류력 변수를 활용하는 방안, 양상 변동(regime shift)을 반영한 산정식 개발을 대안으로 제시하였다. 이러한 새로운 접근은 다양한 조건에서 소류사량 산정의 정확도를 높이는 데 기여할 것으로 기대된다.

키워드
소류사량
경험식
메타데이터 분석
실험 수로
자연 하천
마찰 응력
References
1

Aguirre-Pe, J., Olivero, M.I.A.L., and Moncada, A.T. (2003). "Particle densimetric Froude number for estimating sediment transport." Journal of Hydraulic Engineering, Vol. 129, No. 6, pp. 428-437.

10.1061/(ASCE)0733-9429(2003)129:6(428)
2

Ali, S.Z., and Dey, S. (2017). "Origin of the scaling laws of sediment transport." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 473, 20160785.

10.1098/rspa.2016.0785
3

Ancey, C., and Pascal, I. (2020). "Estimating mean bedload transport rates and their uncertainty. Journal of Geophysical Research: Earth Surface, Vol. 125, No. 7, e2020JF005534.

10.1029/2020JF005534
4

Ancey, C., and Recking, A. (2023). "Scaling behavior of bedload transport: What if Bagnold was right?." Earth-Science Reviews, Vol. 246, 104571.

10.1016/j.earscirev.2023.104571
5

Armanini, A., Cavedon, V., and Righetti, M. (2015). "A probabilistic/ deterministic approach for the prediction of the sediment transport rate." Advances in Water Resources, Vol. 81, pp. 10-18.

10.1016/j.advwatres.2014.09.008
6

Bagnold, R.A. (1966) An approach to the sediment transport problem from general physics. Professional Paper 422-I, United States Geological Survey, Washington, D.C., U.S.

10.3133/pp422I
7

Barati, R., Neyshabouri, S.S., and Ahmadi, G. (2014). Numerical simulation of the sediment transport in the saltation regime. In River flow 2014, Taylor and Francis Group London, London, England, pp. 833-841.

10.1201/b17133-114
8

Batalla, R.J. (1997). "Evaluating bed‐material transport equations using field measurements in a sandy gravel‐bed stream, Arbucies river, NE Spain." Earth Surface Processes and Landforms: The Journal of the British Geomorphological Group, Vol. 22, No. 2, pp. 121-130.

10.1002/(SICI)1096-9837(199702)22:2<121::AID-ESP671>3.0.CO;2-7
9

Boateng, I., Bray, M., and Hooke, J. (2012). "Estimating the fluvial sediment input to the coastal sediment budget: A case study of Ghana." Geomorphology, Vol. 138, No. 1, pp. 100-110.

10.1016/j.geomorph.2011.08.028
10

Brown, C.B. (1950). "Sediment transportation." Engineering hydraulics, Edited by Rouse, H., Wiley, New York, NY, U.S., pp. 769-857.

11

Brownlie, W.R. (1981) Compilation of alluvial channel data: Laboratory and field. W. M.Keck Laboratory of Hydraulics and Water Resource, Report No. KH-R-43B, Pasadena, California Institute of Technology, CA, U.S.

12

Bunte, K., Abt, S.R., Potyondy, J.P., and Swingle, K.W. (2008). "A comparison of coarse bedload transport measured with bedload traps and Helley-Smith samplers." Geodinamica Acta, Vol. 21, No. 1-2, pp. 53-66.

10.3166/ga.21.53-66
13

Bunte, K., and Swingle, K.W. (2021). Description and development of a database for bedload trap measurements in Rocky Mountain streams. US Department of Agriculture, Forest Service, Rocky Mountain Research Station, Fort Collins, CO, U.S.

10.2737/RMRS-GTR-420
14

Camenen, B., and Larson, M. (2005). "A general formula for non- cohesive bed load sediment transport." Estuarine, Coastal and Shelf Science, Vol. 63, No. 1-2, pp. 249-260.

10.1016/j.ecss.2004.10.019
15

Cao, H.H. (1985) Résistance hydraulique d'un lit de gravier mobilea pente raide. Ph.D. Dissertation, École polytechnique fédérale de Lausanne, Lausanne, Switzerland.

16

Cassar, C., Nicolas, M., and Pouliquen, O. (2005). "Submarine granular flows down inclined planes." Physics of Fluids, Vol. 17, No. 10, 103301.

10.1063/1.2069864
17

Cheng, N.S. (2002). "Exponential formula for bedload transport." Journal of Hydraulic Engineering, Vol. 128, No. 10, pp. 942- 946.

10.1061/(ASCE)0733-9429(2002)128:10(942)
18

Cheng, N.S., Wei, M.X., Chiew, Y.M., Lu, Y.S., and Emadzadeh, A. (2020). "Combined effects of mean flow and turbulence on sediment pickup rate." Water Resources Research, Vol. 56, No. 2, e2019WR026181.

10.1029/2019WR026181
19

Claude, N., Rodrigues, S., Bustillo, V., Bréhéret, J.G., Macaire, J.J., and Jugé, P. (2012). "Estimating bedload transport in a large sand - gravel bed river from direct sampling, dune tracking and empirical formulas." Geomorphology, Vol. 179, pp. 40-57.

10.1016/j.geomorph.2012.07.030
20

Deal, E., Venditti, J.G., Benavides, S.J., Bradley, R., Zhang, Q., Kamrin, K., and Perron, J. T. (2023). "Grain shape effects in bed load sediment transport." Nature, Vol. 613, No. 7943, pp. 298-302.

10.1038/s41586-022-05564-636631652
21

du Boys, M.P. (1879). "Étude du régime du Rhône et de l'action exercée par les eaux sur un lit à fond de graviers indéfiniment affouillable." Annales des Ponts et Chaussées, Vol. 5, No. 18, pp. 141-195.

22

Einstein, H.A. (1950). The bed-load function for sediment transportation in open channel flows(Vol. 1026). US Department of Agriculture, Washington, DC, U.S.

23

Engelund, F., and Hansen, E. (1967). A monograph on sediment transport in alluvial streams. Technical University of Denmark, Østervoldgade 10, Copenhagen K, Denmark.

24

Ferguson, R.I. (2012). "River channel slope, flow resistance, and gravel entrainment thresholds." Water Resources Research, Vol. 48, No. 5, W05517.

10.1029/2011WR010850
25

Guo, J. (2015). "Sidewall and non-uniformity corrections for flume experiments. Journal of Hydraulic Research, Vol, 53, No. 2, pp. 218-229.

10.1080/00221686.2014.971449
26

Guo, J. (2017). "Exact procedure for Einstein - Johnson's sidewall correction in open channel flow." Journal of Hydraulic Engineering, Vol,143, No. 4, 06016027.

10.1061/(ASCE)HY.1943-7900.0001260
27

Guo, J. (2021). "Generalized bed-load function based on empirical data." Journal of Hydraulic Engineering, Vol, 147, No. 8, 06021008.

10.1061/(ASCE)HY.1943-7900.0001909
28

Hinton, D., Hotchkiss, R., and Ames, D.P. (2017). "Comprehensive and quality-controlled bedload transport database." Journal of Hydraulic Engineering, Vol. 143, No. 2, 06016024.

10.1061/(ASCE)HY.1943-7900.0001221
29

Hoan, N.T., Stive, M., Booij, R., Hofland, B., and Verhagen, H.J. (2011). "Stone stability in nonuniform flow." Journal of Hydraulic Engineering, Vol. 137, No. 9, pp. 884-893.

10.1061/(ASCE)HY.1943-7900.0000387
30

Hsu, T.J., Jenkins, J.T., and Liu, P.L.F. (2004). "On two-phase sediment transport: Sheet flow of massive particles." Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 460, No. 2048, pp. 2223- 2250.

10.1098/rspa.2003.1273
31

Ikeda, H. (1983). Experiments on bedload transport, bed forms and sedimentary structures using fine gravel in the 4-metre wide flume. Technical Report Paper 2, Environmental Research center. Tsukuba University, Ibaraki, Japan.

32

Jäggi, M. (1984). "Der Geschiebetransport in Flüssen nach der VAW-Formel 1983." Schweizer Ingenieur und Architekt, Vol. 102, No. 47, pp. 940-943.

33

Kim, D., Kim, J., Son, G., and Park, Y.S. (2024). "Experimental evaluation of estimating local bed shear stress using log law in a straight river channel." KSCE Journal of Civil Engineering, Vol. 28, No. 3, pp. 1094-1107.

10.1007/s12205-024-1399-3
34

King, J.G. (2004). Sediment transport data and related information for selected coarse-bed streams and rivers in Idaho (No. 131). US Department of Agriculture, Forest Service, Rocky Mountain Research Station, Fort Collins, CO, U.S.

10.2737/RMRS-GTR-131
35

Krause, P., Boyle, D.P., and Bäse, F. (2005). "Comparison of different efficiency criteria for hydrological model assessment." Advances in Geosciences, Vol. 5, pp. 89-97.

10.5194/adgeo-5-89-2005
36

Kwon, S., Noh, H., Seo, I.W., and Park, Y.S. (2023a). "Effects of spectral variability due to sediment and bottom characteristics on remote sensing for suspended sediment in shallow rivers." Science of The Total Environment, Vol. 878, 163125.

10.1016/j.scitotenv.2023.16312536990231
37

Kwon, S., Seo, I.W., and Lyu, S. (2023b). "Investigating mixing patterns of suspended sediment in a river confluence using high- resolution hyperspectral imagery." Journal of Hydrology, Vol. 620, 129505.

10.1016/j.jhydrol.2023.129505
38

Kwon, S., Seo, I.W., Noh, H., and Kim, B. (2022a). "Hyperspectral retrievals of suspended sediment using cluster-based machine learning regression in shallow waters." Science of The Total Environment, Vol. 833, 155168.

10.1016/j.scitotenv.2022.15516835417723
39

Kwon, S., Shin, J., Seo, I.W., Noh, H., Jung, S.H., and You, H. (2022b). "Measurement of suspended sediment concentration in open channel flows based on hyperspectral imagery from UAVs." Advances in Water Resources, Vol. 159, 104076.

10.1016/j.advwatres.2021.104076
40

Lamb, M.P., Dietrich, W.E., and Venditti, J.G. (2008). "Is the critical Shields stress for incipient sediment motion dependent on channel‐bed slope?" Journal of Geophysical Research: Earth Surface, Vol. 113, F2.

10.1029/2007JF000831
41

Lee, M., Park, Y.S., Lee, M., Song, Y.S., and Park, C. (2024). "Estimation of friction factor and bed shear stress considering bedform effect in rivers." Earth Surface Processes and Landforms, Vol. 49, No. 13, pp. 4154-4167.

10.1002/esp.5954
42

Maager, F., Hohermuth, B., Weitbrecht, V., and Boes, R.M. (2022). "Effect of macrorough sidewalls on flow resistance in steep rough channels." Water Resources Research, Vol. 58, No. 5, e2021WR031490.

10.1029/2021WR031490
43

Martin, Y., and Church, M. (2000). "Re-examination of Bagnold's empirical bedload formulae." Earth Surface Processes and Landforms: The Journal of the British Geomorphological Research Group, Vol. 25, No. 9, pp. 1011-1024.

10.1002/1096-9837(200008)25:9<1011::AID-ESP114>3.0.CO;2-H
44

Meyer-Peter, E. and Müller, R. (1948). "Formulas for bed-load transport." Proceeding 2nd Meeting International Association of Hydro-Environment Engineering and Research, Stockholm, Sweden, pp. 39-64.

45

Noh, H., Kwon, S., Park, Y.S., and Woo, S.B. (2024a). "Application of RGB UAV imagery to sea surface suspended sediment concentration monitoring in coastal construction site." Applied Ocean Research, Vol. 145, 103940.

10.1016/j.apor.2024.103940
46

Noh, H., Park, Y.S., and Lee, M. (2021). "Regional classification of total suspended matter in coastal areas of South Korea." Estuarine, Coastal and Shelf Science, Vol. 254, 107339.

10.1016/j.ecss.2021.107339
47

Noh, H., Park, Y.S., and Seo, I.W. (2023a) "A novel efficient method of estimating suspended‐to‐total sediment load fraction in natural rivers." Water Resources Research Vol. 59, No. 10, e2022WR034401.

10.1029/2022WR034401
48

Noh, H., Son, G., Kim, D., and Park, Y.S. (2023b). "A SVR based- pseudo modified einstein procedure incorporating H-ADCP model for real-time total sediment discharge monitoring." KSCE Journal of Civil and Environmental Engineering Research, Vol. 43, No. 3, pp. 321-335. (in Korean)

49

Noh, H., Son, G., Kim, D., and Park, Y.S. (2024b). "H-ADCP-based real-time sediment load monitoring system using support vector regression calibrated by global optimization technique and its applications." Advances in Water Resources, Vol. 185, 104636.

10.1016/j.advwatres.2024.104636
50

Onyutha, C. (2022). A hydrological model skill score and revised R-squared. Hydrology Research, Vol. 53, No. 1, pp. 51-64.

10.2166/nh.2021.071
51

Paintal, A.S. (1971). "Concept of critical shear stress in loose boundary open channels." Journal of Hydraulic Research, Vol. 9, No. 1, pp. 91-113.

10.1080/00221687109500339
52

Parker, G. (1990). "Surface-based bedload transport relation for gravel rivers." Journal of Hydraulic Research, Vol. 28, No. 4, pp. 417-436.

10.1080/00221689009499058
53

Pazis, G. (1976). Faible transport des sédiments par érosion et déposition dans des canaux alluvionnaires. Ph.D. Dissertaion, École polytechnique fédérale de Lausanne, Lausanne, Switzerland.

54

Pushpalatha, R., Perrin, C., Le Moine, N., and Andréassian, V. (2012). "A review of efficiency criteria suitable for evaluating low- flow simulations." Journal of Hydrology, Vol. 420, pp. 171-182.

10.1016/j.jhydrol.2011.11.055
55

Recking, A. (2009). "Theoretical development on the effects of changing flow hydraulics on incipient bed load motion." Water Resources Research, Vol. 45, No. 4, W04401.

10.1029/2008WR006826
56

Recking, A. (2010). "A comparison between flume and field bed load transport data and consequences for surface‐based bed load transport prediction." Water Resources Research, Vol. 46, No. 3, W03518

10.1029/2009WR008007
57

Recking, A. (2013), "A simple method for calculating reach-averaged bedload transport." Journal of Hydraulic Engineering, Vol. 139, No. 1, pp. 70-75.

10.1061/(ASCE)HY.1943-7900.0000653
58

Recking, A. (2019). BedloadWeb and user manuel. accessed 1 February 2025, <https://www.researchgate.net/publication/332950523_BedloadWeb_User_Manuel>.

59

Recking, A., Frey, P., Paquier, A., Belleudy, P., and Champagne, J. Y. (2008). "Bed-load transport flume experiments on steep slopes." Journal of Hydraulic Engineering, Vol 134, No. 9, pp. 1302-1310.

10.1061/(ASCE)0733-9429(2008)134:9(1302)
60

Revil-Baudard, T., and Chauchat, J. (2013). "A two-phase model for sheet flow regime based on dense granular flow rheology." Journal of Geophysical Research: Oceans, Vol. 118, No. 2, pp. 619-634.

10.1029/2012JC008306
61

Rickenmann, D. (1991). "Hyperconcentrated flow and sediment transport at steep slopes." Journal of Hydraulic Engineering, Vol. 117, No. 11, pp. 1419-1439.

10.1061/(ASCE)0733-9429(1991)117:11(1419)
62

Schwindt, S., Negreiros, B., Mudiaga-Ojemu, B.O., and Hassan, M. A. (2023). "Meta-analysis of a large bedload transport rate dataset." Geomorphology, Vol. 435, 108748.

10.1016/j.geomorph.2023.108748
63

Shields, A. (1936). Anwendung der Ahnlichkeitsmechanik und der Turbulenzforschung auf die Geshchiebewefung, Ph.D Dissertation, Versuchsanstalt fur Wasserbau und Schifbau. Berlin, Germany.

64

Smart, G., and Jaeggi, M. (1983) Sedimenttransport in steilen Gerinnen. Technical Report 64. Mitteilungen 64 der Versuchanstalt Für Wasserbau, Hydrologie und Glaziologie an der Eidgenössischen Technischen Hochschule, Zürich, Switzerland

65

Son, G. (2021). Riverine sediment load measurement technique using acoustic doppler current profilers considering hysteresis. Ph. D. Dissertation, Dankook University.

66

Suszka, L. (1987). Sediment transprot at steady and unsteady flow: a laboratory study. Ph.D. Dissertation, École polytechnique fédérale de Lausanne, Lausanne, Switzerland.

67

Venditti, J.G., Church, M., Attard, M.E. and Haught, D. (2016). "Use of ADCPs for suspended sediment transport monitoring: An empirical approach." Water Resources Research, Vol. 52, No. 4, pp. 2715-2736.

10.1002/2015WR017348
68

Wang, X., Zheng, J., Li, D., and Qu, Z. (2008). "Modification of the Einstein bed-load formula." Journal of Hydraulic Engineering, Vol. 134, No. 9, pp. 1363-1369.

10.1061/(ASCE)0733-9429(2008)134:9(1363)
69

Wilcock, P.R. (1987). Bed-load transport of mixed-size sediment. Ph.D. Dissertation, Massachusetts Institute of Technology, Cambridge, MA, U.S.

70

Williams, G.P. (1970). Flume width and water depth effects in sediment-transport experiments. Technical Report Professional Paper 562-H, United States Geological Survey, Washington, D.C., U.S.

10.3133/pp562H
71

Williams, G.P., and Rosgen, D.L. (1989). Measured total sediment loads (suspended loads and bedloads) for 93 United States Streams. Open-File Report 89-67, US Geological Survey Washington, DC, U.S.

10.3133/ofr8967
72

Wilson, K.C. (1966). "Bed-load transport at high shear stress." Journal of the Hydraulics Division, Vol. 92, No. 6, pp. 49-59.

10.1061/JYCEAJ.0001562
73

Wong, M., and Parker, G. (2006). "Reanalysis and correction of bed-load relation of Meyer-Peter and Müller using their own database." Journal of Hydraulic Engineering, Vol. 132, No. 11, pp. 1159-1168.

10.1061/(ASCE)0733-9429(2006)132:11(1159)
74

Wu, H., Cheng, N.S., and Chiew, Y.M. (2021). "Limiting behavior of the probability distribution in Einstein's bed‐load formula and its improvement." Water Resources Research, Vol. 57, No. 10, e2020WR028900.

10.1029/2020WR028900
75

Yager, E.M., Venditti, J.G., Smith, H.J., and Schmeeckle, M.W. (2018). "The trouble with shear stress." Geomorphology, Vol. 323, pp. 41-50.

10.1016/j.geomorph.2018.09.008
76

Yu, K.K., and Woo, H.S. (1990). "Comparative evaluation of some selected sediment transport formulas." Journal of the Korean Society of Civil Engineers, Vol. 10, No. 4, pp. 67-75.

Information
  • Publisher :KOREA WATER RESOURECES ASSOCIATION
  • Publisher(Ko) :한국수자원학회
  • Journal Title :Journal of Korea Water Resources Association
  • Journal Title(Ko) :한국수자원학회 논문집
  • Volume : 58
  • No :4
  • Pages :329-343
  • Received Date : 2024-12-24
  • Revised Date : 2025-02-21
  • Accepted Date : 2025-03-06
  • DOI :https://doi.org/10.3741/JKWRA.2025.58.4.329
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