Using Lagrangian particle saltation observations for bedload sediment transport modelling Yarko NinÄo 1 and Marcelo GarcõÂa  Hydrosystems Laboratory, Dept of Civil Engng, University of Illinois at Urbana-Champaign, 250 N. Mathews, Urbana, IL 61801, USA Abstract: A Lagrangian model for the saltation of sand in water is proposed. Simulated saltation trajectories neglecting particle rotation and turbulence eects compare fairly well with experimental observations. The model for particle motion is coupled with a stochastic model for particle collision with the bed, such that a number of realizations of the saltation process can be simulated numerically. Model predictions of mean values and standard deviations of saltation height, length and streamwise particle velocity agree fairly well with experimental observations. Model predictions of the dynamic friction coecient are also in good agreement with experimental observations, but they underestimate the value of 0 . 63 proposed by Bagnold for this coecient. The saltation model is applied to the estimation of bedload transport rates of sand using a Bagnoldean formulation. Modelled values of the bedload transport rates overestimate those predicted by commonly used bedload formulae, which appears to be a consequence of problems in the de®nition of the dynamic friction coecient. These results seem to indicate a few problems with the Bagnoldean formulation, particularly regarding the continuum assumption for the bedload layer, which would be valid only for very high particle concentrations and small particle diameters, and also regarding the evaluation of the shear stress exerted on the bed by the saltating particles. # 1998 John Wiley Sons, Ltd. KEY WORDS Lagrangian model; saltation; particle motion; stochastic collision; Bagnold formulation; bedload sediment transport INTRODUCTION Saltation is described as the unsuspended transport of particles over a granular bed by a ¯uid ¯ow, in the form of consecutive hops within the near-bed region. It is governed mainly by the action of hydrodynamic forces that carry the particles through the ¯ow, the downward pull of gravity and the collision of the particles with the bed, which transfers their streamwise momentum into upward momentum, thus sustaining the saltation motion (NinÄ o and GarcõÂa, 1995). This diers from an earlier de®nition given by Bagnold (1973) who assumed that the only upward impulses exerted on the saltating particles were those resulting from the impact of particles with the bed. Thus, Bagnold neglected the eect of hydrodynamic lift and vertical impulses owing to ¯ow turbulence, which have been shown to play an essential role in the saltation phenomenon (e.g. Leeder, 1979a; Bridge and Dominic, 1984; Bridge and Bennett, 1992; NinÄo et al., 1994; NinÄo and GarcõÂa, 1995). Two recent experimental studies on saltation of gravel and sand by NinÄ o et al. (1994) and NinÄ o and GarcõÂa (1997) have given detailed information on the physics of particle saltation. In particular, they have provided a CCC 0885±6087/98/081197±22$1750 Received 23 January 1996 # 1998 John Wiley & Sons, Ltd. Revised 27 September 1996 Accepted 6 July 1997 Hydrological Processes Hydrol. Process. 12, 1197±1218 (1998)  Correspondence to: Marcelo GarcõÂa, Hydrosystems Laboratory, Department of Civil Engineering, Universityof Illinois at Urbana- Champaign, 250 N. Mathews, Urbana, IL 61801, USA. 1 Current Address: Department of Civil Engineering, University of Chile, Santiago, Chile. Contract grant sponsors: NSF and Petroleum Research Fund (ACS). Contract grant numbers: CTS-9210211 and PRF 24328-G2