INTRODUCTION The well-known systematic downstream re- duction of the mean grain size of river-bed sedi- ment has puzzled scientists ever since Sternberg’s (1875) classic study of the Rhine River in Ger- many. Numerous studies have sought to under- stand the phenomenon by developing equations to describe it and investigating its possible causes. Sternberg (1875) attributed downstream fining on the Rhine River to abrasion and developed an ex- pression that describes the downstream decrease in grain size as an exponential function. This func- tion has been widely used to describe fining in both sand- and gravel-bed streams (e.g.,Yatsu, 1955; Pizzuto, 1995; Knighton, 1999). The theory that abrasion drives downstream fining was also supported through laboratory studies using tum- bling mills and revolving currents (Krumbein, 1941; Kuenen, 1956). More recent studies have focused on selective sorting as the primary cause of downstream fining in most fluvial systems. Laboratory abrasion tests of sediment from the Allt Dubhaig, Scotland, pro- duce only a very small fraction of the actual re- duction in median grain size over the equivalent length of reach, implying that selective sorting must be the dominant cause of downstream fining on this river (Ferguson et al., 1996). Laboratory flume studies have produced downstream fining in reaches that are too short for abrasion to be a significant factor in grain-size reduction (Paola et al., 1992; Seal et al., 1997). In support of these findings, numerical models have also shown that downstream fining is principally due to selective particle sorting in resistant lithologies (Parker, 1991; Cui et al., 1996; Hoey and Ferguson, 1997; Robinson and Slingerland, 1998). In this study we aim to understand how sedi- ment sorting operates within a drainage network. The importance of tributary inputs has been rec- ognized in field studies of sorting dynamics at channel confluences (Ichim and Radoane, 1990; Rice, 1998). Pizzuto (1995) used a numerical model to study texture changes in a drainage net- work by applying empirical downstream-fining laws. Despite these notable contributions, how- ever, very little is known about the mechanics of particle sorting within the realm of a branching drainage network. Here we use a numerical model of selective sorting to investigate the link between surface-texture dynamics and the aggregation structure of a drainage network. We deliberately examine equilibrium drainage networks in which there is no deposition and sediment storage in or- der to evaluate whether such factors are neces- sary conditions for downstream fining. The phenomenon of selective sorting arises from selective entrainment and transport of smaller grains in a heterogeneous mixture. Experimental studies reveal that sediment particles on a homo- geneous bed are entrained above a threshold fluid shear stress, which for fully turbulent fluid flows varies with particle diameter (Shields, 1936). En- trainment on a heterogeneous stream bed is com- plicated by grain hiding and protrusion effects, which tend to increase the entrainment threshold for smaller particles and decrease it for larger par- ticles (Andrews, 1983; Komar, 1987; Kuhnle, 1993; Wilcock, 1993). Such effects have been shown to produce equal particle mobility on a reach scale in well-mixed gravels (Parker et al., 1982). Equal mobility describes the condition where all grain sizes in a mixture are equally transportable when scaled by their concentration in the mixture. Recent studies have found that while equal mobility occurs locally in sediment patches with varying mean grain size, patchiness at the reach scale can disrupt equal mobility and produce selective transport (Paola and Seal, 1995; Seal and Paola, 1995). Here we model the general case of a sand and gravel mixture. Wilcock (1998) showed that en- trainment of sediment in such mixtures can be modeled on the basis of the median sizes of the sand and gravel fractions (Fig. 1). On a bed with a small proportion of sand in the sediment, the in- terlocked gravel framework makes entrainment of both sand and gravel difficult. As the bed be- comes sandier, the gravel framework is broken. Gravel particles are spread apart and become eas- ier to entrain because they protrude above the bed, while the sand particles become easier to en- train because they are no longer hidden behind the larger particles. Eventually, the sandy matrix dominates, and entrainment of sand and gravel is no longer affected by further additions of sand. We also use the model to explore the gravel- sand transition, a notable feature of many natural mixed sand- and gravel-bed streams. The gravel- sand transition describes a rapid change from unimodel gravel, to bimodal sediments, to exclu- sively sand material on the bed (Smith and Fer- guson, 1995; Knighton, 1999). The transition has been variously attributed to a local base level control, an excess supply of sand, or the physical breakdown of gravel. For example, sandy min- ing waste supplied to the Ringarooma River, Tasmania, caused a very sharp gravel-sand tran- sition (Knighton, 1999). Yatsu (1955) argued Geology; December 1999; v. 27; no. 12; p. 1079–1082; 3 figures. 1079 Downstream fining through selective particle sorting in an equilibrium drainage network Nicole M. Gasparini* Gregory E.Tucker Rafael L. Bras Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA ABSTRACT The phenomenon of downstream fining has been attributed to both particle abrasion and selective particle sorting; the latter is generally considered to play the dominant role within re- sistant lithologies. It has been recognized that tributaries can disrupt fining patterns; however, few downstream-fining studies have considered the entire fluvial network structure. Here we combine a theory for selective transport with a model of river-basin evolution in order to simu- late the dynamics of selective sorting throughout a drainage network. Previous numerical mod- eling studies of single-thread or braided channels have treated downstream fining as a phenom- enon driven by differential deposition rates. We show, however, that in an eroding drainage network, downstream fining emerges as a natural dynamic adjustment to variable water, sedi- ment, and energy inputs, even under conditions of uniform size distribution in sediment flux. Thus, although selective deposition and abrasion clearly can and do play a role in some fluvial systems, neither is necessary to produce downstream fining within a drainage network. *E-mail: nmgaspar@mit.edu.