Determination of the transport ("diffusion") coefficient, the main parameter of most forward models for generating fluvial stratigraphy, requires finding the average slope required to transport the total sediment load delivered to a given point for a given water discharge. Finding this value, in turn, requires averaging the substantial fine-scale local variability in transport capacity that one encounters in most natural rivers. The problem is especially acute for braided rivers, in which the local capacity varies strongly in time and space as channels migrate, flow shifts from one part of the channel network to another, and confluences, which account for a disproportionate share of sediment flux, form and dissipate. Here, we present a model for computing spatially averaged sediment flux in a sandy braided river system. Coupled with sediment mass balance, the sediment-flux model leads to the usual diffusion equation for surface topography. The problem of indeterminacy of channel width is dealt with by using an empirical constant value of 1.8 for the mean nondimensional (Shields) stress. We test the model by applying it to a mine-tailings fan in which all independent parameters (sediment flux, water flux, grain size, deposition pattern) are well known and constant. The statistical parameters needed to determine the transport coefficient are determined from independent measurements of the river network on the fan. Using these inputs, the model predicts the fan topography well. The model suggests that, for a highly active braided system such as this one, the effect of the fluctuations in sediment flux can increase total sediment flux by a factor of two to four relative to what would be predicted from mean values alone. The data also suggest, however, that some of the key statistical parameters vary significantly downstream along the fan. This variation may result from downstream variation in grain-size distribution, sediment flux, or both.