This dissertation presents an investigation of the effects of a stochastic component of sediment transport in sandy rivers in an attempt to gain information about the transport system and its implications for the evolution of Earth's surface topography. First, a method for characterizing the geometries of bed forms is introduced and compared to previously proposed methods. This new method is then implemented on a field dataset as well as laboratory dataset and the results are compared to those obtained by traditional methods. Second, a method for characterizing the dynamic evolution of the bed geometries is demonstrated. It produces a velocity scale, the mean migration rate of the bed topography, and a deformation scale, the evolutionary departures of the bed topography from pure migration. These scales are calculated for the field and laboratory data and are compared. The flux of bed sediment is then shown to depend on the stochastic component of bed evolution. The fluxes for each dataset are calculated, they are related to the environmental conditions causing the transport of sediment, and suggestions are made for the design of field campaigns that attempt to measure sediment transport by repeated surveys of bed topography. Finally, the implications of stochasticity for sediment transport are investigated. A null hypothesis is formulated for topographic change by a stochastic process. Then the effects of measurement and field collection methods on the null hypothesis are evaluated. The most important prediction is non-trivial behaviors in measurable rates of surface change at short timescales. This prediction is then evaluated with field data from a growing sandy channel network whose behaviors can be determined at timescales of decades to centuries (dendrochronology), tens of thousands of years (cosmogenic radiochemistry), and hundreds of thousands to millions of years (age of channel system and sediments through which it cuts). These three investigations create a coherent account of the expressions and implications of variability in the transport of sediment, and therefore the evolution of topography, in sandy river systems that can then be generalized to changes across Earth's surface. / text