STOCHASTIC MODEL FOR THE DEVELOPMENT OF FLUVIAL BEDFORM CROSS SET BOUNDING SURFACES (Invited Presentation)

Fluvial bedform cross strata have the potential to record dynamics of ancient river systems, yielding insight into past conditions. Bedform geometries and motions respond over short timescales (order minutes to days) to local changes in flow and sediment transport dynamics. Bedforms and their stratigraphic records, therefore, may provide a uniquely detailed snapshot of local flow and sediment transport conditions. Three principle components define the kinematics of bedforms in a streamwise-oriented framework: migration, deformation, and aggradation rates. Dynamics of flow and sediment transport ultimately dictate the kinematic responses of the bed. Thus, considering the stratigraphic preservation of each may provide a path for quantitative reconstruction of past dynamics. While the role of migration, deformation, and aggradation on preservation of bed sets have been individually described, a complete framework combining all three components and their dynamic controls requires investigation over a wide range of parameters difficult to achieve from flume studies alone. To aid this exploration of a broad parameter space, we present a stochastic kinematic model relating bedform migration, aggradation, deformation, and correlations in deformation rates to stratigraphically measureable parameters such as distributions of bed set thickness, length, and bounding surface curvature. This new model, tested with flume data, describes set bounding surface development as a mean reverting random walk, specifically an Ornstein-Uhlenbeck process. We treat migration and aggradation as steady state processes, represented by characteristic rates. Deformation rates, defined as the vertical rate of change of bed elevation in the downstream migrating (Lagrangian) reference frame, are treated as a stochastic process with individual deformations randomly drawn from a distribution. The relaxation timescale over which bounding surfaces tend toward the mean is treated as proportional to the bedform migration timescale (bedform length/migration rate). We find reasonable fit of model stratigraphy to experimental data. The resultant model framework will enable new metrics for inverting dynamic conditions from ancient strata.