This paper matches sediment fluxes, estimated to have passed through an ancient river system, with mapped downstream sediment volumes in a deltaic sink, providing a test of the recently developed fulcrum approach to source-to-sink analysis. This paper uses field measurements (such as channel depth, width, and grain size) to estimate paleodischarge in an ancient trunk channel of the Cretaceous Ferron Sandstone in central Utah. The estimates of instantaneous discharge are then integrated over the geological duration of the river to estimate the total sediment volume delivered to downstream deltaic sinks in an attempt to balance the estimated sediment flux with the mapped deltaic deposits in the sink. The bankfull channel depths, calculated using the scaling relationship between the flow depth and the mean dune height, vary from 3.3 to 5.5 m with an average depth of 4.4 m. The corresponding bankfull channel width estimates vary from 50 to 80 m, with an average value of 65 m, calculated using scaling relationship between channel width and the width of accretion surfaces. Water discharge calculated for these bankfull dimensions vary from 2.7 × 102 m3/s to 8.6 × 102 m3/s, also indicating that these rivers were routinely capable of generating hyperpycnal flows. The instantaneous sediment discharge reaching the fulcrum was calculated using established sediment transport equations. These instantaneous discharge values were first converted to mean annual sediment volume using the bankfull event durations, recurrence intervals, and a factor for the proportion of the total annual sediment load transported during the bankfull period, based on empirical relationships from modern climate analogs, and then projected over the average time duration of individual parasequences in the Ferron Notom clastic wedge, which is approximately 14 kyr. The mass balance across the fulcrum reveals that the average bedload sediment volume derived from the source (about 3 km3) matches with that deposited in the sink within a factor of two. However, underestimation of the bedload volume in the sink suggests sediment escape beyond the limits of currently mapped sink area. Previous models for the Ferron indicate significant SE deflection of sediment due to wave reworking, which may account for the missing sandy sediment. It is also possible that there is an overestimation of time duration for individual valleys, resulting in higher sink-volume estimation and larger source-to-sink mass imbalance. Monte Carlo simulations, based on probabilistic estimation, were used to test the sensitivity of key parameters used in converting bankfull discharge to mean annual discharge. The P10, P50 (median), and P90 values for the average annual bedload volume (Qmas) are 9.1 × 104 m3, 1.7 × 105 m3, and 3.7 × 105 m3, respectively. AQmasvalue between P50 and P90 yields a source-to-sink balance for bedload volume.

The current study establishes a mass balance across the fulcrum with a reduced range of uncertainty for the various parameters used. Uncertainty associated with bankfull channel dimensions has been reduced through inclusion of detailed outcrop data. The uncertainty in estimating average annual sediment volume (Qmas) from bankfull events is less than a factor of three. This uncertainty can be further reduced by incorporating a more robust global-discharge dataset from modern analog river systems. Despite many assumptions and uncertainties, our study shows that the fulcrum method appears to be capable of balancing sediment budgets to within at least an order of magnitude in deep-time sedimentary systems.

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