Source-to-sink interpretations of genetic equivalency between fluvial feeder systems and basin accumulations infer that the sediment and water mass collected and transferred by rivers from the catchment is in balance with the mass ultimately delivered to the depositional basin. This relationship has value for modeling basin-fill volumes, climate and climate change, ocean water mass, and other applications. Executing an estimate of this mass balance is challenging in modern systems but even more difficult in deep-time stratigraphic systems where the catchment is no longer active and critical variables from the source and sink system are either not preserved or preserved with large uncertainties. Available data sets from stratigraphic systems are likewise often limited to a few localized boreholes, scattered outcrop, and/or geophysical surveys. This paper offers a method, the fulcrum test, for estimating mass flux from the source area to the basin sink by calculation of channel paleohydrologic variables extractable from these common stratigraphic data sources. We use the Cenomanian channels of the Bahariya Formation, Egypt, as an example application in a stratigraphic system. The technique may provide greater accuracy in modern systems where more data are available and uncertainties are lower.
Total mass passing through a cross section of all feeder channels over a period of time should match with both the total sediment delivered to the cross section from the source area and the total volume delivered through these channels to the basin. This cross section would constitute a fulcrum across which source and sink sediment and water mass should balance. Bankfull dimensions and representative bedload are measured and sampled from channel stories identified in outcrop and/or subsurface data over a fulcrum cross section within the basin. Flow transport equations are used to estimate bankfull discharge and sediment concentrations using established methods. These concentrations are projected over longer durations to estimate total channel mass through-flux over basin-fill time spans. These estimates can also be tested against other mass-flux methods such as known volumetric basin-fill accumulation rates and/or estimates of drainage-area denudation. In the example case, calculations of mass flux from Bahariya channels that feed the equivalent fluvial-to-marine basin show that these channels were capable of delivering at least three times the sediment actually preserved. Channels were small with average depths of 2.5 m and 0.1 m3/sec bankfull sediment discharges.
The fulcrum test offers a first-order approximation of mass balance, but it remains a nascent method. Key parameters have large uncertainties, which currently limit accuracy to an order of magnitude. This uncertainty could be reduced to a factor of three in stratigraphic systems through improved constraints on channel width and development of better relationships between bankfull and mean annual discharge. Uncertainties can be lowered to a factor of two in extant systems where key variables (e.g., slope, etc.) can be measured instead of estimated. The method also retains intrinsic limitations. It derives a discharge for only a single representative “unit” channel, and the contingency of multiple channels must be detected through other geologic data and integrated independently. The method also does not account for mass extraction through deposition between the catchment and the fulcrum, though fulcrum tests in multiple cross sections longitudinally could potentially lend insight into this issue. Accuracy of the test also depends upon stratigraphic preservation as a valid “statistical sampling machine” for discharge processes, and upon unbiased sampling of discrete channel stories within this preserved sample population.