Quantifying paleodischarge from geological field observations have been for decades, and remains, a key research challenge. Several paleodischarge scaling relationships have been developed for fluvial environments, such as BQART, Fulcrum and regional hydraulic geometry or for river deltas by precluding the role of wave and tide. In deltas where marine (wave, tide) energy causes bidirectional flow, the available paleodischarge scaling relationships are not applicable. Here, the spatial variability of distributary channel widths from a database of 114 global modern river deltas is assessed to understand the limit of marine influence on distributary channel widths. Compiling 4459 distributary channel width measurements enables improvements to distributary channel width-discharge scaling relationships specifically for river-, tide- and wave-dominated deltas. By bootstrapping the channel widths measured from modern deltas, the minimum number of width measurements needed to apply width-discharge scaling relationships to ancient deltaic deposits is estimated as 3 and 30 for upstream and downstream river-dominated deltas, consecutively, 6 for upstream part of tide-dominated deltas and 4 for wave-dominated deltas. This estimate will guide sedimentologists who often have limited numbers of distributary channel widths exposed in the rock record. Statistically significant width-discharge scaling relationships are derived for river- and wave-dominated deltas, with no significant relationships identified for tide-dominated deltas. To test the reliability of these improved width-discharge scaling relationships in the rock record, paleodischarges were estimated for the well-studied Cretaceous lower Mesa Rica Formation, USA. Comparison of these results with the more complex Fulcrum method suggests that these new scaling relationships are accurate. Hence these scaling relationships obtained from modern deltas can be applied to the rock record, and this approach requires less, and easier to measure, data inputs than previously published methods.
Paleodischarge estimation is largely undertaken within fluvial settings, and there are limited paleodischarge estimates specifically from delta deposits, despite their significance globally. Making water paleodischarge estimates for deltas using catchment-based approaches developed using data from fluvial settings requires estimation of parameters from the rock record (e.g. paleotemperature, paleoslope, paleorelief) that may be difficult to determine, and may lead to under- or over-estimation of paleodischarge values due to differences in process-form relationships between alluvial rivers and deltas. When a sediment-conveying fluvial channel starts to debouch into a standing body of water, delta lobes develop through repeating mouth bar deposition due to flow deceleration, forming a deltaic morphology with distributary channel networks that differ morphologically from those developed in unidirectional flowing alluvial rivers. This study provides empirical relationships determined across five climate regions, using 3823 measurements of distributary channel width from 66 river deltas alongside their bankfull discharge, by applying the concept of hydraulic geometry. Empirical relationships are developed from the global delta dataset between bankfull discharge and catchment area (Qb-A) and also bankfull discharge and distributary channel width (Qb-w). These empirical relationships produce very strong statistical correlations, especially between Qb and w, across different climate regions (Qb = 0.34w1.48, R2 = 0.77). However, both Qb-A and Qb-w relationships have outliers that may be explained by particular hydrological or geomorphic conditions. These new empirical relationships derived from modern systems are applied to Cretaceous outcrops (Ferron Sandstone, Dunvegan and McMurray formations). The comparatively simple scaling relationships derived here produced paleodischarge estimates within the same order of magnitude as the paleodischarge values derived from existing, more complex approaches. Our study contributes to source-to-sink investigations by enabling paleodischarge estimates that intrinsically account for climate impacts on channel geometry at the time of deposition, using measurements of channel width or catchment area of a deltaic outcrop.
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