Using delta channel width to estimate paleodischarge in the rock record: geometric scaling and practical sampling criteria

Quantifying paleodischarge from geological field observations remains a key research challenge. Several scaling relationships between paleodischarge and channel morphology (width; depth) have been developed for rivers and river deltas. Previous paleodischarge scaling relationships were based on discharge-catchment area scaling and an empirical flow velocity estimate (e.g. Chézy, Manning formulae) multiplied by channel cross-sectional area to derive discharge. In deltas, where marine (wave, tide) energy causes bidirectional flow within distributary channels, the available paleodischarge scaling relationships are not applicable due to their unidirectional flow assumption. 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. Using 6213 distributary channel width measurements, the median channel widths of distributary channels for each delta were correlated with bankfull discharge for river-, tide- and wave-dominated deltas, the latter two including the effect of bidirectional flow. Statistically significant width-discharge scaling relationships are derived for river- and wave-dominated deltas, with no significant relationships identified for tide-dominated deltas. By reverse 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 4 for the upstream parts of river- and wave-dominated deltas, respectively, increasing to 30 in the downstream parts of river-dominated deltas. These estimates will guide sedimentological studies that often have limited numbers of distributary channel widths exposed in the rock record. To test the reliability of these alternative width-discharge scaling relationships in the rock record, paleodischarges were estimated for the well-studied Cretaceous lower Mesa Rica Sandstone Formation, USA . Comparison of these results with the more complex Chézy-derived method suggests that these new scaling relationships are accurate. Hence, it is proposed that the scaling relationships obtained from modern deltas can be applied to the rock record, requiring fewer, and easier to measure, data inputs than previously published methods.