Trickling down the paleoslope: an empirical approach to paleohydrology

Abstract

This paper provides a review of existing methods for determining paleohydraulic parameters applicable to ancient lithified fluvial strata and attempts to update these formulae using empirical re-evaluation of modern stream data. Linear regression analysis was used to produce a series of equations that can readily be applied to ancient fluvial strata. These new formulae were developed using information from >4000 modern rivers, with depth, width, and grain size, as independent variables, as these can be directly estimated with varying degrees of confidence in the ancient stratigraphic record. Existing methods of estimating paleo-depth from crossbeds may reflect thalweg depth rather than average bankfull stream depth. Dune height (Hd), when corrected for compaction, is considered equal to 2.52 ± 0.7 times the average height of trough crossbeds (Hx). Thalweg depth (dmax) is calculated as 6.5058 x Hd1.111. From this average bankfull stream depth (dbf) is calculated as 0.6095 x dmax0.973. Bankfull channel width (wbf) is then calculated as 16.293 dmax1.198 for low sinuosity rivers (P < 1.3), 17.338 dmax1.168 for intermediate sinuosity rivers (1.3<P>1.7), and 17.458 dmax1.230 for high sinuosity rivers (P>1.7). Bankfull discharge (Qbf) can be calculated as 17.359 dmax1.270. Drainage basin size (DA) can be calculated from bankfull depth as 241 dbf2.17. Slope (S) can then be calculated from bankfull width as 0.0341 wbf-0.7430. Estimates of slope, discharge and drainage area can be further refined using formulae developed for specific Köppen-Geiger climate zones and sub-zones. With all of the above formulae a high degree of uncertainty remains due to the scatter of original data. In addition it is not always possible to establish climate variables in ancient strata. A further complication in comparing modern and ancient systems is discharge variability. This is related both to climate and to potential differences in surface runoff rates linked to the evolution and spread of rooted terrestrial vegetation.