Quantifying weathering on variable rocks, an extension of geochemical mass balance: Critical zone and landscape evolution

We present a statistical model of soil and rock weathering in deep profiles to expand the capacity to assess weathering to heterogeneous bedrock types, which are common at the Earth's surface. We developed the Weathering Trends (WT) model by extending the fractional mass change calculation (tau) of the geochemical mass balance model in two important ways. First, WT log transforms the elemental ratio data, to discern the log-linear patterns that naturally develop from thermodynamic and kinetic laws of chemistry. Second, WT statistically fits log-transformed element concentration ratio data – log(c_j/c_i), the only depth-varying term in tau – as a function of depth to determine characteristic depths of transitions in weathering processes, along with confidence intervals. With no prior assumptions, WT estimates average parent material composition, average composition of the upper weathered zone and mean fractional mass change of each element over the entire weathering profile. WT displays the mean shape of weathering profiles of log-transformed geochemical data bounded by calculated confidence intervals. We share the WT model code as an open-source R package (https://github.com/fisherba/WeatheringTrends). The WT model was designed to interpret two 21 m cores from the Laurels Schist bedrock in the Christina River Basin Critical Zone Observatory in the Pennsylvania Piedmont, where our morphological and elemental data provided inconclusive estimates of bedrock depth. The WT model differentiated between rock variability and weathering to delineate the maximum extent of weathering at 12.3 m (CI 95% [9.2, 21.3]) in Ridge Well 1 and 7.2 m (CI 95% [4.3, 13.0]) in Interfluve Well 2. The water table was 5–8 m below fresh rock at Ridge Well 1, but at the same depth as fresh rock at the lower elevation interfluve. We assess statistical approaches to identify the best immobile element for use in WT and tau calculations.