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Foraminifera are unicellular organisms that inhabit the oceans. They play an important role in the global carbon cycle and record valuable paleoclimate information through the uptake of trace elements such as strontium into their calcitic shells. Understanding how foraminifera control their internal fluid composition to make calcite is important for predicting their response to ocean acidification and for reliably interpreting the chemical and isotopic compositions of their shells. Here, we model foraminiferal calcification and strontium partitioning in the benthic foraminiferaCibicides wuellerstorfiandCibicidoides mundulusbased on insights from inorganic calcite experiments. The numerical model reconciles inter-ocean and taxonomic differences in benthic foraminifer strontium partitioning relationships and enables us to reconstruct the composition of the calcifying fluid. We find that strontium partitioning and mineral growth rates of foraminiferal calcite are not strongly affected by changes in external seawater pH (within 7.8–8.1) and dissolved inorganic carbon (DIC, within 2100–2300 μmol/kg) due to a regulated calcite saturation state at the site of shell formation.

 

Bedload particle hops are defined as successive motions of a particle from start to stop, characterizing one of the most fundamental processes of bedload sediment transport in rivers. Although two transport regimes have been recently identified for short and long hops, respectively, there is still the lack of a theory explaining the mean hop distance–travel time scaling for particles performing short hops, which dominate the transport and may cover over 80 % of the total hop events. In this paper, we propose a velocity-variation-based formulation, the governing equation of which is intrinsically identical to that of Taylor dispersion for solute transport within shear flows. The key parameter, namely the diffusion coefficient, can be determined by hop distances and travel times, which are easier to measure and more accurate than particle accelerations. For the first time, we obtain an analytical solution for the mean hop distance–travel time relation valid for the entire range of travel times, which agrees well with the measured data. Regarding travel times, we identify three distinct regimes in terms of different scaling exponents: respectively, $\sim$ 1.5 for the initial regime and $\sim$ 5/3 for the transition regime, which define the short hops, and 1 for the Taylor dispersion regime defining long hops. The corresponding distribution of the hop distance is analytically obtained and experimentally verified. We also show that the conventionally used exponential distribution, as proposed by Einstein, is solely for long hops. Further validation of the present formulation is provided by comparing the simulated accelerations with measurements. 

Incising rivers may be confined by low-slope, erodible hillslopes or steep, resistant sidewalls. In the latter case, the system forms a canyon. We present a morphodynamic model that includes the essential elements of a canyon incising into a plateau, including 1) abrasion-driven channel incision, 2) migration of a canyon-head knickpoint, 3) sediment feed from an alluvial channel upstream of the knickpoint, and 4) production of sediment by sidewall collapse. We calculate incision in terms of collision of clasts with the bed. We calculate knickpoint migration using a moving-boundary formulation that allows a slope discontinuity where the channel head meets an alluvial plateau feeder channel. Rather than modeling sidewall collapse events, we model long-term behavior using a constant sidewall slope as the channel incises. Our morphodynamic model specifically applies to canyon, rather than river–hillslope evolution. We implement it for Rainbow Canyon, CA. Salient results are as follows: 1) Sediment supply from collapsing canyon sidewalls can be substantially larger than that supplied from the feeder channel on the plateau. 2) For any given quasi-equilibrium canyon bedrock slope, two conjugate slopes are possible for the alluvial channel upstream, with the lower of the two corresponding to a substantially lower knickpoint migration rate and higher preservation potential. 3) Knickpoint migration occurs at a substantially faster time scale than regrading of the bedrock channel itself, underlying the significance of disequilibrium processes. Although implemented for constant climactic conditions, the model warrants extension to long-term climate variation.

 

Fine-grained sediment (grain size under 2,000 μm) builds floodplains and deltas, and shapes the coastlines where much of humanity lives. However, a universal, physically based predictor of sediment flux for fine-grained rivers remains to be developed. Herein, a comprehensive sediment load database for fine-grained channels, ranging from small experimental flumes to megarivers, is used to find a predictive algorithm. Two distinct transport regimes emerge, separated by a discontinuous transition for median bed grain size within the very fine sand range (81 to 154 μm), whereby sediment flux decreases by up to 100-fold for coarser sand-bedded rivers compared to river with silt and very fine sand beds. Evidence suggests that the discontinuous change in sediment load originates from a transition of transport mode between mixed suspended bed load transport and suspension-dominated transport. Events that alter bed sediment size near the transition may significantly affect fluviocoastal morphology by drastically changing sediment flux, as shown by data from the Yellow River, China, which, over time, transitioned back and forth 3 times between states of high and low transport efficiency in response to anthropic activities.

 

Accounting for the burial of tracer particles during bedload transport is an important component in the formulation of tracer dispersal in rivers. Herein we propose a modified active layer formulation, which accounts for the effect of burial and admits analytical solutions, enabling insightful exploration of the phenomenon of superdiffusion of bedload tracers at the intermediate timescale. This phenomenon has been observed in recent numerical results using the 2‐D Exner‐Based Master Equation. By assuming that tracers in the active layer can exchange with nontracer particles in the substrate layer to preserve mass, and that tracers entering the substrate layer get permanently trapped during the timescale of analysis, we are able to deduce governing equations for the tracer concentration in both layers. The active layer tracer concentration is shown to be governed by an advection‐diffusion equation with a sink term, and the increase of tracers in the substrate layer is driven by a corresponding source term. The solution for the variance of tracer population is analytically determined and can be approximated by the sum of a diffusion‐induced scaling (∝t¹) and an advection‐induced scaling (∝t³) terms at the intermediate timescale, which explains the phenomenon of superdiffusion. The proposed formulation is shown to be able to capture the key characteristics of tracer transport as inferred by comparison with available results of numerical simulations.