LOSCAR: Long-term Ocean-atmosphere-Sediment CArbon cycle Reservoir Model v2.0.4

The LOSCAR model is designed to efficiently compute the partitioning of carbon between ocean, atmosphere, and sediments on time scales ranging from centuries to millions of years. While a variety of computationally inexpensive carbon cycle models are already available, many are missing a critical sediment component, which is indispensable for long-term integrations. One of LOSCAR's strengths is the coupling of ocean-atmosphere routines to a computationally efficient sediment module. This allows, for instance, adequate computation of CaCO<sub>3</sub> dissolution, calcite compensation, and long-term carbon cycle fluxes, including weathering of carbonate and silicate rocks. The ocean component includes various biogeochemical tracers such as total carbon, alkalinity, phosphate, oxygen, and stable carbon isotopes. LOSCAR's configuration of ocean geometry is flexible and allows for easy switching between modern and paleo-versions. We have previously published applications of the model tackling future projections of ocean chemistry and weathering, <i>p</i>CO<sub>2</sub> sensitivity to carbon cycle perturbations throughout the Cenozoic, and carbon/calcium cycling during the Paleocene-Eocene Thermal Maximum. The focus of the present contribution is the detailed description of the model including numerical architecture, processes and parameterizations, tuning, and examples of input and output. Typical CPU integration times of LOSCAR are of order seconds for several thousand model years on current standard desktop machines. The LOSCAR source code in C can be obtained from the author by sending a request to [email protected]

orbitN: A symplectic integrator for planetary systems dominated by a central mass -- Insight into long-term solar system chaos

Reliable studies of the long-term dynamics of planetary systems require numerical integrators that are accurate and fast. The challenge is often formidable because the chaotic nature of many systems requires relative numerical error bounds at or close to machine precision (~1e-16, double-precision arithmetic), otherwise numerical chaos may dominate over physical chaos. Currently, the speed/accuracy demands are usually only met by symplectic integrators. For example, the most up-to-date long-term astronomical solutions for the solar system in the past (widely used in, e.g., astrochronology and high-precision geological dating) have been obtained using symplectic integrators. Yet, the source codes of these integrators are unavailable. Here I present the symplectic integrator orbitN (lean version 1.0) with the primary goal of generating accurate and reproducible long-term orbital solutions for near-Keplerian planetary systems (here the solar system) with a dominant mass M0. Among other features, orbitN-1.0 includes M0's quadrupole moment, a lunar contribution, and post-Newtonian corrections (1PN) due to M0 (fast symplectic implementation). To reduce numerical roundoff errors, Kahan compensated summation was implemented. I use orbitN to provide insight into the effect of various processes on the long-term chaos in the solar system. Notably, 1PN corrections have the opposite effect on chaoticity/stability on 100-Myr vs. Gyr-time scale. For the current application, orbitN is about as fast or faster (factor 1.15-2.6) than comparable integrators, depending on hardware. The orbitN source code (C) is available at github.com/rezeebe/orbitN.Comment: Publishe

CO2 perturbation experiments: similarities and differences between dissolved inorganic carbon and total alkalinity manipulations

Increasing atmospheric carbon dioxide (CO2) through human activities and invasion of anthropogenic CO2 into the surface ocean alters the seawater carbonate chemistry, increasing CO2 and bicarbonate (HCO3−) at the expense of carbonate ion (CO32−) concentrations. This redistribution in the dissolved inorganic carbon (DIC) pool decreases pH and carbonate saturation state (Ω). Several components of the carbonate system are considered potential key variables influencing for instance calcium carbonate precipitation in marine calcifiers such as coccolithophores, foraminifera, corals, mollusks and echinoderms. Unravelling the sensitivities of marine organisms and ecosystems to CO2 induced ocean acidification (OA) requires well-controlled experimental setups and accurate carbonate system manipulations. Here we describe and analyse the chemical changes involved in the two basic approaches for carbonate chemistry manipulation, i.e. changing DIC at constant total alkalinity (TA) and changing TA at constant DIC. Furthermore, we briefly introduce several methods to experimentally manipulate DIC and TA. Finally, we examine responses obtained with both approaches using published results for the coccolithophore Emiliania huxleyi. We conclude that under most experimental conditions in the context of ocean acidification DIC and TA manipulations yield similar changes in all parameters of the carbonate system, which implies direct comparability of data obtained with the two basic approaches for CO2 perturbation

The importance of planetary rotation period for ocean heat transport

The climate, and hence potential habitability, of a planet crucially depends on how its atmospheric and oceanic circulation transports heat from warmer to cooler regions. However, previous studies of planetary climate have concentrated on modelling the dynamics of their atmospheres whilst dramatically simplifying the treatment of the oceans, which neglects or misrepresents the effect of the ocean in the total heat transport. Even the majority of studies with a dynamic ocean have used a simple so-called aquaplanet having no continental barriers, which is a configuration which dramatically changes the oceanic dynamics. Here the significance of the response of poleward ocean heat transport to planetary rotation period is shown with a simple meridional barrier – the simplest representation of any continental configuration. The poleward ocean heat transport increases significantly as the planetary rotation period is increased. The peak heat transport more than doubles when the rotation period is increased by a factor of ten. There are also significant changes to ocean temperature at depth, with implications for the carbon cycle. There is strong agreement between the model results and a scale analysis of the governing equations. This result highlights the importance of both planetary rotation period and the ocean circulation when considering planetary habitability

A secular solar system resonance that disrupts the dominant cycle in Earth's orbital eccentricity (g2-g5): Implications for astrochronology

The planets' gravitational interaction causes rhythmic changes in Earth's orbital parameters (also called Milankovi\'c cycles), which have powerful applications in geology and astrochronology. For instance, the primary astronomical eccentricity cycle due to the secular frequency term (g2-g5) (~405 kyr in the recent past) utilized in deep-time analyses is dominated by Venus' and Jupiter's orbits, aka long eccentricity cycle. The widely accepted and long-held view is that (g2-g5) was practically stable in the past and may hence be used as a "metronome" to reconstruct accurate ages and chronologies. However, using state-of-the-art integrations of the solar system, we show here that (g2-g5) can become unstable over long time scales, without major changes in, or destabilization of, planetary orbits. The (g2-g5) disruption is due to the secular resonance $\sigma_{12}$ = (g1 - g2) + (s1 - s2), a major contributor to solar system chaos. We demonstrate that entering/exiting the $\sigma_{12}$ resonance is a common phenomenon on long time scales, occurring in ~40% of our solutions. During $\sigma_{12}$-resonance episodes, (g2-g5) is very weak or absent and Earth's orbital eccentricity and climate-forcing spectrum are unrecognizable compared to the recent past. Our results have fundamental implications for geology and astrochronology, as well as climate forcing because the paradigm that the longest Milankovi\'c cycle dominates Earth's astronomical forcing, is stable, and has a period of ~405 kyr requires revision.Comment: Final revised version in press. The Astronomical Journa

Equilibria, kinetics, and boron isotope partitioning in the aqueous boric acid–hydrofluoric acid system

REZ is grateful to Lance Agavulin and Glen Morangie for their spiritual support. JWBR was supported by the European Research Council (ERC Grant 805246) and the Natural Environment Research Council (NERC grant NE/N011716/1).The aqueous boric, hydrofluoric, and fluoroboric acid systems are key to a variety of applications, including boron measurements in marine carbonates for CO2 system reconstructions, chemical analysis and synthesis, polymer science, sandstone acidizing, fluoroborate salt manufacturing, and more. Here we present a comprehensive study of chemical equilibria and boron isotope partitioning in the aqueous boric acid–hydrofluoric acid system. We work out the chemical speciation of the various dissolved compounds over a wide range of pH, total fluorine (FT), and total boron (BT) concentrations. We show that at low pH (0 ≤ pH ≤ 4) and FT ≫ BT, the dominant aqueous species is BF4−, a result relevant to recent advances in high precision measurements of boron concentration and isotopic composition. Using experimental data on kinetic rate constants, we provide estimates for the equilibration time of the slowest reaction in the system as a function of pH and [HF], assuming FT ≫ BT. Furthermore, we present the first quantum-chemical (QC) computations to determine boron isotope fractionation in the fluoroboric acid system. Our calculations suggest that the equilibrium boron isotope fractionation between BF3 and BF4− is slightly smaller than that calculated between B(OH)3 and B(OH)4−. Based on the QC methods X3LYP/6-311+G(d,p) (X3LYP+) and MP2/aug-cc-pVTZ (MP2TZ),  α(BF3−BF4−) ≃ 1.030 and 1.025, respectively. However, BF4− is enriched in 11B relative to B(OH)4−, i.e., α(BF4−−B(OH)4−) ≃ 1.010 (X3LYP+) and 1.020 (MP2TZ), respectively. Selection of the QC method (level of theory and basis set) represents the largest uncertainty in the calculations. The effect of hydration on the calculated boron isotope fractionation turned out to be minor in most cases, except for BF4− and B(OH)3. Finally, we provide suggestions on best practice for boric acid–hydrofluoric acid applications in geochemical boron analyses.PostprintPeer reviewe