This paper describes the ocean BiogeochemicAl Model for Hypoxic and Benthic Influenced areas (BAMHBI). BAMHBI is a moderate complexity marine biogeochemical model that describes the cycling of carbon, nitrogen, phosphorus, silicon and oxygen through the marine foodweb. It involves 22 state variables, extends from bacteria up to mesozooplankton and includes three phytoplankton functional types (PFTs), two zooplankton size-classes, a microbial loop with several classes of detritic materials. Five optional modules are available allowing to extend the model with the explicit modelling of Chlorophyll a (Chl a) in each PFT, benthic degradation, gelatinous dynamics, particles aggregation and the carbonate system. BAMHBI describes the degradation of organic matter according to oxygenation conditions using an approach similar to that used in the sediment to simulate early diagenesis. The model is particularly appropriate for modelling low oxygen environments and the generation of sulfidic waters. An optional benthic module solves the degradation of sedimentary organic matter and the benthic-pelagic fluxes of solutes using an efficient formulation based on meta-modelling. This paper describes in details model formulations, implementation and coupling with the physics. BAMHBI's code is written in Fortran and can be coupled with many hydrodynamical models. Two case studies of application of BAMHBI in the Black Sea are described. One describes the application of BAMHBI to simulate the biogeochemical dynamics of the northwestern shelf during the eutrophication period. In particular, the ability of BAMHBI to simulate the oxygen dynamics at seasonal and interannual scales is assessed with a focus on the simulation of bottom hypoxia. We highlight the results of the benthic modelling module and its ability to represent benthic-pelagic fluxes. The second case study compares the BAMHBI simulated Chl a, oxygen and nitrate dynamics in the deep sea with respect to biogeochemical Argo.

Due to the exceptionally long atmospheric lifetime of anthropogenic CO2, anthropogenic emissions are expected to affect the timing of the next glacial cycle. This is because glacial inception depends not only on changes in solar insolation, but also on CO2 concentration. Using the fast Earth system model CLIMBER-X, we conduct long-term transient coupled climate–carbon cycle–ice sheet simulations to explore how different levels of cumulative emissions influence the predicted timing of the next glacial inception. Our results show that assumptions about the pre-industrial state of the carbon cycle and the magnitude of cumulative emissions profoundly impact the predicted timing of inception. We find that historical carbon emissions are insufficient to delay the next glacial period, which would naturally occur around 50 kyr AP (kiloyears after present). Cumulative emissions exceeding 1000 PgC are likely to postpone glacial inception until 100 kyr AP, while emissions up to 5000 PgC would still lead to glacial inception within the next 200 kyr. Millennial-scale AMOC variability, particularly its weakening into Stadial conditions, is also shown to play a critical role in the exact timing of the onset of the next glaciation. Despite this, the simulated timing of glacial inception aligns reasonably well with the predicted timing, which was found using the critical insolation–CO2 relation and a dedicated set of coupled climate–carbon cycle experiments. In these experiments, the predicted timing was identified as the point when the simulated atmospheric CO2 concentration drops below the critical threshold required to trigger glacial inception, given a specific value of maximum summer insolation at 65°N. Our study underscores the long-term impact of anthropogenic CO2 emissions on the Earth's climate, and offers new insights on the inherent predictability of glacial cycles.

Coral reefs are currently under threat due to climate change and ocean acidification. However, future atmospheric CO2 levels, climate change and associated impacts on coral reefs remain uncertain. Critically, corals not only respond to atmospheric and climatic conditions but modify them. The calcification of corals modifies the concentration of dissolved inorganic carbon and total alkalinity in the upper ocean, impacting air-sea gas exchange, atmospheric CO2 concentrations, and ultimately climate. These feedbacks between atmospheric conditions and coral biogeochemistry can only be accounted for with a coupled coral-carbon-climate model. To simulate coral-mediated climate-carbon interactions, we have implemented a coral reef calcification module into the iLOVECLIM Earth system model of intermediate complexity. We then performed an ensemble of 210 parameter perturbation simulations to derive carbonate production parameter values that optimise the simulated distribution of coral reefs and associated carbonate production rates. The tuned model simulates the presence of coral reefs and regional-to-global carbonate production values in good agreement with data-based estimates. We have used this new coupled model to project future changes in coral reef carbonate production. The use of a computationally efficient intermediate complexity model allows us to cover a large range of possible futures that encompass different emissions scenarios (SSPs), climate sensitivities (hence different levels of warming) as well as the possibility of coral reefs adapting to higher SSTs which would reduce the risk of bleaching. We found a high sensitivity of the simulations to the ability of corals to adapt to thermal changes and to climate sensitivity, with the possibility of 20 to 100% coral extinction in scenario SSP1-2.6 depending on these parameters. This highlights the importance of improving the constraints on these factors in models and observations.

Human activities are expected to delay the next glacial inception because of the long atmospheric lifetime of anthropogenic CO 2 . Here we present Earth system model simulations for the next 200,000 years with dynamic ice sheets and interactive atmospheric CO 2 , exploring how emissions will impact a future glacial inception. Historical emissions (500 PgC) are unlikely to delay inception, expected to occur under natural conditions around 50,000 years from now, while a doubling of current emissions (1000 PgC) would delay inception for another 50,000 years. Inception is generally expected within the next 200,000 years for emissions up to 5000 PgC. Our model results show that assumptions about the long-term balance of geological carbon sources and sinks has a strong impact on the timing of the next glacial inception, while millennial-scale variability in the Atlantic Meridional Overturning Circulation influences the exact timing. This work highlights the long-term impact of anthropogenic CO 2 on climate.

Coral reefs are under threat due to climate change and ocean acidification. However, large uncertainties remain concerning future carbon dioxide emissions, climate change and the associated impacts on coral reefs. While most previous studies have used climate model outputs to compute future coral reef carbonate production, we use a coral reef carbonate production module embedded in a global carbon-climate model. This enables the simulation of the response of coral reefs to projected changes in physical and chemical conditions at finer temporal resolution. The use of a fast-intermediate complexity model also permits the simulation of a large range of possible futures by considering different greenhouse gas concentration scenarios (Shared Socioeconomic Pathways (SSPs)) and different climate sensitivities (hence different levels of warming for a given level of acidification), as well as the possibility of corals adapting their thermal bleaching thresholds. We show that without thermal adaptation, global coral reef carbonate production decreases to less than 25 % of historical values in most scenarios over the 21st century, with limited further declines between 2100 and 2300 irrespective of the climate sensitivity. With thermal adaptation, there is far greater scenario variability in projections of reef carbonate production. Under high-emission scenarios the rate of 21st century declines is attenuated, with some global carbonate production declines delayed until the 22nd century. Under high-mitigation scenarios, however, global coral reef carbonate production can recover in the 21st and 22nd centuries and thereafter persist at 50 %-90 % of historical values, provided that the climate sensitivity is moderate.

Coral reef development is intricately linked to both climate and the concentration of atmospheric CO2, specifically through temperature and carbonate chemistry in the upper ocean. In turn, the calcification of corals modifies the concentration of dissolved inorganic carbon (DIC) and total alkalinity in the ocean, impacting air–sea gas exchange, atmospheric CO2 concentration, and ultimately the climate. This feedback between atmospheric conditions and coral biogeochemistry can only be accounted for with a coupled coral–carbon–climate model. Here we present the implementation of a coral reef calcification module into an Earth system model. Simulated coral reef production of the calcium carbonate mineral aragonite depends on photosynthetically active radiation, nutrient concentrations, salinity, temperature, and the aragonite saturation state. An ensemble of 210 parameter perturbation simulations was performed to identify carbonate production parameter values that optimize the simulated distribution of coral reefs and associated carbonate production. The tuned model simulates the presence of coral reefs and regional-to-global carbonate production values in good agreement with data-based estimates, despite some limitations due to the imperfect simulation of climatic and biogeochemical fields driving the simulation of coral reef development. When used in association with methods accounting for bathymetry changes resulting from different sea levels, the model enables assessment of past and future coral–climate coupling on seasonal to millennial timescales, highlighting how climatic trends and variability may affect reef development and the resulting climate–carbon feedback.

Abstract. The carbon cycle component of the newly developed Earth system model of intermediate complexity CLIMBER-X is presented. The model represents the cycling of carbon through the atmosphere, vegetation, soils, seawater and marine sediments. Exchanges of carbon with geological reservoirs occur through sediment burial, rock weathering and volcanic degassing. The state-of-the-art HAMOCC6 model is employed to simulate ocean biogeochemistry and marine sediment processes. The land model PALADYN simulates the processes related to vegetation and soil carbon dynamics, including permafrost and peatlands. The dust cycle in the model allows for an interactive determination of the input of the micro-nutrient iron into the ocean. A rock weathering scheme is implemented in the model, with the weathering rate depending on lithology, runoff and soil temperature. CLIMBER-X includes a simple representation of the methane cycle, with explicitly modelled natural emissions from land and the assumption of a constant residence time of CH4 in the atmosphere. Carbon isotopes 13C and 14C are tracked through all model compartments and provide a useful diagnostic for model–data comparison. A comprehensive evaluation of the model performance for the present day and the historical period shows that CLIMBER-X is capable of realistically reproducing the historical evolution of atmospheric CO2 and CH4 but also the spatial distribution of carbon on land and the 3D structure of biogeochemical ocean tracers. The analysis of model performance is complemented by an assessment of carbon cycle feedbacks and model sensitivities compared to state-of-the-art Coupled Model Intercomparison Project Phase 6 (CMIP6) models. Enabling an interactive carbon cycle in CLIMBER-X results in a relatively minor slow-down of model computational performance by ∼ 20 % compared to a throughput of ∼ 10 000 simulation years per day on a single node with 16 CPUs on a high-performance computer in a climate-only model set-up. CLIMBER-X is therefore well suited to investigating the feedbacks between climate and the carbon cycle on temporal scales ranging from decades to >100 000 years.

In the open ocean, calcium carbonates are mainly found in two mineral forms. Calcite, the least soluble, is widespread at the seafloor, while aragonite, the more soluble, is rarely preserved in marine sediments. Despite its greater solubility, research has shown that aragonite, whose contribution to global pelagic calcification could be at par with that of calcite, is able to reach the deep-ocean. If large quantities of aragonite settle and dissolve at the seafloor, this represents a large source of alkalinity that buffers the deep ocean and favours the preservation of less soluble calcite, acting as a deep-sea, carbonate version of galvanization. Here, we investigate the role of aragonite dissolution on the early diagenesis of calcite-rich sediments using a novel 3D, micrometric-scale reactive-transport model combined with 3D, X-ray tomography structures of natural aragonite and calcite shells. Results highlight the important role of diffusive transport in benthic calcium carbonate dissolution, in agreement with recent work. We show that, locally, aragonite fluxes to the seafloor could be sufficient to suppress calcite dissolution in the top layer of the seabed, possibly causing calcite recrystallization. As aragonite producers are particularly vulnerable to ocean acidification, the proposed galvanizing effect of aragonite could be weakened in the future, and calcite dissolution at the sediment-water interface will have to cover a greater share of CO 2 neutralization.

The successful and efficient approach at the basis of SolveSAPHE (Munhoven, 2013), which determines the carbonate system speciation by calculating pH from total alkalinity (AlkT) and dissolved inorganic carbon (CT), and which converges from any physically sensible pair of such data, has been adapted and further developed for work with AlkT & CO2, AlkT & HCO3− and AlkT & CO32−. The mathematical properties of the three modified alkalinity-pH equations are explored. It is shown that the AlkT & CO2 and AlkT & HCO3− problems have one and only one positive root for any physically sensible pair of data (i.e., such that, resp., [CO2] > 0 and [HCO3−] > 0). The space of AlkT & CO32− pairs is partitioned into regions where there is either no solution, one solution or where there are two. The numerical solution of the modified alkalinity-pH equations is far more demanding than that for the original AlkT-CT pair as they exhibit strong gradients and are not always monotonous. The two main algorithms used from SolveSAPHE v.1 had to be revised in depth to reliably process the three additional data input pairs. The AlkT & CO2 pair is numerically the most challenging. With the Newton-Raphson based solver, it takes about five times as long to solve as the companion AlkT & CT pair, while AlkT & CO2 requires about four times as much time. All in all, it is nevertheless the secant based solver that offers the best performances. It outperforms the Newton-Raphson based one by up to a factor of four, to reach equation residuals that are up to seven orders of magnitude lower. Just like the pH solvers from routines from the v.1 series, SolveSAPHE v.2 includes automatic root bracketing and efficient initialisation schemes for the iterative solvers. For AlkT & CO32− pairs of data, it also determines the number of roots and calculates non-overlapping bracketing intervals. An open source reference implementation in Fortran 90 of the new algorithms is made publicly available for usage under the GNU Lesser General Public Licence v.3 or later.

Abstract. The successful and efficient approach at the basis of SolveSAPHE (Munhoven, 2013), which determines the carbonate system speciation by calculating pH from total alkalinity (AlkT) and dissolved inorganic carbon (CT), and which converges from any physically sensible pair of such data, has been adapted and further developed for work with AlkT \u0026 CO2, AlkT \u0026 HCO3− and AlkT \u0026 CO32−. The mathematical properties of the three modified alkalinity-pH equations are explored. It is shown that the AlkT \u0026 CO2 and AlkT \u0026 HCO3− problems have one and only one positive root for any physically sensible pair of data (i.e., such that, resp., [CO2] \u003e 0 and [HCO3−] \u003e 0). The space of AlkT \u0026 CO32− pairs is partitioned into regions where there is either no solution, one solution or where there are two. The numerical solution of the modified alkalinity-pH equations is far more demanding than that for the original AlkT-CT pair as they exhibit strong gradients and are not always monotonous. The two main algorithms used from SolveSAPHE v.1 had to be revised in depth to reliably process the three additional data input pairs. The AlkT \u0026 CO2 pair is numerically the most challenging. With the Newton-Raphson based solver, it takes about five times as long to solve as the companion AlkT \u0026 CT pair, while AlkT \u0026 CO2 requires about four times as much time. All in all, it is nevertheless the secant based solver that offers the best performances. It outperforms the Newton-Raphson based one by up to a factor of four, to reach equation residuals that are up to seven orders of magnitude lower. Just like the pH solvers from routines from the v.1 series, SolveSAPHE v.2 includes automatic root bracketing and efficient initialisation schemes for the iterative solvers. For AlkT \u0026 CO32− pairs of data, it also determines the number of roots and calculates non-overlapping bracketing intervals. An open source reference implementation in Fortran 90 of the new algorithms is made publicly available for usage under the GNU Lesser General Public Licence v.3 or later.

The successful and efficient approach at the basis of the Solver Suite for Alkalinity-PH Equations (SolveSAPHE) (Munhoven, 2013), which determines the carbonate system speciation by calculating pH from total alkalinity (AlkT) and dissolved inorganic carbon (CT), and which converges for any physically sensible pair of such data, has been adapted and further developed to work with AlkT–CO2, AlkT–HCO3-, and AlkT–CO32-. The mathematical properties of the three modified alkalinity–pH equations are explored. It is shown that the AlkT–CO2, and AlkT–HCO3- problems have one and only one positive root for any physically sensible pair of data (i.e. such that [CO2]>0 and [HCO3-]>0). The space of AlkT–CO32- pairs is partitioned into regions where there is either no solution, one solution or where there are two. The numerical solution of the modified alkalinity–pH equations is far more demanding than that for the original AlkT–CT pair as they exhibit strong gradients and are not always monotonous. The two main algorithms used in SolveSAPHE v1 have been revised in depth to reliably process the three additional data input pairs. The AlkT–CO2 pair is numerically the most challenging. With the Newton–Raphson-based solver, it takes about 5 times as long to solve as the companion AlkT–CT pair; the AlkT–CO32- pair requires on average about 4 times as much time as the AlkT–CT pair. All in all, the secant-based solver offers the best performance. It outperforms the Newton–Raphson-based one by up to a factor of 4 in terms of average numbers of iterations and execution time and yet reaches equation residuals that are up to 7 orders of magnitude lower. Just like the pH solvers from the v1 series, SolveSAPHE-r2 includes automatic root bracketing and efficient initialisation schemes for the iterative solvers. For AlkT–CO32- data pairs, it also determines the number of roots and calculates non-overlapping bracketing intervals. An open-source reference implementation of the new algorithms in Fortran 90 is made publicly available for usage under the GNU Lesser General Public Licence version 3 (LGPLv3) or later.

MEDUSA is a time-dependent one-dimensional numerical model of coupled early diagenetic processes in the surface sea-floor sediment. In the vertical, the sediment is subdivided into two different zones. Solids (biogenic, mineral, etc.) raining down from the surface of the ocean are collected by the reactive mixed layer at the top. This is where chemical reactions take place. Solids are transported by bioturbation and advection, and solutes are transported by diffusion and bioirrigation. The classical coupled time-dependent early diagenesis equations (advection–diffusion reaction equations) are used to describe the evolutions of the solid and solute components here. Solids that get transported deeper than the bottom boundary of the reactive mixed layer enter the second zone underneath, where reactions and mixing are neglected. Gradually, as solid material gets transferred here from the overlying reactive layer, it is buried and preserved in a stack of layers that make up a synthetic sediment core. MEDUSA has been extensively modified since its first release from 2007. The composition of the two phases, the processes (chemical reactions) and chemical equilibria between solutes are not fixed any more, but get assembled from a set of XML-based description files that are processed by a code generator to produce the required Fortran code. 1D, 2D and 2D×2D interfaces have been introduced to facilitate the coupling to common grid configurations and material compositions used in biogeochemical models. MEDUSA can also be run in parallel computing environments using the Message Passing Interface (MPI).

Aragonite is about 50% more soluble than calcite in seawater and its pelagic production is dominated by pteropods. Moreover, it could account for a large fraction of marine CaCO3 export. The aragonite compensation depth (ACD, the depth at which accumulation is balanced by dissolution) is generally very close to the aragonite saturation depth, i.e. within a few hundred metres. Conversely, the calcite compensation depth (CCD) can be 1-2 kilometres deeper than the calcite saturation depth. That aragonite disappears shallower than calcite in marine sediments is coherent with aragonite’s greater solubility, but why is the calcite lysocline, i.e. the distance between its compensation and saturation depths, much thicker than its aragonite equivalent? Here, we suggest that at the seafloor, the addition of a soluble CaCO3 phase (aragonite) results in the preservation of a predeposited stable CaCO3 phase (calcite), and term this a negative priming action. In soil science, priming action refers to the increase in soil organic matter decomposition rate that follows the addition of fresh organic matter, supposedly resulting from a globally increased microbial activity (Bingeman et al., 1953). Using a new 3D model of CaCO3 dissolution at the grain scale, we show that a conceptually similar phenomenon could occur at the seafloor, in which the dissolution of an aragonite pteropod at the sediment-water interface buffers the porewaters and causes the preservation of surrounding calcite. Since aragonite-producing organisms are particularly vulnerable to ocean acidification, we expect an increasing calcite to aragonite ratio in the CaCO3 flux reaching the seafloor as we go further in the Anthropocene. This could, in turn, hinder the proposed aragonite negative priming action, and favour chemical erosion of calcite sediments. Reference: Bingeman, C.W., Varner, J.E., Martin, W.P., 1953. The Effect of the Addition of Organic Materials on the Decomposition of an Organic Soil. Soil Science Society of America Journal 17, 34-38.

Abstract In the open ocean, calcium carbonates are mainly found in two mineral forms. Calcite, the least soluble, is widespread at the seafloor, while aragonite, the more soluble, is rarely preserved in marine sediments. Despite its greater solubility, research has shown that aragonite, which could contribute between 10 and 90% to pelagic calcium carbonate production, is able to reach the deep-ocean. If large quantities of aragonite settle and dissolve at the seafloor, this represents a large source of alkalinity that buffers the deep ocean and favours the preservation of less soluble calcite, acting as a deep-sea, carbonate version of galvanization. Here, we investigate the role of aragonite dissolution on the early diagenesis of calcite-rich sediments using a novel 3D, micrometric-scale reactive-transport model combined with 3D, X-ray tomography structures of natural aragonite and calcite shells. Results highlight the important role of diffusive transport in benthic calcium carbonate dissolution, in agreement with recent work. We show that, locally, aragonite fluxes to the seafloor could be sufficient to suppress calcite dissolution in the top layer of the seabed, possibly causing calcite recrystallization. As aragonite producers are particularly vulnerable to ocean acidification, the proposed galvanizing effect of aragonite could be weakened in the future, indirectly boosting calcite dissolution further.

Line-of-sight integration of emissions from planetary and cometary atmospheres is the Abel transform of the emission rate, under the spherical symmetry assumption. Indefinite integrals constructed from the Abel transform integral are useful for implementing remote sensing data analysis methods, such as the numerical inverse Abel transform giving the volume emission rate compatible with the observation. We obtain analytical expressions based on a suitable, non-alternating, series development to compute those indefinite integrals. We establish expressions allowing absolute accuracy control of the convergence of these series depending on the number of terms involved. We compare the analytical method with numerical computation techniques, which are found to be sufficiently accurate as well. Inverse Abel transform fitting is then tested in order to establish that the expected emission rate profiles can be retrieved from the observation of both planetary and cometary atmospheres. We show that the method is robust, especially when Tikhonov regularization is included, although it must be carefully tuned when the observation varies across many orders of magnitude. A first application is conducted over observation of comet 46P/Wirtanen, showing some variability possibly attributable to an evolution of the contamination by dust and icy grains. A second application is considered to deduce the 557.7 nm volume emission rate profile of the metastable oxygen atom in the upper atmosphere of planet Mars.

Aragonite is about 50% more soluble than calcite in seawater and its pelagic production is dominated by pteropods. Moreover, it could account for a large fraction of marine CaCO3 export. The aragonite compensation depth (ACD, the depth at which accumulation is balanced by dissolution) is generally very close to the aragonite saturation depth, i.e. within a few hundred metres. Conversely, the calcite compensation depth (CCD) can be 1-2 kilometres deeper than the calcite saturation depth. That aragonite disappears shallower than calcite in marine sediments is coherent with aragonite’s greater solubility, but why is the calcite lysocline, i.e. the distance between its compensation and saturation depths, much thicker than its aragonite equivalent? Here, we suggest that at the seafloor, the addition of a soluble CaCO3 phase (aragonite) results in the preservation of a predeposited stable CaCO3 phase (calcite), and term this a negative priming action. In soil science, priming action refers to the increase in soil organic matter decomposition rate that follows the addition of fresh organic matter, supposedly resulting from a globally increased microbial activity (Bingeman et al., 1953). Using a new 3D model of CaCO3 dissolution at the grain scale, we show that a conceptually similar phenomenon could occur at the seafloor, in which the dissolution of an aragonite pteropod at the sediment-water interface buffers the porewaters and causes the preservation of surrounding calcite. Since aragonite-producing organisms are particularly vulnerable to ocean acidification, we expect an increasing calcite to aragonite ratio in the CaCO3 flux reaching the seafloor as we go further in the Anthropocene. This could, in turn, hinder the proposed aragonite negative priming action, and favour chemical erosion of calcite sediments. Reference: Bingeman, C.W., Varner, J.E., Martin, W.P., 1953. The Effect of the Addition of Organic Materials on the Decomposition of an Organic Soil. Soil Science Society of America Journal 17, 34-38.

The successful and efficient approach at the basis of the Solver Suite for Alkalinity-PH Equations (SolveSAPHE) (Munhoven, 2013), which determines the carbonate system speciation by calculating pH from total alkalinity (Alk(T)) and dissolved inorganic carbon (C-T), and which converges for any physically sensible pair of such data, has been adapted and further developed to work with Alk(T)-CO2, Alk(T)-HCO3-, and Alk(T)-CO32-. The mathematical properties of the three modified alkalinity-pH equations are explored. It is shown that the Alk(T)-CO2, and Alk(T)-HCO3- problems have one and only one positive root for any physically sensible pair of data (i.e. such that [CO2] > 0 and [HCO3-] > 0). The space of Alk(T)-CO32- pairs is partitioned into regions where there is either no solution, one solution or where there are two. The numerical solution of the modified alkalinity-pH equations is far more demanding than that for the original Alk(T)-C-T pair as they exhibit strong gradients and are not always monotonous. The two main algorithms used in SolveSAPHE v1 have been revised in depth to reliably process the three additional data input pairs. The Alk(T)-CO2 pair is numerically the most challenging. With the Newton-Raphson-based solver, it takes about 5 times as long to solve as the companion Alk(T)-C-T pair; the Alk(T-)CO(3)(2-) pair requires on average about 4 times as much time as the Alk(T)-C-T pair. All in all, the secant-based solver offers the best performance. It outperforms the Newton-Raphsonbased one by up to a factor of 4 in terms of average numbers of iterations and execution time and yet reaches equation residuals that are up to 7 orders of magnitude lower. Just like the pH solvers from the v1 series, SolveSAPHE-r2 includes automatic root bracketing and efficient initialisation schemes for the iterative solvers. For Alk(T)-CO32- data pairs, it also determines the number of roots and calculates nonoverlapping bracketing intervals. An open-source reference implementation of the new algorithms in Fortran 90 is made publicly available for usage under the GNU Lesser General Public Licence version 3 (LGPLv3) or later.

The importance of volcanic CO2 release, continental weathering, and coral reef growth on the global carbon cycle has been highlighted by several different studies. Based on these independent approaches, we here revisit the last 800 kyr with the box model BICYCLE, which has been extended to be able to address these solid Earth contributions to the carbon cycle. We show that the volcanic outgassing of CO2 as a function of sea level change from mid-ocean ridges and hot spot island volcanoes cannot be the generic process that leads during phases of falling obliquity to a sea level-CO2 decoupling as has been suggested before. The combined contribution from continental and marine volcanism, if both lagging sea level change by 4 kyr, might have added up to 13 ppm to the glacial/interglacial CO2 rise. Coral reef growth as suggested by an independent model is during glacial terminations about an order of magnitude too high to be reconciled with meaningful carbon cycle dynamics. Global riverine input of bicarbonate caused by silicate and carbonate weathering is suggested to have been stable over Termination I. However, if weathering fluxes are changed by up to 50% in sensitivity experiments, the corresponding bicarbonate input might contribute less than 20 ppm to the deglacial atmospheric CO2 rise. The overall agreement of results with the new process-based sediment module and the previously applied time-delayed response function to mimic carbonate compensation gives confidence in the results obtained in previous applications of the BICYCLE model without solid Earth processes.

We developed a coupling scheme for the Community Earth System Model version 1.2 (CESM1.2) and the Model of Early Diagenesis in the Upper Sediment of Adjustable complexity (MEDUSA), and explored the effects of the coupling on solid components in the upper sediment and on bottom seawater chemistry by comparing the coupled model's behaviour with that of the uncoupled CESM having a simplified treatment of sediment processes. CESM is a fully coupled atmosphere–ocean–sea-ice–land model and its ocean component (the Parallel Ocean Program version 2; POP2) includes a biogeochemical component (the Biogeochemical Elemental Cycling model; BEC). MEDUSA was coupled to POP2 in an offline manner so that each of the models ran separately and sequentially with regular exchanges of necessary boundary condition fields. This development was done with the ambitious aim of a future application for long-term (spanning a full glacial cycle; i.e. ∼105 years) climate simulations with a state-of-the-art comprehensive climate model including the carbon cycle, and was motivated by the fact that until now such simulations have been done only with less-complex climate models. We found that the sediment–model coupling already had non-negligible immediate advantages for ocean biogeochemistry in millennial-timescale simulations. First, the MEDUSA-coupled CESM outperformed the uncoupled CESM in reproducing an observation-based global distribution of sediment properties, especially for organic carbon and opal. Thus, the coupled model is expected to act as a better “bridge” between climate dynamics and sedimentary data, which will provide another measure of model performance. Second, in our experiments, the MEDUSA-coupled model and the uncoupled model had a difference of 0.2 ‰ or larger in terms of δ13C of bottom water over large areas, which implied a potentially significant model uncertainty for bottom seawater chemical composition due to a different way of sediment treatment. For example, an ocean model that does not treat sedimentary processes depending on the chemical composition of the ambient water can overestimate the amount of remineralization of organic matter in the upper sediment in an anoxic environment, which would lead to lighter δ13C values in the bottom water. Such a model uncertainty would be a fundamental issue for paleo model–data comparison often relying on data derived from benthic foraminifera.