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The Keeling plot analysis is an interpretation method widely used in terrestrial carbon cycle research to quantify exchange processes of carbon between terrestrial reservoirs and the atmosphere. Here, we analyse measured data sets and artificial time series of the partial pressure of atmospheric carbon dioxide (pCO2) and of δ13C of CO2 over industrial and glacial/interglacial time scales and investigate to what extent the Keeling plot methodology can be applied to longer time scales. The artificial time series are simulation results of the global carbon cycle box model BICYCLE. The signals recorded in ice cores caused by abrupt terrestrial carbon uptake or release loose information due to air mixing in the firn before bubble enclosure and limited sampling frequency. Carbon uptake by the ocean cannot longer be neglected for less abrupt changes as occurring during glacial cycles. We introduce an equation for the calculation of long-term changes in the isotopic signature of atmospheric CO2 caused by an injection of terrestrial carbon to the atmosphere, in which the ocean is introduced as third reservoir. This is a paleo extension of the two reservoir mass balance equations of the Keeling plot approach. It gives an explanation for the bias between the isotopic signature of the terrestrial release and the signature deduced with the Keeling plot approach for long-term processes, in which the oceanic reservoir cannot be neglected. These deduced isotopic signatures are similar (−8.6‰) for steady state analyses of long-term changes in the terrestrial and marine biosphere which both perturb the atmospheric carbon reservoir. They are more positive than the δ13C signals of the sources, e.g.the terrestrial carbon pools themselves (−25‰). A distinction of specific processes acting on the global carbon cycle from the Keeling plot approach is not straightforward. In general, processes related to biogenic fixation or release of carbon have lower y-intercepts in the Keeling plot than changes in physical processes, however in many case they are indistinguishable (e.g. ocean circulation from biogenic carbon fixation).

Many sensitivity studies have been carried out, using climate models of different degrees of complexity to test the climate response to Last Glacial Maximum boundary conditions. Here, instead of adding the forcings successively as in most previous studies, we applied the separation method of U. Stein et P. Alpert 1993, in order to determine rigorously the different contributions of the boundary condition modifications, and isolate the pure contributions from the interactions among the forcings. We carried out a series of sensitivity experiments with the model of intermediate complexity Planet Simulator, investigating the contributions of the ice sheet expansion and elevation, the lowering of the atmospheric CO2 and of the vegetation cover change on the LGM climate. The separation of the ice cover and orographic contributions shows that the ice albedo effect is the main contributor to the cooling of the Northern Hemisphere, whereas orography has only a local cooling impact over the ice sheets. The expansion of ice cover in the Northern Hemisphere causes a disruption of the tropical precipitation, and a southward shift of the ITCZ. The orographic forcing mainly contributes to the disruption of the atmospheric circulation in the Northern Hemisphere, leading to a redistribution of the precipitation, but weakly impacts the tropics. The isolated vegetation contribution also induces strong cooling over the continents of the Northern Hemisphere that further affects the tropical precipitation and reinforce the southward shift of the ITCZ, when combined with the ice forcing. The combinations of the forcings generate many non-linear interactions that reinforce or weaken the pure contributions, depending on the climatic mechanism involved, but they are generally weaker than the pure contributions. Finally, the comparison between the LGM simulated climate and climatic reconstructions over Eurasia suggests that our results reproduce well the south-west to north-east temperature gradients over Eurasia.

The total alkalinity–pH equation, which relates total alkalinity and pH for a given set of total concentrations of the acid–base systems that contribute to total alkalinity in a given water sample, is reviewed and its mathematical properties established. We prove that the equation function is strictly monotone and always has exactly one positive root. Different commonly used approximations are discussed and compared. An original method to derive appropriate initial values for the iterative solution of the cubic polynomial equation based upon carbonate-borate-alkalinity is presented. We then review different methods that have been used to solve the total alkalinity–pH equation, with a main focus on biogeochemical models. The shortcomings and limitations of these methods are made out and discussed. We then present two variants of a new, robust and universally convergent algorithm to solve the total alkalinity–pH equation. This algorithm does not require any a priori knowledge of the solution. SolveSAPHE (Solver Suite for Alkalinity-PH Equations) provides reference implementations of several variants of the new algorithm in Fortran 90, together with new implementations of other, previously published solvers. The new iterative procedure is shown to converge from any starting value to the physical solution. The extra computational cost for the convergence security is only 10–15% compared to the fastest algorithm in our test series.

Many sensitivity studies have been carried out, using climate models of different degrees of complexity to test the climate response to Last Glacial Maximum boundary conditions. Here, instead of adding the forcings successively as in most previous studies, we applied the separation method of U. Stein et P. Alpert 1993, in order to determine rigorously the different contributions of the boundary condition modifications, and isolate the pure contributions from the interactions among the forcings. We carried out a series of sensitivity experiments with the model of intermediate complexity Planet Simulator, investigating the contributions of the ice sheet expansion and elevation, the lowering of the atmospheric CO2 and of the vegetation cover change on the LGM climate. The separation of the ice cover and orographic contributions shows that the ice albedo effect is the main contributor to the cooling of the Northern Hemisphere, whereas orography has only a local cooling impact over the ice sheets. The expansion of ice cover in the Northern Hemisphere causes a disruption of the tropical precipitation, and a southward shift of the ITCZ. The orographic forcing mainly contributes to the disruption of the atmospheric circulation in the Northern Hemisphere, leading to a redistribution of the precipitation, but weakly impacts the tropics. The isolated vegetation contribution also induces strong cooling over the continents of the Northern Hemisphere that further affects the tropical precipitation and reinforce the southward shift of the ITCZ, when combined with the ice forcing. The combinations of the forcings generate many non-linear interactions that reinforce or weaken the pure contributions, depending on the climatic mechanism involved, but they are generally weaker than the pure contributions. Finally, the comparison between the LGM simulated climate and climatic reconstructions over Eurasia suggests that our results reproduce well the south-west to north-east temperature gradients over Eurasia.

We are investigating the late Holocene rise in CO2 by performing four experiments with the climate-carbon-cycle model CLIMBER2-LPJ. Apart from the deep sea sediments, important carbon cycle processes considered are carbon uptake or release by the vegetation, carbon uptake by peatlands, and CO2 release due to shallow water sedimentation of CaCO3. Ice core data of atmospheric CO2 between 8 ka BP and preindustrial climate can only be reproduced if CO2 outgassing due to shallow water sedimentation of CaCO3 is considered. In this case the model displays an increase of nearly 20 ppmv CO2 between 8 ka BP and present day. Model configurations that do not contain this forcing show a slight decrease in atmospheric CO2. We can therefore explain the late Holocene rise in CO2 by invoking natural forcing factors only, and anthropogenic forcing is not required to understand preindustrial CO2 dynamics.

A reduction of the carbonate-carbon to organic-carbon export rain ratio during glacial times has been advanced to explain the glacial-interglacial atmospheric CO2 variations. This hypothesis is tested and implications for the dynamics of sedimentary carbonate preservation and dissolution are explored with a multi-box model (MBM) of the ocean carbon cycle, fully coupled to a new transient early diagenesis model (called MEDUSA). A peak reduction of the rain ratio by 40% at the Last Glacial Maximum (LGM) was found to produce a net atmospheric pCO2 reduction of about 40 ppm. Changing shelf carbonate accumulation rates and continental weathering inputs produced a 55-60 ppm reduction. The combination of the two mechanisms generates a PCO2 change of 90-95 ppm, which compares well with the observed data. However, the resulting model sedimentary record does not conform to actual sedimentary records. The changes related to continental shelf processes and variable weathering flux depress the calcite saturation horizon (CSH) by about I kin at the LGM; if rain ratio variations are also considered, that depression increases by another kin. In addition to this large amplitude for the CSH, possibly due to the adopted box-model approach, the changing rain ratio also leads to transition zone changes in the model sedimentary record that are opposite in phase with data-based reconstructions. Realistic changes in the aragonite fraction of the carbonate rain were found to have only a minimal impact on atmospheric PC02. Finally, chemical erosion of deep-sea sediment was shown to reduce the amplitude of variation of the sedimentary CCD by about 10-20%. It may provide a mechanism to improve the model-data agreement.

A new Earth system model of intermediate complexity, LOVECLIM, has been developed in order to study long-term future climate changes. It includes an interactive Greenland and Antarctic ice sheet model (AGISM) as well as an oceanic carbon cycle model (LOCH). Those climatic components can have a great impact on future climate. The few studies in recent literature assessing the impact of polar ice sheets on future climate draw very different conclusions, which shows the need for developing such a model. A set of numerical experiments have been performed in order to study the possible perturbations of climate induced by human activities over the next millennia. A particular attention is given to the Greenland ice sheet. In most of the projections, the Greenland ice sheet undergoes a continuous reduction in volume, leading to an almost total disappearance in the most pessimistic scenarios. The impact of the Greenland deglaciation on climate has therefore been assessed through a sensitivity experiment using the scenario SRES A2. The removal of the Greenland ice sheet is responsible for a regional amplification of the global warming inducing a total melt of Arctic sea ice in summer. The freshwater flux from Greenland generates large salinity anomalies in the North Atlantic Ocean that reduce the rate of North Atlantic Deep Water formation, slowing down slightly the oceanic thermohaline circulation.

The Keeling plot analysis is an interpretationmethod widely used in terrestrial carbon cycle research toquantify exchange processes of carbon between terrestrialreservoirs and the atmosphere. Here, we analyse measureddata sets and artificial time series of the partial pressure of atmosphericcarbon dioxide (pCO2) and of d13C of CO2 overindustrial and glacial/interglacial time scales and investigateto what extent the Keeling plot methodology can be appliedto longer time scales. The artificial time series are simulationresults of the global carbon cycle box model BICYCLE.The signals recorded in ice cores caused by abrupt terrestrialcarbon uptake or release loose information due to air mixingin the firn before bubble enclosure and limited samplingfrequency. Carbon uptake by the ocean cannot longer be neglectedfor less abrupt changes as occurring during glacialcycles. We introduce an equation for the calculation of longtermchanges in the isotopic signature of atmospheric CO2caused by an injection of terrestrial carbon to the atmosphere,in which the ocean is introduced as third reservoir. This is apaleo extension of the two reservoir mass balance equationsof the Keeling plot approach. It gives an explanation for thebias between the isotopic signature of the terrestrial releaseand the signature deduced with the Keeling plot approach forlong-term processes, in which the oceanic reservoir cannotbe neglected. These deduced isotopic signatures are similar(−8.6) for steady state analyses of long-term changes inthe terrestrial and marine biosphere which both perturb theatmospheric carbon reservoir. They are more positive thanthe d13C signals of the sources, e.g. the terrestrial carbonpools themselves (~ −25). A distinction of specific processesacting on the global carbon cycle from the Keeling plot approach is not straightforward. In general, processesrelated to biogenic fixation or release of carbon have lowery-intercepts in the Keeling plot than changes in physical processes,however in many case they are indistinguishable (e.g.ocean circulation from biogenic carbon fixation).

North America warms more than the zonal mean, while Europe warms less than the zonal mean during the next millennia. This asymmetry can be explained by both regional and larger-scale processes. The amplification of the warming in NAM is due in winter and spring to the snow cover feedback and, in addition, to the sea ice feedback in autumn. The poleward heat transport in the Atlantic is reduced by 10%. This weakens the sst increase along European coasts in winter and therefore reduces the warming over the continent during this season.

The glacial/interglacial rise in atmospheric pCO2 is one of the best known changes in paleoclimate research, yet the cause for it is still unknown. Forcing the coupled oceanatmosphere- biosphere box model of the global carbon cycle BICYCLE with proxy data over the last glacial termination, we are able to quantitatively reproduce transient variations in pCO2 and its isotopic signatures (d13C, D14C) observed in natural climate archives. The sensitivity of the Box model of the Isotopic Carbon cYCLE (BICYCLE) to high or low latitudinal changes is comparable to other multibox models or more complex ocean carbon cycle models, respectively. The processes considered here ranked by their contribution to the glacial/interglacial rise in pCO2 in decreasing order are: the rise in Southern Ocean vertical mixing rates (>30 ppmv), decreases in alkalinity and carbon inventories (>30 ppmv), the reduction of the biological pump ( 20 ppmv), the rise in ocean temperatures (15 20 ppmv), the resumption of ocean circulation (15 20 ppmv), and coral reef growth (

The runoff and riverine fluxes of HCO3-, Si and Ge that arise from chemical erosion in non-glaciated terrain, are modelled at six time steps from the Last Glacial Maximum (LGM) to the present day. The fluxes that arise from the Great Ice Sheets are also modelled. Terrestrial HCO3- fluxes decrease during deglaciation, largely because of the reduction in the area of the continental shelves as sea level rises. The HCO3- fluxes, and the inferred consumption of atmospheric CO2 are used as inputs to a carbon cycle model that estimates their impact on atmospheric CO2 concentrations (atmsCO2). A maximum perturbation of atmsCO2 by 5.5 ppm is calculated. The impact of solutes from glaciated terrain is small in comparison to those from non-glaciated terrain. Little variation in terrestrial Si and Ge fluxes is calculated (atmsCO2, and only little influence on the global Si and Ge cycle and marine Ge/Si ratios during deglaciation.