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 >100000 years.
Bundesministerium für Bildung und ForschungPalMod01LP1920B01LP1917D01LP1919B01LP1919C01LP1920CIntroduction
Atmospheric CO2 exerts a profound control on the state of the Earth system. Although it is present only in tiny concentrations
in the present-day atmosphere, by absorbing radiation in the longwave spectral range it has a substantial effect on the energy balance of
the Earth. In the present-day atmosphere, CO2 is the second most important greenhouse gas after water vapour. CO2 is also a fundamental molecule for life on Earth, as it serves as “food” in the photosynthesis process. The atmospheric CO2
concentration is hence a main control on the growth rate of plants on land.
From ice core data it is well known that atmospheric CO2 concentrations showed pronounced variations over the last
million years (e.g. ) that played an important role for the climate evolution over the Pleistocene (last ∼ 2.6 million years)
by amplifying the variations associated with glacial–interglacial cycles (e.g. ). Furthermore, on even longer timescales, a secular decrease in CO2 is thought to have been the main driver of the gradual cooling over the Cenozoic (last 66 million years) (e.g. ).
Over the last few centuries, human activities have strongly disrupted the natural CO2 balance by directly emitting CO2 from fossil sources into the atmosphere. The resulting increase in atmospheric CO2 has been the main factor
for the observed rapid climate warming since the pre-industrial period (e.g. ).
Modelling the atmospheric CO2 concentration is thus fundamental both for understanding past climate changes and for predicting the
future evolution of the Earth system under different anthropogenic emission scenarios.
However, it is far from trivial, because atmospheric CO2 is the result of complex biogeochemical processes on land, in the ocean,
in marine sediments and in the lithosphere. Additionally, because of the long timescales involved in some of the carbon cycle processes, the interactive simulation of atmospheric CO2 has been, and still is, a challenge for state-of-the-art Earth system models.
Fast Earth system models of intermediate complexity have therefore been extensively employed for investigating carbon cycle–climate feedbacks, e.g. Bern3D , cGENIE , CLIMBER-2 , iLOVECLIM , LOVECLIM and Uvic . Among these, CLIMBER-2 has successfully reproduced glacial–interglacial variations in CO2, but some of the processes involved remain uncertain. CLIMBER-X builds on the past experience in modelling the global carbon cycle with CLIMBER-2 but adds an improved and more detailed representation of carbon cycle processes both on land and in the ocean. Improvements include a generally
higher spatial resolution, a 3D ocean model, a state-of-the-art ocean biogeochemistry and marine sediment model, a
more comprehensive description of vegetation and soil carbon processes, including permafrost and peatlands, and a new chemical weathering scheme.
In the following, the biogeochemistry components of CLIMBER-X are presented. The climate core of CLIMBER-X
is described in detail in .
Model description
CLIMBER-X represents the cycling of carbon through the atmosphere, vegetation, soils, seawater and marine sediments. Through sediment burial, chemical weathering of rocks and volcanic degassing, carbon is also exchanged with geological reservoirs.
A schematic illustration of the carbon cycle in the model is shown in Fig. .
The carbon cycle component of CLIMBER-X consists of the ocean biogeochemistry and marine sediment models from HAMOCC6
and the land model PALADYN , which includes dynamic vegetation, a soil carbon model and the
weathering model of and .
The atmospheric CO2 concentration is determined interactively by the exchange of carbon between the atmosphere, seawater, land and lithosphere. The model includes a representation of the dust cycle, with simulated dust deposition determining the input of the micro-nutrient iron into the ocean.
CLIMBER-X also 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.
The model is enabled with the carbon isotopes 13C and 14C, which are tracked through all model compartments.
The different model components are described in more detail in the following sections.
Schematic illustration of the natural biogeochemical cycles in the CLIMBER-X model.
Ocean biogeochemistry and marine sediments: HAMOCC
HAMOCC is a state-of-the-art ocean biogeochemistry model, which is part of the MPI-ESM,
the Earth system model of the Max Planck Institute for Meteorology (MPI). The latest version , which is the version employed by
the MPI in the Coupled Model Intercomparison Project Phase 6 (CMIP6), has been the
starting point for the implementation of the model in CLIMBER-X. As a first step, the original HAMOCC6 code has been adapted to the CLIMBER-X structure.
Notably, for easier parallelization, it has been transformed from a 3D model into a 1D vertical column model in which each water column is independent of the others. This is possible because the biogeochemical processes in the model are restricted to local vertical interactions.
The different columns interact only through horizontal advection by ocean currents, which takes place in the ocean model.
HAMOCC represents the biogeochemical processes in the water column, in the sediments and at the air–sea interface. Marine biology dynamics are based on an extended NPZD (nutrients, phytoplankton, zooplankton and detritus) approach .
The carbonate chemistry in the model follows the latest OMIP protocol , which uses the robust and safe pH calculation routines
from SolveSAPHE-r1 . In the water column, the following biogeochemical tracers are simulated: dissolved inorganic carbon (DIC), total alkalinity (TA),
phosphate (PO4), nitrate (NO3), nitrous oxide (N2O), dissolved nitrogen gas (N2), silicate (SiO2), dissolved bioavailable iron (Fe),
dissolved oxygen (O2), phytoplankton (Phy), zooplankton (Zoo), dissolved organic matter (DOC), particulate organic matter (POC),
opal shells, calcium carbonate shells (CaCO3), terrigenous material (dust) and hydrogen sulfide (H2S).
The composition of organic material follows a constant Redfield ratio (C:N:P:O2=122:16:1:−172) after and for the micro-nutrient iron (Fe:C=4×10-6:1).
The marine sediment module, which is part of HAMOCC, is based on . It essentially simulates the same
processes between dissolved tracers (DIC, TA, PO4, NO3, O2, Fe, SiO2, H2S and N2) in porewater and solid sediment constituents (POC, opal, CaCO3 and dust) as in the water column. Porewater tracers are exchanged with the overlying water column via diffusion. Sedimentation fluxes of POC, CaCO3, opal and dust are added to the solid components of the sediment. Accumulation of solid sediment
material will lead to active sediment layer content being shifted to the burial layer and back if boundary condition changes lead to chemical erosion of previously buried sediment.
Next we describe the changes introduced into HAMOCC as part of its implementation in CLIMBER-X.
N2 fixation is represented by a diagnostic formulation, whereby the nitrate influx into the surface layer is a function
of the nitrate deficit relative to phosphate, multiplied by a constant fixation rate .
Prognostic N2 fixers have recently been included in HAMOCC , based on the physiological characteristics
of the cyanobacterium Trichodesmium. However, for simplicity and because uncertainties in nitrogen fixation remain large (e.g. ), in CLIMBER-X cyanobacteria are disabled by default.
Following , we have implemented a representation of aggregates in the model.
Particulate organic carbon is assumed to form aggregates with the denser calcite and opal built during phytoplankton and
zooplankton growth and with dust particles. The sinking speed of these aggregates depends on their excess density . Note that this approach neglects the effects of e.g. aggregate size distribution and porosity on the sinking speed , and it does not, like other numerically more expensive schemes
(e.g. ), explicitly resolve the biological and physical aggregation and disaggregation processes. The introduction of the ballasting scheme required a re-tuning of the dissolution rates of calcite and opal as shown
in Table .
Following recent evidence that the remineralization of organic carbon depends on temperature (e.g. ), we have introduced a Q10 temperature dependence for the remineralization of POC and DOC , with a default Q10 value of 2. The complete set of remineralization parameters is listed in Table .
In the original HAMOCC, iron complexation by organic substances is assumed when the iron concentration exceeds a given threshold, and dissolved iron is then removed from the water column at a fixed rate.
In CLIMBER-X, we explicitly model iron complexation, differentiating between free and complexed iron forms following
and . The complexed iron is associated with an organic ligand, and only the free iron is available for scavenging. The ligand concentration is assumed to be constant at 1 nmolkg-1 with a ligand
stability constant of 1×1011kgmol-1. The speciation of iron is then determined by equilibrium kinetics.
The scavenging rate of free iron is a combination of a minimum scavenging rate and a scavenging rate that is proportional to
the POC, calcite and opal concentrations following and .
Compared to HAMOCC, we have also increased the stoichiometric iron ratio in organic compounds from Fe:C=3×10-6:1 to Fe:C=4×10-6:1. The parameters related to the iron cycle are also reported in Table .
Modified HAMOCC parameters used in CLIMBER-X compared to HAMOCC6 (i.e. Table 2 in ).
ParameterDescriptionCLIMBER-XHAMOCC6UnitNutrientsμcyanN2 fixation rate0.00250.005d-1λdetrefPOC remineralization rate at temperature Tref0.050.025d-1λNrefDenitrification rate at temperature Tref0.150.07d-1λSrefSulfate reduction rate at temperature Tref0.0050.005d-1Q10Q10 for temperature dependence of remineralization rate21TrefReference temperature for remineralization rate20∘CIron cyclefFedustFraction of iron mass in dust0.0250.035kgkg-1dFeIron solubility in surface water0.010.01RFe:CStoichiometric iron ratio in organic compounds4×10-63×10-6molFemolC-1LTotal ligand concentration1×10-9kmolm-3kLLigand stability constant1×1011m3kmol-1kscavminMinimum free Fe scavenging rate3×10-5d-1kscavPOCSlope of free Fe scavenging rate by POC0.002mmolCm-3-1d-1kscavshellsSlope of free Fe scavenging rate by shells0.002mmol(C/Si)m-3-1d-1Shell materialKSiOHalf-saturation constant for Si(OH)4 uptake5×10-61×10-6kmolSim-3RCa:PCaCO3:P uptake ratio1020molCmolP-1RSi:POpal:P uptake ratio5025molSimolP-1λcalcDissolution rate of calcite shells0.30.075d-1λopalDissolution rate of opal shells0.00250.01d-1Sedimentsλdetsed,refSediment POC remineralization rate at temperature Trefsed0.0250.01kmolO2m-3-1d-1λNsed,refSediment denitrification rate at temperature Trefsed0.10.01d-1λSsed,refSediment sulfate reduction rate at temperature Trefsed2.5×10-52.5×10-5d-1Q10sedQ10 for temperature dependence of remineralization rate21TrefsedReference temperature for remineralization rate in sediments5∘CλcalcsedSediment dissolution rate constant of CaCO30.020.0086kmolCaCO3m-3-1d-1λopalsedSediment dissolution rate constant of opal0.0050.0026kmolSi(OH)4m-3-1d-1
The carbon-13 isotope was recently implemented in HAMOCC by . In CLIMBER-X we extended this approach to also include radiocarbon.
Since the ocean model in CLIMBER-X is a rigid lid model, following the OMIP protocol , we explicitly take
into account the local concentration-dilution effect of the net surface freshwater flux, which changes surface DIC concentration and alkalinity.
Two options are available in the model to implement the dilution effect on DIC and alkalinity. The first one ensures that the net
global surface tracer flux is zero by applying deviations from the global average freshwater flux to the global average surface tracer
concentration. The second (default) option applies the actual local surface freshwater flux to compute a new virtual top ocean layer
thickness and then dilutes the tracers accordingly. In this case, the conservation of tracer inventories is ensured by compensating for imbalances over the global ocean. Additionally, during times when ocean volume is changing because of build-up or melt of land ice, concentrations of all tracers are globally adjusted while conserving tracer inventories. This is a reasonable simplification, considering that land ice volume changes
occur on multi-millennial timescales, over which the ocean can be considered well mixed.
Based on scale analysis, we have excluded fast sinking tracers (CaCO3, opal, POC and dust) from advection, as these particles have
sinking speeds which are large enough so that vertical transfer between different grid cells is more rapid than horizontal transfer by advection
would be, considering the relatively coarse resolution of the ocean model. Following a similar line of thought, short-lived tracers like phytoplankton and zooplankton are also excluded from oceanic transport.
However, convection and wind-driven surface vertical mixing are applied to all biogeochemical tracers.
In CLIMBER-X, HAMOCC is integrated with a time step of 1 d, which is also the time step of the physical ocean model.
Land carbon cycle: PALADYN
PALADYN is a comprehensive land surface–vegetation–carbon cycle model designed specifically for use in CLIMBER-X . It includes a detailed representation of the land carbon cycle.
Photosynthesis is computed following the Farquhar model and depends on absorbed
shortwave radiation, air temperature, vapour pressure deficit between leaf and ambient air, atmospheric CO2 and soil moisture. Carbon assimilation by vegetation is coupled to the transpiration of
water through stomatal conductance. The model includes a dynamic vegetation module with five plant functional types (PFTs) competing for the grid-cell share based on their respective net primary productivity. The model distinguishes between mineral soil carbon, peat carbon,
buried carbon and shelf carbon. Each soil carbon “type” has its own soil carbon pools generally represented by a litter and fast and slow carbon pools in each of the five soil layers. Carbon can be redistributed between the layers by vertical diffusion. For the vegetated macro-surface type, decomposition is a function of soil temperature and soil moisture. Carbon in permanently frozen layers is assigned a
long turnover time which effectively locks carbon in permafrost. Carbon buried below ice sheets and on ocean shelves is treated separately. The land model also includes a dynamic peat module. PALADYN includes carbon isotopes 13C and 14C, which are tracked
through all carbon pools in vegetation and soil. Isotopic discrimination is modelled only during the photosynthetic process.
A simple methane module is implemented to
represent methane emissions from anaerobic carbon decomposition in wetlands and peatlands.
The integration of PALADYN into the coupled CLIMBER-X framework and subsequent sensitivity analyses of the land carbon cycle feedbacks,
which were not performed with the offline PALADYN set-up in , highlighted the need to improve certain aspects of the model. These improvements are described next.
We have updated the parameterization of the roughness length for heat and moisture. Originally, it was simply taken to be proportional to the roughness length for momentum, but there is ample evidence from observations that the roughness length
for scalars can be orders of magnitude lower than that for momentum when the surface roughness is large
(e.g. ). We have therefore implemented the parameterization from , which includes a dependence of the surface roughness length for heat and moisture on the
roughness Reynolds number. With this new parameterization, the exchange coefficient for the turbulent surface fluxes shows a much weaker dependence on the roughness of the surface, which has an impact on the vegetation feedback.
We have introduced a topographic erodibility factor for dust emissions following .
It assumes that a basin with pronounced topographic variations contains a large amount of sediments which have accumulated in the valleys and depressions and which can easily be mobilized by wind. The following topographic
factor is then applied to scale dust emissions:
ftopo=max(0,zmax-z)zmax-zmin5,
where z is the grid-cell mean elevation, and zmax and zmin are the maximum and minimum
surface elevations computed from the high-resolution topography in the surrounding 15×15∘.
The exponent 5 is taken from .
The RuBisCO-limited photosynthesis rate in the version of the PALADYN model described in was based on the “strong optimality” hypothesis of , which assumes that RuBisCO activity and the nitrogen content of leaves vary with canopy position and seasonally so as to maximize net assimilation at the leaf level . However, we found that this formulation led to a relatively small increase in gross primary production
over the historical period, which resulted in an overestimation of atmospheric CO2 in coupled historical simulations. We therefore introduced a new formulation for the maximum RuBisCO capacity, with dependencies on PFT-specific, constant foliage nitrogen concentration, specific leaf area and leaf temperature following as implemented in CLM4.5 .
In the original PALADYN formulation, the internal leaf CO2 concentration used for photosynthesis was computed based on the
Cowan–Farquhar optimality hypothesis . In the new model version, for C3 plants, we have implemented an alternative scheme
following the more general least-cost optimality model with the moisture dependence proposed by .
In the isotopic discrimination during photosynthesis (Δ), we included an explicit fractionation term for photorespiration as recommended by several recent studies :
Δ=4.4ca-cica+27⋅cica-12Γ∗pa,
where ca and ci are the ambient and leaf-internal CO2 concentrations, pa is the ambient partial pressure of CO2 and Γ∗ is the CO2 compensation point.
For the distinction between evergreen and summergreen trees, in addition to a threshold on the coldest month's temperature, we have introduced a PFT-specific threshold on the growing degree days above 5 ∘C, which is set to 600 for needleleaf trees and 900
for shrubs following .
In the dynamic vegetation model, a parameter (λ) is used to partition the net primary production (NPP) between local growth of existing vegetation and lateral expansion (“spreading”) of vegetation coverage within the grid cell,
with all of the NPP being used for growth for small leaf area index (LAI) values and all of the NPP being used for “spreading” for large LAI values. λ is assumed to be a piecewise linear function of the leaf area index between a minimum and maximum LAI. For small leaf area indices, all of the NPP is used for local growth (λ=0); for LAI above a critical value
LAImin, a fraction (λ>0) is used for spreading:
λ=LAI-LAIminLAImax-LAImin.
However, since the simulated leaf area index depends strongly on NPP, which in turn has a pronounced dependence on atmospheric CO2,
this formulation results in a strong dependence of λ on CO2, with an increasingly larger fraction of NPP being used for
spreading as CO2 increases. We have therefore implemented a CO2 dependence in the maximum leaf area index to reduce this effect:
LAImax=LAImaxref⋅1+0.5⋅logCO2/CO2ref.
The fraction of decomposed litter respired directly as CO2 to the atmosphere has been reduced from 0.7 to 0.6 and
the fraction of decomposed litter transferred to the slow soil carbon pool has been doubled from 0.015 to 0.03. Together these
changes result in more carbon accumulating into the soil.
A simple representation of land use change has been introduced into the model following as described in
. A fraction of each grid cell is prescribed as being used for agriculture and land use is then represented
as a limitation to the space available for the woody PFTs to expand into. When forests and shrubs are affected
by land use change, an additional disturbance rate of 1 yr-1 is prescribed on top of the standard background disturbance,
leading to vegetation dying. The resulting dead vegetation carbon is then added as litter to the soil carbon pools,
and a large part will be respired directly to the atmosphere within a few years. Storage of wood from deforestation in products such as paper or wood for construction is not accounted for in the model and soil carbon is assumed to not be directly affected by land use practices.
Following deforestation, the model will grow C3 or C4 grasses, depending on climate conditions.
The partitioning of the soil carbon decomposed under anaerobic conditions into CO2 and CH4 used a prescribed constant ratio
in . We modified this by making the fraction released as CH4 dependent on temperature with a Q10 of 1.8,
following and .
We implemented a chemical weathering model to compute the riverine fluxes of bicarbonate ions (HCO3-) (and therefore dissolved inorganic carbon and alkalinity) to the ocean and the consumption of atmospheric CO2.
The weathering rate depends on the lithology and on the climate variables temperature and runoff.
The lithological map of distinguishing 16 different lithologies is used to describe the spatial distribution of rocks.
The parameters for the chemical weathering equations for all lithologies, except for carbonate sedimentary rocks and loess,
are based on a spatially explicit runoff-dependent model of chemical weathering, which was calibrated for 381 catchments in Japan
, with the additional temperature dependence of .
The effect of soil shielding on the weathering rate suggested by has not been considered since information on soil shielding is
not readily available for periods beyond the recent past. For carbonate sedimentary rocks, the weathering rate follows the approach
of with a dependence on runoff. Alternatively, the temperature-dependent formulation of is available for use in the model.
The weathering rate for loess sediments depends on runoff following . The global distribution of loess cover for the present day and for the Last Glacial Maximum as well as the lithologies of the continental shelves that were exposed at the Last Glacial Maximum are taken from . The weathering fluxes are transferred from the land to the ocean in the same way as water runoff, following the runoff routing scheme.
The carbon isotope fluxes from chemical weathering are computed assuming a δ13C of 1.8 ‰ for carbon originating from carbonate minerals .
Equations describing silicate and phosphorus weathering fluxes are also available as part of the weathering model. However,
silicate and phosphorus riverine fluxes are not considered in the default model set-up, as they would result in further complications related to the conservation of nutrients in the ocean. Instead, as discussed in Sect. , the silicate and phosphorus
budgets are closed by assuming that the sediment burial flux is returned as input at the ocean surface.
The atmospheric CO2 concentration in CLIMBER-X is a globally uniform value. It can either be prescribed
(as constant or time-dependent) or interactively computed by the model from the following prognostic
equation for the total carbon content stored as CO2 in the atmosphere (Catm):
dCatmdt=Focn+Flnd+Fanth-Fweath+Fvolc+FCH4ox.
The source and sink terms on the right-hand side represent, from left to right, the net sea–air carbon flux, the global net land-to-atmosphere carbon flux, the anthropogenic carbon emissions (excluding land use change), the CO2 consumption by silicate and carbonate weathering, the volcanic degassing flux and the CO2 flux from the
oxidation of atmospheric methane originating from non-agricultural sources.
The CO2 consumption by weathering is computed assuming that all carbon in the HCO3- originating from the weathering of
silicate rocks (FHCO3-sil) comes from the atmosphere, while only half of the carbon in the HCO3-
originating from the weathering of carbonate rocks and sediments (FHCO3-carb) comes from the atmosphere:
Fweath=FHCO3-sil+0.5⋅FHCO3-carb.
The constant volcanic degassing rate is set to half the silicate weathering rate (e.g. ) as determined by an equilibrium spin-up simulation:
Fvolc=0.5⋅FHCO3-sil.
The flux from the oxidation of methane, FCH4ox, is computed by the CH4 model as described in Sect. below.
The atmospheric CO2 concentration is then computed from Catm using a conversion factor of 2.12 PgCppm-1.
Equations similar to Eq. () are also used for the carbon isotopes 13C and 14C. The prognostic equation for the stable isotope 13C in atmospheric CO2 is
d13Catmdt=Focn13+Flnd13+Fanth13-Fweath13+Fvolc13.
The 13C fluxes from land and ocean are explicitly computed by the land and ocean carbon cycle models as described in detail
in and .
The δ13C of anthropogenic carbon emissions is prescribed as time-dependent from historical data of , and the 13C flux from CO2 consumption by weathering, assuming no fractionation, is simply computed as
Fweath13=Fweath13CatmCatm.
The 13C of volcanic degassing is computed assuming a δ13C of -5 ‰.
The prognostic equation for radiocarbon 14C in atmospheric CO2 reads as
d14Catmdt=Focn14+Flnd14-Fweath14+Fprod14-14Catmτ14C.
Carbon sources originating from geological reservoirs, i.e. volcanic degassing, are assumed to contain no radiocarbon.
Similarly, radiocarbon is assumed to be absent in anthropogenic carbon emissions from fossil fuel burning, because the age
of fossils far exceeds the half-life of 14C.
The production rate of radiocarbon in the atmosphere (Fprod14) is prescribed in the model and
the radiocarbon decay time is τ14C=8267 years.
Similarly to CO2, atmospheric CH4 is also considered to be well mixed in the atmosphere and is therefore represented as a globally uniform value. The atmospheric CH4 concentration can be prescribed, or it can be interactively computed
by the model from
dCH4dt=Flndemis+Fanthemis-CH4τCH4.
Methane sources include natural emissions from wetlands and peatlands (Flndemis), which are explicitly simulated by
the model as originating from anaerobic decomposition processes of carbon in soils . Other natural sources of methane
are generally smaller (e.g. ) and are neglected here for simplicity. Anthropogenic methane emissions
(Fanthemis) are prescribed in the model.
The sink of methane from oxidation in the atmosphere is computed using a constant residence time of CH4,
τCH4=9.5 years, which is a reasonable first approximation, at least for climate conditions ranging between the Last Glacial Maximum and the present day .
Closed and open carbon cycle model configurations and model spin-up
Two different configurations of the carbon cycle model are available and can be chosen according to the specific needs.
The first (and simplest) set-up consists of ocean, land and atmosphere carbon cycle components only. In this set-up marine sediments are disabled and particulate fluxes that reach the ocean floor are completely remineralized/dissolved in the bottom ocean grid cell. Rock weathering from land is also switched off, so that the carbon exchange between ocean, land and atmosphere
occurs only through air–sea fluxes and through land–atmosphere exchanges. In this set-up the carbon system is closed in the sense that there are no natural sources and sinks from and to geological reservoirs. As a response to an external climate perturbation, carbon is then simply redistributed
between atmosphere, ocean and land, with the total carbon in the system being conserved. This set-up is equivalent to what is used in many state-of-the-art Earth system models for climate change projections on centennial timescales (e.g. ). The model spin-up for this simple set-up is straightforward and requires only that the model is run to steady state with a prescribed atmospheric CO2 concentration for ≈10000 years. The slowest timescale in this set-up is given by the slow decomposition rate of organic carbon in frozen soils, which is limited to a maximum value set by default to 5000 years.
The initial state for the spin-up run is given by observed present-day 3D concentrations of different tracers in the ocean , while the land surface is assumed to be covered by bare soil and with no carbon stored on land.
The closed carbon cycle set-up is applicable to simulations of up to 1000 years. On longer timescales, sediment and weathering processes become important and need to be accounted for when performing long-term transient simulations with interactive CO2.
Although it is unlikely that in reality the slow carbon cycle processes related to marine sediments, peatlands and permafrost
carbon are in equilibrium at any
specific point in time, for practical reasons we assume that such an equilibrium is a reasonable first approximation.
Assuming that the pre-industrial is an equilibrium state of the climate–carbon cycle system allows us to run perturbation experiments with the interactive carbon cycle without having to deal with possible long-term drifts in atmospheric CO2.
However, the long timescale of ∼ 100 000 years involved in ocean sediment processes represents a challenge in running the model into equilibrium, even for a high-throughput model like CLIMBER-X. We therefore implemented a scheme to run
the physical ocean and ocean biogeochemistry models in an offline set-up with prescribed climatological daily input fields at the ocean surface. This set-up results in a speed-up of a factor >2 relative to running the fully coupled climate–carbon cycle model, meaning that ocean carbon cycle and marine sediments can be run into equilibrium in about a week of computing time on a high-performance computer. In detail, the spin-up procedure of the full carbon cycle configuration comprises two different stages. Atmospheric CO2 is prescribed to a constant value throughout the process, at 280 ppm for the pre-industrial case. The first stage aims at spinning up the sediment model. For this purpose the full carbon cycle–climate model is run for 5000 years, and every 300 years the sediment model is run offline for 1000 years. During this stage all net fluxes into the sediments are compensated for and returned as inputs
at the ocean surface in order to approximately conserve water column tracer inventories while the sediments are filling up.
In the second stage we switch to simulated DIC and alkalinity weathering fluxes from land and at the same time also switch to
the more efficient offline ocean–biogeochemistry set-up described above and run the model until an approximate equilibrium is reached after ∼ 100 000 years (Fig. ).
A simplification that is made in the open carbon cycle set-up is that organic carbon and opal that are buried in the sediments, and are therefore effectively leaving the system, are returned in remineralized form to the surface ocean, so that phosphorus and silica inventories of the ocean–sediment system are conserved throughout the simulation.
Open versus closed carbon cycle spin-up for pre-industrial conditions. The figure shows surface input of (a) DIC and (b) alkalinity,
the evolution of (c) DIC and (d) alkalinity inventories in the ocean, and (e) the air–sea CO2 flux. The grey vertical lines indicate the switch between the first and second spin-up phases, as described in the text.
The carbon fluxes among the different model components in the open set-up for equilibrium pre-industrial conditions are schematically illustrated in Fig. . The volcanic degassing rate is equal to half the atmospheric CO2
consumption by silicate weathering, in accordance with theory . Note that not only the carbon budget of the different compartments
(atmosphere, ocean, lithosphere) is well balanced but that the ocean alkalinity budget also is.
CLIMBER-X carbon fluxes and reservoirs in equilibrium with pre-industrial conditions for the open carbon cycle set-up.
Model evaluation for the historical period and present day
Here we present results from a CLIMBER-X simulation with interactive CO2 and CH4 in the open carbon cycle set-up for the historical period (1850–2015) and provide a comprehensive evaluation of model performance against various observational datasets.
The forcings for this simulation include variations in solar radiation , radiative forcing of volcanic
eruptions , globally uniform N2O concentrations from ,
globally uniform CFC11 and CFC12 concentrations from , 3D O3 concentrations and
2D SO42- load from the ensemble mean of CMIP6 models and land use change (pasture and cropland fractions)
from .
The model is initialized from an 80 000-year equilibrium simulation with the open carbon cycle set-up for pre-industrial boundary conditions and a prescribed
atmospheric CO2 of 280 ppm, as described in Sect. and shown in Fig. .
Present day
In the following, different simulated climatological characteristics are compared to observations to assess the model performance for
the present day. Unless stated otherwise, the comparison with observations is for the time interval from 1981 to 2010. To give an overview of how CLIMBER-X compares to state-of-the-art Earth system models based on general circulation models,
we also include results from model simulations
from the recent CMIP6 . The following CMIP6 models are included for ocean biogeochemistry: CESM2, IPSL-CM6A-LR, MRI-ESM2-0, MIROC-ES2L, MPI-ESM1-2-LR, UKESM1-0-LL and CanESM5. For the land carbon
cycle, the following models are used for comparison: ACCESS-ESM1-5, BCC-CSM2-MR, CanESM5, CNRM-ESM2-1, GFDL-ESM4, IPSL-CM6A-LR,
MIROC-ES2L, MPI-ESM1-2-LR, MRI-ESM2-0, NorESM2-LM and UKESM1-0-LL. For ocean biogeochemistry, we highlight how the model compares with results from the MPI-ESM1-2-LR employing the original marine
carbon cycle model HAMOCC6.
Ocean biogeochemistry and marine sediments
An overview of simulated global variables characterizing the ocean carbon cycle are presented and compared to observation-based estimates in Table , providing a summary of model performance for the present day.
Global values of the main ocean biogeochemical variables for the present day.
CLIMBER-XEstimated rangeUnitSourceOcean–atmosphere fluxesPre-industrial CO2 flux0.20.2–0.6PgCyr-1; N2O flux5.01.9–9.4TgNyr-1Surface nutrients and alkalinitySurface alkalinity24102355mmolm-3GLODAPv2, Surface nitrate6.35.2mmolNm-3WOA 2013, Surface phosphate0.510.53mmolPm-3WOA 2013, Surface silicate8.27.5mmolSim-3WOA 2013, Primary productionNet primary production5347–60PgCyr-1; N fixation8851–200TgNyr-1; Export productionPOC export at 100 m5.95.8–12.9PgCyr-1CaCO3 export at 100 m0.620.38–1.8PgCyr-1Opal export at 100 m10594.5–155.5TmolSiyr-1SedimentsPOC sediment deposition0.570.93–3.2PgCyr-1CaCO3 sediment deposition0.270.16–0.4PgCyr-1; Opal sediment deposition7979–84PgCyr-1; POC burial0.090.07–0.7PgCyr-1CaCO3 burial0.190.13–0.45PgCyr-1Opal burial5.32.7–9.9TmolSiyr-1
Representing the ocean ventilation timescale reasonably well is a prerequisite for simulating biogeochemical tracers in the ocean. The ocean uptake of CFCs of anthropogenic origin over the historical period is often used to probe the ventilation of the ocean
on decadal timescales, while the pre-industrial radiocarbon concentration in the ocean provides information on the age distribution of the water masses in an approximate equilibrium state. We therefore start by comparing how well the model reproduces the
CFC11 and radiocarbon distributions in the ocean.
The inventory of CFC11 in the ocean starts to increase after ≈1950 as a consequence of its increase in the atmosphere (Fig. ). Estimates for the CFC11 inventory in the year ≈1994 are available from models from the OCMIP model intercomparison and from direct observations . CLIMBER-X results are generally consistent with these estimates (Fig. ), indicating that, at least at the global scale,
the decadal ventilation timescale in CLIMBER-X is well in line with observations and other models. In terms of spatial distribution, the CFC11 uptake is overestimated in the North Pacific Ocean, in the North Indian Ocean and around Antarctica,
while too small CFC11 concentrations are simulated at mid latitudes in all basins at depths between 500 and 1000 m (Fig. ).
Historical global cumulative ocean uptake of CFC11 in CLIMBER-X compared to observations and OCMIP models .
Zonally averaged CFC11 concentration for the year 1994 in CLIMBER-X (a, d, g) and GLODAP (b, e, h) for different basins:
Atlantic (a–c), Pacific (d–f), and Indian (g–i) oceans. The model bias is shown in panels (c), (f), and (i).
The radiocarbon ventilation age in the pre-industrial gives additional insights into the ocean ventilation under quasi-equilibrium conditions, information which is complementary to CFC11. The radiocarbon ventilation age of the deep ocean is nicely reproduced by CLIMBER-X, while radiocarbon age is systematically
overestimated in the upper kilometre across all ocean basins (Fig. ). The too old (in terms of radiocarbon age) sub-surface waters could be a result of the model not explicitly resolving synoptic processes in the atmosphere and therefore
not representing the non-linear effects of synoptic variability on vertical mixing of tracers. For instance, a one-time mixing
down to 200 m depth by a wind storm could have a large effect on some tracers, which cannot be resolved by using
climatological mean winds. We would expect this non-linear effect to be much more important for radiocarbon than for nutrients.
The analyses of CFC11 and radiocarbon provide important insights into the ocean ventilation in the model and will be useful when discussing model biases in the distribution of other biogeochemical tracers below.
Zonally averaged pre-industrial radiocarbon ventilation age in CLIMBER-X (a, d, g) and GLODAP (b, e, h)
for different basins:
Atlantic (a–c), Pacific (d–f), and Indian (g–i) oceans. The model bias is shown in panels (c), (f), and (i).
The spatial pattern of the air–sea CO2 exchange is well captured by the model (Fig. ), with outgassing generally taking place in the tropics and CO2 being taken up at mid to high northern latitudes and at mid latitudes of the Southern Hemisphere. The main difference compared to the other models is observed around the Equator, with a less pronounced peak in CO2 release simulated by CLIMBER-X (Fig. ), which is likely related to deficiencies in the simulated ocean circulation close to the Equator, where the geostrophic approximation employed in CLIMBER-X reaches its limit of applicability.
In the Southern Ocean, most CMIP6 models tend to overestimate the CO2 uptake compared to observations (e.g. )
(Fig. ), while CLIMBER-X is apparently more consistent with recent estimates, although with substantial differences
in the spatial distribution of the CO2 flux (Fig. ).
Notably, in the Southern Ocean the CLIMBER-X air–sea CO2 exchange diverges from that simulated by the MPI-ESM1-2-LR model (Fig. ), which employs the original HAMOCC6 ocean biogeochemistry model. This is possibly related
to the lower simulated net primary production in the Southern Ocean in CLIMBER-X compared to MPI-ESM (Fig. a).
However, the MPI-ESM seems to be an outlier in the simulated primary production in the Southern Ocean, possibly because of biases in climate,
which are unrelated to the HAMOCC ocean carbon cycle model.
The 1985–2010 average air–sea CO2 flux in (a) CLIMBER-X compared to (b) observations from .
Zonal mean air–sea CO2 flux (1985–2010 average) in CLIMBER-X compared to observations from and
selected CMIP6 models.
The export of particulate organic carbon from the euphotic layer drives the biological pump and generally follows the primary productivity
pattern, with modifications due to varying sinking speeds and remineralization rates of POC in the water column. While the net primary productivity in CLIMBER-X is in line with CMIP6 models (Fig. a) and the globally integrated
value of 53 PgCyr-1 agrees well with observations (Table ), the export production in the model is generally at the lower end of the CMIP6 model range (Fig. b).
CaCO3 and opal export are compared to CMIP6 models in Fig. c, d.
The 1981–2010 average global zonal mean (a) net primary production, (b) particulate organic carbon export at 100 m depth, (c)CaCO3, and (d) opal export at 100 m depth. Results from CLIMBER-X are compared to CMIP6 models.
Primary production in the ocean is limited by the availability of nutrients. Over large parts of the surface ocean, nitrogen concentrations constitute the main limiting factor for photosynthesis in CLIMBER-X (Fig. ). However, over the Southern
Ocean, in the equatorial Pacific and in the North Pacific, production is limited by the availability of iron (Fig. ). This is in accordance with observations showing that iron limitation is usually important where sub-surface nutrient supply is enhanced, such as in oceanic upwelling regions (e.g. ). Since one of the main iron sources in the ocean is from mineral dust deposited at the
ocean surface (e.g. ), iron limitation is confined to regions with low dust deposition. The dust cycle is an integral
part of CLIMBER-X, and the dust deposition is therefore explicitly modelled. The simulated dust deposition compares reasonably well with
estimates from complex ESMs for the present day (Fig. ), although they are relatively poorly constrained. A comparison of dust deposition fluxes with observations over land further indicates that the model is able to capture
the general pattern of the dust deposition rate (Fig. ).
Nutrient limitation of marine net primary productivity in CLIMBER-X.
(a) CLIMBER-X annual dust deposition flux compared to model-based products of (b), (c), and (d). The respective globally integrated deposition values are given in brackets in the panel titles.
Simulated versus observed dust deposition fluxes at different locations available from the AeroCom dataset (, and references therein). The dashed lines indicate 1 order of magnitude deviation from the 1:1 line.
The simulated dissolved iron concentration in surface water is closely related to the dust deposition shown in Fig. .
It is therefore high in the Atlantic and Indian oceans, lower in the Southern Ocean and very small over large parts of the Pacific
(Fig. ). This is broadly consistent with observations (e.g. ), but measurements of iron concentration
in ocean water are still relatively sparse.
Average surface dissolved iron concentration in CLIMBER-X over the period 1981–2010.
The main features of the surface nitrate concentration are well reproduced by CLIMBER-X, with large concentrations in
the Southern Ocean, moderate values in the upwelling region of the eastern equatorial Pacific and in the North Atlantic and North Pacific and low values elsewhere (Figs. and a). The most pronounced model biases
are found in too high nitrate concentrations in the Arctic and too low values in the North Pacific.
The simulated basin-wide vertical distribution of nitrate is in very good agreement with observations (Fig. ).
The 1981–2010 average global zonal mean surface concentrations of the nutrients (a) nitrate, (b) phosphate, (c) silicate, and (d) dissolved iron. CLIMBER-X is compared to observations and CMIP6 model results.
Surface NO3 concentration in (a) CLIMBER-X (1981–2010 average) compared to (b) observations from the World Ocean Atlas 2013 (WOA13, ).
The model bias is shown in panel (c).
Global and basin-wide average profiles of different biogeochemical tracers in the ocean, from top to bottom:
DIC, alkalinity, nitrate, phosphate, silicate, and dissolved iron. CLIMBER-X results (black) are compared to observations (blue) and CMIP6 model results (grey). Results from the MPI-ESM1-2-LR are shown
by the green dashed lines. The boundary of the Southern Ocean is set at 35 ∘S and the Southern Ocean section is
not included in the profiles of the Atlantic, Pacific, and Indian oceans. CLIMBER-X and CMIP6 data are averages over the time period 1981–2010.
The 3D phosphate distribution in the global ocean is nicely captured by the model (Figs. , b, and ), except for too
low concentrations simulated in the surface ocean of the North Pacific and North Indian oceans. The negative bias in the North Pacific is consistent with the too low simulated surface nitrate concentrations, both originating from a too vigorous ventilation
of water masses in the upper kilometre in the physical ocean model.
As a result of reduced primary productivity in the Southern Ocean in CLIMBER-X compared to MPI-ESM1-2-LR, both surface nitrate and
phosphate concentrations are consistently higher in CLIMBER-X (Fig. a, b), as fewer nutrients are assimilated during photosynthesis.
Zonally averaged PO4 concentration in CLIMBER-X, 1981–2010 average (a, d, g), and WOA13 (b, e, h) for different basins: Atlantic (a–c), Pacific (d–f), and Indian (g–i) oceans. The model bias is shown in panels (c), (f), and (i).
Silicate concentration is generally overestimated in the sub-surface ocean and is underestimated in the deep North Pacific and North Indian oceans (Fig. ), similarly to other nutrients (Fig. ).
Zonally averaged Si concentration in CLIMBER-X, 1981–2010 average (a, d, g), and WOA13 (b, e, h) for different basins: Atlantic (a–c), Pacific (d–f), and Indian (g–i) oceans. The model bias is shown in panels (c), (f), and (i).
The large-scale patterns of oxygen concentration in ocean waters simulated by CLIMBER-X are largely consistent with observations (Fig. ), but the extent and depth of the oxygen minimum zones, in particular in the eastern equatorial Pacific, are overestimated. This bias is common to many CMIP5 models (e.g. ). Other biases include a too oxygen-depleted Southern Ocean and too high oxygen concentrations in the upper North Pacific and North Indian oceans, again resulting from the excessive water mass ventilation
in those regions as discussed above.
Oxygen concentration in CLIMBER-X, 1981–2010 average (left column), and WOA13 (middle column) at different ocean depths: from top to bottom, 100, 500, 1000, and 3000 m.
The model bias is shown in the right column.
Both DIC and alkalinity are generally overestimated in the upper ocean (Fig. ), particularly in Antarctic intermediate
water masses, and underestimated in the deep ocean (Figs. and ). These biases in the simulated vertical distribution of DIC and alkalinity could be due to a relatively low CaCO3 export from the euphotic layer (Table ),
which leads to a too weak vertical redistribution.
Additionally, the simulated DIC concentration is generally too low in the North Pacific and North Indian oceans.
Zonally averaged dissolved inorganic carbon in CLIMBER-X, 1981–2010 average (a, d, g), and GLODAPv2 (b, e, h) for different basins: Atlantic (a–c), Pacific (d–f), and Indian (g–i) oceans. The model bias is shown in panels (c), (f), and (i).
Zonally averaged total alkalinity in CLIMBER-X, 1981–2010 average (a, d, g), and GLODAPv2 (b, e, h) for different basins: Atlantic (a–c), Pacific (d–f), and Indian (g–i) oceans. The model bias is shown in panels (c), (f), and (i).
The carbon-13 isotope in the ocean helps to track the distribution of different water masses. The higher δ13C values in the Atlantic Ocean compared to the Pacific Ocean, originating mainly from the pronounced overturning circulation in the Atlantic, which is absent in the Pacific, are generally captured by the model (Fig. ).
The negative biases at 500–1500 m depth are associated with the “nutrient trapping” problem
that is often seen in ESMs. This problem is characterized by high concentrations of remineralized nutrients and carbon and, therefore, low δ13C . The positive biases through the whole water column in the North Atlantic,
North Pacific and North Indian oceans are possibly the result of too strong ventilation in these regions in the model.
Zonally averaged δ13C in CLIMBER-X, 1981–2010 average (a, d, g), and (b, e, h) for different basins: Atlantic (a–c), Pacific (d–f), and Indian (g–i) oceans. The model bias is shown in panels (c), (f), and (i).
Weight fraction of calcite, opal, and organic carbon in marine sediments as simulated by CLIMBER-X (a–c) compared to observations (d–f).
In the Atlantic and Indian oceans, CaCO3 dominates the sediment composition, in accordance with observations (Fig. a, d). However, little CaCO3 is simulated in large parts of the sediment in the eastern Pacific Ocean, where observations indicate widespread
CaCO3 content in the Southern Hemisphere (Fig. a, d). The underestimation of calcite weight fractions in sediments
of the eastern South Pacific Ocean is caused by water being undersaturated with respect to calcite in this area. This leads to dissolution
of most of the calcite produced at the surface before it can even reach the sediments. The strongly undersaturated water is ultimately a
result of deficiencies in the simulated ocean circulation. Some other models show similar deficiencies in the simulated calcite fraction
in Pacific sediments (e.g. ).
Global CaCO3 sediment deposition and burial are in line with
observational underestimates (Table ), with around 25 % of the deposited CaCO3 undergoing dissolution.
The opal content in sediments in CLIMBER-X is overestimated (Fig. b, e), even though the global opal sedimentation
and burial fluxes are fully consistent with observational estimates (Table ). Opal is particularly abundant in the eastern
equatorial Pacific simply as a result of missing CaCO3 in the sediments in that area. Organic carbon is found mainly on the continental margins and in the equatorial eastern Pacific, in agreement with observations (Fig. c, f), although CLIMBER-X tends to underestimate the organic carbon content in sediments, possibly
because of a too small sediment deposition flux of POC (Table ).
Land carbon cycle
A detailed evaluation of the land carbon cycle component has already been presented in the original PALADYN description paper
. However, here we partly repeat the analysis to show the model performance in the coupled climate model set-up and with the additional modifications to the model described above.
A selection of simulated global variables characterizing the land carbon cycle is presented and compared to observation-based estimates in Table , providing a summary of model performance for the present day.
Global values for the main variables of the land carbon cycle.
CLIMBER-XEstimated rangeUnitSourcePrimary productionGross primary production120115–131PgCyr-1Net primary production6742–70PgCyr-1Land carbon poolsVegetation carbon472392–437PgCSoil carbon21453300–4800PgCSoil carbon top 1 m15211200–2000PgCSoil carbon top 1 m 60–90∘ N436314–526PgCPermafrost area19.118.7106×km2; Carbon in permafrost area7961100–1500PgCPeatland area2.44.4106×km2Carbon in peatlands340530–694PgCCH4Maximum monthly wetland area55.1106×km2; Total CH4 emissions214100–217TgCH4yr-1Tropical CH4 emissions18271–155TgCH4yr-1Extratropical CH4 emissions3312–64TgCH4yr-1Weathering (pre-industrial)CO2 consumption22.617–27TmolCyr-1Carbonate weathering20.110–25.4TmolCyr-1Silicate weathering12.610.8–19.7TmolCyr-1Alkalinity flux to ocean32.730–40Tmolyr-1;
(a) Simulated GPP compared to (b) observations . (c) Comparison of zonally integrated GPP.
(d) Simulated vegetation carbon compared to (e) observations . (f) Comparison of zonally integrated vegetation carbon.
(g) Simulated soil carbon compared to (h) observations . (i) Comparison of zonally integrated soil carbon.
(j) Simulated ecosystem carbon turnover time compared to (k) observations . (l) Comparison of zonal mean ecosystem carbon turnover time.
In panels (c), (f), (i), and (l), results from CLIMBER-X are shown in black, observations in blue, and CMIP6 models in grey. CLIMBER-X and CMIP6 data are averages over the time period 1981–2010.
Photosynthesis is the basic process by which carbon enters the land domain. The simulated gross primary production (GPP), which quantifies this
process, is in good agreement with observational estimates, both in terms of global integrals (Table ) and in terms of spatial distribution (Fig. a, b, c).
The total carbon stored in the vegetation, both above ground and below ground, is slightly overestimated in the model (Table ),
but the meridional distribution, mainly originating from large-scale differences in precipitation, is well reproduced (Fig. d, e, f).
Most of the soil carbon in CLIMBER-X is stored in cold soils of the Northern Hemisphere high latitudes, in agreement with observations (Fig. g, h, i). However, compared to estimates from , the soil carbon distribution is too skewed toward high northern latitudes, and there is too little carbon in the tropics. Most CMIP6 models underestimate soil carbon in the tropics as well (Fig. j).
In CLIMBER-X, ∼ 1500 PgC of carbon is stored in the top soil metre, in good agreement with different estimates (Table ). However, with ∼ 2150 PgC, the total soil carbon content seems to be underestimated compared to observations, which suggest
>3000PgC. This indicates that too little carbon is simulated in soil below 1 m depth.
However, total soil carbon content estimates vary widely between datasets (e.g. ), with e.g. 1952±198PgC
in WISE30sec and 3141±893PgC in in the top 2 m of soil.
Most of the carbon in mineral soil layers below 1 m is recalcitrant, and its response to changes in environmental conditions is uncertain. In Earth system models, total soil carbon storage is usually much lower (1206±445PgC, ), as these models account for active carbon responding on centennial timescales. In CLIMBER-X, one possible explanation for underestimated carbon content in deeper soil layers is that the maximum turnover
timescale of soil carbon is set to 5000 years in the model, which limits the amount of carbon that can be accumulated in cold, frozen soil layers.
Other possible reasons include (i) a general underestimation of vertical carbon transport by diffusion, particularly into perennially frozen soil layers, and (ii) a possible depth dependence of soil carbon turnover due to processes other than
temperature and moisture (e.g. ) and that are not included in the model.
Consistently, the carbon contained in areas affected by permafrost is ∼ 800 PgC, which is also a bit lower than
the ∼ 1100–1500 PgC suggested by observations (Table ).
Let us note that, even when models are initialized with the observed permafrost carbon stock of ≈1300PgC, remapping at model resolution and accounting for differences in soil temperatures between models and observations generally
leads to a reduction in permafrost carbon stocks (e.g. ). The CLIMBER-X-simulated peatland extent is lower than estimated , and the peat carbon is also consistently underestimated accordingly (Table ).
The turnover time of terrestrial ecosystem carbon is an integrated quantitative measure of the residence time of carbon on land,
from the time it is fixed by photosynthesis to the time it is returned to the atmosphere through respiration processes. It is
computed as the ratio between land carbon stocks (vegetation + soil) and gross primary production.
The ecosystem carbon turnover time simulated by CLIMBER-X is in line with CMIP6 models, while it is underestimated compared to
observation-based estimates from (Fig. j, k, l).
However, it should be noted that the large uncertainties in soil carbon content result in a rather uncertain estimated ecosystem
carbon turnover time .
The global maximum monthly wetland extent in CLIMBER-X agrees well with observations (Table ), although with substantial
differences in the geographic distribution (Fig. ).
Compared to the multi-satellite product from GIEMS (Global Inundation Extent from Multi-Satellites) , the model simulates a larger wetland extent in tropical forest areas. However, when compared to other wetland products based on data other than from satellites, GIEMS underestimates wetlands below dense forests (e.g. the Amazon forest) (e.g. ). In South-East Asia, the GIEMS wetland extent also includes extensive rice cultivation areas, which are not represented in the model.
Maximum monthly wetland fraction (a) in CLIMBER-X compared to (b) the GIEMS dataset .
In CLIMBER-X, methane is emitted exclusively from wetlands. Because of the dependence of methane emissions on soil carbon decomposition rates and because of the temperature dependence of the fraction of wetland carbon respired as methane,
wetland methane emissions are dominated by tropical sources (Table , Fig. ),
in agreement with observations (e.g. ).
The total CH4 emissions from wetlands are at the high end of recent estimates, which is a result of tuning the emissions
in the model to match the observed emissions from all natural sources.
Natural methane emission simulated by CLIMBER-X for the present day (1981–2010 average).
Chemical weathering fluxes are generally high where runoff is high, with the separation between silicate and carbonate
weathering being modulated by lithological properties (Fig. ).
The global CO2 consumption rate by weathering and the alkalinity flux to the ocean in the form of bicarbonate produced by rock weathering are in good agreement with observational estimates (Table ), while the partitioning between carbonate and silicate
weathering is skewed toward carbonate weathering (Table ).
CLIMBER-X (a) silicate and (b) carbonate weathering flux distribution for the present day (1981–2010 average).
Historical period
As shown by , the historical climate evolution is well simulated by CLIMBER-X.
Here we extend this analysis by focusing on the carbon cycle response.
The historical atmospheric CO2 concentration
is well reproduced by the model, with CO2 at the year 2015 being within ∼ 5ppm of direct measurements
(Fig. ). Biases in simulated CO2 of ∼ 10 ppm are quite common
in state-of-the-art ESMs (e.g. ).
Historical atmospheric CO2 concentration from a coupled CLIMBER-X simulation compared to observations .
The partitioning of the anthropogenic carbon emitted over the historical period among the different spheres is compared with
recent estimates of the Global Carbon Budget (GCB) by the Global Carbon Project in Fig. .
The amount of fossil carbon emitted from anthropogenic activities is prescribed from empirical data and therefore by definition
matches with estimates from . The carbon emissions resulting from land use change practices are
underestimated in CLIMBER-X compared with the GCB, although the actual values remain uncertain (e.g. ). A substantial fraction of this anthropogenic CO2 emission is absorbed by the ocean and the land, while the rest remains in the atmosphere.
In CLIMBER-X, the ocean carbon uptake is a bit lower and the land carbon uptake a bit higher than GCB estimates, but the net effect is a
realistic airborne fraction of carbon remaining in the atmosphere.
The ocean carbon uptake is driven by the chemical disequilibrium between surface air CO2 concentrations and the
concentration of dissolved CO2 in the surface ocean water and is relatively well understood, as also indicated by the
narrow uncertainty range obtained from different CMIP6 models (Fig. a). The CLIMBER-X ocean carbon uptake
falls within this narrow range, although it tends to be at the lower end. The land carbon uptake is largely driven by an increase in gross primary productivity as a response to increasing atmospheric CO2.
The net primary productivity increase simulated by CLIMBER-X over the historical period is in agreement with what is shown by most CMIP6 models
(Fig. b). However, the effect of this NPP increase on vegetation carbon varies widely among models (Fig. c),
also because of the confounding factor of land use change. In CLIMBER-X the net effect is a vegetation carbon stock decrease by ∼ 10 PgC. The historical evolution of soil carbon additionally depends on the response of microbial decomposition to changing environmental
conditions, particularly soil temperatures. The increasing NPP and consequently larger input of litter carbon into the soil dominate over the negative effect of increasing temperatures in CLIMBER-X, leading to an increase in soil carbon by
∼ 50 PgC (Fig. d).
Historical global carbon budget in CLIMBER-X. The dashed lines are estimates from .
Historical anomalies of (a) air–sea CO2 flux, (b) net primary production on land, (c) vegetation carbon, and (d) soil carbon in CLIMBER-X compared to CMIP6 models.
The anomalies are computed relative to the time interval 1850–1880 CE.
Since CLIMBER-X is enabled with carbon isotopes, it also allows for a comparison of isotopic signatures to observations,
thereby providing additional constraints on processes involved in carbon cycle exchanges. As an example,
the historical δ13C of atmospheric CO2 is compared to observations in Fig. .
Historical δ13C of atmospheric CO2 in CLIMBER-X compared with observations .
The general historical trend in atmospheric CH4 is captured by the model (Fig. a).
Prescribed anthropogenic methane emissions are the dominant source for the increase in the atmospheric methane burden, but natural emissions from land are also increasing due to the increase in NPP and soil temperature (Fig. b).
Historical (a) atmospheric CH4 concentration in CLIMBER-X compared to observations and
(b) prescribed anthropogenic CH4 emissions and natural land emissions as simulated in CLIMBER-X.
Carbon cycle feedbacks
Carbon cycle processes both on land and in the ocean are sensitive to changes in climate and atmospheric CO2.
This implies that carbon fluxes between ocean and atmosphere and between land and atmosphere will respond to changes in climate
and CO2 concentration, which will in turn affect CO2 and consequently climate. Quantifying the strength of these
feedbacks is important to understanding how the climate will respond to anthropogenic CO2 emissions. For that, a linear feedback decomposition analysis was proposed by to estimate these feedbacks in Earth system models.
The analysis relies on a set of model simulations under idealized 1 %yr-1CO2 increase experiments, whereby
in one simulation the CO2 increase is seen only by the radiative code in the atmosphere (radiatively coupled), in another
one the CO2 increase is seen only by the carbon cycle (biogeochemically coupled) and in a final one both the radiation and carbon cycle see the increase in atmospheric CO2 (fully coupled). This set of simulations allows us to roughly separate the effect of changes in climate and changes in CO2 on land and ocean carbon fluxes. To a first approximation, the carbon cycle feedback
to climate is usually quantified using global temperature changes, while in reality climate obviously influences the carbon cycle in
more complex ways than just through (global) temperature.
The carbon cycle feedback parameters have been estimated for the C4MIP, CMIP5 and CMIP6 models . In Fig. the carbon cycle–climate (γ) and the carbon
cycle–concentration (β) feedbacks in CLIMBER-X are compared to CMIP6 model results separately for land and ocean.
An increase in CO2 has a positive effect on the uptake of carbon by both land and ocean, resulting in a lowering of
CO2 and therefore a negative feedback on climate (implying positive β, Fig. a, c).
Conversely, climate warming has a generally negative impact on the ability of ocean and land to store carbon, leading to a positive
feedback loop (implying negative γ, Fig. b, d). The β and γ values obtained here are well within the range of
estimates from CMIP6 models , although in CLIMBER-X the CO2 fertilization effect on land is rather high (Fig. a) and the ocean carbon uptake as a response to an increase in
atmospheric CO2 is at the lower end of the CMIP6 models (Fig. c).
Carbon cycle feedbacks in CLIMBER-X compared to CMIP6 models . The (a, c)β and (b, d)γ
parameters are shown at the time of CO2 doubling (year ∼ 70) and at the time of CO2 quadrupling (year ∼ 140) in idealized
1 %yr-1CO2 increase experiments.
The zero emissions commitment
The zero emissions commitment (ZEC) is a measure of the amount of additional future temperature change following a complete cessation
of CO2 emissions (e.g. ). A model intercomparison project has been established in an effort to analyse and compare the ZEC in different Earth system models . Here we use this standardized and idealized experimental set-up to compare the carbon cycle response in CLIMBER-X with results from the Zero Emissions Commitment Model Intercomparison Project (ZECMIP) models for the 1000 PgC emission pulse .
The experiment branches off from a 1 % per year CO2 increase run with CO2 emissions set to zero
at the point of 1000 PgC of total carbon emissions. We performed this experiment with both the open and closed carbon cycle set-ups.
The results of the CLIMBER-X simulations are generally well within the large range of results from state-of-the-art ESMs and EMICs
participating in ZECMIP (Fig. ). Atmospheric CO2 concentration rapidly decreases after stopping the carbon emissions (Fig. b), while global temperature shows a more modest decrease (Fig. a). The ocean continues to take
up carbon throughout the simulation (Fig. c), while the land turns from a sink to a source of carbon roughly at the time
of the peak in CO2 (Fig. d). CLIMBER-X initially shows a relatively weak ocean carbon uptake compared to ZECMIP models,
while the land carbon uptake is at the high end of the ZECMIP model ensemble.
The differences between the experiments with open and closed carbon cycle set-ups are negligible for the first few centuries but continue to grow over time, with CO2 decreasing faster in the open set-up (Fig. b).
Comparison of CLIMBER-X simulations with ZECMIP model results in terms of (a) global temperature, (b) atmospheric CO2 concentration,
(c) cumulative ocean carbon uptake, and (d) cumulative land carbon uptake for the standard ZECMIP experiment with 1000 PgC cumulative carbon emissions.
For CLIMBER-X, results with both the open (solid lines) and closed (dashed lines) carbon cycle set-ups are shown.
Conclusions
We have described the major features of the carbon cycle components of the newly developed CLIMBER-X Earth system model. The model includes a detailed representation of carbon cycle processes on land, in the ocean and in marine sediments, thus
allowing the investigation of the complex interactions between climate and the carbon cycle. Two set-ups of the global carbon cycle, closed and open, are available in CLIMBER-X, allowing both a proper comparison with CMIP6-type models in centennial-scale and multi-millennium simulations. We have evaluated the model performance for the historical period against observations and state-of-the-art CMIP6 models,
showing that many characteristics and feedbacks of the carbon cycle are reasonably well captured by the model.
Biases in the simulated distribution of ocean biogeochemical tracers exist and can mostly be related to deficiencies in the
simulated ocean circulation changes, which can at least partly be attributed to the comparatively coarse resolution of the ocean model
and to the frictional–geostrophic approximation that it rests upon. On land, the carbon in soil layers below
1 m is underestimated, particularly in the permafrost zone, with possible implications for the land carbon cycle response
to global warming.
Some possible directions for future model developments include the extension of the organic carbon cycle, allowing for burial on land and in sediments and fluxes from land to ocean, the refinement of the carbonate chemistry on shelves, including coral growth, and possibly the addition
of the nitrogen cycle on land, which could be important for nitrogen limitation of photosynthesis and would allow for interactive atmospheric N2O, considering that N2O fluxes from the ocean are already available from the ocean biogeochemistry model HAMOCC.
The computational efficiency of CLIMBER-X will enable it to be used for systematic explorations of the coupled climate–carbon cycle evolution over timescales ranging from decades up to ∼ 100 000 years while also allowing a quantification of related uncertainties.
Code and data availability
The source code of CLIMBER-X v1.0 is archived on Zenodo (10.5281/zenodo.7898797, ), with the exception of the HAMOCC model, which is covered by the Max Planck Institute for Meteorology software licence agreement as part of the MPI-ESM
(https://code.mpimet.mpg.de/attachments/download/26986/MPI-ESM_SLA_v3.4.pdf, last access: 5 May 2023).
CMIP6 model data are licensed under a Creative Commons
Attribution-ShareAlike 4.0 International License (https://creativecommons.org/licenses, last access: 5 May 2023) and can be accessed through
the Earth System Grid Federation (ESGF) nodes (for instance https://esgf-data.dkrz.de/search/cmip6-dkrz/, last access: 14 December 2022).
Author contributions
MW and AG designed the model. TI and BL provided the HAMOCC model code and assisted in the implementation of
the model in CLIMBER-X. CH helped with the sediment model set-up and configuration. MP re-arranged HAMOCC into a column model for the purpose of integration into CLIMBER-X. MH implemented and tuned the particle-ballasting
scheme. DD contributed to the improvements in the land carbon cycle model. VB and GM assisted in the implementation and set-up of the open carbon cycle. JB, JH and GRM developed the weathering model and contributed to its implementation in CLIMBER-X. MW coupled the different model components and tuned and tested the model. MW performed the model simulations, prepared the figures
and wrote the paper, with contributions from all the authors.
Competing interests
The contact author has declared that none of the authors has any competing interests.
Disclaimer
Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Acknowledgements
Matteo Willeit, Bo Liu, Malte Heinemann and Janine Börker are funded by the German climate modelling project PalMod supported by the German Federal Ministry of Education and Research (BMBF) as a Research for Sustainability (FONA) initiative (grant nos. 01LP1920B, 01LP1917D, 01LP1919B, 01LP1919C and 01LP1920C). Guy Munhoven is a Research Associate with the Belgian Fund for Scientific Research – F.R.S.-FNRS.
We thank Irene Stemmler for technical support in implementing HAMOCC in CLIMBER-X and Thomas Kleinen for discussions on the methane cycle. We thank the World Climate Research Programme, which, through its Working Group on Coupled Modelling,
coordinated and promoted CMIP6. We thank the climate modelling groups for producing and making available their model output, the ESGF for archiving the data and providing access, and the multiple funding agencies who support CMIP6 and the ESGF. We thank Nuno Carvalhais for providing the soil and vegetation carbon dataset.
The authors are grateful to the European Regional Development Fund (ERDF), the German Federal Ministry of Education and Research and the State of Brandenburg for supporting this project by providing resources on the high-performance computer system at the Potsdam Institute for Climate Impact Research.
Financial support
This research has been supported by the Bundesministerium für Bildung und Forschung (PalMod project, grant nos. 01LP1920B, 01LP1917D,
01LP1919B, 01LP1919C and 01LP1920C).The publication of this article was funded by the Open Access Fund of the Leibniz Association.
Review statement
This paper was edited by Carlos Sierra and reviewed by two anonymous referees.
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