The underlying physical model, ModelE2.1, has been described in Kelley et al. (2020) and includes updates to earlier versions of the NASA GISS model (Schmidt et al., 2006; Hansen et al., 2007; Schmidt et al., 2014). For ease of access and comprehensiveness of model presentation, we will describe key components of the model here as well, although complete information and evaluations of the physical model should be sought in these publications.
The atmospheric model has horizontal resolution of 2 by 2.5° in latitude and longitude respectively and 40 layers in the vertical from the surface to 0.1 hPa in the lower mesosphere; it is coupled to an ocean with 1 by 1.25 horizontal resolution in latitude and longitude respectively and has also 40 layers in the vertical.
Atmospheric dynamics uses Arakawa's B-grid scheme where eastward and northward velocity components are located at primary cell corners; vertical discretization follows terrain‐following (sigma) layers in the troposphere which transition to constant‐pressure layers in the stratosphere. The transition is smooth and centered at 100 hPa with a half‐width of approximately 30 hPa. The vertical discretization in the ocean is 40 vertical layers in mass with higher resolution of 5–20 m near the surface and within the thermocline and about 200 m at depth.
Prognostic variables in the atmosphere are dry air mass, potential temperature, water vapor mixing ratio, and horizontal velocity components. Virtual potential temperature is used for all density/buoyancy-related calculations. Ocean prognostic variables include seawater mass, potential enthalpy that accounts for variations in specific heat capacity, salt and horizontal velocity components on both the C-grid (perpendicular to primary cell edges) and D-grid (parallel to primary cell edges).
Subsurface reservoirs are split into four types: open water (including lakes and oceans), ice-covered water (including lake ice and sea ice), ground (including bare soil and vegetated regions), and land ice/glaciers. Within each type there are further subdivisions (fraction of plant functional types, fractional snow cover, melt pond fraction over sea ice, etc.), which are communicated to the atmospheric model as weighted mean quantities (for example the albedo in the radiation computations). The non-ocean reservoirs include prognostic variables for water mass and heat content, and the sea ice also includes salt content.
The model uses a 30 min time step for physics calculations (i.e. surface interactions, condensation etc). The radiation code is called every five physics time steps (every 2.5 h), however, the zenith angle and sun light intensity are updated every physics time step. The model uses a 225 s time step for the atmospheric dynamics (transports) and 112.5 s time step for ocean gravity wave computations.
Simplifications in atmospheric thermodynamics ignore the sensible heat of condensate. Although latent heat of water vapor is treated correctly, its mass is not added to atmospheric dry mass. Consequently, precipitation and evaporation occur at 0 °C, specific potential enthalpy equals potential temperature times dry specific heat capacity, and humidity affects atmospheric density only in the pressure gradient force computation.
The ocean model is a dynamic ocean model E2.1-G (Russell et al., 1995; Schmidt et al., 2006, 2014; Kelley et al., 2020), non-Boussinesq (i.e. includes density variations in the horizontal as well as vertical momentum equations and in the continuity equation, following Schmidt et al., 2006). It conserves potential enthalpy, freshwater mass, and salt mass, and uses natural boundary conditions (for heat and freshwater). It has a free surface and thus it is not volume conserving. The number of vertical layers varies from 2 to 40. After the dynamics, the mass ratio of layer n and its layer above is fixed in time and space, but this does vary with n. The thickness of layer 1 varies and is approximately 10 m. The vertical coordinate is mass per unit area, including the mass of air, ice and water above any level.
The ocean model solves the dynamical equations via an invariant form. The Coriolis term is computed via the C and D-grid velocities and has latitude dependence. The quadratic upstream advection scheme (Prather, 1986) uses mean, three-dimensional gradients, and second order moments to advect scalar tracers, thus effectively increasing the resolution, in both horizontal and vertical direction. Bottom friction is applied at the lowest layer of each ocean column. The ocean model employs the K-profile parameterization (KPP) for vertical mixing (Large et al., 1994) and the Gent-McWilliams parameterization for eddy induced tracer transports (Griffies, 1998a, b). The mesoscale diffusivity allows for surface‐intensified eddies, by employing an exponential decay of diffusivity with depth that depends locally on the horizontal gradient of potential density (Kelley et al., 2020) which permits eddies to restratify the Southern Ocean over a large depth range, consistent with the observed density structure there, while not overacting in other regions of the World Ocean (such as the North Atlantic). The Rossby radius is replaced by a geographically constant nominal length scale, and the diffusivity is a function of the Brunt‐Vaisala frequency and the slope of isopycnal surfaces.
Mesoscale transport is expressed in local quasi‐isopycnal layers, avoiding difficulties associated with skew-flux representation (1) in regions with weak vertical stratification, e.g. the surface mixed layer and at the ocean surface, where the GM parameterization assumes that eddies transport tracers along isopycnal surfaces. However, near the surface, these surfaces can be highly tilted or intersect the ocean surface, which violates the assumptions of the parameterization. Applying the GM scheme directly in these regions can lead to spurious mixing and incorrect representation of processes like deep convection and mixed-layer re-stratification, (2) near lateral boundaries and the ocean bottom, where the eddy fluxes must be parallel to these boundaries, but the GM scheme's isopycnal-following nature doesn't naturally enforce this, and (3) in areas of strong density fronts (e.g., the Gulf Stream or the Antarctic Circumpolar Current) where the “small-slope approximation” which assumes that the slope of isopycnal surfaces is small and is valid in the deep ocean, breaks down in areas where the isopycnals are steeply tilted. Ventilation of marginal seas through their connecting straits has been increased via two mechanisms in E2.1‐G, reducing salinity biases there. While there is no explicit overflow parameterization in the ocean model, for straits deep enough that density contrasts can drive strong opposing flows at the surface and at depth, the finer upper‐ocean layering in E2.1‐G resolves this structure, in conjunction with a slight tuning of strait depths. Second, horizontal diffusivity was increased in straits that are shallow or have weaker density contrasts. The first mechanism impacted the Red and Black seas, and the second the Baltic and Hudson (Kelley et al., 2020). The first is the sole ventilation mechanism for straits narrower than the nominal resolution, which are parameterized using the Russell et al. (1995) one‐dimensional channel scheme that lacks horizontal mixing.
In addition to KPP, the vertical diffusivity also includes a contribution from tidal dissipation. The ocean model Atlantic meridional overturning circulation (AMOC) is found to be sensitive to tidally driven mixing, which occurs in the shallow waters bordering the North Atlantic following dissipation distributions generated by Jayne (2009).
The Equation of State employed in the ocean model computes specific volume (m3 kg−1) as a function of specific potential enthalpy (J kg−1), salinity (psu), and pressure (Pa). Using constant uniform gravity, pressure at any level is gravity times mass per unit area above the level. The one-to-one relationship between temperature and specific potential enthalpy is computed using the adiabatic lapse rate of sea water as function of temperature, salinity and pressure (IES-1980 et al., 1981) and specific enthalpy of sea water as function of temperature and salinity at atmospheric pressure. Using these formulas, the model's Equation of State can be computed from the specific volume function of temperature, salinity and pressure (IES-1980 et al., 1981). Complex computations for Equation of State, freezing temperature, specific heat capacity, and others are evaluated offline and are stored in tables; the model interpolates the table values as functions of specific potential enthalpy, salinity and pressure (Chen and Millero, 1976). Table resolutions are 4000 J kg−1 of specific potential enthalpy, 1 psu of salinity, and
The ocean carbon cycle model is based on the NASA Ocean Biogeochemistry Model (NOBM), originally developed at the NASA-Global Modeling and Assimilation Office (Gregg and Casey 2007) and later coupled coupled to the GISS climate model under prescribed atmospheric concentrations (Romanou et al., 2013, 2014) and under prescribed emissions (Ito et al., 2020). The model includes four phytoplankton species (diatoms, chlorophytes, cyanobacteria, and coccolithophores), four nutrient species (nitrate, silicate, ammonia, and iron), three detrital pools (nitrate/carbon, silicate, and iron) and one heterotroph species (Fig. 1). Carbon cycling is represented through dissolved organic (DOC) and inorganic carbon (DIC), where carbonate chemistry is solved using MOCSY (Orr and Epitalon, 2015). Ocean carbon interacts with atmospheric CO2 through gas exchange parameterization, following the CMIP6 protocol (Orr et al., 2017). The current version of NOBM (NOBMg) has been expanded to include oxygen and alkalinity (Lerner et al., 2021, 2024) and an updated treatment of iron scavenging (see below). The model equations and parameters used are laid out in Appendix A and in Tables A1–A11 therein. A short description of the model equations is provided below.
Schematic diagram of the ocean carbon cycle model (NOBMg). credit: Jay Friedlander, NASA-GSFC.
All tracers in NOBMg are changed via physical transport and mixing which are following parameterizations of these processes in the physical ocean model.
Phytoplankton species are also subject to sinking, growth via nutrient uptake, respiration and exudation of DOC, senescence and zooplankton grazing. Nutrient distributions are changed via uptake by phytoplankton species for growth, remineralization of particulate organic carbon or nitrogen, and detrital breakdown. Cyanobacteria can also grow via nitrogen fixation, where growth is limited only by light, iron, and temperature. Nitrogen assimilated into organic matter is obtained from N2. Cyanobacterial growth via nitrogen fixation follows the same Michaelis-Menten formulation as cyanobacterial growth that is nitrate limited, with two exceptions. First, the iron half-saturation constant for nitrogen fixation is 33 % higher than that for nitrate-limited growth, as nitrogen fixation generally relies upon an increased availability of iron. Second, nitrogen fixation is inhibited by the presence of nitrate and ammonium, following laboratory culture experiments using
Herbivores grow via grazing of phytoplankton and are lost to heterotrophic consumption and excretion to DOC.
Carbon and nitrate particulates (detritus) are linked via the constant
The model includes prognostic alkalinity which is advected and mixed like all other tracers and follows the Ocean Carbon Model Intercomparison Project parameterizations (OCMIP-2, Najjar et al., 2007), i.e. it is produced via conversion of nitrate to organic N and carbonate dissolution, while it is lost to remineralization of detrital organic carbon
Oxygen interacts with the rest of the ocean biogeochemical tracers via remineralization of organic carbon and by determining when the model switches to slower rates of remineralization that are consistent with denitrification (Eqs. A48–A56; Lerner et al., 2024).
The Ent Terrestrial Biosphere Model (Ent TBM) (
Leaf biophysics is a coupled conductance/photosynthesis model that simulates vegetation stomatal control of both transpiration and uptake of CO2. The coupled leaf photosynthesis/ stomatal conductance model consists of the photosynthesis model of Farquhar and von Caemmerer (1982) and the Ball-Berry model of stomatal conductance (Ball and Berry, 1987), with leaf boundary layer conductances following the approach by Collatz et al. (1991) but with the boundary layer conductance derived from the canopy surface layer conductance of the land surface model; for the cubic equations of coupled photosynthesis/conductance, a numerical solver for net assimilation of CO2 and leaf internal CO2 concentration was developed. C4 photosynthesis follows the scheme of Collatz and Berry (1992). Leaf-to-canopy scaling is achieved through the canopy radiative transfer scheme of Spitters et al. (1986) (introduced to ModelE in CMIP5 in Schmidt et al., 2006) combined with a numerical scheme for vertical layering of the canopy by converging the total canopy fluxes. Vegetation canopy absorbance and transmittance of photosynthetically active radiation thus depend on vertical layering of leaf area index, solar zenith angle, and the fractions of diffuse vs. direct radiation, providing vertical profiles of sunlit and shaded leaf area fractions. Physiological algorithms for water stress, cold hardening in evergreen needleleaf trees, and temperature sensitivity of photosynthetic capacity are detailed in Kim et al. (2015). To account for variation in parameters of the leaf biophysics by climate and seasonality of vegetation, temperature dependence of leaf photosynthetic capacity,
Water stress is modeled after the approach of Rodriguez-Iturbe et al. (2001), in which stress is a factor between 0 (full stress) and 1 (unstressed), as a function of relative extractable water (volume water
For surface albedo, Ent's 12 different vegetation types have different spectral and snow masking depth properties. In E2.1 Ent PFTs are mapped to the 8 biome types of Matthews (1984) for seasonal albedo for radiative purposes.
In Schmidt et al. (2006) and henceforth, all surface conductance of water vapor for vegetated land was assigned to the vegetation, which meant that there was no soil evaporation under canopies. The rationale for this approach (Abramopoulos et al., 1988) was that vegetated land was simply a surface with a particular albedo and conductance. Numerous studies have demonstrated the importance of soil evaporation as a component of evapotranspiration, especially for semiarid ecosystems (e.g., Lawrence et al., 2007). While evaporation from bare soil was included in previous versions of the model, in E2.1 we have added a simple representation of soil evaporation based on the work of Zeng et al. (2005) and Lawrence et al. (2007), by including the evaporative flux from the vegetated soil into the total evapotranspiration scaled as a function of the current leaf area index. Total evapotranspiration never exceeds the potential evaporation.
In E2.1, irrigation is implemented as a prognostic field (Cook et al., 2011, 2014; Krakauer et al., 2016; Puma and Cook, 2010; Shukla et al., 2014) where water demand for irrigation (Wada et al., 2014) is estimated using prescribed irrigation areal extent (Siebert et al., 2015). The water is drawn first from rivers and lakes locally, and if that is insufficient, it is drawn from an external groundwater source (which is tracked diagnostically). Groundwater is assumed to have the same temperature as the soil and default tracer concentrations. Groundwater recharge is not accounted for, and so there is a small increase in total water mass (and eventually, sea level) associated with the net global groundwater draw in these simulations. These effects have a complex impact on freshwater delivery to the oceans (and hence sea level). Irrigation from local surface water sources leads to increased soil moisture and reduced river outflow, but this is dominated by net additions of groundwater which add freshwater to the climate system, about 0.2 mm yr−1 of global sea-level-equivalent in 2010 (Miller et al., 2021). As discussed in Miller et al. (2021) this freshwater imbalance is driven by an underestimate of surface water in lakes and rivers (which means that more groundwater is needed) and also the lack of counteracting increase in reservoirs.
The land carbon dynamics in the fully coupled carbon cycle physics configuration is the same as described in Ito et al. (2020) for the ModelE submission to CMIP6 C4MIP. The leaf biophysics is sensitive to the surface atmospheric CO2 concentration. The model tracks CO2 exchanges between the land and atmosphere in diagnostics for GPP, autotrophic respiration, soil respiration, and carbon fluxes due to land cover change. Land carbon change associated with the annual land cover change is distributed as CO2 fluxes to the atmosphere over the following year to avoid having to add a pulse of CO2.
Schematic diagram of the Ent in GISS ModelE2.1-CC2.
Sea ice and lake ice are computed on the atmospheric grid, and the information is mapped on to the ocean grid. Temperature and salinity profiles in the ice are computed prognostically, and sea ice distribution trends and seasonal cycles are realistic (Kelley et al., 2020).
Salinity in the ice affects basal ice formation/melt and heat diffusion (Schmidt et al., 2006) using brine-pocket (BP) thermodynamics (Bitz and Lipscomb, 1999; Schmidt et al., 2014) and updated in Kelley et al. (2020). Sea ice dynamics use the viscous-plastic formulation of Zhang and Rothrock (2000). Lead fraction is treated differently in the Arctic and Antarctic wintertime thick-ice growth to produce more realistic heat fluxes and sea ice growth rates. Processes relevant to the salt budget (e.g., gravity drainage and flushing of meltwater) are consistently treated with the BP physics.
The mass and energy associated with net snow accumulation over each hemisphere's ice sheets is used to adjust the implicit iceberg calving fluxes into the adjacent oceans over a 10-year relaxation time, and this diagnostic is preserved as glacial melt. This ensures that the model can reach a long-term equilibrium under changed climate forcings but does not imply realism in the response of ice sheets to climate, since the ice sheets are assumed to remain in mass balance.
The total solar irradiance at the top of the model's atmosphere is based on satellite calibrations (Kopp and Lean, 2011) with a base value of 1361 W m−2. Spectral irradiance values are taken from Coddington et al. (2016). The radiation model includes explicit multiple scattering calculations for solar radiation (shortwave, SW) and explicit integrations over both the SW and thermal (longwave, LW) spectral regions (Schmidt et al., 2006; Schmidt et al., 2014; Kelley et al., 2020). SW radiation is absorbed by H2O, CO2, O3, O2, and NO2 using the
Longwave radiation is absorbed by H2O, CO2, and O3 using the correlated
Variations in incoming solar forcing in the 20th Century simulation follow Matthes et al. (2017) and include updated spectral solar irradiance. Orbital parameters that determine the seasonal and latitudinal variation in insolation are calculated each year (updated on 1 January), based on Berger (1978).
The radiation model also includes the effects of 3D cloud heterogeneity via the 3D cloud parameterization (Cairns et al., 2000) to get more realistic albedos from realistic water paths and particle sizes (Schmidt et al., 2006). The procedure rescales optical depth, asymmetry parameter, and single scattering albedo according to the relative variance of the cloud particle density distribution. The partitioning between convective precipitation that descends and has the potential to evaporate in the environment rather than in the downdraft is increased from 0 % to 50 %, thus increasing the sensitivity of humidity to convection. The downdraft buoyancy is based on virtual temperature including condensate loading. Glaciation in the mixed‐phase temperature range has been updated in the stratiform cloud parameterization.
Stratiform cloud formation is done more realistically because there is no restriction in coverage, no dependence on vertical motion, the altitude is taken to be relative to local planetary boundary layer (PBL) height rather than a fixed 850 hPa, better demarcating cloud‐topped boundary layers from the free troposphere where the threshold relative humidity is used for the TOA radiation balancing process (described in Sect. 3.1.1) to maintain top‐of‐the‐atmosphere radiative balance.
The advection of humidity (and other tracers) is done only once every physics time step (30 min) with iterative time stepping to avoid any Courant–Fredrichs–Levy violations. The smaller time steps are used primarily in the stratosphere and upper troposphere where zonal winds are strong or as a result of extremely high flow deformation.
The atmospheric chemistry configuration used in GISS ModelE2.1-CC2 is the basic non-interactive composition (NINT f2 used in CMIP6) in which the background fields of ozone and aerosol concentrations (dust, sea-salt, sulfate, nitrate, ammonium and carbonaceous aerosols e.g. black and organic carbon) are derived from simulations of the interactive one-moment aerosols (OMA) version of the model, run as an atmosphere only model with prescribed SST (Kelley et al., 2020). All anthropogenic and biomass burning emissions of short‐lived species were updated to CMIP6 specifications (Hoesly et al., 2018; van Marle et al., 2017) and were prescribed annually or monthly.
Specifically, with regards to dust, the six dust bins (0.1–0.2, 0.2–0.5, 0.5–1, 1–2, 2–4, and 4–8
Currently in NOBMg within GISS ModelE2.1-CC2, dust iron deposition is obtained from the historical annual cycle climatology extracted from the GISS E2.1-G online dust simulations which include eight externally mixed minerals (illite, kaolinite, smectite, carbonates, quartz, feldspar, iron oxides, and gypsum) plus internal mixtures between seven minerals and iron oxides (Perlwitz et al., 2015a; Perlwitz et al., 2015b). The masses of free and structural iron and their fractions of total iron have been evaluated using measurements from Izaña Observatory (Pérez García-Pando et al., 2016). For more on the dust deposition, see Sect. 3.1.2 on Forcings. In future versions of the model, dust deposition will be interactive with the global carbon cycle.
A second order scheme is used for the transport (Schmidt et al., 2006) of all the tracer fields in the atmosphere which are advected using the highly non-diffusive quadratic upstream scheme (QUS; Prather, 1986), which keeps track of nine subgrid-scale moments as well as the mean within each grid box. This increases the effective resolution of the tracer fields and allows the GISS model to produce reasonable climate fields with relatively coarse nominal resolution.
The radiation model generates spectrally dependent direct/diffuse flux ratios for use in biosphere feedback interactions. The surface albedo utilizes six spectral intervals, in nanometers: nm: VIS (300–770), NIR1 (770–860), NIR2 (860–1250), NIR3 (1250–1500), NIR4 (1500–2200), NIR5 (2200–4000), and is solar zenith angle dependent for ocean, snow, and ice surfaces.
The spectral and solar zenith angle dependence of ocean albedo is based on calculations of Fresnel reflection from wave surface distributions as a function of wind velocity (Cox and Munk, 1956) taking also into account the effects of foam and hydrosols on ocean albedo (Gordon and Jacobs, 1977). The spectral and solar zenith angle dependence of snow and sea ice is modeled following Warren and Wiscombe (1980). Snow “ages” following Loth and Graf (1998) and has a different albedo for wet or dry snow. Ocean ice albedo is spectrally dependent and is a function of ice thickness and parameterized melt pond extent (Schmidt et al., 2006 and references therein).
Light profiles from the atmospheric radiation module are propagated underwater into the ocean and spectrally decomposed to 33 wavebands that are used to compute growth of the phytoplankton groups, sinking profiles, as well as changes in the vertical distribution of ocean temperatures due to biologically mediated absorption and scattering in the water column (Gregg and Conkright, 2002). NOBMg is coupled prognostically to the atmospheric radiation module which is part of ModelE2.1. Direct and diffuse sunlight in 6 wavebands (5 in the near IR and 1 in the visible part of the spectrum) that are computed by the radiation module are decomposed into the 33 wavelengths (250–3700 nm) needed for the absorption and scattering by the different phytoplankton species. The decomposition factors are based on the fractions of direct (diffuse) sunlight at the equator for each wavelength relative to the total radiation as derived from a monthly climatology provided by the Ocean–Atmosphere Spectral Irradiance Model (OASIM) and forced by MODIS data for aerosols and clouds (Gregg and Casey, 2007).
Vegetation spectral albedo is prescribed as seasonally varying by plant functional type (PFT) and is treated as Lambertian, assuming a flat, diffusely reflecting surface. Bare soil is represented as grey, with values from Matthews (1984). Seasonal spectral albedos for vegetation are specified by mapping Ent PFTs to the eight Matthews biome types: tundra (Ent cold-adapted shrubs), C3 grass (Ent C3 perennial, annual, and arctic grasses), shrub (Ent arid-adapted shrubs), deciduous forest (all Ent deciduous trees), evergreen needleleaf forest (Ent evergreen needleleaf trees), tropical rainforest (Ent evergreen broadleaf trees), and crops (Ent crops). Total land albedo is calculated as a weighted average across the corresponding land-cover fractions and linearly interpolated between prescribed seasonal values. When snow is present, snow albedo is included in the weighted average according to its masking fraction.
Separate atmospheric surface fluxes are computed for each subsurface reservoir: open water, sea or lake ice, land ice, snow free and snow-covered ground. ModelE calculates atmospheric turbulence over the entire vertical column. The surface fluxes are calculated using a submodule that is embedded between the surface and the midpoint of the first resolved model layer. In the atmospheric planetary boundary layer (PBL), a formulation for the temperature, moisture, and scalar fluxes is employed and consists of a local (diffusive) term and a countergradient term derived from large-eddy simulation (LES) data (Holtslag and Moeng, 1991) as well as a nonlocal vertical transport scheme for virtual potential temperature, specific humidity, and other scalars (Holtslag and Boville, 1993).
A level-2.5 turbulence model (Cheng et al., 2002; Yao and Cheng, 2012) is applied to this region (using eight sublayers) independently over each surface type where the mixing profile depends on the height of the PBL, which is closely related to the large eddy size and thus characterizes the nonlocality, and the buoyancy and shear effects at the surface. The turbulence length scale formulation is obtained from the large eddy simulation data by Nakanishi (2001).
Above the PBL a second-order closure (SOC) model developed by Cheng et al. (2002) is used, which is based on Mellor and Yamada (1982). The Reynolds stress and heat flux equations have been solved with a more advanced parameterization of the pressure–velocity and pressure–temperature correlations. In addition, a few turbulent time scales are determined by a new two-point turbulence closure model (Canuto and Dubovikov, 1996a, b). The more realistic “Richardson number criterion” rather than the “TKE criterion” to calculate the PBL height, following Troen and Mahrt (1986) and Holtslag and Boville (1993).
The lower boundary conditions for the wind and the potential temperature equations are determined assuming continuity of the respective turbulent fluxes at the surface. To calculate the fluxes through the surface layer, drag and transfer coefficients are set using similarity theory following Hartke and Rind (1997). The roughness length for momentum (
We reduce the saturation specific humidity by 2 % over the oceans (to account for sea salt aerosol effects; Gill, 1982).
Over land, the surface evaporative flux is determined by the vegetation, but to improve estimates of surface humidity by the submodule described above, we calculate the maximum available evapotranspiration and do not allow the atmosphere to draw more water than is available. This requires a change in the humidity surface boundary condition from a variable to a fixed flux in such situations.
Continental runoff occurs at the mouths of rivers as well as small tributaries. Prognostic river runoff is computed within ModelE2.1-CC as part of the simulated global hydrological cycle, thus increases (decreases) due to changes in precipitation and evaporation over land, and delivers accordingly nutrients and carbon components to the coastal ocean (for more details see Sect. 3.1.2 on Forcings).
Coupling between the different components in ModelE is synchronous and at the frequency of the physics time step (30 min). It is always implemented via fluxes of the fundamentally conserved quantities (mass, energy, and tracer). Given the surface conditions, the atmospheric model calculates the precipitation, radiative, and other surface fluxes (surface wind stress, evaporation, and sensible and latent heat) over each surface type. Radiation and precipitation fluxes are first applied directly to the land surface (soils, vegetated ground, and glaciers) and the land surface model computes latent and sensible heat fluxes, as well as land carbon fluxes. Using the atmosphere–ice wind stress, the sea ice dynamics calculates the horizontal ice velocities and the resulting ice–ocean stress. The ocean has finer horizontal resolution than the atmosphere and thus area conserving schemes of horizontal interpolation of fluxes from the atmospheric and the ocean grid are designed to conserve mass, energy, and tracer fluxes.
River flow occurs on the atmospheric grid and is deposited into the ocean by the coupler (Schmidt et al., 2014). Ice-ocean fluxes involving melt, heat conduction, and momentum drag are computed on the ice grid, while ice formation in the ocean occurs on the ocean grid and is then interpolated back to the atmosphere-ice grid ensuring conservation of fluxes.
More than 100 vertically integrated diagnostics for every process in the atmosphere and the ocean are accumulated on each horizontal surface cell. They include fresh and saltwater mass, atmospheric kinetic and static energy, ocean energy, and water and energy for each continental reservoir, as well as all ocean tracer fields. Offline programs utilize these monthly accumulated diagnostics, as well as water mass, tracer and energy amounts for each reservoir at beginning and end of each month and compute the change in reservoirs and compare to flux changes. For both global and regional domains, errors are zero within the restrictions of machine accuracy (real*4 for fluxes and real*8 for reservoirs).
In the atmosphere, the advection scheme is mass conserving for humidity and tracers, and potential enthalpy conserving for heat. All processes including dynamics, cloud schemes, gravity wave drag, and turbulence, conserve energy and air, water, and tracer mass to machine accuracy. All dissipation of atmospheric kinetic energy through various mixing processes is converted to heat globally. In the long-term mean, net top-of-atmosphere (TOA) radiative flux approaches zero in the pre-industrial control simulation.
In atmosphere-coupled experiments, the Ent TBM is currently run in biophysics-only mode without prognostic leaf area index (LAI) or stem growth. Vegetation structure is prescribed from satellite-derived vegetation cover, type, height, and maximum LAI. Maximum LAI is used to compute vegetation demography and cohort densities based on Ent's allometric relations by PFT. For each PFT, we use observed monthly LAI from Moderate Resolution Imaging Spectroradiometer (MODIS) which is interpolated at a daily time step. For land cover/land use change (LCLUC), Ent prescribes only annual historical change in cropland cover, rescaling the natural vegetation cover fractions in a grid cell (Miller et al., 2021; Ito et al., 2020); land use change such as deforestation is included only implicitly as part of the total cultivated land cover change.
Currently, we run Ent in biophysics-only mode where vegetation structure is prescribed, and all carbon pools are prescribed except the soil pools and the labile (non-structural carbohydrate) vegetation carbon pool which are prognostic. The labile carbon pool is dynamic with uptake of carbon through photosynthesis, withdrawal for respiration and leaf growth, and retranslocation with senescence. Any carbon excess, that is since LAI is prescribed, and no stem growth is allowed, is redirected to the litter pool in the soil, and that ensures carbon conservation. As mentioned earlier, land carbon change associated with the annual land cover change is distributed as CO2 fluxes to the atmosphere over the course of the following year. Because the prescribed vegetation structure may not be in equilibrium with the simulated climate due to climate model biases or scenarios of climate change, respiration is restricted when labile carbon balances approach zero or slightly negative, allowing recovery of the labile pool during the growing season. This is also done to ensure carbon conservation.
NOBMg conserves carbon, iron, ammonium and silicate but does not conserve nitrate, due to the fact that the nitrogen cycle is not closed. For nitrogen fixation, we assume an unlimited reservoir N2 is available for diazotrophs. Moreover, while there is an oxygen-dependent switch from faster (aerobic) to slower (anaerobic) remineralization rates, denitrification (the conversion of nitrate to N2) is not represented in NOBMg. Alkalinity is also not conserved since we do not include an explicit calcium carbonate tracer. Hence, rather than exchanges between dissolved and solid-phase carbonate ions being present, dissolved carbonate ions are either removed in near-surface waters by implicit calcium carbonate production (assumed to be proportional to primary productivity), or released by implicit carbonate dissolution in deep waters (assumed to follow a fixed exponential profile).