The Flexible Modeling System (FMS) is the coupler between the different model components of CM2Mc and has been developed at GFDL .

https://www.gfdl.noaa.gov/fms/ (last access: 30 November 2020)

CM2Mc employs the GFDL Modular Ocean Model (MOM) version 5 in a nominal 3∘ × 3∘ lateral grid, with 28 vertical levels . The meridional grid resolution increases to a maximum of 0.6∘ at the Equator to allow the explicit simulation of some equatorial currents. The model uses rescaled pressure vertical coordinates (p*), with the uppermost eight layers having a thickness of 10 dbar, which increases with depth to a maximum layer thickness of 506 dbar . MOM5 utilizes the tripolar model grid of to avoid a singularity at the North Pole and partial bottom cells for a more accurate representation of bottom topography. Where the grid fails to resolve important exchanges of water between ocean basins, the cross-land mixing scheme of is employed. MOM5 in CM2Mc is coupled to the GFDL thermodynamic–dynamic sea ice model (SIS; ). We refer to for a more complete description of the model setup.

Enclosed in the ocean component MOM5, the Biogeochemistry with Light, Nutrients and Gases (BLING) model is run. It was developed at Princeton/GFDL as an intermediate-complexity tool to approximate marine biogeochemical cycling of key elements and their isotopes. More details can be found in .

The atmospheric module in CM2Mc is the GFDL Atmospheric Model version 2.1 AM2;. It uses the finite volume dynamical core as described in and implemented in CM2.1 : a latitudinal resolution of 3∘, a longitudinal resolution of 3.75∘ and 24 vertical levels, with the lowest being at 30 m and the top at about 40 km above the surface. For the coupled setup, we use a general atmospheric time step of 1 h at which variables are exchanged with the coupler. Dynamic motion and the thermodynamic state of the atmosphere are calculated at a 9 min time step, whereas the radiation scheme has a time step of 3 h. The coupled model includes an explicit representation of the diurnal cycle of solar radiation. For a more detailed description of the model and its configuration, see and .

The C main function of LPJmL5 used in the offline version is replaced by a coupler function providing the interface between the internal C functions of LPJmL5 and the Fortran functions of the CM2Mc model. The coupler function is called by FMS at an hourly time step, and it calls the specific update functions of LPJmL5 at the end of each hour, day, month or year, respectively. Ingoing and outgoing data are transferred as array arguments of this function. The mapping of the coarse resolution of the CM2Mc model to the 0.5∘ × 0.5∘ resolution of LPJmL5 is done by the FMS coupler. We found that the FMS land model component must be run at LPJmL5 resolution, which is 0.5∘, so that all model components and the FMS coupler agree on which cells belong to land and which to the ocean. This yields slight changes of the land–sea mask from the original CM2M_coarse_BLING setup.

CM2Mc as well as LPJmL5 can use the message passing interface (MPI) to run the simulation in parallel on a compute cluster. CM2Mc uses FMS to set up a two-dimensional domain decomposition (i.e., it splits the global grid into rectangular domains which are mapped to concurrent MPI tasks). In contrast, the LPJmL5 grid is represented by an unsorted one-dimensional array of land cells, which is evenly distributed onto the MPI tasks. As this LPJmL5 grid is not compatible with the FMS grid exchange framework, a small wrapper library was developed for the data exchange between LPJmL5 and FMS domains. The wrapper library is called for the ingoing and outgoing data, and the time overhead for this data exchange is negligible. The coupler function as well as the wrapper library are part of the LPJmL5 distribution.

The stand-alone version of LPJmL5 does not calculate the essential coupling variables, canopy temperature and humidity, which is remedied in the coupled configuration via the addition of a new canopy module. In this new module, the canopy humidity and canopy temperature and some further quantities linked to those variables are calculated (Fig. ). In this setting, the canopy layer corresponds to the lower boundary for the temperature in the atmosphere. The atmospheric diurnal cycle as well as the seasonal changes depend on the surface energy balance. The canopy humidity, on the other hand, is the lower boundary for the atmospheric humidity and, hence, sets the moisture content and the amount of precipitation in the atmosphere as well as the potential for evapotranspiration at the surface. A schematic overview of the different calculation steps is provided in Fig. .

In the stand-alone version of LPJmL5, climatic input is prescribed; therefore, calculations of processes and fluxes, such as evapotranspiration, do not feed back to the atmosphere. In the coupled version, however, a small perturbation in a positive feedback loop can influence the climate and push the process towards an even larger perturbation. Thus, special attention has to be given to ensure the stability of the model by either ignoring the feedback and implementing a simple, empirical and stabilizing relationship or by increasing the complexity of the implementation, in order to get a more realistic representation of the vegetation embedded in the Earth system. The latter was done in CM2Mc-LPJmL by replacing the former simple Priestley–Taylor approach for calculating potential evapotranspiration ET0 with the more complex and process-based Penman–Monteith evapotranspiration . The Penman–Monteith approximation also accounts for additional parameters, such as humidity, that were previously not available in the stand-alone LPJmL5 model (Fig. ): 1LvET0=dqsatdT(Rn-G)+86400⋅ρaCp(es0-ea)τaνdqsatdT+γ(1+τsτaν), where Lv is the volumetric latent heat of vaporization of 2453 MJ m-3, ET0 is the evapotranspiration (in m d-1), dqsatdT is the slope of the vapor pressure curve (in kPa ∘C-1), Rn is the net radiation at the surface (in MJ m-2 d-1), G is the soil heat-flux density (in MJ m-2 d-1), 86 400 is the conversion factor from seconds to daily values, ρa is the air density (in kg m-3), Cp is the specific heat of dry air (1.013×10-3 MJ kg-1 ∘C-1), es0 is the saturated water vapor pressure (in kPa), ea is the actual water vapor pressure (in kPa), τaν is the bulk surface aerodynamic resistance for water vapor (in s m-1) and τs is the canopy surface resistance (in s m-1). γ is the psychrometric constant (in kPa ∘C-1) and is calculated as follows: 2γ=CpPμλ=0.000665P, where P is the atmospheric pressure at the surface (in kPa), λ is the latent heat of vaporization of 2.45 MJ kg-1 and μ is the ratio of molecular weight of water vapor to dry air (which is 0.622). ET0 is presented here in the general daily form but is applied to the model on the sub-daily timescale; thus, it is divided by the number of time steps per day (in the current version 24).

Equation () uses the canopy surface resistance τs, which is the reciprocal of the non-water-stressed canopy conductance gp (in mm s-1). gp was also slightly changed, compared with , in order to include climate feedbacks. Following , we included a PFT-specific stomatal conductance parameter g1 as defined in and the vapor pressure deficit (D). 3gp=1000τs=g0+1.61+g1DAdtpa, where g0 (in mm s-1) is a PFT-specific minimum canopy conductance scaled by FPC, occurring due to processes other than photosynthesis. pa is the ambient partial pressure of CO2 (in Pa), Adt denotes the daily net daytime photosynthesis and 1000 is the unit conversion factor from millimeters to meters. D (in Pa) can be obtained by the canopy humidity qca and the saturation humidity qsat: 4D=qsat-qca. While the new potential evapotranspiration is calculated at the sub-daily time step, the non-water-stressed canopy conductance is calculated at a daily time step, due to the daily calculation of the photosynthesis in LPJmL5. As climate data from FMS are available on a sub-daily basis, the photosynthesis routine uses a diurnal average of air temperature and photosynthetic active radiation.

The newly calculated potential evapotranspiration, accounting for gp, is then also used in several LPJmL5 routines (e.g., bare soil evaporation or interception) instead of the equilibrium evapotranspiration (Eq), which was based on the Priestley–Taylor formula .

As a next step, we calculate the water-stressed transpiration Etr, using the supply–demand functions of LPJmL5 as follows: the demand is calculated by the newly implemented potential evapotranspiration (Eq. , corrected by the fraction used for interception), and the supply is driven by vertical root distribution and phenology as in. The initial transpiration is then a function of the minimum of supply and demand for water. Following this, transpiration is subtracted from the various soil layers, depending on water availability. If the available water is not sufficient, transpiration decreases. The adjusted transpiration is consequently used in an inverse version of the Penman–Monteith formula in order to calculate the actual canopy conductance, linked to transpiration gtr.

The total canopy conductance is additionally influenced by the conductance of soil evaporation (ge) and plant interception (gi). Therefore, we use a simple approach taking the maximum rainfall interception conductance (GIMAX=10 mm s-1) into account and considering the fraction of rainfall i stored in the canopy of a biome-dependent rainfall regime : 5gi=GIMAX⋅i⋅Pr/ET0⋅fv, where fv is the vegetated grid cell fraction, and Pr is the daily precipitation. Pr and ET0 are applied in millimeters per second (mm s-1) here. The soil-evaporation conductance is calculated for the non-vegetated area of a grid cell and depends on the maximum soil conductance (GEMAX=10 mm s-1; ) and an empirical scaling factor for the dependency of soil-evaporation conductance on soil water status (α0=10, ): 6ge=(1-fv)⋅GEMAX⋅exp⁡(α0⋅(wevap-1)), where wevap is the soil water content relative to the water-holding capacity available for evaporation defined for a certain soil depth . Both conductances are calculated at a daily time step.

We then calculate the total canopy conductance gc by adding gtr, gi and ge and using τaν following . 7gc=ρa1(gtr+gi+ge)+(1-βph)⋅τaν, where βph is the water available for photosynthesis: 8βph=min⁡Wr0.75⋅Wr*,1, with Wr as the actual soil water and Wr* as the maximum available soil water. The increment of the canopy humidity qca per time step is then calculated as follows, using gc: 9dqcadt=ET-qflux+dqsatdT⋅gc⋅dTdtdqfluxdqca+gc, where qflux is the water flux from the canopy layer to the atmosphere, provided by the FMS coupler; dTdt is the gradient of the surface temperature over time; and ET is the final evapotranspiration, consisting of transpiration, evaporation, interception and sublimation from surface or vegetation into the canopy layer. For the calculation of ET, we used the Penman–Monteith equation (Eq. ), now applying the total water-stressed canopy conductance gc (Eq. ). dqfluxdqca is the evaporation–humidity gradient. The total canopy conductance and the final increment of the canopy humidity, which is important for the FMS coupler, are calculated at a sub-daily time step. Equation () is based on and is derived in Appendix C.

It was also necessary to implement the calculation of surface/canopy temperature within LPJmL5, which required major adaptions to the energy cycle in LPJmL5. The stand-alone LPJmL5 model calculates the temperature of different soil layers by employing a temperature transport scheme and considering air temperature as climatic input. In CM2Mc, however, the energy balance is calculated on the surface and then passed to the coupler and the atmosphere. Therefore, we had to implement this energy balance analogously in the coupled version of LPJmL5. While this surface temperature depends on several inputs from the coupler, such as radiation, it also uses several variables connected to the water cycle in LPJmL5 (evaporation, sublimation and melted water). As our approach does not account for a height-dependent canopy temperature, we used the surface temperature as an approximation for the canopy temperature, which is needed to calculate canopy humidity and evapotranspiration. Hence, surface temperature and canopy temperature are assumed to be the same, following the approach in the LaD model .

The soil temperature is still important for internal processes in LPJmL, such as permafrost, but it is not needed in the coupler to calculate fluxes from the land to the atmosphere. The calculation of heat transfer in the soil layers uses the heat-convection scheme as in stand-alone LPJmL5 model by taking the air temperature into account, which highly depends on the canopy temperature. Both temperature calculations, for the surface/canopy temperature and for the soil temperature, operate at the fast time step.

In order to calculate the surface/canopy temperature within LPJmL5, we employed a simple energy balance formulation for the incremental change in temperature ΔT for each time step adapted from: 10ΔT=Rn-m⋅LEf+ET⋅LEv-Qsn-HCs⋅Δt, where m is the melted ice transformed to water (in kg m-2 s-1), LEf is the latent heat of the conversion of ice into water (in J kg-1), LEv is the latent heat of the conversion of water into vapor (in J kg-1), Qsn is the energy released by snow (in W m-2), H is the sensible heat provided by the FMS (in W m-2), Cs is the heat capacity of the soil (in J kg-1) and Δt is the fast time step duration (in s). Rn is used here in watts per square meter (W m-2). While the temperature is calculated individually for each stand, a weighted average over all stands within one grid cell is used in the humidity calculation and passed to the coupler. The heat balance of snow is calculated as performed for the soil layers see, where snow temperature changes (ΔTsnow) depend on the thermal conductivity (λsnow=0.2 W m-2 K-1) and heat capacity (Csnow=630000 J m-3 K-1) of snow as follows: 11ΔTsnowΔt=λsnowCsnow⋅Tair+Tsoil[0]-2⋅TsnowΔzsnow2. The heat flux from snow (Qsnow) is calculated as follows: 12Qsnow=λsnow⋅(Tsnow-ΔTsnow)zsnow, where zsnow is the snow depth, Tair is the air temperature and Tsoil[0] is the soil temperature of the first layer.

Albedo (β), the average reflectivity of the grid cell, is calculated as in , based on a first implementation by and later improved by considering several drivers of phenology by : 13β=∑PFT=1nPFTβPFT⋅FPCPFT+Fbare⋅(Fsnow⋅βsnow+(1-Fsnow)⋅βsoil), where the albedo for bare soil βsoil is defined as 0.3, and the albedo for snow βsnow is defined as 0.7. βPFT is calculated for each PFT depending on the foliage projective cover (FPC) and the stem, litter and leaf albedo of the respective PFT. The value for each parameter is as in . Fsnow and Fbare are the snow coverage and the fraction of bare soil, respectively. Water bodies such as lakes and rivers have a constant albedo value of 0.1.

Roughness length z0m is calculated according to : 14z0m=zbexp⁡-1d and 15d=∑i=1nPFTFPCiln⁡zbz0mi2, where zb is the height of the boundary layer under stable conditions, set to 100 m ; z0mi is the PFT-specific roughness length; and FPCi is the foliage projective cover of each PFT, respectively. The coupler uses the roughness length to calculate aerodynamic resistance and surface drag and provides these variables to the different sub-models of the ESM.

For a global model we also need to consider Antarctica, which has not been part of the standard grid of the stand-alone LPJmL5 modeling configuration. It was implemented using a simplified approach and will be replaced with the Parallel Ice Sheet Model (PISM, ) in the future. For now, Antarctica is assigned the ice soil type and a constant albedo of 0.7. The temperature balance is calculated as on the other continents.

In the stand-alone LPJmL5 model, sublimation is subsumed by a constant global value of 0.1 mm d-1, likely underestimating the sublimation at high latitudes. Especially in wintertime, we do not expect much evapotranspiration; hence, the sublimation changes with meteorological conditions and becomes an important process. For this reason, we implemented the calculation of sublimation Es using the formula from : 16Es=(0.18+0.098u)(es-ea), where u is the wind speed (in m s-1) from the coupler, es is the saturated vapor pressure (in mbar) and ea is the air vapor pressure (in mbar).

Furthermore, the first test runs of the coupled models proved the need to tune some LPJmL5 PFT-specific parameters: we increased the effective rooting depths of the tropical tree PFTs to 2.3 m in order to counter a negative AM2 precipitation bias in northern South America. Therefore, we increased the β value of each tropical tree PFT, describing their vertical fine-root distribution in the soil column from 0.96 as in to 0.99 in this study.

The analysis of the model stability was based on the pi-Control experiment, which ran over 750 years in total (see Sect. 2.5 for details). Here, we evaluate temperature and precipitation in terms of absolute values as well as the rate of change over time and the variability.

After the initial 300 years, the global temperature remains relatively stable at ca. 14.7 ∘C over the remaining simulation period of 400 years with a slight drift of less than of 0.05 ∘C per 100 years (Fig. a). The interannual variability in this period is ca. 0.1–0.2 ∘C. The decreasing temperature over most of the 750-year simulation period can be explained by the energy uptake of the ocean, as deep ocean layers are not yet in equilibrium. The average precipitation follows a similar trend as temperature and reaches a relatively stable state at around 2.88 mm d-1 after ca. 400 years, changing less than 0.01 mm d-1 over the remaining period (Fig. b). The interannual variability is 0.01–0.02 mm d-1.

The temperature evolution over the historical period (and hence the climate sensitivity to changes in atmospheric forcing) is evaluated by comparing the transient temperature increase in the 1880–2018 period of the TR experiment to GISTEMP evaluation data . We further evaluate the spatial impact of historical climate change without land use by comparing the years 2006–2015 of the PNV experiment with the last 10 years of the pi-Control experiment in the Supplement (Sect. S2).

The temperature evolution over the historical period from 1880 to 2018 is well captured as compared to GISTEMP evaluation data (Fig. ). Throughout the displayed period, temperature anomalies are negative before the year 1962 and remain positive afterwards, as climate change is accelerating. While the temperature anomalies are slightly underestimated between 1980 and 2010, GISTEMP and the TR experiment both have an average global temperature increase of 0.75 ∘C in the year 2018 relative to the reference period from 1951 to 1980. Our results are also within the range of CMIP5 models Sect. S4. The interannual variability in CM2Mc-LPJmL is ca. 0.5 ∘C and, thus, larger than in the GISTEMP data (ca. 0.25 ∘C), although the decadal changes are smaller in CM2Mc-LPJmL.

In the PNV experiment, climate change is also well captured, but it is weaker than when land use is included in the model (Fig. S5).

Basic climate patterns are well captured in the annual mean surface temperature (Fig. a), as temperatures are increasing from polar temperatures of below -10 ∘C towards the Equator with a maximum of ca. 25–30 ∘C in the tropics. Desert regions are usually warmer, whereas mountainous regions are colder than the surrounding area. In the high latitudes, ocean cells are usually a bit warmer than land cells due to the ocean's ability to store heat.

Between 1994 and 2003, the average global temperature is 15.6 ∘C compared with 14.3 ∘C in the ERA5 data set with a NME of 0.16. While the temperatures in the tropics and temperate zone are slightly overestimated (by ca. 1 ∘C), the poles and the boreal zone show a large negative temperature bias (up to -10 ∘C) (Fig. b). The Southern Ocean has a significant positive temperature bias (ca. 3 ∘C on average). Large differences between CM2Mc-LPJmL and ERA5 are also visible for mountainous areas, where the temperature bias is partly due to the coarse resolution of the model not adequately capturing the orographic influence of most mountain ranges on climate (e.g., the Andes or Himalaya).

While the seasonal cycle is usually well captured in CM2Mc-LPJmL, especially in Antarctica a strong seasonal temperature bias is partly balanced out in the annual mean temperature. The temperature over Antarctica is largely overestimated during the Southern Hemisphere summer, whereas it is underestimated during the Southern Hemisphere winter (Figs. S1, S2).

The latitudinal distribution of modeled mean temperature between 1994 and 2003 (Fig. c) shows similar values to ERA5 data from high- to midlatitudes in the Northern Hemisphere, but a slight overestimation in parts of the temperate zone and the tropics (between 70∘ S and 40∘ N). Specifically, the cold bias in the boreal zone leads to a slight underestimation of temperature between 60 and 90∘ N.

The comparison of CM2Mc-LPJmL (pi-Control) and pi-CM2Mc-LaD as in shows that similar biases in relation to ERA5 are present in both model versions. For example, both model versions slightly overestimate global temperature (Fig. S6). The strong regional biases compared with ERA5 data are also present in both model setups (Fig. S6) and are, therefore, not due to the implementation of LPJmL5.

The spatiotemporal pattern of global precipitation is well simulated with a global average of 2.86 mm d-1 and a maximum of up to 10 mm d-1 in the tropics close to the Intertropical Convergence Zone (ITCZ; Fig. a). Regions with little to no vegetation, such as deserts and polar areas, receive very little precipitation throughout the year.

Precipitation biases with respect to ERA5 data are, however, stronger than temperature biases, with an NME of 0.50 compared with 0.16 for temperature (Fig. b). The biases are strongest at the Equator with an apparent shift of the ITCZ. While precipitation in the Pacific is underestimated directly at the Equator, it is overestimated north and south of the Equator (Fig. b). Moreover, northern South America shows a large negative precipitation bias.

The seasonal patterns (Figs. S3, S4) confirm the imprecise modeling of the ITCZ, which remains north and south of the Equator for a large part of the year and passes the Equator region relatively swiftly. While precipitation south of the Equator is overestimated, it is underestimated north of it.

The latitudinal annual mean precipitation between 1994 and 2003 (Fig. c) compares well with observations, displaying the global precipitation maximum in the tropics, local minima in the subtropics and very low values at high latitudes. The tropics, however, show a shifted maximum. While the ERA5 global precipitation maximum over the Pacific is at ca. 10∘ N and a local smaller maximum is at -10∘ S, CM2Mc-LPJmL models the global maximum at roughly -10∘ S and a smaller local maximum at ca. 10∘ N. The difference between the two maxima is less pronounced compared with ERA5.

The comparison of the results of CM2Mc-LPJmL with the original pi-CM2Mc-LaD model shows similar biases in relation to ERA5 for both model versions. Neither of the models precisely captures the behavior of the ITCZ, especially over the Pacific. Both models also show a large dry bias in northern South America (Fig. S6).

While the evaluation of temperature and precipitation is performed for the years 1994–2003, we compare average model results for aboveground biomass (AGB) and the dominant PFT for the years 2006–2015 due to availability of evaluation data.

Simulated AGB shows a good pattern overall, with the largest values in the tropics, decreasing biomass in the subtropics, and a local maximum in the temperate and boreal zone (Fig. d). In vegetation-free areas, such as deserts or polar regions, simulated AGB is zero or very close to zero (less than 200 g C m-2). When comparing AGB against GlobBiomass (Fig. a), spatial differences emerge (Fig. c). While simulated AGB is slightly overestimated in boreal North America and Asia, it is underestimated in the European temperate zone and in Scandinavia, extending into eastern Europe and West Siberia. In most of the other temperate, Mediterranean-type and subtropical regions, AGB matches the observed values. In the tropics, AGB is overestimated in semiarid regions, whereas wet tropical rainforests are mostly underestimated, especially the eastern Amazon. AGB shows good agreement in the seasonally dry Cerrado region in South America but appears to be overestimated in the Caatinga in northeastern Brazil. In central Australia, AGB matches observations but is overestimated in the northern part of the continent and underestimated in the southeastern part (Fig. c).

Figure d compares the latitudinal mean of CM2Mc-LPJmL and LPJmL-offline with the evaluation data. LPJmL-offline shows better performance than the coupled model, with a smaller NME (0.35 vs. 0.56) and a better R2 (0.94 vs. 0.64). While both models underestimate biomass in the tropics, biomass in the boreal zone is overestimated by CM2Mc-LPJmL and underestimated by the stand-alone LPJmL5 model compared with GlobBiomass. The LPJmL5 stand-alone version is forced by a reanalysis climatic input with a 0.5∘ spatial resolution, and the model is calibrated to this specific climate conditions; therefore, better model performance is expected. Modeled biomass is also within the range of CMIP5 models (Fig. S7).

The geographic distribution of dominant PFT cover in CM2Mc-LPJmL follows the spatial pattern of the biomass distribution (Fig. a). The tropics are mostly dominated by the evergreen tree PFT. In the tropical savanna areas, the tropical deciduous tree PFT dominates, along with the C4-grass PFT. The temperate zone is dominated by land use with some summergreen trees – most common in areas such as Europe. The boreal zone is correctly covered by boreal needle-leaved and boreal summergreen trees, and the tundra zone is covered with polar grasses. To better visualize the model error for the PFT distribution, we produced an error map that consists of the sum of the square error for each PFT per cell (Fig. b). In tropical rainforests, the error with respect to the evaluation data is relatively small. Drier savanna areas show a much larger error, as do parts of the temperate and the boreal zone. Areas with a small FPC fraction show a small error because the error metric takes absolute errors into account. This applies to desert regions in Africa, the Arabian Peninsula and central Australia.