The lgm simulation is a CMIP6 Tier 1 experiment, as well as one of the two possible PMIP4 entry cards (i.e. one of the two simulations that must be performed by modelling groups wishing to officially take part in PMIP4). The lgm simulation will be compared to the CMIP DECK (Diagnostic, Evaluation and Characterization of Klima) pre-industrial control (piControl) for 1850 CE and the CMIP6 historical experiment (Eyring et al., 2016) and must therefore be run using the same version (including level of complexity and the interactive feedbacks) and resolution of the model and following the same protocols for implementing external forcings as in these two reference simulations.

The minimum set of changes that must be made for the lgm simulation, compared to the set-up of the piControl, are the insolation, GHG, and ice-sheet forcings (see Sect. 4 for the implementation of these changes). There are several plausible alternatives for the ice-sheet forcing and modelling groups can choose between one of three options (Fig. 1): the ice-sheet reconstruction produced for PMIP3 (Abe-Ouchi et al., 2015), the ICE-6G_C reconstruction (Peltier et al., 2015; Argus et al., 2014), or the GLAC-1D (Tarasov et al., 2012; Briggs et al., 2014; Ivanovic et al., 2016). However, if the PMIP4 transient last deglaciation experiment is run (Ivanovic et al., 2016), the modelling groups should ensure consistency between the LGM simulation and subsequent transient phase of the experiment, when possible.

The dust and vegetation forcing in the Tier 1 lgm experiment must be imposed in a manner that is consistent with the DECK simulations. Models that include interactive dust, for example, should allow interactive emissions at the LGM. For this purpose, two alternative reconstructions of LGM dust emission regions are provided for models without dynamic vegetation (Hopcroft et al., 2015; Albani et al., 2016: see the PMIP4 website) and modelling groups are free to choose either one of these. If dust-enabled models do not include dynamical vegetation, then vegetation should be changed in the LGM dust emission regions so that dust emission can occur (e.g. by imposing bare soil or a fractional grass cover). Both dust data sets provide atmospheric mass concentrations, which could alternatively be used to compute a corresponding radiative forcing in a consistent manner as for the reference simulations. Modelling groups can also use a climatology of atmospheric dust mass concentrations produced offline by their own dust model, using dust emission regions and vegetation as above. Otherwise the lgm simulation should be run using the same forcing as for the DECK and historical runs (i.e. with no increase in dust). Unless a model includes dynamic vegetation or interactive dust, the vegetation should be prescribed to be the same as in the DECK and historical runs.

The relative flexibility of the set-up summarized above reflects the range of model configurations foreseen for CMIP6 and PMIP4, in particular in terms of the representation of vegetation and dust. In the case of the ice sheets, it also reflects the uncertainties in our knowledge of the boundary conditions. Taking this uncertainty into account is new to the PMIP LGM experimental design but is essential for evaluating the CMIP6-type models. The differences between the reconstructed ice-sheet altitude can be as large as several hundred metres (e.g. over the North American ice sheet), which can be enough to induce differences in the Atlantic jet stream (Beghin et al., 2016).

The concentrations of the atmospheric trace gases should be set to

190 ppm for CO2,

The astronomical parameters should be set to their 21 ky BP values, according to Berger (1978):

eccentricity = 0.018994,

The ice sheet can be set to one of the following reconstructions (Fig. 1): GLAC-1D (Tarasov et al., 2012; Briggs et al., 2014; Ivanovic et al., 2016), ICE_6G-C (Peltier et al., 2015; Argus et al., 2014), or PMIP3 (Abe-Ouchi et al., 2015). GLAC-1D and ICE_6G-C are the most recent reconstructions and are compatible with the set-up of the PMIP4 deglaciation simulation (Ivanovic et al., 2016). The use of the PMIP3 ice-sheet reconstruction allows direct comparison with the PMIP3 simulations. These ice-sheet reconstructions significantly differ with each other, in particular in terms of altitude, with differences reaching several hundred metres over North America and Fennoscandia (Fig. 1 and Ivanovic et al., 2016, Fig. 2). This uncertainty in the boundary conditions results from the different approaches used for the reconstructions, which are summarized in Ivanovic et al. (2016).

The implementation of the LGM ice sheets will vary from one model to the other. Here, we give the main implementation steps that have been followed for the IPSL climate model (Fig. 3). The details of the implementation may differ for other models, but the same steps should be followed and documented.

The LGM sea-level drop leads to expanded continents and this can mean that prescribed river courses no longer reach the ocean. The North American and European ice sheets also disrupt river courses. At a minimum, the LGM rivers must be set up to ensure they reach the oceans. For instance, the European rivers that today drain into the Nordic and Baltic seas can be redirected to the North Atlantic via the paleo-English Channel (see e.g. Alkama et al., 2006). More realistic river-routing files compatible with the ice-sheet reconstructions will also become available at a later stage.

It is highly possible that the snow mass balance over the ice sheets is positive, resulting in a sink of freshwater in the climate model. If this is the case, the average value of the sink (e.g. the average for a 10-year period) should be computed and released to an adjacent ocean, to guarantee closure of the freshwater budget. This should be done following the same procedures as for the DECK experiments or following the procedure advised since PMIP2, which was to compensate for the sink of freshwater by imposing a freshwater flux in broad regions of oceans adjacent to the ice sheets (e.g. the Arctic and North Atlantic north of 40∘ N for the North American ice sheet). As this decision might have a large impact on the global ocean overturning circulation, it must be precisely documented (cf. Sect. 4.10).

Models including dynamical natural vegetation should use the corresponding module on all unglaciated continents, in the same way it is used for natural vegetation in other CMIP6 simulations. Modelling groups who do not run with dynamical natural vegetation should use the same vegetation cover as for piControl, extrapolated to the lgm land mask, in their PMIP4-CMIP6 experiment. There is insufficient information to construct a reliable global map of vegetation at the LGM, but one way to take account of LGM vegetation changes in models without dynamic vegetation is to run a biogeography or dynamical vegetation model offline, using climate forcing from the LGM simulation, and to then prescribe the simulated vegetation patterns in the coupled climate model. This ensures that the prescribed vegetation will be consistent with the climate forcing for the given model. These simulations will then be PMIP4 sensitivity experiments (cf. Sect. 3.2.1). A minimum change for models with interactive dust modules will be to remove vegetation from (or only to allow grass in) regions of strong potential dust emissions (cf. Sect. 4.6 below).

There are several options for implementing dust forcing according to the model's complexity and to the availability of different data sets. Three series of dust data sets are provided. Two of them are based on model simulations (Albani et al., 2014, 2016; Hopcroft et al., 2015). Both models include a prognostic dust cycle, based on different formulations of the dependency of emissions on wind speed, soil moisture, and vegetation cover arising from the work of Marticorena and Bergametti (1995) and Fécan et al. (1999). In one case (Albani et al., 2014) pre-industrial vegetation is prescribed for physical climate for both PI and LGM climate conditions, but LGM dust emissions at each grid cell are scaled by the non-vegetated fraction, resulting from an offline vegetation reconstruction with BIOME 4 (Kaplan et al., 2003), in equilibrium with LGM climate conditions. In the other case (Hopcroft et al., 2015) a dynamical vegetation model was used to determine the erodible surface. These differences result in different dust emission fields. Furthermore, Albani et al. (2014, 2016) further refined their dust emissions by scaling the soil erodibility at the continental scale in order to have a better match to paleodust observations in terms of deposition fluxes. The third data set (Lambert et al., 2015) is a reconstruction of dust deposition, essentially based on geo-statistical interpolation of paleodust observations. The three data sets have different specifications in terms of dust size distribution: four size bins spanning 0.1–10 µm diameter (Albani et al., 2014), six size bins spanning 0.0316–31.6 µm radius (Hopcroft et al., 2015), and bulk i.e. integrated over the entire observed size range (Lambert et al., 2015). This has implications for imposing proper constraints on the global dust cycle, e.g. magnitude of emissions (Albani et al., 2014), as well as for dust radiative forcing, when considered in combination with the prescribed dust optical properties (Kok et al., 2017). Therefore modelling groups should carefully account for this aspect when integrating one of these data sets into their model framework.

For models with interactive dust modules but without dynamic vegetation, it is advisable to take into account the more extensive dust sources at LGM. These are described by the “erodibility map” from the Albani et al. (2016) data set and a bare soil map for the Hopcroft et al. (2015) data (Fig. 6a and b, respectively). For these regions, vegetation must be set to either low vegetation (grasses) or bare soil; otherwise, the source functions should be adapted depending on the precise formulation of the dust emission module in the particular model (e.g. Ginoux et al., 2001) so that dust emissions are allowed. For models that compute the dust radiative forcing from atmospheric dust mass loading, two data sets are available for the LGM: Albani et al. (2014, 2016) and Hopcroft et al. (2015). The prescribed LGM mass loading should be implemented as perturbations of the piControl loading, i.e. by either adding an anomaly to these piControl loads or by multiplying them by a ratio, the anomaly, or the ratio being computed from the Albani et al. (2014, 2016) or Hopcroft et al. (2015) data sets. Alternatively, modelling groups can compute their own atmospheric dust mass loads offline and use them as prescribed fluxes in their coupled simulations.

Both dust data sets also provide radiative forcing. These should not be used directly because the specified radiative properties of dust vary among models, and using the forcing from the models used to produce the dust fields would be incompatible with other CMIP6 experiments. The dust radiative forcing provided with the data sets is only given with the purpose of broad comparison with the modelling groups' own model output (Fig. 6c and d).

Models including marine biogeochemistry should use LGM dust deposition on the oceans, using the same data set as for the atmospheric forcing (Fig. 6e and f). If LGM dust atmospheric forcing cannot or is not taken into account, then the Lambert et al. (2015) data set can also be chosen (Fig. 6g).

Modelling groups undertaking the implementation of dust in their models are advised to perform a first trial with an atmosphere-only simulation, as run-away effects involving dust, vegetation, and climate have been experienced by some modelling groups (Hopcroft and Valdes, 2015b). In the latter case, it was the choice of parameters in the dynamic vegetation model which proved to be inadequate.

The global amount of dissolved inorganic carbon, alkalinity, and nutrients should be initially adjusted to account for the change in ocean volume. This can be done by multiplying their initial value by the relative change in global ocean volume. Other features that may need adjustment, given the changes in coastlines and bathymetry, include the amount of nutrients brought by rivers and by boundary exchange at the ocean–sediment interface. Modelling groups must document any such changes in the description of their simulations (cf. Sect. 4.10).

First, it is suggested to run the atmosphere model separately, using the sea surface temperatures and sea ice from the ocean's initial conditions, in order for the atmosphere to adjust to the topography and surface-type changes. At this stage, it is advised to check that the total atmospheric mass (or globally averaged surface pressure) is the same as for piControl. This run will yield an initial state for the atmospheric component of the model.

The ocean should be initialized with a salinity 1 psu higher than for piControl, which is consistent with the sea-level difference between LGM and piControl (and the volume of freshwater stored in the ice sheets). Similarly, ocean biogeochemistry models should adjust their alkalinity and models including oxygen isotopes should initialize them with a Standard Mean Ocean Water (SMOW) of +1 ‰. The ocean model can be initialized from a piControl experiment or from previous LGM experiments, to minimize spin-up duration.

Practically, the ocean model can be generally initialized from a piControl ocean state with adjusted salinity (and oxygen isotope, if applicable), or from previous LGM experiments (e.g. with well-stratified glacial ocean states), to minimize spin-up duration. Such ocean states, such as described in Werner et al. (2016), which provide 3-D fields of sea temperature, salinity, and associated stable water isotopes on a regular 1∘ × 1∘ grid, are available on the PMIP4 website and from the PMIP2 and PMIP3 databases.

The model should be spun up until equilibrium. In previous PMIP protocols (in particular http://pmip2.lsce.ipsl.fr) the simulations were considered at equilibrium when the trend in globally averaged SST was less than 0.05∘C/century, the Atlantic Meridional Overturning Circulation (AMOC) was stable and, for models including representations of the carbon cycle or dynamic vegetation, the requirement was that the carbon uptake or release by the biosphere is less than 0.01 Pg C per annum. Recent works give other criteria or recommendations for defining or reaching the equilibrium. For instance, to avoid impacts of potential transient characteristics in the deep ocean on AMOC strength (Zhang et al., 2013), the equilibrium ocean should ensure that the trend in zonal mean sea salinity in the Southern Ocean (south of the winter sea-ice edge) remains small, especially in the Atlantic sector. Marzocchi and Jansen (2017) show that the AMOC has to be monitored on multi-centennial timescales because variability on the timescales of decades to a century prevents a precise determination of the trends, and hence of whether the model is close to equilibrium or not.

It is required that at least 100 years of data from the equilibrated part of the simulation is stored on the ESGF (Earth System Grid Federation). In order to document the approach to equilibrium, we recommend that the modelling groups monitor the variables listed in Table 3 and save them for model documentation (cf. Sect. 4.10). We recommend these data be saved for at least a few hundred years before the period stored on the ESGF and for the ESGF period, so that the trends in these variables can be better determined. This will help characterize the “ESGF period” within the full simulation and make us aware of possible remnant drifts. The same variables should also be provided for the corresponding piControl simulation, for comparison.

Experience gained from previous phases of PMIP suggests there can be several problems setting up an LGM simulation, including

failure to close the freshwater budget, which can arise from either inadequate compensation for a positive snow mass balance over the ice sheets or from rivers not reaching the ocean,

The documentation of the simulations should include

the model version used, in particular in terms of vegetation and dust representations (interactive, prescribed, or absent),

CMIP6 simulations can be documented through their “ripf” code, these letters standing for “realization”, `initialization”, “physics”, and “forcing”. In practice, each of these letters is followed by a number which indicates

after the “r”: the simulation number in the ensemble of simulations with the same characteristics;

The first digit should describe the ice-sheet reconstruction. It should be set to

1 for ICE_6G-C,

The second digit should describe the vegetation. It should be set to

0 if piControl vegetation is used,

The data should be formatted so as to comply with the CMIP6 standards (to be documented in the GMD CMIP6 special issue; cf. Eyring et al., 2016) and PMIP4 data request (Kageyama et al., 2016) so that analyses including other PMIP and CMIP6 simulations can be performed easily. The current list of variables is given in the Supplement but is still subject to potential changes following adjustments of the full CMIP6 list. The PMIP4 data request can be found on the PMIP4 website (https://pmip4.lsce.ipsl.fr/doku.php/database:pmip4request#the_pmip4_request).