The Last Glacial Maximum (LGM; ∼ 21 ka) is of interest to the climate research community because of the relative abundance of proxy data and because it is the most recent profoundly different climatic state of our planet. For these reasons, the LGM is extensively studied in modelling frameworks (e.g. Menviel et al., 2017; Brady et al., 2012; Otto-Bliesner et al., 2007; Bouttes et al., 2011; Buchanan et al., 2016; Lynch-Stieglitz et al., 2016; Kageyama et al., 2017). Model simulations of the past ocean can not only provide a method to gain a mechanistic understanding of marine proxy records, but they can also inform us about model performance in a different climatic state of the Earth system (Braconnot et al., 2012). Typical state-of-the-art tools to simulate the (past) Earth system are climate or Earth system models as used, for example, in the Coupled Model Intercomparison Project phase 5 (CMIP5; Taylor et al., 2011). Besides simulating our present climate, these CMIP5 models are also used to simulate past climate states (such as the LGM) in the Palaeoclimate Modelling Intercomparison Project phase 3 (PMIP3). However, the computational costs and runtime of such fully coupled model frameworks are a major obstacle for their application to palaeoclimate modelling. Palaeoclimate modelling optimally requires long simulations (thousands to tens of thousands of years) in order to provide the necessary time for relevant processes to emerge (e.g. CaCO3 compensation) (Braconnot et al., 2007). Complex fully coupled models can not typically be run into full equilibrium (which requires hundreds to thousands of years of integration) due to computational costs (Eyring et al., 2016). Therefore, the PMIP3 models exhibit model drift (especially in the deep ocean; e.g. Marzocchi and Jansen, 2017). Since significant differences between a (drifting) non-equilibrated state and the equilibrium model state can impede the comparison of model results with proxy data, a well equilibrated model with minimal drift is desirable. The third phase of the PMIP project (Braconnot et al., 2012) limits global mean sea surface temperature drift to under 0.05 K per century and requires the Atlantic Meridional Overturning Circulation to be stable (Kageyama et al., 2018).

We refer to a “forced ocean model” as a model of the ocean–sea-ice–atmosphere system in which the atmosphere is represented by prescribed 2-D forcing fields. Such model set-ups have been extensively used in model intercomparison studies such as the Coordinated Ocean-ice Reference Experiments (COREs; Griffies et al., 2009) and more recently in the CMIP6 Ocean Model Intercomparison Project (OMIP; Griffies et al. 2016). A forced ocean model can be used whenever ocean–atmosphere feedbacks are of minor importance, and it has the advantage of reducing the computational costs – making longer or more numerous model runs feasible. The use of PMIP output in forced ocean modelling is common practice (e.g. Muglia and Schmittner, 2015; Khatiwala et al., 2019). Until now, however, there is no standardized dataset available that can be used to easily derive a Last Glacial Maximum model forcing. Therefore, we present 2-D (surface) anomaly fields of CMIP5/PMIP3 experiments of “lgm” (representing the Last Glacial Maximum state of the Earth system) minus “piControl” (representing the pre-industrial, PI, state) calculated from monthly climatological PMIP3 output. The PMIP3 output is the result of global boundary conditions and forcings (such as insolation and ice sheet cover) applied in the fully coupled PMIP3 models (Braconnot et al., 2012). Our dataset (Morée and Schwinger, 2020) is a unique compilation of existing data, which has been processed and reformatted such that it can be readily applied in a forced ocean model framework that uses a bulk forcing approach similar to Large and Yeager (2004). Since this approach has been popularized through coordinated model intercomparison activities (Griffies et al., 2009), a majority of forced ocean models today use this approach. The 2-D anomaly fields presented here can be added to the pre-industrial forcing of a forced ocean model in order to obtain an atmospheric forcing representative of the LGM. The data are climatological mean anomalies, and as such they are suitable for equilibrium LGM “time-slice” modelling of the ocean. In Sect. 2, a general description of the dataset and data sources is provided alongside an overview of the variables (Table 1). The description of the procedure followed to make this dataset (Sect. 3) should support any extension of the dataset with additional (PMIP-derived) variables if needed. The PMIP4 guidelines (Kageyama et al., 2017) can support users in designing a specific model set-up, for example, regarding the land–sea mask, trace gas concentrations, river run-off, or other conditions and forcings that one would want to apply to a model. Limitations of the dataset are discussed in Sect. 4.

The data presented in this article are 2-D anomaly fields of the LGM versus the pre-industrial state based on PMIP3 (Braconnot et al., 2012). We note that the PMIP3/CMIP5 pre-industrial state, which is the result of piControl experiments, represents the year 1850 and is therefore strictly speaking already influenced by anthropogenic forcing (e.g. Eyring et al., 2016). Our anomaly fields can be used as atmospheric LGM forcing fields for ocean-only model set-ups when added to pre-industrial forcing fields (as done by, for example, Muglia and Schmittner, 2015; Khatiwala et al., 2019) and are optimized for use in combination with CORE forcing fields (Griffies et al., 2009). We note that the CORE forcing is based on modern era (1948–2009) reanalysis and observations and thus is not a pre-industrial forcing. However, the anthropogenic climate signal contained in these data is relatively small, particularly in comparison to the uncertainties of the LGM–PI anomalies (see below). The basis of the anomaly data is monthly climatological PMIP3 output. Any variables presented at sub-monthly time resolutions are therefore time-interpolated. We chose to time-interpolate the variables to their respective time resolution in the CORE Normal Year Forcing format (CORE-NYF; Large and Yeager, 2004). The anomalies are calculated as the mean of the difference between monthly climatologies of the “lgm” and “piControl” PMIP3 model runs. In cases where modelling groups provided more than one ensemble member, we included only the first member in our calculations. The data are the mean anomaly of five PMIP3 models (CNRM-CM5, IPSL-CM5A-LR, GISS-E2-R, MIROC-ESM, and MRI-CGCM3; Table 2) as only these models provide output for all variables. A discussion on the limitations of our dataset is provided in Sect. 4.

The variables are (i) near-surface specific humidity, (ii) downwelling long-wave radiation, (iii) downwelling short-wave radiation, (iv) precipitation, (v) wind (v and u components), (vi) near-surface temperature, and (vii) sea surface salinity (SSS) (Table 1). The SSS anomaly field can be used to adjust SSS restoring in LGM simulations.

All variables (Sects. 3.1–7) of the monthly climatological PMIP3 output have been regridded (Table 3, #1), averaged (Table 3, #2), and differenced (Table 3, #3) to calculate the anomaly fields. Additional procedures for each variable are provided in the respective part of Sect. 3, together with a figure of each variable's annual mean anomaly and model spread. Alongside the lgm–piControl anomaly for each variable, the model spread across all five models has been made available. The individual model anomalies for each of the variables are presented in Fig. A1. In order to give the reader the opportunity to compare the anomaly data with typical pre-industrial values for each of the variables, we provide the multi-model annual mean for the piControl experiment in Fig. A2.

The inter-model disagreement is described for each variable in Sect. 3 and could, for example, be used to guide adjustments to the amplitude of the forcing anomaly for model tuning purposes. Additionally, proxy-based reconstructions are available for some of the variables, which can constrain potential adjustments to the forcing anomaly fields. We note, however, that for none of our variables does a purely proxy-based global reconstruction exist – underlining the value of model-based reconstructions. A combination of model and proxy data makes it feasible to create global coverage for air temperatures (e.g. Annan and Hargreaves, 2013), but we are not aware of similar efforts for any of our other variables. Regional proxy-based reconstructions, although mostly quantitative and only over the continents, exist for humidity (e.g. Alexandre et al., 2018), precipitation (e.g. Mendes et al., 2019), and wind direction and strength (e.g. Markewich et al., 2015). Regarding ocean proxies, salinity reconstructions are highly uncertain (Rohling, 2000) but could also provide some constraint to the model data. We leave the decision to the individual modelling groups whether to adjust their forcing fields for their specific application. All operations were performed with NetCDF toolkits Climate Data Operator (CDO) version 1.9.3 (Schulzweida, 2019) or netCDF Operator (NCO) version 4.6.9. The main functions used are documented in Table 3 and referred to in the text at the first occurrence. The atmospheric anomaly data are on a Gaussian grid with 94 × 192 (lat × long) grid points. The SSS fields are on a regular 180 × 360 (lat × long) grid. Regridding any of the files to a different model grid should be straightforward (e.g. Table 3, #1) as it was ensured that all files contain the information needed for re-gridding. The variables, grid, and time resolution are chosen to be compatible with the CORE forcing fields (Large and Yeager, 2004), which have been extensively used in the ocean modelling community as they are the standard in ocean model comparisons (Griffies et al., 2009, 2016). We anticipate that the variables selected here should be useful in different model set-ups as well. We intend to provide a dataset that is flexible with respect to the use of different land–ocean masks in different models. Therefore, we account for changes in sea level (i.e. a larger land area in the LGM) which can affect variables in coastline areas by applying the following masking procedure: (i) masking the multi-model mean anomaly with the maximum lgm land mask across all models, then (ii) extrapolating the variable over land using a distance-weighted average (Table 3, #4), and (iii) finally masking the data with a present-day land mask (based on the World Ocean Atlas 2013 1∘ resolution land mask) but with the ocean extended in a 1.5∘ radius over land. Therefore, our anomaly forcing dataset can likely be used with any pre-industrial land–sea mask. By following this procedure, the grid points affected by land–sea mask changes are thus filled with the extrapolated model mean anomaly from the LGM coastal ocean. In the case of NorESM-OC (Schwinger et al., 2016), the atmospheric anomaly fields were added to its CORE-NYF fields (Large and Yeager, 2004) to obtain an LGM normal-year forcing under the assumption of unchanged spatial and temporal variability for the respective variable. Note that the addition of the anomaly fields to the user's own model forcing could lead to physically unrealistic and/or non-meaningful results for some variables (such as negative precipitation or radiation). This must be corrected for by capping off sub-zero values (Table 3, #5) after the addition of the anomaly.

The anomaly fields presented here are a model-based “best estimate” of the LGM anomaly relative to the pre-industrial state. There are some important limitations to these data related to the temporal resolution, the use of model means, and the fact that we rely on modelling results only.

Proxy data with global coverage are unavailable for most of the variables needed to force stand-alone ocean models. We do not attempt to constrain the anomaly fields using the spatially limited information from available proxy data. Consequently, where PMIP3 models are in disagreement with proxy data, our dataset will be so, too. The limitations (or uncertainty) of the PMIP3 simulations can be seen through the large inter-model spread which is provided with the anomaly data. This does not preclude the possibility that PMIP3 models collectively (i.e. such that the model spread is small) disagree with available proxy data. Nevertheless, PMIP3 is the state of the art for the modelling of past climates at present (Braconnot et al., 2012; Braconnot and Kageyama, 2015).

By adding multi-model mean anomalies to forcing fields, dynamical inconsistencies (e.g. between wind and temperature fields) will be created. This means that the resulting forcing fields do not strictly obey the equations of state or motion. A forcing dataset would typically be dynamically consistent if the forcing would be the outcome of an atmospheric model or an advanced reanalysis. The advantage of using model mean fields is that large anomalies of individual models will be smoothed out where models disagree. We believe that currently a main challenge for palaeo-modelling activities is to achieve integration times that are long enough. Therefore, using a single forcing (as opposed to using multiple forcings from individual models) seems to be preferable. Regarding the dynamical inconsistencies, it is important to note that the CORE forcing itself (for which our dataset is optimized) is a mixture of reanalysis and observational data products and as such not dynamically consistent.

PMIP3 model output is publicly available only as monthly mean fields, which also results in some limitations for the anomaly forcing dataset. First, although we interpolate the monthly mean anomaly fields to a higher (e.g. 6-hourly) temporal resolution, we implicitly assume that any sub-monthly variability (e.g. the diurnal cycle) is preserved from the pre-industrial climate state to the LGM state. We can currently not quantify the implications of this assumption, but future phases of PMIP (providing simulation output with higher temporal resolution) might alleviate this problem. Second, we are not able to accurately re-reference near-surface temperature and humidity to a different reference height. The CORE bulk forcing method of Large and Yeager (2004) requires near-surface specific humidity and temperature at the same height as the wind forcing (at 10 m). Humidity and temperature are, however, provided at 2 m height in PMIP3 (as in most atmospheric data products). A procedure to re-reference humidity and temperature from 2 to 10 m (e.g. Large and Yeager, 2004) requires input data at a higher (sub-daily) time resolution in order to resolve different boundary layer stability regimes. However, for an anomaly forcing, the re-referencing only has an effect if it leads to different temperature and/or humidity increments under the PI and the LGM state. For the open ocean, this is barely the case, and taking a climatological anomaly of 2 m quantities and applying it at 10 m height is unproblematic. Over sea ice, however, there could be a larger effect of the re-referencing (due to a significantly different atmospheric stability in the LGM state), especially regarding the temperature. Our analysis indicates that this is probably the case over the central Arctic Ocean (not shown). For all other regions, we estimate that the error made in applying the re-referencing approach on monthly climatological-resolved data does not justify its application. In general, the error made by omitting the re-referencing is much smaller than the uncertainties of the anomalies (i.e. the model spread), particularly at high latitudes.

Regarding the robustness of the dataset, we observe that the inclusion of additional model data only leads to minor changes in the anomalies. An example of this is given by comparing version 1 (Morée and Schwinger, 2019) and the current version 3 (Morée and Schwinger, 2020) of this dataset, as the latter also includes the GISS-E2-R model for the calculation of the anomalies. Indeed, individual model anomalies (Fig. A1) show broad agreement, although the magnitude of the anomaly is less agreed on (as discussed in more detail for the individual variables in Sect. 3).

Despite the limitations described here, we believe that using the mean PMIP3 anomaly of coupled models as forcing is currently the best available option for use in stand-alone ocean models. For this purpose, our dataset provides lgm–piControl anomalies in standardized format for the most common variables used in ocean forcing.

The data are publicly accessible at the NIRD Research Data Archive at 10.11582/2020.00052 (Morée and Schwinger, 2020). The .md5 files contain an md5 checksum, which can be used to check whether changes have been made to the respective NetCDF files.

The output of the fully coupled PMIP3 simulations of CNRM-CM5, IPSL-CM5A-LR, MIROC-ESM, MRI-CGCM3 and GISS-E2-R is converted to anomaly datasets intended for use in forced ocean modelling of the LGM. All anomalies are calculated as the difference between the “lgm” and “piControl” PMIP3 experiments. In addition, all data are formatted in a way that further conversions (of, for example, units or the grid) can be applied in a straightforward way. The variables are provided in NetCDF format in separate files and distributed by the NIRD Research Data Archive (Morée and Schwinger, 2020). A climatological LGM forcing dataset can be created for any forced ocean model by the addition of the presented 2-D anomaly fields to the model's pre-industrial forcing. This approach enables the scientific community to simulate the LGM ocean state in a forced ocean model set-up. We expect that if additional forcing is needed for a specific model, the same approach as described above can be followed. This process is simplified by providing all main CDO and NCO commands used in creating the dataset (Table 3). All data represent a climatological year, i.e. one annual cycle per variable. The application of the data is thus suitable for “time-slice” equilibrium simulations of the LGM and optimized for use with the CORE forcing format (Large and Yeager, 2004).

The uncertainty of our anomaly forcing (approximated by the model spread of the PMIP3 models) is generally of similar magnitude as the multi-model annual mean. The complete attribution of the model spread to specific processes is beyond the scope of this article, but our results show that there is considerable uncertainty involved in the magnitude of the anomaly for all variables presented here. Nevertheless, all mean anomalies show a distinct spatial pattern that we expect to be indicative of the LGM–PI changes. Finally, there is currently no other way to reconstruct most of these variables than model simulations with state-of-the-art Earth system models such as those applied in the PMIP3 experiments. For modelling purposes, the inter-model disagreement of PMIP3 provides the user with leeway to adjust the amplitude of the forcing (guided by the size of the model spread, which is therefore provided alongside the variables in the dataset). Such adjustments can improve model–proxy data agreements, such as those described for salinity in Sect. 3.7.