Because the models have interactive dust emissions, wind fields play a prominent role in dust emission and transport . Therefore, this study contrasts two different present-day forcing experiments: one with winds generated by the dynamical part of the climate model (named PD) and the other nudged to reanalysed winds (named PDN) from ERA-Interim . The historical greenhouse gas concentrations are consistent with . The models IPSL and IPSL-4DU were run without explicit gas-phase interactive chemistry activated; therefore, they use the CMIP6 ozone forcing database . The CNRM-ESM2-1 has explicit chemistry in the stratosphere and upper atmosphere . A last simulation wherein aerosols and chemistry emissions are prescribed for 1850 (named PI) is presented as well; see Table . All the simulations are from 2000 to 2014 plus at least 1 year of spin-up (except NorESM-PDN that covers 2001 to 2014). All the simulations implement prescribed sea surface temperatures (SSTs) of present-day conditions according to the input4MIPs dataset . The solar forcing implemented by all the models is derived from the dataset of . The comparison between the PD and PDN experiments provides information on the role of wind fields in explaining model diversity. The difference between PD and PI dust emissions allows us to evaluate whether the effects in the climate system due to non-dust emissions have a discernible impact on the global dust cycle (as both PD and PI have been prescribed with the same SSTs). A summary of the properties of the model experiments is given in Table .

This dataset comprises deposition flux observations described in composed of several measurement campaigns over land and ocean (Fig. a), hereafter named Network-H2011, plus an additional set of measurements at stations in the Mediterranean and Sahel regions (Fig. b), hereafter named Network-SET-M, for which data values are shown in Table S.MD.5.

The set Network-H2011 gives deposition fluxes estimated from sedimentation corresponding to the DIRTMAP (Dust Indicators and Records of Terrestrial and MArine Palaeo-environments) database , while direct measurements of deposition fluxes were acquired during the SEAREX campaign , mostly in the Northern Hemisphere. describe 28 sites where dust deposition is inferred assuming a 3.5 % fraction of iron. The compilation also includes observations of deposition fluxes deduced from ice core data according to . The dataset covers a range of total dust flux deposition from 10-3 to 0.5×103 gm-2yr-1 but without a homogeneous distribution of values over this range. Only two stations have observational values larger than 100 gm-2yr-1, and the bulk set of stations comprised values between 0.1 and 75 gm-2yr-1.

The dataset Network-SET-M includes field measurements for 20 additional stations located in the Mediterranean and Sahel regions to represent deposition both near dust sources and at intermediate distances from them . The values in this dataset ranges from 4.2 to 270 gm-2yr-1 and allow us to visualise regional differences in the dust deposition flux. The INDAAF (International Network to study Deposition and Atmospheric composition in Africa) stations provide us with an estimation of the inter-annual variability, which is large in the Sahel region (see the Table S.MD.7)

The first part of the climatological dataset for dust concentrations (see Table S.MD.4) at the surface has been adopted from estimations done by the University of Miami Oceanic Aerosols Network (UMOAN) whose instruments are filter collectors deployed in the North Atlantic and Pacific oceans . This dataset provides climatological monthly averages with a standard deviation that represents inter-annual variability. The second part of the climatological dataset is based on yearly values from the station data shown in . The dataset comprises 36 stations with values from 5×10-2 to 100 µgm-3 distributed within the full range of values but grouped in clusters correlated with the geographical regions they belong to.

The multi-instrument network was deployed in the framework of the African Monsoon Multidisciplinary Analysis and belongs to the INDAAF set of data stations. described the collocated measurements of wet and dry deposition as well as surface concentrations (of particulate matter smaller than 10 µm) at three stations in the Sahel region; see Tables S.MD.6 and S.MD.7 and Fig. b. The stations also measured precipitation, wind velocity and surface temperature. Additionally, in the same locations there are AERONET sun photometers to measure aerosol optical depths.

The AERONET (aerosol robotic network) database implemented in our comparisons relies on the version 3 (level 2.0) algorithm. Based on this new algorithm the entire database of observations was reprocessed in 2018 . The database comprises aerosol optical depths and Ångström exponents, as well as fine and coarse optical properties obtained with a new cloud-screening quality control scheme. The actual division threshold between fine and coarse particles is ascertained by the inversion algorithm that aims to differentiate aerosol particles from ice crystals, and it lies between 0.44 and 0.99 µm.

The network database provides daily data, allowing for event analysis, and there is also a monthly time resolution dataset used here to examine decadal, yearly and seasonal properties. We processed data from 300 stations of the full network to explore general properties. For the dust analysis we selected stations where all the models together considered dust to be an important contributor to the aerosol composition (at the geographical location of the AERONET station). This subset is called the dusty set of stations here, which are shown in Fig. . It comprises 39 stations divided into two subsets: stations where the dust has a dominant role in terms of the optical depth (τ440dust>0.5τ440all-aer for all models and all the months of the year, with τ440all-aer referring to optical depth at 440 nm of all aerosols and τ440dust the optical depth of mineral dust aerosols at 440 nm) and those where the dust is important although not necessarily dominant for all the models (even if the dust optical depth from a single model contributes more than 50 % of the total aerosol optical depth). The first subset comprises 21 stations, and it is denoted with uppercase letters in Fig. . The second comprises 19 stations, and it is denoted with lowercase letters. The dusty station set over Africa is consistent with the stations analysed by based on the criteria, but it has been extended with stations in Australia, South America, North America and Asia, consistent with . Figures with the seasonal cycle of aerosol optical depth for the dominantly dusty and important stations that highlight the classification criteria are shown in the Supplement (Figs. S.DOD.10 and S.DOD.11).

Interactions between dust and radiation are defined through three optical properties: dust optical depth (DOD), single-scattering albedo (ω) and the asymmetry parameter, which defines the ratio of the radiation scattered forward over the radiation scattered backward. For the dust coarse mode, the dust optical depth can be estimated using the Moderate Resolution Imaging Spectroradiometer (MODIS) enhanced deep-blue (DB) aerosol optical depth as done by with the additional support of the MODIS product of single-scattering albedo (ω) and Ångström exponent (α). The rationale of the method relies on the properties of these three optical parameters applied to aerosol particles. First, α is very sensitive to particle size, so there are parameterisations of aerosol optical depth that use it to separate each mode contribution. Second, aerosols with low absorption and large scattering like sea salt have ω≃1, whereas mineral dust is considered an absorbing aerosol. Third, the dependency of α(λ) on wavelength contains a signature of the aerosol composition. Given this information, we have considered two different MODIS dust-optical-depth-related datasets. One of them is a pure filter of aerosol optical depth to differentiate pixels wherein dust is expected to be the dominant contribution to aerosol optical depth, but without an attempt to estimate the actual fraction of mineral dust, so it is considered here to be an upper threshold for the actual DOD of the coarse mode (because particles of dust with diameters below 1 µm are thought to contribute less than 10 % to the total dust optical depth). The other method aims to explicitly separate sea salt and proceeds to rescale the aerosol optical depth to ascertain an actual value of DOD; according to it may be considered a lower bound for the DOD. Additional information and a comparison of these created products are given in the Supplement; see Figs. S.MD.2 and S.MD.3.

The Multi-angle Imaging Spectroradiometer (MISR) is a sensor on board the Terra satellite which takes advantage of its multi-angle measurement capabilities. It is able to ascertain the presence of non-spherical particles in the aerosol products at four different wavelengths. The optical depth at several wavelengths has been used to compute the Ångström exponent between March 2000 and December 2014 from MISR and compare with the models' Ångström exponent based on the same information. This product gives us information on how the models represent the spectral dependence of optical depth. Our computation using the 446 and the 672 nm wavelengths has been compared with the MISR Ångström exponent product to validate our computations; see Fig. S.GL.8.

The global dust cycle has been analysed in terms of global climatological values and complemented by a study of the role of the particle size distribution in the direct radiative effects (based on the IPSL model with four dust modes).

The dust particle size distribution is physically constrained by emission, transport and deposition (wet and dry), whereas other aerosol processes like aerosol nucleation, condensation and coagulation have a minor role in the evolution of the size distribution . Therefore, the first step to describe the global atmospheric dust cycle in climate models consists of a characterisation of the emission and deposition fluxes at the surface. This analysis is complemented by the analysis of two size-integrated properties: the dust optical depths and loadings. Other phenomena present in the Earth system dust cycle more relevant for paleoclimate studies, like those derived from the stabilisation of dust deposition on the surface on long timescales, are not considered in this work.

The global dust budget is analysed for the whole time period of the simulations over the three different simulations considered: PD, PDN and PI. Table  presents the mean global values of each model. It describes the dust mass balance in terms of emission as well as dry and wet deposition. A parameter Rdep is defined to represent the ratio of total dry to total wet deposition. In addition, Δ represents the fraction (%) of the emissions not deposited relative to the total emission. This last parameter is used to ascertain if the dust cycle from emission to deposition is consistent in terms of global mass conservation or, on the contrary, whether the model transport introduces any inconsistency in the modelled dust cycle. In particular, the parameter Δ is used to identify the models and experiments that will be included in the multi-model ensemble mean to ensure internal consistency in the ensemble.

In this regard, the mass budget of the CNRM-3DU model is closed to within Δ≃3% as its dynamical core is based on a semi-Lagrangian method , which is not fully mass-conservative in terms of its tracers. In the case of the PDN experiment there is an increase to Δ≃4.3% because the excess of mass in the deposition with respect to the emissions is similar for all the experiments, but the emissions of CNRM-3DU decrease with nudged winds by 30 %. The deposition value is therefore biased by an approximately constant amount of 75 Tgyr-1 independently of the wind field. Given in any case the value of Δ<5%, we have included the CNRM-3DU model in the ensemble means. In the case of the CNRM-6DU model the consequences of its dynamical core properties are the same; hence, there is also a bias. However, it is close to 600 Tgyr-1 in total deposition, producing a value of Δ larger than 15%. Therefore, this model is not included in the ensemble means. In both cases (the CNRM-3DU and the CNRM-6DU models), the bias in total deposition implies an excess of mineral dust in the atmosphere not consistent with the actual modelled emissions. A further complication is that the bias leads to other biases in variables like concentrations, load and optical depths. For this reason the CNRM-6DU model is not used in our analysis to draw conclusions about the dust cycle. But it is kept in the other analyses to be compared with future developments of the model that improve or fix the mass conservation and subsequently better highlight the implications of these kinds of numerical instabilities in dust modelling. For the other models, Δ<0.1%, with NorESM and EC-Earth presenting values closest to zero.

The multi-model mean global emissions for the PD and PI simulation experiments are 2836 and 2835 Tgyr-1, respectively, with standard deviations of 2680 and 2627 Tgyr-1. The PDN experiment shows an ensemble mean value of 1614 Tgyr-1, which is significantly smaller because of the models included (see Table ), but also because of an important decrease in the CNRM-3DU total emissions. Indeed, the decrease in emissions with nudged winds is even higher in CNRM-6DU. As a consequence, our ensemble mean value for the PDN experiments agrees well with recent estimations when large particles (diameter ≤ 20 µm) are not included. But it also agrees well with previous estimations of 1500 Tgyr-1 based on the DEAD model for particles with diameters smaller than 10 µm. At the same time, when nudged winds are used (PDN ensemble), the standard deviation of total emissions (278 Tg yr-1) is significantly smaller than for the PD or PI cases. For the PD experiment, the multi-model ensemble mean total emission, for the same models as available for PDN, has a mean value of 1843 Tgyr-1 with a standard deviation of 544 Tgyr-1, which is significantly larger than the standard deviation of the PDN experiment. Therefore, nudged winds decrease model diversity in terms of global emissions. Indeed, the CNRM-6DU and CNRM-3DU models have total emissions with nudged winds similar to the CRESCENDO ESM ensemble mean, but they produce higher emissions without nudged wind fields, i.e. 2600 Tgyr-1 in the CNRM-3DU model (diameters up to 10 µm) and 3500 Tgyr-1 for CNRM-6DU (diameters up to 100 µm; see Table ). These values are similar to the 3000 Tgyr-1 reported by for particle sizes between 0.1 and 50 µm. Finally, due to the presence of particles with diameters up to 62 µm, the UKESM has notably higher emissions (although in this case we cannot assess the role of surface winds).

This higher value of total emissions due to large particles is not directly correlated with the modelled dust load in the atmosphere. The reason is that the lifetime of dust particles in the atmosphere depends on the size, and these large particles sediment faster. For instance, the UKESM has monthly mean global loading values close to the other models and a smaller lifetime of dust in the atmosphere (less than 12 h, a characteristic value of the largest particles). In fact, the dry deposition of larger particles for UKESM (which for this model includes sedimentation) is truly dominant, resulting in a wet deposition close to other models, like IPSL, without the largest particles modelled. In contrast, the CNRM-6DU wet deposition is 2 times larger than that of the UKESM and IPSL model in the PD simulation (with CNRM-6DU being the only model for which wet deposition exceeds total dry deposition) but close to IPSL with nudged winds. Because larger particles are deposited faster by gravitational settling, it is expected that Rdep would be larger for models including the largest particles, but it is only obvious for the UKESM. For the CNRM-6DU model that is not the case. EC-Earth has double the value of Rdep of IPSL, and NorESM is 6 times larger. Previously, reported values for Rdep between 1.03 and 8.1, also uncorrelated with the size range of the dust particles modelled. The multi-model ensemble mean for total dry deposition without gravitational settling is 622 Tgyr-1 for the PD experiment and 558 Tgyr-1 for PDN. In the case of wet deposition, we estimated 623 and 531 Tgyr-1 for the multi-model mean for the PD and PDN experiments, respectively. Despite the similar values of our ensemble mean, the standard deviation of dry deposition is more than 2 times that from wet deposition. To summarise, each of the processes (sedimentation, wet deposition and dry deposition – without sedimentation) has a similar contribution in the ensemble mean for all the experiments, but this is masking strong differences in these three properties from each of the models.

As explained above, the impact of the largest particles on the global behaviour of loading and dust optical depth is considered less important than coarse particles (up to 10 µm), so this hypothesis allows us to compare all models with observational constraints that rely on optical depth measurements. Figure a compares the PD experiment with the proposed values of dust optical depth and total load. We also derive the mass extinction efficiency (MEE) field as the ratio of dust optical depth to loading field; see Table .

Figure  indicates that, aside from the CNRM-6DU model, all models have dust loadings smaller than 20 Tg, with the loading of NorESM half that of the ensemble median value. As already noted above, the load of the CNRM-6DU model is subject to a bias due to the artificial mass introduced during transport. Therefore, the set of models included in our ensemble mean (Table ) agrees with the AeroCom Phase I models or which the fine dust dominates with a total load ensemble mean value of 15 Tg.

Also based on AeroCom Phase I, reported an MEE multi-model median of 0.72 m2g-1, which is similar to the global MEE value of 0.6 m2g-1 used by to compare DOD and dust loadings of CMIP5 models. Recently, estimated a mean from 13 observational stations, giving a value slightly smaller than 0.6 m2g-1. Our estimation of MEE shows that EC-Earth and NorESM depart from that value, whereas the other models remain reasonably close to the hypothesis and the AeroCom Phase I median value. The larger MEE values of EC-Earth and NorESM can be due a combination of factors: they have the lowest dust loadings and both do not model particles larger than about 8 µm. In the case of NorESM, the imaginary part of the refractive index is also the largest of all the models analysed. Our results highlight the fact that the MEE depends on the modelled dust particle size distribution (in particular the presence of large particles) but with a significantly smaller inter-annual variability than dust optical depth and loading. This fact explains its use for ad hoc relationships between dust optical depths and loadings with a constant factor .

We note that the global mean values for the models, as shown in Fig. a, are partially influenced by ocean or land regions with low dust loadings. To complement this analysis, we present two additional comparisons in the Supplement. The first is shown in Fig. S.GL.1 for the case when only values over land are considered. The second is shown in Fig. S.GL.2 for the case when the annual values are estimated over the dust belt that covers most of the Sahara and the Middle East. Both figures still indicate important differences between models.

To further understand the properties of dust optical depth, we calculated the distribution of values for each model with a kernel density estimation based on the histogram of the annual global values of dust optical depth. The results shown in Fig. b indicate the presence of two main groups for our model ensemble: the first one centred around a value close to 0.01 and the second one around 0.025, which is a value closer to the proposed constraint. The solid black line shows the distribution of dust optical depth at 550 nm proposed by , and the vertical lines indicate the mean of that distribution and the AeroCom Phase I median value. The EC-Earth model actually agrees in terms of both the central value and typical inter-annual variability (as represented by the width of the distributions). These results should also be interpreted in the context of the total aerosol optical depth (AOD, Fig. c). We observe that the UKESM has the lowest values of dust optical depth but actually the largest values of total aerosol optical depth, with similar global mean values as those obtained by MODIS at 550 nm but with a narrower distribution. The EC-Earth model has AOD values slightly smaller than MISR estimates but with similar inter-annual variations. Fig. c indicates model discrepancies in the magnitude of the inter-annual variability (as measured by the width of the distribution) and an overall underestimation of AOD at 550 nm with respect to these satellite platforms.

A specific PDN experiment with the IPSL model was run for 5 years (2010 to 2014) to analyse how the representation of the dust size distribution influences the dust cycle. In this simulation, named IPSL-4DU, the dust scheme is based on four dust insoluble modes (m1, m2.5, m7 and m22; the number indicates the MMD – mass median diameter – value of that log-normal mode) covering the whole range of sizes from 0.1 to 100 µm, and nudged winds were used. The results shown in the Supplement Table S.GL.7 are consistent with the impact of larger particles on dust emissions and loadings in UKESM, and they allow us to discuss the role of each mode independently. The total emissions for IPSL-4DU are dominated by the largest particles, which are those of mode m22, but are promptly removed from the atmosphere through their sedimentation, which is very rapid compared with the typical lifetime of mineral dust, as shown in Table . When comparing the total load for each mode, the coarse size mode m2.5 is actually more abundant than m22. Amongst all the modes, mode m7 has the largest contribution, with 2/3 of the total, which is comparable to the large particles represented in the CNRM-6DU model, consistent with . Note that the dust loads in CNRM-6DU model are larger than in CNRM-3DU to a degree that cannot be explained solely by the larger emissions of CNRM-6DU. An explanation for this difference is that the bin that includes particle sizes from 2.5 to 20 µm in CNRM-3DU is split into different bins in the CNRM-6DU model, which have different lifetimes in the atmosphere, and that non-conservative transport could create larger aerosol mass in the CNRM-6DU configuration. In contrast to emissions, optical properties are dominated by the contributions of accumulation to coarse size particles compared to the largest particles of mode m22, which does not play a large role in the contribution to aerosol extinction. Those values are then used for assessments of modal contributions to direct radiative effects.

Mineral dust aerosol interaction with solar and terrestrial radiation results in both absorption and scattering of light. These interactions are strongly dependent on dust mineralogical composition and particle size distribution; hence, they differ regionally . We estimated the respective roles of the different modes (that represent different particle size ranges) and note that in the case of multi-modal distributions the estimations of direct radiative effects (DREs) by each mode are somewhat non-linear . This is illustrated by the sum of the contribution of the DRE from each mode, which is not exactly equal to the multi-modal dust contribution. Appendix  shows how, with an estimation of DRE per mode based on the combination of two different methods, we determined modal values of DRE that, when combined, come close to the multi-modal DRE estimation. This is summarised in Table  where the estimates per mode of DREs for each method are shown together with their mean. The sum of these mean values per mode is now consistent with the multi-modal DRE. It is remarkable how the estimations of DRE at TOA-SW (top of the atmosphere in the shortwave) for m7 for each method differ by a factor of 2. The non-linear effects at the surface in the SW are also important, with differences in the sum of the four modes between methods of 0.3 Wm-2.

The analysis of direct radiative effects (DREs) by mode, shown in Table , indicates that the largest particles (mode m22) have a minor impact on the DRE in both the LW and SW according to the IPSL-4DU model. In contrast, the inclusion of the mode with the smallest particles contributes to SW cooling, although it is the coarse size mode that dominates the net direct radiative effects at the top of the atmosphere. At the surface, however, mode m7 has the largest effect on both SW and LW, but its net contribution (LW+SW) is smaller than the coarse mode m2.5. It is important to note that the DRE shown in Table  is estimated without scattering in the LW (only absorption). To neglect the LW scattering in the case of mineral dust implies an underestimation of TOA-DRE-LW , mostly in cloud conditions.

A global picture of the dust cycle is shown in Figs.  and , which describe temporal mean properties of dust in CRESCENDO ESMs (PD simulations) over 15 years. The spatial resolution and vertical levels of the models are introduced in Table .

First, models that have a sectional representation of the DPSD (CNRM-6DU, CNRM-3DU and UKESM) are shown in Fig. . For all these models, emission and dry deposition show strong spatial correlations because gravitational settling of large particles occurs close to dust sources, whereas wet scavenging dominates the deposition process over the oceans. The extension of regional emissions over the Sahel and Somalia is more pronounced for UKESM than for the CNRM models. Although the Chalbi Desert in Kenya is also a location for emission in the CNRM models, the extent over which emissions occur in the UKESM is significantly larger. The figure also suggests differences in deposition for the CNRM models: the CNRM-3DU model has higher values of dry deposition than CNRM-6DU, but the opposite is true for wet deposition. These differences in wet deposition are pronounced over the North Atlantic and the Indian Ocean. In contrast, wet deposition is more intense over the Sahel and the Indian subcontinent in the UKESM, which indicates the strong role of the monsoon in scavenging dust. It is also noticeable that the CNRM-3DU annual mean wet deposition decreases from west to east over the Indian Ocean, while the inverse is true for UKESM. Despite systematic smaller values for UKESM optical depth compared to CNRM-3DU, they have rather similar spatial distributions, except in Australia. Analogues of Fig.  for PI and PDN are shown in Figs. S.GL.3 and S.GL.5, respectively. The figures for the PI experiment demonstrate no differences from the PD experiment, but the PDN experiment for CNRM models show smaller values of deposition and optical depth but with similar spatial patterns due to the decrease in their dust emissions with nudged winds.

Second, the models with a modal description of the DPSD (IPSL, EC-Earth3-AerChem and NorESM) are shown in Fig. . Dust emissions from EC-Earth are more intense in Asia than for the other models, whereas EC-Earth has the smallest emissions from the northern Sahara. This causes the trans-Pacific transport of dust to peak in this model compared to others and the transport across the Atlantic to be smaller. Northern Sahara emissions from NorESM are more localised but with larger peak values. Like for sectional models, dry deposition correlates well spatially with emissions, whereas wet deposition dominates over oceanic regions. EC-Earth shows both larger wet deposition and optical depth over East Asia extending into the Sea of Japan. For all models with a modal scheme, wet deposition over the Indian Ocean mostly occurs over its western part. Analogues to Fig.  for the PI and PDN experiments are shown in Figs. S.GL.4 and S.GL.6, respectively. Here, the results of PI and PDN draw a picture with similar global properties of the dust cycle as the PD experiment.

The dust emission rate is defined as the surface mass flux of mineral dust in the vertical direction Fd. This flux is derived in climate models as a function of surface winds, but there are different schemes depending on the complexity of the description. classify all dust emission schemes in three different categories named α,β and γ schemes. The α schemes are those whereby Fd is directly described in terms of the wind speed (with a non-linear function including a friction velocity threshold) with an imposed empirical size distribution at emission. IPSL-INCA uses this approach. The β schemes instead estimate the vertical flux from the dust horizontal mass flux, which can itself be parameterised depending on a geographical erodibility factor and the surface wind. Although this erodibility factor depends on soil properties and moisture, sub-daily global patterns of dust emission are tightly correlated with wind fields and therefore with the atmospheric general circulation . Examples of β schemes are those described by and that are respectively used by the NorESM and UKESM. It is also used in the EC-Earth model whose horizontal flux is estimated with the scheme described by , which distributes particles in four bins with values up to 8 µm. Those values are mapped in the modes described in Table S.MD.9. In the case of UKESM the horizontal flux is also calculated based on into nine bins with diameters between 0.064 and 2000 µm but mapped for transport into six bins described in Table S.MD.9. Similarly, the CNRM models have a drag partition according to , but the size distribution at emission follows that defined by . The γ schemes aim to describe the physical process driving the size-resolved vertical flux, but they require additional information on the underlying soil properties and are not used by CRESCENDO ESMs.

Despite the different schemes all of them agree that the regions where most dust is uplifted are subtropical arid and semi-arid regions. Such regions are characterised by atmospheric stability and scarce rainfall. This global pattern is, however, modulated by Intertropical Convergence Zone (ITCZ) oscillations, monsoons and orography, as visible in Figs.  and . Because the Himalayan mountains filter the water vapour transport from the Indian Ocean all the models have important dust sources in northern Asia (such as the Taklamakan and Gobi deserts), but the specific location of Asian sources and their relative contribution to global emissions differ significantly between models.

Nowadays, we understand how regional climate influences dust emissions and their variability, together with the atmospheric systems linked to dust emission episodes. But dust emission modelling still constitutes an active research field . In particular, the dust particle size distribution (DPSD) at emission is critical for a better description of the global dust cycle , but its modelling needs to be improved for three main reasons: (1) because there is not a unified approach, (2) because there are discrepancies in the role of wind speed at emission for larger dust particles , and (3) because the quantitative link between soil properties and dust emission fluxes still needs additional research.

Regardless of the several sets of parameterisations of DPSD at emission , the actual modelling of dust in global climate models is highly influenced by a balance of the different elements involved (vertical flux at small scale, soil erodibility, wind fields), which explains that during the last decade the estimation of dust emissions when online-coupled with meteorological fields has improved their results significantly. On the one hand, the modelled wind surface friction velocity and speed agree better with actual meteorological conditions; e.g. . On the other hand, the description of the soil surface properties has become more accurate due to both improvements in soil texture databases and the use of satellite retrievals to better describe the roughness length; e.g. and .

All those facts explain why the comparison (Table ) of the emissions (PD experiment) over large regions is fairly consistent among models: they agree on the main source of mineral dust being located in the Saharan desert but represent 39 % of total global emissions in the EC-Earth model and 66 % in CNRM-3DU. Previous studies estimated the contribution of Africa to dust emissions in the range from 50 % to 68 % but also including Namibian desert emissions. The consistency is larger when we consider larger regions like hemispherical contributions, for which all the models show more than 85 % of global dust emissions from the Northern Hemisphere. When smaller regions are considered, the differences in relative contributions between models increase, which is also expected when turbulence at small scale and/or convection play a role in dust events. If we evaluate total values rather than relative contributions, the driving factor that explains differences between modelled emissions is the upper threshold of particle sizes at emission.

Dust emissions by region (which are shown in Fig. ) and their intensities (in Tgyr-1) are listed in Table  for the PD experiment. The most intense source of dust for the EC-Earth model is located over the Gobi Desert, while the northern Sahara, a key emitting region in all other models, constitutes only the fourth most intense region in emissions (after the Taklamakan and the Kyzyl Kum). The Bodélé is a remarkably important dust source across all CRESCENDO ESMs. As expected from the analysis of dust optical depth over Asian regions, the Taklamakan, Kyzyl Kum and Thar deserts exhibit substantial differences. Regarding UKESM, it has an additional and extended dust source over the Somali desert (see Fig. 5), which is only a relatively small source in other models. Analogues of Table  for the PDN and the PI experiments can be found in Tables S.DE.1 to S.DE.4, respectively, showing similar model differences.

If we want to realistically compare global climate model emissions over smaller regions, we need to account for the different model resolutions. We opted to display normalised emission estimations over a common grid for all the models. Our method interpolates the emission flux from each model grid to that with the highest spatial resolution (NorESM). We use a near-neighbour interpolation method, which conserves the flux in each model when compared to the flux integrated over the original model resolution. This method does not introduce any ad hoc information on how the emission tendency is distributed within the original grid pixel. A monthly time series of normalised emitted dust mass per grid pixel, with respect to global monthly emissions, is produced using this method. These normalised emissions over a common grid allow us to pick up differences over locations that are caused either by the formulation of the source function or by the dust particle size distribution imposed during the emission process.

A direct comparison of dust emission maps with observations is challenging because it would require the translation of the observed frequency of dust events into a dust emission flux rate . Assuming the hypothesis of for this mapping, the hot spots of their Spinning Enhanced Visible and InfraRed Imager (SEVIRI) emission-normalised product can be compared with our normalised maps (in terms of the relative contribution of different pixels over North Africa). In particular, they suggest that beyond the Bodélé Depression an important source is in the Hoggar Mountains (west of Bodélé Depression). This feature is only captured by the CNRM models.

The annual average of these monthly maps is presented in Fig.  for the PD and PDN experiments. The models CNRM-6DU and CNRM-3DU show similar values per grid cell, which indicates the use of the same information on soil properties, but the normalised emissions, although similar, are not identical, reflecting the differences in dust size distribution at emission. In these models, the normalised emissions over Australia are higher than for the other models, and this difference also appears in the optical depths simulated at the AERONET station of Birdsville. Their description of semi-desert areas in northern India has many similarities to the IPSL model. Emission tendencies from the UKESM extend to areas where other models do not simulate emissions, and the pattern of emissions is more smooth. In particular, significant emissions occur over the Sahel, Ethiopia, Somalia and India. For these regions, higher dust emissions in UKESM could have a stronger impact on African and Asian monsoons. The most granulated pattern is found for NorESM due to the higher resolution of the source functions implemented. The last row in Fig.  corresponds to the normalised emission maps for the PDN experiment, and it indicates that although there are important differences between the PD and PDN experiments in terms of total emissions (see Table ), the spatial patterns of emissions are similar once they are normalised. We can ascertain this fact by comparing the CNRM-6DU normalised emission maps for the PD and the PDN experiment. The analysis for the PI experiment is in the Supplement: Fig. S.DE.5.

Previous studies show that total deposition of dust, when compared with in situ measurements, agrees globally only to within a factor of 10. Part of the reason is that dry deposition and wet deposition are dependent on the dust particle size distribution, whose representation is challenging for current global climate models. Indeed, processes driving dry deposition such as turbulent motions of particles and gravitational settling are both particle-size-dependent, as the aerodynamic resistance and the terminal velocity due to friction depend on the effective dust particle diameter. Wet deposition during precipitation events also depends on the size of the particle , but measurements of aerosol lifetimes below clouds are scarce. Furthermore, other aerosol processes inside clouds modify the aerosol size distribution, as well as their optical properties, essentially due to potential aggregation of water-coated aerosols . Thereby, the first step of the analysis is a comparison of dry and wet deposition at a regional scale.

In fact, as the gravitational settling of large particles is dominant close to dust sources, regions remote from the main emission sources are well suited to compare models with different emission schemes and evaluate their respective total dry and wet deposition. Close to dust sources the upper threshold of the emitted dust particle sizes plays a role in the comparison with measurements. In particular, wet deposition over oceanic regions is enhanced relative to dry deposition, which motivates targeting these specific regions for comparison. Tables  and show the regional analysis of wet and dry deposition (including the sedimentation–gravitational settling) over oceans. These results are globally consistent with those shown by . The two main oceanic regions where dust deposition occurs are the North Atlantic and the Indian Ocean, even though the EC-Earth model simulated the largest dust wet deposition over the western Pacific Ocean. For all models, the fraction of dry and wet deposition over the oceans is smaller than over land. Wet deposition over oceans represents 40 % and 45 % of the total wet deposition for IPSL and EC-Earth, respectively. But for NorESM it represents 26 % of the global wet deposition. Dry deposition over oceans ranges from 3 % to 12 % of global dry deposition. For the UKESM, the dry deposition over land is 97 % of the total dry deposition due to the gravitational settling of large particles close to emission regions. Tables  and also show slightly better consistency in the total dry deposition over oceans in the model ensemble (from 67 to 250 in Tgyr-1) than in the wet deposition (72 to 392 in Tgyr-1), as we exclude CNRM-6DU from the model ensemble. Results for the PDN and PI experiments are included in Tables S.DD.1 to S.DD.4.

The simulated dust optical depth (DOD) by climate models has been previously compared with those retrieved through a network of ground-based sun photometers but also with products derived from satellite retrievals . There are also intercomparisons between global climate models . The overall agreement reported by these studies between retrieved and simulated dust aerosol optical depth is within a factor of 2. Those results support the reliability of global estimations of the radiative effect from mineral dust. However, given that it is a vertically integrated parameter, it masks larger differences present in partial column estimates.

Our study focuses first on the comparison in regions defined in Fig. . We compare the DOD of the CRESCENDO ESMs with satellites and intercompare simulated dust optical depth. Figure  shows the seasonal cycle (relative to the annual mean value of each model) and the MODIS DOD product during the period 2001–2014 for the PD experiment (the PDN and PI experiments are shown in Figs. S.DOD.1 and S.DOD.2). We can hence analyse the seasonal amplitude relative to the annual background signal per region for each model. The Supplement Fig. S.DOD.3 shows the direct comparison of the seasonal cycle without relative values.

Over the most prominent preferential dust source regions (first row of Fig. ), the amplitude of the seasonal variability is systematically larger in all the models (with respect to the MODIS DOD product), with a slight offset in the maximum value of the seasonal cycle towards springtime, particularly over the northern Sahara. It is remarkable that in these regions CNRM-3DU and NorESM show consistency in the seasonality with respect to MODIS DOD, whereas EC-Earth and UKESM show more discrepancies in the seasonal cycle in both the amplitude and the phase. The CNRM-6DU model and IPSL have slight discrepancies in these four regions. Over the Asian deserts (the Taklamakan and Gobi) the seasonal maximum is reasonably represented in the spring with relatively good agreement for EC-Earth, although the seasonality is not well represented for the Thar Desert. The UKESM, NorESM and CNRM-3DU models overestimate summer dust optical depth over the Taklamakan desert. A common feature between all the models is that over the Asian desert the winter values are smaller than those of MODIS DOD. Previous studies concluded that the seasonal cycle of the Taklamakan desert is controlled by later spring and summer emissions, which most models capture, whereas the Gobi and the associated northern China deserts have maximum emissions during late winter and early spring. CRESCENDO ESMs reproduce the maximum values of DOD in spring for the Gobi Desert, and UKESM and EC-Earth capture that seasonality over the Taklamakan as well. Given the structural differences in the soil properties of these Asian regions (more stony at the Gobi, mostly sandy at Taklamakan) and the additional role of snow cover over the Gobi Desert, further model studies of Asian dust emissions are needed to better constrain the way dust scheme parameterisations capture emissions in these regions. Ideally, these studies should be backed up by in situ surface concentration measurements. Regarding the Middle East, the combined region of the northern and southern Middle East is in agreement with the study based on CMIP5 models.

We quantified the performance skill of the CRESCENDO ESMs by estimating the Pearson's correlation between the time series of dust optical depth provided by each model for each of the seasons and the same time series of dates given by the MODIS DOD product for the period between January 2001 and December 2014.

Figure displays the values for this Pearson's correlation. The overall assessment indicates marked differences between models for the same season and over the same region. In the case of the PD experiment (middle panel), the correlation between MODIS DOD and CRESCENDO ESMs is positive over winter except in the Australia and southern Africa regions, which are regions particularly challenging for the ESMs analysed as we reported negative correlations, whereas South America is one of the regions with a correlation closer to zero across all the seasons (and models). The overall correlation decreases in spring (with respect to winter), as we notice multiple regions where the Pearson correlations are close to zero. In summer, except in the Gulf of Guinea, the correlation is also smaller than in the winter season. Finally, in autumn the performance over the Middle East and the Kyzyl Kum region is improved. The better behaviour of all the models is given over the Bodélé in the winter season and the Arabian region (northern and southern Middle East), which shows reasonable agreement all year for almost all models. Most of the features remain similar with pre-industrial aerosol–chemistry forcings (PI experiment), and the CNRM-6DU and CNMR-3DU behave identically in the PI experiment.

The agreement with satellite platforms is significantly improved for the PDN simulations, and the consistency between models is enhanced. In particular, the Saharan region shows a marked improvement in the simulated dust optical depth. Australia and southern Africa are still the regions where most discrepancies are found, and South America systematically has the correlation closest to zero.

We extended the analysis based on the Pearson correlation by using the Spearman coefficient, which allows detecting non-linear correlations. The results for the Spearman rank coefficient can be found in the Supplement in Fig. S.DOD.7; they yield similar conclusions, and both methods are consistent.

The stations were chosen to cover a range of dust values from low to moderate dust concentrations, mainly located at a distance from the main dust emission regions. According to the instrument location, the Sahel and the west coast of North Africa (green and grey squares), together with the Middle East stations (grey diamonds), report the highest values of surface concentrations; see Fig. . The group represented by black circles shows moderate values, indicating transport of dust from arid and semi-arid regions of East Asia. The lowest values correspond to Antarctica and the Pacific Ocean (blue triangles). The values of the dataset are shown in Table S.MD.4 of the Supplement.

The comparison between the CRESCENDO models and a network of stations that measure dust surface concentrations is shown in Fig.  for the PD and PDN experiment and in Fig. S.DSC.10 for the PI experiment. The agreement falls into the same range as previous comparisons with the Community Atmospheric Model (CAM) wherein the full range for the expected differences in annual mean values is close to 10. This range of differences between models compares well with the previous study from .

CNRM-3DU underestimates dust concentrations over the Pacific Ocean. This behaviour over regions remote from dust sources could be partly due to the non-conservative semi-Lagrangian transport scheme that accentuates the differences with the distance of transport (a fact also consistent with their values of the Pearson correlation, mainly in nudged simulations). All models except IPSL underestimate the concentrations at the Antarctica station. This could be due to the larger emissions from Patagonia that cause an increase in the correlation coefficient for this model. Over northern Europe, all models except CNRM tend to underestimate dust concentrations and do not reproduce the range of variability found in the observations. When comparing PD and PDN simulations, IPSL and NorESM show slightly better agreement in PDN conditions, whereas the two CNRM models show higher correlations when using nudged winds but similar differences over the Pacific Ocean.

The correlation between the models and observations is significant for all models. The RMSE values are influenced by the stations with the highest concentrations and are hence more representative of the concentrations near the Sahara and the Middle East. In this regard, the NorESM and CNRM-3DU models show the best agreement over these regions. The EC-Earth model, however, shows the smallest bias because it better captures dust concentrations over Japan and eastern China, where the other models underestimate concentrations. Values of normalised bias and normalised mean absolute error complement the previous metrics and give us a characterisation of global differences equally accounting for the stations with the lowest concentrations (see Table ). The normalised statistics indicate that the nudged wind simulations generally show better agreement with observations.

Although the 36 stations cover many regions, a complete assessment of the model performance at the surface is not possible due to the absence of stations in South America and Asia and the presence of only one station inland over North America and Africa. Therefore, the global observational constraints, in terms of the surface concentrations, are only partial.

The comparison of the seasonal cycle of surface concentrations against 14 stations is shown in Fig.  for the PD experiment. The stations Cape Verde and Barbados are at the same latitude on opposite sides of the Atlantic; therefore, they have a signature of the trans-Atlantic transport of mineral dust from the Sahel region. The IPSL, CNRM-6DU and UKESM overestimate the early winter contributions to the seasonal cycle in Cape Verde. The models reproduce the concentrations within a factor of 2 from May to September (except CNRM-6DU model) with a general overestimation except for EC-Earth. However, in the case of Barbados, UKESM after April and CNRM-6DU before May reproduce the surface concentrations very well. All the other models, although with a similar seasonal cycle, underestimate the total surface concentrations by a factor of 2 to 4. The stations Izaña, Bermuda and Miami also have similar latitudes and represent the Atlantic transport from the western Sahara. Izaña Observatory is not at sea level, and all the models have difficulties reproducing the seasonal cycle. The seasonal cycles of Bermuda and Miami are well reproduced, with a general underestimation of the surface concentrations values; only UKESM and IPSL show consistency within a factor of 2. Cheju and Hedo are stations on the western Pacific coast, and their measurements represent the dust transport from China. The EC-Earth model reproduces the seasonal cycle well but with an overestimation of spring concentrations by a factor of 3. The seasonal cycle and values are well represented by the CNRM-6DU and IPSL models. Enewetak is located between the Philippines and Hawaii in the middle of the Pacific Ocean, and EC-Earth and UKESM overestimate the spring concentrations, whereas all the other models underestimate them. A similar situation is found in Hawaii and Midway. The rest of the stations are in the Southern Hemisphere where the dust concentrations are smaller and the seasonal cycle is only partially reproduced. The results for the PDN experiment (see the Supplement DSC) are similar with a slight improvement in the seasonal cycle but with a general underestimation of surface concentrations. All the models with nudged winds exhibit problems in reproducing the observations in Izaña.