Evaluation of natural aerosols in CRESCENDO-ESMs: Mineral Dust

This paper presents an analysis of the mineral dust aerosol modelled by five Earth System Models (ESM) within the Coordinated Research in Earth Systems and Climate: Experiments, kNowledge, Dissemination and Outreach (CRESCENDO) project. We quantify the global dust cycle described by each model in terms of global emissions together with dry and wet depositions, reporting large 5 differences in ratio of dry over wet deposition across the models not directly correlated with the range of particle sizes emitted. The multi-model mean dust emissions was 2954 Tg yr−1 but with a large uncertainty due mainly to the difference in maximum dust particle size emitted. For the subset of ESMs without particles larger than 10 μ m we obtained 1664 (σ=650) Tg yr−1. Total dust emissions with identical nudged winds from reanalysis give us better consistency between models 10 with 1530 (σ=282) Tg yr−1. Significant discrepancies in the globally averaged dust mass extinction efficiency explain why even models with relatively similar dust load global budgets can display strong differences in dust optical depths. The comparison against observations has been done in terms of dust optical depths based on MODIS satellite products, showing a global consistency in terms of preferential dust sources and transport across the Atlantic. However, we found regional 15 1 https://doi.org/10.5194/acp-2020-1147 Preprint. Discussion started: 19 November 2020 c © Author(s) 2020. CC BY 4.0 License.

Dissemination and Outreach (CRESCENDO) project. We quantify the global dust cycle described by each model in terms of global emissions together with dry and wet depositions, reporting large 5 differences in ratio of dry over wet deposition across the models not directly correlated with the range of particle sizes emitted. The multi-model mean dust emissions was 2954 Tg yr −1 but with a large uncertainty due mainly to the difference in maximum dust particle size emitted. For the subset of ESMs without particles larger than 10 µ m we obtained 1664 (σ=650) Tg yr −1 . Total dust emissions with identical nudged winds from reanalysis give us better consistency between models 10 with 1530 (σ=282) Tg yr −1 . Significant discrepancies in the globally averaged dust mass extinction efficiency explain why even models with relatively similar dust load global budgets can display strong differences in dust optical depths. The comparison against observations has been done in terms of dust optical depths based on MODIS satellite products, showing a global consistency in terms of preferential dust sources and transport across the Atlantic. However, we found regional 15 and seasonal differences between models and observations when we quantified the cross-correlation of time-series over dust emitting regions. To faithfully compare local emissions between models we introduce a re-gridded normalization method, that also can be compared with satellite products derived from dust events frequencies. Dust total depositions are compared with instrumental network to assess global and regional differences. We found that models agree with observations distant from 5 dust sources within a factor 10, but the approximations of dust particle size distribution at emission contributed to a misrepresentation of the actual range of deposition values when instruments are close to dust emitting regions. The observational dust surface concentrations also are reproduced within a factor 10. The comparison of total aerosol optical depths with AERONETv3 stations where dust is dominant shows large differences between models, however with an increase of the inter-model 10 consistency when the simulations are conducted with nudged-winds. The increase of the model ensemble consistency also means a better agreement with observations, which we have ascertained for dust total deposition, surface concentrations and optical depths (against both AERONETv3 and MODIS-DOD retrievals). We estimated the direct radiative effects of a multi-modal representation of the dust particle size distribution that includes the largest particles measured at FENNEC experiment. 15 We introduced a method to ascertain the contributions per mode consistent with the multimodal direct radiative effects.

Introduction
Mineral dust is a key element of the Earth system. It plays an important role in our planet's energy 20 budget, in both the long-wave (LW) and the short-wave (SW) spectrum, by direct radiative effects and feedbacks on the climate system (Knippertz and Stuut, 2014). It also contributes significantly to the global aerosol burden. Kok et al. (2017) estimated that global emissions are 1700 Tg yr −1 (with a range between 1000-2700 Tg yr −1 and particle diameters up to 20 µm) which indicates that mineral dust, together with sea spray, have the largest mass emission fluxes of primary aerosols. It 25 is transported by the atmospheric flow from emission source regions to distant remote regions up to thousands of kilometres (Kaufman et al., 2005;Li et al., 2008). When it is deposited over the ocean (Schulz et al., 2012) dust constitutes a source of minerals, in particular iron (Wang et al., 2015;Mahowald et al., 2005;Mahowald, 2011) and phosphorus (Wang Rong et al., 2014), therefore it indirectly participates in the carbon cycle and the ocean removal of carbon dioxide from the at- 30 mosphere (Gruber et al., 2009;Shaffer et al., 2009). When dust is deposited over land it impacts on Table 1. Main characteristics of the CRESCENDO models used in this study and the experiments analyzed.
Resolution is given in degrees (longitude x latitude), and all dust emissions are interactively driven by wind speed. Additional information of the dust schemes can be found in the references mentioned. DPSD (Boucher et al., 2020) ecosystems and snow albedo (Painter et al., 2007). In the troposphere dust contributes to heterogeneous chemical reactions (Tang et al., 2017;Dentener et al., 1996;Perlwitz et al., 2015;Bauer, 2004) and ice nucleation (Tang et al., 2016;Atkinson et al., 2013;Hoose and Möhler, 2012;Prenni et al., 2009) but also behaves as cloud condensation nuclei (Bègue et al., 2015), presenting additional interactions with precipitation (Solomos et al., 2011). Air quality studies link dust concentrations with 5 health effects (Monks et al., 2009) but also with visibility (Mahowald et al., 2007). Additionally, transport and deposition of dust plays a role in the design and maintenance of solar energy stations in semi-desert areas (Piedra et al., 2018), whereas at Earth's surface fine dust particles (diameter smaller than 2.5 µm can cause long-term respiratory problems (Pu and Ginoux, 2018a;Longueville et al., 2010). At regional scales dust has been reported to influence the West African (Strong et al.,10 2015; Biasutti, 2019) and Indian monsoons (Sharma and Miller, 2017).
As a consequence, the dust cycle is actively analysed on regional (Pérez et al., 2006;Konare et al., 2008) and global scales, based on observations and models, covering aspects related to optical properties, mineral composition, emission processes, transport and deposition (Tegen and Fung, 1994).
Current global models represent reasonably well the atmospheric lifetime of dust particles with a 15 diameter of less than 20 µm (Kok et al., 2017), supporting a consistent modeling of the dust atmospheric cycle: emission, transport and deposition. Very large dust particles with diameters of several tens of micrometers are, however, seldomly represented in these models, and have become an active area of research (van der Does et al., 2018;Biagio et al., 2020).
Detailed comparisons between observations and models indicates that the latter are not yet captur- 20 ing the full dust spatial and temporal distribution in terms of its various properties. This is due to the fact that current Earth system models are limited to approximate phenomenological descriptions of the dust mobilization (Zender et al., 2003). These dust emissions schemes are based on either a saltation process (Marticorena and Bergametti, 1995) or a brittle fragmentation model (Kok, 2011), but in both cases the momentum transfer between the wind in the boundary layer and the soil particles is conditioned by erodibility or roughness surface parameters, which sometimes are simply scaled to be in agreement with observations of aerosol index and/or aerosol optical depth. These constrains 5 allow for the models to reproduce reasonably well the dust optical depth (Ridley et al., 2016) but cannot fully constrain the whole range of dust particle size distribution. This explains considerable differences in terms of surface concentrations and vertical deposition fluxes when global models are evaluated against dust observations at regional and local scales. These challenges increase in regions with strong seasonal cycles and sparse vegetation cover, that require a description of the evolving 10 vegetation, like Sahel or semi-arid regions. Others difficulties emerge when the anthropogenic component of the atmospheric dust has to be ascertained, as it requires to account for land use change and agricultural activities. Optical properties of mineral dust aerosols are another field of research as both the refractive index and the particle shape introduce uncertainties on the estimation of scattering and absorption properties (Nousiainen, 2009). Finally, the total mass of mineral dust emitted to 15 the atmosphere is mostly conditioned by few events with intense surface winds, as the dust emission flux has a non-linear dependence on the wind speed, which the models pursue to capture. Actually, the meteorological phenomena conditioning these events exhibit regional dependencies, e.g.
in West Africa deep convection (Knippertz and Todd, 2012) and nocturnal low-level jets (Heinold et al., 2013;Washington and Todd, 2005) have been found to be key drivers, while recently, (Yu 20 et al., 2019) reported differences in the frequency of dust events between the Gobi and Taklamaklan deserts.
The relevance of dust on the Earth system implies that most climate models have introduced parametrization schemes to describe properly the dust cycle in the last two decades. Woodward (2001b) describes the parametrization implemented in the Hadley Centre climate model, Miller et al. 25 (2006) introduces the NASA Goddard dust model, Schulz et al. (1998) and later Schulz et al. (2009) show the implementation of dust emissions in the INteraction of Chemistry and Aerosols (INCA) module of the IPSL model. Pérez et al. (2011) for the BSC-DUST model, and more recently other models either incorporate new dust schemes or improved on previous ones, e.g. Albani et al. (2014) and Scanza et al. (2015) in the CAM climate model, LeGrand et al. (2019) for the GOCART aerosol 30 model, (Klingmüller et al., 2018) in the EMAC atmospheric-chemistry climate model, Colarco et al. (2014) in the NASA GEOS-5 climate model, Astitha et al. (2012) and Gläser et al. (2012) in the ECHAM climate model. Therefore comparisons to ascertain how the models are improving the description of dust related processes are needed to make progress in the above challenges. A broad comparison of 15 AeroCom models (including both climate models and chemistry transport models) 35 compare the ESMs against observations in terms of optical properties (dust optical depth, Ångström exponent), surface concentration, wet and dry deposition, and dust emission, and how these aspects evolve in time and space. The paper is structured as follows: section 2 describes the models analysed, which is followed by section 3 describing the observational datasets used, and the methods (section 4). The results of the comparison are presented first at the global scale (Section 5.1), showing also its 15 climatological spatial patterns (Section 5.2). Followed by sections describing: dust emission (Section 5.3), dust deposition (Section 5.4), dust optical depths (Section 5.5) and surface concentrations (Section 5.6). These results are then discussed in section 6 and the main conclusion are summarised.
The supplementary information is a single document but organised according with the several sections of the main paper: Supplement MD has additional information of sections 2 (models) and 3  Table   S.MD.8 for further details, named here CNRM-6DU (with 6 bins) and CNRM-3DU (with 3 bins).
The UKESM model includes 6 bins, with both UKESM and CNRM-6DU covering also particles with diameters larger than 20µm, with two bins in the case of the UKESM model and one bin in 15 the case of the CNRM-6DU model. In the case of modal description the evolution of the size distribution is controlled by balance equations of mass and number concentrations of each mode, as they effectively constrain a log-normal distribution with fixed width. In CRESCENDO there are two main approaches: EC-Earth and NorESM are considering bi-modal size distributions (one fine or accumulation mode and one coarse mode) but mixed with other aerosols, whereas IPSL is con-20 sidering a non-mixed single dust coarse mode (see Table S.MD.9). The limit between coarse and fine particles is located at about 1 µm (while accumulation refers to fine particles from 0.1 µm to 1 µm). Several experiments aimed to estimate the typical parameters of a multi-modal description of the dust size distribution: first confined to the range of sizes typical of accumulation and coarse modes (Denjean et al., 2016) but also including larger particles (Ryder et al., 2018). Several studies 25  propose that the coarse mode, and more specifically those particles with diameter larger than 20 µm are important to better understand the global dust cycle. Therefore, we also compared the CRESCENDO ESMs modal dust schemes, with a new dust scheme of the IPSL model with 4 insoluble dust modes (Albani and et al, 2020;Biagio et al., 2020) whose properties are based in FENNEC campaign (Rocha-Lima et al., 2018). Table MD.9 shows the modal approaches 30 in CRESCENDO, and how they compare with the IPSL-4DU.
All the models provide standard approaches that estimate dust mobilization based on a velocity threshold, information on soil texture (clay/silk) and erodibility factors (including soil moisture or accumulated precipitation). Conceptually, a fraction of the horizontal flux of dust particles, dominated by sandblasting, is actually transformed into a vertical flux with a mass efficiency factor and then effectively transported by the atmosphere. EC-Earth emissions are calculated following the scheme described by Tegen et al. (2002) based on the horizontal dust flux proposed by Marticorena and Bergametti (1995), which is also used in the UKESM dust scheme (Woodward, 2001a). The

5
NorESM emissions are estimated with the DEAD model (Zender et al., 2003). The IPSL dust emission has been described by Schulz et al. (2009Schulz et al. ( , 1998, and the CNRM model (Nabat et al., 2012) used also (Marticorena and Bergametti, 1995) with an emitted size distribution based on (Kok, 2011). Although none of the models implements an explicit mineralogical description of dust particles, the optical refractive index effectively accounts for global average of the mixture of minerals present 10 in the mineral dust aerosol. Therefore those optical properties are representative for the global mineralogical composition rather than a description of the soil-type dependence of the mineralogy that would imply local differences on emitted optical properties. This approximation is considered to drive specific bias on those regions with the fraction of hematite or goethite minerals induce larger values of optical absorption. 15 In all the models the particle size is described by the geometric diameter, where the dust particles with irregular shapes are modelled by spherical particles with the same effective volume. Regarding optical properties they are calculated based on Mie scattering, this approximation is reasonable as far as the orientation of the particles is randomly distributed, but any physical process that breaks this hypothesis, like preferential transport of specific geometries or physical processes that promote 20 a specific orientation of the particles, will imply bias in the methodology. Additionally, the spherical approximation is considered to underestimate the optical extinction of mineral dust (Kok et al., 2017). This hypothesis also affects the actual area of the global mineral dust surface which is important in heterogeneous chemistry (Bauer, 2004) and influences tropospheric chemistry. The geometry of the particles also affects the gravitational settling, and therefore the transport of particles with 25 specific geometries (Li and Osada, 2007) and their lifetime in the atmosphere.

Model experiments
Because the models have interactive dust emissions, wind fields play a prominent role on dust emission and transport (Timmreck and Schulz, 2004). Therefore, this study contrasts two different present-day forcing experiments: one with winds generated by the dynamical part of the climate 30 model (named PD), and the other nudged to re-analysed winds from ERA-Interim (named PDN). The historical greenhouse gases concentrations are consistent with (Meinshausen et al., 2017). The models IPSL and IPSL-4DU without explicit gas-phase interactive chemistry activated use the CMIP6 ozone forcing database (Checa-Garcia et al., 2018;Checa-Garcia, 2018). The CNRM-ESM2-1 has

Observational datasets
The observational datasets used to ascertain the performance of the CRESCENDO ESMs in their representation of mineral dust are based on a compilation of ground-site and satellite measurements. Table 2 summarizes the different available datasets used, and the spatial and temporal scales applied 10 in the analysis. Additionally, this table includes datasets representative of either a monthly or a yearly climatology (respectively referred as CM and CA in Table 2). In this section these datasets are briefly described but we refer to original publications for further details. For those datasets with specific pre-processing the additional details are given in the supplementary material. The set Network-H2011 gives deposition fluxes estimated from sedimentation corresponding to DIRTMAP database (Kohfeld and Harrison, 2001), while direct measurements of deposition fluxes were acquired during the SEAREX campaign (Ginoux et al., 2001) mostly in the Northern Hemisphere. Mahowald et al. (2009) describes 28 sites where dust deposition is inferred assuming a 3.5% 10 fraction of iron. The compilation also includes observations of deposition fluxes deduced from ice core data according to Huneeus et al. (2011). The dataset covers a range of total dust flux depositions from 10 −3 to 0.5· 10 3 g m −3 yr −1 but without a homogeneous distribution of values over this range.
Only two stations have observational values larger than 100 g m −2 yr −1 and the bulk set of stations comprised values between 0.1 and 75 g m −2 yr −1 .

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The dataset Network-SET-M includes field measurements for 20 additional stations located in the Mediterranean and Sahel regions to represent both deposition near to dust sources (O'Hara et al., 2006), as well as at intermediate distances from them (Vincent et al., 2016). The values in this dataset ranges values from 4.2 to 270 g m −2 yr −1 and allow us to visualize regional differences in dust deposition flux. The INDAAF stations (Marticorena et al., 2017) provide us with an estimation 20 of the inter-annual variability which is large on Sahel region (see the Table S.MD.7)

Surface concentrations
A 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 25 (Prospero and Nees, 1986;Prospero and Savoie, 1989). 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 stations data shown in (Mahowald et al., 2009). The dataset comprises 36 stations with values from 5·10 −2 to 100 µ g m −3 distributed within the full range of values but grouped in clusters correlated with the geographical regions they belong 30 to. Oceanic Aerosols Network) and also those described by Mahowald et al. (2009). Colors represent the region where each station belongs to. The regions correspond to those used for the regional analysis of dust deposition over the ocean: North Atlantic (0), South Atlantic (1), North-Indian Ocean (2), South-Indian Ocean (3), Pacific East (4), Pacific North-West (5), Pacific South-West (6) and Antarctic Ocean (7).  (14), North-America (15). Table 3. Given the mass mixing rations Xs, airmass amass, optical depths τs per specie s and air density ρair.
We indicate here the method used to estimate other diagnostics. (i,j) are the coordinates/index of each cell grid, l represent the level/layer. A(i, j) is the area of (i,j) grid cell, l0 represent the surface layer

Diagnostic Symbol Equation Units
Grid cell area A(i, j) Diagnostic provided by models kg Mass mixing ratio Xs(i, j, l) Diagnostic provided by models kg kg −1 Air-mass amass(i, j, l) Diagnostic provided by models kg Optical depth at 550nm τs(i, j) Diagnostic provided by models -

INDAAF stations of data
The multi-instrument network was deployed in the frame of the African Monsoon Multidisciplinary Additionally, in the same location there are AERONET sun-photometers to measure aerosol optical depths.

AERONET optical properties
The AERONET database implemented in our comparisons rely on the Version 3 (Level 2.0) algo-10 rithm. Based on this new algorithm the entire database of observations has been reprocessed in 2018 (Giles et al., 2019). 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 The network database provides daily data, allowing for events analysis, and there is also a monthly time resolution dataset, used here to examine decadal, yearly and seasonal properties. We processed the 300 stations from the full network to explore general properties and we selected those stations where it is considered that mineral dust is an important part of the aerosol composition based on the Statistic Estimator

MODIS dust related products
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 15 the radiation scattered forward over the scattered backward. For the dust coarse mode, the dust optical depth can be estimated using the Moderate Resolution Imaging Spectro-radiometer (MODIS) enhanced deep-blue (DB) aerosol optical depth (Sayer et al., 2014) as done by Pu and Ginoux (2018b) with the additional support of the MODIS product of single-scattering albedo (ω) and Ångström 13 https://doi.org/10.5194/acp-2020-1147 Preprint. Discussion started: 19 November 2020 c Author(s) 2020. CC BY 4.0 License. exponent (α). The rationale of the method relies on the properties of these three optical parameters applied to aerosols particles. First, α is very sensitive to particle size, so there are parametrizations of aerosol optical depths 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) in wavelength contains a signature of the aerosol 5 composition. Given this information, we have considered 2 different MODIS dust optical depth related datasets. One of them is a pure filter of aerosol optical depth to differentiate those pixels where dust is expected to be the dominant contribution to aerosol optical depth, but without the attempt to estimate the actual fraction of mineral dust, so it is considered here as an upper threshold of the actual DOD of the coarse mode (because particles of dust with diameters below 1 µm are thought 10 to contribute less and 10% to total dust optical depth). The other method aims to explicitly separate sea-salt, and proceed to re-scale the aerosol optical depth to ascertain an actual value of DOD, according to Pu and Ginoux (2018b)   This product gives us information on how the models represent the spectral dependence of optical depth. Our computation using the 446 nm and the 672 nm wavelength, has been compared with MISR Ångström exponent product to validate our computations, see Figure S.GL.8.

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Along this study we calculated several diagnostics not directly provided by the different models. Table 3 shows how they has been estimated together with the units used. Regarding the statistical methods, Table 4 shows the statistics definitions used for the comparison of models with network of instruments. The skill of the models to ascertain the dust optical depth over dust source regions has been calculated based on the Pearson correlation. Given that this statistics is not robust and it is 30 unable to inform about non-linear relationships, the skill is also estimated based on the Spearman rank correlation.  Table 4 summarizes the statistical metrics used to evidence differences between models and ob-10 servations. The surface concentration and total deposition comparison are presented as scatter-plots together with three associated statistics: the Pearson correlation (evaluated in log-scale), the bias and the RMSE. These last two metrics can be used to characterize quantitative differences between each model and observations. Tables 10, 11 and 12 include in addition, the normalized bias and the normalized mean absolute error which help us understand how the models differ when scaled to the 15 observation values.

Results
The whereas the other based on PI simulations help us to evaluate a possible role of prescribed emissions.

Global dust properties
The global dust cycle have been analysed in terms of global climatological values and complemented 30 by an study of the role of the particle size distribution on the direct radiative effects (based in the IPSL model with 4 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 on the evolution of this size distribution . Therefore, the first step to describe the global atmospheric dust cycle in climate models consists of a characterization of the emission and deposition fluxes at surface. This analysis is complemented by the The global dust budget is analysed for the whole period of the simulations over the three different 10 simulations considered: PD, PDN and PI. Table 5 presents the mean global values of each model.
It describes the dust mass balance in terms of emission, dry and wet deposition, and the parameter ∆ ascertains the fraction (%) of the emissions not deposited relative to the total emission. R dep represents the ratio of total dry to total wet deposition.
For global emissions, the PD and PI experiments the multi-model mean 2954 Tg yr −1 and 3011 Tg yr −1 respectively. The PDN experiment shows an ensemble mean value of 1530 Tg yr −1 which is significantly smaller as UKESM is not present but also because an important decrease on the CNRM-3DU and CNRM-6DU total emissions. This value agrees well with recent estimations (Kok et al., 2017) when large particles (diameter ≤ 20 µm) are not included, and previous estimations of 1500 Tg yr −1 based on the DEAD model (Zender et al., 2003) for particles with D<10µm. Also when nudged winds are used (PDN ensemble), the standard deviation of total emissions (282 Tg yr −1 ) is 5 significantly smaller than in PD or PI cases. For the PD experiment the multimodel ensemble total emission for the same models that those of PDN experiment has a mean value of 2268 Tg yr −1 with a standard deviation of 1000 Tg yr −1 .
The CNRM-6DU and CNRM-3DU models have total emissions with nudged winds similar to the CRESCENDO-ESMs ensemble mean, but they produce higher emissions without nudged wind-10 field, i.e. 2600 Tg yr −1 in CNRM-3DU model (diameters up to 10 µm), and 3500 Tg yr −1 for CNRM-6DU (diameters up to 50 µm, see Table 1). These values are similar to the 3000 Tg yr −1 reported by Tegen and Fung (1994) for particle sizes between 0.1 and 50 µm. Due to the presence of particles with diameters up to 62 µm, the UKESM model has notably higher emissions (although in this case we can't assess the role of surface winds). These large particles sediment faster as shown 15 by the monthly mean global loadings with values close to the other models, and the smaller lifetime of dust in the atmosphere (less than 12 hours, a characteristic value of larger particles).
The mass budget of CNRM-6DU and CNRM-3DU models are only closed within ∆ 4.5% as their dynamical cores are based on a semi-Lagrangian method (Voldoire et al., 2012(Voldoire et al., , 2019 which is not fully mass conservative in terms of the tracers. The deposition value therefore represents a 20 lower threshold to actual values since a fraction of the emitted mass is effectively deposited (during long-term transport) but not accounted for in deposition fluxes. For the other models ∆ < 0.1%, with NorESM and EC-Earth presenting values closest to zero. Regarding the deposition of larger particles for UKESM the dry deposition (which for this model includes sedimentation) is truly dominant, resulting in a wet deposition close to other models without the largest particles modelled like IPSL.

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In CNRM-6DU wet deposition is two times larger than those of UKESM or IPSL models at PD for R dep between 1.03 and 8.1 also uncorrelated with the size range of the dust particle modelled.
The multimodel ensemble mean for total dry deposition is 562.7 Tg yr −1 for PD experiment and 430 Tg yr −1 for PDN, in the case of wet deposition we estimated 920 and 577 Tg yr −1 multimodel mean for PD and PDN experiments respectively.   Figure 3. In brackets the order of the 10 regions with largest emissions.
The multimodel ensemble the table includes the mean values ± the standard deviation for all the models, and for all the models without UKESM. On the supplement material (section E), the tables E1 to E4 have the analogous information for PI and PDN experiments. 118.7 (7) 118.8 ( 3) 142.4 (4) 198.7 (7) 377.4 (7) 198 ( The impact of the largest particles on global behaviour of dust optical depth and loadings is considered less important than coarse particles (up to 10 µm), so this allows us to compare with observational constrains that rely on optical depth measurements. Figure 4 (top panel) compares the PD experiment with the Kok et al. (2017) proposed values of dust optical depth and total load, whereas in addition we derived the mass extinction efficiency (MEE) field as the ratio of dust optical depth 5 to loadings fields, see Table 3. 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 depths and loadings. This fact explains the use of MEE for ad-hoc relationships between dust optical depths and loadings with a constant factor (Pu and Ginoux, 2018b).
Based on the histogram of the annual global values of dust optical depth we estimated the distribu- Our estimation of MEE shows that EC-Earth and NorESM depart from that value, whereas the other models remained close reasonably to (Pu and Ginoux,30 2018b) hypothesis and AeroCom median value.
We note that the global mean values for the models, as shown in Figure 4 (top panel) are partially conditioned by ocean or land regions with low dust loadings. To complement this analysis, we present two additional comparisons in the supplementary material. The first is shown in Figure   GL1, for the case when only values over land are considered. The second is shown in Figure GL2 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. Recently,  proposed that the total load of dust in the atmosphere is higher than typical estimation and give a mean value close to 30 Tg yr −1 , where the contribution of coarse mode is more important than the fine mode. In this case the estimation of CNRM-6DU model would be the Mineral dust aerosol interaction with solar and terrestrial radiation results in both absorption and 25 scattering of light. These interactions are strongly dependent on dust mineralogical composition and particle size distribution, hence they differ regionally (Ginoux, 2017;Kok et al., 2017). We estimated the respective roles of the different modes (that represent different particle sizes ranges), we remind that in the case of multi-modal distributions the estimations of direct radiative effects (DRE) by each mode is, somewhat non-linear (Biagio et al., 2020). This is illustrated when the sum of the 30 contribution of the DRE from each mode is not exactly equal to the multi-modal dust contribution.
The Appendix A show how, with an estimation of DRE per mode based on the combination of two different methods, we ascertained modal values of DRE that combine close to the multi-modal DRE estimation. This is summarised in Table 6   The analysis of direct radiative effects (DRE) by mode, shown in Table 6, indicates that the largest particles (mode m 22 ) have a minor impact on the DRE in both LW and SW. In contrast, the inclusion 5 of the mode with the smallest particles contributes to the SW cooling although it is the coarse size mode the one that dominates the net direct radiative effects at the top of the atmosphere. At the surface however, the mode m 7 has the largest effect on both SW and LW but its net contribution (LW+SW) is smaller than the coarse mode m 2.5 .  Figure 5. For all these models, emission and dry deposition show strong spatial correlations because gravitational settling of large particles is happening close to dust sources, whereas wet scavenging dominates the deposition process over the oceans. The extension 15 of regional emissions over Sahel and Somalia is more pronounced for UKESM than for 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: CNRM-3DU model has higher values of dry deposition than CNRM-6DU but the opposite is true for wet deposition. These differences in wet 20 deposition are pronounced over the North Atlantic and the Indian Ocean. In contrast, wet deposition is more intense over the Sahel and the Indian sub-continent in the UKESM model which indicates the strong role of the monsoon at 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, 25 they have rather similar spatial distributions.

Dust global spatial patterns
Models with a modal description of the DPSD (IPSL, EC-Earth3-AerChem and NorESM) are shown in Figure 6. Dust emissions from EC-Earth are more intense in Asia than other for 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 30 to be smaller. Northern Sahara emissions from NorESM are more localized but with larger peak values. Like for sectional models, dry depositions 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,

Dust emissions
The dust emission rate is defined as the surface mass flux of mineral dust in the vertical direction F d .
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. Shao and Dong (2006)  Although this erodibility factor depends on soil properties and moisture, sub-daily global patterns 10 of dust emission are tightly correlated with wind fields, and therefore with the atmospheric general circulation (Shao et al., 2011). Examples of β-schemes are those described by (Zender et al., 2003) and (Woodward, 2001b) that are used respectively by NorESM and UKESM models. But also the EC-Earth model whose horizontal flux is estimated with the scheme described by Marticorena and Bergametti (1995) which distributes particles in four bins with values up to 8 µm. Those values are 15 mapped in the modes described in the Table S.MD.9. Similarly the CNRM models have a drag partition according to Marticorena and Bergametti (1995) but the size distribution at emission follows that defined at (Kok, 2011). The γ-schemes aim to describe the physical process driving the size Nowadays we understand how regional climate influences the dust emissions and its variability, together with the atmospheric systems linked to dust emission episodes. But dust emission modelling 30 still constitutes an active research field (Shao, 2008). In particular, the dust particle size distribution (DPSD) at emission is critical for a better description of the global dust cycle ) but its modelling need to be improved for three main reasons: first because there is not an unified approach; second because there are discrepancies in the role of wind speed at emission for larger dust particles (Alfaro et al., 1998(Alfaro et al., , 1997; and third, because the quantitative link between soil properties and dust emission fluxes still need additional research. Despite the several set of parametrizations of DPSD at emission (Kok, 2011;Alfaro and Gomes, 2001;Shao, 2001Shao, , 2004) the modeling 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), 5 which explains that during last decade the estimation of dust emissions when online coupled with meteorological fields have improved their results significantly. On one side the modelled wind surface friction velocity and speed agree better with actual meteorological conditions, and on the other side the description of the soil surface properties has become more accurate.
All those facts explain why the comparison (Table 7) of the emissions (PD experiment) over large 10 regions is fairly consistent among models: they agree on the main source of mineral dust located in the Sahara desert but representing, from 39% of total global emissions in the EC-Earth model to 66% CNRM-3DU. Previous studies (Shao et al., 2011) estimated the contribution of Africa to dust emissions on a range from 50% to 68% but also including Namibia Desert emissions. The consistency is larger when we considered larger regions like hemispherical contributions where all 15 the models show emissions beyond 85% in 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 (Allen et al., 2015) plays a role in dust events. If we evaluate total values rather than relative contributions, the driving factor to explain differences between modelled emissions relies in the upper threshold of particle sizes at emission. 20 Dust emissions by regions (which are shown in Figure 3) and their intensities (in Tg yr −1 ) are listed in Table 7 for the PD experiment. The most intense source of dust for the EC-Earth model is located over the Gobi Desert, while North Sahara, a key emitting region in all other models, constitutes only the 4th most intense region in emissions (after the Taklamakan and the Kyzyl-Kum).
The Bodele is remarkably an important dust source across all CRESCENDO ESMs. As expected 25 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 Somalia Desert (see Fig. 5) which is only a relatively small source in other models. If we want to compare realistically global climate model emissions over smaller regions, we need to account for the different model resolutions. We opted to display normalized emissions 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 orig-presented at (Huneeus et al., 2011), whose stations are mapped in Figure 1  inal model resolution. This method is not introducing any ad-hoc information on how the emission tendency is distributed within the original grid-pixel. A monthly time-series of normalized emitted dust mass per grid-pixel, with respect to global monthly emissions, is produced using this method.
These normalized emissions over a common grid allow us to pick up differences over spots that are caused either by the formulation of the source function or by the dust particle size distribution 5 imposed during the emission process.
A direct comparison of dust emission maps with observations is challenging because it would require to translate the observed frequency of dust events into a dust emission flux rate (Evan et al., 2015). Assuming the hypothesis of Evan et al. (2015) for this mapping, the hot spots of their SE-VIRI emission normalized product can be compared with our normalized maps (in terms of relative

Dust deposition
Previous studies (Huneeus et al., 2011;Albani et al., 2014) show that total deposition of dust, when compared with in-situ measurements, agree globally only within a factor ten. Part of the reason is

31
https://doi.org /10.5194/acp-2020-1147 November 2020 c Author(s) 2020. CC BY 4.0 License. Table 10. Statistical properties of the comparision of the CRESCENDO-ESMs total deposition against the network-SET-M (see Figure 1 panel b). Statistic metrics used in this table are described on Table 4 that dry and wet deposition depend on the dust particle size distribution, whose representation is challenging for current global climate models.
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 on precipitation events also 5 depends on the size of the particle (Seinfeld and Pandis, 1998) 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 .
As the gravitational settling of large particles is dominant close to dust sources, regions remote 10 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 on 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 8 and 9 show the regional analysis of wet and dry de-  Table 11. Statistical properties of the comparision of the CRESCENDO-ESMs total deposition against the network-H2011 (see Figure 1 panel a). Statistic metrics used in this table are described on 45% respectively of the total wet deposition for IPSL and EC-Earth. But for NorESM it represents 26% of the global wet depositions. Dry deposition over oceans ranges from 3% to 16% of global dry depositions. For the UKESM model, 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 8 and 9  All the models agree that Antarctica and Southern Ocean has the lower values of total deposition.
However, UKESM and IPSL tend to slightly overestimate the total flux whereas CNRM models tend to underestimate the flux (with also a larger range of total deposition values than the range re- If we compare the observations against the model total depositions obtained from the experiment with nudged winds (last row in Figure 8 the correlation coefficients are similar, but differences 15 between models are reduced, specially for the CNRM models. This is illustrated in Table 11 with a negative bias for all models (from -9.4 to -11.8), and the ratio of standard deviations Σ range between 0.11 and 0.18 (for PD experiment between 0.1 and 0.41).
In Figure 9 we analyze the ability of ESMs to reproduce deposition fluxes regionally and closer to sources (for PD and PDN experiments). We focus on the Mediterranean Sea and include three However this implies an understimation over Sahel for CNRM-6DU model that also has the largest interannual variability over the West-Wediterranean. The statistics metrics are shown in Table 10.

Dust optical depth
The simulated dust optical depth (DAOD) by climate models has been compared previously with those retrieved through a network of ground-based sun-photometers (Huneeus et al., 2011) but also 5 with products derived from satellite retrievals (Pu and Ginoux, 2018b;Peyridieu et al., 2013). There are also inter-comparisons between global climate models (Shindell et al., 2013). The overall agreement reported by these studies between retrieved and simulated aerosol optical depth is within a factor of two. 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 10 present in partial columns estimations.
Our study focuses first on the comparison in regions defined in Fig. 3. We compared the DOD of the CRESCENDO ESMs with satellite, as well as inter-compare simulated dust optical depth. Figure   10 shows Gobi the seasonal maximum is reasonably represented in the spring with a relative 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 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 (Laurent et al., 2006) concluded that seasonal cycle of 30 Taklamakan desert is controlled by latter spring and summer emissions which most models capture, whereas 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 deserts, and UKESM and EC-Earth models capture that seasonality over Taklamakan as well.    pero and Nees, 1986;Prospero and Savoie, 1989). The colors of the points indicate the region to which the measurement station belongs. Climatological datasets were obtained from observations over the period from 1991 to 1994. For the PI experiment see Figure S.SDC.10. value of grid pixel to which the station belongs. As we are considering dusty stations, the correlation of the time-series represents how well the seasonal cycle is captured or not, while the representation of the amplitude of the cycle is measured by the standard deviation. Therefore the ratio of standard deviations is an indication of the agreement in seasonal amplitude between model and observations.
Those statistics are compared using the normalized Taylor diagram (Taylor, 2001). These diagrams

Surface Concentrations
The stations were chosen to cover a range of dust values from low to moderate dust concentrations,

10
The comparison between the CRESCENDO models and a network of stations that measure dust surface concentrations is shown in Figure 13 for PD experiment and in Figure   ing equally for the stations with the lowest concentrations (see Table 12), the normalized statistics indicate that the nudged-wind simulations generally show a better agreement with observations.
Although the 36 stations are covering 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 only one station inland over North America and Africa. Therefore, the global observational

Discussion
The analysis of the results provides insight on how both modelling and measuring dust can be used to improve our understanding of the dust cycle. More specifically, through comparison of emission and total deposition fluxes we are able to propose specific areas for which improvements are needed.
Annual global dust emissions are dependent on the dust particle size distribution (DPSD) representation and models that account for particles with diameters larger than 10 µm produce higher total fluxes. To overcome the challenge of comparing models with different DPSD, we introduced normalized emission maps, showing first by a comparison between PD and PDN simulations that 5 wind fields do not affect substantially these normalized emission estimates. This led us to interpret differences in regions where dust was emitted as reflecting differences in underlying effective soil erodibility information among models (including soil moisture effects) With the aim to reproduce dust observations at different model resolutions, models have introduced correction factors to those soil erodibility (see for example Knippertz and 10 Todd, 2012)). But our normalized emissions indicate effective model differences, both in intensity and location, on preferential dust sources. Those differences are the largest over Asia and are also significant over Australia. Hence we identified these regions as two source regions that would benefit from further comparison of dust emission observations with actual model occurrences in emission fluxes. Additional research is also needed to ascertain seasonality disagreements in dust sources. 15 The model ensemble values of total emissions with nudged winds has less dispersion. We stress however that dust column loads are a better quantity when comparing models with different size distribution at emission than compare to total emission fluxes, since gravitational settling gets rid of the very large particles over a short time span. For dust loads, all models are in a range between 9.1 and 15.2 [Tg/yr] which can serve as a baseline to study model improvements. Another important 20 point of discrepancy between models is the ratio between wet and dry deposition over similar particle size range, indicating that specific sensitivity studies should focus on the treatment of deposition. We also evidenced significant differences in deposition over oceans, in particular over the Indian Ocean and over the Pacific East, both of which are affected by dust source distributions over Asia.
Regarding the direct radiative effects, it is important to ascertain an uncertainty range for each 25 model. Based on a calculation with 4 modes over a range from 0.1 to 100 µm, we observe that those models without the smallest particles (without mode m 1 ) will underestimate the short-wave contribution at TOA by up to 20%. Models without the largest particles (those represented by the m ww , ie. for bins with radius larger than 40µm) are expected however to not be significantly affected in their estimations of DRE in the SW. 30 Because the dust emissions depend on mineralogy, on land surface properties and on regional meteorology, a few in-situ measurements are not sufficient to constrain the dust cycle at any scale.
It appeared logical to try to constrain the dust cycle by relying on dust optical depth (DOD) estimated from the satellite observations. (Ridley et al., 2016) used retrievals from instruments onboard MODIS and MISR to estimate global values for DOD between 0.020 and 0.035 which place 35 two models (CNRM-C6 and UKESM) outside this observational range. Although DOD should be proportional to the mineral dust total column, models with the lowest dust loadings are not those with smaller DOD. This is illustrated in the differences on mass extinction efficiency between the different models. The magnitude of this property is a good indicator of intrinsic model properties due to its relatively small seasonal cycle. Mass extinction efficiency is affected by the DPSD and optical 5 properties of mineral dust modelled. Note however that there are a sensible difficulty in estimate DAOD from satellite retrievals with the method of (Ridley et al., 2016) because it still lies on model simulations to ascertain the fraction of non-dust optical depths. As shown by our results in supplement material (section DOD), the non-dust fraction of optical depths can have large inter-model differences. 10 Therefore, based on MODIS satellite estimations of DOD based upon algorithm described in (Pu and Ginoux, 2018b), we compared the regional dust optical depth over dust source regions. This comparison allowed us to evaluate the skill of each model by evaluating the correlation between the regional time series of observations versus each model. A significant increase in the skill was revealed for the simulations using nudged winds, indicating that a consistent reproduction of the 15 seasonal cycle depends critically on how the strong surface winds are represented. This part of the wind distribution being more consistent when using winds from the ERA-Interim re-analysis. The correlation is not informing on differences in the scale of the signal, and Figure DOD.3 shows that there are regions where the seasonal cycle is well reproduced but the mean annual signal is actually underestimated, see also (Pu and Ginoux, 2018b). 20

Conclusions
This paper analyses the representation of the mineral dust cycle in five ESMs through diagnostics used for the evaluation of their performance with regards to observations. Although the agreement in terms of aerosol optical depth is better than surface fluxes or concentrations, we separate the models into two groups based on the simulated global mean dust optical depth. Those models with 25 values closer to 0.025 (CNRM, EC-Earth, IPSL and UKESM) are more consistent with the proposed satellite estimations (Ridley et al., 2016). Given that the optical depths depends on column loadings rather than dust emission fluxes, the inter-model convergence can be achieved even for those models that are not implementing particles with radius larger than 10µm. Also, to achieve an inter-model convergence in terms of optical depths is important to better constrain the dust radiative forcings 30 and direct radiative effects (DRE). Note that according to (Biagio et al., 2020) and to our results of Table 6 the DRE at the top of the atmosphere and at the surface have an important contribution from particles with diameters larger than 10µm altough the contribution of the fraction of particles larger than 40µm is marginal. The DOD seasonal cycle asserted by MODIS satellite estimates (see (Pu and Ginoux, 2018b)) gives us a key reference to understand the sources of the model discrepancies as illustrated by figure 11. The second diagnostic that we find useful is the mass extintion efficency (MEE) coefficient has a smaller inter-annual variability are reflects modelling properties such as assumptions on the size distribution modelled. 5 The models exhibit important differences in preferential dust sources, in particular a better agreement of preferential sources found over Asia and Australia would give us more consistency on global dust transport over the Indian and the Pacific Oceans. Although there is an scarcity of measurement campaigns over Asia compared to the Sahara and Sahel, studies based on empirical relationships between visibility and dust surface concentrations give us an additional insight on dust sources over 10 these regions (Shao and Dong, 2006). Compared to (Huneeus et al., 2011) we added AERONET stations over Asia, which resulted to be challenging for the CRESCENDO-ESMs in terms of the comparison provided by Taylor diagrams (see figure 12).
Currently, the dust source disagreements/differences between models make it difficult to quantify the fraction of the uncertainties of dust emission due to those small-scale atmospheric phenomena 15 not well represented by global models. The use of wind fields from reanalysis datasets reduces the differences between models, but a benchmark reference dataset regarding dust sources is needed to establish a range for those uncertainties.
Note also that the global description of dust cycle in terms of the amount of aerosol mass mobilized needs to be extended to larger particles as they can significantly increase the total emissions, and 20 according to recent studies the fraction of dust mass in the atmosphere due to the coarser particles would be dominant with respect to fine mode . However, still the method in which they are incorporated in the models can drive strong differences in total emissions with ranges from 3500 Tg yr −1 of CNRM-6DU to 7000 Tg yr −1 of UKESM model. Even more these differences in total emissions are not directly translated in proportional loadings because of the 25 differences in deposition between models and therefore in the lifetime.
Regarding total deposition one priority should be given to analyze the large differences in the ratio between dry and wet deposition between models and observations which is only partially explained by the modelled size distribution. From the aerosol micro-physical point of view differences in the dominance of wet scavenging over ocean regions could account for part of these differences. 30 Whereas, as indicated by (Shao et al., 2011) observations of dry deposition velocities in wind tunnels are not reproduced by current dry deposition schemes. At present, all models have difficulties to estimate local values wet/dry depositions, which can exceed a factor of 10. et al. (2013); Heald et al. (2014). This imbalance is conceptually different from the radiative forcing (either defined as an stratospherically adjusted instantaneous radiative forcing or by an effective radiative forcing) which is a comparison between a pre-industrial and a present day. In our case the estimations of direct radiative effects are estimated during a single simulation with present day conditions but with multiple calls to the radiative transfer model implemented in the climate model. The 10 aerosols in the climate model have actually direct, indirect and semi-direct effects along the simulation but the method only estimated the direct radiative effects due to scattering and absorption of specific aerosol species. Therefore there are observational based estimations of the direct radiative effects of the aerosols (Yu et al., 2006). However, from the point of view of aerosol modeling based on multi-modal approaches it has been reported a non-linearity properties for the estimation of each 15 mode contribution (Biagio et al., 2020) here the two different approaches and a joint new method with four calls to the radiative scheme are described.
In general, in the calculation done by current radiative transfer schemes it is considered a state of the atmosphere with several aerosols species X , Y, . . . where each specie is possibly described by a multi-modal distribution with modes X 1 , . . . , X n . The state with all the aerosol species is named 20 hereafter A, therefore A = X ∪ Y ∪ Z ∪ . . . . We define another state named A that includes all the modes of every aerosol specie except those modes corresponding of the specie X . Therefore, A = A ∪ X . The radiative effect of the aerosol X described by several modes X 1 , ..., X n , would be, where R represents the radiance obtained in our radiative transfer scheme which is intrinsically 25 a non-linear forward model. δ represents all others elements considered by our radiative scheme beyond the aerosol species which are invariant for both estimation of the radiance.
However, in order to disentangle the contribution of each mode X i of the specie X , there results differs depending on the methodology used due to the non linearity of R. We define here two methods: the first approach considers each X i mode added individually to A with respect to the 30 experiment given by A, hereafter we name this as method in. The second approach compares a experiment A with a scenario A where all the modes X j with j = i are included, named hereafter method out.
The method A would be written for the radiative effects of X i as, whereas the method B is written as, we note that F X = F X but F Xi = F Xi . In particular, we have both, i F Xi = F X and i F Xi = 5 F X . However, the results for 4 modes of mineral dust of IPSL showed at Table 6 indicate that 1 2 i ( F Xi + F Xi ) ≈ F X = F X . Therefore the joint method based on four calls to the radiative scheme to calculate the direct radiative effect is providing estimations per mode that combine linearly to reproduce the multimodal direct radiative effect.