The MODerate Resolution Imaging Spectroradiometer (MODIS) is mounted on board the polar-orbiting Aqua and Terra satellites operated by NASA. For this study, we use monthly Collection 6.1 level 3 550 nm AOD observations covering the period 2003–2024 , produced with the Dark Target retrieval algorithm over land and sea .

We also use daily MODIS Nd retrievals produced by combining Level 2 MODIS 2.1 µm retrievals of cloud optical thickness τ and cloud-top effective radius (re) under adiabatic (non-precipitating, non-mixing) cloud assumptions. Nd values are retrieved only for liquid-phase clouds with cloud-top temperature larger than 268 K . Several Nd datasets are included in , each resulting from different sampling strategies aimed at targeting systematic error sources affecting satellite retrievals. The least restrictive sampling strategy follows (Q06) and selects pixels with re>4 µm and τ>4. A second follows (G18) and also requires a pixel cloud fraction larger than 0.9 as well as minimal thresholds for satellite and solar zenith angles, to address errors associated with cloud measurements under slanted views . A third follows (BR17) and, on top of all the above-mentioned filters, imposes a stacking order for re, that must increase with the wavelength of the deployed near-infrared channel (1.6, 2.2 or 3.6 µm) to discard non-adiabatic cloud profiles.

We use the Q06, G18 and BR17 Nd retrievals averaged to monthly means on the original 1°×1° rectangular grid for the period 2003–2020. We use Q06 as the optimisation target due to its broader spatio-temporal coverage, and define error bars as the full spread across the three datasets at each grid-point. This approach captures the sensitivity to known retrieval artifacts without assuming a specific error model.

The Visible Infrared Imaging Radiometer Suite (VIIRS) is mounted on board the Suomi National Polar-orbiting Partnership (SNPP) and NOAA-20 satellites, operated by NOAA. We use the Level 3 monthly 550 nm AOD and 550–865 nm Angstrom exponent (AE) products for the period 2023–2024, produced with the Deep Blue algorithm over land and the SOAR algorithm over the ocean.

The Aerosol Robotic Network (AERONET) is an extensive network of ground-based sun photometers, providing measurements of aerosol optical properties . We use daily cloud-cleared, quality-assured and fully calibrated (Level 2) 550 nm AOD and 440–870 nm AE observations, as well as daily cloud-cleared, quality-controlled (Level 1.5) aerosol PSD inversion products for a selection of observational sites. We used all data between 2003 and 2024 available at each site.

The Clouds and the Earth's Radiant Energy System (CERES) instruments for the measurement of top-of-atmosphere (TOA) broadband shortwave (SW) and longwave (LW) radiation are mounted on board the Aqua, Terra, SNPP and NOAA-20 satellites. For this study we use TOA broadband shortwave (SW) all-sky monthly fluxes from Edition 4.2 Energy-Balanced and Filled (EBAF) dataset for the period 2023–2024.

The activation process of a population of aerosol particles can be summarized in such a way that, depending on local aerosols, thermodynamics (Ssat) and kinetics (timescales of ascent and water vapor condensation), for each species all particles larger than a critical size activate into a droplet. Consequently, to describe Nd, a number PSD description is needed, while their mass PSD is required to compute the mass scavenged by precipitation. Depending on the aerosol species and cloud regime, it might be consistent to assume low variability for mass activated fractions (as done by the IFS-COMPO by assigning a prescribed value to each species) while still diagnosing a variable number activated fraction.

We used the adiabatic parcel ascent model by (Pyrcel) to simulate activation of heterogeneous aerosol particle populations. We stored the results of the offline simulations in a lookup table (LUT) that takes as input the parcel updraft velocity and the number concentration of a set of pre-defined CCN-providing aerosol species and returns number and mass activated fractions, as well as critical dry radii for each of them. Atmospheric variables are set to describe an air-parcel ascent with initial pressure 850 hPa, temperature 278 K and 98 % relative humidity, lifted for a minimum of 100 m until peak Ssat is reached.

Previous studies found weak dependency of the activation process on cloud-base pressure and temperature, especially for warm phase regimes (above 273 K) . We perform simulations for a range of vertical velocities w (updrafts) to also describe regimes with relatively high CCN concentrations (greater than 1000 cm⁻³, updraft-limited) . To keep the number of simulations manageable, we define a small set of 6 internally-mixed CCN-providing aerosol species derived from those in Table , by grouping together those species with similar physico-chemical properties and assigning hygroscopicity κ with typical values inferred from . Their definitions are reported in Table . We performed activation simulations for every combination of number concentration for each species and vertical velocity (between 0.1 and 10 m s⁻¹) over seven geometrically-spaced values resulting in a total of 823 543 simulations. Subsequently, these results were integrated over Gaussian distributions of vertical velocities with seven values of mean w‾ in the range [-0.2 m s⁻¹, 0.2 m s⁻¹] (symmetric around zero, absolute values geometrically spaced) and seven geometrically-spaced values of standard deviation σw in the range [0.05 m s⁻¹, 2.5 m s⁻¹]. The integration is performed only for w>0 as in . The final size of the LUT is 5 764 801 elements.

The LUT returns activated number fraction (ax) for each CCN-providing species x listed in Table  for a given mixture of particles and configuration of w‾ and σw. The activation scheme is in this sense a wrapper of the LUT accessor with pre- and post-processing capabilities that extracts the nearest-neighbor value along the aerosol concentrations dimensions, and linearly interpolates along the w‾ and σw dimensions. As a final step, the scheme computes the number of droplets Nd using Eq. () and returns it to the caller. The diagnosed Nd can be used online by the IFS radiation scheme to compute liquid droplets re (see below). Similarly, the LUT can be accessed offline to estimate Nd from a given aerosol population and updraft conditions. When running the IFS with prognostic aerosol tracers, the activation scheme can also be called a second time by the wet deposition code to diagnose the activated mass fraction for each hydrophilic species.

The IFS (CY49R1) has a single-moment cloud microphysics scheme with prognostic variables for cloud fraction and water content for cloud liquid (LWC), cloud ice (IWC), rain (RWC) and snow hydrometeors. The radiation scheme diagnoses re needed for the all-sky radiative calculations: 5re=4(RWC+LWC)3πρwγNd1/3 where γ=rvre3, with rv mean volumetric ratio, ρw is the density of water and Nd the cloud droplet number concentration.

The IFS uses a wind-dependent parametrisation derived from , such that, for 10 m winds between 0 and 10 m s⁻¹ Nd∈[40cm-3,70cm-3] over the ocean and Nd∈[140cm-3,170cm-3] over land. γ derives from the studies by and , and uses the values of 0.77 over ocean and 0.69 over land, with adjustments to represent increased dispersion of the cloud droplet PSD when drizzle is present. We redirect the reader to the IFS documentation for further details.

In the setup for this study, the IFS radiation scheme can diagnose Nd with a call to the activation scheme described above by providing as input w‾, σw and aerosol mass concentrations of all aerosol species required to construct the CCN providers of Table . w‾ is set equal to the large-scale vertical velocity, which is typical for climate models . σw for turbulent boundary layers is generally diagnosed from turbulent kinetic energy (TKE) or eddy diffusivity ; however, these are not available as ERA5 fields, therefore for this study we used the Deardorff velocity scale w∗ for convective boundary layers , scaled by a factor 0.6 to diagnose σw, in line with relationships found in observations and numerical simulations . A minimum value of σw=0.1 m s⁻¹ is imposed to ensure physical activation conditions e.g..

Autoconversion rates of cloud water to rain are computed using the parametrisation from assuming fixed Nd values over land and sea, and this behaviour is left unchanged within this study, so that our setup does not include any direct impact of aerosols on cloud lifetime.

To perform the offline Nd computations needed by the optimisation procedure we relied on stored aerosol fields originally produced for verification purposes from lower-resolution (triangular-linear TL255, ≈78 km) 1 d CAMS simulations initialised from ERA5 over the period 2003–2020. Evaluations of the CAMS aerosol system (with and without assimilation of observations) can be found in and in the CAMS validation reports released periodically (see e.g. ); near real-time validations are also publicly accessible using tools such as Aeroval (https://aeroval.met.no, last access: April 2026). Simulated aerosol fields were stored on 16 pressure levels between 10 and 1000 hPa; the 11 pressure levels below 100 hPa have thicknesses ranging between ≈640 and ≈2300 m, with the highest resolution found in the lower troposphere and lowest resolution in the mid-troposphere. Such a low vertical resolution is clearly suboptimal for the purpose of extracting accurate aerosol concentrations at cloud level; however, using these data enables us to assess the current state of the model and the potential of the optimisation procedure, which may partially compensate for resolution-driven inaccuracies.

We extracted from ERA5 the following fields for the period 2003–2020: pressure (p), temperature (T), cloud cover (f), liquid (LWC) and ice (IWC) water content. These cover the lowest 57 of the 137 IFS model levels, which correspond to up to 10 km altitude. For each data stream, we select within each month every fifth day starting on the third day of the month; for each day, we use 3-hourly data (00:00, 03:00, 06:00, …, 21:00 UTC). All fields are interpolated to the same 1°×1° grid of the Nd retrievals datasets.

For each column, only points with local time between 09:30 and 15:30 UTC are retained, to reflect the typical daytime overpasses of the Aqua and Terra satellites. Only cloudy model grid-boxes are then retained, defined as those with at least 10 % cloud fraction. For each column, we estimate the cloud optical thickness τ across all cloudy grid-boxes and retain only those columns for which τ>4 in line with .

We define the representative cloud-top level as the level at which the cumulative optical thickness from the top crosses the threshold of τ=2 and the cloud bottom where it reaches 95 % of the total cloud τ. Optical thickness is diagnosed offline assuming a constant extinction efficiency of Qext=2. We chose the cloud-top threshold for consistency with MODIS cloud-top properties being typically within τ≈1 in the infrared , given that the extinction efficiency for wavelengths of ≈10 µm in liquid clouds is between 1 and 2 . Stratocumulus clouds also have optically thick and geometrically sharp cloud tops, spanning several units of optical thickness within one model level, which makes the results relatively insensitive to the precise choice of the optical thickness threshold for cloud-top identification. For completeness, we tested the sensitivity to cloud-top threshold values of τ=1 and τ=7, consistent with the bounds provided by correction formulas in for re retrievals. This affected cloud-top height location by less than 30 hPa for the thickest clouds and produced variations within 0.7 % in the global loss function (see below for its definition). Within a cloudy model column, we select liquid-phase clouds as those where at cloud top T>268 K, and IWC/(LWC+IWC)<0.1 similarly to the observational filtering criteria, but allowing for some ice within the gridbox due to the coarse resolution of the model fields (1°×1°) compared to the Level-2 data from which the Nd datasets were derived .

For a cloud layer with constant Nd profile, the instantaneous finite relative change in τ obtained by a change in Nd, assuming all other variables unchanged is given by Nd1/3 scaling, while the relationship with ΔNd/Nd holds only for small perturbations: 6Δττ=ΔNd1/3Nd1/3=13ΔNdNd+OΔNdNdΔNd/Nd→02

Throughout this study we set γ=0.8 consistently with the Nd retrieval methods by . Despite the potentially regime-dependent impact of γ on cloud microphysics , there is currently no consensus on how this parameter should be represented in models. However, typical errors of assuming a fixed value for γ are estimated between 10 % and 14 % (see and references therein), which translate into a relative error in τ of approximately 4 %, which we show below to be of secondary importance relative to that induced by aerosol number concentrations.

At each stored time and for each column of the domain, we interpolate aerosols to the identified cloud-top level p and calculate aerosol number concentrations using Eq. (). Given the relatively low vertical resolution of the aerosol dataset, the aerosol population extracted at cloud level represents a vertically smoothed average of actual simulated populations above and below the cloud level. The activation LUT is then used offline as a mapping function to diagnose Nd,IFS values from local aerosols and vertical velocity diagnostics. These are then averaged into monthly means, using only locations with at least three identified warm-phase cloud cases within the month. For each year, the simulated monthly-mean Nd are evaluated against the observed monthly-mean Nd,Q06 fields using the following loss function L: 7L(Nd,IFS)=Nd,IFS1/3-Nd,Q061/3ΔÑd,MODIS1/328ΔÑd,MODIS1/3≡max⁡Q06,G18,BR17Nd1/3-min⁡Q06,G18,BR17Nd1/3 where ‖…‖2 indicates the area-weighted average on the spherical surface and the source of Nd can be the offline diagnostics (IFS) or one of the three MODIS sampling strategies: Q06, G18, BR17 . Among the retrievals, Nd,Q06 was chosen as the optimisation target since Q06 is the least restrictive sampling strategy, which implies the largest number of valid retrievals.

As an optimisation algorithm for the loss function L we use Nelder-Mead with free bounds, a popular minimisation method belonging to the class of direct search methods, i.e. that do not require knowledge of the gradients of the function, for functions of the kind f(Rn)→R, which is the case for the constructed L. The algorithm uses n-dimensional simplexes and performs a series of reflection, expansion and contraction operations to converge on function minima see e.g.. Across the many setups considered, we never encountered important convergence issues.

The optimisation procedure is illustrated in the flowchart of Fig. . For each year from 2003 to 2020, L is evaluated on monthly Nd using aerosol number concentrations from Eq. (). The procedure is repeated in a loop leaving the median radius rmed as a free parameter for each CCN species excluding the coarse sea salt mode (Ssc), for which the median radius is fixed to 10rmed,ssf.

While aerosol and cloud data are spatially co-located, only monthly mean values are compared, so that L can be seen as a statistical evaluation of the simulated Nd. This implies that the optimisation targets large-scale and seasonal Nd signals, with variability on monthly and longer timescales. As a result, the sensitivity to the co-location in time and space of cloud fields and satellite overpasses is reduced. At the same time, by considering a smaller number of samples within each month we can substantially reduce the volume of data processed, keeping the procedure manageable.

As a result, a collection of optimised median radii for each species x and year y is obtained, rmed,x,y. We finally define the optimal PSD as those using the effective median radius rmed,x‾≡medy(rmed,x,y), i.e. the median across the 18 years of the optimised median radii. Within this framework, the resulting optimised aerosol PSDs are constrained by the cloud-top Nd observations and represent an effective description of aerosol number consistent with these observations; their realism is conditioned by non-represented processes (e.g. diagnostic representation of Nd and absence of prognostic droplet microphysics) and aerosol biases (e.g. speciation and vertical structure), and is therefore evaluated a posteriori through independent observations of aerosol optical properties.

The optimal median radii and implied number scaling for all three optimisation setups are reported in Table , while Fig.  shows how the simulated Nd compares with the optimisation target (Nd,Q06) before (prior, CAMS default PSDs) and after optimisation (optimised), for the InCloud and ClBase3 setups. These are represented as relative differences in Nd1/3, defined as 9RDND=ΔNd1/3Nd,Q061/3=Nd,IFS1/3-Nd,Q061/3Nd,Q061/3 which serves as a proxy quantity for expected first-order relative changes in τ (see Eq. ). The absolute zonal-temporal Nd1/3 RMSE is also shown in Fig. .

The optimal PSDs resulting from the InCloud setup imply reduced number per unit mass J for nitrate (Nit, ×0.69) and organics (Org, ×0.08) CCN species but an increased value for sulfate (Sul, ×1.11) and fine sea salt (Ssf, ×3.96) (see Table ). Figure  shows that the optimal PSDs globally improve the simulated Nd, corresponding to a reduction of the prior evaluation of the loss function L (Eq. ) by 13 %, from 1.85±0.02 to 1.60±0.02. The strongest reductions in absolute Nd1/3 (-0.25 to -0.5 cm⁻¹) are at the equator, where the prior Nd have a strong positive bias associated with OM-dominated CCN over Central Africa (RDND⪆0.50), and at latitudes south of 30° S, where model Nd are negatively biased (RDND⪅-0.50). However, moderate (RDND up to ≈0.2) residual bias patterns persist throughout the tropics and at latitudes south of 45° S, as shown by Fig. . Subtropical open-sea regions are also visibly degraded after the optimisation (RDND from ≈0.05 to ≈0.15). The low Nd bias over Australia worsens after optimisation (RDND from ≈-0.15 to ≈-0.3) as a result of the reduction of J for Org species.

We selected eight regions to better investigate remaining biases after the optimisation procedure: north tropical Africa (NTA), mid-Atlantic (MAT), central Africa (CAF), north tropical Pacific (NTP), Southern Indian Ocean (SIO), Southern Pacific (SOP), Europe (EUR) and India (IND). Their extents are reported in Table  and illustrated in Fig. . Figure  shows that the NTA, MAT, CAF, NTP regions all suffer from a high Nd residual bias relative to Nd,Q06 after the InCloud optimisation (RDND between ≈0.15 and ≈0.30), while SIO and SOP regions are biased low (-0.15⪆RDND⪆0). For these two groups of regions, monthly observed and simulated Nd are illustrated as spider plots in Fig. . In the NTP region, both prior and optimised model Nd are within the uncertainty range of the observations, while for the SIO and SOP regions, despite a significant increase in simulated Nd after optimisation, these remain below the lower end of the uncertainty range, typically found at ≈60 cm⁻³. Finally, in the NTA, MAT and CAF regions, the prior simulated Nd exceeds the upper bound of the uncertainty range with a clear seasonal pattern: December–February for NTA, December–March and June–September for CAF, July–October for MAT. After optimisation, Nd values fall within the uncertainty range in all three regions, but tend to remain near the upper bound and biased high with respect to Nd,Q06 (Fig. ) during these periods. Aerosol speciation in these three regions indicates that 60 %–90 % of simulated Nd originates from OM and BC particles (not shown), which are typically associated with wildfires.

If BC is excluded from the CCN calculations, the resulting optimal aerosol PSDs produce effects qualitatively consistent with InCloud, but with a significantly weaker reduction for Nit (×0.93) and Org (×0.31) CCN species (Table ). For this setup, optimal PSDs for all species except fine sea salt (Ssf) are closer to the prior PSDs than for InCloud (Table ). At the end of the InCloudNoBC optimisation, L=1.62±0.03, so that the final result is not significantly different from that of InCloud (L=1.60±0.02). Similarly, we found no significant difference in RDND between the optimised InCloudNoBC and InCloud Nd (not shown).

If Nd is diagnosed using aerosols located three model levels below cloud base, optimal PSDs imply a strongly reduced J for Sul (×0.44), Nit (×0.52) and Org (×0.16), and a higher J for Ssf (×2.55) (see Table ). For all species except Ssf, the optimal rmed values are significantly larger than for the InCloud setup. For the optimised ClBase3 setup, L=1.38±0.03; this setup is markedly better than InCloud at matching MODIS Nd due to the lower Nd1/3 RMSE (Fig. ) at latitudes south of 30° S over the ocean, where |RDND|⪅0.15.

Figure  shows that the optimised (InCloud) PSDs for the group of aerosols including SS and NI tend to slightly increase AOD, with a larger relative impact at mid- to high latitudes in the Southern hemisphere, while the low-latitude signal is dominated by the reduced AOD from the group of OM, SOA, SOB aerosols. Overall, the mean and local impact (not shown) on total visible AOD remains typically within a 15 %, partly also due to a compensation between the two aerosol groups. The increase in SS AOD at latitudes south of 30° S provides the largest relative change in total AOD, which improves the DJF season and degrades the JJA season.

The change in AE due to the optimised (InCloud) PSDs is dominated (> 90 %) by the SS2 and SS3 aerosol (not shown). This is detrimental at the latitudes higher than 45° in the Summer hemisphere, where the model tends to be biased low, but mostly beneficial everywhere else. As a result, the global AE RMSE is reduced by more than 34 % for both seasons, as shown by Fig. .

Figure  shows aerosol size spectra as observed by AERONET and simulated from CAMS aerosols for sites located close to the NTA and CAF regions. The plotted quantity is the PSD of the total spherical geometrical cross-section: 10dσdln⁡r=πr2rdNdr weighted by the Mie extinction efficiency Qext(r) at 550 nm for a real refractive index 1.3. Stations north and south of the equator present a peak in AOD during the DJF and JJA seasons, respectively, which is consistent with regional wildfire seasons. Multimodal size spectra are found for the stations north of the equator, with peaks at ≈0.1 µm, ≈0.6 µm and ≈2 µm. The two coarser peaks are also present in simulated spectra and are produced by mineral dust likely advected by northerly trade winds from West Africa. The finest-mode peak produced by the model is found at ≈0.3 µm (associated with OM aerosol), while it is located at less than 0.2 µm or even 0.1 µm in the AERONET data. Despite the particle number being generally underestimated by the model, the overall area below the graph in the r<1 µm regime is in fairly good agreement between model (prior) and observations. Using the optimised (InCloud) PSD definitions (see Table ) produces a modest shift in the size spectra of the finest peak, which is associated with OM aerosol, toward larger values, resulting in visibly degraded size spectra and deepening the low aerosol number bias against AERONET.

To test the sensitivity of ACI to aerosol wet removal in mixed-phase clouds, we performed a series of online IFS-COMPO simulations. These use meteorological initial conditions from ERA5 analyses, while chemical and aerosol tracers are restored from the previous forecast day at valid time +24 h, thus leaving them free to evolve. These runs have a resolution of ≈39 km.

Figure  displays a cross-section of the simulation output for a case study on 18 September 2024, after a 10 d spin-up. We use aerosol number mixing ratios (computed from prior CAMS PSDs), i.e. aerosol number concentration per unit mass of air, for Sulfate (SU), Sea Salt bin 1 (SS1) and Organic matter (OM) as an upper-bounding proxy (CCNmax⁡) for CCN concentrations. This case shows that for the control simulation CCNmax⁡ drops to extremely low values (well below 10 cm⁻³) in mixed-phase clouds simulated over the Southern Ocean. With the MOD2 version of the model, CCNmax⁡ is significantly higher throughout the same ice-containing cloud profiles, with values up to 100 cm⁻³. CCNmax⁡ is also increased at lower latitudes, where snow is present aloft, which is particularly evident at 42° S, between 650 and 250 hPa.

We also tested MOD1 and MOD2 by performing more extended simulations over the boreal winter (DJF) 2023–2024 and boreal summer (JJA) 2024 seasons. These setups use a 1-month spin-up to ensure that tracers are aligned with the climate of the model. For these cases, the “Control” experiment uses the default IFS CY49R1, where Nd do not depend on aerosols, “InCloud” diagnoses Nd from aerosols (ACI) at cloud level using the InCloud optimal PSDs, while MOD1 and MOD2 experiments add the corresponding IN-SCAV modifications on top.

Figure  shows the top-of-atmosphere (TOA) biases in simulated SW fluxes against CERES for the DJF 2023–2024 season experiments. The InCloud (ACI) experiment exhibits both larger absolute bias (+3.5 W m⁻²) and error standard deviation (STDE, +2.1 W m⁻²) than Control. The strongest contribution to this degradation is over the Southern Ocean, where TOA SW biases are increased by ≈20 W m⁻² in the sense of reduced cloud albedo. With the InCloud-MOD1 and InCloud-MOD2 experiments, STDE is reduced respectively by 1.1 and 1.7 W m⁻² compared to InCloud, with reflected SW radiation over the Southern Ocean increasing by up to ≈20 W m⁻².

We evaluate mean model outputs using mean observations of all available AERONET 550 nm AOD, 440–870 nm AE and size spectra over the period 2004-2024 at several high-latitude stations, six in each hemisphere. These are shown in Fig.  and cover the summer season (DJF for the southern and JJA for the northern hemisphere).

Figure  shows AOD and AE boxplots for the selected AERONET stations. The control simulation produces comparable 550 nm AOD with respect to AERONET, but tends to be biased low relative to the colocated MODIS AOD for most sites with enough valid retrievals. The model also tends to produce systematically low AE (up to ≈-0.8) against AERONET, but this difference is only occasionally larger than the joint model-observations interquartile range. The MOD1 and MOD2 simulations result in generally increased AOD (up to +0.05) and decreased AE (up to -0.5) for all locations, which represent a degradation with respect to mean AERONET observations.

Figure  shows the total-column AERONET and model size spectra (expressed as weighted cross-section size distributions, see Eq. ) during the summer season at the selected high-latitude stations. For each location, total-column number concentrations are reported, obtained by integrating dNdr over the domain r∈[0.1µm,7µm], over which the errors of the retrieved dV/dln⁡r are estimated within 10 % . For all stations at latitudes higher than 60° N and 60° S the Control simulation has lower particle counts (with differences up to 300 × 10⁻³ µm²), while MOD1 and MOD2 produce significantly higher particle number concentrations than the Control simulation (factor 1.5 to 2) resulting in better agreement with AERONET (see numbers after each label in Fig. ). The size spectra illustrate that this is associated with an increased aerosol mode centred around 0.3 µm which tends to be coarser and with larger amplitude than the finest AERONET mode (around 0.15 µm). This pattern holds consistently for all stations except CEILAP-RG (Argentina), which is the lowest-latitude (52° S) location of the whole set.

The optical thickness in the simulated spectra is dominated by modes shifted to larger sizes compared with AERONET; these larger modes are also amplified in MOD1 and MOD2 that, despite providing better agreement in particle number concentrations, tend to be biased high in AOD relative to AERONET. It must be noted that this contrasts with the validation against satellite AOD. In fact, Fig.  shows that at high latitudes the model's AOD tends to be biased low compared to MODIS, and biased high compared to AERONET. This discrepancy between MODIS and AERONET AOD seems consistent with the analysis by , but this case also shows that a more accurate quantification of biases of AOD from satellite at relatively high latitudes (above 60°) would give significant insights for systems like CAMS operationally assimilating global observations of AOD from satellites. The MOD1 and MOD2 experiments have systematically higher AOD at high latitudes, but tend to have lower AE than AERONET, which indicates too large a contribution to AOD by coarse mode aerosols. These discrepancies are, however, difficult to interpret due to the relative scarcity of observations from sun photometers at high latitudes especially in the Southern Hemisphere, as well as the almost complete absence of observations over open sea regions.

As a final global evaluation of the sensitivity experiments, Fig.  shows the evaluation of zonal-mean 550 nm AOD and zonal RMSE against MODIS for the experiments. The largest impact of MOD1 and MOD2 is at mid- and high latitudes towards increased aerosol burdens, with up to ≈0.05 increase for MOD2. This leads to a significant reduction in zonal RMSE for the summer hemisphere by up to ≈-0.1, and increased by the same amount over the winter hemisphere.

While the magnitude of the reduction of L by only 13 % may raise doubts about the effectiveness of the optimisation, it actually indicates that the prior (CAMS default) PSDs yield Nd values already close to the optimisation target. The main limitations of the optimisation lie in the prescribed spatial aerosol patterns from the model fields, and the restricted number of free parameters (the PSD rmed for five species). This is illustrated by the ClBase3 optimisation setup, where the prior Nd prediction has much larger errors throughout the tropics; in this setup, the improvement brought by the optimisation is significantly stronger, with a reduction of L by 21 %.

The optimised (InCloud) SU median radius rmed is close to the prior 0.11 µm, keeping the increase in particle number below 11 % and the optical effect non-detectable. This PSD description was independently updated in IFS-COMPO CY49R1 (from rmed=0.0355 µm and σ=2.0) and we found that using the old PSD led to significantly larger number concentrations of activated SU by up to a factor ×2.7 (not shown), which the optimisation would then need to correct. While the new prior SU performs fairly well globally, observations of tropical marine sulfate aerosol have indicated mass transfer from Aitken (r≈0.04 µm) to accumulation (r≈0.1 µm) mode . However, the IFS-COMPO does not currently represent changes in aerosol PSDs over time, and in general no transfer of mass across bins is allowed . Other models like the Met Office Unified Model do represent Aitken and accumulation modes for sulfate, and assess typical local mass ratios of 1 : 9 . This variability in sulfate PSD may contribute the pattern of simulated Nd over the oceans, with high Nd biases over subsidence regions, and neutral-to-low in convective regions, indicating a potential benefit of an additional Aitken aerosol mode, either as sulfate or internally-mixed aerosol.

The fixed mass wet scavenging coefficients used by the IFS (between 0.7 and 0.9) for most hydrophilic species tend to be smaller than the typical mass activation rates close to unity provided by the activation scheme. Therefore, we performed an online IFS-COMPO simulation (setup as for simulations in Sect. ) using scavenging rates diagnosed from the activation scheme and found the resulting changes in total aerosol mass to be within 5 % for SS, SOA, SOB, within 10 % for OM, and within 15 % for SU and NI species (see Appendix ). For most species (SS, SU, AM, OM) the resulting reduction in aerosol burdens would tend to increase the prior Nd biases for the optimisation. For OM, however, these reductions are too small to explain the reduction by a factor ×0.08 to ×0.31 required by the optimisation.

MODIS Nd retrievals are known to suffer from an optical penetration bias due to the assumption that the spectrally-retrieved re values are representative of the droplet PSD at cloud top, leading to overestimated Nd (MODIS 2.1 µm) retrievals between 20 % and 40 % for marine clouds. Bias-correction of retrievals has been shown to occasionally improve agreement with in-situ measurement campaigns, but implications on Nd budgets are still unclear . This translates to an upper-bound effect of 12 % in Nd-1/3 over marine regions within 30° latitude.

At latitudes higher than 60° N and 45° S our method struggles to sufficiently increase Nd to match observations. MODIS cloud retrievals are known to suffer from viewing geometry errors with large satellite and solar zenith angles , potentially degrading high latitude observations. According to , at latitudes higher than 60° Nd are overestimated by 16 cm⁻³ or less, which is potentially significant over relatively pristine regions over the ocean, with typical retrieved Nd values between 75 and 100 cm⁻³. These effects are included in one of the sampling strategies (BR17) and contribute to the error bars that we assigned to the MODIS Nd observations.

The optimisation results highlight that carbonaceous (OM, BC) aerosols are important contributors to simulated Nd over Africa and, as such, require a more detailed discussion of their representation. Particles with radii < 15 nm are weakly activated into cloud droplets, especially when characterised by low hygroscopicity, as in the case of soot. Representing BC with the same PSD as pristine soot might overestimate the number of particles, but underestimate their activation rates. This is because such an approach implicitly neglects the property of soot to form large chain-like clusters e.g., resulting in a reduction of the effective number of independent particles available for activation. At the same time, this approach cannot represent the growth of such clusters into larger structures incorporating SU or OM particles e.g., making them more efficient CCN providers. In addition, sensitivity of the activation efficiency to updraft velocity is expected in such aerosol-rich regimes; this sensitivity highlights both the relevance of ongoing efforts to better characterise updraft variability in global models e.g. and the difficulty of applying alternative approaches in our offline framework. However, updraft velocity plays a secondary role compared to aerosol number in determining the Nd bias, therefore the discussion will focus on the aerosol-related processes.

For black carbon CCN (defined as soot in Table ), the median simulated number activation rate is around 0.5 %. If BC were represented in the form of aged aggregates of hundreds to thousands of monomers often incorporating organics and sulfate crystals, this would imply a reduced total amount of aggregates by two to three orders of magnitude which, however, readily activate due to internal mixing with larger and more hydrophilic particles. Moreover, BC ageing is an open area of research, and future work is needed to better characterise the role and relevance of aged BC and its representation on CCN simulations.

Sensitivity calculations of simulated optical properties (AOD, AE, spectra) indicate that the optimal PSD for OM is likely compensating for processes not represented in the optimisation. In fact, the optimised (InCloud) PSD visibly degrades the shapes of the aerosol size spectra and worsens the low bias in total column number concentrations (Fig. ). The fact that InCloudNoBC produces Nd of similar quality, but with a neutral impact on aerosol optics, suggests that the compensated biases are related to the co-existence of BC and OM aerosol. Additionally, most of the aerosol counts from AERONET spectra are significantly higher than the model and associated with the fine-mode part of the size distribution (r⪅0.15 µm), which corresponds to BC in the model. However, a precise evaluation in this fine size regime is limited by the quickly decaying sensitivity of the retrieval for r<0.1 µm, where the number contribution to CCN aerosol particles increases. However, the substantially flatter tail of the model spectra is consistent with the above-discussed limitations in the representation of OM and BC ageing.

In the IFS-COMPO, carbonaceous aerosol emissions are controlled by satellite observations of wildfires via the Global Fire Assimilation System (GFAS). Figure  shows that wildfire carbonaceous aerosol emissions from GFAS correlate well with observed Nd in both regions (normalized covariance of 0.71 and 0.90) and the difference between observed and simulated Nd (normalized covariance of 0.85 and 0.72) for the north tropical Africa (NTA) and central Africa (CAF) regions, mirroring the seasonal biases in model Nd of Fig. . This does not hold for other regions like India (IND) and Europe (EUR), where wildfires are instead a weak predictor of Nd. The seasonality of Nd over NTA and CAF, and downstream over the mid-Atlantic, can therefore be associated with simulated wildfire emissions. This opens the possibility of using these results to support validation of related processes under active development for the wildfire assimilation systems, such as representation of wildfire types and associated smoke plumes.

We tested the robustness of the optimisation by excluding BC from the CCN calculations (InCloudNoBC). The rationale behind this is that the externally-mixed CAMS aerosol representation for this species is unsuited for describing the process by which BC is mostly scavenged in aggregated form with other, more efficient aerosol particles, and that therefore its contribution to the overall number of CCN is neutral. Results of the optimisation for this setup excluding BC from the CCN (labelled InCloudNoBC) are reported in Table  and are significantly closer to the prior definitions in the case of Org and Nit CCN providers. The almost identical final value of LInCloudNoBC to the InCloud setup indicates that excluding BC brings no significant change to the optimised Nd. Furthermore, the InCloudNoBC optimal PSD for OM has a nearly neutral effect on simulated OM AOD, which makes it a preferred option for its consistency with the current optical definitions; such a neutral impact can also be appreciated by visually comparing the typical mass extinction efficiency at rmed=0.09 µm and rmed=0.13 µm for OMH in Fig. . Given the equivalence of the resulting Nd, the higher consistency with OM aerosol optics and the significantly smaller size of the required LUT, InCloudNoBC emerges as a preferable configuration until CAMS BC representation is further improved.

The AE and AOD signal from SS aerosol (Fig. ) strongly depends on the decision to keep the two SS PSD modes geometrically spaced by a factor 10 (see Table ). The rigid displacement of the entire bimodal SS PSD towards smaller sizes during the optimisation is therefore driven by the number values associated with Ssf, for which the mass contributions from SS1 and SS2 are typically 70 % and 30 %. By design, Ssc provides extremely low CCN number concentrations (order of the unit against a background of dozens to hundreds cm⁻³); moreover, its role in reducing the activation efficiency of smaller, less hygroscopic particles, that we quantified within 15 %–20 % in the subtropical stratocumuli (not shown), provides too weak a signal in the overall simulated Nd to allow independent constraint of Ssc during the optimisation. However, the beneficial impact of decreasing AE over the ocean between 45° N and 45° S indicates that the current representation is plausibly underestimating the optical contribution of the coarse SS aerosol particles, and potentially also their relevance during aerosol activation.

Testing the activation scheme (InCloud optimisation) with online IFS-COMPO experiments shows a widespread and strong decrease (up to ≈35 W m⁻²) of reflected solar radiation at latitudes south of 45° S, covering all the Southern Ocean (SO). Since the IFS, like many global models , generally underestimates the amount of reflected solar radiation over the SO, this signal directly translates into a significant degradation of TOA SW fluxes. The understanding that these regions are strongly characterised by mixed-phase, boundary-layer cloud regimes motivated sensitivity tests targeting the aerosol wet removal for freezing clouds. For these clouds, air is typically supersaturated with respect to ice but subsaturated with respect to water, so that ice crystal growth occurs via deposition of water vapour produced by evaporating cloud droplets, a mechanism known as the Wegener-Bergeron-Findeisen (WBF) process . From the standpoint of aerosols, this implies evaporation of activated CCN into interstitial cloud space, therefore limiting the efficiency of aerosol removal by precipitation compared to warm-phase clouds, where only liquid water is present.

Based on observations at one station in the Swiss Alps, produced two parametrisations to modulate scavenging efficiency in mixed-phase clouds, one temperature-dependent and the other phase-dependent, ζ(T) and ζ(IWR), to scale the activated number fraction of aerosol particles with diameter larger than 100 nm. Since the IFS IN-SCAV scheme already applies ζ(T) to rescale the mass-scavenging rates whenever snow is produced , we experimented with two model changes adding complexity to the IN-SCAV scheme; the first uses a phase-dependent parametrisation of scavenging efficiency for both liquid and ice phase (MOD1); the second explicitly treats mixed-phase conditions and riming processes (MOD2).

When evaluating global TOA SW biases, the MOD1 and MOD2 setups still increased STDE relative to control, but this degradation was significantly smaller than that of InCloud (default IN-SCAV scheme) respectively, by 52 % (MOD1) and 86 % (MOD2). In the MOD1 and MOD2 experiments relative to the standard InCloud setup, the SW flux change is dominated (more than 90 %) by reduced cloud re because of higher diagnosed Nd by the activation scheme over the SO. This response is driven both by increased SS and SU aerosol burden (and associated AOD) at high latitudes, and by their longer persistence inside ice-precipitating clouds. Because no new optimisation was applied to MOD1 and MOD2 setups, the radiative response reflects the impact of the modified wet removal processes. The increased aerosol burden improves agreement in aerosol total-column number concentrations for most high-latitude AERONET sites, but tends to progressively overestimate AOD and underestimate AE, suggesting that the model is overestimating the size of aerosol particles at those locations.

The increased aerosol loads for MOD1 and MOD2 significantly improve AOD with respect to satellite observations over the summer hemisphere, but lead to a significant overestimation over the winter hemisphere, indicating a failure in capturing the seasonal variability of aerosols over marine mid- and high-latitudes. A possible explanation is that the IFS, despite linking SU production to the oxidation of available dimethyl sulfide (DMS), has no representation of sea-borne marine organic aerosols. These are likely linked to photosynthetic activity of phytoplanktons and are found to significantly contribute to spatio-temporal variability of cloud Nd . Therefore, considering sea spray as containing only SS might result in an overestimated burden of SS, with boundary layer aerosols lacking the correct seasonal cycle.

The MOD1 and MOD2 tests have demonstrated high sensitivity of simulated Nd to the representation of aerosol removal by precipitation from mixed-phase clouds. However, particles released by evaporating droplets also incorporate information on microphysical processes occurring before evaporation, e.g. collection, collision-coalescence or nucleation, resulting in internal mixtures with increased particle size . Such evolution cannot be effectively represented with the single-moment cloud scheme of the IFS, since no memory of cloud particle number concentrations is preserved. Nonetheless, our investigation indicates that this is a plausible process limiting the effectiveness of the Nd optimisation at mid- to high latitudes.

The optimal Nd values from the ClBase3 optimisation perform markedly better than those from InCloud at mid- and high southern latitudes. This likely does not reflect better physical realism, because of the inconsistency with vertical tracer transport to cloud top (see discussion in Sect. ), but rather a more meridionally uniform aerosol background found below cloud base than inside the cloud. To illustrate this point, Fig.  shows the amount of diagnosed Ssf particles (represented with the prior PSDs) during the InCloud and ClBase3 setups. In principle, low Ssf number concentrations are expected, as sea-spray is a secondary CCN provider e.g.. However, coarse sea salt significantly impacts Nd in pristine regions via activation competition mechanisms of heterogeneous aerosol populations , making a realistic representation of marine aerosol profiles essential to predict Nd. While particle concentrations at cloud level are typically between ≈7 and ≈20 cm⁻³ at subtropical latitudes, these sharply fall below 5 cm⁻³ with increasing latitude. Such meridional contrast is not found when diagnosing Ssf CCN just below the cloud base (with significantly higher values up to ≈30 cm⁻³), so that for ClBase3 their concentrations over the SO are of similar or higher magnitude than subtropical values. As a result of this substantially different aerosol background, the optimisation for ClBase3 yields significantly better agreement, although it does not guarantee physical consistency, highlighting the need for independent observational constraints. Nonetheless, this makes the ClBase3 approach a viable workaround for improved model Nd in IFS-COMPO until aerosol concentrations inside clouds are improved, with the important caveat of a trade-off between correcting Nd biases and preserving consistency with optics and vertical transport of tracers.