The mineral dust samples used to investigate dust ice nucleation activity were collected during field campaigns in Morocco (2019) and Iceland (2021). The Morocco campaign was organized by the European Research Council project entitled FRontiers in dust minerAloGical coMposition and its Effects upoN climaTe (FRAGMENT) and the Iceland campaign co-organized between FRAGMENT and the project Iceland as a model for high-latitude dust sources – a combined experimental and modeling approach for characterization of dust emission and transport processes (HiLDA) e.g.. Soil sampling in Morocco was carried out in September 2019 in the area of L'Bour (29°49^′30^′′ N, 5°52^′25^′′ W), a dry lake located in the lower Draâ valley at the edge of the Sahara. The zone consists of a flat surface with a smooth hard crust in which under favorable weather conditions dust was frequently emitted. For a detailed characterization of the area and aerosols, the reader is referred to , and . Icelandic soil samples were collected from a terminal lake connected to a nearby glacier (N 64°54^′55^′′, W 16°46^′35^′′, 710 m a.s.l.) in the Vatnajökull National Park in August 2021 . The area was flat and devoid of substantial roughness elements. Flooding from the nearby glacier regularly supplied fresh sediment to the area. A detailed description of the study site and sediment characteristics is presented in and of the properties of the emitted dust in . For both locations, sampling was done with a metallic shovel (50 cm2 area, and 2 cm depth) in a stratified random sampling approach across 9 equally sized squared strata covering a total area of 100 × 100 m². After collection, samples were stored in plastic bags and transported to the laboratory where they were dried for 24–48 h at 50 °C. Three samples were collected within each stratum and then combined to three separate representative samples (hence each consisted of one sample per each stratum). Size-segregated samples for injection into AIDA (Sect. ) were generated from the collected samples using both sieving and a cascade impactor. The procedure is described in . In short, a cascade impactor (Retsch TYP PI-1) was used, allowing separation into a maximum of seven stages ranging from 0.3 µm to >20 µm in diameter. Approximately 0.2 g of the sample that had been previously sieved through a 63 µm mesh was placed into the initial stage of the impactor, as instructed by the manufacturer. The air flow through the impactor was held constant at 2.4 m3 h-1 with a compressed air pressure of 3–20 bars to disaggregate the particles before entering the impactor. To determine the mass of the sample collected in each stage, each ring of the impactor was weighed before and after the segregation process using a balance (with a precision of 0.0001 g).

Subsequently, the particle size distribution (PSD) was measured using a Malvern Mastersizer 2000 (Malvern Instruments Ltd), which employs the laser diffraction method based on Mie scattering theory (ISO 13320-1). The instrument determines PSDs from the angular distribution of scattered light of an ensemble of particles rather than detecting individual particles; thus, all particles within the laser beam contribute to the measurement signal. The nominal measurable size range is approximately 0.02 to 2000 µm. Ethanol was used as dispersant. The refractive index for the dispersant and particles was 1.360 and 1.520, respectively. The technique yields volume-based particle size distributions, reporting diameters of equivalent spheres assuming a spherical shape. Uncertainties in the retrieved PSD arise from assumptions in the inversion algorithm (e.g., refractive index), particle shape effects, and sample dispersion. Under controlled conditions, the reproducibility of laser diffraction measurements is typically within a few percent (ISO 13320), but variability may be higher for irregular particles such as mineral dust. Furthermore, reproducibility was further assessed through n=2 to 6 replicates per sample. The mean bin-wise coefficient of variation of the surface area distribution, defined according to CV‾=1N∑iσi/μi, where μi and σi are the across-replicate mean and standard deviation of the surface area distribution, respectively, and N is the number of replicated measurements, was below 6 % for 5 of 7 samples, reaching 12 % and 6 % for the Morocco samples (Fig. b and c, respectively). This metric captures point-by-point shape variability across the full distribution. These results indicate high repeatability of the Malvern measurements for the analyzed samples. It should be noted that the PSDs derived from Malvern measurements were used to qualitatively compare the PSD obtained from freshly segregated samples with the PSD measured during the MICOS campaign inside the AIDA chamber, rather than being used in any calculation.

The Dust-induced ice nucleation: Effects of MIneralogical COmposition and Size (MICOS) campaign took place from 21 November to 9 December 2022 with a total of 32 expansions in the Aerosol Interaction and Dynamics in the Atmosphere (AIDA) chamber. Our main focus was to study the ice nucleation activity of coarse (2.5≤D<10 µm) and super-coarse (10≤D<62.5 µm) particles defined in terms of the volume-equivalent (geometric) diameter (D). To this end, the INA of the samples was investigated using four complementary techniques, each fulfilling a distinct and necessary function that could not be covered by a single instrument. AIDA (Sect. ) and INSEKT (Sect. ) were used in combination to extend the temperature range of the INAS density measurements. While AIDA operates at colder temperatures, INSEKT reaches warmer temperatures through offline filter-based freezing assays, together providing a more complete characterization of the temperature dependence of ns. AIDAm (Appendix ) was used to characterize the temporal evolution of the INAS density at a higher temporal frequency than AIDA, by performing multiple consecutive expansions on aerosol sampled directly from AIDA. This is particularly relevant for the extended size range considered in this study, as larger particles are subject to gravitational settling inside the chamber, which could progressively alter the size distribution of the aerosol during an experiment and therefore affect the measured INAS density. The AIDAm time series therefore allowed to investigate whether the INA changed with changing PSD. Finally, the IR-DROFA (Sect. ) provided an independent cross-check of the INAS density using a bulk suspension approach combined with BET-derived specific surface area measurements. This approach is complementary to the aerosol-based surface area estimates used in AIDA and INSEKT, and allows us to compare the derived ns values obtained with the different surface area estimation methods. The following sections describe each instrument and its specific measurement approach in detail.

Additional measurements of INAS density were conducted using a modified version of the droplet freezing assay (IR-DROFA) setup. The basic configuration of this instrument is described in . The modified version includes an infrared (IR) camera (model PI640i, OPTRIS GmbH), which is used to detect the temperature jump associated with the release of latent heat upon freezing of a suspension droplet. Suspensions were prepared using the samples sieved through a 20 µm mesh. Droplets with a volume of 17 nL were deposited onto a 10 × 10 mm2 Si wafer in a square array consisting of 80 to 95 individual droplets. The fraction of frozen droplets as a function of temperature was measured using an initial suspension with 1 wt %, which was then diluted tenfold twice, resulting in suspensions with concentrations of 0.1 wt % and 0.01 wt %. Each IR-DROFA measurement was performed twice at a cooling rate of 3 Kmin⁻¹.

In order to obtain the differential nucleus concentration (k(T)) or the cumulative nucleus concentration, INAS density (ns(T)) (Sect. ) the surface area of the particles is needed. Previous studies have assumed that mineral dust particles can be approximated to spherical shapes . However, newer studies on the shape of mineral dust have found that ellipsoids are better shape approximations . Furthermore, the deviation of the aspect ratio (AR) from unity (AR-1) and the height-to-width ratio (HWR) of these ellipsoids both follow a log-normal distribution . Using ellipsoids as approximation for mineral dust shape, we computed the surface area using the globally averaged values of the AR and HWR distributions, i.e. a median AR of 1.70 ± 0.03, a median HWR of 0.40 ± 0.07, a geometric standard deviation for AR-1 of 0.70 ± 0.02 and for HWR of 0.73 ± 0.09 . Following a similar procedure as in , volume-equivalent (geometric) diameters of ellipsoidal dust particles were obtained with Monte Carlo sampling from the AR-1 and HWR log-normal distributions. The surface area of each generated ellipsoidal dust particle is computed. Then, particles with the same volume-equivalent geometric diameter are grouped and the mean surface area is obtained. Figure b presents the surface area for the volume-equivalent geometric diameter for both ellipsoidal and spherical shapes. Larger differences in surface area between spheres and ellipsoids become noticeable at approximately 30–40 µm.

The dust aerosol number PSDs were obtained with APS, SMPS, and OPC. One APS was located at the top of the chamber sampling with a vertical line, and another APS and SMPS were located at an intermediate height sampling with a horizontal line. The additional vertically sampling APS was installed to identify and avoid possible losses from gravitational settling in the horizontal lines. For large particles, the number PSDs were measured with Welas 2 (an explanation of the threshold used is provided below). SMPS and APS were combined by merging overlapping size bins. The size distribution of the mobility diameter from the SMPS and the size distribution of the aerodynamic diameter from the APS were converted to size distributions of the volume equivalent (geometric) diameter, defined as the diameter of a sphere that has the same volume as the measured particle, independent of its actual shape. Welas measurements were converted from optical to geometric diameter considering triaxial ellipsoidal shapes. The complex refractive index for Morocco was set to n=1.49+0.0015i, where the real part 1.49 accounts for the refraction (phase velocity) and the imaginary part 0.0015 for the absorption . For Iceland, the complex refractive index was set to n=1.59+0.004i . Combining the properties of our optical sensor , with a wavelength centered at 0.44 µm, and a scattering angle from 85 to 95°, and the refractive index of our samples, the conversion from optical to geometric diameters was carried out based on Table S1 reported in . Figure a depicts the relationship between optical and geometrical diameter for the characteristics of our sensors and samples. It can be observed that for sizes smaller than 1 µm the geometric and optical diameters are similar. However, for larger sizes, the relationship changes. Initially, the optical diameter is smaller than the geometric diameter up to approximately 7 µm, and becomes larger thereafter.

To reduce measurement noise and minimize rapid fluctuations in concentration, particularly for smaller particle sizes, bin averaging was applied to the SMPS-APS data. After converting both datasets (SMPS-APS and Welas) to their respective geometric diameters, they were overlaid for comparison. Due to the reduced efficiency of the APS at larger particle sizes (beyond ≈3–4 µm), a decline in measured particle counts is observed, while Welas reported higher concentrations at the same diameters. We used the intersection of measurements from APS and Welas, i.e. the transition point where the APS measurements fall below those of the Welas, as the threshold beyond which we utilized Welas data. However, due to the decreased efficiency of both instruments near their overlapping zone, the merged size distributions often exhibit an unrealistic dip in the transition region. However, this does not significantly affect the final results (see Sect. ). Additionally, two other issues were encountered during the measurement of PSDs in AIDA. The first was the presence of residual monodisperse polystyrene latex (PSL) spheres used for calibrating the optical sensors. The second was that the CPC measured a lower particle concentration than the optical sensor during expansion, which is not physically realistic because the CPC's measurement range is broader than that of the optical sensor. The first issue was easily addressed, as the PSL particles exhibited a characteristic and clearly noticeable peak at the same diameter in all measurements, making them easy to identify and exclude from the PSD. The second issue was resolved by scaling the initial PSD (prior to expansion) to the maximum concentration observed during expansion. This approach is justified based on a common assumption in AIDA experiments, in which all particles nucleate into CCN. Therefore, the total particle number before and after expansion is conserved. Figures  and  show the surface area size distribution of the samples injected into AIDA, as well as the mean surface area size distribution of multiple experiments with the same sample ID for samples in AIDAm. The mean values and standard deviations of the multiple expansions in AIDAm are shown in Figs.  and  for Morocco and Iceland, respectively, prior to expansion for each experiment, as obtained using the approach described earlier. It is important to mention that due to technical problems with AIDAm in 7 out of 30 experiments (IDs 5, 10, 11, 12, 14, 20, and 21), no AIDAm expansions were carried out in those experiments. Additionally, Figs.  and  present the surface area distribution measured with laser diffraction (LD, Sect. ) after sieving the samples. Although it relies on a different measurement principle than the other sensors, laser diffraction yields PSDs that are in reasonable agreement with those obtained from the combined SPMS-APS-Welas approach. The largest differences between the two methods are observed for IDs 5, 9, 10, 12, and 34, where the surface area distribution obtained with the combined instruments (SMPS-APS-Welas) tends to show higher values for diameters larger than 10 µm than the LD distributions. Conversely, experiment ID 29 exhibited a different behavior compared to both the combined instruments (IDs 25 and 28) and the LD technique. The reasons for this behavior are not clear.

In addition to the surface area estimates obtained using the methods described in Sect.  and , the specific surface area (SSA) and porosity of samples from Morocco and Iceland sieved to 20 µm was determined with the Brunauer–Emmett–Teller (BET) method using the Anton Paar (Quantachrome) Autosorb iQ device. The analysis was performed for N2 and H2O gases with cell type 9 and 6 mm w/o rod, respectively. Characteristics of the measurement of each sample and gas and the measurement results are summarized in Table .

Particle morphology was investigated with scanning electron microscopy (SEM, ThermoFisher Scientific, ESEM FEI Quattro S) on a single analyzed filter collected with the vertical sampling for experiment IDs 20 and 22 for Morocco and Iceland, respectively. All samples were collected on a Nuclepor^® membrane filter, pore size 0.2 µm, and coated with 1.5 nm Pt before analysis. Most Icelandic dust particles are compact agglomerates of densely packed plate-like fragments as shown in Fig. a and b. In contrast, Moroccan particles are either solid particles (presumably mixtures of chlorite, plagioclase, clays, among others) as shown in Fig. c or porous loosely packed agglomerates of nanometer-size fragments, the composition of which is characteristic for montmorillonite (Fig. d). The presence of swelling phyllosilicate (montmorillonite) and the intrinsic porosity of such particles is likely responsible for (1) the enhanced gas adsorption capacity of Moroccan dust (Appendix ), and (2) the strong difference of SSA measured with N2 and water vapor, which is not observed for Icelandic dust (Table ). However, it is important to note that the SEM analysis performed on these samples does not allow for a quantitative estimation of the frequency of agglomerates. A preliminary estimate suggests that the agglomerate frequency lies between 5 and 10 % (Appendix ). However, the frequency distribution of agglomerates across sizes is not considered. Consequently, the increased adsorption observed in the Moroccan samples cannot be unambiguously attributed to the presence of agglomerates, and further tests are required.

Assuming that ice nucleation occurs at the interface between the particle and the liquid droplet in which it is immersed, the particles have a characteristic number density of ice nucleation active sites (ice nuclei) on their surface at which ice germs form at defined temperatures, i.e. ice formation occurs at this site instantaneously once the characteristic temperature is reached. Considering the average number of ice nuclei that are active in an infinitesimal change of temperature on the surface of a particle, the differential nucleus concentration is defined as 2k(T)=1SareaN0(T)dNdT, where k(T) [m-2K-1] is the differential nucleus concentration of active sites per surface area and temperature change at temperature T, Sarea is the surface area of the particle, and N0 is the number of unfrozen droplets at temperature T. It is worth noting that the use of the original equation proposed by has been altered changing volume to surface area . It is possible to relate the change in the number of frozen and unfrozen droplets through dN=-dNf, with dN being the change in the number of unfrozen and dNf that in the number of frozen droplets. Considering that the probability of finding one or more active sites within dT follows a Poisson distribution and noting that the presence of one or more active sites on the surface of the particle at temperature T leads to the freezing of the droplet, we obtain for a monodisperse aerosol 3dNfN0(T)=1-e-k(T)SareadT It is possible to extend Eq. () to the case of a polydisperse aerosol as 4∑j=1pdNf,j=∑j=1pN0,j(T)[1-e-k(T)Sarea,jdT] with j being the jth size bin and p the number of size bins in the distribution. A common metric used to express the ice activity of particles is the cumulative nucleus concentration, also called INAS density, ns(T), which represents the number of active sites per surface area between temperature T to T+dT. It is possible to obtain ns(T) in two different ways. The first involves the use of Eq. () and the relationship k(T)dT=-dns. By integrating Eq. () and extending it to a polydisperse aerosol population, Eq. () is obtained: 5∑j=1pNf,j=∑j=1pN0,j[1-e-ns(T)Sarea,j] Noting the similarities of Eqs. () and (), the procedure to obtain either k(T) or ns(T) is the same. Expressing the exponential term as a Taylor series, we obtain: 6∑j=1pfj=∑j=1pqjbj-bj22!+bj33!-… where fj is dNf,j or Nf,j, qj is N0,j(T) or N0,j, and bj is k(T)Sarea,jdT or ns(T)Sarea,j, respectively, for Eqs. () or (). Assuming that both k(T) and ns(T) are independent of particle size, and that k(T)Sarea,jdT≪1 and ns(T)Sarea,j≪1, non-linear terms can be neglected, which leads us to the approximated equations for k(T) and ns(t): 7ak(T)=-1dT∑j=1pdNf,j∑j=1pN0,jSarea,j7bns(T)=∑j=1pNf,j∑j=1pN0,jSarea,j

The second method consists of computing k(T) according to Eq. () (linear approximation) and from there estimate ns(T) as 8ns(T)=∑hqkhΔTh where q represents the number of ΔT intervals required to arrive at T from the initial temperature T0, and kh is the differential nucleus concentration at temperature Th.

As presented in Sect. , the use of Eqs. () and () assumes that the exponential of Eqs. () and () are much less than 1. Given that we are considering particle sizes that expand over three orders of magnitude (i.e. from 10-1 to more than 101), it is relevant to evaluate whether or not this assumption and therefore the approximated solutions are valid. For this purpose, we computed ns(T) (a) with Eq. () and (b) including higher powers (up to 5 for stability reasons) in the Taylor series (Eq. ) to obtain k(T) and ns(T). For the case in which k(T) is computed, Eq. () allows to obtain ns(T). We then quantified the difference between these methods as the relative error, 9RE=|ns,app-ns′|ns,app×100, where ns,app is the approximate value of ns(T) calculated with Eq. (), and ns′ is the value obtained including 5 terms in Eq. () (to obtain ns(T) directly) or with Eq. () (to obtain ns(T) through k(T)). To obtain the roots of Eq. () different approaches were evaluated, and Newton's method proved to be the most stable. Fig.  shows the resulting relative error for Moroccan dust for experiments with AIDA (Fig. a–b) and INSEKT (Fig. c–d). It can be noticed that for INSEKT experiments, there is no appreciable difference between the approximated solution and the one considering higher-order terms (Fig. c–d). This is due to the low IN activity present at the temperatures in which INSEKT experiments were carried out. On the other hand, substantial differences are observed for AIDA experiments. Experiments 5, 13, 14, 16, and 29 present the biggest differences for both methods with a relative error closer to 90 % when INAS is computed with a polynomial of degree 5 (Fig. a) and around 40 % to 80 % when it is obtained with k(T) (Fig. b). The relative error increased with decreasing temperature during an experiment. For example, RE increased from experiment 26 to 29 and the start temperature in those experiments decreased from 251.9 K in experiment 26 to 250.7 K in experiment 29 (Table ). Experiments conducted at the warmest temperatures (experiment IDs 9, 10, 20, 21, 23, 24, and 25) have a relative error of less than 40 %. Generally, for the coldest temperatures, the error increases because the ice nucleation activity is higher (measured either through k(T) or ns(T)) making higher-order terms in the polynomial expression more relevant. Moreover, the use of a 5th-degree polynomial in the general expression (Eq. ) is still an approximation that may be affected by numerical instability. For example, large values can cause high-degree terms to grow excessively.

Figure presents the relative error for the Iceland experiments for AIDA and for INSEKT. The difference in the ns(T) values obtained with the different methods is almost zero for all INSEKT experiments. This is due to the low INA that the Icelandic samples presented at temperatures between 252–255 K. As was the case for the Moroccan experiments, there is a larger difference for AIDA experiments compared to INSEKT and a similar trend is observed, i.e. experiments at colder temperatures show larger relative differences.

Given that for most of our experiments the difference between both approaches was lower than 50 % or even 30 % (labels b, c, and d for Figs.  and ), and considering more terms in the computation of INAS did not change significantly the final fit, we will use the standard equations (Eqs.  and ). However, it is important to note that in some experiments the difference exceeded 50 %, which makes it plausible that with samples with a higher INA, or at lower experimental temperatures, the difference could grow even larger. For this reason, it is suggested that the commonly used assumption that ns(T)Sarea,j≪1 (or equivalently k(T)Sarea,jdT≪1) needs to be revised when the surface area distribution covers several orders of magnitude and in particular when the INA is high.

The values of k(T) and ns(T) obtained with Eqs. () and () are shown in Fig.  for Morocco and Fig.  for Iceland as a function of temperature and colored depending on the mean diameter of the surface area size distribution of the probed sample. Figure a and b present the experimental results obtained with AIDA and c and d with INSEKT. The differential nucleus concentration, k(T) (Fig. a, c) displays a larger variation from a linear behavior as the temperature is decreased for the same experiment. This is because k(T) is more sensitive to variations in ice crystal number concentration than ns(T). While ns(T) generally increases with each new temperature step due to its cumulative nature, k(T) can increase, decrease, or remain constant, reflecting the dynamic changes in ice nucleation. When comparing metrics obtained with the same experiment techniques (Fig. a, b for AIDA and Fig. c, d for INSEKT) it is notable how similar the slopes of the linear regressions are: 0.75 for ln⁡(k(T)) and 0.80 for ln⁡(ns(T)) for AIDA, and 0.72 for ln⁡(k(T)) and 0.74 for ln⁡(ns(T)) for INSEKT. Interestingly, the different size distributions, indicated by their mean diameter, did not have a notable impact on the values obtained for k(T) and ns(T), i.e. no color gradient is apparent across k(T) or ns(T) for a given temperature in Fig. . For example, experiments 9 and 23, which started at similar temperatures, but tested dust aerosol with different mean diameters, presented almost the same behavior and ice nucleation activity.

Figure  presents k(T) and ns(T) obtained from AIDA and INSEKT experiments for Icelandic dust. It can be noticed that the logarithm of the differential nucleus spectrum for AIDA does not present a clear linear increment with the decrease in temperature, but rather a more dispersed behavior around the linear fit. Whereas ln⁡(k(T)) shows considerable deviation and dispersion around a linear behavior, ns(T) follows a linear relationship well and with smaller dispersion, particularly for the INSEKT results.

Figure  combines our results from AIDA and INSEKT and shows INAS densities, ns(T), for Morocco (Fig. a) and Iceland (Fig. b) together with results from previous studies. For the temperature span of AIDA and INSEKT experiments, a notable spread in INAS densities of ∼ 1.5 orders of magnitude for Morocco and ∼ 2 orders of magnitude for Iceland can be observed. The disagreement between these two techniques is not new, and our results are consistent with previous observations . Table presents the coefficients for the linear regression (a+bx, P1) for both dust sources, Morocco and Iceland. Besides our own experimental results, Fig. a also shows results from previous studies as a reference. It can be observed that our AIDA results are closer to previous fits for temperatures lower than 250 K, approaching the parameterization proposed by , which is also based on AIDA experiments. Compared with , we obtained lower values for INAS densities from our experiments. However, our results are within the scaled values of 1% and 20% reported by for K-feldspar, which agrees with the measured feldspar content of our samples (Sect. ).

INAS densities for Iceland (Fig. b) show a greater spread than those for Morocco: ∼ 3 orders of magnitude in the 95 % confidence interval compared to ∼ 2 orders of magnitude for Morocco. Similar to our results for Morocco, INSEKT experiments yielded lower INAS densities than AIDA experiments in the temperature range in which they overlapped. The presented AIDA data (slope -0.35, Fig. b) is closer than the INSEKT data (slope -0.64, Fig. d) to the parameterization of (slope ≈-0.46). It is important to note that the comparisons in Sect.  were always performed between experiments using the same instrument, ensuring that methodological offsets between AIDA and INSEKT did not affect our conclusions regarding sample properties. Nevertheless, we acknowledge that the systematic offset between AIDA and INSEKT affects the absolute ns values and therefore the parameterizations derived from the combined dataset (Table , Fig. ). Although its cause remains unclear, this offset is consistent with previously reported inter-instrument discrepancies and introduces an additional source of uncertainty in the proposed parameterizations (as accounted for in the confidence intervals). Disentangling instrument-related from sample-related contributions to the observed spread in the overlapping temperature range has been the subject of previous studies and would require dedicated intercomparison experiments using identical aerosol samples measured with both techniques, which is beyond the scope of the present study. For this reason, the fits obtained with each individual technique are also presented (Figs.  and ). As mentioned in Sect. , experiment IDs 5, 9, and 10 for Morocco, and IDs 12 and 34 for Iceland, exhibited surface area distributions skewed toward larger sizes compared to those obtained using the LD technique. To assess the impact of these experiments on the derived INAS density fits, we performed a sensitivity analysis. This involved computing the INAS fit for Morocco and Iceland (one fit per location) under three different conditions: (1) using all experiments from Morocco and Iceland, (2) excluding the experiments that showed a skewed distribution, and (3) using only the experiments that exhibited a skewed distribution. The fits obtained for each case are shown in Fig. . For Moroccan fits, the difference between all experiments and the experiments without the skewed size distribution is minimal, while the discrepancy between the case considering all experiments and only the skewed experiments reaches a maximum of approximately 60 % at the lowest temperature (around 246 K). Similarly, Fig. b presents the ns(T) fits for Iceland. In this case, the differences among the fits remain below 20 %. These results indicate that the influence of experiments with deviating surface area distributions relative to those obtained with the LD technique on the ns(T) fits do not exceed one order of magnitude. These variations lie within the confidence intervals shown in Fig. a and b for Morocco and Iceland, respectively.

Figure shows INAS density, ns(T), from the IR-DROFA measurements, calculated from the fraction of frozen droplets using the total area of all particles in a droplet (see Sect. ). This total surface area was estimated either from BET-based SSA values (SSABET_H2O) or by assuming that all particles in a droplet are spherical with a diameter of 15 µm (see Appendix. ) and a particle density of 2.65 gcm-3 (SSAGEO).

The IR-DROFA measurements (MOR and ICE SSAGEO in Fig. ) are in good agreement with measurements of Icelandic and Moroccan dust obtained using other methods (AIDA and INSEKT). For Icelandic dust, the agreement is almost perfect (solid blue line and open blue symbols in Fig. ), whereas the ns(T) values for Moroccan dust follow a less steep curve than the exponential fit to the AIDA and INSEKT data (solid red line and open reddish symbols in Fig. ). This deviation is not totally clear but it may be attributed to the different particle sizes used in the experiments: while the sieved fraction was confined to particles with geometric diameters below 20 µm, the coarse particles in the cloud chamber extended up to 50 µm and beyond. Furthermore, similar behavior was observed in Fig. , which shows deviations in the results obtained from different experimental techniques, such as AIDA and INSEKT. Further studies are required to elucidate the main reasons behind the discrepancies among these techniques. Nevertheless, an overall good agreement is observed.

In addition to differing fractions of ice-nucleating minerals (such as feldspar, Sect. ) present in the two samples, the variation in IN behavior can also be attributed to differences in the internal surface area accessible to water within the particles. Since Moroccan dust exhibits a fourfold higher SSA, a single particle of a given size presents four times more surface area available for ice nucleation compared to an identically sized Icelandic particle. This effect is illustrated by the INAS densities calculated for both dust sources using the water vapor adsorption-based SSA (solid symbols in Fig. ). As a result, the ns(T) values of both dust types nearly coincide.

It is important to note that calculating the INAS density based on water adsorption-derived SSA has limited practical application, as the SSA of natural dust aerosols is generally not accessible. Nonetheless, this result underscores the necessity of carefully considering surface area measurements for each potential atmospheric aerosol acting as an INP.

A comprehensive analysis of our Moroccan samples was carried out in . Here, we focus on the mineralogical single-particle composition and its dependence on size. In short, analyzed more than 300 000 freshly emitted individual particles using offline analysis with scanning electron microscopy (SEM) coupled with energy-disperse X-ray spectrometry (EDX). In their analysis, quartz was found to be the second largest constituent of the analyzed particles behind clay minerals. Furthermore, externally mixed feldspar represented 3.2 % of all particles by mass, and a 10th of it was estimated to correspond to K-feldspar. It is important to note that this is externally mixed K-feldspar and there is additional internally mixed K-feldspar, however, this cannot be isolated by the technique used in . An important finding of the Moroccan samples analyzed was that the relative amount of externally mixed feldspar and K-feldspar was invariant across particle size. In contrast, the mass fractions of complex quartz-like and feldspar-like particles increased with particle size, ranging from 5 % to 18 % for feldspar-like particles.

However, determination of the composition of larger particles is inherently limited. While the elemental composition obtained is most probably representative for the whole particle, as all of the particle's cross-section is scanned, the SEM-EDX technique used in identifies only the dominant mineral type in each particle. No actual phase identification is carried out, all particle classes are therefore labeled “-like” to reflect similarity in elemental fingerprints rather than confirmed mineral phases. This ambiguity is particularly relevant for larger particles, as the proportion of internally mixed aggregates increases with particle size, making the attribution of the EDX signal to a specific mineral such as K-feldspar increasingly uncertain. Nevertheless, a specific particle size threshold beyond which classification becomes uncertain is not defined, and the limitation is described qualitatively as a progressive effect with increasing particle size. As shown in Sect. , INAS densities obtained from our experiments fell within the 1 % and 20 % K-feldspar scaled fits and that the values obtained with AIDA aligned with the 20 % K-feldspar scaled fit (Fig. a). Although quartz is the second largest constituent by mass of our samples, we observed a higher ice nucleation activity than that obtained for quartz by (Fig. a). In order to understand the possible role of quartz in promoting ice nucleation, it is important to mention that our samples were collected in September 2019 and stored in plastic bags. Later, in November 2022, they were sieved and stored in small plastic containers. Finally, one month later, they were used in AIDA and INSEKT experiments. The fact that our samples did not exhibit INA similar to quartz might suggests that, despite quartz being larger in mass contribution than feldspar, most of its active sites may have become inactive or the quartz contribution was masked by the more active components like feldspar. found that the INA of quartz samples decreased substantially after exposure to air during storage, as well as after exposure to water . Consequently, the primary source of active sites in our Moroccan samples likely comes from the less abundant, but more aging-resilient feldspar active sites.

The single-particle composition, size, shape, and mixing state of our freshly emitted Icelandic particles were studied in . The size-resolved chemical and physical composition of over 190.000 individual particles with geometric diameters spanning from 0.1–120 µm were analyzed with computer controlled scanning electron microscopy/energy dispersive X-ray spectroscopy (ccSEM/EDX). It was found that the most abundant particle composition was Medium-Al mixed silicate particles (volcanic glass-like particles) varying between 35 % and 93 % by volume of the total aerosol population. Furthermore, a proportion of the Icelandic particles presented sulfate particles, suggesting the contribution of volcanic emissions. Potassium was almost absent from the samples. It was also observed that the relative volume fraction of the quartz-like particle group decreased with size, disappearing at 4 µm. In the same way, pyroxene occupied a higher relative volume fraction for smaller sizes, disappearing almost completely for diameters larger than 16 µm. However, the complex quartz-like structure was almost constant with size. As pointed out, notable differences emerge when comparing the mineralogy of Moroccan and Icelandic samples. For example, Icelandic dust consisted mainly of glass, intermediate plagioclase, and pyroxene. On other hand, Moroccan samples were dominated by clays, feldspar, quartz, and calcite. Therefore, differences in the ice nucleation activity between these two dust sources are expected, confirming our experimental results (Fig. ).

The INA of samples from Iceland and, more generally, close to volcanoes was already the focus in previous studies . In Fig. , we present a comparison between our parameterization and experimental data and other parameterizations from earlier studies. It can be seen that our parameterization (Table ) predicts values almost one order of magnitude lower than previous studies for Iceland and pyroxene . Pyroxene is particularly relevant because it has been suggested to be one of the most important minerals promoting the INA in volcanic samples . As the reason for this, it has been hypothesized that exsolution and the presence of perthitic microtextures (surface features that serve as ice-active sites) can occur in minerals commonly seen in volcanic ashes such as pyroxenes . Contrasting our parameterization with the one obtained by , at first sight a large discrepancy appears. Nevertheless, upon closer inspection, interesting features can be noticed. First, the spread of ns values derived with the same technique , i.e. INSEKT or AIDA experiments, for the whole temperature range is close to 1 order of magnitude (Fig. ). Second, comparing the values obtained at the same temperature but with different techniques (AIDA vs. INSEKT) the spread increases to ≈ 2 orders of magnitude (Fig. ). Additionally, data derived only with AIDA shows to agree more with parameterization. This variability of values between experiments might point to a variability in mineralogical content or other properties of the particles which might have a stronger impact at temperatures higher than 250 K given that for lower temperatures the ns values tend to agree more for the considered experiments. Therefore, additional studies are needed to understand the differences in IN values when wet and dry techniques are used and whether these differences are related to the mineralogical composition of the samples.

As said before, pyroxene is considered one of the most ice-active groups present in samples of volcanic origin. The values obtained by are larger than those expected from pyroxene. However, the particles analyzed by are airborne samples making it feasible that their composition and INA is altered in comparison with samples obtained at surface level.

In the previous section, links between ice nucleation activity and mineralogy were considered. In this section, we discuss how the relationship between mineralogy and ice activity depends on particle size. For example, as mentioned in Sect. , the relative volume fraction of the complex feldspar-like and feldspar mixtures increased with particle diameter for our Moroccan samples. The subsequent question is therefore whether this size dependence has any influence on the INA of the samples. To answer this, we compared experiments carried out with the same start temperature, but with different surface area concentration ratios of the three modes (Sfr, Scr and Sscr) defined as 101=SfST+ScST+SscST=Sfr+Scr+Sscr where ST is the total surface area concentration. Sf, Sc, and Ssc is the surface area concentration coming from fine, coarse and super-coarse particles.

The previous results (Table ) were calculated with the standard assumption that ns(T) is independent of size, i.e. the density of active sites is constant for all size bins. However, under the assumption that the INA of a sample can be linked to the content of a specific mineral or group of minerals, the probability of finding an active site over the surface will not be the same as for all sizes when the relative fraction of that mineral varies with size. This is the case for both of our samples, Morocco and Iceland, where the relative fractions of feldspar and pyroxene vary with particle size.

If enough information about the mineral composition of a sample is known (as well as its size dependence) and if there is a group of minerals that dominates the INA (for example, feldspar), we hypothesize that accounting for this information when computing the surface area will improve the obtained value of ns(T) to predict the concentration of INPs. To test this hypothesis, we calculated ns(T) again, but this time we scaled the surface area to the fraction of feldspar or pyroxene present in each size bin (effective surface area) according to . Figure  presents the obtained fit for ns(T) (ln⁡(ns(T))=211.5026-0.7669T for Iceland and ln⁡(ns(T))=291.6934-1.0845T for Morocco) using the effective surface area (“Iceland_S_eff, This study” and “Morocco_S_eff, This study”). The main effect of incorporating this new surface area for Iceland is an increase in the ns value by ≈1.5 orders of magnitude. Additionally, the new fit agrees with previous measurements of samples with similar origin or mineralogy, such as those reported by and . This result can be interpreted as a good indicator that the INA of Icelandic samples can be scaled to the content of pyroxene at each size of the considered PSD.

Regarding Morocco, the effect of considering the effective surface area is less pronounced as for Iceland, Fig.  shows that the difference between both parameterizations is less than 1 order of magnitude and is within the 95 % confidence interval of the parameterization obtained with the complete surface area. This can be understood in terms of the mineral composition dependence on size, there is low variation of the relative volume fraction of feldspar (and k-feldspar) with size and accounting for almost 30 % for all sizes .

The differential nucleus concentration is a less commonly used metric in comparison with ns. Nevertheless, it provides additional information that cannot be derived from ns(T), for example, the computation of w=Δln⁡(k(T))/ΔT allows comparing the freezing activity of samples when the temperature is varied ΔT. In this way, nearly constant values of w indicate that the freezing activity of the sample varies in a constant fashion when temperature is changed. This metric was presented in Fig.  for Morocco and Fig.  for Iceland. Moroccan samples presented a similar slope (w, especially for AIDA experiments) and less spread of the data around the linear fit, while Icelandic samples showed a larger difference in slope for AIDA experiments and a pronounced deviation from a linear behavior for INSEKT experiments. Upon closer inspection, it can be noticed that for our Moroccan samples, k(T) decreased nearly exponentially with temperature (Fig. a), whereas a more complex shape is observed for our Icelandic samples, where for temperatures warmer than 248 K the data presents a larger spread than for colder temperatures (Fig. a). In the work of , w was analyzed for several previously published experiments and it was found that no general trend in the behavior of w was present, i.e. deviations from the linear trend were quite frequent, and no possible sources of the deviations were suggested. Taking into account the characteristics of the mineral size dependence of our samples, as well as the results from preceding works discussed in previous sections and our own results, we hypothesize that one reason for the change in the exponential decrease of k(T) with temperature is the variation of the presence of the same dominant factor promoting ice nucleation. In the context of our experiments, this dominant factor was linked to mineralogy. In our Moroccan samples, all size bins presented contributions from K-feldspar and feldspar, and the biggest difference in the INA for samples of different surface area ratio contributions from fine, coare, and super-coarse particles was observed at warmer temperatures. On the other hand, we observed a strong dependence with size of the fraction of pyroxene, one of the main minerals for ice nucleation in our Icelandic samples. Pyroxene was mainly present in particles smaller than 8 µm and almost absent in particles with diameters larger than 16 µm. In this way, once the smaller and more active sizes nucleate at relatively warm temperatures, the subsequent nucleation are likely dominated by other minerals or a different probability of finding active sites on the surface of the remaining particles, changing the behavior of nucleation and the slope of w. To test this hypothesis, further experiments are required using samples of which the size dependence of their mineralogy is known and in which different size distributions/fractions are considered.