The HyICE-2018 campaign took place at the SMEAR II measurement station in Hyytiälä, Finland , located within a sub-Arctic boreal environment at 61°51^′ N, 24°17^′ E and 181 m above sea level. The station setup and details during HyICE-2018 are fully described in . For the purposes of this study, the time period of interest is from 19 February 2018 to 10 June 2018, during which time two continuous flow diffusion chambers (CFDCs; PINC – Portable Ice Nucleation Chamber and PINCii – second-generation PINC) sharing design characteristics were operated to sample ambient aerosol and measure INPs with high time resolution.

Although INP concentration is highly temperature dependent, for much of the heterogeneous freezing temperature spectrum (between ≈ -38 and 0 °C), INPs represent a small fraction (as low as one in a million) of all particles . That means that there is significant scientific interest in identifying tracers or other indicators of freezing activity that can be used to follow INP concentration.

Detailed instrument specifications for the HyICE-2018 campaign instruments are provided in ; metadata for the full SMEAR II monitoring suite are available via the SmartSMEAR portal .

The machine-learning analysis employed random forest and decision tree models to derive feature importance rankings and principal component analysis (PCA) together with K-means clustering for dimensionality reduction and pattern exploration. These algorithms were applied as exploratory importance-ranking tools; no train–test data splitting or cross-validation was performed as the objective was hypothesis generation rather than predictive modelling. Prior to analysis, all variables were harmonised to a common 20 min time base; variables measured at a coarser resolution were assigned to the nearest 20 min interval, and those at a finer resolution were averaged. The analyses were implemented in R: random forests with the randomForest package, decision trees with rpart, and PCA and K-means with the base functions prcomp and kmeans. Random-seed sensitivity is quantified by running the random forest under 50 independent seeds; the seed-resolved importance scores are archived with the analysis code (see the “Code availability” section).

In addition to the INP measurements, for the purpose of this investigation, 509 individually monitored variables that are continuously recorded at SMEAR II were interrogated (data are available online at ). Those measurements, recorded with high time resolutions, are mostly atmospheric in character and can be broadly categorised as meteorological, radiological, soil, characteristics of aerosols and gases, and associated data products of the aforementioned. Naturally, the resulting multidimensional data include many potential redundancies and/or irrelevancies in terms of illuminating connections to INPs. Therefore, data filtering techniques were implemented to reduce the dimensionality and redundancy within the data. As a first pass, data features were not considered if they contained the following: (I) excessive NaN (Not a Number) values, often generated when concentrations are below instrument sensitivities; (II) data with little or no variability, i.e. constant values; and (III) data which were duplicated, like the same parameter sampled at different heights but without showing systematic differences.

The study also employs the Wideband Integrated Bioaerosol Sensor (WIBS), a real-time, single-particle instrument designed for atmospheric bioaerosol detection. The WIBS uses dual ultraviolet excitation wavelengths and subsequent fluorescence emission measurement to infer the presence of biological material in individual aerosol particles. Light scattering from a 635 nm diode laser determines particle size > 0.5 µm;.

It is important to note that these machine-learning methods were applied here as importance-ranking and exploratory tools and not to build or evaluate a predictive model; no train–test data splits were applied.

The following instrument specifications are provided to establish the conditions under which INP concentrations were measured (particularly the lamina temperature and humidity, which define the INP activation threshold) and to facilitate comparison with other CFDC-based INP studies.

Specifically, we test whether new particle formation (NPF) events generate particles that grow into the INP-relevant size range (> 0.5 µm); whether primary biological aerosol (proxied by fluorescent particle counts from the WIBS) is a dominant INP source in this environment; and whether aerosol chemical markers – including black carbon, nitrate, and organic aerosol mass – can serve as practical INP proxies.

Of the operational sampling units from the HyICE-2018 campaign, two CFDCs have time resolutions that make their data practical to compare with other parameters sampled at high frequency and have been directly compared by . PINC and PINCii are parallel-plate CFDCs designed to measure INPs, present in a sample air flow that is sandwiched between clean sheath air. Ice nucleation conditions within the sample air flow are modelled for CFDCs based on measured wall temperatures and the known saturation vapour pressure for the ice-covered walls .

PINC, the first-generation instrument, has been widely used in field campaigns for over a decade . Originally built for airborne deployments, it features a compact design with a main chamber (568 mm in length) and a 230 mm evaporation section. It is effective for ambient INP measurements but has limitations in terms of cooling power, wall temperature control, and laminar flow stability. Its operation typically involves fixed temperature and humidity conditions that target mixed-phase cloud scenarios. During HyICE-2018 PINC was operated from 19 February to 2 April at a fixed sample lamina temperature of Tl = -31 °C and a relative humidity with respect to water of RH_w = 105 %. PINC utilised a 1 L min⁻¹ dried (RH ≤ 30 %) sample flow with an inline cyclone impactor used to eliminate sampling particles larger than 2.5 µm. PINC measurements from HyICE-2018 are presented in detail in .

PINCii was originally designed and built based on upgrading PINC , utilising knowledge gained from more than a decade of experimental use , and thus significantly enhancing the PINC design and capabilities. PINCii is fully described in . It has a much larger chamber, approximately twice the length(s) in both the main (1000 mm) and the evaporation (440 mm) sections, which provides extended residence time for aerosol particles and ice nucleation and crystal growth. These longer sections – and, thus, increased growth time - improve the counting statistics and the instrument resolution. PINCii incorporates a pre-cooled sheath air system, as well as an enhanced wall temperature control and monitoring, with dense thermocouple arrays and a sophisticated cooling system that allows cooling to ≈ −67 °C. PINCii also introduces improved methods for thermodynamic measurements by accounting for wall inhomogeneities and ice layer thickness, increasing the accuracy of RH and temperature estimations. During HyICE-2018, PINCii also utilised a dried sample aerosol flow of 1 L min⁻¹ (measuring from 22 April to 10 June) with aerosol lamina temperature Tl = -32 °C and RH_w = 105 % and a 2.5 µm cyclone impactor.

Both PINC and PINCii operate with the same measurement cycle: a 5 min background (particle-free) period followed by a 15 min ambient sampling period, cycling continuously. Each INP concentration value is derived from the ambient-period particle count minus the interpolated background, yielding one data point every 20 min . At a sample flow rate of 1 L min⁻¹, the 15 L sample volume per data point is sufficient for statistically meaningful INP counts even at the low concentrations observed during winter (< 1 L⁻¹). Instrumental constraints and availability made it impossible for PINC and PINCii to operate simultaneously during HyICE-2018. However, their operation in succession means that, for the bulk of the campaign, there exists high-frequency data coverage, which appears to be self-consistent. An instrument comparison summary is available within the campaign measurement report , where the inconsistencies with another parallel-plate CFDC chamber, SPectrometer for Ice Nuclei (SPIN), make plain its absence here. The comparison showed that PINC and PINCii agree within a factor of 2 during the overlapping measurement period, with both instruments capturing the same general trends in INP concentrations; minor differences in absolute concentration are attributable to the 1 K difference in operating temperature (Tl = -31 °C for PINC, -32 °C for PINCii) and instrument-specific detection efficiencies.

The time series of INP concentrations measured by PINC and PINCii, each with a 15 min ambient sampling window (one data point every 20 min) , are presented in Fig. a. INP concentrations were measured at Tl = -31 °C (PINC) and Tl = -32 °C (PINCii). Each point represents a 15 min ambient sampling period (with 5 min background periods before and after, yielding one data point every 20 min) with a subtracted background interpolated from particle-free measurements before and after the sampling periods. Between instruments and across the entire campaign period no significant differences in the absolute concentrations and spread of measurements are noted. However, by visual inspection of Fig. a, the PINCii spring and early-summer time series appear to be somewhat more spread on the logarithmic concentration axis than the PINC winter series, consistent with seasonal changes in aerosol sources and meteorology; we do not report distribution fits or geometric moments here because PINC and PINCii did not operate simultaneously, and so we restrict the comparison to this qualitative description.

Also depicted in Fig.  are the time series of several other key monitored variables. Some, like temperature (Fig. b) and snow depth (Fig. b, grey trace), reflect the seasonal change from winter to spring and summer, while others are quite commonly associated with INP abundance (e.g. particle number concentrations, Fig. c). Given that previously published results from daily and/or multi-day samples have demonstrated seasonal variability for Hyytiälä INPs and linked observed trends with biogenic emissions , the time evolutions of aerosol mass fractions are also plotted (Fig. e). The most notable change in that time series is the increasing organic aerosol fraction with the change in season from winter to summer.

Finally, the time series of sub-micron particles (Fig. f) clearly exhibits the characteristic “banana” curves, indicative of new particle formation, that Hyytiälä is well-known for . New particle formation events are relevant here because freshly nucleated particles can grow into the INP-relevant size range during sustained growth episodes, potentially contributing to the INP-active aerosol population.

The seasonal progression visible in Fig.  – the transition in temperature and snow depth, the spring–summer increase in fluorescent biological particles, the shift in aerosol chemical composition (increasing organic fraction, panel e), and the apparent co-variability of INPs with these tracers – motivates a more objective evaluation of how INP variability relates to the broader set of concurrently measured parameters. Given the large number of variables and their inherent covariance, simple visual or pairwise analyses are insufficient to robustly rank their relevance. Therefore we apply statistical and machine-assisted approaches to explore the reduction of the feature space and to identify consistent associations with INP concentrations.

The variables presented in Fig.  are a small subset of the total of 509 recorded variables that were investigated within this study. Of those 509 sampled variables the previously outlined first-pass dimensional reduction left 84 variables. The remaining 84 parameters were further interrogated using several machine-supported analysis techniques, including random forest models (Fig. ), along with pairwise correlation, decision tree, principal component, and K-means clustering analyses. While it was difficult to extract quantitative results in all cases, to quantify the random-seed sensitivity of the random forest feature importance we ran the analysis with 50 independent random seeds (1 … 50). Figure  reports the per-variable median importance with 5th–95th-percentile whiskers across seeds; the top-ranked variables discussed below remain in the top group across all seeds. A formal multi-method comparison (e.g. side-by-side feature rankings from random forest, decision tree, and PCA) is not shown but was verified by the authors during analysis; these approaches consistently highlighted similar top-ranking variables.

The feature importance rankings from random forest models (e.g. Fig. ) consistently assign high importance to variables that are known to be strongly correlated with INP concentration. For example, biological particles that yield a fluorescence signal serve as a tracer for primary biological aerosol, which may include INP-active species, and are among the most studied INP types in forest environments . The connection(s) between other highly ranked quantities that emerge and INP are sometimes less clear, but suggest closer investigation. Several other highly ranked variables (e.g. acetone, methanol concentrations) are not examined individually because they largely co-vary with the selected predictors (particularly nitrate) and thus provide redundant information for the purposes of this exploratory analysis. A systematic investigation of all high-ranking but unexpected variables is an important avenue for future work.

In Fig.  six variables are selected to illustrate their pairwise correlation with INPs. The six variables were selected on two complementary grounds: (i) a high importance rank in the random forest analysis and (ii) an established physical or empirical connection to INP in prior literature or at this specific site (> 0.5 µm particle number concentration as per ; organic aerosol mass as per the biogenic seasonality documented by ). For example, in Fig. , fluorescence and nitrate are more closely examined, but acetone and methanol, which largely co-vary with nitrate, are not. Ice nucleation has a documented dependence on particle size that emerges in many parameterisations and combined with mass accounts for volume. Indeed, nitrate and acetone concentrations correlate positively with total aerosol mass during the PINCii spring–summer period (r ≈ 0.5–0.6), suggesting that their association with INPs may partly reflect the total aerosol burden rather than a specific chemical mechanism. Several indicators of black carbon (BC) are surprisingly highly ranked, given that many INP studies suggest weak ice activity for BC . Notably, also reported a positive correlation between BC and INP concentrations at short timescales during the HyICE-2018 campaign at the same site (their Fig. 5), independently supporting this finding. Possible mechanisms include enhancement of BC's ice-nucleating ability through atmospheric ageing, oxidation, and coating with organic material . Finally, because of Hyytiälä's well-documented legacy in organic aerosol measurements and new particle formation , organics are added as a variable of interest.

In Fig.  measured INPs are plotted on the vertical axis. In the upper panels variables with previously established linkages to INPs are plotted on the horizontal axes (fluorescent biological aerosol particles from the WIBS; total particle mass from the aerosol mass spectrometer (AMS); > 0.5 µm number concentration from the particles larger than 0.5 µm (Aerodynamic Particle Sizer, APS)). In addition to fluorescent biological aerosol particles (WIBS), particle number concentrations for particles larger than 0.5 µm (APS) are plotted. Particle concentrations of this size appear in several, widely used INP parameterisation schemes . Particle mass concentration, again largely a proxy for the number of large particles present in the aerosol, is plotted in Fig. b. In the bottom panels several highly ranked variables that constrain aerosol chemistry are plotted. For all of these cases, the organic mass concentration (Fig. d), nitrate mass concentration (Fig. e), and black carbon mass concentration (Fig. f; all three from the AMS except BC, which is from the aethalometer), the direct correlation is as good as or better than what is demonstrated in the upper panels for variables with previously established links to ice activity. Data for PINC and PINCii are shown separately because the two instruments operated in different seasons (winter vs. spring–summer) with distinct ambient aerosol and INP characteristics; combining them would conflate seasonal differences and obscure the key finding: the observed correlations are specific to the PINCii spring–summer subset and do not hold generally across the full campaign (the PINC winter data show no meaningful correlation with any of the examined predictors). The Pearson correlation coefficients were calculated from the raw (untransformed) data; the log–log axes are used for visualisation only to accommodate the wide dynamic range of the measurements. Using 20 min data instead of hourly means yields qualitatively similar results, suggesting that the dominant co-varying processes operate on timescales exceeding 20 min (diurnal or synoptic scale) rather than at sub-hourly variability. This subset-specific character of the correlations has broader implications for campaign-based INP correlations reported in the literature: INP–aerosol correlations derived from short, season-specific field campaigns are conditioned on the ambient regime of the measurement period and should be interpreted with caution when generalised to other seasons, sites, or ecosystems.

While the individual learning algorithms that were tested were consistent and succeeded in bringing to light several variables that also exhibit strong pairwise correlation with INP, they identify statistical associations between predictor variables and INP concentrations but cannot establish causal relationships. This is perhaps unsurprising as, taken holistically, the highly ranked variables simply suggest that more dirty, mixed aerosol with higher particulate concentrations is more likely to contain INPs. The correlations likely reflect co-varying air mass properties rather than direct INP composition: INPs are a vanishingly small fraction of the total aerosol (∼ 1 in 106), and, without single-particle analysis of ice crystal residuals, the identity of the actual ice-nucleating species remains undetermined . Similar observations have been made previously in several diverse ecosystems, from the subtropical marine boundary layer to ocean basins , and globally distributed land-based samples ranging from Arctic to equatorial latitudes . In those studies it has been noted that INP concentrations measured remotely from strong sources often exhibit log-normal frequency distributions (Fig. a). This observation is directly analogous to random mixing (dilution) of trace pollutant species and suggests that the dominant INP signal originates from long-range transport of well-mixed aerosol. Log-normal concentration distributions arise naturally from the multiplicative dilution and mixing of aerosol during atmospheric transport , consistent with INPs at this site originating from diverse, distant sources. This interpretation aligns with the findings of , who hypothesised that long-range transport is the dominant INP source at SMEAR II based on the same PINC dataset. Lagrangian back trajectories or dispersion models (e.g. HYbrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT, , and the FLEXible PARTicle dispersion model, FLEXPART, ) can contextualise air mass history and are often used together with chemical tracers or receptor modelling to assess long-range transport, but they do not by themselves uniquely verify INP provenance or the dilution interpretation above: trajectory errors, mixing along the path, and the lack of INP-specific tagging in kinematic histories mean that such analyses complement – rather than uniquely test – inferences from local correlations and distribution shape. We highlight combined trajectory–tracer or trajectory–receptor studies as a priority for future work. In Fig.  the relative frequency distributions of INP concentrations measured with PINC (blue) and PINCii (red) are plotted with unimodal (a) and bimodal (b) fitted curves. From the χ2 statistics (using raw bin counts; see caption), the formal tests reject the simple unimodal log-normal null at conventional significance for both PINCii (χ2 = 81.98, p = 0.001) and PINC (χ2 = 157.19, p < 0.001). Nevertheless, the histograms are broadly similar in shape and scale, and so log-normality remains a useful approximate description of the bulk distribution. A modest elevated tail in the PINCii histogram motivates the bimodal decomposition in Fig. b: for PINCii, χ2 decreases to 63.54 (p = 0.028), whereas for PINC the bimodal fit does not improve overall agreement (χ2 = 242.72, p < 0.001). We therefore do not interpret the PINCii tail as evidence for a statistically robust separate population at the 5 % level, and we caution that the χ2 values indicate residual structure beyond ideal unimodal log-normal behaviour for both instruments.

If the dominant INP signal originates from long-range transport, local parameterisations based on co-located measurements will have limited predictive power – a prediction directly borne out by the PINC winter results below. The modest success of the PINCii spring–summer parameterisations may then reflect a local biogenic INP contribution that augments the transported background during the growing season.

The limited correlations identified in Sect. 3.2 suggest that existing parameterisations – which rely on variables, such as nAP > 0.5 µm, that do not strongly correlate with INPs in this dataset – are unlikely to reproduce the observed INP variability. Testing them nonetheless serves two purposes: (i) it quantifies the parameterisation failure against a comprehensive boreal dataset, and (ii) it motivates the exploration of alternative local proxies in Sect. 3.3.2.

The qualitative connections that emerge between INP and aerosol characteristics (Fig. ) from the machine-learning algorithms (Fig. ) signal an opportunity to explore the parameterisation space. We expect existing parameterisations to account for the observed correlations related to aerosol particle abundance and biogenic origin (top panels in Fig. ). In contrast, the connections to aerosol chemical composition (bottom panels in Fig. ) are less obvious, and, in fact, despite considerable explorations, black carbon is typically observed to have limited ice activity , especially when it occurs as fresh soot. That said, there is some evidence that transport, oxidation, and ageing enhance soot's ice activity .