Under the framework of the NASCENT campaign , ambient INP measurements and aerosol characterization took place at the Arctic field site in Ny-Ålesund, Svalbard (78.9∘ N, 11.9∘ E) during October–November 2019 and March–April 2020. Ny-Ålesund is located on the southern coast of the Kongsfjorden in western Svalbard, and it is a well-established international site in the Arctic for scientific research. We configured ambient INP and aerosol measurements in a container used as the temporary observatory, which was placed at the southern end of the Ny-Ålesund town (see Fig. a). In addition to the minor anthropogenic emissions from the town, the container was approximately 600 m from the coast of Kongsfjorden and was surrounded by mountains and glaciers.

The experimental setup is shown in Fig. b. Ambient aerosol was sampled through a custom-built total aerosol inlet of 4.5 m vertical length, which was kept at a maximal temperature of 40 ∘C. During cold periods with strong winds (e.g., ambient temperature of -30 ∘C with wind chill below -50 ∘C in March 2020) the temperature of the inlet temporarily dropped but never went below 0 ∘C. Downstream of the inlet, a flow splitter (custom-built) directs the aerosol inflow into INP and aerosol instruments. For INP measurements, as shown in Fig. b, the first sampling branch was regulated with a steady total flow of 300 Lmin-1 through the inlet to the high-flow-rate impinger (Coriolis^® µ, Bertin Instruments, France). The inlet diameter was 50 mm, which was tapered to 25 mm (KF-25 pipe standard) after the flow splitter. A detailed sketch of the applied setup has previously been used in Fig. 1e of . Secondary sampling lines that branched off the flow splitter had a diameter of 6 mm and were used by different instruments operating at flow rates between 0.283 stdLmin-1 and 1 Lmin-1. The INP sampling and auxiliary aerosol measurements are explained in more detail below.

In this study, we aimed to predict the INP concentrations solely as a function of the observed nucleation temperatures (explained in Sect. ). Using linear regression to fit the relationship between the logarithmic space of INP concentrations and nucleation temperature requires the ordinary least-squares technique to estimate the regression coefficients. A critical assumption behind this method is homoscedasticity, i.e., constant variance of errors for all observations regardless of the value of regressors. However, in reality, this is hardly achieved, in particular for real-time observational data in the field, since INP concentrations naturally vary several orders of magnitude at a given temperature. In addition, the INP concentrations at each measured temperature are not evenly distributed, which are limited by inter-instrumental differences and available sample sizes. As a result, we observed a non-constant variance in the errors (i.e., heteroscedasticity) of INP concentrations over the investigated temperatures (see Fig. S1 in the Supplement). We therefore applied weighted factors in fitting our parameterization to obtain unbiased regression coefficients. The details are given in Sect. S1 of the Supplement.

An overview of the observed INP number concentrations as a function of nucleation temperature at Ny-Ålesund (Svalbard, Norway) within the framework of the Ny-Ålesund AeroSol Cloud ExperimeNT (NASCENT) campaign for autumn 2019 and spring 2020 is shown in Fig. . INP concentrations at -30 ∘C were measured using the horizontal ice nucleation chamber (HINC, ). INP spectra above -22 ∘C were measured with the DRoplet Ice Nuclei Counter Zurich (DRINCZ, ) using the liquid samples collected by a high-flow-rate impinger (further details given in Sect. ). The INP measurements at T<-22 ∘C were lacking because all droplets froze in most cases, hindering the calculation of INP concentrations. While concerning observations at T>-5 ∘C, most INP concentrations were below the limit of detection (LOD) of the instrument due to the volume of air sampled, and thus could not be reliably derived. Overall, in Fig.  the INP concentrations were found to increase in a log-linear pattern with decreasing temperature for both observing periods (orange line). For INP concentrations observed in autumn 2019 and spring 2020, we performed unpaired t tests to infer if there is a significant seasonal difference at the 95 % confidence interval level (p<0.05). Overall seasonal variation of INP concentrations at the investigated nucleation temperatures is unidentifiable for the months during which we sampled INP concentrations.

State-of-the-art parameterizations predict INP concentration based on an aerosol property such as number and surface area concentration (e.g., D10, N12, T13, D15, M18) or meteorological properties such as ambient temperature e.g.,S21. We investigated the effectiveness of aerosol and meteorological properties as predictors for INP concentration at different temperatures. Figure  shows the observed INP concentrations at different investigated temperatures for both seasons as a function of the concentration of particles with a diameter larger than 0.5 µm (n0.5). Similarly, Fig.  shows an example of the observed INP concentrations with a nucleation temperature of -15 ∘C for both seasons as a function of (Fig. a) surface area concentration (S) and (Fig. b) fluorescent particle concentrations (additional temperatures are presented in Figs. S4 and S5 in the Supplement). Moreover, predictions based on a selection of existing INP parameterizations using the three presented aerosol properties (n0.5, S, and fluorescent particle concentrations) are shown in the corresponding panel as a reference (Figs.  and , and more temperatures are shown in Figs. S4 and S5 in the Supplement). Note that the mentioned parameterizations represent air masses dominated by specific aerosol types, which are likely different from our observations in the Arctic region. Therefore, it is unsurprising that the three parameterizations (D10, N12, T13) overestimate and one parameterization (M18) underestimates the INP concentrations (Figs. , and S4). recently proposed a multiplicative calibration factor of about 0.02 for D10 predictions of INP applicable to the remote region of the Alps, which reduces the predicted concentrations by nearly 2 orders of magnitude, moving the predictions near the center of the scattered data. A special case is given by D15 (for T>-20 ∘C), which underestimates INP concentrations in autumn and overestimates INP concentrations in spring at all the temperatures shown in Fig. . However, despite the predictions of D15 lying within the observed data, the parameterization was designed for dust-dominated air masses, and it remains weakly constrained at temperatures warmer than -20 ∘C (shown in dashed black lines in Fig. ).

From Figs.  and a, the difference in aerosol loading between the observed seasons is non-negligible. Indeed, ambient aerosol number concentrations were on average 6 times higher in spring 2020 than in autumn 2019 (see Fig. S2 in the Supplement). Such an enhancement in INP concentration was not observed between the seasons (Fig. ), although from Figs.  and a, a stronger correlation between INP concentration and aerosol properties was observed for spring 2020. The Spearman's rank correlation coefficients increased from 0.11 and 0.07 in autumn 2019 to 0.43 and 0.51 in spring 2020 for INP concentrations measured at -15 ∘C versus n0.5 and S, respectively. As a result, no strong correlation between the INP concentration and aerosol properties is expressed for the data of both seasons combined (Table S1 in the Supplement). It is important to mention that for our INP observations, any INP parameterization using a season-dependent variable, such as aerosol number concentration or surface area concentration, could induce a bias in the INP prediction (e.g., higher INP concentrations with higher aerosol loading).

Aside from aerosol properties, meteorological variables were explored to predict INP concentration (Table S1). showed the usability of the ambient temperature in the prediction of INP concentration, representative of season-dependent INP sources. For our observations, such a dependence of INP concentration on ambient temperature was absent (see Table S1). As argued above for the particle concentration, the absence of a strong relationship can be explained as the mean ambient temperature differed between seasons while the INP concentration did not. We investigated the usability of other temperature quantities such as virtual temperature, potential temperature, and equivalent potential temperature (Table S1). However, the correlation behavior did not differ substantially from the coefficients found for the ambient temperature. Lastly, weakly season-dependent variables such as relative humidity, pressure and wind were investigated. No relation of INP concentration to ground-measured relative humidity, pressure, and wind direction could be found (Table S1). In turn, a weak correlation was found between INP concentrations and ground wind speed. Reasons behind these observations could potentially be increased transport and advection of INPs with the associated synoptic wind system or local source enhancement. For the latter, e.g., enhanced aerosolization of local soil dust cf. or stronger activity of bubble-bursting-induced sea spray aerosol enrichment , are conceivable reasons.

In this section, we investigated the potential of different aerosol and meteorological properties as predictors of ambient INP concentrations. No parameters with a consistently moderate or strong relationship to INP concentration could be identified. Furthermore, it was illustrated that any season-dependent variable (e.g., aerosol concentration, or ambient temperature) would induce a seasonal bias in INP concentration that was not observed. Given these obstacles to the inclusion of an additional property in the prediction of the ambient INP concentration in the Arctic, we aimed to develop an INP parameterization insensitive to abruptly changing atmospheric aerosols (e.g., peak events or seasonality) that can be implemented for long-span predictions. In Sect. , we investigate the prediction of INP concentrations solely based on ice nucleation temperature.

The improved accuracy of advanced INP parameterizations relies on a robust relationship between INP concentration and aerosol or meteorological properties – which was not evident in our in-situ observations (Sect. ). Alternatively, average INP concentrations can be predicted solely by a nucleation-temperature-dependent parameterization. For a few decades, it has been known that the temperature dependence of INP parameterizations is critical to represent cloud properties accurately . We present a methodology to optimally fit the slope of INP concentration frequency distributions as a function of investigated nucleation temperature.

Figure  shows the relative frequency distribution of our observed INP concentrations at different measured temperatures for the two campaigns in autumn and spring combined. The adequate log-normal fits of the observed distributions of INP concentrations per temperature support the hypothesis of (see Sect. ). Figure S7 (see Supplement) provides more evidence based on the approximate linearity between the observational and theoretical quantiles of the log-normal distribution, particularly at lower temperatures (T<-12 ∘C), where the closeness of data to the red line assesses the likelihood that the data set follows the theoretically log-normal distribution (see more details in Sect. S5 in the Supplement). The nature of log-normal INP distributions has been previously reported from the long-term INP monitoring in Svalbard and the subtropical maritime boundary layer . Thus, we propose an INP parameterization that fits the median value of the log-normal distribution and investigated nucleation temperatures, represented as follows: 3NINP(T)=ea(T-273.15)+b, where NINP is the INP number concentrations in std L-1, T is the temperature in kelvin, and a and b are fit parameters with the value given in Table . Note that instead of using an linear regression based on ordinary least-squares (OLS), we applied a weighted least-squares (WLS) approach (see Sect. S1 in the Supplement) to address the heteroscedasticity of frequency distributions of INP concentrations over different temperatures. In addition, we also report the dominant INP concentration distributions within the 95 % confidence interval (i.e., median ±2× standard deviation), based on the WLS fit of log-normal distributions. The fitting parameters for the lower and upper bounds of the predicted INP concentration distribution are also given in Table .

In Fig. , we compare to previous INP parameterizations that are only dependent on temperature . Our fit predicts at least 1 or 2 orders of magnitude lower INP concentrations than these parameterizations. Note that these three parameterizations were derived from the observations in different environments (not during the seasonal transition months in the Arctic). The INP concentration predicted by is closer to our parameterization but still slightly overestimates our values.

We gathered observations of INP concentrations from previous field measurements in the Arctic from 1976 to the latest 2021 as a reference data set to test the parameterization developed for background INP concentration in this study. Generally, INP data that was clearly archived at locations further north than 66∘34′ were considered in this study (see positional information in Fig.  and detailed data features in Table S3 in the Supplement). Overall, 32 155 observations of INP concentration as a function of nucleation temperature were applied to evaluate the background INP parameterization developed from the Ny-Ålesund campaign data in this study. Figure  compares the measured INP concentrations in this study and the selected reference Arctic measurements. In general, our probed INP concentration range was in agreement with that reported in previous Arctic studies, with this study being one of the few to measure the INP concentrations in the Arctic at temperatures as low as -30 ∘C. However, a few studies (e.g., ; ; ) observed consistently higher INP concentrations in the summer, indicating enhanced sources of local emissions due to the decreased ice and snow cover. We note that the parameterization herein was derived from the measurements during transition seasons (autumn and spring), aiming to predict the background level of INP concentrations in the Arctic. Therefore, applying it to generate INP concentrations, particularly in the Arctic summer, could introduce a low bias. On the other hand, the log-normal-distribution-based parameterization developed from high-frequency INP measurements (over 4000 observations in 12 weeks) is insensitive to peak events, i.e., local INP enhancement from instantaneous cases. It is therefore recommended to be implemented for longer-span predictions.

In addition to the seasonal differences, we summarized the INP concentrations at -15 ∘C by classifying the Arctic INP concentration data by measurement platform (Fig. ). The measured INP concentration ranges overlap between different measuring platforms, except for , which observed systematically higher INP concentrations (air-borne) compared to other studies, possibly due to the presence of mineral or soil dust. The overall level of ground-based measured INP concentrations was slightly higher than the shipborne measurements at this temperature, indicating a relative enhancement from terrestrial INP sources. Besides, only two studies measured INP concentrations from flight campaigns, challenging the comparison with the other two categories (i.e., ground-based and shipborne).

To evaluate our parameterization, we compared the predicted INP concentrations to observations from previous Arctic field measurements in Fig. . From a total of 32 155 comparison observations, 81 % of the INP concentrations are predicted within the 95 % confidence interval, revealing notable predictability of the proposed Arctic parameterization, given that approximately 2 to 3 orders of magnitude of the variation of INP concentrations are naturally observed. However, the INP concentrations tend to be overestimated, particularly towards warm temperatures (T>-15 ∘C), because the INP concentrations are highly variable and rather low at these temperatures. More interestingly, the predictions of INP concentrations retain their performance when the evaluation is categorized for seasons (see Fig. b). Particularly in spring and autumn, a higher percentage of observations from other studies fall into the 95 % confidence interval of the proposed parameterization. However, more INP concentrations are overpredicted in winter (Fig. b, e.g., data from ), particularly towards warmer temperatures, likely due to decreasing INP loading from regional emissions when the surface was covered with more ice and snow. This finding agrees with our previous discussion that the LOD of DRINCZ imposed limitations fitting the low INP concentrations at warm temperatures, notably when overall INP loading declines and the log-normal distributions become biased towards the higher INP concentrations that were observed above the LOD. Based on this explanation, the performance of the parameterization should improve in the summer when overall INP concentrations increase due to the increasing local emissions , which is, however, contradictory to what is shown in Fig. b. The predicted INP concentrations are still overestimated, mainly due to the inclusion of 11 804 data points from the filter samples by , who observed universally lower INP concentrations during a ship-based campaign in the Arctic Ocean around Svalbard compared to the provided distribution-based (i.e., 95 % confidence interval) predictions. They potentially measured in a region where comparably lower INP concentrations were prevailing, i.e., when measured within the sea ice pack, INP concentrations were systematically lower compared to the ice-free ocean. Another possibility could be the degradation of the filter samples during transport and storage, supported by the fact that the INPs measured by SPIN (an online instrument based on the same measurement principle as HINC) were consistently higher than filter samples measured by their drop freezing method, LINA (see Fig. ). The above reasons could explain why the filter data from are substantially lower than previous measurements. If data are removed from the evaluation, we achieve approximately 97 % of the data falling within the confidence interval for the summer (not shown). However, our parameterization underestimates the INP concentrations measured in SPIN's temperature range during summer, which could be explained by the increased local terrestrial source (e.g., mineral dust) in the season when the surface is free of ice and snow.