Ambient aerosol particles were collected on 47 mm Whatman nuclepore track-etched polycarbonate membrane filters with a pore size of 0.2 µm. The filter sampling line and the filter holder are made of stainless steel and were installed in a cottage in the forest, with a rooftop PM10 inlet connected to the other sampling components installed indoors. The inlet height is approximately 4.6 m above ground and, therefore, approximately 17.2 m below the forest canopy. A vacuum pump, in combination with a critical orifice, ensured a constant sampling flow rate of about 11 std L min-1. Because the PM10 inlet provides a precise 10 µm cut-off size for a flow rate of about 16 std L min-1, it is possible that larger particles were also collected. However, the deviation of total aerosol number and surface concentration from the PM10 concentrations is <1 %. We, therefore, refer to PM10 number concentration and PM10 surface concentration when comparing the INP concentrations and calculating INAS (ice nucleation active surface site) densities. Filters were pre-cleaned with 10 % H2O2 and rinsed with deionized water that was passed through a 0.1 µm Whatman syringe filter before being dried for use in sampling. After sampling, the filters were stored in sterile petri dishes, wrapped in aluminium foil and frozen until the sample were analysed for their INP content.

The INP content of the collected aerosol samples was quantified using the INSEKT (Ice Nucleation Spectrometer of the Karlsruhe Institute of Technology) method described in Schiebel (2017). The INSEKT is based on an ice spectrometer developed at the Colorado State University, which is described in Hill et al. (2016). INSEKT measures INP concentration as a function of the activation temperature in the immersion freezing mode between about 247 and 268 K. For the INP analysis, the collected aerosol particles are washed from the filter membranes by immersion in 8 mL of nanopure water, which was passed through a 0.1 µm Whatman syringe filter. The sample solution was spun on a rotator for approximately 20 min, and subsequently, the aerosol suspension was diluted with 15- and 225- or 10- and 100-fold volumes of filtered nanopure water. Small volumes of 50 µL are pipetted into two 96-well polymerase chain reaction (PCR) plates. The wells are partitioned into different groups, including a group for the undiluted suspensions, the two diluted samples and for the filtered nanopure water that serves to determine background freezing levels. Filter handling and suspension preparation always occur in a clean flow cabinet using tweezers which have been pre-cleaned in the same manner as the filter membranes. The filled PCR plates are then placed into the INSEKT instrument, which consists of two aluminium blocks, each with openings for holding a 96-well PCR plate. The aluminium blocks are connected to a chiller (LAUDA Dr. R. Wobser GmbH & Co. KG.; Proline RP 890), which pumps ethanol cooling liquid through the aluminium blocks at a constant cooling rate of 0.25 K min-1. A total of eight evenly distributed temperature sensors measure the temperature distribution inside the blocks with a 2 Hz resolution. The aluminium blocks are placed in a PVC box insulated with 2 cm of Armaflex insulation material. The upper part of the PVC box is equipped with an antireflection and depolarized glass pane, which covers the PCR plates and prevents contamination from the ambient air. In order to avoid condensation on the glass, the interior of the PVC box and the upper side of the glass pane are continuously flushed with particle-free synthetic air at a constant flow rate of about 80 L h-1. A camera with a 60 cm focal distance detects brightness changes in the small suspension volumes that are related to freezing during the cooling process. LabVIEW software is used to control and monitor the cooling rate, temperature and brightness changes. Using this setup, the frozen fraction of the small aerosol suspension volumes are determined as a function of temperature. From the fraction frozen, the INP concentration per standard litre of sampled air is calculated, binned on a 0.5 K grid and corrected by the background from the filtered nanopure water, using the procedure described in Vali (1971). Error is estimated by determination of 95 % confidence intervals using the Wilson score interval (Wilson, 1927) in the form described by Agresti and Coull (1998). Data points with a ratio of upper to lower confidence interval higher than eight are considered insignificant and neglected. A systematic error due to the preparation process and flow measurements is added. Applying a simple linear error propagation on the formulas given in Vali (1971) and inserting the error-containing parameters like the pipetted suspension volumes, the flow rate systematic errors of 4 % for the undiluted suspension, 5 % for the first dilution step, 8 % for the third dilution step and 11 % for the fourth step are calculated. The systematic error increases with each dilution step because the additional pipetting step adds uncertainty. In addition, INP concentrations derived from handling blank filters, which were collected without flowing air through the membranes, are subtracted. Heat treatment tests of the collected aerosol samples provide additional information about the heat sensitivity of the containing INPs and have been applied in various previous INP studies (Hill et al., 2016; O'Sullivan et al., 2018; Wilson et al., 2015). For these tests, a test tube filled with 2 mL of the aerosol suspension is kept in boiling water for approximately 20 min. Afterwards, the treated sample is analysed with the INSEKT in the same way as previously described. INAS densities were calculated as described in Eq. (2) in Ullrich et al. (2017), where ice number concentrations are normalized by the aerosol surface area concentration. Assuming that every INP triggers the formation of one ice crystal, the ice number concentrations are equal to the INP concentrations, which are determined by the INSEKT measurements. The aerosol surface area concentrations are derived from continuous size distribution measurements of the PM10 atmospheric aerosol at SMEARII. Details on the size distribution measurements are given in the following section.

To characterize the sampled aerosol particles further, atmospheric aerosol size distributions were continuously measured with a differential mobility particle sizer (DMPS). The covered size range was 3–1000 nm in electrical equivalent diameter, with 10 min time resolution (Aalto et al., 2001) with a closed loop flow arrangement (Jokinen and Mäkelä, 1997). The instrument was operated following guidelines from Aerosols, Clouds and Trace gases Research InfraStructure (ACTRIS; Wiedensohler et al., 2012). The aerosol sample was taken from 8 m height inside the canopy through a total suspended particle (TSP) inlet. The super-micron aerosol size distribution was determined with a TSI aerodynamic particle sizer (APS), model 3321, for the size range 0.5–10 µm in aerodynamic diameter. The sample was drawn through a vertical sampling line to avoid particle losses. The inlet is at a height of 6 m above the ground and consists of a total suspended particle inlet (DIGITEL Elektronik GmbH). The inlet was heated to 40 ∘C to prevent condensation and to ensure that fog droplets are evaporated and the RH remains below 40 %.

The intense measurement period during the HyICE-2018 campaign also provides additional aerosol instrumentation, like a long time-of-flight aerosol mass spectrometer (L-ToF-AMS) to measure the aerosol chemical composition and a wideband integrated bioaerosol sensor (WIBS-NEO) to derive information about biogenic fluorescent aerosol particles. The WIBS-NEO (Droplet Measurement Technologies, Longmont, CO, USA) is a bioaerosol sensor that provides information on the fluorescence properties, size and asphericity ratio of individual aerosol particles. It operates with an inlet flow of 0.3 L min-1 and detects particles with diameters between 500 nm and 30 µm. From 11 March to 2 April 2018, the WIBS was located about 50 m from the aerosol filter sampling line used for the INP analysis. There, it was attached to a total aerosol inlet, which is characterized in Vogel (2018). On 3 April 2018, the WIBS was moved and installed directly next to the filter sampling line and attached to a PM10 inlet, which is described in Schmale et al. (2017). For the WIBS data analysis, particles from 0.5 to 10 µm were considered. To analyse the fluorescence of the particles, the WIBS sensor utilizes two xenon flashlamps as excitation light sources (optically filtered at wavelengths of 280 and 370 nm) and two emission detection channels (wavelength bands 310–400 and 420–650 nm). Optical size information is acquired by utilizing elastic scattering from a continuous wave laser with a wavelength of 635 nm and a photomultiplier tube located orthogonally with respect to the laser. The excitation pulses are fired into the sample volume at different times, and both detection channels record the emission(s) from both excitations, leading to three distinguishable excitation–emission combinations (the 370 nm light saturates the 310–400 nm detection channel and, therefore, does not provide any information). Thus, the fluorescence can be divided into the following seven unique fluorescence groups based on the excitation–emission wavelength pairs and their combinations after Perring et al. (2015) and Savage et al. (2017): A (only FL1 – excitation 280 nm; emission 310–400 nm), B (only FL2 – excitation 280 nm; emission 420–650 nm), C (only FL3 – excitation 370 nm; emission 420–650 nm), AB (FL1 and FL2), BC (FL2 and FL3), AC (FL1 and FL3) and ABC (FL1 and FL2 and FL3). The WIBS performs an empty chamber background signal check every 8 h, during which the excitation pulses are fired into the optical chamber without any present particles. The background check collects a multitude of emission intensities that form a baseline for particle fluorescence. In this study, a particle is considered fluorescent if the associated emission peak intensity is larger than FT + 9σ. FT is the mean value of the forced trigger intensities, and σ is their standard deviation. A more commonly used method would be to compare the emission peak intensity to FT + 9σ. However, some non-biological particle types, such as wood smoke, African dust and black carbon are weakly fluorescent and, therefore, might satisfy the lower threshold value, leading to an overestimation of biological particle concentration. Furthermore, the stricter threshold only marginally affects the detection efficiency of biological particles because they tend to have stronger fluorescence (Savage et al., 2017). More detailed descriptions on the WIBS are also available in Savage et al. (2017) and Perring et al. (2015). Daily size distributions measured by the DMPS and APS combination are compared with the size distributions measured by the WIBS from 11 March to 13 May 2018 and are shown in Fig. A3. In summer, WIBS tends to measure slightly more particles with diameters larger than about 3 µm compared to the APS. However, the size distributions agree well for the other time periods and the smaller size ranges.

The size-resolved chemical composition of ambient aerosol was measured with the L-ToF-AMS. Its application in the same campaign has been described in Paramonov et al. (2020). It builds on the functionality and characteristics of the high-resolution ToF-AMS (DeCarlo et al., 2006). However, due to the longer time-of-flight chamber, the L-ToF-AMS has a better resolution (8000 M/ΔM) than the standard ToF-AMS (2000 M/ΔM in V-mode). Detailed descriptions of the instrument, measurements and data processing are available in other publications (Canagaratna et al., 2007; DeCarlo et al., 2006). In general, the L-ToF-AMS measures the size-resolved, non-refractory composition of submicron aerosols, including organic, sulfate, nitrate, ammonium and chloride. The aerodynamic lens has a 100 % transmission range of 75–650 nm (in vacuum aerodynamic diameter; Liu et al., 2007) and focuses particles into a narrow beam that impacts the surface of a porous tungsten vaporizer heated to 600 ∘C, followed by ionization by a 70 eV electron source. Ions are detected by a long time-of-flight mass analyser (Tofwerk AG). The sample flow of 0.09 L min-1 is extracted from an extra suction flow (3 L min-1) that is used to avoid aerosol losses in the inlet line. A PM2.5 cyclone mounted at the inlet removes large particles to avoid clogging the critical orifice (100 µm), and before entering the L-ToF-AMS, the samples are dried by a Nafion dryer to keep the RH (relative humidity) below 30 %. The L-ToF-AMS data were analysed using standard ToF-AMS data analysis toolkits (Squirrel V1.61B and PIKA1.21B) using Igor Pro software (V6.37; WaveMetrics Inc.). To calculate mass concentrations, an ionization efficiency (IE) was determined using 300 nm, size-selected, dry ammonium nitrate particles, and a relative ionization efficiency (RIE) for ammonium of 3.7 was determined. The default RIE values of 1.1, 1.2, 1.3 and 1.4 for nitrate, sulfate, chloride and organics, respectively, were applied. A composition-dependent collection efficiency (CE) was applied based on the principles proposed by Middlebrook et al. (2012).

Various meteorological parameters are continuously monitored at SMEARII. For this study, we used five basic variables, including ambient air temperature, relative humidity, wind speed, snow depth and precipitation. The ambient air temperature was measured 4.2 m above ground with a Pt100 sensor inside a ventilated, custom-made radiation shield. This 4.2 m temperature measurement is the closest to ground-level at SMEARII, and thus, we utilize this as the ground-level ambient air temperature in the following. The RH was measured at 35 m height by a Rotronic MP102H RH sensor. For wind speed measurements, we used a Thies 2D ultrasonic anemometer at 34 m above the ground. The snow depth was measured by a Jenoptik SHM30 snow depth sensor, which is based on an opto-electronic laser distance sensor, in an open field about 500 m southeast of the aerosol collection area of SMEARII. The precipitation, the liquid water equivalent, was measured by a Vaisala FD12P weather sensor at 18 m height.

All INP temperature spectra measured from 11 March 2018 to 31 May 2019 are shown in Fig. 1 in a monthly representation. The INP concentrations range from about 10-4 to 10-2 std L-1 at the highest and from about 100 to 102 std L-1 at the lowest temperatures. These concentration values fall within the range of INP concentrations measured during previous globally distributed field studies, which are summarized in Kanji et al. (2017). This indicates that primary ice formation in boreal forest areas is comparable to other regions on Earth, despite the lack of anthropogenic and dust sources. In our study, we observe both INP concentrations and spectral shape to be highly variable from day to day and to show clear seasonal trends. INP temperature spectra in March, December, January and February constitute the lowest of the entirety of INP temperature spectra, whereas the INP temperature spectra with the highest INP concentrations are recorded in May and September. Figure 2a depicts the full time series of INP concentrations, measured as a function of activation temperature, with a time resolution between 24 and 144 h. The colour contours represent the seasonal cycle of INP concentrations, which are lowest in wintertime from December to March and highest in the summer months, especially during May and September, as shown in Fig. 1. An additional peak is found in the beginning of July. The INP concentrations in the middle temperature range around 257 K show the most distinct seasonal cycle. The variability in INP concentrations at the lower and upper end of the temperature range is less pronounced. Figure 2b shows the time series of INAS densities, which are calculated by normalizing the INP concentration measured by INSEKT with the aerosol surface concentration of atmospheric PM10 aerosol particles derived from DMPS and APS. The INAS densities show the similar seasonal trend and annual variability as the INP concentrations. For comparison, the time series of PM10 aerosol number concentrations and PM10 aerosol surface concentrations are shown in the Appendix Fig. A1.

To investigate factors that influence the abundance of INP and might explain the daily and seasonal variability of INP concentrations, the INP time series are compared with other data sets like meteorological and aerosol data. As the seasonal trends and variability are most pronounced at activation temperatures around 257 K, the INP time series at 257 K is used for this comparison. In Fig. 3, the monthly averaged INP time series at 257 K is compared with the monthly fraction of NPF event days and snow coverage measured alongside the INP measurements at SMEARII and with the averaged concentrations of pollen and other PBAP. We have defined snow coverage as measured snow depth >1 cm. The analysis of NPF events is based on permanent measurements at SMEARII and was provided by Simo Hakala, University of Helsinki. As there were no simultaneous direct measurements of pollen and other PBAP available for the period of our INP measurements, we compare them to pollen and PBAP measured in 2003 and 2004 by Manninen et al. (2014) at SMEARII. Manninen et al. (2014) collected aerosol samples in a Hirst-type volumetric spore trap (Burkard Manufacturing Co. Ltd.; Hirst, 1952), located at SMEARII, 3 m above the forest canopy. The trap is driven by a clockwork mechanism and collects aerosol particles larger than approximately 3 µm on an adhesive, transparent, plastic tape with a sampling flow rate of approximately 10 L min-1. The analysis of the collected particles was performed according to standard methodology adopted by the Finnish pollen information network and following the principles of the European Aeroallergen Network (https://www.polleninfo.org/, last access: 15 October 2020) and Rantio-Lehtimäki et al. (1994). The observed INP peak in spring coincides with the peak in pollen concentrations, whereas the peak in September is found to correlate with enhanced concentrations of other PBAP. Maxima in NPF event fractions are recorded in spring and in autumn, which has also been observed in many years dating back to 1996 (Dall'Osto et al., 2018; Kulmala et al., 2004; Nieminen et al., 2014). Snow-free periods are characterized by relatively high INP concentrations, whereas complete snow cover yields low concentrations.

Figure 4 shows the INP time series at 257 K focussing on the intensive measurement period of the HyICE-2018 campaign from March to May 2018. After a period of rather constant INP concentrations in March, we observe a steady increase of INP concentrations in April, which comes along with the snowmelt period at SMEARII. After the snowmelt, INP concentrations are again on a rather constant but higher level. During the HyICE-2018 period, more comprehensive aerosol characterization was done, including measurements with the L-ToF-AMS and the WIBS shown in Fig. 4a and b. Here, we define the number concentration of fluorescent particles as the number concentration of aerosol particles, whose fluorescence emission intensity produces a fluorescent signal in the fluorescence group ABC (see Sect. 2.3 for details on the categorization in fluorescence groups). The time series of the number concentration of particles with a fluorescence signal in other fluorescence groups is shown in the Appendix in Fig. A2. In this Figure, the strongest seasonal increase in the transition period from winter to summer is observed in the group ABC. Consequently, this fluorescent group correlates best with the measured INP concentrations (see Fig. 4a). The characteristics of each fluorescence group are comprehensively investigated and reported in Savage et al. (2017), who examined the fluorescence emissions of different types of pollen, fungi, bacteria, biofluorophores, dust, HULISs (humic-like substances), PAHs (polycyclic aromatic hydrocarbons), soot and brown carbon. Using the FT + 9σ threshold for defining a particle as fluorescent, nearly all dust and HULIS types show no fluorescence signal at all. Some of the soot and brown carbon types only show weak signals in A and B, BC and A, respectively. Nearly all of the bacteria types show fluorescence only in group A. The fluorescence of fungal spores are also mainly detected in group A but also in AB and ABC. The investigated biofluorophores show mainly fluorescence in the groups BC (riboflavin – NAD), A (pyridoxamine), AB (tryptophan) and ABC (ergosterol). PAHs show fluorescence mostly in groups ABC and A. Finally, most pollen types show fluorescence in groups ABC and AB. Some pollen types also show a fluorescence signal in groups A and B. Both the organic aerosol mass concentration measured by the L-ToF-AMS and the number concentration of fluorescent particles measured by WIBS tend to increase during the transition period from winter to summer (Fig. 4a and b). The number concentration of atmospheric PM10 aerosol measured by the APS and DMPS (Fig. 4c) does not show this trend. However, a slight seasonal trend is visible in the PM10 surface concentration (Fig. 4d). The number and surface concentration of PM10 atmospheric aerosol for the whole time period from March 2018 to May 2019 is shown in the Appendix in Fig. A1.

Figure 5a depicts the whole time series of INP concentrations in comparison to the measured ground-level ambient air temperature from March 2018 to May 2019, which clearly shows the INP time series following the course of the ground-level ambient air temperature. Only for ground-level ambient air temperatures about >15 ∘C is the deviation of the two time series is higher. However, the general seasonal trend in the ground-level ambient air temperature is the same as we observed in the INP time series. Besides a significant correlation of INP concentrations to the ground-level ambient air temperature, the snow depth also showed a significant correlation. Figure 5b shows a direct comparison of the INP time series with the measured snow depth. Periods of decreasing INP concentrations clearly overlap with snowmelt periods, whereas an increasing snow depth comes along with increasing INP concentrations. Figure 5c shows the comparison of the INP time series with the time series of relative RH measured 35 m above ground. Over the entire time period, no clear relationship between RH and INP concentrations is observed. For a shorter time period, from June to September 2018, there seems to be some correlation between the INP concentration and the RH, during which the peaks in the INP concentration in June correspond to a RH peak. In Fig. 5d, we compare the time series of INP concentrations with the time series of wind speed measured 34 m above the ground, which is also above the forest canopy. A relationship between measured INP concentrations and wind speed is not observed. In Figure 5e, the time series of the INP concentration is compared to the occurrence of precipitation. Although other studies like Prenni et al. (2013), Huffman et al. (2013) and Iwata et al. (2019) report increasing INP concentrations during and after rain events in forested sites, we do not consistently observe this behaviour. In this respect, increased INP concentrations are observed only during two of the strongest precipitation events in June and September 2018. However, it should be noted that, in the cited studies, INP concentrations were measured with higher time resolutions from minutes to hours. Huffman et al. (2013) reported increased INP and biological particle concentrations during rain events and up to 1 d after rain events. With our sampling (and therefore averaging) time of 24 h or more, rain-induced enhancements of INP concentrations may have been missed. Therefore, this type of sampling strategy may not be appropriate to deterministically link INP concentrations with rain events.

In the wintertime, complete snow cover seems to suppress biogenic particle emissions, resulting in comparably low INP concentrations. Such a correlation is also supported by the peaks of pollen and PBAP concentrations in snow-free periods in spring and in autumn and by the increases in the organic aerosol mass concentration and fluorescent particle numbers of group ABC observed in spring. According to the study of Savage et al. (2017), we assume particles of fluorescence group ABC to be mainly pollen, particles containing PAHs or ergosterol or fungal spores. The non-refractory organic components measured by AMS include the commonly observed primary organic aerosol (POA) and oxygenated organic aerosol (OOA). As the surface concentration of PM10 particles is more sensitive to larger particles, the increase in PM10 surface concentration (see Fig. 4d) indicates that the observed seasonal increase may be due to larger particles, which are expected to be mainly of biogenic origin. No day-by-day relation of NPF events and INP peaks are identified, but this is not unexpected given that particles formed during NPF events are initially smaller than 5 nm in diameter and events are more likely when condensation sinks are low (Dada et al., 2017). However, we consider the enhanced NPF event frequency as an indicator of generally higher biological activity in the forest. Enhanced biological activity means more biogenic INP emissions from the vegetation, which agrees with the seasonal dependencies from the previous findings. Any direct impact of NPF events on the boreal forest INP abundance remains uncertain and requires more investigation.

The exemplary INP spectra in Fig. 6 demonstrate that the INP concentrations show an exponential trend with activation temperature (an approximately linear shape of the log(cINP) T spectra) during the wintertime, whereas summertime spectra show enhanced concentrations at around 260 K, resulting in curvature in the spectra. After heating the INSEKT samples in boiling water for approximately 20 min, the resulting INP spectra are shifted towards lower concentrations by 1 to 2 orders of magnitude throughout the temperature range. However, the characteristic bulge in the summertime spectra is conserved or even more pronounced after the heat treatment. The observed shift of INP spectra after the heat treatment reveals the presence of heat-labile INP types, which hints at particles of biogenic origin containing ice-active proteinaceous material (Hill et al., 2016; Morris et al., 2004). As a significant number of residual heat-resistant INPs still remains after heat treatment, this indicates that not all measured INPs are associated with heat-labile biogenic materials. However, the majority of the INP population seems to be dominated by heat-labile materials, which is shown by the systematic shift in INP temperature spectra. The characteristic differences in the shapes of the INP spectra further indicate that different aerosol types dominate the INP populations in winter- and summertime. These differences are consistent for the observations in 2018 and in 2019, suggesting a systematic seasonal behaviour.

The observations presented in Figs. 1–6 indicate that the INP populations in boreal environments are dominated by biogenic emissions from the vegetation in the forest. We provide evidence that INP concentrations experience a seasonal cycle, which we link to seasonal trends in biogenic aerosol. The observational data we have presented poses new challenges for quantitative INP predictions, as it is essential to incorporate seasonal trends to achieve accurate descriptions. In Fig. 7a–d, the measured INP concentrations are plotted versus the INP concentrations predicted by current parameterizations (DeMott et al., 2010; Tobo et al., 2013; Ullrich et al., 2017). DeMott et al. (2010) and Tobo et al. (2013) have developed temperature-dependent parameterizations that use the number concentration of aerosol particles with diameters >0.5 µm (Fig. 7a and b). Tobo et al. (2013) provide an additional temperature-dependent formulation using the FBAP (fluorescent biological aerosol particle) concentration (Fig. 7c). Ullrich et al. (2017) use the measured aerosol surface area concentration to formulate a temperature-dependent parameterization of the INAS density of mineral dust (Fig. 7d). Among the selected parameterizations, Tobo et al. (2013) reproduce most of the data points by predicting 63 % (Fig. 7b) and 80 % (Fig. 7c) of the measurements to within 1 order of magnitude. Note that, for the application of the Tobo et al. (2013) parameterization using FBAP concentrations, only data from the HyICE-2018 time period could be used as the fluorescence measurements from the WIBS are only available in this period. Therefore, the number of data points in Fig. 7c is lower than in the other panels. The aerosol-specific parameterization of Ullrich et al. (2017) best matches the temperature trend, but overestimates the measured INP data, reproducing only 23 % of the data points to within a factor of 10. This is not surprising, as the boreal forest aerosol is not dominated by mineral dust. The predictions of DeMott et al. (2010) and Tobo et al. (2013) overestimate INP concentrations, especially in wintertime. These comparisons emphasize the need for a parameterization that accounts for seasonality.

Given the need to represent seasonality, we suggest two new formulations to describe the seasonal variability of boreal forest INPs. Our first new non-aerosol-specific approach assumes that the atmospheric INP concentration is predominantly determined by the boreal forest as the major INP-emitting source with a magnitude that naturally changes with the seasons. Using ground-level ambient air temperature averaged over the aerosol filter sampling times as a proxy for the seasonal cycle, the observed INP concentration is quite well overlaid (see Fig. 5a). This clear relationship motivates us to use this parameter for the formulation of the new parameterization. The measured INP temperature spectra between 250 and 265 K were used to create a least squares fit between the activation temperature T in K and the natural logarithm of INP concentrations cINP in std L-1. This describes the activation behaviour of INPs in temperature space. To account for seasonal dependencies in this formulation, the linear relation between the ambient air temperature Tamb in kelvin measured close to the ground at 4.2 m height (called ground-level ambient air temperature) and the natural logarithm of the time series of INP concentrations cINP in std L-1 was used to establish a prefactor which shifts the parameterized INP temperature spectra to higher or lower INP concentrations, depending on the ground-level ambient air temperature. The resulting parameterization is as follows: 1cINP=0.1⋅exp⁡a1⋅Tamb+a2⋅exp⁡b1⋅T+b2stdL-1, with a1=0.074±0.006 K-1, a2=-18±2, b1=-0.504±0.005 K-1, b2=127±1 and with the activation temperature T and ground-level ambient air temperature Tamb in kelvin (measured at 4.2 m height). This new parameterization is able to reproduce 97.22 % of the data to within a factor of 10. 88.21 % and 49.79 % are reproduced within a factor of 5 and 2, respectively. In Fig. 8a, measured INP concentrations are compared to those predicted by the new parameterization, underlining the good agreement with a goodness of fit of R2=0.82. This new parameterization approach describes the annual variation in the near-surface INP concentration in the boreal forest, which provides a temperature-dependent source of these INPs. We did not directly detect or quantify the INP source but found a strong correlation of the measured INP concentration with the ground-level ambient air temperature. This leads to the assumption that the near-surface INP concentration in the boreal forest may be dominated by local or regional sources, and that this parameterization may be used in models to formulate the source strength or concentration of INPs in boreal forests near the surface. It should be noted that this is a mechanistic approach, which cannot necessarily be applied to regions other than boreal areas or to higher altitudes where the INP spectrum may be influenced by other sources. It is, furthermore, important to note that INPs might undergo changes in their size distribution and chemical composition when they are transported from their sources to higher altitudes, which could affect their ice nucleation ability.

Our second formulation is aerosol specific and describes the ice nucleation efficiency of boreal forest aerosol types using the INAS approach (Ullrich et al., 2017; Vali, 1971). As the seasonal cycle of INAS densities (see Fig. 2b) and the heat test results described earlier (see Fig. 6) indicate a seasonal change in INP types, we suggest specific parameterizations for different seasons. For the INAS density parameterization for boreal forest INPs, an exponential relation, as suggested by Ullrich et al. (2017), is assumed and has the following form: 2nS=exp⁡a1⋅T+a2m-2, where T is the activation temperature of INPs in kelvin. The INAS density nS in m-2 is calculated by normalizing the measured INP concentration by the total surface area concentration derived from DMPS and APS size distribution data. We adjusted the parameters in Eq. (2) to our measured INAS densities, considering the data set in three different periods corresponding to winter, summer and transition periods. The periods are defined by the measured snow depth s (s=0 cm corresponds to summertime, s>10 cm corresponds to wintertime and 0<s≤10 cm is the transition period). The new fits yield a1 =-0.543±0.007 K-1 and a2=154±2 for summertime (R2=0.78), a1=-0.495±0.008 K-1 and a2=141±2 for wintertime (R2=0.78) and a1=-0.49±0.01 K-1 and a2=140±3 for the transition period (R2=0.85). In Fig. 8b, the INP concentration calculated with these new parameterizations is compared to the measured concentrations. In summertime 92.57 % (79.40 % and 41.32 %) of the data are reproduced by the INAS density fit within a factor of 10 (5 and 2); in wintertime 97.32 % (86.30 % and 47.80 %) and in the transition period 99.11 % (95.56 % and 56.89 %) are reproduced.