MY05 is a bulk cloud microphysics parameterization with one-, two- and three-moment versions. We use the two-moment version available in WRF-Chem. It includes the following prognostic variables: the mass mixing ratio qx and the number concentration Nx, with x∈(c,r,i,s,h,g) respectively representing cloud liquid water (c), cloud ice water (i), rain (r), snow (s), hail (h) and graupel (g). The time evolutions of the hydrometeor mass mixing ratio and number concentration are respectively governed by the following prognostic equations: 1∂qx∂t=-1ρ∇⋅(ρqxU)+∇⋅(K∇qx)+1ρ∂∂zρqxVQx+dqxdt|s, and 2∂NT,x∂t=-∇⋅(NT,xU)+∇⋅(K∇NT,x)+∂∂zρNT,xVNx+dNT,xdt|s, where ρ is the density of air, U the 3D velocity vector, VQx the mass-weighted fall speed, NT,x the total number concentration per unit volume, VNx the number-weighted fall speed and K the turbulent diffusion matrix. The right-hand side terms of both equations respectively represent advection and divergence, turbulent mixing, sedimentation, and microphysical tendencies (marked by the “s” subscript).

The mass of a single hydrometeor for the x category is parameterized as a power law of the form 3mx(D)=cxD3, where cx=ρxπ6, with ρx the bulk density (Table ) for spherical particles x (cloud liquid water, rain, snow, graupel and hail). Cloud ice crystals are assumed to be bullet rosettes with ci=440 kgm-3. The size spectrum of each category is described by a common generalized gamma distribution function of the form 4Nx(D)=NT,xνxΓ(1+αx)λxνx(1+αx)Dνx(1+αx)-1exp⁡-(λxD)νx, where Nx(D) is the number concentration of hydrometeor x per unit volume per unit diameter D, αx is the shape parameter controlling the size dispersion, λx is the slope and νx is a second size dispersion parameter. The size distribution of cloud droplets is represented in MY05 by αx=1 and λx=3. For all other hydrometeors νx=1, leading to the form 5Nx(D)=N0xDαxexp⁡(-λxD), where N0x is the intercept parameter given by 6N0x=NT,x1Γ(1+αx)λx(1+αx).

The four ice-phase hydrometeors follow the size distribution above. The cloud ice water category represents pristine ice crystals. The snow category includes crystals with radii greater than 100 µm and aggregates. The graupel category includes moderate-density graupel formed from heavily rimed ice or snow. The hail category corresponds to high-density hail and frozen raindrops. For each ice-phase hydrometeor x, the total number concentration NT,x (kg-1) and the mass mixing ratio qT,x (kgkg-1) are respectively given by 7NT,x=∫0∞N0xDαxexp⁡(-λxD)dD, and 8qT,x=∫0∞mx(D)N0xDαxexp⁡(-λxD)dD, where mx(D) is obtained from Eq. ().

Microphysical processes represented in MY05 are summarized in Table , where processes are listed according to the hydrometeor category. The source and sink terms for the two-moment (mass content) scheme are from previous studies and depend on the size distribution function. The primary sources of ice crystals in the atmosphere are heterogeneous and homogeneous ice nucleation. Homogeneous freezing is the spontaneous freezing of a water (or haze) droplet. According to , the homogeneous freezing rate of cloud droplets is dominant at temperatures below ∼-32 ∘C. In the range -30 to -50 ∘C, MY05 follows with 9ΔNfreeze=∫0∞(1-exp⁡(-JVΔt))NTc(D)dD.

In a given time step Δt, ΔNfreeze is the number of droplets freezing homogeneously and J is the nucleation rate for pure water. For homogeneous nucleation, 10log⁡10(J)=-606.3952-52.6611Tc-1.7439Tc2-2.65×10-2Tc3-1.536×10-4Tc4, with the volume V approximated by the mean droplet diameter in centimeters. Therefore, the fraction of cloud droplets freezing in one time step may be written as 11Ffreeze=ΔNfreezeNTc1-exp⁡(-Jπ6Dmc3Δt), where Dmc is the mean volume diameter of cloud droplets. Heterogeneous ice nucleation needs INPs, a minor fraction of the tropospheric aerosol, which exhibits micro surface structures to facilitate the formation of ice crystals. In the presence of INPs, if thermodynamic conditions are favorable, ice crystals can form by heterogeneous nucleation through four different modes. Deposition nucleation and condensation freezing can occur without the presence of supercooled droplets. For clouds below 0 ∘C primarily composed of supercooled liquid droplets, ice crystal can form by immersion and contact freezing. This conceptual definition of heterogeneous ice nucleation is used in MY05. Contact freezing follows wherein the number concentration of contact INPs is a function of temperature according to . In the contact-freezing formation mode, ice nucleation occurs on a solid particle colliding with a supercooled liquid droplet. Immersion freezing of raindrops and cloud water droplets follows the parameterization of . The deposition mode involves the growth of ice directly from the vapor phase, whereas condensation freezing occurs if the ice phase is formed immediately after condensation of water vapor on a solid particle as liquid intermediate. In the original version of MY05, deposition and condensation freezing are functions of water vapor supersaturation with respect to ice, Si, following : 12Nm,i(Si)=1000exp⁡12.96(Si-1)-0.639, where Nm,i is the number of ice crystals predicted per unit volume due to deposition and condensation freezing. The parameterization for deposition and condensation freezing depends only on supersaturation. It was derived from ground-based measurements. These approximations may lead to an overestimation of Nm,i when the number concentration of particles acting as INPs is low, such as in Arctic conditions . Moreover, the immersion-freezing mode from has been extended to include freezing of immersed INPs inside an aqueous solution or wet aerosol , which is a significant process of Arctic ice cloud formation .

The new parameterization focuses on heterogeneous ice nucleation for uncoated INPs and for sulfuric-acid-coated INPs in the deposition mode, i.e., in water-subsaturated conditions. In this approach, INPs are assumed to be mineral dust particles following . For contact freezing and immersion freezing from supercooled cloud droplets, the parameterizations remain unchanged. As condensation freezing is uncertain , this process is no longer included in the model. The modified version of MY05 including our new parameterization described below is hereafter referred to as MYKE.

The parameterization is based on the CNT, a stochastic approach in which the nucleation rate Jd depends on the contact angle between an ice embryo and its INPs. Following CNT, in each time step Δt the number concentration of nucleated ice crystals Nf is given by 13Nf(Δt)=Ntexp⁡1-JdAdΔt, where Ad is the total surface area of dust particles and Nt is the total number concentration of available INPs. In previous studies using this approach , Ad and Nt were prescribed and constant over time, although the concentration of atmospheric INPs varied tremendously in time and space, as well as in their composition and origins. The new MYKE parameterization within WRF-chem now considers the temporal and spatial variation of Ad and Nt. Jd, the nucleation rate of embryos per unit surface of particles , is defined as 14Jd=Bexp⁡-ΔG∗kT, where B=1026 cm-2s-1 is the kinetic coefficient , k is the Boltzmann constant (JK-1), T is the temperature in Kelvin, and ΔG∗ is the critical Gibbs free energy for the formation of an ice embryo (J) and is defined as 15ΔG∗=16πσiv3f(cos⁡θ)3ρi2Rv2T2ln⁡2Si, where σiv=106.5×10-3 Jm-2 is the surface tension between ice and water vapor, ρi=0.5 gcm-3 is the bulk ice density and Rv=461.5 Jkg-1K-1 is the gas constant for water vapor. The function f(cos⁡θ) is a monotonic decreasing function of the cosine of the contact angle θ as defined by for a curved substrate: 16f(cos⁡θ)=121+1-qcos⁡θϕ3+q32-3(q-cos⁡θϕ)+q-cos⁡θϕ3+3q2cos⁡θq-cos⁡θϕ-1, where ϕ=1-2qcos⁡θ+q2 and q=rnrg, with rg being the critical germ size expressed as 17rg=2νwσivkTln⁡(Si), where νw is the volume of a water molecule.

In the CNT, the contact angle θ is a very important variable because it represents the ability of an INP to form ice. The lower the contact angle, the better an INP the aerosol is. Numerous laboratory studies have found realistic values of θ based on the physicochemical composition of aerosols (e.g., ). The CNT approach using these values was subsequently applied successfully in climate and forecast models at different scales . For example, using the parameterization of based on laboratory studies from , were able to simulate Arctic clouds forming in polluted and clean air masses with a prescribed contact angle of 26 and 12∘, respectively. These studies were, however, limited because the contact angles represent extreme cases that must be prescribed arbitrarily before the simulation, and they assumed homogeneity of the degree of acidity of clouds in space and time throughout the whole domain.

For the first time, a real-time variable contact angle is used here in the CNT approach by coupling MY05 with the chemical module in WRF-Chem. This coupling is between MY05 and the MOSAIC (Model for Simulating Aerosol Interactions and Chemistry) aerosol module . MOSAIC simulates a wide variety of aerosol species: sulfates, methanesulfonate, nitrate, chloride, carbonate, ammonium, sodium, calcium, black carbon (BC), primary organic mass (OC), liquid water and other inorganic mass (OIN). OIN represents unspecified inorganic species such as silica (SiO2), other inert minerals and trace metals lumped together assimilated to mineral dust. MOSAIC uses a sectional approach to represent aerosol size distributions by dividing the size distribution for each species into several size bins (four or eight available in WRF-Chem) and assumes that the aerosols are internally mixed in each bin. MOSAIC considers the major aerosol processes of inorganic aerosol thermodynamic equilibrium, binary aerosol nucleation, coagulation and condensation but does not include secondary organic aerosol (SOA) formation in the version used in this study. MOSAIC is a good compromise between accuracy and computing performance. It is used in WRF-Chem with four chemical mechanisms.

The coupling is done by expressing θ as a function of the aerosol neutralization fraction fn in dust particles internally mixed with sulfate, nitrate and ammonium , which is between 0 and 1 and is defined as 18fn=NH4+2SO42-+NO3-.

This was motivated by several previous studies suggesting that the acidification of ice nuclei by the oxidation of sulfur dioxide forming sulfuric acid in the Arctic greatly alters the microphysical response of ice clouds. Such ice clouds tend to have bigger and fewer ice crystals than ice clouds formed in pristine environments. For instance, showed that, except for quartz, acid-coated dust makes less effective INPs in the deposition mode but has similar effectiveness in the immersion-freezing mode, i.e., in water-supersaturated regime. Based on X-ray diffraction analyses, they argued that acid treatment caused structural deformations of the surface dust, and the lack of structured order reduced the ice nucleation properties of coated particles in the deposition mode. Moreover, they suggested that, at water-supersaturated conditions, surface chemical reactions might not change the original ice-nucleating properties permanently because coating material could be removed by dissolution. concluded that sulfuric-acid-treated kaolinite particles could result in the formation of aluminum sulfate that can easily be dissolved in water. Considering these recent findings and our objective to develop a simplified parameterization to limit computational time, we choose to use the CNT formula for deposition mode but with a specific factor, the neutralization fraction fn, indicating the degree of acidity of the coating of dust particles.

Moreover, θ has been derived by from heterogeneous nucleation rates on kaolinite particles obtained in laboratory measurements. As a best fit, they found limiting values of θ=26∘ in polluted air and θ=12∘ in clean air. Kaolinite represents a significant component of mineral dust . It is also found to be an efficient ice nucleus in the deposition mode, requiring relative humidity with respect to ice (RHi) below 112 % in order to initiate ice crystal formation . This is a typical microphysical condition found in Arctic ice clouds. Recent studies from showed that

the relevance of quartz particles as atmospheric INPs is uncertain,

Table  presents biases (Bias), Pearson correlation coefficients (Cor) and root mean square errors (RMSE) for the temperature T and relative humidity over ice RHi for the three simulations (REF, MYKE2 and MYKE4) and above the 500 hPa level. According to , the uncertainties on the measurements are estimated at ±0.5 ∘C for T and ±11 % for RHi. Note that vertical profiles of T and RHi for flights F13, F21 and F29 are very close to results obtained by . As expected, due to the nudging, the new heterogeneous ice nucleation parameterization does not significantly impact T and RHi. The lowest temperatures at the top of the clouds, where the process of heterogeneous ice nucleation is important, are relatively well reproduced by MYKE2 and MYKE4 simulations with similar statistics (Cor ≃0.99, RMSE ≃2, Bias ≃-2 ∘C), except along F21 flight (Cor ≃0.82, RMSE ≃3.3, Bias ≃-3 ∘C), for which the observed increase in temperature caused by the heat exchanged at cold temperatures is not adequately represented by the model. For that flight, the three simulations underestimate RHi by ±50 % at the top of the cloud. These biases are consistent with the large-scale GFS FLN fields and result in an underestimation of the altitude of the top of the cloud by the model for F21.

Figure  shows the comparison between observed and simulated (REF, MYKE2 and MYKE4) vertical profiles of total aerosol number concentrations (Na). The Passive Cavity Aerosol Spectrometer Probe (PCASP) externally mounted under a wing of the Convair-580 aircraft sampled ambient clear air just before entering the cloud regions for all flights except F21. The optical particle counter (PCASP) provided particle size distributions and number concentrations in the geometric diameter size range 0.12–3 µm. To allow a fair comparison between WRF-Chem-simulated and PCASP-measured Na, the model concentrations are summed over bins 3 to 6, corresponding to sizes between 0.156 and 2.5 µm. According to , the uncertainty in number concentration measured by the PCASP is approximately 10 %. First, the model does not reproduce the observed vertical variability. This may be due to the small sampling domain and time taken during ISDAC, which make comparisons between model simulations and the observed variability difficult, especially at the low horizontal resolution of 10 km used here. For F13, the air mass is relatively clean, with a weak vertical variability of aerosol number concentrations remaining mostly below 210 cm-3 on the whole column with mean concentrations around 73 cm-3, very close to the simulation mean of 86 cm-3. For F29, the PCASP shows that there is a much higher concentration of aerosol particles in the lower troposphere (more than twice that observed during F13, e.g., larger than 400 cm-3), particularly at altitudes above 550 hPa near cloud top where peak concentrations exceeding 1000 cm-3 have been measured. Comparing the two flights, between 550 hPa and 400 hPa, the simulated aerosol number concentration is overestimated by a factor of 3 above observations for flight F13 and underestimated by 1 order magnitude for flight F29 (Fig. ). These discrepancies are consistent with , who analyzed aerosol concentrations during polar night around Fairbanks and showed an overestimation of aerosol concentrations over the nonpolluted site and an underestimation at an polluted site by using WRF-Chem. They concluded that discrepancies result from uncertainty in emissions, especially at Fairbanks. While most models agree that Arctic aerosols can be attributed to a mixture of anthropogenic sources, mesoscale models have difficulty properly simulating aerosol concentrations over the Arctic . Moreover, even if the simulated results show the same order of magnitude for Na above 550 hPa (Fig. ), whereas observations show a large difference between the two flights, we expect that the differences between simulated results for cloud microphysical properties for these two flights could be mainly explained by a combination of differences in the physicochemical properties of aerosols and the altitude of the simulated cloud top.

Figure  presents simulated (REF, MYKE2 and MYKE4) vertical profiles of sulfate (SO4), ammonium (NH4) and nitrate (NO3) molar aerosol concentrations along flights F13, F21 and F29, respectively. Unfortunately, no observation of the aerosol chemical composition was available during the campaign to evaluate those results. Vertical distributions indicate a rather constant structure of aerosol molar concentrations for F13, with a mean value around 6.2 nmolcm-3 for both SO4 and NH4 and a value of 0.5 nmolcm-3 for NO3 (Fig. ). For F21 and F29 simulated results show peak aerosol concentrations in the mid-troposphere up to a factor of 2 compared to F13 and a larger vertical gradient, with large and moderate depletion in the boundary layer for F21 and F29 (Fig. b and c). F21 and F29 have NH4 mean values of 8 and 10.2 nmolcm-3, respectively, and SO4 mean values both around 7 nmolcm-3. These values and the vertical structures correspond relatively well with mean observed concentrations for NH4 and SO4 of 7 nmolcm-3 seen during the ARCTAS (Arctic Research of the Composition of the Troposphere from Aircraft and Satellites) and ARCPAC (Aerosol, Radiation, and Cloud Processes affecting Arctic Climate) campaigns in April 2008 . showed that volcanic sources (Aleutian Islands and Kamchatka) accounted for 12 %–24 % of the sulfate at all altitudes, with a peak contribution in the mid-troposphere. The volcanic source is discharged directly in the free troposphere and is thus less affected by deposition than surface sources. This is also supported by satellite observations from the Ozone Monitoring Instrument (OMI) over the North Slope of Alaska, which shows much larger SO2 concentrations at the end of ISDAC. Clouds sampled during both F21 and F29 appear to form mostly in air masses containing dust and smoke, possibly with a highly acidic coating.

Figure  presents the vertical profile of the neutralization fraction fn (full line, see Eq. ) and the contact angle θ (dashed, see Eqs.  and ) for MYKE2 (Fig. a) and for MYKE4 (Fig. b) along the top of the three flights F13, F21 and F29. Results obtained with MYKE2 and MYKE4 using the same value of the neutralization fraction are very similar. Results from the two simulations are therefore discussed together. The difference lies in the curve shape of the contact angle θ: MYKE4 simulates a more rapid decrease for 0<fn<0.5 than MYKE2 (Fig. ). This prescription substantially increases θ values in MYKE4 more than in MYKE2 along the vertical profile by up to 3∘, especially at the cloud top where nucleation is the dominant process. This change has a positive impact on the nucleation rate: a smaller contact angle in the MYKE2 simulation indeed tends to decrease the critical Gibbs free energy to form ice embryos (Eq. ), hence leading to a higher nucleation rate of ice crystals. The θ profile in F13 presents a constant shape with values around 17.5 and 20.5∘ for MYKE2 and MYKE4, respectively. Focusing on MYKE4 for F21, the large contact angle around 21∘ corresponds to acid INPs, i.e., a smaller fn than F13, and a decrease in the nucleation rate. Although F29 also shows significant acidity around 400 hPa (Fig. b), with higher concentrations of SO4 than F13, it tends to neutrality around 500 hPa in relation to the increase in ammonium at this altitude in comparison to higher altitudes and the negligible amount of nitrate in the upper part of the cloud (Fig. b and c).

Our results reveal that the model broadly reproduces Na from the ground to the 500 hPa level, but it has difficulty representing Na in the upper part, even if observations and model results remain of the same order of magnitude. MYKE2 and MYKE4 simulations show higher θ values at cloud top for F21 and F29 in comparison to F13, thus differencing the acidic from the nonacidic cases as expected. In the following section, we will examine the effect of interactive chemistry on the cloud microphysical variables.

Details of the retrieval of cloud microphysical properties and associated uncertainties from the several cloud probes onboard the Convair-580 aircraft are given in . Figure  presents the comparison of the observed and simulated (REF, MYKE2 and MYKE4) vertical profiles of IWC (uncertainties: ±75 %) along the three flights. Observed IWC vertical profiles for F13 and F29 continuously decrease between 800 and 400 hPa, with values in the range of 10-1 to 10-2 kgkg-1. For flight F21, observed IWC shows a large variability in its vertical structure. IWC values simulated by both MYKE2 and MYKE4 are very similar, with a slight improvement for MYKE2 simulating more IWC. This agrees with the θ difference between MYKE2 and MYKE4 (Fig. ). A smaller contact angle in the MYKE2 simulation tends to decrease the critical Gibbs free energy to form ice embryos (Eq. ), hence leading to a higher nucleation rate of ice crystals and higher IWC. Both MYKE2 and MYKE4 broadly capture observed values with a low bias: +1.2×10-2 and +8.1×10-3 gkg-1 for F13; -3.2×10-3 and -3.5×10-3 gkg-1 for F21; -2.1×10-3 and -8.1×10-3 gkg-1 for F29. In contrast, REF strongly underestimates IWC values with a negative bias of 0.01 gkg-1 for F13 and 0.03 gkg-1 for F29. Note that REF does not have any noticeable IWC cloud at these levels in flight F21.

Figure  presents a comparison between observed and simulated (REF, MYKE2 and MYKE4) vertical profiles of ice number concentration (Ni) (uncertainties: ±50 %) in the upper part of the cloud where heterogeneous ice nucleation processes are dominant above 500 hPa during flights F13, F21 and F29. The airborne ISDAC vertical profile for the TIC1 observed during F13 varies between 70 and 200 L-1 and is rather constant with altitude. The REF simulation strongly underestimates Ni by 2 orders of magnitude, corresponding rather to a TIC2. MYKE2 and MYKE4 reproduce the observed Ni within the ranges of uncertainties well, while MYKE4 is slightly closer to observations with a bias of 25 L-1. The TIC2 cloud type observed along F21 and F29 flight tracks is characterized by a small concentration of ice crystals ranging between 1 and 30 L-1. For F21, while REF is not able to simulate a persistent cloud, both MYKE2 and MYKE4 show a cloud with Ni close to observations typical of TIC2 under 450 hPa in the range of uncertainties (±50 %). As expected, due to the biases of temperature and relative humidity over ice, the model underestimates the cloud-top altitude for F21. For F29, both MYKE2 and MYKE4 show an increase in Ni compared to REF, which has the best statistics, while MYKE2 and MYKE4 simulations are overestimated by 1 order of magnitude. However, it is reasonably close to satellite observations as analyzed by . Their analysis revealed a large discrepancy in Ni between ISDAC flights and satellite estimations for F29 in the upper part of the cloud. We can notice here that the order of magnitude of Ni for F29 estimated from satellites can call into question the classification of F29 as a TIC2, especially as , using a flight track above Barrow (now Utqiagvik) instead of Fairbanks, classified this cloud as a TIC1. This discrepancy between airborne measurements, simulated results and satellite observations can be due to the small sampling domain during ISDAC versus the low resolution of satellite products and of the model grid.

Figure  presents the comparison of the observed and simulated (REF, MYKE2 and MYKE4) vertical profiles of the mean ice crystal radius (Ri) with uncertainties of ±97 %) along the F13, F21 and F29 flights. Observations show that, although having the same IWC magnitude (Fig. ), the TIC1 and TIC2 differ in their Ni (Fig. ) and Ri values. Flight F13 (TIC1), with a large Ni concentration, has Ri values around 25 µm, while both F21 and F29 refer to TIC2 with a low Ni and Ri at least a factor of 2 larger. The INP acid coating in TIC2 inhibits the ice nuclei properties of the INPs, slowing the rate of ice nucleation in comparison to uncoated Ni. Subsequently, this decrease in the nucleation rate increases the amount of available supersaturated water vapor and allows the rapid growth of activated ice crystals. It could explain the persistence of low Ni and the large Ri. For flight F13, MYKE2 and MYKE4 simulate the TIC1 formation above 450 hPa relatively well in the observation range, while below 450 hPa they both overestimate Ri by a factor of 2. For this TIC1 cloud, MYKE2 and MYKE4 give the smallest error in comparison to REF. For flight F21, MYKE2 and MYKE4 improve the comparison of simulated Ri against observations, showing large ice crystals even if the cloud-top altitude is underestimated. For flight F29, observed values of Ri are even larger. MYKE2 and MYKE4 show a little improvement in comparison to REF but only above around 450 hPa, with larger simulated ice crystals than REF. For flights F21 and F29, MYKE2 and MYKE4 underestimate the observed Ri by a factor of 2.

Our analysis shows the poor performance of the original REF parameterization in representing ice heterogeneous nucleation with low IWC and reveals that the MYKE parameterization can significantly improve the representation of the IWC at all vertical levels in polluted or unpolluted air masses. Along the three flights, RHi is therefore lower in the MYKE2 and MYKE4 simulations than in the REF run at cloud top. This may be due to the new parameterization promoting ice nucleation through a reduction of the available supersaturated water vapor. The new parameterization, with the variation in time and space of Ad and Nt, better represents Ni and Ri values at the top of TICs for flights F13 and F21 where the nucleation occurs. The pronounced slope of observed Ri above the 500 hPa level in TIC2 cases (Fig. ) indicates rapid growth of the ice crystals, which consume supersaturated water vapor faster than it is made available in the model. Finally, for flight F29, the new parameterization slightly improves Ri at the top of the clouds, while under around the 450 hPa level, simulated results show better agreement for the REF simulation. The reason for that is not clear. However, Fig.  shows a decrease in θ with altitude between 450 and 500 hPa in connection with an increase in the ammonium molar concentration (Fig. b), which leads to a more efficient heterogeneous nucleation of ice at this altitude with smaller ice crystals and larger concentrations.

Finally, from the comparison of the three simulations, we can assess the ability of the new scheme to discriminate TIC1 and TIC2 clouds. For F13, while REF results in a TIC2 cloud, MYKE2 and MYKE4 simulations produce a TIC1 in agreement with observations. As shown before, the orders of magnitude of Na at the top of the cloud for F13 and F29 are similar, but the neutralization fraction fn shows more acidic aerosols for F29. For both cases, close values of IWC allow us to compare MYKE results for Ni and Ri. Looking at the top of the cloud (above the 440 hPa level), Ni is lower for F29 than for F13 and Ri is larger for F29 than for F13, responding to acid aerosol through the variation of the contact angle. Within the limit of our calculation, the new parameterization significantly improves the representation of nucleation in TIC1 for F13 versus TIC2 for F29 at the cloud tops, despite the model bias of simulated aerosols by WRF-Chem over the Arctic . The comparison between simulations of F21 and F13 cases with MYKE is not so clear. Even if, at the top of the cloud, Ni is lower for F21 than for F13 as expected, Ri is smaller for F21 than for F13, which is not consistent with TICs. However, the comparison of the fn fraction at the cloud tops shows similar values for F21 and F13 near acid neutrality. This result highlights the importance of a consistent simulation of aerosol physicochemical properties to create a valuable simulation of microphysical ice cloud properties with our new parameterization of heterogeneous ice nucleation.

In general, regarding overall simulated results, MYKE4 shows better agreement with observations than MYKE2 for TIC1 and TIC2 clouds. It is well known that the effect of acid coating on INPs is to reduce their ability to form ice crystals, and this effect increases with the amount of acid . Moreover, our results suggest that even a low acidity on INPs leads to an important decrease in the heterogeneous ice nucleation rate because, for MYKE4, θ increases more rapidly when acid coating increases, i.e., decrease in the fn fraction (Fig. ).