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# H_{2}SO_{4}–H_{2}O binary and H_{2}SO_{4}–H_{2}O–NH_{3} ternary homogeneous and ion-mediated nucleation: lookup tables version 1.0 for 3-D modeling application

### Alexey B. Nadykto

### Jason Herb

Formation of new particles in the atmosphere has important
implications for air quality and climate. Recently, we have developed a
kinetically based H_{2}SO_{4}–H_{2}O–NH_{3}-ion nucleation model
which well captures the absolute values of nucleation rates as well as
dependencies of nucleation rates on NH_{3} and H_{2}SO_{4} concentrations, ionization rates, temperature, and relative humidity
observed in the well-controlled Cosmics Leaving Outdoor Droplets (CLOUD)
measurements. Here we employ the aforementioned recently developed kinetic
nucleation model to generate nucleation rate lookup tables for
H_{2}SO_{4}–H_{2}O binary homogenous nucleation (BHN),
H_{2}SO_{4}–H_{2}O–NH_{3} ternary homogeneous nucleation (THN),
H_{2}SO_{4}–H_{2}O-ion binary ion-mediated nucleation (BIMN), and
H_{2}SO_{4}–H_{2}O–NH_{3}-ion ternary ion-mediated nucleation
(TIMN). A comparison of nucleation rates calculated using the lookup tables
with CLOUD measurements of BHN, BIMN, THN, and TIMN is presented. The lookup
tables cover a wide range of key parameters controlling binary, ternary, and
ion-mediated nucleation in the Earth's atmosphere and are a cost-efficient
solution for multidimensional modeling. The lookup tables and FORTRAN
codes, made available through this work, can be readily used in 3-D
modeling. The lookup tables can also be used by experimentalists involved in
laboratory and field measurements for a quick assessment of nucleation
involving H_{2}SO_{4}, H_{2}O, NH_{3}, and ions.

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_{2}SO

_{4}–H

_{2}O binary and H

_{2}SO

_{4}–H

_{2}O–NH

_{3}ternary homogeneous and ion-mediated nucleation: lookup tables version 1.0 for 3-D modeling application, Geosci. Model Dev., 13, 2663–2670, https://doi.org/10.5194/gmd-13-2663-2020, 2020.

Particles in the troposphere either come from direct emission (i.e., primary
particles) or in situ nucleation (i.e., secondary particles). Secondary
particles formed via nucleation dominate the number of concentrations of
atmospheric particles (Spracklen et al., 2008; Pierce and Adams, 2009; Yu
and Luo, 2009) that are important for air quality and climate. Nucleation in
the atmosphere is a dynamic process involving various interactions of
precursor gas molecules, small clusters, and pre-existing particles (Yu and
Turco, 2001; R. Zhang et al., 2012; Lee et al., 2019). H_{2}SO_{4} and
H_{2}O are known to play an important role in atmospheric new-particle
formation (NPF; e.g., Doyle, 1961). It has been long known that while
binary homogeneous nucleation (BHN) of H_{2}SO_{4}–H_{2}O may play a
dominant role in the cold upper troposphere, it cannot explain nucleation
events observed in the lower troposphere (e.g., Weber et al., 1996). Several
alternative nucleation theories have been proposed, including ternary
homogeneous nucleation (THN) involving NH_{3} (Coffman and Hegg, 1995;
Napari et al., 2002), ion-mediated nucleation (IMN) considering the role
of the ubiquitous ion in enhancing the stability and growth of
prenucleation clusters (Yu and Turco, 2001), and nucleation involving
organic compounds (e.g., Zhang et al., 2004). The laboratory measurements in
the CLOUD (Cosmics Leaving Outdoor Droplets) chamber experiments at CERN
show that both ammonia and ionization can enhance H_{2}SO_{4}–H_{2}O
nucleation (Kirkby et al., 2011). In order to reach a deep and insightful
understanding of the physicochemical processes underlying the observed
enhancement effect of ammonia and ions, Yu et al. (2018) developed a kinetic
ternary ion-mediated nucleation (TIMN) model for the
H_{2}SO_{4}–H_{2}O–NH_{3}-ion system with thermodynamic data
derived from laboratory measurements and quantum chemical calculations. The
model is able to explain the observed difference in the effect of NH_{3}
in lowering the nucleation barriers for clusters of different charging
states and predicts nucleation rates in good agreement with CLOUD
observations (Yu et al., 2018).

The main objective of this work is to employ the recently developed kinetic
nucleation model (Yu et al., 2018) to generate nucleation rate lookup
tables for four different nucleation pathways: H_{2}SO_{4}–H_{2}O
binary homogenous nucleation (BHN), H_{2}SO_{4}–H_{2}O–NH_{3}
ternary homogeneous nucleation (THN), H_{2}SO_{4}–H_{2}O-ion binary
ion-mediated nucleation (BIMN), and H_{2}SO_{4}–H_{2}O–NH_{3}-ion
ternary ion-mediated nucleation (TIMN). With the lookup tables and simple
interpolation subroutines, the computational costs of the binary and ternary
nucleation rate calculations were significantly reduced, which is critically
important for multidimensional modeling. The computed nucleation rates of
BHN, THN, BIMN, and TIMN based on the lookup tables were evaluated against
CLOUD measurements.

The H_{2}SO_{4}–H_{2}O–NH_{3}-ion kinetic nucleation model, as
described in detail in Yu et al. (2018) solves the dynamic interactions of
various clusters and offers a physics-based explanation of the different
concentrations of NH_{3} needed to induce nucleation on neutral clusters, positive
ions, and negative ions. The model is designed for a nucleating system
consisting of H_{2}SO_{4}–H_{2}O–NH_{3} in the presence of
ionization (i.e., ternary ion-mediated nucleation, TIMN). In the absence of
NH_{3}, the model transforms into binary homogeneous nucleation (BHN)
or binary ion-mediated nucleation (BIMN) and reduces to BHN or ternary
homogeneous nucleation (THN) in the case when no ions are present. It is
important to note that in the H_{2}SO_{4}–H_{2}O–NH_{3} ternary
system, binary H_{2}SO_{4}–H_{2}O clusters coexist with ternary
H_{2}SO_{4}–H_{2}O–NH_{3} ones, while in the system with ions,
neutral clusters coexist with charged clusters. Therefore, BIMN includes
BHN, THN includes BHN, and TIMN includes both BIMN and THN.

For the benefit of different applications and for enabling one to evaluate
the contribution of different nucleation pathways (binary versus ternary,
neural versus ion-mediated), we run the model to generate nucleation lookup
tables separately for the four different nucleating systems, i.e.,
H_{2}SO_{4}–H_{2}O (BHN), H_{2}SO_{4}–H_{2}O–NH_{3} (THN),
H_{2}SO_{4}–H_{2}O-ion (BIMN), and
H_{2}SO_{4}–H_{2}O–NH_{3}-ion (TIMN). One can accurately determine
the role of NH_{3} by looking into the difference between BHN (BIMN) and
THN (TIMN) rates and the role of ionization by examining the difference
between BHN (THN) and BIMN (TIMN) rates. Another benefit of generating
separate lookup tables is that for the users who are only interested in BHN,
BIMN, or THN, the corresponding lookup tables are much smaller than that of
TIMN and much easier to handle.

For many practical applications, steady-state nucleation rates under given conditions are required. Nucleation rates are conventionally calculated at the sizes of critical clusters (Seinfeld and Pandis, 2016). Since the kinetic nucleation model explicitly solves the evolution of clusters of various sizes, it can calculate steady-state particle formation rates at any sizes larger than critical sizes (Yu, 2006). In many laboratory studies new-particle formation rates have been measured at certain detection sizes, typically much larger than critical sizes. For example, the nucleation rates measured in the CLOUD experiment are for particles with a mobility diameter of 1.7 nm. For atmospheric modeling with size-resolved particle microphysics, the sizes of the first bin are generally much larger than the critical sizes, and the nucleation rates calculated at the critical sizes (which vary with the atmospheric conditions) have to be extrapolated to the sizes of the first bin based on the assumed growth rates and coagulation sinks of freshly nucleated particles that may lead to additional uncertainties. To compare model nucleation rates with typical laboratory measurements and to facilitate the application of the obtained results in a size-resolved particle microphysics model whose first bin can have a size of down to around 1–2 nm. Nucleation rates are calculated at 1.7 nm mobility diameter (corresponding to mass diameter of ∼1.5 nm; Yu et al., 2018).

Lookup tables of steady-state nucleation rates for BHN (*J*_{BHN}), THN
(*J*_{THN}), BIMN (*J*_{BIMN}), and TIMN (*J*_{TIMN}) have been generated
under a wide range of atmospheric conditions. There are six parameters
controlling *J*_{TIMN}: sulfuric acid vapor concentration
([H_{2}SO_{4}]), ammonia gas concentration ([NH_{3}]), temperature (*T*), relative
humidity (RH), ionization rate (*Q*), and surface area of pre-existing
particles (*S*). Compared to *J*_{TIMN}, there is one fewer controlling
parameter for both *J*_{BIMN} (no [NH_{3}] dependence) and *J*_{THN} (no *Q*
dependence), while *J*_{BHN} only depends on four parameters
([H_{2}SO_{4}] *T*, RH, and *S*). Table 1 gives the range of each dependent
variable dimension, total number of points in each dimension, values at each
point, and controlling parameters for the four nucleation pathways. The
range and resolution in each parameter space are designed based on the
sensitivity of nucleation rates to the parameter, its possible range in the
troposphere, and a balance between the accuracy and sizes of the lookup
tables. *T* ranges from 190 to 304 K (resolution: 3 K), and RH (with respect
to water) ranges from 0.5 % to 99.5 % (resolution: 4 %). For
[H_{2}SO_{4}], we use 31 points to cover 5×10^{5} to
5×10^{8} cm^{−3} plus one additional point at
$\left[{\mathrm{H}}_{\mathrm{2}}{\mathrm{SO}}_{\mathrm{4}}\right]=\mathrm{5}\times {\mathrm{10}}^{\mathrm{9}}$ cm^{−3}. For [NH_{3}], we
employ 31 points to cover 10^{8} to 10^{11} cm^{−3} plus two
additional points at [NH_{3}]=10^{5} and 10^{12} cm^{−3}. *Q* ranges from 2 to 23 ion pairs ${\mathrm{cm}}^{-\mathrm{3}}\phantom{\rule{0.125em}{0ex}}{\mathrm{s}}^{-\mathrm{1}}$ with the
resolution of five values per decade (geometric) plus one additional point at *Q*=100 ion pairs ${\mathrm{cm}}^{-\mathrm{3}}\phantom{\rule{0.125em}{0ex}}{\mathrm{s}}^{-\mathrm{1}}$ (noting that *Q*=0 ion pairs
${\mathrm{cm}}^{-\mathrm{3}}\phantom{\rule{0.125em}{0ex}}{\mathrm{s}}^{-\mathrm{1}}$ is covered under BHN or THN). *S* ranges from 20 to 200 µm^{2} cm^{−3} with two points. Almost all the possible
tropospheric conditions relevant to NPF shall be covered with the above
parameter ranges. The lookup tables are designed to calculate nucleation
rates in the troposphere. For conditions in the stratosphere (RH<0.5 %) and on other planets (such as on Venus, as discussed in
Määttänen et al., 2018), it is unclear whether the model is valid or not
as measurements under such conditions are not available to validate the
model.

The lookup table for *J*_{TIMN} is the largest, being composed of
*J*_{TIMN} at more than 17 million points ($\mathrm{32}\times \mathrm{33}\times \mathrm{39}\times \mathrm{26}\times \mathrm{8}\times \mathrm{2}=\mathrm{17}\phantom{\rule{0.125em}{0ex}}\mathrm{132}\phantom{\rule{0.125em}{0ex}}\mathrm{544}$) and
with a total text format size of ∼103 MB. For
comparison, the smallest lookup table (for *J*_{BHN}) has just 64 896 points
and a total text format size of ∼0.38 MB. For any given
values of [H_{2}SO_{4}], [NH_{3}], *T*, RH, *Q*, and *S* within the
ranges specified in Table 1, nucleation rates can be obtained using the
lookup tables with an efficient multiple-variable interpolation scheme as
described in Yu (2010). For conditions out of the ranges specified in Table 1, which may occur occasionally in the atmosphere, linear extrapolation is
allowed only for surface area, for which the tables only give values at two
surface area points (*S*=20 and 200 µm^{2} cm^{−3}). The
dependence of nucleation rates on the surface area, which serves as
a coagulation sink (not a condensation sink because [H_{2}SO_{4}] is fixed),
is relatively linear, and thus extrapolation (linearly between Log_{10}*J*
versus surface area) will not cause unphysical values. The *J*_{BHN},
*J*_{THN}, *J*_{BIMN}, and *J*_{TIMN} lookup tables can be accessed via the
information given in the data availability section and can be used to
calculate nucleation rates efficiently in 3-D models.

Compared to those based on the full model, the deviation of nucleation rates
based on the lookup tables is generally within a factor of 2, well within
the corresponding uncertainty of CLOUD measurements. The dependence of
nucleation rates on the surface area is relatively linear, and two points for
*S* provide reasonable accuracy (compared to the uncertainties in the model
itself and measurements). In the atmosphere, the surface area of
pre-existing particles not only serves as a coagulation sink but also as a condensation sink for H_{2}SO_{4}, and thus it has a more profound impact
because nucleation rates are highly sensitive to [H_{2}SO_{4}]. For the
lookup tables, [H_{2}SO_{4}] is fixed, and therefore the dependence of
nucleation rates on surface area is relatively weaker. It should be noted
that most existing nucleation parameterizations do not take into account the
effect of surface area.

Dunne et al. (2016) reported CLOUD-measured nucleation rates under 377
different conditions (Table S1 of Dunne et al., 2016). These data can be
divided into BHN, THN, BIMN, and TIMN based on the values of [NH_{3}] and
*Q* in the chamber. Nucleation is classified as neutral (BHN or THN) when
*Q*=0 and as binary (BHN or BIMN) when [NH_{3}]<0.1 ppt. As a
result, 15, 27, 110, and 225 of these CLOUD measurements correspond to BHN,
BIMN, THN, and TIMN, respectively. Figures 1–4 present the comparisons of
the nucleation rates calculated from the lookup tables (*J*_{model}) with
corresponding values observed during CLOUD experiments (*J*_{obs}) under
BHN, BIMN, THN, and TIMN conditions. The error bars give the *J*_{model} range as a result of the measured [H_{2}SO_{4}] uncertainty
(−50 %, +100 %). The uncertainties in *J*_{obs} (overall a factor of
2) and those associated with the uncertainty in measured [NH_{3}]
(−50 %, +100 %) are not included.

Because of the increase in the contamination (both unwanted ammonia and
amines) with the CLOUD chamber temperature (Kürten et al., 2016), binary
nucleation measurements (i.e., without ammonia, [NH_{3}]<0.1 ppt) are only available at very low *T* (Figs. 1–2). Both BHN and BIMN
predictions based on the lookup tables overall agree well with the available
CLOUD observations within the uncertainty range. As pointed out earlier,
binary H_{2}SO_{4}–H_{2}O clusters coexist with ternary
H_{2}SO_{4}–H_{2}O–NH_{3} ones in the ternary system, while neutral
clusters coexist with charged clusters in the system containing ions.
Therefore, the nice agreement of BHN and BIMN model predictions with
observations provides a good foundation for the more complex THN and TIMN
models. CLOUD experiments have more data points for THN and TIMN within a
wide temperature range covering the lower troposphere. For THN (Fig. 3),
the model prediction is consistent with measurements at a low temperature
($T=\sim \mathrm{205}$–250 K) but deviates from measurements at high
*T*, with the level of model underprediction increasing with increasing *T*. As
pointed out in Yu et al. (2018), the level of contamination in the CLOUD
chamber appears to increase with temperature (Kürten et al., 2016); the nice
agreement at lower *T* and the deviation at higher *T* may be associated with
contamination (such as amines, etc.) in the CLOUD (Kirkby et al., 2011)
that increases with temperature (Kürten et al., 2016). In contrast to THN,
*J*_{model} for TIMN (Fig. 4) agrees with CLOUD measurements within the
uncertainties under nearly all conditions. *J*_{model} for TIMN at *T*=292–300 K is slightly lower than the corresponding observed values, which is likely a
result of similar causes of the THN underprediction at higher *T* (Fig. 3).
As demonstrated in Yu et al. (2018), the nucleation of ions is typically
stronger than that of neutral clusters for both binary and ternary
nucleating systems with ammonia. The ubiquitous presence of ionization in
the Earth's atmosphere calls for regional and global aerosol models to take
into account the effect of ionization in NPF. The BIMN and TIMN lookup
tables, derived from a physics-based kinetic nucleation model and validated
against the state-of-the-art CLOUD measurements, provide an efficient way to
incorporate the role of ionization in new particle formation in 3-D models.

Many global models explicitly calculate nucleation rates, but different
models and studies employ quite different nucleation schemes (e.g., Wang and
Penner, 2009; Zhang et al., 2010; Yu et al., 2010, 2012; Liu et al., 2012; K. Zhang et al., 2012; Williamson et al., 2019). For example, the BHN scheme of Vehkamäki et
al. (2002; hereafter V2002) was used by the CAM5 (Liu et al., 2012) and
ECHAM5-HAM (Stier et al., 2005) models. The H_{2}SO_{4}–H_{2}O ion-induced
nucleation (IIN, similar to BIMN defined in this study) of Lovejoy et al. (2004) and Kazil and Lovejoy (2007) was considered in the ECHAM5-HAM2 model
(Kazil et al., 2010; K. Zhang et al., 2012). The H_{2}SO_{4}–H_{2}O ion-mediated nucleation
scheme of Yu and Turco (2001) and Yu (2010) was employed by the GEOS-Chem
(Yu et al., 2010) and CAM5 (Yu et al., 2012) models. In addition, some aerosol
models (Wang and Penner, 2009; K. Zhang et al., 2012) used the empirical
nucleation parameterization for the boundary layer (e.g., Kuang et al., 2008)
in combination with the binary nucleation scheme. It is of interest to
understand the differences in nucleation rates predicted by different
nucleation schemes under the well-controlled CLOUD conditions.

Figure 5 compares nucleation rates calculated based on lookup tables
presented in this work and several other aerosol nucleation
parameterizations with the CLOUD measurements. The nucleation
models and parameterizations considered in Fig. 5 include this study (i.e., the
lookup tables described in this paper); BHN of Kulmala et al. (1998; hereafter K1998)
and Vehkamäki et al. (2002; hereafter V2002); BHN and BIMN of Yu (2010; hereafter Y2010) and
Määttänen et al. (2018; hereafter M2018); IIN (same as the BIMN) of Modgil et al. (2005; hereafter M2005), which is a parameterization based on Lovejoy et al. (2004);
THN of Napari et al. (2002; hereafter N2002); empirical activation nucleation (EAN)
parameterization of Riipinen et al. (2007; hereafter EAN-R2007; $J=\mathrm{3.5}\times {\mathrm{10}}^{-\mathrm{7}}$ [H_{2}SO_{4}]); and empirical kinetic nucleation (EKN)
parameterization of Kuang et al. (2008; hereafter EKN-H2008; $J=\mathrm{2.5}\times {\mathrm{10}}^{-\mathrm{13}}$ [H_{2}SO_{4}]^{2}). The EAN and EKN parameterizations were
derived from atmospheric nucleation measurements in the boundary layer (with
the presence of ammonia and ionization) and thus are compared with the TIMN
scheme (Fig. 5d). For THN (Fig. 5c), N2002 scaled by 10^{−5} has been used
in some modeling studies (e.g., Williamson et al., 2019), and thus values of
N2002 $\times {\mathrm{10}}^{-\mathrm{5}}$ are also given in Fig. 5c for comparisons. It can
be seen from Fig. 5 that there exist large differences in the nucleation
rates predicted by different nucleation schemes and parameterizations, and the
CLOUD measurements provide useful constraints to the nucleation schemes. Among
the schemes considered in Fig. 5, the lookup tables presented in this work
are in the best agreement with CLOUD measurements for all four nucleation
pathways in terms of not only the absolute nucleation rates but also the
correlation coefficients. BHN rates based on K2008, V2002, and M2018 are
generally 1–4 orders of magnitude higher than the observed values, with
K1998 having the lowest correlation coefficient (*r*=0.48). For BIMN, M2005
generally underpredicts while M2008 overestimates the rates by up to
∼2 orders of magnitude. For THN, N2002 significantly
overestimates the rates by 5–9 orders of magnitude. The scaling of N2002
by 10^{−5} reduces the overestimation, but the correlation coefficient
remains low (*r*=0.32). The empirical parameterizations (both EAN and EKN)
depend only on [H_{2}SO_{4}] and, unsurprisingly, have very low
correlation coefficients (*r*=0.08) with CLOUD measurements. Care should be
taken in employing the empirical parameterizations in global models as both
EAN and EKN may give incorrect spatial distributions (Yu et al., 2010) and
temporal variations of nucleation rates in the atmosphere. It should be
noted that the TIMN scheme can be directly applied to calculate nucleation
rates in the whole troposphere (including the boundary layer), and thus one
shall not combine the BHN, THN, BIMN, and TIMN schemes presented in this study with
empirical boundary nucleation parameterizations (i.e., EAN and EKN) in
regional and global simulations.

The code and lookup tables can be accessed via the zenodo data repository (https://doi.org/10.5281/zenodo.3483797; Yu, 2019). For quick calculation of BHN, THN, BIMN, and TIMN rates under specified conditions, one can use the online nucleation calculators, which we have developed based on these lookup tables and made available to the public at http://apm.asrc.albany.edu/nrc/ (last access: 15 June 2020).

FY designed and generated the lookup tables. FY, ABN, GL, and JH contributed to the kinetic model used to generate the lookup tables. FY wrote the paper with contributions from all coauthors.

The authors declare that they have no conflict of interest.

This research has been supported by the US National Science Foundation (grant no. AGS1550816) and the Russian Science Foundation and the Ministry of Science and Education of Russia (grant nos. 1.6198.2017/6.7 and 1.7706.2017/8.9).

This paper was edited by Samuel Remy and reviewed by three anonymous referees.

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- Abstract
- Introduction
- Nucleation rate lookup tables for BHN, THN, BIMN, and TIMN
- Comparison of BHN, THN, BIMN, and TIMN rates from the lookup tables with CLOUD measurements
- Comparison of BHN, THN, BIMN, and TIMN rates based on the lookup tables with those based on other models and parameterizations
- Code and data availability
- Author contributions
- Competing interests
- Financial support
- Review statement
- References

- Abstract
- Introduction
- Nucleation rate lookup tables for BHN, THN, BIMN, and TIMN
- Comparison of BHN, THN, BIMN, and TIMN rates from the lookup tables with CLOUD measurements
- Comparison of BHN, THN, BIMN, and TIMN rates based on the lookup tables with those based on other models and parameterizations
- Code and data availability
- Author contributions
- Competing interests
- Financial support
- Review statement
- References