Impact of Air Refreshing and Cloud Ice Uptake Limitations on Vertical Profiles and Wet Depositions of Nitrate, Ammonium, and Sulfate

The impacts of cloud mixing and uptake on wet scavenging are not adequately resolved in global models which can lead to an overestimation of the removal of water‐soluble gases and aerosols from the atmosphere. To address this issue, we develop and implement novel parameterizations to consider the impacts of these processes. Our analysis of vertical profiles of nitric acid, inorganic nitrate, ammonium, and sulfate concentrations during the Atmospheric Tomography Mission periods indicates that air refreshing limitation has a significant impact above 800 hPa, while cloud ice uptake limitation plays an important role above 500 hPa. Incorporating these two processes resulted in a reduction of wet depositions of these species across source regions and a slight increase in their downwind regions. Wet depositions of nitrate, ammonium, and sulfate were reduced in source regions by 22.7%, 8.4%, and 8.3%, respectively and increased in downwind regions by 10.1%, 7.0%, and 4.3%, respectively.

Plain Language Summary Atmospheric species in cloud-free or rain-free air need time to be transported and mixed with those in cloudy or rainy air before being influenced by wet scavenging.Additionally, the efficiency of rainout of water-soluble aerosols for cold clouds is expected to be limited by cloud ice uptake.The removal of water-soluble aerosols from cold clouds only occurs when they are taken up by ice crystals.However, current models do not adequately address these two processes.In this study, we derived new approaches that consider the effects of air refreshing and cloud ice uptake limitations on wet scavenging.We found that these new approaches have significant impacts on the vertical profiles and wet deposition fluxes of nitrate, ammonium, and sulfate.
• Air refreshing and cloud ice uptake limitations are not well resolved in global models • Air refreshing limitation impacts vertical concentration profiles <800 hPa, while cloud ice uptake limitation is important above 500 hPa • In combination, the two processes reduced wet depositions across source regions and slightly increased wet depositions in downwind regions

Supporting Information:
Supporting Information may be found in the online version of this article.
of clear air to be 3,600 s.This approach may overestimate the impact of entrainment-limited cloud uptake in unstable clouds and underestimate such impact in stable clouds.
Cold cloud wet scavenging is sensitive to the fraction of species incorporated in ice crystals (Liu et al., 2001).Liu et al. (2001) studied the impact of 0% and 100% partitioning of aerosols into ice crystals on cold cloud wet scavenging and found that the 100% partitioning assumption can prevent overestimations of 210 Pb and 7 Be in the middle and upper troposphere.Moreover, Luo et al. (2020) showed that GEOS-Chem significantly underestimated nitric acid and sulfate over the Northern Hemisphere during northern winter in the upper troposphere.These biases may be caused by the uncertainties of cold cloud wet scavenging but need further investigation.
In this study, we derive new approaches to simulate air refreshing and cloud ice uptake limitations in GEOS-Chem.
The approaches are described in Section 2. Their impacts on vertical profiles of nitric acid, inorganic nitrate, ammonium, and sulfate during the Atmospheric Tomography Mission (ATom) campaign periods and wet depositions of nitrate, ammonium, and sulfate are discussed in Section 3.

Approaches
We use air refreshing limitation to account for wet scavenging limited by subgrid air mixing between cloudy and cloud-free air and cloud ice uptake limitation to account for cold cloud rainout limited by interstitial scavenging by ice crystals.

Air Refreshing Limitation
Wet scavenging of species with grid mean mass mixing ratio C (kg species per kg air) is treated as: where ΔC is the grid mean mass loss (kg kg −1 ), f is the cloud or rainfall fraction, R i is the in-cloud or under-rain removing rate (s −1 ), and Δt is the time step (s).In Equation 1, the air mass in grid box is assumed to be well-mixed instantaneously.To take into account the impact of subgrid air mixing, air refreshing limited grid mean mass loss rate (R A , s −1 ) is determined by the time of in-cloud or under-rain removal (1/R i ) and the time of grid refreshing by cloud-free or rain-free air (τ A ): When τ A is 0, R A = fR i is as that used in current models.When τ A is large, R A is smaller than fR i which indicated wet scavenging is slowed down by air mixing.
The time of grid refreshing by cloud-free or rain-free air (s) is: where K A is cloud-free or rain-free air refreshing rate (s −1 ).
As inflow air mass equals outflow air mass, the change of C can be expressed as: where K i is the cloudy or rainy air refreshing rate (s −1 ).
Substituting Equation 4 into Equation 3, we get: Cloudy (rainy) air is exchanged with cloud-free (rain-free) air via turbulence.The information of the subgrid concentration gradient can help accurately simulate the exchange of species between cloudy and cloud-free areas within grid box.However, due to the lack of such information in current models, we assume that the concentration in the cloud-free area is C and the interstitial concentration in the cloudy area is 0. The assumption of interstitial concentration is based on that GEOS-Chem assumed aerosol in subgrid covered by clouds can be 100% activated and captured by clouds and then be impacted by precipitation.Mass exchanges at x, y, and z directions are: where u′, v′, and w′ are turbulence velocities (m s −1 ), and Δx, Δy, and Δz are grid spacing (m).Cloud volume fraction is needed to identify the cloudy and cloud-free areas inside one grid cell.However, cloud fractions in x, y, and z directions are not available.Therefore, we assume that cloud fractions in x and y directions equal   1 ∕2 and cloud fraction in z direction equals 1.
1 ∕2 is to account for the 2-d nature of cloud fractions.
Based on Stull (1988), turbulence velocities are dependent on the turbulence kinetic energy (TKE, m 2 s −2 ): By assuming   ′ =  ′ =  ′ as found by Pinto (1998), we obtain turbulence velocities as that of Morrison and Pinto (2005): Therefore, the refreshing rate can be calculated via turbulence velocities: More details about simulation of TKE in GEOS-Chem are described in Text S1 of the Supporting Information S1.

Cloud Ice Uptake Limitation
In GEOS-Chem, the original rainout efficiency of water-soluble aerosols for cold clouds was prescribed as 1 (Liu et al., 2001).This indicated not only aerosols activated in the clouds but also aerosols captured by the clouds are impacted by precipitation.Cold clouds are formed at high altitude Tropical and Polar Regions, where water-soluble aerosol particle sizes are usually small and hardly be activated in-cloud.Due to the long lifetime of cold clouds, water-soluble aerosols are captured by ice crystals by coagulation and then removed by precipitation.Therefore, cold cloud rainout efficiency is expected to be limited by cloud ice uptake.Cold cloud rainout efficiency equals the fraction of water-soluble aerosols in cloud ice due to uptake (F I ) which can be calculated as: where R A,U is air refreshing limited cloud ice uptake rate (s −1 ) which can be calculated by cloud ice uptake rate R U via Equation 2: Cloud ice uptake of aerosols depends on the coagulation rate of aerosols and ice crystals.Due to large uncertainties of aerosol sizes in bulk aerosol schemes, it is difficult to quantify cloud ice uptake rates in reasonable ranges via the coagulation rates.In this study, we assume cloud ice uptake of water-soluble aerosols is similar to that of nitric acid (R U,HNO3 ) which is (Jacob, 2000): where N I is ice number concentration (cm −3 ), S I is ice surface area (cm 2 ), r is ice crystal radius (cm), D g is gas phase diffusion coefficient (cm 2 s −1 ), M is molar mass (g mole −1 ), T is temperature (K), and γ is uptake efficiency.
Based on Hudson et al. (2002), γ of nitric acid is calculated as: Treating cloud ice uptake of water-soluble aerosols as that of nitric acid may not hold true as the dominant process for water-soluble aerosols is the uptake of coagulation, while molecular uptake dominates for nitric acid.As ice uptake of nitric acid is more efficient than that of aerosols, this assumption leads to the overestimation of cold cloud wet scavenging of aerosols.

Results
We use GEOS-Chem-v14.1.1 (Text S2 in Supporting Information S1) to assess the impacts of the new approaches.
There are three cases: (a) BSL for the baseline simulation, (b) AR considering only the impact of the air refreshing limitation, and (c) ARIU considering the combined effect of the two approaches.

Impacts on Vertical Profiles of Nitric Acid, Inorganic Nitrate, Ammonium, and Sulfate During ATom1-4 Campaign Periods
Aircraft measurements of nitric acid (HNO 3 ), inorganic nitrate (InOrgNIT), ammonium (NH 4 ), and sulfate (SO 4 ) during ATom1-4 were used to study the impacts of new approaches on their vertical profiles (Text S3 in Supporting Information S1).Model simulations generally captured the gradients of aircraft measurements (Figure 1).The Pearson's correlation coefficients between the simulations and observations varied within the ranges of 0.71-0.83(HNO 3 ), 0.66-0.80(InOrgNIT), 0.94-0.97(NH 4 ), and 0.91-0.93(SO 4 ).As shown in Table 1, after  considering air refreshing limitation, concentrations of these species increased 44.2%, 99.7%, 43.4%, and 25.6% between 800 and 500 hPa and 11.6%, 283.0%, 114.4%, and 30.3% above 500 hPa.These values were much larger than those below 800 hPa, due to the usually strong turbulence in the planetary boundary layer.Strong turbulence resulted in small air refreshing limitation.Cloud ice uptake limitation showed negligible impacts below 800 hPa due to negligible cold cloud removal.By contrast, the impacts of cloud ice uptake limitation were obvious above 500 hPa, where cold cloud scavenging is important.Here, the changes caused by cloud ice uptake limitation were 2.8-5.5 times higher than those caused by air refreshing limitation.It indicated that cloud ice uptake limitation is important for wet scavenging in the mid-to-high altitude atmosphere.

Impacts on Wet Depositions of Nitrate, Ammonium, and Sulfate
Wet deposition fluxes of simulated nitrate (HNO 3 + NIT), ammonium (NH 3 + NH 4 ), and sulfate (SO 2 + SO 4 ) were compared with the National Trends Network (NTN) observations across the US (Figure 2) and the European Monitoring and Evaluation Programme's (EMEP) Chemical Co-ordinating Centre (CCC) observations across Europe (Figure 3).More details about the comparison are provided in Text S4 of the Supporting Information S1.Normalized mean biases of BSL case for nitrate, ammonium, and sulfate were 61.3%, −4.3%, and −15.2% at NTN and 36.8%,−2.2%, and 14.2% at CCC (Table 2).BSL case overestimated wet depositions of nitrate at  the two networks and underestimated wet deposition of sulfate at NTN.We found the correlation coefficient of observed and simulated wet deposition of sulfate is low at NTN.One of the reasons for the low correlation is that the model resolution is too coarse to represent the urban-rural gradient as shown in Figure 2c.When we ran the model at the higher 0.5° × 0.625° resolution, the correlation coefficient increased to 0.39.The impacts of air refreshing and cloud ice uptake limitations on wet depositions at NTN and CCC sites are shown in Table 2.The results simulated by AR and ARIU cases were close to each other.It indicated cloud ice uptake limitation has a negligible impact on wet depositions at these sites.By contrast, air refreshing limitation shows obvious impacts.Due to air refreshing limitation, wet depositions of nitrate, ammonium, and sulfate were changed by −38.2%, −5.0%, and −7.2% at NTN and −34.7%, −10.6%, and −9.5% at CCC.We noticed that the impacts of our new approaches on the wet deposition of nitrate are larger than those on ammonium and sulfate.It is caused by the different vertical concentration gradients of nitric acid, ammonia + ammonium, and sulfur dioxide + sulfate.As shown in Table S1 of the Supporting Information S1, nitric acid scavenging dominates HNO 3 + NIT wet deposition, while gas scavenging and aerosol scavenging both have considerable contributions to NH 3 + NH 4 and SO 2 + SO 4 wet depositions.We analyzed the vertical profiles of mean concentrations of nitric acid, NH 3 + NH 4 , and SO 2 + SO 4 at NTN sites (Figure S1 in Supporting Information S1) and found their C 800-600hPa / C P>800hPa ratios are 0.43, 0.26, and 0.21, respectively.The higher value of C 800-600hPa /C P>800hPa indicated that a larger proportion of mass is distributed in the upper layer where the effect of air refreshing limitation is stronger.
Figure 4 shows the BSL global distributions of wet depositions of nitrate, ammonium, and sulfate and the impacts of new approaches on them.Global mean wet depositions of these species were 0.72 kgN ha −1 a −1 , 1.05 kgN ha −1 a −1 , and 1.04 kgS ha −1 a −1 , respectively.Wet depositions were unevenly spread across the world.Hotspots of wet depositions were found in South Asia, East Asia, Europe, Eastern North America, Central Africa, and Southern Brazil.Wet depositions across land were 3.9, 5.0, and 1.9 times higher than those across the ocean.Figures 4d-4f summarized the impacts of the new approaches.We found global mean wet depositions of these HNO 3 + NIT (kgN ha −1 a −1 ) NH 3 + NH 4 (kgN ha −1 a −1 ) SO 2 + SO 4 (kgS ha −1 a −1 )   species were reduced by 18.1%, 3.8%, and 4.8%, respectively.Wet depositions were reduced across land and increased slightly in downwind regions such as North Pacific, North Atlantic, and South Ocean.This is because the two limitations reduced wet scavenging near source regions which extends lifetimes of these species and leads to more of them being transported and deposited in downwind regions.As a result of the spatial shifting, wet depositions of nitrate, ammonium, and sulfate were reduced in source regions by 7.2 TgN a −1 , 3.1 TgN a −1 , and 3.3 TgS a −1 , respectively and increased in downwind regions by 0.5 TgN a −1 , 1.2 TgN a −1 , and 0.6 TgS a −1 , respectively.

Summary and Discussions
To improve the accuracy of wet scavenging simulations, we derived air refreshing limitation and cloud ice uptake limitation approaches in this study.Our comparisons of model simulations with observations indicate that both approaches substantially improved model performances.Air refreshing limitation increased the concentrations of nitric acid, inorganic nitrate, ammonium, and sulfate by 44.2%, 99.7%, 43.4%, and 25.6% in the layers between 800 and 500 hPa and by 11.6%, 283.0%, 114.4%, and 30.3% in the layers above 500 hPa.Cloud ice uptake limitation played an important role in the layers above 500 hPa, causing an increase in the concentrations of these species by 32.2%, 843.8%, 478.9%, and 166.8%, respectively.By employing both approaches in wet scavenging, global mean wet depositions of nitrate, ammonium, and sulfate were reduced by 18.1%, 3.8%, and 4.8%, respectively.The developed novel parameterizations in this study do not only work for GEOS-Chem but also work for models which do not resolve the impacts of cloud mixing and uptake on wet scavenging.
Although the derived new approaches improved the simulation of nitric acid, inorganic nitrate, ammonium, and sulfate concentrations in the upper troposphere, there remain significant biases.One limitation of the current approaches is treating cloud ice uptake of water-soluble aerosols as that of nitric acid.Additional aircraft measurements and sectional aerosol microphysics simulations of the size distributions of nitrate, ammonium, and sulfate at cold temperatures and lab-measured uptake coefficients of these species on ice crystal surfaces are expected to reduce these biases.Uncertainties also exist in the parameterizations of ice size and surface area.Further investigations on the impacts of different ice parameterizations on cloud ice uptake limitation are underway.Follow-up studies on the broad geophysical implications of this work (e.g., the impacts on aerosol lifetime, distribution, and nitrogen nutrients to the global terrestrial ecosystem) will be carried out.

Figure 2 .
Figure 2. Horizontal distributions of HNO 3 + NIT, NH 3 + NH 4 , and SO 2 + SO 4 wet depositions across the contiguous US simulated by (a-c) BSL case and (d-f) ARIU case.Filled circles are annual mean wet depositions at NTN sites modified by the ratio of simulated precipitation to observed precipitation.

Figure 3 .
Figure 3.The same as Figure 2 but across Europe.

Figure 4 .
Figure 4. Global horizontal distributions of (a-c) HNO 3 + NIT, NH 3 + NH 4 , and SO 2 + SO 4 wet depositions and (d-f) their differences between the ARIU and BSL cases.Panel subheadings note the global (G), land (L), and ocean (O) mean values.

Table 2
Observed and Simulated HNO 3 + NIT, NH 3 + NH 4 , and SO 2 + SO 4 Wet Depositions at NTN Sites Across the US and CCC Sites Across Europe