Estimating the potential cooling effect of cirrus thinning achieved via the seeding approach

. Cirrus thinning is a newly emerging geoengineering approach to mitigate global warming. To sufﬁciently ex-ploit the potential cooling effect of cirrus thinning with the seeding approach, a ﬂexible seeding method is used to calculate the optimal seeding number concentration, which is just enough to prevent homogeneous ice nucleation from occurring. A simulation using the Community Atmosphere Model version 5 (CAM5) with the ﬂexible seeding method shows a global cooling effect of − 1 . 36 ± 0 . 18 Wm − 2 , which is approximately two-thirds of that from artiﬁcially turning off homogeneous nucleation ( − 1 . 98 ± 0 . 26 Wm − 2 ). How-ever, simulations with ﬁxed seeding ice nuclei particle number concentrations of 20 and 200 L − 1 show a weak cooling effect of − 0 . 27 ± 0 . 26 Wm − 2 and warming effect of 0 . 35 ± 0 . 28 Wm − 2 , respectively. Further analysis shows that cirrus seeding leads to a signiﬁcant warming effect of liquid and mixed-phase clouds, which counteracts the cooling effect of cirrus clouds. This counteraction is more prominent at low latitudes and leads to a pronounced net warming effect over some low-latitude regions. The sensitivity experiment shows that cirrus seeding carried out at latitudes with solar noon Author contributions. JL derived the formula for optimal seeding number concentrations. XS and JL designed the model experiments and developed the model code. JL processed and analyzed the raw model output data and wrote the XS helped to explain the results. Both authors contributed to improving and the


Introduction
Global warming has been proven by observations and has demonstrated many adverse effects on the environment and economy (Alexander et al., 2006;Feely et al., 2009;Lenton et al., 2019;Milne et al., 2009;Myhre et al., 2013). Sav-ing energy and reducing greenhouse gas emissions are regarded as the primary strategies to counteract global warming, but these strategies may not be satisfactory (Fuss et al., 2018;IEA, 2019;Rogelj et al., 2015;Solomon et al., 2009). Therefore, geoengineering as a backup tool against climate warming has been receiving increasing attention in recent years (e.g., Gasparini et al., 2020;Jones et al., 2018;Keith and MacMartin, 2015;Lawrence et al., 2018;Lohmann and Gasparini, 2017;Macnaghten and Owen, 2011). Geoengineering is usually divided into two categories: carbon dioxide removal (CDR), which aims to permanently eliminate CO 2 from the atmosphere, and solar radiation management (SRM), which proposes artificial intervention in the radiation budget (Caldeira et al., 2013;Heutel et al., 2018;Irvine et al., 2016;Kravitz et al., 2011;Vaughan and Lenton, 2011).
It is well known that cirrus clouds (ice clouds) typically reflect less incoming solar radiation but block more of Earth's outgoing longwave radiation, which warms our planet (Berry and Mace, 2014;Hong et al., 2016;Matus and L'Ecuyer, 2017). Cirrus thinning geoengineering, which allows more longwave radiation to escape to space, leading to a cooling effect on the planet, has been investigated as a new SRM approach and has been proposed in Geoengineering Model Intercomparison Project Phase 6 (GeoMIP6; Kravitz et al., 2015). In GeoMIP6, cirrus thinning is simulated by artificially increasing the sedimentation velocity of ice crystals (ICs). Simulations with this idealized approach indicate that cirrus thinning can produce the desired globally averaged cooling effect (∼ −2.0 W m −2 ; e.g., Gasparini et al., 2017;Jackson et al., 2016;Muri et al., 2014). Considering the physical feasibility, simulating cirrus thinning by seeding with ice nuclei particles (INPs) is a better approach that can prevent homogeneous nucleation from occurring, thereby decreasing the number concentration of ICs (e.g., Gruber et al., 2019;Storelvmo et al., 2013). Previous studies have shown that the cooling effect achieved via the seeding approach is sensitive to the seeding number concentration (N seed ), and even the strongest cooling effects are not strong enough (above −1.0 W m −2 ; e.g., Gasparini and Lohmann, 2016;Gasparini et al., 2017;Penner et al., 2015). Note that the N seed used in these model simulations is fixed (usually in the range of 0.1 to 200 L −1 ), and the seeding strategy is uninterrupted (i.e., seeding occurs at every model time step). This study shows that the potential cooling effect of cirrus thinning cannot be sufficiently exploited due to the fixed seeding method. Moreover, a flexible seeding method is introduced to calculate the optimal N seed (N seedopt ) based on the cirrus formation condition. The major purpose of this study is to estimate the potential cooling effect of cirrus thinning achieved via the seeding approach.
In this study, the cooling effects of cirrus thinning with different seeding methods are estimated. The paper is organized as follows. The flexible seeding method and its advantages are introduced in Sect. 2. This section also introduces the models and experimental designs that are employed. Comparisons of the cooling effects among different seeding methods and the main mechanism for the cooling effect are presented in Sect. 3. Finally, Sect. 4 presents the conclusions and discussion.

Cirrus thinning by seeding with ice nuclei particles
To better understand the seeding methods used in this study, it is necessary to briefly introduce the mechanism of cirrus thinning by seeding with INPs. In cirrus clouds, ICs are formed by homogeneous nucleation on soluble aerosol particles or heterogeneous nucleation on insoluble aerosol particles (Pruppacher and Klett, 1998). As ice-phase supersaturation (S i ) rises, heterogeneous nucleation occurs earlier with the aid of INPs (i.e., insoluble aerosols). A few ICs (usually less than 100 L −1 ) are generated due to the relatively low number concentration of INPs. These newly formed ICs consume water vapor via deposition growth and then hinder S i from rising (DeMott et al., 2003;Hoose and Möhler, 2012;Lohmann et al., 2008). The threshold S i for homogeneous nucleation (S ihom ) is relatively higher. Therefore, homogeneous nucleation cannot occur (i.e., S i cannot reach S ihom ) if there are enough newly formed ICs from heterogeneous nucleation. However, homogeneous nucleation can produce a large number of ICs once it takes place (usually much greater than 100 L −1 ) because the number concentration of soluble aerosols in the upper troposphere is abundant (Barahona and Nenes, 2009;Kärcher, 2002). Therefore, seeding the clouds with a few INPs (usually less than 100 L −1 ) can prevent S i from reaching S ihom (Barahona and Nenes, 2009;Liu and Penner, 2005;McGraw et al., 2020). As a result, the in-cloud IC number concentration (N i ) is usually decreased, which decreases the cirrus cloud optical depth (i.e., cirrus thinning; Storelvmo et al., 2013).

Models and parameterizations
In this study, we use a cloud parcel model to illustrate the impact of seeding on the ice nucleation process. The parcel model presents the IC formation process in an adiabatically rising air parcel with a constant updraft vertical velocity (W ). Equations that describe the evolution of temperature (T ), pressure (P ), ice water mixing ratio (Q i ), and ice particle size (R i ) can be found in Pruppacher and Klett (1998). The S i is diagnosed from the conservation equation of total water (i.e., water vapor plus ice water). The homogeneous nucleation rate (J ) of sulfate aerosol particles is calculated based on the water activity (Koop et al., 2000). The heterogeneous frozen fraction of dust aerosol particles is calculated by the classical nucleation theory (CNT; following Barahona and Nenes, 2009) with a freezing efficiency of 1.0 (i.e., 100 % dust aerosols can act as INPs). More details about this cloud parcel model can be found in Shi and Liu (2016).
The climate model used in this study is version 5.3 of the Community Atmosphere Model (CAM5; Neale et al., 2012) with an improved ice nucleation parameterization that considers the effect of preexisting ICs and incloud vertical velocity fluctuations (Shi et al., 2015;Shi and Liu, 2016). The ice nucleation parameterization considers the competition between heterogeneous freezing on coarse-mode dust aerosol particles and homogeneous freezing on sulfate aerosol particles. Here, 100 % coarse-mode dust aerosols can act as INPs (Liu and Penner, 2005;Shi et al., 2015). Considering that sulfate aerosol particles may transform into a glassy state at very low temperatures (Murray et al., 2010), homogeneous nucleation is switched off below −68 • C (∼ 205 K), which could cause the modeled N i to be close to observations (Shi et al., 2013). Note that there is no homogeneous nucleation in mixed-phase clouds (0 • C ≥ T > −37 • C). The sub-grid vertical velocity (W sub ) derived from the turbulent kinetic energy is used to drive ice nucleation parameterization (Gettelman et al., 2010). The effect of preexisting ICs on ice nucleation is parameterized by reducing the vertical velocity for ice nucleation (W pre ; Barahona et al., 2014;Kärcher et al., 2006;Shi et al., 2015). In the improved ice nucleation parameterization, the newly nucleated IC number concentration (N inuc ) is calculated as a function of T , P , S i , W sub , W pre , the number concentration of coarse-mode dust aerosols (N dust ), and the number concentration of sulfate aerosols (N sul ). The cloud microphysics is represented by a two-moment scheme (Morrison and Gettelman, 2008).
J. Liu and X. Shi: Potential cooling effect of cirrus seeding 10611

Flexible seeding method
According to the mechanism of cirrus thinning caused by seeding with INPs, it is clear that N seedopt is the minimal number concentration to prevent homogeneous nucleation from occurring. If N seed is less than N seedopt (underseeding), the newly formed ICs from heterogeneous nucleation are insufficient; thus, homogeneous nucleation still occurs and produces a relatively large N inuc . If N seed is larger than N seedopt (overseeding), despite homogeneous nucleation being suppressed, N inuc remains somewhat larger due to excessive N seed . Notably, in terms of consuming water vapor and hindering homogeneous nucleation, it is clear that ICs are superior to INPs (Pruppacher and Klett, 1998;Kärcher et al., 2006;Shi et al., 2015). In other words, ICs can act as cheaper, cleaner, and safer INPs. Therefore, ICs are used as the seeding material in the flexible seeding method introduced by this study. The formulas for calculating N seedopt are introduced in the Appendix. N seedopt is a function of cirrus ambient conditions, aerosol properties, and radius of seeding ICs (R seed ). R seed is a tunable given parameter. It is important to point out that seeding with ICs occurs only where homogeneous nucleation would occur without seeding (i.e., flexible seeding strategy). Figure 1a illustrates the advantage of N seedopt . Parcel model results show that without seeding (REF, black lines), heterogeneous nucleation takes place at S i > 10 % and produces 10 L −1 of ICs. Because these newly formed ICs are too few in number to prevent S i from increasing, homogeneous nucleation takes place at S i > S ihom (∼ 56 %) and produces a large number of ICs (2937 L −1 ). The final N i (i.e., N inuc ) is 2947 L −1 . In the simulation with pure heterogeneous nucleation (HET, green lines), the final N i is 10 L −1 . In the simulation with seeding of 28 L −1 (N seedopt is 28 L −1 ) of ICs (OPT, red lines), the newly formed ICs from heterogeneous nucleation (10 L −1 ) and seeding ICs are just enough to prevent S i from reaching S ihom . The final N i (i.e., N inuc + N seedopt ) is 38 L −1 . In the simulation with seeding of 20 L −1 of coarsemode dust aerosol particles (INP20, blue lines, underseeding), heterogeneous nucleation produces more ICs (30 L −1 ) than the REF simulation. However, homogeneous nucleation still occurs and produces 715 L −1 of ICs. The final N i is 745 L −1 . In the simulation with seeding of 200 L −1 of coarse-mode dust aerosol particles (INP200, orange lines, overseeding), the newly formed ICs from heterogeneous nucleation (210 L −1 ) are large enough to prevent homogeneous nucleation from occurring. The final N i is 210 L −1 . Overall, seeding with INPs/ICs can lead to a lower N i , and N i from the OPT simulation is closest to the HET simulation.
Additionally, we run large-ensemble ice nucleation offline experiments to show the advantage of the flexible seeding strategy (Fig. 1b). A total of 1000 cirrus formation cases are sampled from the CAM5 simulation without seeding. The input variables (T , P , S i , W sub , N dust , and N sul ) used to drive ice nucleation parameterization in CAM5 are used to drive these offline experiments. Homogeneous nucleation events account for 7.4 % (i.e., 74 homogeneous nucleation cases). Five experiments corresponding to the parcel model simulations are carried out. Each experiment is driven by the same 1000 cases. In the two fixed seeding experiments (i.e., the INP20 and INP200 experiments), INPs (i.e., coarse-mode dust aerosols) are added for all 1000 cases, even if there was no homogeneous nucleation (i.e., uninterrupted seeding strategy). Compared with the REF experiment, all large N i cases (dots with N i > 500 L −1 ) totally vanish in the HET experiment because only heterogeneous nucleation events occur. The N i distribution in the OPT experiment is similar to that in the HET experiment, except for some low N i (< 10 L −1 ) cases. In the INP20 experiment, there are some large N i cases because homogeneous nucleation still occurs in 36 cases. In the INP200 experiment, there are no large N i cases because almost all homogeneous nucleation cases are suppressed, whereas the N i from all cases is greater than 200 L −1 due to the large N seed . In short, the flexible seeding method is better than the fixed seeding method.

Experimental setups
CAM5 model experiments are carried out to estimate the cooling effect of cirrus thinning. Table 1 summarizes all the experiments performed in this study. The REF, HET, OPT, INP20, and INP200 experiments correspond to the offline experiments discussed above. In the INP20 and INP200 experiments, the N dust used for driving ice nucleation parameterization (cirrus clouds only) increases by 20 and 200 L −1 (i.e., the N dust from the aerosol module plus 20 and 200 L −1 ), respectively. Note that the seeding INPs are added at every model time step but only impact the ice nucleation process (i.e., theN dust in the aerosol module is not influenced by the seeding INPs). In the OPT experiment, the seeding ICs are directly added into the cloud microphysics scheme. As a result, these seeding ICs would affect both the ice nucleation process and other cloud microphysics processes. Notably, it is unnecessary to consider water conservation because the seeding ICs are made from ambient atmospheric water vapor.
Additionally, we set up two sensitivity experiments for the flexible seeding method (Table 1). First, the tunable parameter R seed is investigated. R seed is 10 µm in the R10 experiment, whereas R seed is 50 µm in the OPT experiment. Second, the seeding region is investigated. Cirrus thinning also leads to more incoming solar radiation (warming effect), which counteracts the cooling effect from more outgoing longwave radiation, especially for the low solar noon zenith angle regions . Furthermore, this study also finds that the cooling effect over low-latitude regions is less susceptible to cirrus seeding for other reasons (see Sect. 3.1). Thus, another sensitivity experiment with a specific geographical target (i.e., the GT experiment) is examined. Similar to the study of  Panel (b) shows the N i from ice nucleation parameterizations driven by the same 1000 datasets of input variables (one dot denotes one offline result), which are sampled from the CAM5 simulation. The horizontal coordinate axis is N i , and the vertical coordinate axis is meaningless. Sensitivity experiments for the flexible seeding method R10 Similar to OPT, but R seed is set to 10 µm. GT Similar to OPT, but seeding occurs over target regions, where the solar noon zenith angles are greater than 12 • . , cirrus seeding is only carried out at latitudes where the solar noon zenith angles are greater than 12 • , which compose approximately 80 % of the Earth's surface.
In this study, all CAM5 experiments are atmosphere-only simulations with the same prescribed climatological ocean surface conditions. All experiments run for 11 model years at a horizontal resolution of 1.9 • × 2.5 • and a model time step of 30 min. The first year is considered to be a spin-up period, and the last 10 years are used in the analyses. The standard deviations, which are estimated from the averages of each year, are used for variability analysis.
3 Estimating the cooling effect of cirrus thinning

Comparisons among different seeding methods
First, we analyze the impact of cirrus seeding on the ice nucleation process (Fig. 2). The contribution of homogeneous nucleation to cirrus formation (F hom ) is essential for the radiative properties of cirrus clouds Shi and Liu, 2016). Here, F hom is quantified as the ratio of the homogeneous nucleation occurrence frequency to the ice nucleation occurrence frequency (F nuc ). In the REF experiment, F hom is low near dust source regions (e.g., the Saharan Desert and Arabian Desert). F hom is high over other tropical regions due to the large W sub (not shown). Generally, F hom is low (< 20 %) in most regions, which is consistent with observations that heterogeneous nucleation is the dominant mechanism for cirrus formation (Cziczo et al., 2013;Jensen et al., 2013). Although F hom from the INP20 exper-iment is decreased substantially, there are still some homogeneous freezing events (3.38 % of all cirrus and 5.20 % at 233 hPa). In the INP200 experiment, there are only a few homogeneous freezing events (0.42 % of all cirrus and 0.63 % at 233 hPa) due to the larger N seed of INPs. Both the INP20 and INP200 experiments show that the averaged number concentrations of ICs produced from heterogeneous freezing events (N ihet ) are increased. This increase would lead to more intense competition between homogeneous and heterogeneous nucleation. As a result, the averaged number concentrations of ICs produced from homogeneous freezing events (N ihom ) from the INP20 and INP200 experiments are substantially decreased compared with the number concentration of ICs from the REF experiment. As expected, F hom and N ihom are zero from the HET and OPT experiments. It is noteworthy that a large number of small ICs (e.g., homogeneous nucleation occurs) would exist for a long time, consuming water vapor via deposition growth and then hindering subsequent ice nucleation (Shi et al., 2015). Therefore, F nuc from the REF experiment is very low (< 4 %) in most regions, and F nuc from the cirrus thinning experiments (i.e., the HET, OPT, INP20, and INP200 experiments) is obviously increased due to the decreases in F hom and N ihom . This finding suggests that the impact of cirrus seeding (including the HET experiment) on the ice nucleation process is very complicated. There is not only the direct instantaneous impact but also the indirect impact caused by subsequent changes. Figure 3 shows the impact of cirrus seeding on cloud properties. In the cloud microphysics scheme, the in-cloud IC number concentration (i.e., N i ) mainly depends on the ice nucleation process (i.e., N inuc , Shi et al., 2015;Shi and Liu, 2016). Therefore, the annual averaged N i from the cirrus thinning experiments is decreased significantly in most cirrus clouds (ice clouds), especially from the HET and OPT experiments. The N i from the INP20 experiment is not significantly decreased over the tropical regions because there are still many homogeneous freezing events (F hom and N ihom in Fig. 2). Compared with the REF experiment, N i from the INP200 experiment is obviously increased in the tropical upper troposphere and the polar troposphere. This increase occurs because the homogeneous nucleation contribution (i.e., F nuc × F hom × N ihom ) from the REF experiment is relatively low, and the heterogeneous nucleation contribution (i.e., F nuc × N ihet ) from the INP200 experiment increases dozens of times over these regions (Fig. 2). Similarly, the vertically integrated N i (i.e., column N i ) from the HET and OPT experiments is significantly decreased in most regions. In contrast, the changes in column N i from the INP20 and INP200 experiments are not notable. The changes in ice water content (IWC) and ice water path (IWP) from the INP20 and INP200 experiments are also non-significant in most regions. In the HET and OPT experiments, both N i and IWC in the middle and lower mixed-phase clouds are obviously increased. The main reason might be that the deep convective activity becomes more vigorous because cirrus thinning reduces atmospheric stability via the radiative budget (not shown). The ratio of ice to total cloud condensate detrained from the convective parameterizations is a linear function of temperature between −40 and −10 • C (Morrison and Gettelman, 2008). Furthermore, the ICs can grow through the Bergeron process in mixed-phase clouds (Morrison and Gettelman, 2008). This might be the reason that the relative increases in IWC in mixed-phase clouds are stronger than the relative increases in N i . Although the increases in IWC in mixed-phase clouds counteract the decreases in IWC in ice clouds to some extent, the IWP is still significantly decreased in most regions from the HET and OPT experiments. However, the IWP is significantly increased over a few regions (e.g., central Africa and northern Brazil) because the decreases in IWC in ice clouds are slight and even smaller than the increases in IWC in mixed-phase clouds over those regions (not shown). The changes in liquid water content (LWC) and liquid water path (LWP) from the INP20 and INP200 experiments are non-significant in most regions, whereas both the LWC and LWP from the HET and OPT experiments are significantly decreased in some low-and mid-latitude regions. One possible reason is that falling ICs accrete by riming of cloud droplets Storelvmo et al., 2013), and the conversion efficiency of cloud droplets to precipitation is increased. Another possible reason is that cirrus thinning leads to stronger convective precipitation (Kristjánsson et al., 2015;, which would consume more cloud water Rapp et al., 2011). The above analyses are in agreement with previous studies, which show that cirrus thinning might result in complex impacts on mixed-phase and liquid clouds (Gasparini and Lohmann, 2016;Gruber et al., 2019).
The cooling effect of cirrus thinning is usually quantified by the anomaly in cloud radiative effect ( CRE; Mitchell and Finnegan, 2009;. For convenience of expression, " " indicates the difference between the cirrus thinning experiments and the REF experiment. In addition to the model standard diagnostics of CRE, CRE from ice clouds (iCRE), mixed-phase clouds (mCRE), and liquid clouds (lCRE) is also diagnosed separately. Note that cirrus clouds are clouds at temperatures below −37 • C and above 440 hPa (Boucher et al., 2013), so we refer to them as ice clouds in this study. Furthermore, the cooling radiative effect is quantified by a negative value, even if it has been declared a cooling effect. For convenience, the global annual mean cloud radiative effects from all experiments are listed in Table 2.
The iCRE and its shortwave (iCRE SW ) and longwave (iCRE LW ) components are analyzed first (Fig. 4). The globally averaged iCRE from the REF experiment is 6.49 W m −2 (net warming effect), with a shortwave component (iCRE SW ) of −5.30 W m −2 (cooling effect) and a longwave component (iCRE LW ) of 11.79 W m −2 (stronger warming effect). This globally averaged iCRE is within the possible range reported in recent studies (4.5-6.8 W m −2 ; Gasparini    . The annual mean spatial distribution of ice cloud shortwave radiative effect (iCRE SW , first row), ice cloud longwave radiative effect (iCRE LW , second row), ice cloud radiative effect (iCRE = iCRE SW + iCRE LW , third row), and cirrus seeding effectiveness (fourth row) from the REF experiment (first column) and the differences (" ") from the HET, OPT, INP20, and INP200 experiments with respect to the REF experiment (second to fifth columns). Note that regions with absolute value of iCRE < 1.0 W m −2 from the REF experiment are excluded for calculating cirrus seeding effectiveness. Global mean values are shown in the upper right corner, and the corresponding standard deviations calculated from the difference of each year for 10 years are shown in brackets. The shadow denotes that the differences between two experiments are not significant at the 95 % level based on Student's t test. and Lohmann, 2016;Gasparini et al., 2020;Hong et al., 2016;Lohmann and Gasparini, 2017;Muench and Lohmann, 2020). The globally averaged iCRE SW from the HET, OPT, INP20, and INP200 experiments increases (less negative, warming effect) by 3.39, 3.25, 0.38, and 0.30 W m −2 , respectively. The decrease in iCRE LW (cooling effect) from all cirrus thinning experiments is stronger, especially from the HET (−6.84 W m −2 ) and OPT (−6.29 W m −2 ) experiments. Although iCRE LW from the HET and OPT experiments shows significant cooling effects over most regions, there are still a few regions with warming effects (central Africa and northern Brazil) due to higher ice cloud occurrence frequencies (not shown). The spatial patterns of iCRE SW and iCRE LW are generally in agreement with the changes in IWP and column N i (Fig. 3). In terms of iCRE, the HET (−3.45 W m −2 ) and OPT (−3.04 W m −2 ) experiments show much stronger cooling effects than the INP20 (−0.44 W m −2 ) and INP200 (−0.01 W m −2 ) experiments. Following Gasparini et al. (2020), the cirrus seeding effectiveness (−100 × | iCRE/iCRE|) is used to show what proportion of iCRE is eliminated by cirrus seeding. The globally averaged cirrus seeding effectiveness from the HET and OPT experiments is 56.19 % and 49.40 %, respectively. These values are much higher than those from the INP20 (6.69 %) and INP200 (−2.22 %) experiments. The fixed seeding method restricts the cirrus seeding effectiveness. Notably, over some tropical regions, the cirrus seeding effectiveness from the HET and OPT experiments is somewhat low, although the iCRE is relatively strong (< −5 W m −2 ). One reason is that iCRE is relatively strong (> 10 W m −2 ), but convective detrainment (anvil cirrus, which is not influenced by cirrus seeding) contributes more to iCRE (not shown). Another reason is that the ratio of iCRE SW to iCRE LW is higher over tropical areas due to the small solar noon zenith angles (not shown).
In addition to iCRE, mCRE and lCRE are also obviously influenced by cirrus thinning (Fig. 5). Compared with the REF experiment, mCRE from the HET and OPT experiments is significantly increased in most ocean regions. The corresponding globally averaged mCRE is 1.06 and 1.09 W m −2 , respectively. This warming effect (i.e., positive mCRE) mainly comes from the increasing longwave component (not shown), which is consistent with the increase in IWC in mixed-phase clouds (Fig. 3). The globally averaged lCRE from the HET and OPT experiments increases (warming effect) by 1.06 and 0.94 W m −2 , respectively. The lCRE is strong (> 2 W m −2 ) over some lowand mid-latitude regions that couple with the decreases in LWP (Fig. 3). Both mCRE and lCRE from the HET and OPT experiments show that the globally averaged values are several times larger than the corresponding standard deviations (0.11-0.14). This finding indicates that cirrus thinning with the HET/OPT method leads to a significant globally averaged warming effect from mixed-phase clouds ( mCRE) and liquid clouds ( lCRE), although mCRE and lCRE are not statistically significant in most regions. Unlike the HET and OPT experiments, both mCRE and lCRE from the INP20 and INP200 experiments are weak and uncertain. The overall cooling effect of cirrus thinning (i.e., CRE) from the HET and OPT experiments is −1.98 ± 0.26 W m −2 and −1.36 ± 0.18 W m −2 , respectively (Fig. 5). Compared with the cooling effect of ice clouds (i.e., iCRE, Fig. 4), these values drop by approximately half due to the warming effect exerted by mixed-phase and liquid clouds. The INP20 and INP200 experiments show a weak cooling effect (−0.27 ± 0.26 W m −2 ), and even a small warming effect (0.35 ± 0.28 W m −2 ), respectively. It is clear that cirrus seeding with the flexible method could produce a notable global cooling effect, which is much better than the fixed methods. Furthermore, the cooling effect with the flexible seeding method is significant over most midlatitude and high-latitude regions. Some low-latitude regions show a pronounced warming effect because cirrus seeding leads to a stronger warming effect introduced by mixed-phase and liquid clouds (i.e., mCRE and lCRE). This finding suggests that cirrus seeding over low-latitude regions might be redundant.

Sensitivity experiments with the flexible seeding method
To better understand cirrus thinning with the flexible seeding method, this section investigates sensitivity experiments of the cooling effect on R seed (R10 experiment) and the seeding region (GT experiment). Figure 6 shows the seeding number concentration (N seedopt ) and seeding frequency (F seed ). As expected, the OPT and GT experiments show similar N seedopt in midlatitude and high-latitude regions. In these two experiments, N seedopt is less than 40 L −1 in most regions. Because N seedopt increases with decreasing R seed (see Appendix), N seedopt from the R10 experiment is larger than that from the OPT and GT experiments. In these seeding experiments (i.e., the OPT, R10, and GT experiments), it becomes easier for the ice nucleation process to reach S ihom (i.e., cirrus seeding occurs) because the large number of long-lived small ICs produced by homogeneous nucleation is cut off. As a result, F seed from the seeding experiments is much larger than the homogeneous freezing occurrence frequency (F hom × F nuc ) from the REF experiment (much less than 1 %, Fig. 2). However, F seed from the seeding experiments is still relatively low (< 4 %) in most regions. F seed from the GT experiment is even lower than 2 % in most regions. The smaller ICs usually have a longer lifetime in cirrus clouds, so F seed from the R10 experiment (1.01 % of all cirrus and 1.05 % at 233 hPa) is lower than that from the OPT experiment (1.13 % of all cirrus and 1.43 % at 233 hPa). Similar to the spatial distribution of F hom from the REF experiment, F seed from the cirrus seeding experiments is much higher in the low-latitude regions. This is the reason that the globally averaged F seed from the GT ex- Figure 5. Similar to Fig. 4 but for the mixed-phase cloud radiative effect (mCRE, first row), liquid cloud radiative effect (lCRE, second row), and the all cloud radiative effect (CRE, third row). periment (0.82 % of all cirrus and 0.80 % at 233 hPa) is about one-third lower than that from the OPT experiment. Figure 7 shows the cooling effects from the R10 and GT experiments. The globally averaged iCRE from the R10 experiment is −2.58 W m −2 . This ice cloud cooling effect is obviously weaker than that from the OPT experiment (−3.04 W m −2 ) because the seeding ICs in the R10 experiment (larger N seedopt and smaller R seed ) could exist for a longer time in cirrus clouds. Correspondingly, the cirrus seeding effectiveness from the R10 experiment (43.02 %) is also less than that from the OPT experiment (49.40 %). Similar to the OPT experiment, the R10 experiment also shows that cirrus seeding induces an obvious global warming effect of mixed-phase and liquid clouds ( mCRE and lCRE, Table 2). Notably, these warming effects (i.e., mCRE and lCRE) are weaker than those from the OPT experiments (Table 2). Thus, CRE from the R10 experiment is −1.25 ± 0.22 W m −2 , which is close to that from the OPT experiment (−1.36 ± 0.18 W m −2 ). Compared with the OPT experiment, iCRE from the GT experiment becomes weaker over the regions without seeding (Figs. 7 and 4). Thus, the globally averaged iCRE only decreases by −2.34 W m −2 from the GT experiment. Correspondingly, the cirrus seeding effectiveness from the GT experiment is also obviously less than that from the OPT experiment, except in high-latitude regions. As mentioned in Sect. 3.1, cirrus seeding would lead to a strong warming effect of mixed-phase and liquid clouds at low latitudes. As expected, in the GT experiment, this warming effect is constrained to some extent ( Table 2). The globally averaged cooling effect ( CRE) from the GT experiment is −2.00 ± 0.25 W m −2 , which is much stronger than that from the OPT experiment (−1.36±0.18 W m −2 ) and even stronger than that from the HET experiment (−1.98 ± 0.26 W m −2 ). This finding suggests that cirrus seeding without low solar noon zenith angle regions might produce a better global cooling effect.

Conclusions and discussion
The major purpose of this study is to estimate the potential cooling effect of cirrus thinning. Based on the mechanism of cirrus thinning by the seeding approach, a flexible seeding method is used to calculate the optimal seeding number concentration, which is just enough to prevent homogeneous ice nucleation from happening. Furthermore, the cirrus seeding approach could move further by injecting ice crystals (ICs) instead of ice nuclei particles (INPs). In terms of hindering homogeneous nucleation and environmental safety, ICs are better than INPs. More importantly, the problem of INP transportation discussed in previous studies might be solved because ICs can be made from ambient atmospheric water vapor.
Both parcel model simulations and large-ensemble ice nucleation offline experiments show that the flexible seeding method has obvious advantages over the fixed seeding method. Furthermore, the CAM5 simulations with the flexible seeding method (implementing seeding globally) show a notable global cooling effect, −1.36 ± 0.18 W m −2 from seeding with ICs of 50 µm (OPT experiment) and −1.25 ± 0.22 W m −2 from seeding with ICs of 10 µm (R10 experiment). However, simulations with fixed seeding number con- centrations of 20 and 200 INPs L −1 show a weak cooling effect of −0.27 ± 0.26 W m −2 and a warming effect of 0.35 ± 0.28 W m −2 , respectively. Note that some previous work using CAM5 with the fixed seeding method showed a notable cooling effect (∼ −2 W m −2 ; e.g., . This is attributed to the contribution of homogeneous nucleation to cirrus formation (F hom ) from the default CAM5 model used in their study (Penner et al., 2015). The F hom from default CAM5 simulations is relatively higher because the default version neglects the effect of preexisting ICs (Shi et al., 2015). Penner et al. (2015) tuned the main ice nucleation mechanism in CAM5 to limit F hom and found that cirrus thinning with a fixed seeding number concentration cannot produce a definite global cooling effect. In this study, F hom is also limited to a low level (Fig. 2). Our results with the fixed seeding method are similar to the study of Penner et al. (2015). However, with the benefits of the flexible seeding method, cirrus seeding could produce a considerable cooling effect.
This study also analyzes the main mechanism for the cooling effect achieved via cirrus seeding. Simulation results show that cirrus seeding not only impacts ice clouds, but also significantly impacts mixed-phase and liquid clouds. In terms of ice clouds, cirrus thinning with the flexible seed- ing method could lead to a notable cooling effect. However, cirrus seeding also leads to a significant warming effect of mixed-phase and liquid clouds, which counteracts the cooling effect of cirrus clouds. Because the counteraction is more prominent over low-latitude regions, the low-latitude regions are less susceptible to cirrus seeding. This finding agrees with the previous finding that cirrus thinning is more effective at mid and high latitudes because of more insolation caused by cirrus thinning when the sun is overhead . The warming effect of liquid clouds from the OPT experiment (0.94 ± 0.11 W m −2 ) is similar to the study of Gasparini et al. (2017;Table 5, 0.96 ± 0.25 W m −2 from the ECHAM-HAM model simulation with seeding of 1 L −1 of 50 µm INPs). There seems to be a relatively solid mechanism whereby cirrus thinning reduces atmospheric stability, leading to the warming effect of liquid clouds. However, the warming effect of mixed-phase clouds from the OPT experiment (1.09 ± 0.11 W m −2 ) is several times stronger than that reported in their results (0.15±0.10 W m −2 ). This difference suggests that the climatic response to cirrus seeding is complex and might differ among different climate models and seeding methods. Finally, it is necessary to point out that the compensating effects introduced in this study (i.e., the warming effect of mixed-phase and liquid clouds) are derived from the atmosphere-only simulations, and with prescribed ocean surface conditions, the coupled model simulations might show different results (e.g., Gasparini et al., 2017).
Sensitivity experiments with the flexible seeding method show that the seeding method with smaller ICs (i.e., the R10 experiment) leads to a weaker global cooling effect of ice clouds due to the larger seeding number concentration and smaller ICs. The warming effects of mixed-phase and liquid clouds are also reduced to some extent because the convective activity from the R10 experiment is not as strong as that from the OPT experiment (not shown). Thus, the global cooling effect from seeding with smaller ICs (−1.25 ± 0.22 W m −2 ) is not obviously weaker than seeding with larger ICs (−1.36 ± 0.18 W m −2 ). Avoiding seeding over low-latitude regions can limit some warming effects due to changes in mixed-phase and liquid clouds and thus lead to a more pronounced global cooling effect. Sensitivity experiments show that seeding carried out at latitudes with solar noon zenith angles greater than 12 • yields a stronger global cooling effect of −2.00 ± 0.25 W m −2 , which is close to that of artificially turning off homogeneous nucleation over the whole Earth (−1.98 ± 0.26 W m −2 ). In addition, we carried out sensitivity experiments with other threshold values (23.5, 18, and 8 • ). With increasing thresholds, the global cooling effect of ice clouds decreases, and the global warming effects of mixed-phase and liquid clouds also decrease. The overall cooling effect is maximized when using a solar zenith angle threshold of 12 • . In short, the global cooling effect is more sensitive to seeding regions than to the radius of seeding ICs. The global cooling effect can thus be maximized when limiting seeding to the most suitable regions and times of the year. However, estimating the cooling effect of cirrus seeding based on commercial airliners (i.e., with a limited time and place) is more realistic. We plan to investigate this method in our future work.
Appendix A: The formula of optimal seeding number concentration (N seedopt ) For the ice nucleation parameterization with the preexisting IC effect, the seeding ICs are considered to be preexisting ICs. The optimal number concentration of ICs (N seedopt ) depends on the ice nucleation parameterization, especially for its treatment of the preexisting IC effect.
Without the preexisting ICs or seeding ICs, the temporal evolution of S i is governed by the following (Kärcher et al., 2006): where the parameters a 1 , a 2 , and a 3 only depend on the ambient temperature and pressure. W is the updraft velocity, and dQ nuc dt denotes the growth rate of newly nucleated ICs. To account for the effect of preexisting ICs and seeding ICs, the deposition growth of preexisting ICs dQ pre dt and seeding ICs dQ seed dt are added to Eq. (A1): Equation (A2) can be rewritten as the following form: The effect of preexisting ICs on ice nucleation can be taken as reducing the vertical velocity (W pre ; Barahona et al., 2014). Details about how to calculate W pre are introduced in Shi et al. (2015). Here, the reduced vertical velocity from seeding ice (i.e., W seed ) is similar to W pre . W seed is a function of seeding ice number concentration (N seed ) and its radius (R seed ). Assuming all seeding ICs have the same R seed , the growth rate is given by where ρ i is the ice density, and m w is the mass of a water molecule. b 1 = αν th n sat (S i −1)/4, b 2 = αν th n sat /4D. α is the water vapor deposition coefficient on ice, ν th is the thermal speed, n sat is the water vapor number density at ice saturation, and D is the water vapor diffusion coefficient from the gas phase to the ice phase (Kärcher et al., 2006).
Under a given R seed , W seed increases with increasing N seed . That is, the more ICs that are added, the more they will reduce W . The minimal N seed (i.e., N seedopt ) is calculated based on the minimal W seed , which can prevent homogeneous ice nucleation from occurring. The default ice nucleation parameterization (Liu and Penner, 2005; LP parameterization) provides a threshold updraft velocity (W thre ) for homogeneous ice nucleation, where T is the ambient temperature, a = −1.4938 ln N INP + 12.884, b = −10.41 ln N INP − 67.69. N INP is the INP (e.g., dust aerosol particle) number concentration. Homogeneous ice nucleation does not occur (i.e., only heterogeneous nucleation) if the effective updraft velocity (W eff , W eff = W − W pre − W seed ) is less than W thre . Thus, the minimal W seed is calculated as W seed = W − W pre − W thre . If W seed < 0, there is no need for seeding. The minimal number concentration of seeding ICs (i.e., N seedopt ) can be calculated based on Eqs. (A5) and (A6) at threshold S i for homogeneous freezing (S ihom ). In this study, with the given R seed , N seedopt is given by Because the impact of deposition growth on preexisting ICs is neglected in calculating W pre (Barahona et al., 2014;Shi et al., 2015), the increase in R seed caused by deposition growth during the ice nucleation process is also neglected. As a result, N seedopt might be overestimated, especially for a small given R seed . The LP parameterization provides a critical number concentration of INPs (N lim ) for the only heterogeneous freezing scenario. N seedopt cannot exceed N lim because ICs are superior to INPs in hindering homogeneous nucleation.
Code and data availability. The modified code of CAM5 and the output data used in this study are available online at https://doi.org/10.5281/zenodo.4507001 (Liu and Shi, 2021).
Author contributions. JL derived the formula for optimal seeding number concentrations. XS and JL designed the model experiments and developed the model code. JL processed and analyzed the raw model output data and wrote the paper. XS helped to explain the results. Both authors contributed to improving and reviewing the manuscript.
Competing interests. The authors declare that they have no conflict of interest.
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Acknowledgements. The authors would like to thank Blaž Gasparini for suggesting plotting the cirrus seeding effectiveness. The model simulation was conducted in the High Performance Computing Center of Nanjing University of Information Science & Technology.
Financial support. This research has been supported by the National Key Research and Development Program of China (grant no. 2018YFC1507001) and the National Natural Science Foundation of China (grant nos. 41775095 and 42075145).
Review statement. This paper was edited by Martina Krämer and reviewed by Blaž Gasparini and one anonymous referee.