We conduct our seeding experiments using the ECHAM6.3–HAM2.3 aerosol-climate GCM . We use the horizontal resolution T63 (1.875∘ × 1.875∘), with 47 vertical levels (L47) up to 0.01 hPa, which corresponds to a vertical resolution of around 1 km in the upper troposphere at cirrus altitudes. The model timestep is 7.5 min.

The two-moment ice microphysics scheme by , used in the default version of ECHAM6.3-HAM2.3, was succeeded by the Predicted bulk Particle Properties (P3) scheme by that was ported to ECHAM-HAM by . It replaces an earlier method of artificially separating ice particles into different size classes , rendering the use of the tuning parameter for the rate of snow formation unnecessary . Instead, ice is represented with a single prognostic category based on mass-to-size relationships. With the single ice category no longer differentiating between in-cloud and precipitating ice, vertical advection and precipitation processes were also updated to include a sub-stepping approach for prognostically solving ice sedimentation. This allows for sedimenting ice to be subjected to cloud processes as it falls and for numerical stability within the cloud scheme . For more specific information on P3 and its implementation within ECHAM6, please refer to .

A separate scheme by that was adapted for ECHAM-HAM by handles in situ ice nucleation within cirrus clouds. It simulates the competition for water vapour between heterogeneous and homogeneous nucleation and between depositional growth onto pre-existing ice particles from existent cirrus clouds or those that are transported into the cirrus regime from deep convective detrainment or from stratiform mixed-phase clouds. The scheme uses a sub-stepping approach to simulate the temporal evolution of the ice saturation ratio (Si) in an air parcel rising adiabatically during the formation stage of a cirrus cloud. Ice formation occurs only when Si reaches the critical values for heterogeneous or homogeneous nucleation (see below). The evolution of Si is determined by the balance between the adiabatic cooling rate of rising air and the diffusional growth of ice particles that consume the available water vapour. As the cooling rate and therefore the magnitude of Si are directly related to the strength of the vertical velocity, a fictitious downdraft that counteracts the vertical velocity is introduced at the start of each timestep of the cirrus sub-model to quantify the effect of water vapour consumption on pre-existing ice particles, which includes new ice formation in the previous cirrus sub-model timestep . This “effective vertical velocity” (updraft and fictitious downdraft), therefore, determines the magnitude of Si and is calculated at the end of a single sub-timestep of the cirrus scheme. It is used in the subsequent sub-timestep to update Si.

Vertical velocity is represented by a grid-mean value plus a turbulent component based on the turbulent kinetic energy (TKE) . Orographic effects on vertical velocity as well as small-scale gravity waves in the upper troposphere are not included in this study. We provide a short analysis that verifies our model without orographic effects in Appendix . In summary, by using the new P3 ice microphysics with the in situ cirrus ice nucleation scheme , including orographic effects acts to drastically increase cirrus ICNC while reducing spatial heterogeneity, in worse agreement with observations. updated the water vapour consumption by ice, following the diffusional growth equation . The temporal change in the saturation ratio follows such that if the updraft is stronger than the water vapour consumption by pre-existing ice and heterogeneous INPs, then it may reach a suitable magnitude for homogeneous nucleation to occur. The opposite is true in weaker updraft regimes or in high INP concentration environments . The sub-stepping approach in the cirrus scheme is computed dynamically based on a 1 % rate of change in the ice saturation ratio between each sub-timestep.

To simulate the competition between homogeneous and heterogeneous nucleation, several freezing modes are introduced into the cirrus scheme (Table ), including pre-existing ice. In general, the cirrus nucleation scheme follows an “energy-barrier” approach, with pre-existing ice and the most efficient INP, dust (in the default set-up), consuming water vapour at a lower Si. An ice formation event in each mode can occur as either a threshold freezing process or as a continuous freezing process . The former is based on the original cirrus scheme by , whereby ice forms by a particular mode when its critical ice saturation ratio (Si,crit) is reached. In our set-up, homogeneous nucleation of liquid-sulfate aerosols with a temperature-dependent Si,crit between 1.4 and roughly 1.75 and immersion freezing of soluble-material-coated dust with a Si,crit of 1.3 act as threshold freezing modes. As a threshold process, all aerosol particles associated with the mode form ice that proceeds to deplete available water vapour and reduce Si. For dust immersion freezing, only 5 % of the total dust aerosol concentration from the aerosol module, HAM, acts as an INP within the mode, following . introduced the latter, continuous freezing process to account for the saturation-dependent activated fraction (AF) of INPs available for heterogeneous nucleation. We include deposition on insoluble accumulation and coarse-size-mode dust particles as continuous freezing modes. The AF is calculated using temperature-dependent Si,crit thresholds of 1.2 for T > 220 K and 1.1 for T ≤ 220 K based on laboratory measurements by . At every timestep in the cirrus scheme, the AF of these modes is calculated, and if ice forms, it is added to the ice concentration.

Following , we introduce seeding particles as a separate threshold freezing mode into the cirrus scheme for temperatures below 238 K, increasing the competition for available water vapour. All seeding particles can nucleate ice with a Si,crit (hereafter the seeding particle critical ice saturation ratio, Si,seed) of 1.05 and later with Si,seed=1.35 (Sect. ). The seeding particles have a modal radius of 0.5 µm like in . We perform uniform global seeding with no spatial or temporal variability in seeding particle concentration for comparability to previous GCM studies, except for an altitude restriction below 100 hPa to minimize seeding of the stratosphere. This seeding restriction to altitude levels below 100 hPa (i.e. higher pressure levels) is in line with proposed real-world delivery mechanisms for seeding particles with commercial aircraft .

Cloud cover is based on the diagnostic approach by , hereafter referred to as S89, that assumes fractional cloud formation exists due to relative humidity (RH) variability within the grid box. The formulation was developed for liquid (warm) clouds, using a critical RH (RHcrit) above which fractional cloud cover in a grid box can occur. Full grid-box coverage occurs when grid-mean RH reaches 100 % with respect to liquid water. This formulation works well for warm clouds, but as and note, it breaks down for mixed-phase clouds (T < 273 K) that may or may not include ice, presenting a difficult choice between RH with respect to liquid (RHl) or ice (RHi) to determine the cloud fraction. The S89 approach for pure ice clouds (T < 235 K) is analogous to warm clouds in earlier versions of our model, where instead of liquid water saturation, full grid-box coverage occurs at ice saturation. As explain, when accounting for the ice supersaturation required for homogeneous or heterogeneous nucleation, this leads to full grid-box coverage of freshly nucleated cirrus clouds, an inconsistency between cloud fraction and the microphysics scheme . This may also explain the high cirrus CRE in ECHAM6 found by . updated the cloud fraction formulation for pure ice clouds to differ from liquid clouds by updating the RH conditions in which an ice cloud can partially cover a grid box. In this new scheme (hereafter D19) that we use in this study, ice saturation (Si = 1.0) is set as the lower boundary condition for partial ice cloud fractions. The upper boundary condition for full grid-box coverage for ice clouds is set following the theory for homogeneous nucleation of solution droplets by . The difference between the two schemes is illustrated in Fig. . As a contextual example, if ice were to form at 233 K in an environment with Si = 1.2, then D19 would calculate an ice cloud fraction <1.0, whereas S89 would adjust the ice supersaturation down to ice saturation and would produce a cloud fraction of 1.0.

Additional ice number and mass mixing ratio tracers were added to the model, following , to trace the origin of in situ cirrus ice directly. We include two tracers for ice from homogeneous and heterogeneous nucleation, with additional tracers for heterogeneously formed ice on dust and seeding particles, the sum of which equates to the total in situ heterogeneously nucleated ice tracer. The implementation of these tracers highlighted an error when accounting for the number of aerosols that previously nucleated ice. The aerosol concentration of each freezing mode of the cirrus scheme was scaled by the total amount of pre-existing ice. This approach overestimated the concentrations of in-cloud aerosols and underestimated the interstitial aerosol concentration. We updated the scaling of each aerosol concentration mode to account for the fraction of each mode out of the total pre-existing ice concentration. These updates warranted a re-tuning of the model to primarily target the balance between global annual mean TOA SW and LW fluxes . A summary of the model configuration we utilize in this study compared to the “HET_CIR” simulation by is presented in Table . Ice self-collection (γislf) was increased from its original value in the base version of the model to 5.5 to account for too small TOA SW and LW fluxes. This adjustment strengthened both TOA fluxes, but the LW flux remained too weak. Therefore, to compensate, the autoconversion rate from cloud liquid water to rain within convective cores was increased to 1.75. In addition to radiative flux imbalance, we found that the model produced a global mean liquid water path value that was beyond the upper value of the observations reported by . To address this issue, we halved the convective cloud mass flux above the level of non-buoyancy (γctop) to 0.1. As reducing this flux leads to more frequent and thicker boundary layer clouds , we compensated for this by increasing the autoconversion rate within stratiform liquid clouds (γr) to 8.3 to maintain radiative balance. All other tuning parameters were kept the same as the “HET_CIR” configuration in . We also note a too negative net CRE after tuning. state that this points to a possible structural problem within the model, which is related to the coarse vertical resolution that results in the underprediction of low-level clouds .

We performed cirrus seeding simulations using P3 with the cirrus scheme coupled to the new ice cloud fraction approach (D19) described above. We examined seeding with full nucleation competition between heterogeneous, homogeneous, and pre-existing ice. Additionally, we tested the original S89 ice cloud fraction approach within the framework of the P3 scheme; we did not re-tune the model for simulations using S89 in order to examine the sensitivity of cirrus seeding to the ice cloud fraction scheme. Previous CCT studies include additional simulations in which they allow only homogeneous nucleation to occur in cirrus. Here, we chose to pursue full nucleation competition as a more realistic approach to examine the impact of seeding particles, mimicking a real-world implementation. For both model configurations (see Table ), we implemented seeding particles as an additional heterogeneous freezing mode in the cirrus ice-nucleation scheme continuously at every timestep, following on from previous approaches (i.e. without accounting for those that already formed ice). Only grid boxes that are supersaturated with respect to ice (i.e. Si > 1.0) are seeded. We test four seeding INP concentrations of 0.1, 1, 10, and 100 INP L-1 to represent the spread of concentrations tested in previous studies . Each simulation was conducted for 5 years between 2008 and 2012, inclusive, with 3 months of spin-up from 1 October 2007. Monthly mean sea surface temperatures and sea ice coverage are prescribed, and emissions are from the year 2010 following the CMIP6 methodology .

The Si,seed of 1.05 follows and and is based on suggestions of a hypothetical, highly efficient seeding particle material. However, it is unclear whether this Si,seed can be applied to a realistic seeding particle material. suggested bismuth tri-iodide, but the specific ice-nucleating properties of this material are unknown. Therefore, to test the sensitivity of ice nucleation competition to Si,seed, we conducted additional seeding simulations with all the seeding particle concentrations described above, with a Si,seed of 1.35 (Table ). We chose this relatively high Si,seed value to ensure that seeding can occur in ice-supersaturated environments below the lower homogeneous nucleation Si,crit threshold of roughly ≥ 1.40 and, in order to be less competitive with background heterogeneous nucleation processes, above the maximum Si,crit for dust of 1.3.

We take particular care to quantify significance in our results, following the false discovery rate (FDR) method by . The updated approach for conducting independent t tests accounts for the high spatial correlation of neighbouring grid points; i.e. the null hypothesis cannot be as widely rejected when calculating significance. We calculate a 5 % significance based on the inter-annual variability over the 5 years of simulation (Sect. ). The inter-annual variability is also used to calculate the 95 % confidence interval around the 5-year mean.

We start by evaluating the model with the new P3 ice microphysics scheme and the new D19 ice cloud fraction approach for the unseeded reference case, by comparing ICNC data to the latest compilation of in situ aircraft measurements by in Fig. . Model results represent the 5-year mean temperature versus ICNC between 2008 and 2012. The observational data comprise multiple in situ aircraft field campaigns between 1999 and 2017, totalling around 90 h of flight data , with different meteorological situations captured in the tropics, mid-latitudes, and the Arctic; southern high latitudes are not included. Although this is a much more significant compilation of observational data than was previously available, there remains a caveat that these data are not representative of the entire atmosphere .

The median ICNC per temperature bin between 180 and 250 K is also shown for both data sets, with the observational median also presented with the model data for comparison. Model-median ICNC values agree rather well with the observational median at temperatures between roughly 205 and 230 K. Between 230 and 240 K the model median diverges above the observational median, where it does not capture the more frequent occurrence of lower ICNC values. Both the model and observations capture the tailing off of ICNC at temperatures warmer than 240 K, with the model being slightly lower than the observations. The small disagreements in these two temperature ranges may be linked to the default parameterization for heterogeneous nucleation on mineral dust particles in mixed-phase clouds in ECHAM. The results of offer an explanation in this regard. In their study, they conducted several sensitivity tests with ECHAM-HAM using the default rate-based immersion freezing scheme by and a newer AF approach based on dust particle surface area and active site density. They found better agreement with satellite-based observations using the AF approach in combination with higher dust particle freezing efficiency as compared to the default rate-based approach, and they noted an underprediction of mixed-phase ice with the latter that led to a higher abundance of cloud droplets being transported into the cirrus regime where they could undergo homogeneous nucleation. Our model-median ICNC values between 230 and 250 K indicate a similar behaviour. The higher ICNC values between 230 and 240 K, as compared to the observations, are likely of liquid origin, whereas the lower ICNC values above 240 K are likely due to the underprediction of mixed-phase ice using the default rate-based scheme for dust immersion freezing. The study suggests using a different approach for mixed-phase cloud glaciation for better comparability to observations and to address this issue of an overabundance of liquid-origin cirrus ice. suggest that these liquid-origin cirrus clouds in the mid-latitudes originate from warm conveyor belts or mesoscale convective systems. Therefore, their formation is tied to a stronger dynamical forcing that allows for abundant homogeneous nucleation from numerous cloud droplets being transported into the cirrus regime. As CCT targets in situ formed cirrus in regions with less dynamical forcing , we deem this overprediction of ICNC values insignificant relative to our study.

The model diverges from the observed median at temperatures below about 205 K. According to , ICNC values at such cold temperatures likely originate from tropical deep convection. Between 195 and 205 K the model-median ICNC is higher than the in situ measurements. This may be linked to a lack of cloud top measurements at these cold temperatures or the fact that high ICNC values in this temperature range are short-lived and therefore difficult to capture by aircraft . The model also does not capture the ICNC occurrence at temperatures below roughly 195 K. A simple analysis of the number of data points belonging to this temperature regime shows that, in the observations, there is a large drop-off in the number of recorded points (not shown). Therefore, these measurements make up a small portion of the total observational data set. Furthermore, CCT in a real-world context would target in situ formed cirrus away from systems with strong dynamical forcing , like in the tropics. The model also does not capture the wide variability of ICNC values as seen in the in situ measurements, like the higher frequency of low ICNC values between roughly 205 and 250 K. This is due to the fact that we compare 5-year annual mean model data to instantaneous values recorded during various aircraft campaigns. However, for the purposes of our CCT analysis, we find that the model-median ICNC as a function of temperature agrees well with the measurements for in situ formed cirrus.

The net global-mean radiative balance between TOA SW and TOA LW fluxes, including the net CRE, is presented in Fig. a and c, respectively, for Si,seed = 1.05. The results are tabulated along with the constituent SW and LW CRE fluxes in Table , with the 95 % confidence interval; CRE fluxes are discussed below. We find no net negative mean TOA anomalies for any of our simulations except Full_D19 Seed1 (Table ). Some cooling may be evident within the range of uncertainty surrounding the mean anomalies for the Seed0.1 (D19 and S89) and Seed1 (D19-only) simulations. However, as the uncertainty is high relative to the mean, a clear response at these low seeding particle concentrations is unclear from a TOA perspective. For larger seeding concentrations (≥ 10 L-1), the radiative anomalies indicate a certain warming response likely from overseeding. Furthermore, the differences between the two cloud cover approaches become abundantly clear. The largest warming occurs for Seed100, with 4.9 W m-2 (D19) and 9.9 W m-2 (S89). These responses are an order of magnitude larger than the maximum TOA anomaly found by of 0.5 W m-2 at the same seeding particle concentration and for a similar configuration of the cirrus scheme. Instead, our results more closely resemble their simulations where seeding was applied to cirrus that could form only by homogeneous nucleation but are more than 2 times what they found at a seeding concentration of 100 L-1. This difference in results further highlights the importance of a consistent approach to simulating cirrus ice microphysics and will be discussed further in Sect. . In addition, the maximum responses shown here are well above the latest available IPCC estimate of the effective radiative forcing from a doubling of atmospheric CO2 from the pre-industrial period of 3.9 W m-2 , highlighting the potential dangerous side-effects of cirrus seeding.

Cloud effects are the largest contributor to the TOA radiative anomalies (Fig. c and Table ). In the Seed100 case, the net CRE anomalies make up roughly 85 % and 90 % of the total TOA radiative anomalies for both D19 and S89. Like the TOA anomalies, there is slight evidence of cooling at lower seeding particle concentrations (< 10 L-1) within the range of uncertainty. At higher concentrations, it is clear that clouds exert a positive forcing on the atmosphere, which is fuelled by positive LW CRE anomalies (Table ). These large anomalies are only partially counteracted by increasingly negative SW CRE anomalies at higher seeding particle concentrations, indicating perhaps a shift in the cirrus formation pathway towards optically thicker liquid-origin cirrus or a feedback on lower-lying liquid and mixed-phase clouds.

To examine the cloud impacts further, in particular the overseeding at high seeding particle concentrations, we show the zonal mean cloud fraction anomalies between each seeding simulation and their respective reference simulation for both cloud fraction schemes in Fig. . Firstly, the difference between D19 and S89 stands out from the respective reference simulations (top panels). With the larger Si bounds for ice cloud fractions in D19, there is a clear cloud fraction reduction within the cirrus regime, above the blue dotted line (238 K isotherm) in Fig. , which leads to less warming in the reference simulation compared to S89. The new cloud fractions in D19 were found to agree better with the observed satellite product from CALIPSO than the original S89 approach . Secondly, a significant pattern in the zonal cloud fraction does not emerge until Seed1, with small regions of cirrus cloud fraction reductions larger than about 4 %. S89 Seed1 shows a small region of positive cloud fraction anomaly in the stratosphere over the northern high latitudes; however, the signal is not clear, as all the anomalies are insignificant. A clearer pattern emerges for Seed10 and Seed100, where what appears as a shift in cloud height starts developing within the cirrus regime at these seeding concentrations and reaches a maximum for Seed100. Seeding decreases cloud fraction by up to 8 % and 12 % in D19 and S89, respectively, in the mid-troposphere between 300 and 800 hPa at higher latitudes and between 300 and 100 hPa in the tropics. Note that the tropopause is located at roughly 200 hPa in polar regions and at 100 hPa in the tropics, as shown by the black line in Fig. . There are noticeable cloud fraction increases around the tropopause by more than 12 % over the southern high latitudes for D19 and over all latitudes for S89. The difference between the two cloud fraction approaches in this case is also clear, with S89 showing much more extensive regions of cirrus cloud fraction increases in the stratosphere than D19. The difference between the cloud fraction approaches is discussed further in Sect. . There are small regions in the lower tropical to mid-latitude troposphere (pressure > 500 hPa) that show positive cloud fraction anomalies of up to 4 % and 8 % for D19 and S89, respectively. The reduction in lower-lying cirrus and an apparent shift to more frequent higher-altitude cirrus explains the large positive LW CRE anomalies in Table . This shift outweighs the stronger (i.e. more negative) SW CRE anomalies that likely originate from the small positive cloud fraction anomalies for lower-lying clouds. Meanwhile, the overseeding response is amplified by the unrealistic increases in cloud fraction in the stratosphere.

Next, we examine the microphysical response to seeding in Fig. , which shows the total ICNC anomalies for Seed1 (Fig. a–b) and Seed100 (Fig. c–d) for both D19 and S89. Determining an exact ICNC response for Seed1 is rather difficult due to ICNC anomaly heterogeneity. For D19 Seed1 (Fig. a), in some areas we find that seeding produces more ice particles in widespread areas throughout the troposphere, with few areas of negative anomalies that also extend into the lower stratosphere. The S89 signal is similar, being mixed throughout the tropopause and extending into the lower stratosphere, but it is less pronounced than D19. For both cases, the positive ICNC anomalies at lower altitudes, in some regards, are in line with one of the desired outcomes of CCT to produce ice at lower altitudes, i.e. warmer temperatures, which emits more LW than higher-altitude ice, thus inducing a cooling effect. However, for both our Seed1 cases, our FDR analysis reveals that the Seed1 ICNC anomalies contain high uncertainty. As a result, the net CRE (Fig.  and Table ) also shows a high magnitude of uncertainty relative to the mean response.

The ICNC anomalies are much clearer and certain for the extreme case, Seed100, than for the Seed1 anomalies (Fig. c–d). Positive ICNC anomalies exceeding 200 L-1 are shown at all latitudes throughout the troposphere and into the lower stratosphere at higher latitudes. The anomaly heterogeneity around the tropics is likely due to the proficiency of seeding particles in nucleating ice and hampering homogeneous nucleation in convective outflow regions around the tropopause. The ICNC anomalies at lower altitudes and towards higher latitudes are much clearer. Here the ICNC anomalies are in line with the cloud fraction anomalies in Fig. . There is a loss of the lowermost ice crystals that also extends into the mixed-phase regime (below the blue dashed line in Fig. ), while the ICNC in the cirrus regime increases. This is likely due to the proficiency of seeding particles in nucleating ice, leading to more numerous and smaller ice crystals that do not sediment into the mixed phase regime as readily compared to the unseeded case. In fact, we find that ice crystals decrease in size on average by more than 4.0 µm in the cirrus regime for Seed100 (not shown). In addition, with numerous seeding particles available up to 100 hPa, ICNC increases in the lower stratosphere above higher latitudes. This leads to large cloud fraction increases (Fig. i–j) in these regions, where in the unseeded case there were fewer clouds (Fig. a–b). Therefore, for the Seed100 case it is the combination of multiple effects that contributes to the strengthening of the LW CRE by roughly 7.4 and 14.8 W m-2 in D19 and S89 (Table ), respectively, and the strong positive Seed100 net TOA anomalies for both cases in Fig. .

It is clear that seeding particles lead to an overseeding effect at higher concentrations, with wide impacts on the total ICNC. For a direct view of the impact of seeding particles on ice nucleation competition, Fig.  shows the cirrus ice number tracer (Sect. ) anomalies for Seed100 for D19 and S89. The tracers include in situ cirrus ice numbers from homogeneous and heterogeneous nucleation, with additional tracers for heterogeneously formed ice on mineral dust particles and seeding particles. Firstly, the anomalies presented in Fig.  are mainly constrained to the cirrus regime, the area above the blue dashed line, and the lower stratosphere, with some extension of anomalies into the lower-lying mixed-phase regime following ice crystal sedimentation. In terms of ice nucleation competition, Seed100 shows the desired effect by decreasing homogeneously nucleated ice by more than 200 L-1 in the middle to upper troposphere in both D19 and S89. The opposite effect occurs in the stratosphere, where homogeneously nucleated ice increases. The shift in homogeneous nucleation to lower pressure levels (Fig. a–b) is likely due to increased LW cloud top cooling from thicker cirrus cloud following seeding . This also impacts heterogeneous nucleation on mineral dust particles in the lower stratosphere. As this latter process is not sufficient at consuming water vapour, homogeneous nucleation proceeds to form additional ice crystals. This cloud top cooling effect likely also explains the heterogeneity of the total ICNC anomaly around the tropical tropopause (Fig. ). As there is a clear separation between the troposphere and the stratosphere, these phenomena point to a complex impact on the stratospheric circulation, which we discuss in Sect. .

The reduction in homogeneous nucleation in the troposphere is outweighed by the wider-spread increases in heterogeneous nucleation globally throughout the middle to upper troposphere and into the lower stratosphere for both ice cloud fraction approaches, leading to the positive net TOA and CRE anomalies (Fig. ). For Seed100 the heterogeneous signal is clearly dominated by seeding particles that act to dampen natural processes, including heterogeneous nucleation on dust as well as homogeneous nucleation. While this effect occurs in both D19 and S89, the spatial extent of the ICNC responses is more widespread in the latter, in line with the smaller Si bounds for calculating ice cloud fractions.

We also find ice crystals formed on seeding particles from the cirrus regime ending up in the mixed-phase regime (below the dashed line in Fig. ), pointing to potential impacts on lower-lying cloud layers from seeding. In fact, vertical profiles of IWC and liquid water content (LWC) for D19 in Fig.  confirm this behaviour. The positive Seed100 IWC anomaly within the cirrus regime right of the vertical black line in Fig.  is in line with the total ICNC (Fig. ) and cirrus ice tracer (Fig. ) anomalies. We also find that ice increases to a smaller extent in the upper portion of the mixed phase regime, also in line with the tracer anomalies above. The main impact of seeding appears as a reduction in IWC in wider areas of the mixed-phase and liquid regimes, the latter of which includes sedimenting ice that has not had sufficient time to melt. This is likely due to amplified ice residence times in the cirrus regime fuelled by smaller ice crystals that weaken the sedimentation flux. With less ice falling into the mixed-phase regime at lower altitudes, LWC anomalies responded positively (Fig. b) due to less efficient riming and/or cloud droplet depletion via the Wegener–Bergeron–Findeisen (WBF) process. This is in line with the positive, albeit small, anomalies of lower-lying cloud fractions in the tropics and mid-latitudes in Fig. . With a higher frequency of these lower clouds, the SW CRE strengthens by about -3.3 W m-2 for D19 Seed100 (Table ). However, this is outweighed by the larger LW CRE positive anomaly of 7.4 W m-2 due to optically thicker in situ cirrus . To a smaller extent, a similar pattern is reflected in the Seed10 IWC vertical anomaly, in line with the positive LW CRE (Table ); however, the LWC vertical anomaly is much less clear, and therefore the SW CRE anomaly is much smaller, with higher uncertainty relative to the mean value. It is unclear why LWC decreases by up to 0.5 mgm-3 in liquid clouds for D19 Seed0.1. This may point to an enhanced precipitation efficiency from the few seeding particles in this case that form ice that sediments into warmer regimes and, thus, consumes available water and depletes lower-lying clouds. The SW CRE anomaly in Table  suggests that this may be the case; however, as the uncertainty is high and there is no significant signal in the cloud fraction anomalies in Fig. , it is unclear whether this feedback mechanism is present.

The patterns found in the TOA radiative anomalies and the ICNC and IWC anomalies can be explained by the competition for water vapour during the formation of in situ cirrus ice. The cirrus scheme is called during every timestep in the model, and the nucleation of new ice crystals occurs only if cirrus conditions (T < 238 K) are met. Seeding particles efficiently form new ice crystals with a relatively low Si,seed = 1.05. In addition, our simplified method of including seeding particles as INPs in our cirrus scheme, using a globally uniform approach (i.e. every grid box includes the same concentration of seeding particles), results in accumulation of their impacts. This resulted in ICNC anomalies that were larger than the seeding particle concentration (Figs.  and ). As seeding particles consume water vapour with increasing efficiency at higher concentrations, they leave little supersaturated vapour left for other processes to occur, as indicated by the reduction in homogeneous nucleation and heterogeneous nucleation on mineral dust particles. This phenomenon goes beyond the traditional understanding of overseeding, where only homogeneous nucleation suppression was documented, coupled to a higher number of ice crystals nucleated on seeding particles . Rather, our results show that overseeding leads to an ice nucleation competition alteration with the suppression of heterogeneous nucleation on mineral dust particles on top of homogeneous nucleation suppression. In relation to the cloud fraction responses (Fig. ), overseeding in our model appears to lead to the desired reduction in mid-troposphere clouds. However, at higher altitudes, seeding particles overtake natural processes to form higher cloud fractions. As these clouds are in general colder, increases in their coverage lead to the larger TOA warming described above.

Overseeding occurs with both D19 and S89 ice cloud fraction approaches but is more widespread with the narrower Si bounds used in the latter. With seeding particles being present in every grid box of the cirrus scheme and their relatively low Si,seed, even small increases in the number of INPs and hence the amount of ice in an ice-supersaturated environment can lead to dramatic cloud fraction increases with S89. In addition, the low Si,seed = 1.05 “outcompetes” all other freezing modes to alter nucleation competition away from natural processes and towards seeding particles with both schemes. As this critical saturation ratio threshold is somewhat arbitrary, we investigate CCT sensitivity using seeding particles with a higher critical Si,seed = 1.35 for nucleation.

Additional sensitivity tests were conducted by increasing Si,seed to 1.35 (1.35 seeding) in an effort to limit the overseeding found with Si,seed = 1.05 (1.05 seeding). Figure b presents the net TOA radiative anomaly for both cloud fraction approaches for 1.35 seeding; results are also presented along with the 95 % confidence interval in Table . Note the difference in scale to the 1.05 seeding TOA plot (Fig. a); 1.35 seeding leads to a drastic reduction in the net TOA anomalies by a whole order of magnitude for both D19 and S89. We find TOA anomaly maxima of 0.33 and 0.37 W m-2 for both D19 and S89, respectively, for the Seed1 case, with only S89 showing certainty in the 95 % confidence level. For both cases, the positive TOA anomalies are driven by positive CRE anomalies, fuelled mainly by weaker SW CRE (i.e. positive anomalies). This indicates a reduction in lower-lying mixed-phase or liquid clouds. In fact, for all S89 cases, the net CRE anomalies either match or exceed the net TOA anomalies, meaning rapid cloud adjustments are likely contributing to the larger CRE anomalies. For example, for the S89 Seed0.1 case, the net CRE anomaly even contrasts with the TOA anomaly. For D19, the TOA anomalies are driven mainly by weaker (i.e. positive) SW CRE anomalies, except for the Seed100 case, where we find a stronger positive LW CRE of 0.18 W m-2 (Table ).

Consistent across both cloud fraction approaches is the large uncertainty relative to the absolute response, leading to uncertainty in the net TOA radiation and CRE in Fig. c, d. The only exception is for S89 Seed1, which at the 95 % confidence level shows a net warming effect (Table ). However, with high uncertainty in the net TOA balance and the net CRE for 1.35 seeding with both ice cloud fraction approaches, plus the use of the unrealistic ice saturation threshold for full grid-box coverage for ice clouds in S89 (Sect. ), we focus our comparison for the rest of this study between 1.05 seeding and 1.35 seeding with D19 only.

As the Seed1 case showed the largest amount of cooling for 1.05 seeding and the largest warming for 1.35 seeding, we examine the microphysical response by comparing the zonal mean in situ ice tracer anomalies for Seed1 and Seed1_1.35 in Fig. . There is no clear response in the homogeneously nucleated ice number anomalies within the cirrus regime (above the 238 K isotherm, dashed line in Fig. ) for both 1.05 seeding and 1.35 seeding. Plus, the overall zonal mean anomalies for both cases are uncertain according to the FDR analysis. The signal is clearer in the in situ heterogeneous tracer anomaly, where positive values are much more widespread and certain for 1.05 seeding than 1.35 seeding. Heterogeneous nucleation increases by more than 10 L-1 in most regions for 1.05 seeding and to a lesser extent with 1.35 seeding, where there is much wider-spread uncertainty. The 1.05 seeding signal is less certain towards higher latitudes in the Northern Hemisphere (NH), where it shows mixed responses, as well as in the 1.35 seeding case. The differences between 1.05 seeding and 1.35 seeding are clearer in the anomalies for heterogeneous nucleation on mineral dust (Fig. e, f). With the former, we find a similar situation to before, where heterogeneous nucleation on dust is overtaken by heterogeneous nucleation on seeding particles. For Seed1 this switch to seeding-particle-dominant heterogeneous nucleation within cirrus clouds appears to replace some homogeneous nucleation throughout the troposphere and leads to a small negative TOA effect (Fig.  and Table ). We find the opposite behaviour in the TOA response with Seed1_1.35, with the total heterogeneous nucleation anomaly closely resembling that for heterogeneous nucleation on mineral dust particles. Seeding particles in this case, and only in some areas, decrease the number of ice particles formed by homogeneous nucleation but are not effective at shutting off background heterogeneous nucleation processes. In fact, the amount of dust-driven nucleation increases throughout the troposphere, except for a small region at roughly 45∘ N. However, both homogeneous and heterogeneous nucleation ice tracers for 1.35 seeding contain high uncertainty, as shown by the stippling in Fig. . The seeding ice tracer anomaly is more certain and shows increases between 1 and 10 L-1 in the tropics and is much less widespread than the 1.05 seeding scenario. This is due to the fact that a Si of 1.35 occurs much less often in the atmosphere than a Si of 1.05. Therefore, seeding particles with a higher Si,seed are much less efficient in this case at consuming water vapour to overtake other nucleation modes like in the 1.05 seeding scenario, leading to the insignificant zonal ice tracer anomalies, despite a clear significant positive anomaly of heterogeneous nucleation on seeding particles (Fig. h). Our results in this case only partially support the idea of an optimal seeding particle concentration around 1 INP L-1 .

The global mean TOA radiative anomalies as well as the zonal mean ICNC tracer anomalies are mostly inconclusive for both 1.05 seeding and 1.35 seeding. Therefore, we examine the zonal mean TOA anomalies for each seeding concentration for both Si,seed thresholds in Fig. . The most striking finding is that increasing Si,seed to 1.35 reduces the likelihood of overseeding, producing more regions of cooling for all seeding particle concentrations. For Seed100 with Si,seed = 1.05 (Fig. a), the maximum positive TOA anomaly is around 13.6 W m-2 in the Southern Hemisphere (SH), whereas Seed100_1.35 (Fig. b), the maximum positive radiative forcing anomaly, is about 1.5 W m-2. There are small regions of negative forcing (i.e. a cooling effect) for all seeding particle concentrations for 1.35 seeding and seeding particle concentrations ≤ 10 L-1 for 1.05 seeding. For the 1.05 seeding case, Seed0.1 and Seed1 show some degree of negative forcing between roughly 40 and 15∘ S and between around 30 and 60∘ N. The cooling for Seed1 around 50∘ N is the only appreciable signal at roughly -1.1 W m-2. Seed10 shows only a small degree of cooling around 30∘ S, with a small region with a maximal cooling of -0.7 W m-2 at roughly 35∘ N. As the Seed1 global mean anomaly showed the largest amount of cooling in the global mean net TOA anomalies for 1.05 seeding (Table ), we added the 95 % confidence interval, which shows high uncertainty for 1.05 seeding.

The 1.35 seeding shows negative forcings in similar latitude regions but for all seeding particle concentrations (Fig. b). The 95 % confidence interval is shown here as well. For the Seed1 anomaly, three regions, between 90 and 60∘ S, at around 15∘ N, and at roughly 45∘ N, show the largest amount of cooling. The largest negative anomaly is -1.2 W m-2 in the southern polar region. It is significant at the South Pole, perhaps indicating a higher CCT efficacy towards higher latitudes as well as in our model . However, in other regions like the 1.05 seeding case, the uncertainty around the Seed1 zonal mean anomaly is high. Therefore, it is difficult to determine the exact radiative response around the regions with the largest amount of cooling.

The indication that high-latitude seeding may lead to a negative response in the Seed1_1.35 zonal anomaly in Fig.  is in line with previous findings by and . To examine these higher-latitude regions further, Table  presents the 5-year mean net TOA anomalies between 60 and 90∘ N/S as well as the 95 % confidence interval around the mean. For 1.05 seeding, the only cooling response occurs for Seed0.1 in the NH but contains an uncertainty 1 order of magnitude higher than the mean.

There is a clear overseeding response in both hemispheres for Seed100, with mean responses exceeding the net TOA anomaly (Table ). As shown previously, the positive anomalies are drastically reduced for 1.35 seeding, which shows negative anomalies for Seed0.1 and Seed1 in the SH. The largest cooling response of about -0.45 W m-2 occurs for the Seed1 anomaly in the SH, but, consistent with the other responses, it is highly uncertain.

Figure  shows the vertical profiles of IWC and LWC anomalies for each seeding particle concentration, like in Fig.  but for 1.35 seeding. Unexpectedly, we find that 1.35 seeding does not impact IWC within the cirrus regime and leads to only very small anomalies in the mixed-phase and liquid regimes. There does appear to be a feedback on lower-lying clouds as the LWC anomalies are larger. LWC increases in the lower part of the mixed-phase regime and the uppermost part of the liquid regime by a small amount only for Seed10_1.35 and Seed100_1.35. At warmer temperatures, the LWC decreases for all seeding particle concentrations. For Seed0.1_1.35 and Seed1_1.35, the LWC decreases in the lowermost mixed-phase regime. It is unclear why there is a shift from negative to positive LWC anomalies in the mixed-phase regime with increasing seeding particle concentrations. The lack of an IWC response, combined with the increase in heterogeneously nucleated ice on seeding and mineral dust particles for Seed1_1.35 (Fig. ), indicates that seeding, to some extent, impacts the ice crystal size, which in turn affects sedimentation from the cirrus regime. Ice crystal size anomalies are also highly uncertain for the 1.35 seeding case (not shown), with a mixed signal in the cirrus regime. At least at lower seeding particle concentrations, it may be that seeding forms larger ice crystals that sediment into the mixed-phase regime and consume liquid water more efficiently via the WBF process or riming. At higher seeding particle concentrations, ice growth may be limited and therefore cirrus ice crystals may be smaller, which weakens the sedimentation flux into the mixed-phase regime. The lack of large ice crystals in the mixed-phase regime reduces cloud droplet consumption via the WBF process or riming and increases LWC for at least two of our scenarios. In these cases, the positive LWC anomalies in the upper mixed-phase regime may equate to smaller cloud droplets that lead to a weaker sedimentation flux, which may result in few cloud droplets in the liquid regime. Overall, however, the cirrus seeding signal on lower-lying cloud feedbacks is ambivalent for 1.35 seeding, as uncertainty surrounding the responses in the cirrus regime remains high.

Our annual mean results for 1.35 seeding cannot confirm the findings from previous studies that higher-latitude regions are the most desirable for CCT implementation . Therefore, we examine whether there is a seasonal sensitivity to CCT efficacy. Figure  shows the NH winter and summer zonal mean TOA radiative anomalies as well as the constituent SW and LW flux anomalies for 1.35 seeding. The net TOA is presented in the first column for NH winter (top) and summer (bottom), with the SW and LW flux anomalies in the second and third columns, respectively. Uncertainty is plotted around the Seed1_1.35 mean anomaly. A clear seasonal pattern is difficult to decipher from the TOA anomalies, except that there appear to be more widespread positive TOA anomalies during NH winter.

In the northern polar regions (north of 60∘ N), only the Seed10 and Seed100 TOA anomalies show any cooling during NH winter, but at specific latitudes. Due to the negligible SW flux at high latitudes during winter, the net TOA response is entirely driven by LW anomalies. Our model suggests that seeding particles in this case act to enhance the large LW CRE in this region (roughly 11 W m-2 in the unseeded case) to produce mostly positive TOA anomalies. However, the uncertainty around the Seed1 mean anomaly in this region is high (Fig. ). We find smaller regions of cooling with net negative TOA responses for Seed1 during NH winter in the northern mid-latitudes (between 30 and 45∘ N) and in the southern polar regions (south of 60∘ S) (Fig. a). The cooling in the northern mid-latitudes is driven by a large decrease of around -2.5 W m-2 in the net TOA LW flux coupled to a weaker TOA SW flux in the same region. This is the same region where we find the negative homogeneous nucleation and total heterogeneous nucleation ice anomalies in Fig. , indicating that seeding particles in this region may cause a shift in the cirrus formation pathway or have an impact on lower-lying mixed-phase clouds. The smaller net cooling for the SH in the same time period appears to be driven by a stronger TOA LW that is partially compensated for by a stronger TOA SW.

During NH summer the net TOA response is similar to that during NH winter, with the exception of the northern polar regions, where the maximum positive anomaly for Seed10_1.35 is nearly 5.0 W m-2. There are a few regions of cooling in the NH that are driven primarily by SW anomalies. The maximum amount of cooling of -2.5 W m-2 for Seed1_1.35 occurs around 70∘ N and is driven by a weaker TOA SW flux, indicating a feedback on lower-lying clouds that is partly compensated for by a weaker (i.e. more positive) TOA LW flux. We also find a similar pattern in the NH tropics around the location of the Intertropical Convergence Zone (ITCZ). Thicker in situ cirrus clouds to some extent reflect more SW , similar to the Twomey effect for lower-lying liquid or mixed-phase clouds (MPCs). However, they also induce a strong compensating LW effect as a result of seeding. In the southern polar region we find a cooling response for Seed1_1.35 of nearly 2.5 W m-2. Similar to before, the cooling in this region is driven by LW emissions due to a lack of SW radiation during SH winter; however, the uncertainty is wide enough in this case that we cannot determine whether the net TOA anomaly is indeed neutral.

So far, our analysis has focused on the changes in the troposphere leading to the TOA overseeding presented in Fig. . However, our findings also point to stratospheric effects as a result of seeding, particularly the positive ICNC anomalies in the lower stratosphere (Fig. ) and the subsequent cloud fraction increase (Fig. ). The former can be partially explained by the seeding strategy we utilize in our cirrus scheme. Seeding particles are available in every grid box of the cirrus scheme up to the 100 hPa pressure level. This places some of our seeding particles firmly within the troposphere in the tropics but in the lower stratosphere at the mid and high latitudes. Therefore, seeding particles are present in environments with little competition between mineral dust (i.e. low INP environments) or liquid sulfate particles, leading to wide extents of the lower stratosphere with large positive ICNC anomalies. Cloud fraction increases accordingly with larger ice crystal number concentrations from seeding. This effect is more widespread with S89 than D19 due to the ice saturation threshold for full grid-box coverage of ice clouds used in the former.

What remains unclear is the positive in situ homogeneously nucleated ice number anomaly at the mid-latitudes and towards the poles in the lower stratosphere (Fig. , top panel) and the higher cloud fractions that extend to pressure levels less than 100 hPa (i.e. at higher altitudes). As both cloud fraction approaches are RH-based, the patterns observed in stratospheric cloud fractions indicate a dynamic response to the INP perturbations by increasing temperature and consequently enhancing upwelling of water vapour into the stratosphere from the tropical troposphere as shown in Fig. . The anomalies for lower seeding concentrations and for all simulations with Si,seed = 1.35 are insignificant. Here, we only present the anomalies at pressure levels lower than 300 hPa (higher altitudes) to focus on the effects in the upper troposphere and the stratosphere.

Overseeding in Seed100 leads to a positive temperature anomaly of more than 4 K in the tropical troposphere (Fig. a). As a result of warmer temperatures, the saturation-specific humidity increases. Therefore, the specific humidity can increase as well (Fig. b). This appears to enhance water vapour upwelling into the lower stratosphere from the tropical troposphere, as indicated by the positive specific humidity anomaly above the tropopause (Fig. b) that also extends into the middle stratosphere. Water vapour in the stratosphere has a cooling effect , as indicated by the temperature response above the tropopause in the tropics and between 45 and 90∘ N/S. In the same region, updraft velocities increase by more than 0.2 cm s-1. As we observe larger ice cloud fractions in this region (Fig. ), enhanced LW cloud top cooling likely fuels the observed positive updraft anomaly. We find LW cooling in the tropics in the upper troposphere and in the extra-tropics in the stratosphere in Fig. . The latter is likely due to the positive water vapour anomaly in the lower stratosphere (Fig. b). At lower levels we find LW warming, likely caused by more trapping from more frequent and optically thicker cirrus clouds. The increase in updraft velocity, in combination with the positive specific humidity anomaly, not only allows the seeding particles to form abundant ice particles, but also allows air parcels to reach the critical saturation for homogeneous nucleation. There are also small areas in the lower stratosphere where the anomaly of ice formed heterogeneously on mineral dust particles is positive (Fig. ). This enhancement of natural ice formation processes at lower levels in the stratosphere in response to overseeding in the troposphere (Sect. ), plus the widespread positive anomaly of ice formed on seeding particles in the same region, leads to a higher abundance of clouds that likely contributes to the overall TOA warming effect (Fig. ).

The temperature anomaly presented in Fig. a is not restricted to the lower stratosphere where we find enhanced ice formation, which indicates that seeding could impact the wider stratosphere as a whole via a dynamic feedback on the Brewer–Dobson circulation (BDC) . The BDC describes the global mass transport from the troposphere into the stratosphere, where air rises in the tropics and descends over higher latitudes. One of the main findings following numerous studies on greenhouse-gas-driven climate change is a speeding up of this overturning circulation, with enhanced tropical mass upwelling, leading, in general, to a cooler stratosphere and a warmer troposphere . studied the enhancement of gravity-wave-fuelled tropical upwelling into the stratosphere during warm El Niño–Southern Oscillation (ENSO) events. They found that during such events tropospheric warming paired with tropical stratospheric cooling enhances the meridional temperature gradient. This strengthens the sub-tropical jet, as seen by the increase in the zonal mean zonal wind, which is proportional to enhanced gravity-wave drag forcing that fuels increased tropical upwelling . Our results show a similar response with the positive temperature anomaly in the tropical tropopause (Fig. a) that subsequently intensifies the sub-tropical jet, which we diagnosed from the zonal mean zonal wind anomaly in Fig. d. The updraft anomaly in Fig. c on the one hand shows a negative updraft anomaly in the troposphere as a result of enhanced atmospheric stability due to a warmer upper troposphere, similar to the stabilization found by following stratospheric sulfur injections. On the other hand, the positive updraft anomaly indicates a small enhancement of tropical upwelling in the stratosphere that would indicate a strengthening of the BDC. However, with this effect, the downward branch of the BDC leads to stronger warming in the stratosphere at higher latitudes (see Fig.  from ) due to adiabatic compression. Our results show a negative temperature anomaly at high latitudes, in contrast to BDC enhancement findings, rather pointing to a weakening of the downward branch. Instead, our results point to enhanced radiative cooling of the lower stratosphere in response to positive specific humidity anomalies.