Ice crystal number concentration aomaly (ΔNi; perturbation minus control) is shown in Fig. . At flight altitude in Case 1, the ΔNi remains above 1000 L⁻¹ for up to 60 min after initialization, with more than 20 % of the contrail area still exceeding this threshold at that time. By 90 min, ΔNi remains above 500 L⁻¹ across most of the contrail, while 15 % of the area still exhibits ΔNi values exceeding 1000 L⁻¹. At 120 min, ΔNi decreases further, with values remaining above 200 L⁻¹, though a small fraction (0.5 %) of the area continues to exceed 1000 L⁻¹. By 150 min, ΔNi exceeds 100 L⁻¹ in approximately 30 % of the area, with 0.5 % maintaining values above 500 L⁻¹.

At flight altitude in Case 2, ΔNi remains above 1000 L⁻¹ for up to 60 min after initialization, with over 30 % of the contrail area exceeding this threshold at that time. By 100 min, ΔNi decreases to values above 500 L⁻¹, while 20 % of the area still retains ΔNi values exceeding 1000 L⁻¹. At 150 min, ΔNi remains above 200 L⁻¹, with 0.5 % of the area still maintaining values above 1000 L⁻¹. By 180 min, ΔNi remains above 100 L⁻¹, with 25 % of the area exceeding this value, and 0.5 % of the area still exhibiting ΔNi values greater than 500 L⁻¹. These results demonstrate a gradual decline in ΔNi over time, while the contrail persists with a still substantial ΔNi for over 2 to 3 h, albeit at progressively lower concentrations.

In Case 6, Ni remains elevated at flight altitude for an extended period, with values exceeding 500 L⁻¹ up to 90 min and remaining above 200 L⁻¹ until 140 min. Among all eight simulations, these three cases (1, 2, 6) exhibit the most prolonged presence of high Ni at flight altitude. This suggests a delicate balance where ice crystals are neither too small nor the air too dry to induce rapid sublimation, while also preventing excessive humidity and rapid crystal growth that would accelerate sedimentation. Comparing the contours of Case 1 and Case 2 reveals distinct differences in their vertical evolution. In Case 1, the 200 L⁻¹ contour extends up to four layers below flight altitude, whereas in Case 2, it reaches only two. However, Case 1 does not ultimately exhibit greater vertical expansion. Over time, Case 2 develops a larger vertical extent, as indicated by the 30 and 10 L⁻¹ contours. This difference is primarily attributed to the greater average ice-supersaturated (ISS) thickness below flight altitude in Case 2, which supports sustained contrail growth and facilitates continued vertical development. Evaluating the vertical development of Case 6 and Case 7 reveals that their growth is more restricted and shallower than in other cases. This limitation stems from the thin ISS layer below flight altitude, which constrained crystal growth as the contrails spread downward. In contrast, in all other cases the ΔNi extends well below the saturated layer, indicating that contrail ice crystals had more opportunity to grow while sedimenting in saturated air. By the time they reached the subsaturated layer, these larger crystals were able to persist, enabling the contrail to develop beyond the saturated region, as evident in Cases 1, 3, and 5. The vertical development of Case 7 is somewhat larger than in Case 6, with ΔNi contours decreasing more gradually and without the sharp reduction observed when Case 6 enters the subsaturated region. This contrast reflects differences in how relative humidity falls below the saturation threshold – gradual in Case 7 but abrupt in Case 6. Observational studies, such as , have shown that contrail cirrus can persist in slightly ice-subsaturated air, rather than being restricted to strictly saturated or supersaturated conditions. Consistent with this, the 80 % relative humidity contours in Case 1 decline only slowly after 100 min, indicating a much more gradual transition from saturation compared to earlier in the simulation. This slow decrease is mirrored in the ΔNi patterns, particularly in the 30 and 10 L⁻¹ contours, reinforcing that the rate of humidity decline in subsaturated air strongly influences contrail growth and ice crystal survival.

Beyond these ΔNi variations, a broader implication is that the thickness of the supersaturated layer below flight altitude influences contrail vertical development in two related ways:

A thicker supersaturated layer provides sedimenting ice crystals with additional supersaturated air for continued growth, and

The control run for Case 4 reveals a deep layer of near-saturated conditions, as indicated by the relative humidity contours (Fig. ). The vertical cross-section of IWC in the background weather condition shows high values extending from lower altitudes upward (Appendix Fig. ), consistent with cloud formation driven by strong vertical transport. As shown later in this study the natural cloud in Case 4 has a strong greenhouse effect related to its high optical thickness. These characteristics point to a liquid-origin ice cloud , making Case 4 a clear example of this cloud type.

In this case, the contrail is initialized in a deep but only slightly supersaturated layer. Such conditions should, in principle, permit unrestricted vertical extension through fall streak development, since the ISS layer imposes no thickness constraint. Yet the 30 and 10 L⁻¹ ΔNi contours in Fig.  show a vertical extent comparable to cases with a thinner supersaturated layer (e.g., Cases 3, 5, and 8), indicating that additional factors may be limiting the contrail's vertical growth. While ISSRs are essential for persistent contrail formation, but the mere presence of an ISSR does not determine how far contrails may ultimately grow. The following sections examine additional atmospheric variables that shape contrail growth and their radiative effects.

In Case 4, ΔNi at flight altitude decreases more rapidly than in other cases, as seen in the 1000, 500, and 200 L⁻¹ contours. While part of this reduction results from horizontal spreading, dilution, and vertical extension through fall streak development, the comparatively higher rate of decrease suggests that a larger fraction of ice crystals undergo in-situ sublimation at flight altitude. The distinguishing feature in this case is a continuous decrease in relative humidity from the beginning of the simulation (blue contours in Fig.  and panel c in Fig. ). Unlike in cases with higher or sustained humidity, where crystals undergo rapid initial growth , ice crystals here remain growth-limited from the outset and, without a continuous water vapor supply, a larger fraction sublimate before they can develop further.

Moreover, part of the contrail was initialized within a fine-scale gravity-wave–induced ice cloud and remained in the simulation domain for about 60 min before advecting out (Fig. ). Gravity wave dynamics generate small-scale fluctuations that create localized subsaturated regions and restrict mixing with the surrounding supersaturated environment. While contrails in other cases can sustain growth by drawing in water vapor from the edges through mixing with ISSRs, this inhibited spreading likely enhanced ice crystal sublimation here.

Contrail ice crystals in Case 8 exhibit a pronounced upward development above flight altitude (Fig. ). While some vertical extension occurs in all cases due to turbulence, mixing, and wind shear, the ΔNi countours 1000, 500, and 200 L⁻¹ rise more prominently here. As previously noted, young contrails act as strong moisture sinks, leading to high deposition rates that are evident in the RH_ice fields (Fig. ). This deposition reduces humidity toward saturation and releases latent heat, producing a small positive temperature anomaly (Appendix ). The resulting temperature increase is minor – typically only a few tenths of a degree – and its buoyancy effect is likely negligible compared to background wind shear, turbulence, and the overall stability of the upper troposphere.

Case 8 shows a distinctly lower Brunt–Väisälä frequency at flight altitude in the control run (Table ), indicating weaker atmospheric stability. In such conditions, even small temperature perturbations from latent heat release can produce relatively large vertical displacements. The evolution of this case therefore suggests that atmospheric stability may influence not only the cross-sectional area of young contrails during the vortex phase , but also may influence their subsequent vertical expansion as they develop into contrail cirrus.

Figure  is similar to Fig. , but shows the ice water content anomaly (ΔIWC) – that is, the change in IWC within the contrail region in the perturbation run relative to the corresponding region in the control run. In contrast to ΔNi, the ΔIWC increases as the contrail ages. The maxima of IWC and Ni anomalies generally do not coincide in space or time, with Case 4 as the only exception. In the other simulations, the maximum IWC anomaly occurs well below flight altitude. The ΔIWC contours suggest that the thickness of the ice-supersaturated layer beneath the contrail strongly controls both the location and magnitude of this peak, with the maximum positioned just above the subsaturated layer. In Cases 2, 3, 5, and 8, which have thicker ISS layers below flight altitude, contrails reach peak ΔIWC about 2.5 h after formation. Even in Cases 6 and 7, where the ISS layer is much thinner, the maximum occurs after roughly 90 min. Overall, in contrail cirrus (long-lived contrails), the ΔIWC maximum tends to occur near the base of the supersaturated layer, while the ΔNi maximum at that time remains close to flight altitude.

When comparing the cases, the largest ΔIWC is simulated for Case 5, where growth starts gradually at low values and peaks around 160 min after contrail initialization. The maximum anomaly, averaging 6 mg m⁻³, occurs just above the saturation contour. Case 3 follows a similar growth pattern, albeit with lower peak values.

Case 8 reaches a maximum similar to Case 3, but with a different development over time. The ΔIWC increases rapidly at first, reaching 2 and 3 mg m⁻³ much earlier, after which ΔIWC growth decelerates. Another distinct feature of this case is its much stronger vertical growth (fall streak) compared to all other cases, despite the ISS layer beneath not being the deepest. Here, the gradual transition between the 100 % and 80 % RH_ice contours plays a key role in sustaining the downward growth of the contrail. This indicates that, beyond ISS thickness beneath flight altitude, the structure of the slightly subsaturated region – especially its depth and the rate of humidity decrease – strongly influences contrail ice growth and the resulting IWC anomaly and facilitates continued descent of the fall streak. Hence, when planning flight management strategies, it is essential to account not only for the vertical structure and thickness of ISSRs beneath flight level, but also for the characteristics of the slightly subsaturated layer below, which influence contrail growth potential. This aligns with the study of , which detected contrail signals a few hundred meters below flight altitude in cloudy regions using satellite-based observations; similar evidence was reported by , who observed enhanced extinction and ice water content below flight altitude in cirrus perturbed by embedded contrails.

By contrast, several cases exhibited only weak ΔIWC. Aviation-induced IWC is weakest in Cases 1, 2, and 4 (Case 7 is omitted from this discussion because the contrail advected out of the domain before its development could be analyzed). The control simulations for Cases 1 and 2 (Appendix ) show very low background IWC, particularly near flight altitude. These two cases involved contrail initialization at higher altitudes (Case 1 at 12 138 m and Case 2 at 11 800 m) under extremely low ambient temperatures (T<215 K). Such cold conditions likely explain the weaker contrail-induced IWC anomalies in these cases. Case 4 also recorded a low ΔIWC, but under markedly different background conditions. Here, the contrail formed at 10 664 m with an average temperature of about 221 K – roughly 10 K warmer than Cases 1 and 2 – and within a deep ISSR. Unlike those cases, the control run shows relatively high background IWC, indicating a background environment capable of sustaining higher ice water content due to the warmer temperatures. Despite this contrast, the contrail-induced IWC anomaly remained among the lowest.

Although both contrails and natural ice clouds consist of ice crystals, their microphysical properties differ markedly. Young persistent contrails are characterized by exceptionally high ice crystal number concentrations composed of extremely small ice crystals – a feature rarely observed in natural clouds. Owing to their large surface-area-to-volume ratio, these numerous small crystals have very short deposition and sublimation timescales. As a result, young persistent contrails efficiently consume available moisture in ISSRs, rapidly depleting excess water vapor and creating a near-saturated environment at flight altitude (as was shown in Fig. ). However, natural ice clouds do not necessarily deplete excess water vapor rapidly upon formation. Observations show that highly supersaturated conditions often persist within natural cirrus clouds , highlighting a fundamental distinction from contrails. Therefore, the excess water vapor mass – defined here as the mass of water vapor exceeding the saturation threshold over ice at a given temperature and pressure – plays a critical role in contrail evolution within ISSRs. This parameter strongly influences contrail-induced IWC anomalies, as discussed in detail by .

In this study, the saturation vapor pressure over ice, esi, was computed using the formulation implemented in the ICON-2.6.6 version used for our simulations, in order to maintain internal consistency between the post-processed excess-water-vapor diagnostic and the model thermodynamic fields. The corresponding saturation vapor density, ρsi, was then obtained from the ideal gas law (Eq. ), where Rv=461.5 J kg⁻¹ K⁻¹ is the specific gas constant for water vapor and T is the temperature in Kelvin. The actual water vapor density was calculated from the specific humidity, qv, and air density, ρ, as in Eq. (). Excess water vapor mass was then determined as Eq. ()

2ρsi=esiRvT[kgm-3]3ρv=qvρ[kgm-3]4ρexcess=ρv-ρsiwhenρv>ρsi(kgm-3)

Figure  illustrates the time-height evolution of excess water vapor density (mg m⁻³), averaged over the contrail region in the control simulations (only natural cloud). This representation reflects the moisture availability in the contrail region without contrail influence.

The largest IWC anomalies were simulated for Cases 5, 3, and 8, respectively, while Cases 1 and 2 were among the weakest. Case 4 showed a distinct pattern, with an initial increase in IWC followed by a gradual reduction over time (Case 7 is omitted from this discussion because the contrail advected out of the domain before its development could be fully analyzed). Notably, Cases 1, 2, and 6 were among those with the highest Ni, which remained elevated at flight altitude for an extended period. Cases 1 and 2 formed at higher altitudes (≈ 12 km) under very low temperatures (T<210 K). Although relative humidity was high (above 110 %), the absolute amount of excess water vapor is small (less than 2.5 mg m⁻³ throughout), owing to the cold conditions. This limited moisture supply restricted ice crystal growth, resulting in their persistence near flight altitude. Consistently, these two cases showed prolonged Ni anomalies at flight altitude but only minimal increases in IWC anomalies. In agreement, reported that contrails forming at higher altitudes tend to persist longer and exhibit increased lifetimes. We note that our simulations assume a constant initial ice crystal number concentration, while in reality colder conditions at higher altitudes would likely activate more during the contrail formation.

Although both Cases 1 and 2 had limited excess water vapor, Case 2 showed slightly higher values and a distinct temporal pattern: a gradual, steady increase that sustained moisture supply to the contrail region. This behavior is consistent with , who highlighted the role of sustained moisture availability – often linked to prolonged but weak updrafts – in supporting contrail persistence. Consequently, Case 2 maintained a high ice crystal number concentration throughout the 3 h simulation and exhibited greater IWC growth than Case 1.

A similar trend was observed at flight level in Case 6, where excess water vapor initially remained low (below 1 mg m⁻³) but gradually increased over time, supporting relatively longer ice crystal persistence at flight altitude compared with other cases of similar altitude and temperature.

In both Cases 5 and 3, the contours show a gradual increase over time, but Case 5 begins at lower values and eventually exceeds those of Case 3. This excess water vapor availability is clearly reflected in the contrail-induced IWC anomalies over the contrail lifetime, though it may not be readily apparent when examining relative humidity alone.

In Case 8, the excess water vapor reached 4–5 mg m⁻³, yet the IWC anomalies did not attain comparable values. The high moisture supply was present mainly at the beginning of the simulation and then gradually diminished. This initial abundance accelerated ice crystal growth and sedimentation, causing the IWC anomaly to rise more rapidly than in other cases to intermediate values (∼ 3 mg m⁻³). However, it did not continue to develop further, illustrating that not only the total amount of available water vapor but also its temporal distribution strongly influences contrail growth potential.

As discussed previously, Case 4 exhibits unique behavior in both Ni and IWC anomalies. Here, the maxima occur only at a very early stage, after which the contrail gradually decays. This case, marked by a deep supersaturated layers with only moderate ice supersaturation, resembles the conditions usually linked to liquid-origin ice clouds. Both Figs.  and show that the contrail initially formed and evolved in a region with positive excess water vapor, which gradually decreased over time and even reached negative values. Time series of excess water vapor density for the natural cloud (control run) and the contrail-affected region (perturbation run) is provided in Fig. . These results reveal that while excess water vapor declines gradually in the control run – likely due to weakening mesoscale updrafts – its depletion is markedly accelerated in the presence of a contrail. In the perturbation run, excess water vapor decreases sharply at first and then stabilizes near zero, consistent with the rapid initial increase in the IWC anomaly followed by stalled growth and, eventually, a decline as sublimation is required to maintain near-saturated conditions.

To summarize, these findings emphasize that the development potential of persistent contrails is determined not only by the presence of supersaturation conditions but also, critically, by the quantity and temporal availability of excess water vapor within ISSRs.

Figure  presents the time series of terrestrial infrared, or longwave (LW), radiative flux at the top of the atmosphere (TOA). Negative values indicate outgoing radiation and energy loss to space. Less negative values correspond to reduced outgoing radiation, signifying increased greenhouse effects and greater energy retention.

The smallest contrail-induced radiative impact is simulated for Case 4. This case features relatively high thermal flux in the control run, consistent with the presence of optically thick, liquid-origin ice clouds, which typically exert stronger radiative effect than in situ-origin cirrus clouds due to their higher optical thickness . In contrast, the strongest impacts occur in Cases 3, 5 and 8. Case 5 shows the largest anomaly, 24 W m⁻² after 120 min, exemplifying contrail growth under near-optimal conditions: not too high to limit excess water vapor (unlike Case 2), benefiting from a steady, gradual moisture supply, and supported by deep ISSRs below flight altitude (unlike Case 6, where growth was constrained by a thin subsaturated layer).

Case 8 also exhibits a substantial radiative impact, peaking at 23 W m⁻² after only 60 min. This rapid onset mirrors its early IWC anomaly growth. Interestingly, Case 2 – despite forming at higher altitude with limited water vapor – still reaches 18 W m⁻² after 150 min, a value comparable to cases with greater moisture availability.

Figure  also includes the time evolution of IWP. As expected, Case 4 has the largest values in the natural cloudy region (control). However, the contrail-induced change in IWP remains minimal in this case, though a slight increase is still noticeable. A potential relationship between changes in thermal net flux at the top of the atmosphere and IWP anomalies is evident from the analysis. We computed the pointwise distance correlation between contrail-induced changes in IWP and thermal net flux. The coefficient, shown in Appendix , indicates a positive association between these variables – suggesting that larger increases in IWP correspond to greater reductions in outgoing longwave flux. This is in line with , who found that the strongest net radiative forcing of embedded contrails was associated primarily with increases in ice water content. This relationship holds across the simulations, except in Case 4.

To assess solar, or shortwave (SW), radiative effects, all cases were normalized to a standardized reference irradiance corresponding to 1 March at a latitude of 34°. This normalization enables direct comparison of net solar flux across cases, based on a reference value of Sref=231 W m⁻². Figure  presents the time series of solar net flux at the top of the atmosphere for all cases, together with the corresponding albedo time series.

Although the perturbation and control runs show similar overall temporal evolution, the presence of contrails consistently enhances local atmospheric reflectivity, thereby reducing the incoming solar radiation. The largest reductions in solar net flux are observed in Cases 3, 5, and 8, while Cases 1, 4, and 7 exhibit comparatively smaller effects.

In our study, although contrails exhibit a cooling effect from the shortwave (solar) perspective, their warming impact due to the trapping of outgoing longwave radiation (greenhouse effect) remains dominant. A version of Fig. , normalized using a standardized reference irradiance corresponding to 21 June – when solar irradiance typically reaches its annual maximum – is provided in Appendix . Even under these peak solar conditions, the cooling effect from reduced solar flux cannot fully compensate the warming caused by longwave radiation trapping.